Order Code RL31949
Issues in Dynamic Revenue Estimating
Updated April 26, 2007
Jane G. Gravelle
Senior Specialist in Economic Policy
Government and Finance Division

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Issues in Dynamic Revenue Estimating
Summary
Dynamic revenue estimating, which accounts for macroeconomic feedback
effects on revenue costs of tax changes, has become increasingly important. An
analysis of these effects is now required before a tax bill can come to the House floor.
The initial study of the President’s budget proposals for 2003 by the
Congressional Budget Office (CBO) revealed a wide range of effects — from a 30%
decrease in revenues to a 15% increase. Subsequent studies and studies by the Joint
Committee on Taxation and the Treasury Department also find varying results.
These differences reflect the types of effects included, the models used, and the
behavioral responses. There are three types of effects: short-run stimulus, or
Keynesian, effects, which reduce costs; crowding out effects of deficits, which
increase costs; and supply side effects, which could go in either direction. There are
four basic types of models: neoclassical growth models, short-run models with
unemployed resources, and infinite horizon and life cycle intertemporal models.
Only the second type includes Keynesian effects. All include supply side effects.
Deficit effects can be included but eventually have to be resolved in certain
intertemporal models or the models cannot be solved.
Arguments have been made that Keynesian effects not be considered. These
effects also apply to spending, are not the objective of permanent tax policy, and are
dependent on how tax cuts are financed and the reaction of the Federal Reserve. The
two models CBO used with Keynesian effects found opposing effects. Some also
argue that the effects of deficits should not be considered because these effects, as
well, apply to spending and, eventually, deficit issues must be resolved.
Supply side effects in neoclassical growth models include labor supply response,
savings response, and the ability to substitute labor and capital. Given reasonable
savings elasticities, savings effects are not very important in the short run; the main
issue is labor supply. Most evidence suggests, however, that labor supply response
is small (so that assuming no response is probably reasonable). It is even less likely
that labor can respond in the short run, where considerable institutional barriers exist.
Intertemporal models are based on individual optimization over a long period
of time. There are three reservations about these models. First, do they represent
actual behavior of individuals? Second, the outcomes are sensitive to many
assumptions and the behavioral responses in many of these models (including those
used by CBO) result in much larger savings and labor supply responses than are
justified by empirical evidence. Finally, intertemporal models with foresight cannot
be solved without some presumption about how the budget deficit is dealt with, and
the choice can make a great deal of difference in the outcome (indeed, it changes the
direction of effects). These models cannot address a stand-alone tax cut.
The range of results in the Congressional Budget Office study would be even
larger if further sensitivity analysis for supply response were undertaken; in
particular, such sensitivity analysis would probably cause larger additional costs
(rather than revenue offsets) from feedback effects. This report will not be updated.

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Contents
Types of Effects and Types of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Short-Run Stimulus Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Deficit Effects and Crowding Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Supply Side Effects in the Basic Neoclassical Growth Model . . . . . . . . . . . . . . . 9
Labor Supply Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Theoretical Issues: Why Labor Supply Elasticities Are Probably
Small, Can Be Negative, and May Be Falling . . . . . . . . . . . . . . . 11
Using Empirical Evidence on Elasticities for Dynamic Scoring
Purposes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
The Production Function and Factor Substitution Elasticities . . . . . . . . . . . 17
Savings Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Intertemporal Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Are Intertemporal Models Realistic Representations of Behavior? . . . . . . . 20
Correspondence to Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Sensitivity to Method Used to Address the Balanced Budget Constraint . . 25
Summary of Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
The Effects of Different Models and Assumptions: A Summing Up . . . . . . . . . 27
Appendix A. Revenue Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Revenue Feedback Effect: Partial Equilibrium . . . . . . . . . . . . . . . . . . . . . . 29
Revenue Feedback Effect: General Equilibrium, Short Run . . . . . . . . . . . . 29
Appendix B. Labor Supply Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Historical Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Cross Section Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Experiments: Natural and Otherwise . . . . . . . . . . . . . . . . . . . . . . . . . 34
Theoretical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
The Elasticity for Hours of Work and the Hours Constraint . . . . . . . . 35
Participation Responses: Example of the Logit Formula . . . . . . . . . . 37
Application to Revenue Feedbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Uncertainties About Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Cross Income Elasticities for Married Couples . . . . . . . . . . . . . . . . . . 41
Appendix C. Intertemporal Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Intertemporal Substitution in Consumption . . . . . . . . . . . . . . . . . . . . . . . . 42
Studies of the Intertemporal Labor Supply Elasticity with Respect
to Wages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Theoretical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

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List of Tables
Table 1. Percentage Change in Labor Employed with a Percentage Change in
Tax (Fixed Capital Stock) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

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Issues in Dynamic Revenue Estimating
Dynamic revenue estimating, which accounts for macroeconomic feedback
effects of tax changes on revenues, has become increasingly important. The Joint
Committee on Taxation (JCT) has been engaged for some time with a study of how
to include these effects and has been attempting to develop a model for this purpose.
In early 2003, a rule adopted by the House required a macroeconomic analysis to be
prepared (or a reason given for why it cannot be prepared) before tax legislation can
come to the floor, and this rule has been retained by subsequent Congresses.
Also in 2003, the Congressional Budget Office (CBO) presented its first
dynamic analysis of the President’s budgetary proposals, using a variety of models
and assumptions (hereafter CBO study).1 These proposals provided for permanent
tax cuts in individual rates and on income from capital. A range of effects, both
positive and negative (although generally small) was reported in these analyses, with
feedback effects on budgetary costs ranging from a 15% increase in cost to a 17%
decrease in cost. The CBO study examined both spending and tax changes and
considered effects on the entire budget (including effects of increased interest on the
debt). The CBO has subsequently produced studies of both the President’s budget
and other proposals. The most recent study was of the President’s FY2008 budget
proposal.2 As with the 2003 study, feedback effects were relatively small and ranged
from positive to negative.
Subsequently, the JCT prepared an analysis of the tax cut passed in the House
on May 9, 2003 (hereafter JCT study).3 This tax cut was temporary in nature and
many of the provisions directly affecting wage income had effects only in the first
five years because they were accelerations of existing tax cuts. The JCT analysis
focused only on revenue effects (and not the entire budget). Average effects over the
10-year period were a reduction in revenue costs (ranging from 2.6% to 23.4%).
However, its study, while estimating positive effects on real output in the first five
years, found negative effects in the second five years (and these effects would be
expected to continue to be negative). The JCT has continued its studies; the most
recent study was of a income tax reform proposal that would broaden the base and
lower the rate.4 This proposal was not a tax cut, but a revenue neutral reform, and
1 Congressional Budget Office. An Analysis of the President’s Budgetary Proposals for
Fiscal Year 2004, March 2003.
2 Congressional Budget Office. An Analysis of the President’s Budgetary Proposals for
Fiscal Year 2004, March 2003.
3 “Macroeconomic Analysis of H.R. 2, the ‘Jobs and Growth Reconciliation Tax Act of
2003,’” Prepared by the Staff of the Joint Committee on Taxation.
4 Joint Committee on Taxation, Macroeconomic Analysis of a Proposal to Broaden the
(continued...)

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resulted in output increases ranging from 0.1% to 1.2% for the first five years,
depending on the model used.
The Treasury Department’s Office of Tax Analysis prepared its first dynamic
analysis in 2006 with a study of the proposals by the President’s Advisory Panel on
Tax Reform, also a revenue neutral tax change.5 For the income tax reform, the
effects on output in the budget window ranged from 0.1% to 0.4%. For the
consumption tax proposal, the effects ranged from 0.1% to 1.9%.6 A subsequent
analysis examined the effects of the 2001-2004 tax cuts.7 This study did not report
revenue feedback effects, but CRS calculations indicate revenue costs would be
reduced by 7% in their base case and would range, depending on responses in the
models, from less than 1% to 18%.8 Treasury also reported some short-run effects
in its mid-session review.9
The estimates of feedback effect depend on the kinds of effects included, the
nature of the model used, and a variety of assumptions regarding underlying
behavioral responses. This report explains these issues and discusses the empirical
evidence on some of the crucial supply-side behavioral responses. Some of the more
technical material and details are presented in appendices.
The first section explains the three basic sources of feedback effects that can be
considered: short-run stimulus, deficit crowding-out, and supply side; and how these
three effects relate to the four basic types of models. The following sections discuss
the issues surrounding each type of effect.
Types of Effects and Types of Models
There are three types of revenue feedback effects:
! short-run stimulus, or Keynesian effects
! crowding out effects of deficits
4 (...continued)
Individual Income Tax Rate and Lower the Base, JCX-53-06, December 14, 2006.
5 Robert Carroll, John Diamond, Craig Johnson, and James Mackie III, A Summary of the
Dynamic Analysis of the Tax Reform Options Prepared for the President’s Advisory Panel
on Federal Tax Reform, U.S. Department of the Treasury, Office of Tax Analysis, May 25,
2006, prepared for the American Enterprise Institute Conference on Tax Reform and
Dynamic Analysis, May, 2006.
6 This analysis is discussed in greater detail in CRS Reform in CRS Report RL33545, The
Advisory Panel’s Tax Reform Proposals, by Jane G. Gravelle.
7 Office of Tax Analysis, United States Department of the Treasury, A Dynamic Analysis
of Permanent Extension of the President’s Tax Relief, July 25, 2006.
8 CRS Report RL33672, Feedback Effects from the 2001-2004 Tax Cut, by Jane G. Gravelle.
9 U.S. Office of Management and Budget, Fiscal Year 2007 Mid-Session Review, Budget of
the U.S. Government, July 11, 2006.

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CRS-3
! supply side effects.

The first two — the short-run stimulus effect in an underemployed economy
and the crowding out effects of deficits — apply to spending increases as well as tax
cuts. Spending increases actually have a more powerful effect than most tax cuts
because some fraction of a tax cut is not spent. Some have argued that the first effect
or even the first two effects should not be included in dynamic revenue estimates.
The third type of effect is commonly called a supply side effect because it refers to
the effects of tax or other policies on the amount of labor supplied or the amount of
savings (which would affect the size of the capital stock). This supply side effect is
more closely associated with tax changes although it could apply to certain spending
programs as well. (For example, spending on infrastructure such as bridges or
highways would affect productivity.)
There are also four basic types of economic models; all of these models can
incorporate supply side effects, but they vary in whether and how they incorporate
the Keynesian or deficit crowding out effects:10

! Basic neoclassical growth models (also called Solow models);
! Short-run models with underemployed resources typically used for
short-run forecasting. These models are also referred to as ISLM 11
models and usually transition or are made to transition to a
neoclassical growth model;
! Infinite horizon intertemporal models, also called Ramsey models or
referred to as “Barro-type” models; and,
! Life cycle intertemporal models (also called overlapping generation
or OLG models).
Only the second type of model can include short-run stimulus effects because
all of the other models are full employment models.
All of the models include supply side effects but they introduce them in different
ways. In the basic neoclassical growth model and the ISLM-growth model, the
savings rate and the labor supply depend (or can be made to depend) on after-tax
rates of return on savings and after-tax wage rates, and the elasticities (percentage
change in quantity divided by percentage change in price) used are derived directly
from statistical estimates of these parameters (referred to as reduced forms). A
change in tax rates on labor or capital income induces changes in savings rates and
labor supply that affect output in this period and the capital stock in the next period.
The change in the capital stock alters the return on capital and wage and induces
another adjustment in the savings rate and labor supply. This process continues over
10 This report does not address direct estimates of tax revenue response to specific tax
changes since these responses cannot be generalized across different tax cuts.
11 ISLM refers to the two basic demand side equations in a short-run model that determine
aggregate demand levels and interest rates: an investment-savings relationship where output
is the sum of spending on consumption, investment, government expenditures, and net
exports, and a money demand equation where individuals trade off liquidity against interest
rates in determining how much assets are held in money versus bonds.

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a period of time until it approaches a new equilibrium where the savings generated
in the economy just equals the amount of net investment needed to grow the economy
at a steady state. The effects are determined by three responses: the savings
elasticity, the labor supply elasticity, and the factor substitution elasticity; the last
reflects the ease with which labor and capital are substituted in the production
process.
In the infinite horizon and life cycle models, savings (and, depending on the
model, labor supply) arise from an optimization of spending over time — over
infinity in the infinite horizon model and over a lifetime in the life cycle model. The
size of these effects depends on many different factors, but some of the important
ones are the willingness of individuals to substitute leisure for consumption within
a time period (measured by the intratemporal substitution elasticity), the willingness
of consumers to substitute over time (the intertemporal substitution elasticity), and
the factor substitution elasticity. Another very important feature of these models for
the short run is the amount of available hours which directly affects the labor supply
response that arises from the model.
All of the models can deal with deficit effects, but the infinite horizon model
and some versions of the life cycle model (those with foresight) cannot permit
deficits to run indefinitely because deficits eventually cause the model to explode
(i.e., the cumulating deficit will grow without limit). These types of models rely on
future values to solve even the very short run and must be subject to a government
budget constraint which requires the budget deficit eventually to be addressed. How
the budget deficit is addressed can make a great deal of difference to the outcome.
Each of these model types has been used in dynamic analysis of tax provisions.
The Joint Committee on Taxation (JCT) convened a number of researchers in 1996
for a study for fundamental tax reform (with results published in 1997, hereafter
referred to as the JCT Symposium): models there represented two of the first type,
three of the second type, one of the third type, and three of the final type.12 These
studies focused largely on supply side effects because the groups modeled revenue-
neutral tax substitutions, although the disruptions from changing tax collection
sources caused some negative short-run effects in models with unemployment. The
two recent studies presented in March and May of 2003 respectively also used a
variety of model types. The CBO study analyzed the President’s budget proposals
using all of these model types; the JCT study used the two models of the second type
and one of the fourth type.13 More recently, JCT has used one model of each except
the first type, although the infinite-horizon intertemporal model was substantially
modified to include a share of individuals who simply spend all of their income.
Treasury initially used the first, third, and fourth type in its analysis of the tax reform
12 The results were presented in Joint Committee on Taxation: Tax Modeling Project and
1997 Symposium Papers, Joint Committee Print JCS-21-97, U.S. Government Printing
Office, 1997.
13 Note that although the JCT refers to its Macroeconomic Equilibrium Growth model as a
neoclassical growth model, it actually falls in the category of models with underemployment
equilibrium which become similar to neoclassical growth models in the long run.

