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THE IMPLICATIONS FOR TAX POLICY OF UNCERTAINTY ABOUT LABOR-SUPPLY AND SAVINGS RESPONSES WILLIAM C. RANDOLPH* & DIANE LJM ROGERS*

INTRODUCTION

When economists predict the economic effects of tax policies, uncertainty is inevi- table and yet is often ignored. How people and firms respond to changes in the tax base or tax rates can greatly influence the revenue, efficiency, and distributional effects of policies. While economists often have a wide variety of opinions and much uncertainty about the correct values of behavioral parameters, policy forecasts are usually presented based on particular, subjectively chosen values. In the rare instances where a parameter sensitivity analysis is conducted, the results fail to convey a quantitative understanding of the likelihoods of alternative forecasts. Yet it is certainly possible to do so. If we quantitatively characterize our subjective uncertainty about behavioral parameters, we can translate this into quantitative statements of uncertainty about the policy forecasts. Formally showing what we

*Congressional Budget Office, Washmgton, D C 20515

do not know can help us make more ac- curate statements about what we do know.

The uncertainty is well illustrated in the case of current proposals to replace our income-tax system with a consumption- based tax. In this paper, we examine what we do and do not know about two types of behavioral responses most critical to the consumption-tax versus income-tax debate. We show how our uncertainty about the sizes of these behavioral responses can be translated into statements of uncertainty about the economic effects of a switch from an income tax to a consumption tax.

BEHAVIORAL RESPONSES THAT MATTER MOST

When economists compare the relative efficiencies of Income tax and consumption tax systems, the predictions depend critically on two aspects of individual tax- payer behavior: (1) the responsiveness of savings to the rate of return, and (2) the responsiveness of labor supply to wages. A comprehensive income tax reduces the

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rate of return to savings and the return ‘to working. If either saving or labor-supply changes, the income tax can result In lost welfare. In contrast, a broad-based consumption tax is equivalent in the long ru,n to a tax on wage income alone. To raise the same amount of revenue as the income tax, tax rates on the narrower wage income base must be higher than they would be under the cornprehensive income tax, and the tax rate on Income from saving would be zero. If savtng is very responsive and labor supply is not, the consumption tax will tend to be more economically efficient th13n the income tax. The economic efficiency comparison depends critically, t houg’l not exclusively, on the size of the saving and labor-supply responses.

Economists often use colnputable general equilibrium (CGE) rnodels to forecast the relative efficiencies of different tax systems. These are complex computer simulation models of whole economies built up from the level of individual economic decision makers. To compare tax systems, an analyst would use a CGE model to compute equilibrium prices and quantities of all goods produced and consumed under each tax system. The simulations would also determine wages, capital costs, and the associatecl labor and capital supplies in each equilibrium. Compari- son of equilibria under each tax system would allow predictions about relative efficiencies of the different tax systems.

The current state of the art in CGE mod- eling of tax systems is characterized by the use of dynamic life-cycle models.’ In dynamic CGE models, consumers live out complete lifetimes and have children, to whom they may bequeath part of their ‘wealth. An advantage of these models over older models is that they explicitly model life-cycle savtng behavior, whereas the older models typically characterized ‘saving in a more ad hoc: manner.*

For the best known dyr)amic CGE models, the critical savings and labor-supply responses (are determine essentially by two d parameters, the intertebporal and intratemporal elasticities of $ubstitution. The intertemporal elasticity of substitution is most important as a determinant of saving. The intratemporal elasticity is most important as a determinant of labor sup- PlY.

Intertemporal Elasticity of Substitution

In the life-cycle model, individuals choose quantities of goods and nonmarket time, “leisure,” to consume dt each age, given the size of their initial wealth endow- ments and the prices arhd wage rates they face at each age. Depemding on their tastes, the prices and initerest rates may cause them to consume! less when they are young than when they are older (to save) or 10 consume relptiveiy more when they are younger (to boirrow or dissave). Economy-wide rates of saving will depend on the chosen patterns ,of lifetime consumption.

The Intertemporal elasti(city of substitution measures how the pattern of lifetime consumption changes in response to changes in the relative @rices of consumption at dtfferent ages. Fpr example, fol- lowing a reduction in income tax rates, an initial increase in the after-tax rate of return would make future consumption relatively cheaper, which would cause people to shift consumotion into the future by saving more or borrowing less. This shift is the intertemporal substitution effect. The increase in the after-tax rate of return would also inqrease the wealth of savers, which would cause them to want to consume moreNat every age. This change is the income effect. The substitution and income effects act in opposite directions on current consumption. Whether savings would rise or fall after the tax reduction would depend on the

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relative sizes of the offsetting intertemporal substitution and income effects.

