Issues in Dynamic Revenue Estimating
Prepared for Members and Committees of Congress
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
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.
Types of Effects and Types of Models.............................................................................................2
Short-Run Stimulus Effects.............................................................................................................5
Deficit Effects and Crowding Out...................................................................................................7
Supply Side Effects in the Basic Neoclassical Growth Model........................................................8
Labor Supply Response.............................................................................................................9
Theoretical Issues: Why Labor Supply Elasticities Are Probably Small, Can Be
Negative, and May Be Falling.......................................................................................10
Using Empirical Evidence on Elasticities for Dynamic Scoring Purposes.......................13
The Production Function and Factor Substitution Elasticities................................................15
Conclusion .............................................................................................................................. 17
Are Intertemporal Models Realistic Representations of Behavior?........................................18
Correspondence to Empirical Evidence..................................................................................20
Sensitivity to Method Used to Address the Balanced Budget Constraint...............................23
Summary of Issues..................................................................................................................23
The Effects of Different Models and Assumptions: A Summing Up............................................24
Table 1. Percentage Change in Labor Employed with a Percentage Change in Tax (Fixed
Appendix A. Revenue Feedback...................................................................................................26
Appendix B. Labor Supply Response...........................................................................................28
Appendix C. Intertemporal Models...............................................................................................38
Author Contact Information..........................................................................................................41
ynamic 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 D
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
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 1
study). 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 2
recent study was of the President’s FY2008 budget proposal. 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 3
(hereafter JCT study). 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
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 4
reform proposal that would broaden the base and lower the rate. This proposal was not a tax cut,
but a revenue neutral reform, and 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 5
neutral tax change. For the income tax reform, the effects on output in the budget window ranged 6
from 0.1% to 0.4%. For the consumption tax proposal, the effects ranged from 0.1% to 1.9%. A 7
subsequent analysis examined the effects of the 2001-2004 tax cuts. This study did not report
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 2008, March 2007.
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 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 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
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 89
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
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.
There are three types of revenue feedback effects:
• short-run stimulus, or Keynesian effects
• crowding out effects of deficits
• 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
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 10
• Basic neoclassical growth models (also called Solow models);
President’s Tax Relief, July 25, 2006.
8 CRS CRS Report RL33672, Revenue Feedback from the 2001-2004 Tax Cuts, 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
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.
• Short-run models with underemployed resources typically used for short-run 11
forecasting. These models are also referred to as ISLM 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
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 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
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
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.
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 12
third type, and three of the final type. 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 13
type. 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 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 14
There are issues surrounding the estimation and even the appropriateness of including these
various effects, which are discussed in turn.
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.
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.
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 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 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 15
in constant dollars.
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 16
and Washington University Macro Model (WUMM). 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 17
so much that output is fixed).
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
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.
their subsequent 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.
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 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.
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 also had small
effects, with a total elasticity of 0.05 in the base case and 0 in the low elasticity case. 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
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
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 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 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:
• 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
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.
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).
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 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.
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 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 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.
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
19 Moffitt and Wilhelm, “Taxation and the Labor Supply of the Affluent,” In Does Atlas Shrug?, Ed. Joel Slemrod,
New York, Russell-Sage, 2000.
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 20
eventually converge to those of men.
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.
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 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
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.
20 See Heckman, James J., “What Has Been Learned About Labor Supply in the Past Twenty Years,” American
Economic Review, vol. 83, May 1993.
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.
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.
The first challenge in seeking an elasticity, or elasticities, to use in dynamic scoring for tax
purposes is choosing 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 21
labor elasticity is too large and a negative one should be even more negative).
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.
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 22
for men and the magnitude for women. Details are presented in Appendix B.
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 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.
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.
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.
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
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.
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
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)
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 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 23
increased this value to 0.5 to 0.7).
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 24
a long panel data set. 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
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 Elasticity,”
Working Paper, October 2002.
smaller in the short run, when technology combining capital and labor cannot easily be changed,
than in the long run.
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 25
be considered relatively high. 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 capital stock increased by less than 2% after 10
years, and output increased by only 0.4%.
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
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.
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
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.
• 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?
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
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 of their children, their 26
grandchildren, and, indeed, all future generations. 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 27
optimizing over a long period of time. (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
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 the assumption must be made that these patterns reflect the execution of plans that
were carried out in anticipation of lifetime prices and incomes.
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.
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
modeler to 0.4. The CBO models used 0.5 and the JCT 0.25. 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) 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
28 Jorgenson and Yun, Investment, op. cit.
summarized in Appendix C). The JCT’s estimates are 0.15 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 T
consumption is (1/(1+r)) 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 29
(substituting a flat rate income tax with a consumption tax and a wage tax). 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. 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
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.
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
• 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
• 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 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
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
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 30
and allowing an open economy with perfectly mobile capital. (Note, however, that an open
economy is not possible for the infinite horizon model.)
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.
The recent CBO study demonstrated the dramatic differences in the results of intertemporal 31
models when different choices are made. 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.
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
30 These features are also discussed in Gravelle, “Behavioral Responses to a Consumption Tax,” op cit.
31 See Congressional Budget Office. An Analysis of the President’s Budgetary Proposals for Fiscal Year 2004, March
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
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.
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
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
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
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 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.
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).
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 ^
refers to a percentage change):
where a is the capital share of income and a ^ refers to a percentage change.
The first order conditions of the production function result in:
where S is the factor substitution elasticity. In these equations, ˆT refers to the change in tax
divided by (1-T).