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proposals. It has used the second, third, and fourth types in its analyses of the 2001-
2004 tax cut.
Different models have different strengths and weaknesses. Moreover, because
of the complexity of modeling, within each type of model, certain aspects may
modeled in great detail and others simplified. For example, of the three life cycle
models represented in the 1997 JCT Symposium, one model used perfect foresight
(the assumption that consumers can project the effects of their behavior on future
rates of return and wage rates), but had a single good and a single representative
income level. Another life cycle model had considerable detail with respect to
different industry sectors, different types of assets, and different income levels of
individuals, but did not assume agents could predict and act on future prices. A third
life cycle model had neither perfect foresight nor disaggregation but allowed for risk,
uncertainty, and precautionary savings. Comparative studies have shown that these
models are sensitive to a variety of parameters and assumptions and numerous
characteristics that can influence effects on behavior in life cycle models.14
There are issues surrounding the estimation and even the appropriateness of
including these various effects, which are discussed in turn.
Short-Run Stimulus Effects
A number of issues arise with respect to including the effects of short-run
stimulus of the economy (Keynesian effects), where real output increases because of
the employment of involuntarily unemployed labor. The effect is relatively
straightforward: output rises by some multiple of the tax cut, called the multiplier,
that arises from successive rounds of spending (the original tax cut, the spending of
those who receive income from the individual round, and so forth). That increase
results in a feedback effect, at least for the time the output is increased. Multipliers
typically rise as the fiscal stimulus spreads through the economy but then fall as the
economy returns to full employment. If the multiplier is 1 for a given year, and the
tax rate is 0.2, then there is a 20% revenue feedback effect for that year arising from
the stimulus.
The first issue is whether these stimulus effects should be included at all,
especially if the dynamic estimate is to be the official estimate for budget scoring
14 These characteristics include presence of endogenous labor, myopia vs. perfect foresight
regarding pretax rates of return and wage rates, uncertainty, the presence of bequests and
the bequest determination (arising from intergenerational altruism, joy-of-giving, uncertain
life-span, fixed size of bequest), existing consumption tax treatment, substitution elasticities
(intertemporal, intratemporal and factor substitution), use of a Stone-Geary utility function
which requires a minimum consumption in each time period, inclusion of depreciation,
assumed size of potential work hours, single vs. multisector economy, and open vs. closed
economy. For the tax substitution experiment, the presence and form of transition relief was
also important. For a table characterizing the directional effect of these features on short
and long run gross output effects, see Jane G. Gravelle, “Behavioral Responses to a
Consumption Tax,” in United States Tax Reform in the Twentieth Century, Ed. George R.
Zodrow, and Peter Mieszkowski, New York, Cambridge University Press, 2002.

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purposes (a use not currently contemplated), rather than for informational purposes.
A principal reason for excluding these effects is that they also apply to spending
increases, and to consider short-run effects for tax changes and not for spending
changes would create a misperception of the relative costs of these alternatives.
Moreover, if the purpose of the tax cut is as a stimulus it is unclear what the value of
calculating the feedback effect is. The relevant public policy issue is not the cost
after feedback, but rather the desirable size and effectiveness of the initial tax cut on
output, an assessment that requires knowing the cost without feedback. If the
purpose is a permanent tax cut, however, then any short-run feedback effect is
transitory, and to include it in assessing the cost of a tax cut can make the cost appear
artificially small.
Aside from these issues of whether to include the stimulus effect, there are a
number of reasons that such an effect is difficult to assess. Since the effect depends
on how close the economy is to full employment, several tax cuts considered
separately would have a larger summed up effect on output than a combined tax.
Indeed, the feedback effect might be different at the time a tax is proposed, compared
to the time it is actually enacted.
Moreover a tax cut bill may be considered to be financed by a deficit (in which
case it would have a stimulus effect), by a spending offset (in which case it would
probably have a slightly contractionary effect), or by an offsetting tax increase. Any
analysis that includes a stimulus effect is making an implicit judgment about whether
the tax cut would be financed by borrowing.
Another reservation about incorporating short-run effects is that they depend on
the actions taken by the Federal Reserve Board. In theory, any fiscal stimulus could
be offset by contractionary monetary policy (or accommodated with expansionary
policy, although this effect is less likely under current monetary regimes). The
degree to, and speed with which, the monetary authorities act to offset (or magnify)
the effects of a tax cut will determine how large the effect will be, which means that
each analysis implicitly includes an assumption about the behavior of another
government agent. A tax change might also induce behavioral changes by foreign
governments that affect the impact.
The final problem is the accuracy with which the stimulus effect can be
estimated. The effect of a tax cut on output depends crucially on several factors on
which the economics community does not have a consensus. For example, there is
considerable disagreement about how much of an individual tax cut will be spent,
depending on how expectations about the future are presumed to be formed, whether
a tax cut is permanent or temporary, whether it is received by higher or lower income
individuals, and whether it is received in a lump sum form or through withholding.
Effects of an investment stimulus provided to firms are even more uncertain, because
of a lack of empirical evidence on the responsiveness of business investment to tax
subsidies. The effects are also influenced by the degree to which interest rates rise
as income expands (and the subsequent crowding out of private investment). The
degree of openness of the economy is also crucial; in a flexible exchange rate
environment with very mobile capital, a fiscal stimulus has little power other than in
the very short run because the associated rise in interest rates which induces an
inflow of foreign capital will cause the price of the dollar to rise and reduce net

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exports. In such a model, investment crowding out is greatly reduced but so is the
output effect. Finally, a shift in aggregate demand will cause some increase in output
and some increase in price level; the relative shares depend (or should depend) on
how close the economy is to full employment. To the extent that prices rise,
feedback effects can become very confusing unless they are expressed in constant
dollars.15
The estimated stimulus effect depends on which model is used. A study by
economists at the Federal Reserve Board (holding nominal interest rates fixed, which
produces the largest multipliers via an accommodative Fed stance) found that
multipliers, while larger for a spending change than a tax cut, varied substantially
across four models considered: the Federal Reserve’s own model, an older Federal
Reserve model and two commercial macroeconomic models: DRI and Washington
University Macro Model (WUMM).16 After two years, multipliers for tax cuts
ranged from 1 to 1.75. The overall effect on deficits (which depends not only on
output change but interest rate effects) also varied substantially. The authors suggest
that the multipliers in the Federal Reserve’s model tend to be smaller because they
have forward looking expectations. The multipliers would all, of course, be smaller
if money supply were contracted, or even held constant, rather than expanded.
Gregory Mankiw, for example, reports the tax multiplier in a major macroeconomic
model (Data Resources Inc., or DRI, a predecessor of DRI-WEFA and, in turn, a
predecessor of Global Insight) is 1.19 if the interest rate is held constant (which
would require a monetary expansion), 0.26 if the money supply is held constant (the
interest rate would rise but output could also rise), and zero if the inflation rate is
held constant (the interest rate rises so much that output is fixed).17
As an illustration of the differences in the models, the 2003 CBO study of the
President’s proposal compared simulations on two commercial macro models,
Macroeconomic Advisors which is the current version of WUMM and Global
Insight, a model that resulted from a merger of DRI with another modeling firm.
Feedback effects varied from positive to negative because of the offsetting effect of
deficits (discussed next) and differed substantially across models (ranging from an
increase in cost of 9% in the first five years to a decrease of 29%). It is clear from
the disaggregation reported by CBO that the effects on revenues were largely
composed of short-run Keynesian effects. In its initial study in 2003, the JCT used
its own model termed Macroeconomic Growth Model or MEG (adapted from
Macroeconomic Advisors) and the Global Insight model to assess effects on real
revenues (and thus did not include the direct effects of higher interest costs arising
from the deficit, only the crowding out effects on capital income and their subsequent
15 If effects are expressed in nominal dollars, a cut in taxes can appear to be less costly
because the increase in price level increases the nominal level of receipts. This price effect
also increases any spending that is tied to inflation, but since much spending is set in
nominal terms, this change will also cause the nominal deficit to fall, basically by effectively
reducing the real level of government spending.
16 Eileen Mauskopf and David Reifschneider, “Dynamic Scoring, Fiscal Policy, and the
Short-run Behavior of the Macroeconomy,” National Tax Journal, vol. 50, September 1997,
pp. 631-655.
17 N. Gregory Mankiw, Macroeconomics, 5th Edition, New York: Worth Publishers, p. 287.

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effects on revenues). Results for the first 10 years varied significantly depending on
the model and Federal Reserve action: from a 3.6% revenue offset for MEG with an
aggressive Fed offset to a 23.4% for MEG with Fed neutrality. For Global Insight
which has a delayed Fed offset, the feedback was 11.8%. For the House tax bill,
clearly the dominant effect was short-run stimulus, but that effect is partly due to the
transitory nature of the tax cuts and the focus on the revenue side.
Deficit Effects and Crowding Out
While the short-run stimulus effect acts to reduce the revenue cost of a tax cut,
the effect of deficits causes tax cuts to cost more. One cannot have a short-run
stimulus without a deficit, but one can have a deficit without a short-run stimulus (for
example, if the monetary authorities offset the fiscal stimulus).
There are three types of deficit effects. First, the interest on debt issued to
finance the tax cut increases spending costs directly. For dynamic studies of budget
effects, such as those done in the CBO study, these interest rate effects are already
included in initial budgetary costs. Deficits also crowd out investment and reduce
the capital stock and thus reduce long run output and taxes on that output — effects
that show up as a feedback increasing revenue costs. Deficits also add to budgetary
costs because they raise interest rates and increase the cost of debt service.
Some of the same reservations about including stimulus effects also apply to
including deficit effects, mainly that deficit effects occur with spending increases as
well as tax cuts.
While the effect of deficit finance is probably more certain than the effects on
short-run stimulus, there are some major uncertainties. First, if a tax cut is saved
rather than spent, it does not have an effect on interest rates or crowding out (nor
does it have an effect on stimulating the economy). However, empirical elasticities
suggest that even tax cuts that reduce marginal taxes on savings are unlikely to
unleash enough savings to offset the deficit effect.
The effects of deficits on interest rates and crowding out of investment can be
partially or even fully offset by inflows of capital (which again reduce or eliminate
the stimulus effect given flexible exchange rates). If a full offset occurred there
might still be an additional cost to revenues because foreign owners of capital do not
pay U.S. individual income taxes in most cases, and interest on debt, which is more
mobile, is deductible by U.S. firms. (The amount of income available to U.S.
citizens would decline, however, because more of the capital stock would be owned
by foreigners.)
One other problem with deficits is that, while they can simply be allowed to
occur in models that do not rely on long run variables to solve, the deficit must be
addressed in order to solve the infinite horizon model or the perfect foresight life
cycle model. Deficits running indefinitely cause an explosive growth of the debt
which eventually supplants all the capital stock leading to a long run economy with
no output. Two issues arise: how long might one wait to resolve the deficit issue and

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CRS-9
how should the deficit be corrected? These issues are intertwined with the supply
side effects in these intertemporal models and will be discussed in the subsequent
section.
Supply Side Effects in the Basic Neoclassical
Growth Model
Fundamental supply side effects occur largely through increased labor supply
or increased saving (although note that either can be positive or negative due to
income and substitution effects). An increase in the labor supply or the savings rate
in response to a tax cut would produce additional income and taxes that would reduce
the cost of the tax cut. However, increased saving is unlikely to have much effect on
federal revenue in the revenue estimating time frame, while labor supply changes can
be important. The CBO study has relatively small income and substitution effects that
average out to a total elasticity of about 0.1 for an across-the-board wage change. Its
neoclassical model yielded negative feedback effects because the labor supply
elasticities were small while additions to the debt caused additional interest costs.
The JCT study of the House tax cut did not formally report its elasticities (although
they are apparently reflective of empirical evidence and therefore modest). The JCT
model is not a pure neoclassical model even with an aggressive Fed reaction case,
and the estimates reported are only for the effects on revenues. However, its
feedback was relatively small, 9.8% in the first five years and 3.6% in the next 10
years. Real output fell in the second five years, presumably because of the temporary
nature of the tax cuts affecting wages in the tax bill coupled with some budgetary
crowding out.
A simple example can be used to illustrate why labor supply is crucial to effects
on output. Empirical evidence on savings elasticities suggests values that range from
slightly negative to slightly positive. But even taking the highest of these elasticities,
0.4, a 10% increase in rate of return would lead to a 4% increase in the savings rate.
If the capital stock is growing at, say, 3% in real terms, savings would be only 3% of
the capital stock. Thus a 4% increase in the savings rate would lead to a 0.12% (0.03
X 4%) increase in the capital stock. Assuming capital income accounts for one
quarter of net income, total income would increase by about .03% (0.25 X 0.12%),
that is, only 3/100 of 1 percent. This effect does not account for interaction with
demand. An elasticity of 0.4 for labor supply would lead to an output effect of 3%
with a 10% increase in the wage (again without accounting for demand interaction),
an effect 100 times as large. The savings effects will grow over time but will be
small initially.
Another way of thinking about this effect is to think of feedback effects, again
before considering effects of the production function interaction. If an elasticity is
0.2 then, roughly speaking, the revenue feedback effect is on the order of 20% times
the ratio of tax rate to after tax share (see Appendix A). For example, if the tax rate
is 0.3, a reduction in wage tax will lead to an offset of about 9% (20% X0.3/(1-0.3))
That effect means that even small labor supply responses can potentially have
significant feedback effects. Thus, in order to get an accurate measure of the revenue
response, it is crucial to have a good measure of labor supply response. The factor