The intertemporal elasticity of substitution measures the size of the intertemporal substitution effect. For a percentage change in the relative prices of current and future consumption, the intertemporal elasticity is defined as the resulting percentage change in the ratio of future to current consumption, after compensating for the income effect. The intertemporal substitution elasticity is either zero or positive. A compensated increase in the rate of return will either increase current saving or leave it unchanged.

The intertemporal elasticity of substitution is important for tax policy analysis because, when we measure the welfare loss from a tax on the rate of return to saving, for example, the size of the welfare loss is essentially determined by the size of the inter-temporal elasticity of substitution. A large intertemporal elasticity of substitution implies that people will significantly alter their lifetime consumption and savings patterns in response to changes in the after-tax rate of return caused by changes in tax rates. A large value makes it more likely that there are large efficiency gains from switching to a consumption-based tax.

lntratemporal Elasticity of Substitution

The intratemporal elasticity of substitution is another important measure of tastes in the life-cycle model. At each age, people choose the quantities of goods to consume and how much time to work in the labor market. Their ability to consume is an increasing function of how much they work and earn. By choosing a level of labor supply, they effectively make a trade- off between the consumption of goods and leisure time.

If the after-tax wage is increased, even though the return to work increases, peo-

ple may decide to either increase or decrease labor supply, depending on the relative sizes of the intratemporal substitution and income effects. Because a higher income is earned at the higher after-tax wage, for a given level of market work, people may decide to consume more leisure and, so, supply less labor. This is the income effect of the wage increase. However, because the higher wage makes leisure more expensive relative to other goods, people may decide to consume less leisure and more goods. This is the substitution effect. The income and substitution effects act in opposite directions, so whether an increase in the after-tax wage increases or decreases labor supply depends on the relative sizes of the Income and substitution effects.

In the life-cycle models of behavior used for the dynamic CGE models, individuals choose a combination of market labor to supply and goods to consume at each age. The intratemporal substitution elasticity measures, in percentage terms, how the desired ratio of goods to leisure changes in response to a change in the ratio of wages to the price of goods at a particular age, compensating for the income effect of the wage change. A large intratemporal elasticity of substitution implies, for example, that a decrease in the after-tax wage caused by an increase in the tax rate would lead to a large compensated decrease in labor supply. Thus, a larger value of the elasticity increases the possibility that a switch to a consumption tax will reduce efficiency.

EMPIRICAL STUDIES

To use a CGE model for policy prediction, values must be chosen for the behavioral parameters. Modelers usually choose the values of inter-temporal and intratemporal elasticities based on the estimates provided in two bodies of published empirical literature. One literature provides di-

rect estimates of the intertemporal elasticity of substitution. The other litera- tlJre deals with labor-supply behavior.

What Is Known about the Intertemporal Elasticity of Substitution

Researchers have followed three general approaches to estimate the intertemporal elasticity of substitution. The first and most natural approach measures how life-cycle goods consumption decisions are affected by changes in interest rates. The second approach, the life-cycle labor supply approach, measures how people change their labor supply as their wage rates change with age. The third approach, the rational expectations approach, measures how people change consumption over time in response to changes in expectations about real interest rates.

Researchers who follow the life-cycle consumption approach have used aggregate time-series data to estimate the parameters of an aggregate life-cycle consumption function. In the life-cycle theory, consumption depends on income, wealth, interest rates, and demographic variables. The rntertemporal elasticity of substitution can be estimated by measuring the effects of interest rates on consumption after controlling for the other variables.

By studying U.S. time-series data from 1930-65, excluding 1941-6, Weber (‘1970) produced estimates of the intertemporal elasticity of substitution that ranged from 0.13 to 0.41. One problem is that the estimates were based on ob- slerved nominal interest rates, whereas the theory implies that the intertemporal elasticity measures a response to changes in real interest rates. In a later study, We- bier (1975) used real interest rates and added 5 years of data. The later study produced estimates of the intertemporal

elasticity of substitution that ranged from 0.56 to 0.76.