The percentage change in price is a weighted average of the wage rate and the rate of return:
Finally, define the numeraire as a fixed price:
In the short run, a labor demand function can be derived from these equations, assuming that the
capital stock is fixed:
Note however, that the wage rate can change; in order to solve for the wage rate, introduce the
labor supply elasticity, such that:
Combine (5) and (6) to solve for ˆW so that:
which results in
In turn, total output is:
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 32
overtime pay requirements for workweeks in excess of 40 hours in many jobs.
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 thth
labor disputes in the 19 century and early 20 century involved movements for shorter work 33
days and work weeks; hours fell from 70 hours a week in 1856 to 40 hours in 1940. 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
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 positive labor supply response to
higher wages, while participation rates provide a mixed message.
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.
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 34
-0.29. 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 35
reports similar results. The finding of small and possibly negative responses to wages is 36
confirmed in some later studies.
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 37
more recent studies have tended to find small offsetting effects.
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 th
true in earlier years of the 20 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.
34 John Pencavel, “Labor Supply of Men,” in Handbook of Labor Economics, vol. 1, Ed.Orley Ashenfelter, New York,
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, “Work
Disincentive Effects of Taxes: A Reexamination of Some Evidence,” American Economic Review, vol. 82, May 1992.
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 38
variations even within studies based on methods used. A smaller range of effects was found in 39
the smaller number of studies that included taxes: -0.3 to 2.30. A critic of these studies argued
that certain methodological choices tended to bias the estimates upward and concluded that the 40
hours response was actually similar to that of men. Two additional studies since that time found 41
elasticities of around 1, with 70 to 80% of the response a participation response. 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 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, 43
from an estimated 0.8 or 0.9 in 1980 to 0.6 in 1990 and 0.4 in 2000. 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.
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 44
elasticities for men that also tended to be small and either positive or negative. 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 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
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.
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.
high income men), although one study of the response of very high income women to the 1986 46
tax reform act suggested an elasticity of 0.6 to 1. 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 th
less educated women towards the end of the 20 century, which most people agree could have
reflected many other factors than wages. The paper above tried to control for these effects by th
comparing women whose family income placed them in the 99 percentile, with those who are in thth
the 90 or the 75 percentile. Surprisingly, the elasticities were larger with the former 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 47
supply responses (more early retirement and less work during retirement).
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 48
work effort. Again, this evidence suggested a small response for men.
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).
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.
47 Hausman, “Taxes and Labor Supply,” op. cit.
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.
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 50
are not easily free to make small changes in hours in their current positions.
This section of the appendix presents the mathematics for several topics discussed in this report,
including the characteristics of derived participation and hours elasticities.
To obtain the formula for elasticity:
(11/S) (11/S) 1/(11/S)[(1 a)C aL ]−−−−+
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:
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
Or denoting E as the elasticity and setting r = zero:
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%.
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.
A study of time allocation for men in the United States indicated that in 1981 men worked 44 51
hours, commuted for 3.5 hours, slept for 57.9 hours and spent 10.3 hours on personal care. 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 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 52
by very high income men.
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.
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:
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.
52 Moffitt and Wilhelm, “Taxation and the Labor Supply of the Affluent,” op. cit.
(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.
Differentiating this equation, and denoting bw as the coefficient for wages provides a slope of
(1 e )+
and the elasticity of participation
(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 = bw(1-P)(1-bwPW).
Since the sign of the second term can be positive or 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 53
further response? Consider the reasons for not working. 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
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
3% indicate a lack of interest in working and 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.
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 54
the sign of labor supply response for men and the magnitude for women.
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 th
confidence interval would fall well into the negative range. (The estimate was zero at the 25 th
percentile and 0.10 at the 75 percentile, but as a confidence interval, this is a narrow range.)
Compensated elasticities had a mean of 0.22 and a median of 0.18, with a standard deviation of thth
For women the values were a 0.45 mean and 0.30 median, with a larger standard deviation of thth
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.
Compensated elasticities were a 0.59 mean, a 0.43 median, and a 0.44 standard deviation. The thth
25 and 75 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 55
supply response of men). 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.
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, and CBO has reduced elasticities in the neoclassical and 56
short-run models (but not their intertemporal ones).
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
55 It is also possible that some respondents forgot to put down minus signs even though they were reminded in the
56 Congressional Budget Office, The Effect of Tax Changes on labor Supply in CBO’s Microsimulation Tax Model,
-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 58
range of largely cross section elasticities, an average of -0.28 from the survey of studies 5960
incorporating taxes, and a value of -0.33 from a later panel study. 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
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.
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.
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 62
have led to skepticism about real business cycle theories. Auerbach and Kotlikoff 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 63
were not very satisfied with the model) yielded an estimate of 0.39. Elmendorf 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 64
the elasticity is probably below 0.5.
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,
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, 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
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 65
difficulty of shifting labor across time periods. Pencavel’s 1986 survey 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 666768
Reilly and one additional study yielded a similar average of 0.20. French also reports some
other studies whose values were not clear from their studies but, according to French, fell below
Looney and Monica examined hours for both women and men and found no effect.
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
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 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.
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 70
slightly smaller). 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, γ and ρ (new notation is chosen to conform to a reference equation)
multiplied by the share of leisure over labor, or:
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 vt/vt-1 should not be
raised to the power -ρ and note also that equation 3.11 has an error in that the term α should be
raised to the power ρ 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, γ is 0.5, ρ 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) (ρ-γ) a
which in the CBO model would be about 0.265. Making the change in leisure would reduce it to
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
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
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:
If r is .05 and γ 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
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 substitution elasticity could be obtained by reducing the leisure share, and
also by reducing the intertemporal elasticity itself. In the JCT model, the intertemporal
subsitution elasticity is lower, at 0.25, and the ratio of leisure to labor is less than one (0.43), so
the elasticity of substitution for leisure over time is smaller.
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.
Jane G. Gravelle
Senior Specialist in Economic Policy