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CRS-10
substitution elasticity, to which little attention has been paid in many models, can
also play an important role as it determines both the demand for labor (which
interacts with supply to produce a final amount of labor, also derived in Appendix
A).
The first section of this part therefore addresses labor supply responses. It is
specifically addressed to whether adequate evidence on a point elasticity exists to
incorporate labor supply response into a revenue estimate, what such an estimate
might be, and whether a range of effects might be considered. The information is
presented in the body of the paper in summary form, but details are presented in
Appendix B. The next sections discuss the factor substitution elasticity and
elasticity of savings responses.
Labor Supply Response
Labor supply response is directly incorporated through an elasticity estimate,
which may be disaggregated into income and substitution effects and by type of
worker in the neoclassical growth models. The labor supply elasticity in inter-
temporal models is derived from a particular function and will be discussed
subsequently.
The supply of labor can rise or fall with an increase in wages due to opposing
income and substitution effects. A rise in wages causes an increase, through the
income effect, of consumption of both goods and leisure, which reduces labor supply.
This income effect can also arise from changes in average tax rates. The rise in
wages also causes leisure to become relatively more costly, inducing a substitution
of consumption for leisure, which causes the labor supply to rise. This substitution
effect is governed by marginal changes in wages which are affected by marginal tax
rates. Thus evaluating labor supply response to tax changes involves knowing the
relative sizes of the income and substitution effects as well are the net effect of wage
changes on labor supply. Labor supply can also reflect changes in hours, or changes
in participation; the latter has particularly been of interest in the case of women’s
labor supply, since women, because of marriage and children, may not participate in
the labor force.
This section begins with a overview of the empirical evidence, followed by a
discussion of theoretical problems associated with that evidence, and then by the
implications of both for incorporating labor supply response in scoring of tax
legislation. The survey of econometric estimates indicates that both positive and
negative labor supply responses to wage rate increases can be justified by the
empirical evidence, findings consistent with economic theory. Empirical estimates
from the literature also likely overstate the elasticities appropriate to dynamic
revenue estimating for several reasons.
Empirical Evidence. Empirical evidence on labor supply can be classified
into several types: historical patterns, cross section regressions, experimental
approaches (natural or otherwise), and even survey data. Appendix B provides a
more detailed discussion of the evidence, but the findings can be summed up as
follows:

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CRS-11
! History suggests a declining or, more recently, relatively unchanging
number of hours worked per week despite dramatic changes in real
wages, findings consistent with very small and possibly negative
elasticities. Participation rates are mixed: participation of older and
younger men has declined, participation of prime working age men
has been constant, and participation of women has increased (but is
now leveling out). Institutional and cultural factors may play an
important role in these findings.
! Cross section evidence,18 which is the most plentiful, suggests small
income and substitution effects, with a net negative, but small, labor
supply response for men (probably of around -0.1). For married
women, labor supply response is more likely to be positive and the
estimates vary significantly. These studies are fraught with
numerous econometric problems. More recent evidence suggests
that married women’s labor supply response has declined and is
converging toward that of men.
! Experimental approaches were of two types. Actual experiments
with lower income individuals tended to find small elasticities of
mixed signs and “natural experiments” (such as tax changes) tended
to find virtually no effect. In the latter case, one study found
elasticities of 0.6 to 1 for high income married women although this
measure may have reflected only substitution effects and the effects
were quite sensitive to controls; other aggregate studies and studies
of high income men found essentially no response.
! Survey data asking individuals about their behavioral responses are
often held to be unreliable, but they have suggested a small response
by affluent men. Survey data on actual knowledge and work
experience have suggested that individuals do not know their
marginal tax rates (and might not respond for that reason) and that
many individuals do not work their optimal hours (which suggests
institutional factors may restrict behavioral response).
Theoretical Issues: Why Labor Supply Elasticities Are Probably
Small, Can Be Negative, and May Be Falling. Reduced-form empirical
estimates of labor supply (estimates that relate outcomes, such as hours worked or
participation, to wage rates) suggest small elasticities in most cases. For example,
hours of work by men with significantly different hourly earnings actually tend to
vary very little. To understand more about the responses, and to prepare for
understanding labor supply in intertemporal models, we consider how labor supply
responses arise from a more formal model of individual optimization. It is important
to understand several theoretical issues: labor supply response is limited by the
18 Cross-section evidence compares the hours different individuals work in a given time
period and relates these hours to their wages. Cross section evidence can be contrasted to
time series evidence which examines changes in average hours as related to changes in
average real wages over time.

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CRS-12
amount of hours in the day, labor response is limited by the number of potential
workers: any labor supply response to wages presents an important dilemma for
growth accounting, and institutional factors play a potentially important role in
limiting labor supply response, particularly in the short run.
Constraints on Hours. The labor supply elasticity is derived from the
substitution between consumption and leisure; that is a reason to expect it might be
small. Suppose that we make the assumption that leisure and goods consumed by
individuals increase by the same percentage when income increases in a way that
does not affect the marginal wage. (Technically, this assumption means use of a
utility function for leisure and consumption that is a constant returns to scale utility
function, and thus has an income elasticity of one). Also assume that the substitution
elasticity between goods and consumption with respect to the marginal wage is
constant. (See Appendix B for a derivation). We keep the problem simplified by
allowing no savings behavior and designate W as the wage rate, H as the hours
available, L as leisure, C as consumption, and r as the ratio of non-labor income to
labor income. With no non-labor income, we obtain a mathematical expression for
the labor supply elasticity of the form:
E = (S-1) L/H
where S is the substitution elasticity.
What value might we expect to find for S? For many types of choices we would
think of high substitution elasticities as those above one and low elasticities as those
less than one. The more disparate commodities are, the more likely that there is not
a lot of substitution between them. If, for example, one considers consumption of
goods and leisure to be very different commodities one might not expect them to be
easily substitutable.
The S term determines the effect of a rise in wages on increasing work effort
through the substitution effect, while the 1 term determines the effect of a rise in
wages in reducing work effort through the income effect. Labor supply response can
be positive, negative or zero, depending on the size of S. A small labor supply
response could be the result of large or small offsetting income and substitution
elasticities.
However, as the formula indicates, even if leisure and consumption have a
unitary substitution elasticity, the effect of this substitution elasticity on labor supply
is smaller, and perhaps much smaller than the substitution elasticity itself because it
is multiplied by the ratio of leisure to available hours. This effect makes sense: a
person who is working every available minute cannot add to labor supply because his
labor supply is constrained by an exogenous amount of time. As discussed in the
appendix, this ratio of available leisure that can be diverted to work could be quite
small if one allows for other necessary uses of time.
The other point illustrated by this formula is that the labor supply elasticity is
not constant even if the underlying income and substitution elasticities with respect
to consumption and leisure are. As work increases, the elasticity falls. This point is
important, because it suggests that one should not impose a simple labor supply

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CRS-13
elasticity across any significant period of time, but (assuming a rise in real wages)
should have an elasticity that falls over time (becomes a smaller absolute value if
positive and work is increasing and a larger absolute value if negative and work is
decreasing). Moreover, it suggests that elasticities are smaller for those working
more hours, a reason mentioned by Wilhelm and Moffitt in their study finding little
labor supply response by very high income men.19
The example of hours response discussed here is meant only to be illustrative,
as it is based on a specific form of utility function that includes unitary income
elasticities and constant substitution elasticities. Adding non-labor income or
requiring a subsistence amount of consumption, other things equal, is likely to
increase in the first case and decrease in the second case the likelihood of a positive
elasticity and the size of the substitution elasticity. There are many other types of
functional forms where elasticities vary across consumption bundles and income
elasticities can differ for leisure and consumption. However, the constraints of labor
supply exist and those constraints exert limits on elasticities regardless of functional
form: people working every available hour can work no more.
Constraints on Participation. Like the amount of hours worked per week,
the participation rate is also constrained. The share of people participating cannot
fall below zero or rise above one. The almost complete participation of men under
65 in either work or school (and school is largely an investment in future earnings)
over time has resulted in little attention to their participation response. However, for
married women, who may not participate in the work force, participation response
is the most important estimated labor supply response. If the participation response
rises for exogenous reasons (e.g. a change in tastes, a decline in marriage or fertility),
the elasticity should become smaller, and at some point it should decline if it
increases because of wage increases. This point is addressed in the appendix:
elasticities, particularly high elasticities, tend to decline when participation rises;
indeed, such growth has raised the question of whether women’s labor supply
elasticities may eventually converge to those of men.20
Also discussed in the appendix are survey data which illustrate how close
women have now come to male labor supply and how little room for response
remains. A positive labor supply response given wage growth cannot continue for
long without running out of available workers.
The Labor Supply Response Is Incompatible with Steady-State
Growth Unless Elasticities Become Zero. Labor supply analysis is filled with
many troubling issues. Why, for example, did the work week decline for 70 years
and in an uneven fashion, and then largely stabilize (except for World War II) for the
next 60 years at around 40 hours per week? Of course, there were laws adopted that
tended to limit hours, but why were they not changed over time? Moreover, a
troubling problem for any long term model of the U.S. economy is that a positive or
19 Moffitt and Wilhelm, “Taxation and the Labor Supply of the Affluent,” In Does Atlas
Shrug?, Ed. Joel Slemrod, New York, Russell-Sage, 2000.
20 See Heckman, James J.,”What Has Been Learned About Labor Supply in the Past Twenty
Years,” American Economic Review, vol. 83, May 1993.

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CRS-14
negative labor supply response is inconsistent with steady state growth. Growth
economists typically model economies as converging to a steady state, with growth
rates usually (although not always) exogenous. Some models simply fix labor
supply. However, for those that allow endogenous labor supply along with technical
progress that increases real wages, such models technically would converge at corner
solutions, with people either virtually not working at all, or working every available
moment, unless elasticities are zero. Thus a steady state growth model is
incompatible with an aggregate labor supply response, and modelers who wish to
incorporate technical progress must also impose some arbitrary rule (such as
constantly changing preferences that move with the growth rate).
If elasticities are very small (either positive or negative) the change over time
might become so small that, for practical purposes, they can be ignored in growth
models. However, even small elasticities can lead to significant changes over an
extended period of time. For example, a positive elasticity of 0.1 with a current work
week of 40 hours plus other constraints on time that result in leisure being half of
available hours, and assuming a real wage growth of 0.015 over time would result in
projected hours of 43 in 50 years, which would not seem unreasonable. But it would
also imply that individuals worked only 34 hours a week 100 years ago, and 28 hours
200 years ago, a finding at odds with history. If the elasticity were 0.3, the
implication would be a rise to 49 hours in 50 years, with 23 hours 100 years ago and
11 hours 200 years ago, projections that seem completely unreasonable.
Institutional Issues. Modern work activities are performed in groups and
work hours are not easily adjustable for an individual worker. Indeed, as noted
earlier, survey evidence indicates that a large fraction of individuals are not working
their preferred hours. In the case of taxes, economic theory strongly suggests
observations should be bunched at kinks in the budget constraint. But, in fact, they
are not. If anything, they are bunched at what appears to be an institutional norm of
around 40 hours a week which is an aggregate work week span adopted as reasonable
by implication due to the legislation on overtime. In general, one of the arguments
for still allowing hours responses is that individuals do have some flexibility in
choosing hours by choosing employers and jobs, and some flexibility still remains.
However, this type of flexibility is constrained by adjustment costs that present a
potential barrier to variation in hours in the short run.
Using Empirical Evidence on Elasticities for Dynamic Scoring
Purposes. This section addresses the specific issue of turning to the empirical
evidence on labor supply elasticities for purposes of dynamic scoring. In addition to
the inherent uncertainties of labor supply response, other issues are: the likelihood
that female elasticities are lower as the female participation rate has increased, the
need to incorporate cross elasticities between husbands and wives in an aggregate
elasticity, and the expectation that short-run responses will be much more constrained
by adjustment costs and institutional factors. Overall, the discussion suggests that
one cannot necessarily expect a positive labor supply response to tax cuts. Therefore,
the presumption of a fixed labor supply for revenue estimating purposes is a quite
reasonable assumption.
Variability and Uncertainty in Estimates. The first challenge in seeking
an elasticity, or elasticities, to use in dynamic scoring for tax purposes is choosing

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CRS-15
one compatible with empirical evidence and economic theory. Not only do labor
supply elasticity estimates vary considerably, actually moving from positive to
negative, but they are also uncertain because of a number of problems with
measurement and specification. These issues are discussed in a number of the survey
articles cited in the appendix. Even considering the relatively simple case of male
labor supply, there are difficulties in measuring non-labor income (usually from
assets), which is used to identify income effects as separate from substitution effects.
Progressive tax rates create kinked budget constraints and complicate estimation,
although new computer techniques have simplified the mechanics of doing such
estimates. Most studies do not adjust for cost-of-living differences that could affect
real wages in different localities. And with any econometric studies there are often
measurement problems, assumptions of uniformity in certain aspects of the
preference function, variations in the choice of other regressors, and variations in
functional form that can affect estimated coefficients. In some ways, it may be
considered a heroic assumption to posit that the tastes and preferences for work of
high income individuals are the same as lower income individuals. But even
seemingly minor issues can have effects that could actually change the sign when
elasticities are low in the first place. For example, one study found that the use of
actual hours rather than desired hours in estimated labor supply equations biased the
elasticity upward (in this case by 0.1, i.e., a positive labor elasticity is too large and
a negative one should be even more negative).21
More serious complications arise in the case of female labor supply. To correct
for sample selection bias (individuals working may not be representative) as well as
estimate participation response involves including data for non-working individuals
where no wage is observed, requiring the inclusion of instrumental variables
associated with wage. Many characteristics correlated with wages, such as
experience and schooling, may not only directly affect wages but may also reflect
tastes for working. Moreover, the dynamics of families are not completely
straightforward either: do wives make their choices about working given husbands’
choices, or does the couple make a joint utility-maximizing decision, or do they
engage in a bargaining solution? The estimation process and the measurement of
income will vary substantially depending on what assumption is made.
A recent survey of economists, which included a survey of the views of 65 labor
economists on their best estimates of labor supply elasticities for prime age men and
women, is suggestive of the existing professional disagreement and lack of consensus
about the sign of labor supply response for men and the magnitude for women.22
Details are presented in Appendix B.
Using Out-of-Date Estimates. Most estimates of labor supply are based on
data from the sixties, seventies or at best the eighties. Even a more recent study
published in 1998 (Pencavel) used data from the early seventies to the mid nineties
21 Shulamit Kahn and Kevin Lang, “The Effect of Hours Constraints on Labor Supply
Estimates,” The Review of Economics and Statistics, vol. 75, November 1991, pp. 605-611.
22 Victor R. Fuchs, Alan B. Krueger, James M. Poterba. “Economists Views about
Parameters, Values and Policies: Survey Results in Labor and Public Economics,” Journal
of Economic Literature, vol. 36, September 1998.