There are reasons to be cautious about the available estimates based on the life- cycle lconsumption approach. To interpret the results as estimates of the intertemporal elasticity of substitytion many un- tested aggregation assumptions have to be satisfied. Further, even If the aggregation assumptions are all justified, it is not clear that the parameter estimates iden- tify the causal effect of real interest rates on consumption. The esbimates may also measure the correlations of consumption and interest rates with other economic changes tlrlat take place over the business cycle.

Researchers who follow the second approach, the life-cycle labor supply approach, h(3ve measured how changes in relative current and future wages affect the pattern of labor supply as people get older. In the life-cycle theory of labor supply, people choose how Inuch to consume of both goods and leisure at each age. Just as the rate of return to saving affects the relative prices, of consuming goods at early rather thain later ages, changes in wages as pedple get older also affect the relative pt$ces of consuming lelsureb at early rather’ than later ages. For example, if someone’s wage will be highest during midlife, they may choose to work the longest hours then, when leisure is most expensive, aInd take more time off at other ages. The intertemporal elasticity of substitution qan be measured by observing how people make such trade-offs.

The life-cycle labor-supply studies are based on information about t.he behavior of individuals and ideally use longitudinal data, as in MaCurdy (1981). MaCurdy (1981) used data on just over 500 white, prime-age males, whose labor-supply decisions were observed over as many as 10 years. His estnmates of the intertemporal

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1 IMPLICATIONS FOR TAX POLICY

elasticity of substitution range from 0.1 to 0.45. The most precise estimate, 0.25, has a standard error of 0.1 and a 95 percent confidence interval between 0.05 and 0.45. However, this estimate is derived under an assumption that real interest rates are constant over time. When he relaxes this assumption, the best estimate is 0.3, which has a standard error of 0.18 and a 95 percent confidence interval between -0.05 to 0.65.

According to MaCurdy (1981), his estimates are consistent with the estimates from earlier life-cycle studies by Ghez and Becker (1975) and Smith (1977). Esti- mates from later life-cycle labor-supply research by Altonji (1983) also yielded results consistent with MaCurdy’s results.

The life-cycle labor-supply studies have an advantage over the consumption studies because they are based on longitudinal data about individuals, so the models and inferences do not depend on strong aggregation assumptions. In principle, a similar approach could be taken to study intertemporal goods consumption, but longitudinal microdata have not been generally available for broad enough classes of goods consumption.

As with existing estimates based on the life-cycle consumption, however, caution should be applied to estimates based on the life-cycle labor supply. A widely recognized problem with the dynamic and static labor-supply studies is that the two really important variables, hours worked and wages, are often measured poorly. Evidence based on research by Bound et al. (1989) suggests that the typical measures of hours worked contain systematic measurement errors that would bias estimates of the parameters of labor-supply models, especially life-cycle labor-supply models.

As an additional reason for caution, the estimated inter-temporal wage effect from

MaCurdy’s life-cycle labor-supply model can only be interpreted as the intertemporal elasticity of substitution due to certain functional form assumptions, which may be overly restrictive. In particular, the model assumes that lifetime utility is addi- tively separable over time. Although this assumption is standard as a theoretical device, there is little reason to think it is empirically valid.

A third approach, the rational expectations approach, is best characterized by a study by Hall (1988). Hall’s (1988) study incorporated a model based on the permanent income theory of consumption when consumers are uncertain about future income and real rates of return. They consume out of permanent income based on expectations about the uncertain future real rates of return. The theory implies that changes in consumption are affected by expected real interest rates. The theory also shows how lagged (or future) interest rate expectations and changes in consumption can be incorporated as instrumental variables to derive consistent estimates of the intertemporal elasticity of substitution from time-series data.

Hall’s (1988) study is based on aggregate time-series data about consumption, real interest rates, and investment return data such as measures of returns in the stock market. The model and estimation methods are based on the assumption that aggregate consumption is determined in the same way as Individual consumption under a rational expectations, permanent income hypothesis.