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CRS-16
and thus tends to reflect on average the early eighties. As discussed earlier,
elasticities are expected to change over time, so there is always a question of relying
on existing estimates. In particular, the larger elasticities associated with female labor
participation should be falling, perhaps substantially, particularly if one weights
elasticities by current wage shares (which reflect increased participation rates for
women). Female labor participation increased from about 43% in 1970 to 52% in
1980 to 58% in 1990. Moreover, because the elderly population share was growing
during this time (for example, the elderly share of the over 15 population grew by
about 5 percentage points between 1980 and 2000 for women), the participation rate
among those able to work grew even more. There is also some direct evidence of a
decline in supply response. Of course, the perceptions of labor economists reported
above may reflect acknowledgment of the higher participation rates.
Cross Income Elasticities. A simple weighting of male and female
elasticities by their respective wage shares is an incomplete measure, since there are
cross elasticities between husbands and wives which should be negative. That is, the
income effect may not only affect your own labor, but also your spouse’s labor. In
models that treat women as the secondary earner, such a response would be confined
to wives. As shown in Appendix B, elasticities derived from weighting male and
female wage elasticities would be reduced by between 0.05 to 0.10 if this effect were
accounted for.
Short-Run Elasticities Should be Smaller, and Asymmetrically So,
Than Long Run Ones. There are several reasons why the short-run response is
likely to be smaller than the long run (the effect measured in cross section studies),
and this is particularly true for changes that induce a positive rather than a negative
labor response.
First consider hours. A large share of the currently employed labor force has no
direct control over hours; surveys suggest that many individuals would like to work
more or fewer hours than they now do. Economists recognize these constraints but
generally presume that individuals do have hours choices by changing employers and
jobs (and perhaps even professions). This presumption is reasonable in the long run,
which is the basis of most cross section studies. But in the short run, even over
several years of the estimating horizon, these adjustments cannot easily be made.
While self-employed individuals or individuals whose pay is closely tied to
performance may work more to earn higher wages or salaries, some self employed
individuals may still follow group norms, such as standard hours of opening for retail
businesses. Individuals wishing to expand labor hours through a second job find this
choice to be discrete, and perhaps not yielding the same pay. But even given these
options, it should be clear that the hours elasticity should be smaller, perhaps much
smaller, in absolute value, in the short run.
A similar argument applies to a participation response, but applies
asymmetrically with respect to expansion versus contraction. Entering the labor
force requires, at a minimum, some amount of job search, and may also require some
additional period of education and training. Child care arrangements must be made
in many cases and require some period of search. Deciding to enter the labor force,
and being able to do so at a desirable salary and with desirable working conditions,
is a much more challenging process than an original decision made when young to

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CRS-17
stay in or leave the work force. For an individual who has retired, such a re-entry
may be especially difficult and unlikely, in part because of health and in part because
a very short time might remain to work in any case. However, exiting the labor force
is relatively easy.
The Production Function and Factor Substitution Elasticities
In the long run, workers tend to create their own capital, but in the short run, the
capital stock is fixed or relatively fixed. As a result, dynamic feedback effects can
be quite sensitive to assumptions regarding the substitution between capital and labor
in production (which determines the degree to which the labor demand curve slopes).
Despite the importance of this effect, some modelers have paid little attention to the
production function and whether the assumptions (often including use of a unitary
factor substitution elasticity) are appropriate.
Consider first the total effect on labor used, which is due to the interaction of
labor supply and labor demand. The formula for the percentage increase in the labor
supply divided by the initial percentage increase in after tax wage due to a tax change
is ES/(aE+S) where E is the labor supply elasticity, S is the factor substitution
elasticity and a is the share of income received by capital (see Appendix A). To
convert this value to output effects, the percentage change must then be multiplied
by the labor income share (1-a). Thus if labor income is two thirds of the output
share, the percentage change in output will be two thirds of the percentage change in
labor employed.
The elasticity of labor quantity actually used as a function of the labor supply
elasticity and the factor substitution elasticity is shown in Table 1. The large factor
substitution elasticities are shown not so much because they are likely to be realistic,
but rather because they illustrate the pattern of effects.
Table 1. Percentage Change in Labor Employed with a
Percentage Change in Tax (Fixed Capital Stock)
Labor supply
elasticities
Factor substitution elasticities
0.2
0.4
0.5
0.7
1.0
1.5
2.0
-0.2
-0.31
-0.24
-0.23
-0.22
-0.22
-0.21
-0.21
0.0
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.1
0.09
0.09
0.09
0.10
0.10
0.10
0.10
0.2
0.15
0.17
0.18
0.18
0.19
0.19
0.19
0.4
0.24
0.30
0.31
0.33
0.35
0.37
0.37
0.6
0.29
0.39
0.42
0.46
0.50
0.53
0.54
Source: CRS calculations, see text.
It is clear that the production function does not matter very much when
elasticities are small positives but for either backward bending labor supply curves

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CRS-18
or as positive labor supply responses rise, they can matter significantly. For example,
for an elasticity of 0.1, the amount of labor employed with a factor substitution
elasticity of 0.1 is 91% of the effect that would occur with a elasticity of 1.0, while
for an elasticity of 0.6 the effect is 66%.
Many modelers have not devoted much attention to the choice of production
function and a number of them use a simple form (called the Cobb-Douglas) which
has an elasticity of 1.0. The major macroeconomic modelers (ISLM models) use a
unitary elasticity as do all of the models in the CBO study. However, three of the
nine modelers in the 1997 JCT Symposium used lower elasticities (of 0.2, 0.3, and
0.8, although the modeler using 0.2 (Jorgenson) has recently increased this value to
0.5 to 0.723).
Most empirical estimates of elasticities fall under the value of 1.0, in some cases
well under that value. In a survey of estimates from numerous studies, Chirinko
suggests a value of about 0.4, approximately the same value he recently estimated
with two co-authors in a working paper using a long panel data set.24 Note also that
this choice could matter more if one is averaging a high female elasticity with a
negative (and small in absolute value) male elasticity and the markets are largely
segregated (i.e. if women work at different occupations). Moreover, the elasticity
could be smaller in the short run, when technology combining capital and labor
cannot easily be changed, than in the long run.
Savings Responses
Neoclassical models have savings rate elasticities that usually combine income
and substitution effects and thus can be either positive or negative. Studies of direct
savings elasticities are generally based on aggregate times series data, but few have
been done recently because of the growing interest in more sophisticated
intertemporal models discussed in the next section. Most studies report results that
are very small and can be negative; in general, an elasticity of 0.4 would be
considered relatively high.25 Certainly a model that simply held the savings rate
constant would reflect a central tendency based on this evidence. However, even
large elasticities would have little impact . Using the 0.4 elasticity in a simulation
that eliminated the income tax entirely (and replaced it with a consumption tax), the
23 The most recent version is presented in detail in Dale W. Jorgenson and Kun-Young Yun,
Investment: Volume 3: Lifting the Burden: Tax Reform, the Cost of Capital and U.S.
Economic Growth, Cambridge: The MIT Press, 2001. Other modelers have written books
presenting their models in detail. See, Alan Auerbach and Laurence J. Kotlikoff,, Dynamic
Fiscal Policy, Cambridge, MIT Press, 1987 and Don Fullerton and Diane Lim Rogers, Who
Bears the Lifetime Tax Burden, Washington, DC, The Brookings Institution, 1993.
24 See Robert S. Chirinko, “Corporate Taxation, Capital Formation, and the Substitution
Elasticity between Labor and Capital,” National Tax Journal, Vol. 55, June, 2002, p. 339-
354; Robert S. Chirinko, Steven M. Fazzari, and Andrew P. Meyer, “That Elusive Elasticity:
A Long-Panel Approach to Estimated the Capital Labor Substitution Elasticitiy,” Working
Paper, October 2002.
25 See Jane G. Gravelle, The Economic Effects of Taxing Capital Income, Cambridge: MIT
Press, 1994, pp. 27 for a brief summary of this work.

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CRS-19
capital stock increased by less than 2% after 10 years, and output increased by only
0.4%.
Conclusion
The analysis in this section is suggestive that the labor supply elasticity, the
main response that matters for a neoclassical model in the short run, is so small and
so close to zero that a serious question arises as to whether it is worth incorporating
in a dynamic scoring effort. Based on a review of the cross section data, the
estimates are highly variable, although the central tendencies are very small. At the
least, elasticities derived from the body of econometric studies should be adjusted to
take account of the following considerations when used for revenue estimating:
! Participation elasticities, which are the main contributors to positive
response to wage increases, are largely out-of-date and the dramatic
rise in participation since these studies were made suggests lower
elasticities; the higher the initial elasticity, the more it should have
fallen today.
! A simple weighting of elasticities of men and women does not take
into account cross elasticities for wives; if this effect were averaged
in it could easily transform a small average positive response to a
small negative one.
! The response in the short run is likely to be much smaller than the
long run permanent response reflected in most econometric studies
because of institutional constraints and adjustment costs.
! A given positive labor supply elasticity in the short run will have a
more modest effect after interaction with demand in the short run if
the initial elasticity is large, especially if the model uses the small
demand elasticities that are probably more appropriate to the short
run, when capital and labor substitution is less likely.
Intertemporal Models
Intertemporal models are much more complex and formalized than models
relying on reduced form effects. These models are based on consumers choosing
how much to work and save by optimizing over a long period of time. Savings and
labor response derive from fundamental parameters in the individual’s utility
function (a mathematical representation of the value received from consumption).
There are three important issues to consider when evaluating these models:
! Are these models realistic representations of individual behavior?
There are reasons to expect that they might not be.

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CRS-20
! Many behavioral features of these models, particularly when they
occur over a long period of time, have not been tested empirically.
But certain relationships that can be derived from these models can
be directly compared with econometric estimates. Are these
responses consistent with empirical evidence?
! Can models that are so dependent on unspecified policies to deal
with the government budget constraint be useful for dynamic
revenue estimating?
Are Intertemporal Models Realistic Representations of
Behavior?
The formal structure of intertemporal models is consistent with economic theory
depicting individuals making rational decisions over time, and those theoretical
aspects have made them popular in the classroom and the academic journals. But
whether the responses derived from these models constitute a realistic depiction of
actual behavior is a question that has largely not been tested empirically. That is
because, although certain types of empirical estimates are used to construct these
models, the results rely strongly on a variety of other assumptions, including the
mathematical form of the utility function, the motivation for bequests, and
assumptions that individuals are well informed and capable of making precise
allocations over a long period of time.
These models basically depict an individual as having to make a choice, given
a projection of potential lifetime wealth (which includes the present value of future
wage earnings, and any assets on hand or expected to be inherited), choosing how
much consumption goods to purchase and how much leisure to enjoy (that is, how
much to work). The allocation of consumption and leisure over time depend on the
after tax wage rates in different periods and the after tax rates of return. As in the
basic neoclassical model, income and substitution effects offset each other. One
important difference from typical neoclassical models is that changes in rates of
return can have a dramatic effect on labor supply response as individuals shift leisure
between the present and future, in those models that treat labor supply as
endogenous. This effect is often the most powerful supply side response in the short
run, and yet one that would probably be greeted skeptically by many economists.
There are two basic forms of inter-temporal models:
! Infinite horizon models which represent all of the individuals in the
economy as a single, infinitely lived representative investor.
! Overlapping generations models, which consider individuals of
different ages optimizing over their own remaining lifetimes. As the
economy moves through time, new generations are born and older
generations die.
Infinite horizon models may seem bizarre, but can theoretically be justified by
intergenerational altruism — that individuals include in their own welfare the welfare

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CRS-21
of their children, their grandchildren, and, indeed, all future generations.26 Many
economists have reservations about this assumption, given evidence that many
bequests do not appear to arise from altruistic motives and that many individuals
leave little in the way of bequests or have no children. Moreover, the model cannot
be applied to heterogenous classes of individuals (e.g. in different permanent income
classes or subjected to different tax regimes, such as differing national or state or
local taxes).
Life cycle models may appear more realistic, but even in these models
individuals tend to be optimizing over a long period of time.27 (Note that life cycle
models can have perfect foresight about future prices which is required of infinite
horizon models, or they can be myopic, where individuals assume that current pre-tax
wage and interest rates will continue). Are these models, which assume an enormous
amount of information and planning skills, representative of actual behavior (given,
for example, that individuals often do not know their marginal or average tax rates)?
Even if one does imagine individuals actually making lifetime plans for savings
and consuming that respond to changes in taxes and interest rates, there are a variety
of institutional constraints. These models presume that individuals are free to borrow
and lend at the same interest rate and that no individuals are liquidity constrained.
Moreover, although some models assume labor supply (and leisure) are fixed, others
treat labor as a choice variable. When modeling leisure (and thus labor supply),
models presume that individuals can easily change hours of work or that individuals
can periodically leave and enter the labor force on a voluntary basis due to changes
in interest rates as well as wages. Thus, they do not account for the fact that wage
rates and earnings may depend on past employment history. Practically speaking,
most people cannot easily plan a lifetime working career with periodic deliberate
periods of unemployment. And many economists may doubt that the interest rate
affects most worker’s employment decisions.
Moreover, although some of the behavioral responses in the model can be based
on empirical estimates, the functional form of the models force some particular
relationships (for example, that consumption in periods far apart have the same
intertemporal substitution effects as those close together and that these effects are
based on expectations and planning.) While it is possible to estimate profiles of
behavior over time, the best type of data (panel data) still falls short of a lifetime, and
26 This type of model, also called a Ramsey model, underlies a theory referred to as
Ricardian equivalence (and also causes the model to be referred to as a Barro-type model,
after the economist who wrote about Ricardian equivalence, Robert Barro). Ricardian
equivalence means that deficits never matter because individuals, knowing that they will
have to be repaid in the future, will save enough to make up for the debt plus interest and
leave those amounts to their children as bequests. This theory precludes any stimulus effect
or crowding out effect. Intertemporal models always converge to the same long run steady
state equilibrium and basically involve an infinite long-run savings elasticity.
27 Bequests in the life cycle model must be motivated by something other than
intergenerational altruism. One can assume no bequests (although such a model is hard to
calibrate to the economy), fixed bequests, bequests that are treated as, or similarly to, a last
period of consumption (joy of giving), or bequests that occur because individuals need a
hedge against living too long.