Hall examines aggregate time-series data on U.S. consumption measured over time periods starting in 1919. He produces different estimates of the inter-temporal elasticity by using alternative measures of the expected rate of return. The estimation results led him to conclude that the intertemporal elasticity of substitution is likely to be positive but very small. The esti-

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mates tend to be about zero, less than 0.1, and they have relatively large standard errors. For example, one reasonable estimate equals 0.1, but has a standard error of 0.23 and a 95 percent confidence interval between --0.35 and 0.55. Hall demonstrates that earlier, larger intertemporal elasticity estimates from Han- sen and Singleton (1983), who also used a rational expectations approach, were biased because they used instrumental variables that were faulty according to Hall’s consumption model. In later studies, researchers such as Campbell and Mankiw (1989) have estimated rnodified versions of the rational expectations model. The later studies produced intertemporal elasticity estimates that are also positive, small, and imprecise.

Like the aggregate time-series studies t:hat follow the life-cycle consumption approach, the rational expectations rnodel used in this literature is based on many strong implicit aggregation assumptions. Research by Attanasio and Weber (1993) shows that violation of even the simplest aggregation assumptions can affect the parameter estimates for these consumption models substantially. Further, even at the level of the individual decision makers, before aggregation, the theory on which these models are based is not en- tirely plausible. The theory assumes, among other things, that people act as if they live forever, adjust consumption to new information instantly, do not form consumption habits, and do not base consumption on life-cycle factors such as age and children.

In summary, although there have been quite a few empirical studies of the intertemporal elasticity of substitution, the empirical results provide very little infor- rnation upon which to base a confident judgement about the exact value of the elasticity. Existing estimates suggest the value is small, but the estimates are also

consistent with a wide rgnge of possibili- ties.

What Is Known about the Labor- Supply Response

The empirical labor-supply literature is much more expansive. There are rnany good surveys of this litelature. See, for example, Heckrnan (19913), Killingsworth (1983), KIllingsworth anti Heckman (1986), and Pencavel (1986). Empirical labor-supply studies usually stay within strict bounds in order to’ make use of available data and simplify the estimation problems. The researchers typically only examine data about people of prime working ages. Empirical labor-supply studies also usually abstrtact from individual decisions about retirpment and educa- tion, although there are many studies about each subject.

In the studies, labor supply is almost always defined narrowly ;~ls hours per week, weeks per year, qr hours per year. The studies do not anal$ze the determi- nants of work effort su P plied. In theory, labor supply should be defined as hours actually worked and should make some allowance for the intensity and quality of work effort. Due to instikutional con- straints on the hours of Lvork. and costs associated with changing jobs, changes in the intensity of work effprt may be one of the principal ways in which people who work vary their labqr supply, especially in the short run. In,the long run, people may choose occdpations or jobs based on how many hours they want to work and the desired work intensity.

Empincal labor supply stpdies also do not usually treat on-the-job human capital investment as an economic decision. People may spend part of their time at work ac- quiring job skills. The stydies apply a theory about the relationshjp between wage rates and hours worked ito study an observed relationship betwpen wages and

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the sum of hours worked plus hours spent learning.

Finally, most of the labor-supply literature is static in the sense that it does not treat labor supply as a decision that takes place over time as people age, that is, there is no intertemporal substitution. In static models, the elasticity of labor supply with respect to the wage is determined by the rate at which people substitute leisure for other consumption in response to a change in the wage relative to other prices.

A 20-year-old, and still growing, literature on life-cycle labor supply, however, suggests that intertemporal substitution is important and should be accounted for when we try to interpret the results of static labor-supply studies. The life-cycle labor-supply literature suggests that people vary their labor supply differently in response to different types of wage changes. Some wage changes occur nor- mally as people age and they acquire or lose job skills. Some wage changes, such as a change in tax rates, may affect all future wages for each individual. The life- cycle model suggests that these two types of wage change will have different effects on labor supply, whereas the static labor-supply model ignores such differences. Static labor-supply elasticity estimates may, therefore, reflect some unknown combination of intratemporal and intertemporal substitution behavior.

These bounds describe some of the ways that researchers have tried to ask answer- able empirical questions about labor supply. Even within these limits, the estimation and measurement issues can be very difficult. We can, however, learn a fair amount about labor supply from past studies. As discussed in the surveys by Kil- lingsworth (1983), Killingsworth and Heckman (1986), and Pencavel (1986), several broad historical labor-supply patterns have been observed over the twen-

tieth century. As productivity and wages have risen, male hours worked and labor force participation have declined. Female labor force participation has risen substantially. On the surface, the historical patterns suggest that, for labor-supply decisions about hours of work, income effects have dominated substitution effects. That is, the uncompensated elasticity of hours worked with respect to wages appears to be negative, given labor force participation. Further, because the effects of wage increases on aggregate hours and participation have been observed to differ in magnitude and, for females, in sign, the historical patterns suggest that hours and participation decisions should be treated distinctly in labor- supply models.

In Heckman’s (1993) review of what we have learned about labor supply, he clas- sifies individual labor-supply decisions into decisions at the intensive and extensive margins. Decisions at the intensive margin determine how much people work, given that they are in the labor force and have chosen an occupation. Decisions at the extensive margin determine whether people work, where they work, and what oc- cupations they work in. There is now con- siderable empirical evidence that the nature of decisions at the intensive and extensive margins can differ substantially. Hours worked decisions can be very different from participation decisions, and can be affected very differently by changes in income and wages, say, due to changes in tax rates.

As an econometric issue, starting with Heckman’s work in the early 197Os, empirical labor-supply studies now routinely treat hours and participation decisions as distinct, but related decisions. Results of these studies generally suggest that male labor supply is not very sensitive to wages at either the extensive or intensive margins, although some recent evidence sug-

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gests that the participation of low-skilled male workers IS signiificantly affected by wage changes (Juhn, Murphy, and Topel, 1991). The prevailing estimation results suggest that the hours decision for the general male population is negatively affected by increases in the wage, that is, that the income effect dominates the substitution effect.

There are notable exceptions to the prevailing results about male labor supply. S’ome studies are based on a model that carefully incorporates the effects of taxes on labor supply, as Hausman (1985) surveyed. These studies, contrary to standard riesults, suggest that the small negative uncompensated wage elasticity typically found in other studies is a combination of large offsetting income and substitution effects. This would be important because a large substitution effect would irnply that taxes on labor income, for example, result in a large welfare loss. Recent evi- clence by MaCurdy, Green, and Paarsch (1990), however, suggests that the Haus- man-type results are not reliable because they depend heavily on particular restric- tions on functlonal form that appear to be inconsistent with the data.

Studies of female labor supply have ofterl produced elasticities that are quite different from male labor-supply elasticity estimates. This is true for both decisions albout hours and, especially, about female labor force participation, which appears to be very sensitive to wages. Many fe- rnale labor-supply studies have found the hours worked decision to be sensitive to vvages, with a substitution effect that clominates the income effect, that is, a positive uncompensated wage elasticity. A study by Mroz (1987), however, suggests that many of the large positive uncompensated female wage elasticity esti- rnates from previous studies were biased upwards.

Mroz’s study searches for the reasons vvhy previous studies of female labor sup-

ply produced a wide variety of results. Be- cause some of the variation between studies resulted from da$a differences, Mroz use!, a single set of data to repro- duce estimates using the different methods used by previous studies. After controlling for the data diffdrences, any remaining differences in ,estimation results can be explained by the differences in model specification and estimation methods. Mroz’s study concentrates mainly on estimates of the effects of wages and In- come at the Intensive m&-gin, that is, on hours worked.

Mroz’s results irnply that, several well- known previous female labor-supply studies used methods that cqused an over- statemeni of the elasticily of hours with respect to wages. Some of the studies produced relatively large, elasticity estimates because they used an estimation method that treated actual previous labor force experience as an independent exogenous source of variation in wages. Previ- ous a#ctual experience, however, is corre- lated with unobserved tqstes for market work. Unobserved tastes. affect both current labor supply and pr$vious actual experience, which implies that both labor supply and previous expqrience should be treated as endogenous vlariables. Because actual previous experience is treated as an exogenous source of wape variation when it is not exogenouy;, part of the variation in wages explaineq by previous experience :,erves as a proqy for tastes and biases the wage elasticity estimate upwards.

Mroz also observed that some of the studies obtained large wage and income elasticity chstimates because they imposed a restriction of the Tobit Iregression model that labor force participdtion and hours decisions *are determined by the same wage and income pararrieters. Mroz finds that the Toblt restriction can be statisti- cally rejected when previlous labor force

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experience is treated as an exogenous variable. When the Tobit restriction is re- laxed, however, even if previous experience is treated as exogenous, the hours decision appears to be much less wage and income elastic. Mroz concludes that some of the previous wage and income elasticity estimates were too large because the studies used a Tobit model and treated previous experience as exogenous.