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CRS-22
the assumption must be made that these patterns reflect the execution of plans that
were carried out in anticipation of lifetime prices and incomes.
Correspondence to Empirical Evidence
There are four basic measures that influence the behavioral response in these
models (along with a variety of mathematical assumptions):
! The intratemporal substitution elasticity.
! The intertemporal substitution elasticity.
! The factor substitution elasticity.
! The ratio of leisure to hours available to work.
Corresponding to these parameters are the direct estimates of elasticities from
statistical studies discussed in the previous sections. They include the labor supply
elasticities estimated from cross section studies which are composed of offsetting
income and substitution effects, each of which tends to be quite small on average
(perhaps in the neighborhood of absolute values of 0.1 to 0.3). These labor supply
elasticities depend on functional form, the intratemporal substitution elasticity and
the ratio of leisure to hours available. These elasticities also include the factor
substitution elasticity whose average value is often estimated to be less than 0.5.
There have also been attempts to estimate some of the intertemporal responses,
as discussed in Appendix C. They include attempts to directly estimate the
intertemporal substitution of consumption with respect to rates of return; these
estimates have produced a range of returns, but with most studies falling well under
0.5. Modelers in the 1997 JCT Symposium used values of 0.25, 0.3, a range of 0.15
to 0.5, and 1.0, although the last measure has now been reduced by the modeler to
0.4.28 The CBO models used 0.5. (The JCT has not formally provided elasticities
but its elasticities are apparently consistent with other models) Although these values
are often estimated using short panels reflecting close together periods, as applied to
intertemporal models, which measure the response to long periods apart (even
infinitely far apart), they can produce very large savings responses.
Another set of estimates is the intertemporal substitution of labor supply with
respect to changes in the wage rate over time, which tend to be very small, typically
averaging about 0.2, and often not statistically significant. This elasticity must be
derived from the intratemporal elasticity, the intertemporal elasticity and the leisure
shares of hours available.
In general, as discussed in further detail in Appendix C, the labor supply
responses in current intertemporal models appear to be high (and in the case of CBO
much higher than in their neoclassical models), in large part because the functional
form drives models towards income elasticities for leisure with respect to wages to
1, which requires a correspondingly high substitution elasticity to avoid large
backward bending labor supply curves. These elasticities drive both parametric labor
supply elasticities (responses to a proportional change in wages in each period)
28 Jorgenson and Yun, Investment, op. cit.

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CRS-23
making income and substitution effects quite large (as large as 0.6 in some models),
and the intertemporal labor supply elasticity. Most models probably set this latter
elasticity far higher than suggested by the intertemporal substitution estimates,
because they have such a high share of leisure in available hours. Not all models
provide sufficient detail to calculate these derived elasticities, but they appear to be
about 0.76 in the Auerbach-Kotlikoff model and about 1.1 in the CBO models (see
Appendix C). Thus the CBO implicit intertemporal elasticities are over five times
the size of most empirically estimated elasticities (estimated at around 0.2 as
summarized in Appendix C). The JCT’s estimates are slightly below 0.2 and are in
line with the econometric evidence on both intratemporal and intertemporal labor
supply response). The Treasury initially began at 0.75 for one model and 0.5 for
another, but is now at 0.4. Consumption also theoretically responds to changes in
wages over time, although those elasticities have not been estimated directly and tend
to be small in most models. Because of the leisure share of income, the intertemporal
substitution of labor supply with respect to the interest rate is actually larger than the
intertemporal substitution of consumption in many models — about 0.375 in the
Auerbach-Kotlikoff model and about 0.75 in the CBO model.
The easiest way to cause these elasticities to reflect empirical evidence is to set
the leisure share of hours quite low (an approach taken by JCT), but this parameter
is one that has attracted little attention in most cases.
The particular form of utility chosen to allocate consumption throughout the life
cycle (or throughout infinity) also plays an important role in determining the
behavioral response because it leads to equal substitution elasticities between time
periods. But since the price of future consumption is (1/(1+r)) T where T is the time
period, the elasticity of savings with respect to the interest rate can be very large
because of the far apart periods (see discussion in Appendix C).
In 1997, three of the modelers who participated in the JCT study presented a
paper that tested the sensitivity of a tax change to various parameters, based on
revenue neutral tax changes (substituting a flat rate income tax with a consumption
tax and a wage tax).29 Both substitutions would eliminate the tax on new investment
and increase the rate of return. They found the first would have only a negligible
effect on the wage rate, but the second would have a significant effect. In both cases
there are no aggregate income effects in the model although in a life cycle model a
switch to a consumption tax imposes higher taxes on the elderly and lower ones on
the young and a switch to a wage tax does the opposite. They used a base case of a
standard infinite horizon and life cycle model reflecting the parameters of the then
existing Auerbach Kotlikoff model: the intertemporal substitution elasticity set at
0.25, the intratemporal elasticity set at 0.8, the factor substitution elasticity set at 1.0
and the ratio of leisure to hours available 0.6. Because the intratemporal substitution
elasticity is set at 0.8 and the income effect is 1, these effects imply an income
elasticity of labor supply to a proportional change in the wage of 0.6, a substitution
effect of 0.48 and an overall backward bending labor supply elasticity of -0.12.
29 Eric Engen, Jane Gravelle, and Kent Smetters. “Dynamic Tax Models: Why They Do the
Things They Do,” National Tax Journal, vol. 50, September 1997, pp. 657-682.

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CRS-24
These are very high offsetting effects, although the net elasticity is in the empirical
range. Most of the effects in the model are driven by interest rate effects, however.
Some of the important findings of these explorations for the intertemporal
models (referring to the consumption tax substitution and looking at the first five
years) were:
! Results are sensitive to model type. Positive effects of a switch to
a consumption tax in the life cycle model were larger in absolute
size than those in the infinite horizon model for the consumption tax
change, but a large part of that probably reflects the return of retirees
into the work force due to the lump sum tax on old people that is
imposed by a shift from income to consumption. Effects are also
about 20% larger in a life cycle model with myopia as compared to
perfect foresight (both fixed labor models). However, effects were
reduced by about 50% in this myopic fixed labor model when
uncertainty was introduced.
! Although capital expands faster than in the case of the neoclassical
growth model when taxes on capital income are eliminated with
little effect on the wage, the predominant effect is the labor supply
response. The output results for the model with endogenous labor
were about 3½ times the effects for models with fixed labor.
! The savings response was enormous. Eliminating the tax on the
return to capital in these simulations caused the rate of return to
initially rise by about 25% (although the effect was eventually
smaller as the capital stock adjusted). In a myopic life cycle model
(individuals expect pretax wages and rates of return to persist) with
fixed labor, where the rate of return can be treated as fixed and the
25% number holds, savings increased by 127% in the first year,
implying an elasticity of about 5. This response is huge by any
standards and would have been even greater if labor had been
endogenous (in the perfect foresight models, the savings response in
the first year was 60% larger in the infinite horizon model and 26%
larger in the life cycle model, when labor was made endogenous, as
individuals increase work to produce savings to finance future
leisure). By contrast, the percentage increase in the neoclassical
growth model was only 9.5%. Thus the savings rate was over 13
times as large as that in a neoclassical model.
! Results are sensitive to elasticities. In the infinite horizon model,
increasing the intertemporal substitution elasticity from the base of
0.25 to 0.5 increased the average output effect over the first five
years by about 80%. Lowering it to 0.05 reduced the effect by 90%.
(These effects were smaller, 30% and 45%, in the life cycle model).
Because the wage tax rate changed very little, sensitivity analysis to
the intratemporal substitution elasticity is not as meaningful.
Nevertheless, because effective taxes on wages went up, at least in
the short run, changing the intratemporal elasticity to 0 increased

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CRS-25
output by 13%. Reducing the factor substitution elasticity to 0.5
reduced the effect by about 20%. Even the introduction of
depreciation reduced net output increases by 12%.
! Results are quite sensitive to available labor. If the leisure/hours
ratio is set at 0.2 rather than 0.6 to conform them more closely to
empirical estimates of labor supply, the effect fell by 53%.
! Effects can be considerably reduced (by about a half) when
uncertainty is introduced.
The study also indicated significant differences in model type with a shift to a
wage tax, where taxes on wages went up significantly. The life cycle model
produced significant negative effects in the short and the long run, while the infinite
horizon model produced small initial negative responses and positive long run
effects. The short-run effects were positive but smaller in the fixed labor models. In
the life cycle model, reducing the intertemporal elasticity to 0.05 caused the negative
effect to triple, while increasing it to 0.5, turned a negative output effect to a positive
one.
These results suggest a great deal of variability can be expected in the results of
intertemporal models depending on the model type and the elasticities and parameters
used. Moreover, this exploration is limited to comparing simple, one-sector, closed
economy models with relatively simple utility functions. There are many other
features that can alter behavioral response, such as requiring a minimum subsistence
level of consumption in each period, introducing many sectors and allowing an open
economy with perfectly mobile capital.30 (Note, however, that an open economy is
not possible for the infinite horizon model.)
Sensitivity to Method Used to Address the Balanced Budget
Constraint
Intertemporal models with perfect foresight cannot be used to solve the short-
run effect of a stand alone tax cut because the model relies on long run steady state
solutions to be solved at all. While life cycle models can assume individuals behave
as if current rates of return and wages will persist and only taxes change (these are
often called myopic models), these models tend to produce even more unrealistic
savings responses (because they do not account for the eventual fall in the pre-tax
rate of return as the capital stock expands in response to a reduction in taxes on
capital income). Any model with expectations must rely on some other assumed
policy. Policies that retain the income effect (such as assuming that government
spending will be cut) will have a smaller effect on labor supply and savings than
policies that eliminate most or all of the income effect (such as lump-sum tax
changes). Yet a different effect would derive from eventually raising marginal tax
rates, which would lead to a temporary rather than permanent intertemporal shift.
30 These features are also discussed in Gravelle, “Behavioral Responses to a Consumption
Tax,” op cit.

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CRS-26
The recent CBO study demonstrated the dramatic differences in the results of
intertemporal models when different choices are made.31 For the infinite horizon
model in the first five years, choosing to cut government spending resulted in a
budgetary feedback effect of 3% (i.e. the deficit was 3% less than expected) while
imposing a lump sum tax resulted in a feedback of 15%. In the second five years,
these effects are -4% (an increase in budgetary costs) and 17%. With a life cycle
model (closed economy) effects were -6% and 7% in the first five years, -15% and
5% in the second five years. The CBO study could have closed the budget balance
by introducing a future tax increase; such a change probably would have produced
very small effects since it would have eliminated the power of interest rate changes
to induce large short-run labor supply responses to higher rates of return.
The JCT study also used two methods: spending increases and marginal rate
increases; its feedback effects were 3% for the first case and 2.6% for the second.
However, the method of closing the deficit was not as important to its study because
of the temporary nature of tax cuts.
Summary of Issues
This section has outlined a variety of problems associated with intertemporal
models. The interest in these types of models arose from the growing development
of interest in rational expectations and in modeling the economy as agents concerned
with forward looking behavior Many economists doubt that such complex and
sophisticated models can actually describe the behavior of most individuals. The
models produce behavioral responses that are quite large and are governed not only
by estimated parameters that are uncertain in magnitude, but also by functional forms
and assumptions that are somewhat arbitrary. They produce results that are difficult
to believe and that are not supported by the statistical literature. They may propose
elasticities that seem reasonable but may produce factor supply responses outside the
range of empirically estimated results, a point stressed by Charles Ballard who was
the discussant of the intertemporal models in the JCT Symposium. Ballard urged
modelers to try to fit their models to empirical estimates. He also pointed out that
there is no empirical evidence to support the notion that labor supply responds to the
interest rate and that anyone who builds such a response in a model is “shooting in
the dark.” Yet this particular behavioral response is one of the most important ones
in affecting short term response in intertemporal tax models because it produces both
labor supply and savings.
As mentioned in the introduction, there are many other features of these models
that can influence the results. But certainly one of the most troublesome ones is that
intertemporal models with foresight cannot be solved unless some assumption is
made about addressing exploding deficit effects. Thus, no study of a stand alone tax
cut can be made using these models.

31 See Congressional Budget Office. An Analysis of the President’s Budgetary Proposals
for Fiscal Year 2004, March 2003.

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CRS-27
The Effects of Different Models and Assumptions:
A Summing Up
Different types of models will yield substantially different results, depending on
the form of model and the behavioral responses built into the model. These effects
have been demonstrated in a variety of studies that consider the same policy
including the JCT studies published in 1997 and the 1997 study by Engen, Gravelle
and Smetters. The JCT comparisons had first year effects on output of replacing the
income tax with a consumption tax ranging from -2.3% to 7.8% (reflecting both
model differences and elasticity differences). After four years, the effects ranged
from -12.5% to 14.5%. Eliminating the most negative and most positive studies
resulted in a smaller, but still significant range of -1.8% to 5.8% in the first year and
-0.8 and 4.2% after four years. These differences reflected a range of model types
and a range of elasticities used by the nine modelers.
A series of comparisons was done by the Congressional Budget Office for the
President’s budgetary proposals. In the initial (2003) study, for the two models with
unemployed resources, one model led to a reduction in revenue costs of about 30%
that began at 27% and rose slightly over six years until it reached 33%. The other
model began with a 16% reduction which declined and eventually led to a 28%
increase in cost, for an average additional cost of 9%. These models reflect all three
effects (short-run stimulus, deficit, and supply side), and part of the effect is that a
rise in inflation increases nominal revenues and improves the deficit because of an
assumption that appropriations will not be affected by price levels (i.e. a real decline
in government spending).
In the neoclassical model, which incorporated labor supply elasticity (averaging
about 0.1, with a 0.2 substitution effect and a -0.1 income effect) consistent with the
cross section empirical evidence, the feedback effects increased the revenue cost by
6% in the first five years and by 11% in the next five years.
The infinite horizon model led to a reduced revenue cost by 3% or an increased
cost by 4% if lower government spending is used to close the deficit gap. Higher
lump sum taxes led to a reduced revenue cost of 15% and 17%. These latter numbers
reflect the relatively large factor supply responses built into the model which are not
offset by income effects when the budget deficit is closed by lump sum taxes.
In addition to versions of the life cycle model with different ways of closing the
deficit gap, the CB0 study also considered closed and open economies. For the lower
government spending option that leaves income effects intact, feedback would
increase costs by 6% in the closed model and 10% in the open model in the first give
years and by 15% and 5% in the second five years. For the lump sum tax closure that
eliminates some income effects, costs are reduced by 7% in the closed and 6% in the
open economy models in the first five years, and by 5% to 8% in the second five
years.
Overall, the study shows a large range of effects. If supply side responses are
modest and multipliers are small or nonexistent, the eroding effects of the budget
deficit lead to an increase in revenue costs. These supply side effects can be small

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CRS-28
when the elasticities themselves are modest (as in the neoclassical model) or
substitution elasticities are small enough to be largely offset by income effects (as in
the life cycle models). However, when multipliers are large or when supply side
effects are large because of large substitution elasticities that are not offset by income
effects, the revenue cost can be decreased substantially.
Of course the CBO studies do not capture the full range of factor supply
elasticities which can quite reasonably fall in the zero or negative range, so that while
the upper limit of a feedback that reduces revenue may be reflected in its results, the
upper limit of a feedback that increases revenue probably is not. Some sensitivity
analysis, including setting of the elasticities in CBO’s intertemporal model to
correspond more closely to empirical evidence and to the assumptions used in its
neoclassical growth model, and allowing for alternative budget and macro
assumptions regarding how the deficit is closed (e.g. marginal tax rate increases) and
how the monetary authorities might respond would provide a more complete picture
of the range of effects that one might find in these models. Of course, such analysis
would likely increase an already broad range of effects that vary from a reduction in
costs of 30% to an increase in costs of 15%, largely by expanding the latter.
The first JCT study in 2003, while examining only revenue effects from a
temporary tax cut, also showed a wide range of effects from a 2.6% revenue feedback
to a 23.4% one. Variable effects have persisted in later studies and in the Treasury’s
studies.
The discussion of the various studies that provided sensitivity analysis in this
section and in the previous section on intertemporal models points to two important
caveats about dynamic revenue estimating: it is very difficult to obtain a good
estimate because of uncertainty about behavioral responses and very difficult to study
a tax cut without making some sort of assumption about accompanying policies.
Moreover, if the analysis is restricted to supply side effects as some might suggest,
a reasonable estimate of the results based on empirical evidence is likely to be a
negligible effect, reflecting the very modest factor supply elasticities of uncertain
sign.