To summarize the results of female labor- supply studies, Mroz discards the results of studies that either treat experience as exogenous or impose the Tobit model restriction. He finds that elasticities from the remaining studies fall inside a fairly narrow range that is consistent with his estimation results. He finds that the larg- est estimate of the uncompensated wage effect are consistent with an elasticity of 0.12 at the data means, with a confidence interval of -0.21 to 0.45. Simi- larly, the estimated income effect is negative and precise, but very small. Mroz’s results suggest that the hours decision for women is not nearly as wage elastic as many previous studies suggested. The uncompensated and compensated wage elasticity estimates for hours worked, though somewhat imprecise, are similar to the elasticity estimates for males.

Why Don’t We Know More?

Even defined in the narrow way it is by empirical studies, labor-supply behavior has apparently been very difficult to study. Not surprisingly, the studies have produced many varied estimates of elasticities. The same is true for studies of the inter-temporal elasticity of substitution. There are several reasons why these problems have been so difficult.

One of the most fundamental problems has been a lack of adequate data. Ideally, studies of the intertemporal elasticity would be based on longitudinal micro-

data about consumption. Currently, such longitudinal consumption data are only available for narrow classes of consumption, such as food, or else for time periods that are too short. Studies of labor- supply behavior should not only be based on longitudinal data about individuals, which are readily available, but should be able to incorporate information about the complexities of different compensation schemes, fringe benefits, and work effort. Good information about these latter aspects are missing from the data. Further, the best theories allow for both intratemporal and intertemporal substitution between goods and leisure. Inter-temporal and intratemporal substitution would be ideally studied jointly based on longitudinal data about labor supply and comprehensive measures of consumption. Such data are not available.

Because the ideal data are not available, researchers have had to get by with only pieces of the empirical information necessary to understand labor-supply and consumption behavior. The best studies start with a reasonably general theory and then reduce it, by assumption, so that the parameters can be estimated from available data. It is not easy to test these sim- plifying assumptions because many of the most important assumptions are made about things that are not observed in the available data. There is little evidence whether the Implications of these assumptions, such as the forms of labor- supply or consumption functions, are correct. If the assumptions are wrong, the parameters of empirical models may simply represent empirical regularities that are not useful for making reliable behavioral predictions.

Even if the empirical models are right, however, the data often provide poor measures. The consumption data do not measure consumption as it is defined in theory, that is, the consumption of a flow

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of services provided by goods. Many studies of the intertemporal elasticity of substitution have examined data about expenditures on nondurable goods and services, whereas the theory applies to the consumption of services derived from all goods and leisure.

,As discussed above, studies of labor supply are based on measures of hours and wages that appear to contain important ‘systematic measurement errors. The total measurement error may be even larger (and result from problems more fundamental than inadecluate survey designs. Hours spent at work is something that (can be measured perfectly, though not easily, with the right survey device. Work (effort, which is likely to be an important (part of labor supply, is not so easily meats- lured. Further, the price of an extra hour, (as defined by the labor-supply theory, may often lack a simple empirical coun- terpart. As widely recognized, though often ignored, this price is not the average wage, that is, earnings dtvided by hours. IFurther, many labor compensation schemes are designed to encourage current work effort, which often requires longer hours, by offering delayed incen- tives such as future bonuses, awards, pay raises, and promotions. However, the typical labor-supply study treats the labor supply as if it simply operates as a spot market where labor is supplied and paid lfor contemporaneously. Some of the diffi- culty in measuring (3 spot wage may result because there is no spot wage rate at the margin for many workers.

WHAT THE BEHAVIORAL RESPONSES IMPLY ABOUT TA.X POLICIES

13ased on the empirical studies, it is very difficult to decide what parameter values should be used for makrng policy predictions. Although economists have learned from the exis ’ 3 trnc empirical studies, there is still a high degree of uncertainty about

the exact values of paralmeters. One fore- casting aiternative would be to avoid ac- counting for saving and’ labor-supply behavior, but this approach can not be justified based on existing studies. While many of the studies suggest that the behavioral effects are sma I, there is still consrderable risk that fdrecasts would lead to misinformed pollicy decisions if the behavioral effects are in fact more important.

Forecasts that reflect the uncertainty about behavioral parameters may improve the outcome of the policy process, even If forecasts show that the economic effect of a particular policy is highly uncertain based on existin evidence. Unfor- F tunately, when a policy forecast is made, it is after presented as a point estimate without any indication of the often vast level of uncertainty forebasters may have about the economic reaboning and behavioral parameters.

As we discussed earlier in thus paper, economists often use CGE models to de- termline the efficiency effects of alternative tax policies. The typical analysis involves the use of a specific set of parameter values for a central-case com- putatron, qualified by some limited varia- tlon of a few of these v#ues in order to determine the sensitivity of the qualitative results to these parameters. The problem with the ‘standard sensitiivity analysis is that it does not easily trbnslate into a systematic understanding of either uncertainty about the parameters or how that uncertainty translates into uncertainty about the simulation outcomes.

In this section, we show how uncertainty about some of the underlying parameters of a CGE simulation can1 be used to rnake useful statements about~ the implied uncertainty about tax policy forecasts. We use the life-cycle CGE model of Fullerton and Rogers (1993) to analyze the poten- tial efficiency gains associated with a

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IMPLICATIONS FOR TAX POLICY

switch to a proportional, flat-rate consumption tax. The replacement of a progressive income tax with a proportional consumption tax is a useful exercise because the efficiency gains are due to both the flattening of tax rates and the switch in the tax base. We first determine economic outcomes under different values of the intertemporal and intratemporal elasticities of substitution, analogous to a typical sensitivity analysis. We then show how information about the distribution of uncertainty about parameter values can be used to make systematic statements about the uncertainty of model predictions.

The Fullerton-Rogers Model

As described by Fullerton and Rogers (1993), their CGE model includes a disag- gregate production side, with corporate and noncorporate producers, 19 indus- tries, five types of capital, and labor. Con- sumers maximize lifetime utility by borrowing and saving so that consumption is smooth relative to annual incomes. Capi- tal markets are assumed to be perfect. The Fullerton and Rogers (1993) study distinguishes among consumers according to the levels of their lifetime incomes and emphasizes the distributional effects of the various types of U.S. taxes. The model is especially appropriate for studying the overall welfare effects associated with a switch to a consumption-based tax because of the way it characterizes consumer decisions.

In the Fullerton-Rogers model, both the amount of labor supplied and the timing of consumption over the lifetime are endogenous. Consumers first allocate lifetime full income (the lifetime value of human capital) across periods. Within each period, consumers decide how much to work and how to allocate consumption among the available consumer goods. Through the specification of elasticities of substitution in the utility function of con-

sumers, the model allows for direct ma- nipulation of the size of labor-supply and intertemporal substitution behavioral responses.

In the model, lifetime utility, U, is defined as a constant-elasticity-of-substitution (CES) function of age-dated composite commodities (composites of goods and leisure), x,:

(J = [ c &‘/’ ) $“, - WE>]& - 1) t=1

where T is the individual’s certain date of death, E, is the intertemporal elasticity of substitution, and the weighting parameter, a,, depends on a specified subjective rate of time preference. The larger the value of E,, the larger the responsiveness of the timing of household consumption to changes in the net rate of return to capital caused by capital taxation. The composite commodity in each period, x,, is in turn defined as:

+ (1 - at)lle’ p - lKE>]BA~~ - 1)

where c, is the amount of composite goods consumption at t, I, is the amount of leisure consumed at t, and E, is the intratemporal elasticity of substitution between consumption and leisure. The larger the value of E,, the larger the responsiveness of labor supply to changes in the net real wage rate (i.e., changes in the price of leisure relative to the price of goods).3

Simulating a Switch to a Fiat-Rate Consumption Tax

We simulate the replacement of the personal and corporate taxes present in the benchmark year (1984) with a propor-

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tional tax on consumer goods, which in the Fullerton-Rogers model is equivalent to a value-added tax levied at each stage of production. The proportional tax rate on consumption is that which is necessary to make the replacement a revenue-neu- 1:ral one.

The switch from a progressive income tax to a proportional consumption tax can be characterized as having two distinct effects on tax efficienicy. First, the switch to a less progressive tax-rate structure is expected to reduce the distortionary effects of taxes. Second, the switch from an income base to a consumption base In- volves a reduction in the intertemporal distortion in exchange for a larger labor- supply (or leisure-consumption) distortion, and so may increasle or decrease the inef- ificiency of the tax systerrl. The welfare gains associated with a switch from a progressive income tax to a proportional consumption tax are expected to be positively related to the magnitude of the intertemporal elasticity because gains fron- the proportionality and the change in Ibase are positively related to this elasticity. However, the gains are ambiguous with respect to the magnitude of the la- Ibor-supply elasticity because, while gains .from proportionality are positively related to this elasticity, gains from the switch in lbase are inversely related to it.