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CRS-29
Appendix A. Revenue Feedback
Revenue Feedback Effect: Partial Equilibrium
Consider a labor tax at a proportional rate t. The revenue from the tax is tWl,
where W is the wage rate and l is the labor supply. With a small change in t, the
revenue cost is dtWl. The feedback effect is tWdl. The after tax wage is W(1-t).
Holding W constant, the change in the after tax wage is -Wdt, and the percentage
change is -dt/(1-t). Since the elasticity is defined as percentage change in labor
divided by percentage change in wage, dl = -ElWtdt/(1-t). Therefore, the revenue
feedback percentage is -Et/(1-t).
Revenue Feedback Effect: General Equilibrium, Short Run
If we denote Q as output, K as the capital stock, W as the wage rate, R as the
rate of return, with the tax rates and elasticities defined as above. The production
function results in (where the ˆ refers to a percentage change):
(1) $
Q = (1 − a) $L + a $
K
where a is the capital share of income and a ˆ refers to a percentage change.
The first order conditions of the production function result in:
(2) $ = $
L
K
+ S( $R+ $

T − $

W)
where S is the factor substitution elasticity. In these
equations, refers to
the change in tax divided by (1-T).
$T
The percentage change in price is a weighted average of the wage rate and the
rate of return:
(3) $P = (1 −
$
a)W + a( $R + $T)
Finally, define the numeraire as a fixed price:
(4) $
P
= 0
In the short run, a labor demand function can be derived from these equations,
assuming that the capital stock is fixed:
(5) $
L
= (
− S/a $
)(W)

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CRS-30
Note however, that the wage rate can change; in order to solve for the wage
rate, introduce the labor supply elasticity, such that:
(6) $
L = E
$ − $
s (W
T)
Combine (5) and (6) to solve for $
W so that:
(7) $
W = − [aE
+
$
s/(aE s
S)]T
which results in
(8) $L = − [E
+
$
sS / aE s
S)]T
In turn, total output is:
(9) $
Q = − [E
+
$
sS / (aE s
S)]T

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CRS-31
Appendix B. Labor Supply Response
Empirical Evidence
Historical Trends. While it is difficult to use time series to estimate
regressions (because of the endogeneity of the wage rate) the patterns are
nevertheless instructive. Historically, the average hours worked by those in the labor
force has declined over time, from 40.3 hours per week in 1947 to 34.2 in 2001.
Some industries have had virtually no change (manufacturing hours were 40.3 in
1947 and 40.7 in 2001, with very little fluctuation). Since both of these time periods
were associated with rising real wages, they are suggestive of an aggregate zero or
negative response in hours. However, they may also have reflected differing hours
of changing participants in the work force and may also reflect kink points that arise
from institutional constraints on the work week, in particular the overtime pay
requirements for workweeks in excess of 40 hours in many jobs.32
Participation rates have changed over time but not in ways that are especially
meaningful with respect to a wage effect. Male labor force participation rates for
those 15 and over have been declining (falling from 86.1% in January of 1948 to
74.1% in June of 2002). Female participation has been increasing (rising from 32%
in January of 1948 to 59.7% in June of 2002). The decline in the former may reflect
in part the aging of the population as well as some earlier retirement and extended
schooling. Female participation rate increases were especially pronounced in the
seventies and eighties as baby boomers entered the workforce, but their increased
participation may reflect efficiencies in household technology, changes in social
norms, later marriage and declines in fertility. This period was, in fact, not a period
of overall wage growth, although cause and effect cannot be separated (i.e. wage
growth may have slowed because of new entrants).
Over a longer period of time, however, there is a clear fall in labor hours;
indeed, many of the labor disputes in the 19th century and early 20th century involved
movements for shorter work days and work weeks; hours fell from 70 hours a week
in 1856 to 40 hours in 1940.33 During the 1930’s, legislation to mandate a 30-hour
week was debated. Hours rose during World War II, but then fell after the war.
Some of the further decline in the workweek may have come as a result of more part
time jobs in the retail and service industries, reflecting the end of blue laws requiring
Sunday closing.
These observations about work weeks and participation suggest that there are
powerful institutional factors that may constrain a labor supply response in the short
run. In general, the time series evidence on average workweek does not support a
32 For covered employment, payment for overtime is time and a half. Employers thus find
it costly to have workers work in excess of 40 hours (and they might also find that worker’s
productivity declines eventually). At the same time, they may be reluctant to employ part
time workers because of fixed benefits costs (e.g. health insurance). These effects make the
40-hour work week a kink point that may likely be chosen by employers.
33 See “The Workweek in American Industry 1850-1956,” Monthly Labor Review, January
1958.

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CRS-32
positive labor supply response to higher wages, while participation rates provide a
mixed message.
Cross Section Evidence. A second form of evidence, and the one that
receives the most attention from economists, is based on cross section statistical
studies. Indeed, because wages vary across individuals, labor supply has been a
fertile field for econometric studies and the advancement of econometric techniques.
These studies typically compare the labor supply of individuals with different
wage rates. In general the overall elasticities for male labor supply (percentage
change in hours worked divided by percentage change in the wage) are relatively
small and span zero. Indeed, there is a fair amount of reason to believe that the labor
supply elasticity for men is negative: higher wages result in lower work as the income
effect dominates the substitution effect. Pencavel, in his summary of empirical
studies in 1986, reports a wage elasticity for men that ranges from 0.06 to -0.29.34
He reports the central tendency as between -0.17 and -0.08, and the simple average
as -0.12. In a survey confined to a limited number of articles that explicitly included
taxes, Hausman reports similar results.35 The finding of small and possibly negative
responses to wages is confirmed in some later studies.36
An important issue for tax analysis is whether these small elasticities are the
result of offsetting large or small income and substitution effects. Most studies have
found them the result of small offsetting elasticities, which suggests small supply
side effects from changes in tax rate progressivity. A study by Hausman found larger
offsetting income and substitution effects that suggested a more important role for
tax policy; that study has been subject to some criticism and more recent studies have
tended to find small offsetting effects.37
34 John Pencavel, “Labor Supply of Men,” in Handbook of Labor Economics, vol. 1,
Ed.Orley Ashenfelter, New York, Elsiever, 1986.
35 Jerry Hausman, “Taxes and Labor Supply,” Handbook of Public Economics, vol. 1, Ed.
Alan J. Auerbach and Martin Feldstein, New York, North Holland, 1985.
36 See Richard Blundell and Thomas MaCurdy, “Labour Supply: A Review of Alternative
Approaches,” Handbook of Labor Economics, vol. 3, Ed. Orly Ashenfelter and David Card,
Elsiever, 1999 where three additional U.S. studies using panel data and a piecewise budget
constraint found elasticities between 0 and 0.05. Some later studies tended to find higher
positive elasticities but Pencavel argues that those studies are actually picking up
intertemporal substitution elasticities (which are expected to be positive). Pencavel finds
a negative elasticity which becomes more negative with more schooling. However,
elasticities can vary depending on specification. Overall he finds an elasticity of -0.12 for
white men and -0.08 for black men. See John Pencavel, “A Cohort Analysis of the
Association between Work and Wages Among Men, Journal of Human Resources, spring
2002, vol. 37.
37 The study finding large offsetting effects used kinked budget constraints and the criticism
involved statistical restrictions placed on the estimates. In addition to Blundell and
MaCurdy, and Jerry Hausman, cited above, see Thomas MaCurdy, David Green and Harry
Paarsch, “Assessing Empirical Approaches for Analyzing Taxes and Labor Supply,” Journal
of Human Resources, vol. 25, summer 1990. A more accessible article is Thomas MaCurdy,
(continued...)

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The estimation of responses for women is much more complicated and has been
the subject of more attention. While a large majority of men of primary working age
participate in the labor market, a significant fraction of women (at any age) do not
participate, and that was particularly true in earlier years of the 20th century. A
concern that greatly preoccupied econometricians was that estimates of labor supply
response based on women in the labor force would be biased because these women
are not randomly selected (they are self-selected). This aspect of women’s labor
supply creates significant econometric problems which researchers have struggled to
address. In addition, part of the response to wage changes can be not only in hours
of those working, but also in changes in the number of individuals who work.
Considering only those studies (mostly of married women) that have corrected
for selection bias, the range of elasticities is extremely large, ranging from -0.90 to
14, and there are enormous variations even within studies based on methods used.38
A smaller range of effects was found in the smaller number of studies that included
taxes: -0.3 to 2.30.39 A critic of these studies argued that certain methodological
choices tended to bias the estimates upward and concluded that the hours response
was actually similar to that of men.40 Two additional studies since that time found
elasticities of around 1, with 70 to 80% of the response a participation response.41
One of these studies also estimates the response of married women to changes in
husband’s wages (which is negative) finding that the hours response is as large (i.e.
a proportional change in all wages would leave hours unchanged) and that an
increase in the husband’s wage slightly reduces participation as well.42
A recent study that examined changes in women’s labor supply response
indicated that the elasticity of married women’s labor supply had declined
substantially in the past two decades, from an estimated 0.8 or 0.9 in 1980 to 0.6 in
37 (...continued)
“Work Disincentive Effects of Taxes: A Reexamination of Some Evidence,” American
Economic Review, vol. 82, May 1992.
38 Mark Killingsworth and James Heckman, “Female Labor Supply: A Survey.” In
Handbook of Labor Economics, Vol. 1, Ed. Orley Ashenfelter , New York, Elsiever, 1986.
39 Hausman, “Taxes and Labor Supply,” op. cit.
40 Thomas A. Mroz, “The Sensitivity of an Empirical Model of Married Women’s Hours of
Work to Economic and Statistical Assumptions.” Econometrica, vol. 55, July 1987.
41 Richard Blundell and Thomas MaCurdy, “Labour Supply: A Review of Alternative
Approaches,” op cit.; John Pencavel, “The Market Work Behavior and Wages of Women.”
The Journal of Human Resources, vol. 33, fall 1998. Curiously, this latter study also
included single women and found a larger participation response for them than for married
women, which is difficult to reconcile with theory. During this period the wages of married
women as well as their participation rates increased, and it is possible that the results are
reflecting social trends rather than wage response because the data are from repeated cross
sections and thus capture a time dimension.
42 Pencavel, “The Market Work Behavior and Wages of Women,” op. cit.

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CRS-34
1990 and 0.4 in 2000.43 The study also found a decline in response to the husband’s
wage, from -0.3 to 0-0.4 in 1980 to -0.2 in 2000.
Experiments: Natural and Otherwise. A third type of measure uses data
to compare the response of different individuals to a particular change. In the late
1960s and early 1970s a series of experiments with negative income taxes (where
some households were given the benefit and some were not) resulted in estimates of
elasticities for men that also tended to be small and either positive or negative.44
There was also some evidence of a significant withdrawal from the workforce due
to the income effect for married women and a smaller, but still significant effect for
female household heads. There were many problems with these studies, however, and
they relate only to lower income individuals, although they do accord with cross
section data that suggest women are more responsive than men.45
Another type of study that has received increasing attention is the “natural
experiment,” which examines labor supply response to tax changes by comparing
how individuals with different tax rate changes changed their behavior. Most of
these studies have not indicated any response of labor supply to tax changes ( for
aggregate labor income, labor supply of men, or labor supply of high income men),
although one study of the response of very high income women to the 1986 tax
reform act suggested an elasticity of 0.6 to 1.46 About half of the response was due
to participation response, less than is usually thought the case. However, these
elasticities are not comparable to the ones cited above: as noted by the author, they
are more likely to represent the compensated elasticities which reflect only
substitution effects. Uncompensated estimates (such as those discussed above)
which reflect both income and substitution effects would be smaller, but it is difficult
to know what adjustments to make.
Natural experiments face their own problems, and in particular could reflect
trend and cycle effects. For example, women with higher educations increased their
participation rates relative to less educated women towards the end of the 20th
century, which most people agree could have reflected many other factors than
wages. The paper above tried to control for these effects by comparing women
whose family income placed them in the 99th percentile, with those who are in the
90th or the 75th percentile. Surprisingly, the elasticities were larger with the former
43 Blau, Francine D. and Lawrence M. Khan. “Changes in the Labor Supply Behavior of
Married Women: 1980-2000” NBER Working Paper No. 11230 (2005).
44 Pencavel, “The Labor Supply of Men,” op. cit.
45 Hausman, “Taxes and Labor Supply,” op cit.
46 See a review and analysis in Nada Eissa,” Tax Reforms and Labor Supply,” Tax Policy
and the Economy, Ed. James M. Poterba, Cambridge, MIT Press, 1996. In addition to the
work reviewed by Eissa, a working paper by Martin Feldstein (The Effect of Marginal Tax
Rates on Taxable Income: A Panel Study of the 1986 Tax Reform Act, National Bureau of
Economic Research Working Paper 4496) found no clear pattern of response of wage and
salary income (using tax data) to the rate changes in the 1986 act. A detailed study of labor
supply response to the 1986 act focusing on high income men also found essentially no
effect; see Robert A. Moffitt and Mark O. Wilhelm, “Taxation and the Labor Supply of the
Affluent,” In Does Atlas Shrug?, Ed. Joel Slemrod, New York, Russell-Sage, 2000.

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CRS-35
comparison than the latter. Because of trend and cycle effects, one might feel more
sanguine about the results of natural experiments if the results held for a tax increase
as well as a decrease. The 1993 tax increase was an obvious choice as another study
episode; unfortunately studies of the labor supply effects of this change have not
been made.

Studies of social security retirement age changes and earnings tests have also
suggested labor supply responses (more early retirement and less work during
retirement).47
Surveys. Economists have usually been hesitant to rely on survey data.
However, a number of years ago several surveys of affluent men were made, which
included questions about the effect of taxes on work effort. Again, this evidence
suggested a small response for men.48
Some related survey evidence is also interesting: surveys of whether individuals
actually know their average and marginal tax rates and surveys that indicate most
individuals cannot choose their optimal hours.
There is some evidence that marginal tax rates are not reported with much
accuracy.49 In that case, individuals may not respond, particularly to changes in
marginal tax rates. Changes in average tax rates may be more likely to elicit some
effect (or at least their consequences on wages become known, since changes in
average tax rates would be reflected in paychecks).
Survey data also indicate that a large fraction of individuals report that they are
not currently working their optimal hours (some would prefer more hours and some
less), which suggests they are not easily free to make small changes in hours in their
current positions.50
Theoretical Issues
This section of the appendix presents the mathematics for several topics
discussed in this report, including the characteristics of derived participation and
hours elasticities.
The Elasticity for Hours of Work and the Hours Constraint. To obtain
the formula for elasticity:
47 Hausman, “Taxes and Labor Supply,” op. cit.
48 Ibid.
49 See Steven M. Sheffrin, “Perceptions of Fairness in the Crucible of Tax Policy,” in Tax
Progressivity and Income Inequality, Ed. Joel B. Slemrod, New York, Cambridge
University Press, 1994.
50 Shulamit Kahn and Kevin Lang, “The Effect of Hours Constraints on Labor Supply
Estimates,” The Review of Economics and Statistics, vol. 73, November 1991.

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CRS-36
[(1 a)C(1−1/S) aL(1−1/S) ]1/(1−1/S)
−
+
(10) Max
Subject to C = W(H-L) + Y
where C is consumption , L is leisure, W is the wage, Y is nonlabor income, H is
hours available and S is the substitution elasticity.
The first order condition is:
S
S
(11) L/C = [(1−
−
a)/a] W
Now by substituting in the budget constraint, differentiating and making further
substitutions, and denoting hours of labor as l and r as the ratio of non-labor to labor
income, the elasticity can be derived as:
(12) (dl / l) / (dW / W) = [S(1 + r) − 1][L / H][1 / (1 + r[H − L] / H]
Or denoting E as the elasticity and setting r = zero:
(13) E = [ −
S 1][L / H]
Even for typical work weeks, this ratio could be quite small. Available hours,
however, are not all that straightforward to measure. If one just took a 40 hour work
week and a seven day, 24 hours a day available hours, the ratio would be about
three-fourths. However, all hours are not available. For example, there is the
biological necessity for sleep. If one allowed eight hours of sleep per night, about
60% of available hours would be spent in leisure, and thus a unitary elasticity would
fall to a 0.6 elasticity. But even that elasticity is too high. There are certain
minimum requirements for working, that include at least some amount of travel to
work, often a lunch period embedded in the work day, as well as preparation time for
personal hygiene (shaving, bathing, etc.). If we allow, say, two hours per work day
and add it to work, we get a ratio of 55%; if three hours, we get a ratio of 50%.
A study of time allocation for men in the United States indicated that in 1981
men worked 44 hours, commuted for 3.5 hours, slept for 57.9 hours and spent 10.3
hours on personal care.51 If commuting is assigned to work, these findings suggest
a ratio of about between 0.48 and 0.52, depending on whether personal care is added
to work, or excluded from available hours. Moreover, there are many other uses of
time that are highly constrained by necessary household chores or other needs
(eating, shopping, paying bills) or family responsibilities (spending time with spouse
and kids), so that this ratio could be even smaller. Some individuals may also not to
work on particular days for religious reasons (and consider those constraints to be
51 F. Thomas Juster and Frank P. Stafford, “The Allocation of Time: Empirical Findings,
Behavioral Models and Problems of Measurement,” Journal of Economic Literature, vol.
29, June 1991.

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CRS-37
strict). Thus, one would expect to find low labor supply elasticities (for hours) not
only because of netting of income and substitution but also because each of these
effects is small. These observations also make the initial findings of high offsetting
income and substitution elasticities using kinked budget constraints to seem
somewhat implausible.

The other point illustrated by this formula is that the labor supply elasticity is
not constant even though the underlying income and substitution elasticities with
respect to consumption and leisure are. As work increases, the elasticity falls. This
point is important, because it suggests that one should not impose a simple labor
supply elasticity across any significant period of time, but (assuming a rise in real
wages) should have an elasticity that falls over time (becomes a smaller absolute
value if positive and work is increasing and a larger absolute value if negative and
work is decreasing). And, as mentioned earlier, it suggests that elasticities are
smaller for those working more hours, a reason mentioned by Wilhelm and Moffitt
for the lack of a labor supply response by very high income men.52
The example of hours response discussed in this section is meant only to be
illustrative, as it is based on a specific form of utility function that includes unitary
income elasticities and constant substitution elasticities. Adding non labor income
or requiring a subsistence amount of consumption, other things equal, is likely to
increase in the first case and decrease in the other case the likelihood of a positive
elasticity and the size of the substitution elasticity. There are many other types of
functional forms where elasticities vary across consumption bundles and income
elasticities can differ for leisure and consumption. However, the constraints of labor
supply exist and those constraints exert limits on elasticities regardless of functional
form: people working every available hour can work no more.
Participation Responses: Example of the Logit Formula. The effects
of constraints on participation can be most easily seen in the case of the logit
formula. For the logit case, high elasticities tend to decline when participation rates
rise due to wage increases, but low elasticities could rise. The larger the initial
elasticity, the more quickly the elasticity is likely to fall over time. Participation
responses are also constrained and the growing participation rate of women should
lead to lower elasticities; indeed,
The logit form of the participation response can be manipulated mathematically
to illustrate what one might expect as participation rates change:
bx
e
(14) P =
bx
(1+e
)
where P is the probability of being employed, bx is a series of regressors and their
coefficients, including w, and e is the natural constant.
52 Moffitt and Wilhelm, “Taxation and the Labor Supply of the Affluent,” op. cit.

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CRS-38
Differentiating this equation, and denoting b as the coefficient for wages provides
w
a slope of form:
bx
b e
w
(15) dp /dw =
= b WP(1 − P)
bx 2
w
(1 + e
)
and the elasticity of participation
b W
w
(16) Ep =
= b W(1 − P)
bx
w
(1 + e
)
If the change in P is the result of non wage factors, the elasticity should fall as P rises.
In the change in P is the result of wage changes, the elasticity may either rise or fall.
Differentiating equation with respect to W, and substituting from (5), results in
dEp/dw = b (1-P)(1-b PW). Since the sign of the second term can be positive or
w
w
negative, the elasticity can either fall or rise as W rises. One can calibrate this
relationship by the relationships between estimated elasticities, participation rates and
wages, from (7) and eventually the elasticity must fall.
How close have women have come to male participation rates and how much
room is there fore further response? Consider the reasons for not working.53 For
those between 15 to 19, about 54% do not work, and 87% of those do not work
because they are attending school. (About 3% of those who do not work can’t find
a job, about 2% have a temporary or chronic disability, about 2% are taking care of
children, about 2% are not interested in working and about 2% have other reasons).
For those over 65, 85% do not work and 92% of those cite either retirement or
disability as a reason.
The prime working years of 20 to 64 are where the differences in the sexes
emerge. In those groups, about 14% of men do not work, while 27% of women do
not. Most of that differential (about 10 percentage points) reflects differences in
child care responsibilities (or care of others). In each case about 2% are looking for
a job or laid off, almost 5% have chronic disability (and about 1% have a temporary
disability), about 2% are in school. Less than 5% of prime age males are not working
for other reasons; over half of these are retired. Except for minor retirement, virtually
all prime age men are either in the labor force, can not be in, have not succeeded in
entering the labor force, or are preparing to be in the labor force.
About 18% of women are not working for reasons other than these, and over
10% are not working because they are taking care of children or others. Slightly
under 1% are not working because of pregnancy or childbirth, which may or may not
be a voluntary absence. Slightly under 3% indicate a lack of interest in working and
53 See Mai Weismantle, “Reasons People Do Not Work,” 1996, U.S. Census Bureau, Issued
July 2001. Data on labor force non-participants from this study were compared with
population data from the March 1996, Current Population Survey.

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slightly under 3% are retired (the remainder fall into the “other” category). The vast
majority of women who indicate that they are caring for children (or others) are
married. The increase in the ratio of women working over time is partly due to less
marriage and partly due to fewer children or more women with children working.
It may be difficult to expect a significant increase in labor supply from
participation response with these levels of participation. If real wages were to grow
at 2% a year, the real wage would increase by 10% in five years. If there were an
average elasticity of one over that time, there would need to be an increase in female
workers of over 8% of the population. If drawn proportionally from all categories
except the already retired, half of mothers caring for children would have to re-enter
the work force.
There are two other types of participation responses that might be considered,
but both are ambiguous in their effects. First, wages may affect retirement decisions,
but there might, again, be income and substitution effects from higher or lower wages
over a lifetime. Most attention to retirement decisions has focused on the larger
effects of pensions and Social Security. In any case, the fraction of the workforce
over 65 and the fraction of the under-65 workforce not participating because of
retirement is very small (3% in the former case and 2% in the latter in 1996). The
second issue is the choice between spending more time on schooling versus more
time on work. Teenage workers are a small but significant fraction of the workforce
and young adults may also not be working because of schooling. However, the effect
of higher wages may be to increase schooling as the returns increase. Higher wages
also increase the part of the cost of schooling that is in the form of forgone earnings,
but not the direct costs. Thus, one might expect higher wages to increase schooling
and in fact schooling has increased over the years.
Application to Revenue Feedbacks
Uncertainties About Responses. Many of the articles discussed above
contain extensive commentary on the econometric problems encountered in studying
labor supply response, in particular the response of women.
A recent survey of 65 labor economists asking for their best estimates of labor
supply elasticities for prime age men and women is suggestive of the existing
professional lack of consensus about the sign of labor supply response for men and
the magnitude for women.54
For men, the mean was 0.10, a little higher than the evidence that generally
suggests a backward bending labor supply. The median was zero and the standard
deviation was 0.27; hence a standard confidence interval would fall well into the
negative range. (The estimate was zero at the 25th percentile and 0.10 at the 75th
percentile, but as a confidence interval, this is a narrow range.) Compensated
54 Victor R. Fuchs, Alan B. Krueger, James M. Poterba. “Economists’ Views about
Parameters, Values and Policies: Survey Results in Labor and Public Economics,” Journal
of Economic Literature, vol. 36, September 1998.

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CRS-40
elasticities had a mean of 0.22 and a median of 0.18, with a standard deviation of
0.18 (0.08 at the 25th percentile and 0.28 at the 75th percentile).
For women the values were a 0.45 mean and 0.30 median, with a larger
standard deviation of 0.57 (a range that would fall into the negative). The 25th and
75th percentiles were 0.10 and 0.70. Compensated elasticities were a 0.59 mean, a
0.43 median, and a 0.44 standard deviation. The 25th and 75th percentiles were 0.20
and 0.80. The values for women were lower than much of the empirical evidence for
married women, which may reflect an adjustment for single women (who would be
expected to have lower elasticities) and perhaps the growth in participation rates over
time that should move women’s elasticities closer to those of men.
The large standard deviations are suggestive of a great deal of uncertainty in the
measurement of labor supply. Moreover, a significant fraction of respondents did not
answer the question (15% for men’s elasticities and one third for women’s). The
inescapable conclusion is that if the sign of the elasticity matters, we cannot say with
confidence based on the informed judgement of labor economists that it is positive.
One should not make too much of this type of survey data. Labor economists
specialize in particular areas outside of labor supply and many may not be familiar
with all of the literature. Backward bending labor supply curves present certain
difficulties with modeling of business cycles, and economists focused in these areas
may tend to think of labor supply elasticities as positive (otherwise, the survey seems
at odds with the findings of a backward bending labor supply response of men).55
But the survey data do tend to accord in a general way with the assessment made of
the literature: elasticities are probably small but there is a great deal of uncertainty
about them and about whether they are significantly different from zero.
Using Out-of-Date Estimates. Most estimates of labor supply are based on
data from the sixties, seventies or at best the eighties. Even a recent study published
in 1998 (Pencavel) used data from the early seventies to the mid nineties and thus
tends to reflect on average the early eighties. As discussed earlier, elasticities are
expected to change over time, so there is always a question of relying on existing
estimates. In particular, the larger elasticities associated with female labor
participation should be falling, perhaps substantially, particularly if one weights
elasticities by current wage shares (which reflect increased participation rates for
women). Female labor participation increased from about 43% in 1970 to 52% in
1980 to 58% in 1990. Moreover, because the elderly population share was growing
during this time (for example, the elderly share of the over 15 population grew by
about 5 percentage points between 1980 and 2000 for women), the participation rate
among those able to work grew even more. Of course, the perceptions of labor
economists reported above may reflect acknowledgment of the higher participation
rates. As noted above, recent evidence has suggested lower elasticities for women,
55 It is also possible that some respondents forgot to put down minus signs even though they
were reminded in the question.

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CRS-41
and CBO has reduced elasticities in the neoclassical and short-run models (but not
their intertemporal ones).56
Cross Income Elasticities for Married Couples. One would expect cross
section income elasticities (effects of husband’s income on wife’s work effort) to be
negative and at least one study found them to be significant, with a magnitude of
-0.5.57 An aggregate elasticity constructed for the economy based only on own
elasticities should be an overstatement of the true elasticity for purposes of across the
board changes.
With initial small elasticities, this correction could reverse the sign of the
aggregate supply response. With a composite elasticity of 0.1, the median values for
men and women in the survey results with men weighted at 60% and women at 40%
(to reflect both women’s slightly smaller numbers and the female to male wage ratio
of 0.7). If we look back on the empirical evidence for U.S. women, we find a value
for the income elasticity of about -0.20 from the survey of the wide range of largely
cross section elasticities,58 an average of -0.28 from the survey of studies
incorporating taxes,59 and a value of -0.33 from a later panel study.60 These are a
little higher than the mean and median elasticities for all women (computed by
subtracting the Hicksian demand from the Marshallian demand elasticities) from the
survey of labor economists mentioned above, which are -0.13 to -0.14 but it is
commonly thought that married women have more elastic responses in general. A
range from -0.13 to -0.33 seems to reflect a reasonable assumption about these
elasticities. Based on married women’s participation and wages, they would receive
a weight of about 0.25. However, since these weights were corrected for a gender
wage gap, it is appropriate to multiply the elasticities by 1/.7: this yields a range of
-0.19 to -0.47 to reflect the effects of husband’s proportional wage changes.
Multiplying these numbers by 0.25 suggests that any aggregate elasticity computed
by weighting men’s and women’s responses would be reduced by 0.05 to 0.12. At
the lower end, this change would cut the elasticity in half, from 0.10 to 0.05. At the
upper end, this change would transform the 0.10 positive elasticity to a -0.02
(negative elasticity).
56 Congressional Budget Office, The Effect of Tax Changes on labor Supply in CBO’s
Microsimulation Tax Model, April 2007.
57 Pencavel, “The Market Work Behavior and Wages of Women,” op. cit. This study
examined cohorts and is thus not strictly a cross section study; as noted earlier, it is not clear
that controls for social and other changes were incorporated. The estimate is at the high
end of the values discussed subsequently below.
58 Averaged over negative values excluding zeros and positives. See Killingsworth and
Heckman, “Female Labor Supply,” op. cit.
59 Hausman, “Taxes and Labor Supply,” op. cit.
60 This is the 1990 study of Triest, summarized in MaCurdy and Blundell: “Labour Supply:
A Review of Alternative Approaches,” op. cit.

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Appendix C. Intertemporal Models
Empirical Evidence
Empirical evidence relative to this model includes the evidence on labor supply
response in a cross section study which examines the supply response across
individuals, as discussed above. This evidence largely suggests relatively small
income and substitution effects. The evidence regarding the factor substitution
elasticity, again being relatively small, is also directly applicable to intertemporal
models.
Another type of econometric evidence that is relevant to the intertemporal
models is the substitution elasticity across time. These studies have in some cases
employed macroeconomic data, and in others panel data on individuals. There are
two types of evidence. In some studies the change in consumption over time is
estimated as a function of changes in the interest rate. In others, changes in labor
supply are estimated over time as a function of changes in the wage rate. The first
set of studies is relatively straightforward as a direct estimate of the intertemporal
substitution elasticity in a model where labor is fixed or for a combination of leisure
and consumption with certain functional forms (such as those frequently used in tax
models). The intertemporal labor supply elasticity with respect to wage changes has
an interpretation that depends on functional form, discussed below.
Intertemporal Substitution in Consumption
In an early paper on the business cycle, Prescott61 chooses a value of around 1;
he reports three studies that range from 0.5 to 1. The real business cycle model he
was pursuing requires a large substitution elasticity to be viable, however. Indeed,
growing questions about these elasticities have led to skepticism about real business
cycle theories. Auerbach and Kotlikoff62 report the results of nine different studies
which ranged in value from less than 0.1 to more than 1. The median value was
around 0.3 and a weighted average of eight of them using the mid-point of each range
(and excluding a study by Mankiw, Rotemberg and Summers in which it is clear the
authors were not very satisfied with the model) yielded an estimate of 0.39.
Elmendorf63 undertakes a survey of the studies most commonly cited and obtains a
weighted average of 0.37; he uses 0.33 in his work. More recent studies were mostly
consistent with these general results, namely that the elasticity is probably below
0.5.64
61 Edward C. Prescott, “Theory Ahead of Business Cycle Measurement,” In Carnegie-
Rochester Conference on Public Policy, vol. 24, pp. 11-44, 1986.
62 Alan A. Auerbach and Laurence J. Kotlikoff, Dynamic Fiscal Policy, New York:
Cambridge University Press, 1987, p. 50.
63 Douglas W. Elmendorf, “The Effect of Interest-Rate Changes on Household Saving and
Consumption,” Federal Reserve Board, June 1996.
64 Annette Vissing-Jorgenson, “Limited Asset Market Participation and the Elasticity of
Intertemporal Substitution,” National Bureau of Economic Research working paper 8896,
(continued...)

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Studies of the Intertemporal Labor Supply Elasticity with
Respect to Wages
Intertemporal substitution elasticity estimates of labor supply with respect to
wages have been very small. These studies which generally look at patterns of labor
over time as wages change (the time profile of earnings) and small elasticities are
perhaps not surprising given the greater difficulty of shifting labor across time
periods. Pencavel’s 1986 survey65 reflected a median value of 0.26 and an average
of 0.21, with some results not statistically significant. Adding an additional study
reported by Auerbach and Kotlikoff along with three referred to in Ham and Reilly66
and one additional study67 yielded a similar average of 0.20. French 68 also reports
64 (...continued)
April 2002 found an elasticity less than 0.1 in aggregate. Ogaki Masao and Carmen M.
Reinhart, “Measuring Inter-temporal Substitution: The Role of Durable Goods, “ Journal
of Political Economy, vol. 106, no. 5 (October 1998), pp. 1078-1098 found an elasticity of
0.2-0.4. Abdullahi O. Abdulkadro and Michael R. Langemeier, “Using Farm Consumption
Data to Estimate the Intertemporal Elasticity of Substitution and Relative Risk Aversion
Coefficients,” Agricultural Finance Review, vol. 60, 2000, pp. 61-70, found 0.158-0.351.
Other studies that confined their analysis to food also found low elasticities. Motohiro
Yogo, “Estimating the Elasticity of Intertemporal Subsitution when Instruments are Weak,”
Review of Economics and Statistics, v. 86 (August 2004), pp. 797-810, found an elasticity
less than one that was not statistically significant across eleven deceloped countries. Pierre-
Olivier Gourinchas and Johnathan A. Parker find elasticities ranging from 0.7 to almost 2
(depending on certain weights used) in “Consumption over the Life Cycle,” Econometrica,
v. 70, (June, 2002), pp. 47-89, but this approach presumes powerful precautionary savings
effects. Two unpublished studies have included nuances in mesuring the discount rate.
Jonathan Gruber, A Tax Based Estimate of the Elasticity of Intertemporal Subsitution,
National Bureau of Economic Research, Working Paper 11945, January 2006, finds a very
high elasticity when using the marginal tax rate on interest, but stresses the need for further
work. Fuad Hasanov, in his dissertation (University of Texas), Residential Housing,
Household Portfolio, and Intertemporal Elasticity of Subsitution, finds an elasticity of 0.15
to 0.30 when including housing returns in the portfolio for measuring interest rates. Studies
that try to determine this parameter by fitting it to a single aggregate value are not referred
to here because such calibration approaches can be extremely sensitive to model features.
See Owen Evans, “Empirical Tests of the Life Cycle Model: Comment,” in American
Economic Review, vol. 84, March 1984, pp. 254-257, for a discussion.
65 Pencavel, The Labor Supply of Men, op. cit. Taking medians of ranges, the studies
reported values of 0.26, 0.31, 0. 32, and 0,10.
66 Auerbach and Kotlikoff, Dynamic Fiscal Policy, op. cit. rely largely on a study by Ghez
and Becker that had an elasticity of 0.28. John C. Ham and Kevin T. Reilly, “Testing
Intertemporal Substitution, Implicit Contracts and Hours Restrictions Models of the Labor
Market Using Micro Data,” American Economic Review, vol. 92, September 2002, pp. 905-
927 refer to Altonji (1986), Ham (1986) and French (2000), all with elasticities below 0.1
Their own tests reject the intertemporal model.
67 Chul-In Lee, “Finite Sample bias in IV Estimation of Intertemporal Labor Supply Models:
Is the Intertemporal Substitution Elasticity Really Small?” Review of Economics and
Statistics, vol. 83, no. 4, November 2001
68 Eric Fench, “The Labor Supply Response to (Mismeasured but) Predictable Wage
(continued...)

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some other studies whose values were not clear from their studies but, according to
French, fell below 0.5. French also summarizes some specialized or event studies
that found widely varying results. Looney and Monica examined hours for both
women and men and found no effect.69
Theoretical Issues
The intratemporal substitution elasticity is the parameter governing the
substitution of consumption and leisure within a period. It also governs the response
to an equal percentage change in wages in all time periods, thus becoming the
lifetime analog of the basic substitution elasticity that is reflected in the labor supply
equation presented earlier. Moreover, most models use functions that set income
elasticities to one, so the wage elasticity of labor supply elasticity is given a
proportional change in wages across all periods and ignoring capital income on hand
is (L/H)(S-1), where L is leisure, H is hours available, and S the intratemporal
substitution elasticity. (This formula is somewhat modified in the intermediate term
for those who have already accumulated non labor income; the substitution effect
will be slightly larger and the income effect slightly smaller).70 If the elasticities are
not set to yield a steady state growth, which means that aggregate labor supply cannot
respond to wage growth, some assumption must be made in the model to correct for
it. For that reason, it is difficult to justify a very small or very large substitution
elasticity. To keep the income and substitution elasticities in line with empirical
evidence from cross section labor studies, the ratio of leisure to hours available
should be set quite low, probably around 0.2. It often is not, leading to very large
labor supply elasticities that are inconsistent with evidence.

A similar problem can arise with conforming to the relatively low intertemporal
substitution elasticities for labor with respect to wage rate changes. The effects
depend on the functional form of the model, but in the nested utility functions that
are commonly used in tax models, the intertemporal substitution elasticity is a
weighted average of the intertemporal and intratemporal substitution elasticities, (
and D (new notation is chosen to conform to a reference equation) multiplied by the
share of leisure over labor, or:
(17) [L/(H− L)][ a
γ +ρ(1 −a)]
68 (...continued)
Changes.” Federal Reserve Bank of Chicago, Working Paper No. 2000-08, August 2000.

69 Adam Looney and Monica Singhal, “The Effect of Anticipated Tax Changes on
Intertemporal Labor Supply and the Realization of Taxable Income,” Finance and
Economics Discussion Series, 2005-44. This study that used the loss of a dependent to
identify an expected change in the marginal tax rate and found no change in labor supply
(either in participation, or in hours worked by existing participants). The study did find a
curious increase in labor income of men, which is not easily explained, although it is
possible that there was a shifting of income over time periods or a shift to fringe benefits,
or perhaps an increase in work intensity.
70 The substitution elasticity is (1+x)S*L/[H(1+x)-xL] where x is the share of nonlabor
income. The income elasticity is L/[H(1+x)-xL)].

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where L is leisure and a is the share of total consumption spent on leisure
(wL/(c+wL)) where w is the wage rate and c is expenditure on goods). This formula
can be derived from the transition equation for leisure in equation 3.12 of the
Auerbach and Kotlikoff’s book, Dynamic Fiscal Policy, making use of 3.11 and 3.9.
(Note that 3.12 has an error, which is that v v should not be raised to the power -D
t/ t-1
and note also that equation 3.11 has an error in that the term " should be raised to the
power D rather than being multiplied by it.)
This formula would also require leisure to be a relatively small part of hours
(and small relative to labor) in order to keep the intertemporal labor elasticity with
respect to wage relatively low. For example, in the CBO model, ( is 0.5, D is 1.0, a
is 0.53 and L/(H-L) is 1.5 because leisure is 60% of hours available. That result is
1.1, but if the leisure were set at 20% (which would change a to 0.2 and L/(H-L) to
0.25), it would be 0.225, in the neighbor hood of the empirical estimates. A
reduction in the intertemporal elasticity itself would reduce it even further.

In these nested functions consumption over time is also affected by available
wages, but in this case, the elasticity is (derived from equation 3.10 in Dynamic
Fiscal Policy):
(18) (D-() a
which in the CBO model would be about 0.265. Making the change in leisure would
reduce it to 0.1, and changing the intertemporal elasticity to 0.25 would change it to
0.15.
The final set of substitution elasticities is the change in consumption and leisure
with respect to the interest rate. This value is estimated directly but not always over
a long period of time. This elasticity rises as periods become farther apart because
of the compounding of interest and the percentage change in current consumption r-
the percentage change in consumption T years in the future is equal to:
(19) -(T(r/(1+r))
If r is .05 and ( is 0.5, the one period apart, the elasticity is -0.024, for two periods
apart, -0.048, for ten 0.24, and for 50 -1.19. However, if we convert it to an elasticity
of substitution between savings in each period, which has a magnitude more closely
corresponding to the reduced form savings estimates, the elasticity should be divided
by the savings rate, which is usually well under 0.10. Using 0.06 as an example, the
percentage change in savings today minus the percentage change in savings in the
future would be 0.40 for times one period apart, 4 for 10 years apart and 20 for 50
years apart. Thus, the implied elasticities of savings with respect to the interest rate
are very large.
There is also substitution elasticity for leisure over time which leads to an
intertemporal labor supply response to the rate of return. In this case, it’s size also
depends on the ratio of leisure to labor; thus it is larger that the substitution between
consumption in many models because it is multiplied by leisure over labor. If leisure
over labor is 1.5 as in the CBO model it is 50% larger; however, a much lower

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substitution elasticity could be obtained by reducing the leisure share, and also by
reducing the intertemporal elasticity itself.
Note that the income effects are more complicated in these models. There is an
offsetting income and substitution effect that affects the price of future consumption
goods so that if the intertemporal substitution effect were unitary these effects would
offset each other. With an intertemporal substitution elasticity of less than 1, these
types of income effects would result in more consumption with a rise in the interest
rate because future consumption is discounted at a higher rate. However, an increase
in the interest rate also reduces the present value of human wealth, and this latter
effect would reduce consumption and increase savings. At the same time, there is
existing income from capital in the model that can be affected. Therefore, how these
effects occur depends on a variety of factors in the model and what fraction of the tax
cut affects average versus marginal rates of interest.
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