IElasticity Variants

lln Fullerton and Rogers (1993), the standard parameterizatlon uses a value of 0.50 for both the intertemporal and leisure-consumption elasticities of substitution. We include this case in our set of lparameterizations, but also simulate low and high extremes for the two elasticities. ‘We vary the intertemporal elasticity, E,, by computing a low extreme of 0.15 and ,a high extreme of 0.70. The nature of the model does not allow us to simulate an Intertemporal elasticity below 0.15, be- (cause at very low intertemporal elastici-

ties, aggregate life-cycle saving is so small (actually negative) that it is irnpossible to compute an equilibrium given benchmark data. This limitation does not imply that the economy would not equilibrate at a smaller value, but just that equilibrium is not computable from thiis model. Simi- larly, interternporal elasticities that are too high are Inconsistent wiih the benchmark; we found a high&t plausible value of 0.70, at which value life-cycle savings accounts for the entire capital stock (with zero bequests).

We vary I:he leisure-conqumption elastic- lty, E,, by computing a low extreme of 0.10 and a high extreme of 0.90. We find that ,these values imply uncompensated labor-supply elasticities, 77, of 0.008 and 0.40, respectively, based on a simulated change in the net wage rate. The central- case value of 0.50 for the leisure-consumption elasticity implies that the uncompensated labor-supply elasticity equals 0.11. In our simqlations, the implied labor-supply elasticities are insensi- tive to changes in the value of the intertemporal elasticity.

Efficiency Gains

Although- the distributional results focus on a steady-state generation, our measure of effictency gain aiccounts for any Intergenerational redistqibutions that may take place by computing the present- value sum 0.f welfare gains across all generations. While the steady-state generation enjoys an overall increase in welfare under all nine parameteirizations, older generations alive at the time of the tax switch always lose. This is because in the switch to a consumption tax, the older households, who have dlready paid much or all of ihelr wage incdme taxes, are suddenly subjected to ap additional tax on the consumption out of that wage income. This double tax has implications for efficiency, intergenerational equity, and aggregate saving. First, lit actually im-

440

I IMPLICATIONS FOR TAX POLICY

proves efficiency by introducing a lump- sum (unavoidable) component to the tax system. Second, the heavier burden on the old allows an immediate reduction in the share of the tax burden placed on the young. Third, the intergenerational redistribution implies a redistribution of incomes away from those with relatively high marginal propensities to consume; hence, aggregate savings are increased (which leads to higher labor incomes in the future owing to a larger capital stock). To the extent that the double taxation of older generations is unrealistic, the simulations will overstate the im- provement in saving and the size of efficiency gains.

Table 1 summarizes the percentage increase in steady-state saving and efficiency gains associated with the switch to a flat-rate consumption tax under nine alternative combinations of behavioral parameter values. The percentage increase in aggregate saving is positive under all nine simulations and is sensitive to the value of the intertemporal elasticity. The positive relationship between the intertemporal elasticity and the savings response has two sources: (1) a higher elasticity implies that the saving of households in general exhibits greater sensitivity to the initial increase in the net rate of return to capital; and (2) a higher intertemporal elasticity also implies a

slightly greater redistribution of income toward the lifetime rich, who are more adversely affected by inter-temporal distortions, but are also the bigger savers. Be- cause efficiency gains are equal to the present-value sum of equivalent variations across all generations, and because older generations lose from the new tax, the numbers for efficiency gains are smaller than are overall steady-state gains. Never- theless, nearly all of these efficiency numbers are positive. This is not a surprising result, given the two features of the policy change-flatness and greater neutrality. The neutrality of the tax system is im- proved not only because the consumption tax is inter-temporally neutral compared with the personal income tax, but also because it eliminates the interasset and intersectoral (corporate-noncorporate) distortions that are present under the corporate income tax.4

Our main focus in conducting these simulations, however, is on the sensitivity of these numbers to the intertemporal and labor-supply elasticities. It may not be ob- vious why, as the labor-supply elasticity increases, the efficiency gains from the switch to the flat-rate consumption tax are larger. As discussed earlier, theoreti- cally, a higher labor-supply elasticity would imply greater inefficiency associated with high marginal tax rates as well as greater distortrons associated with a la-

TABLE 1 CHANGES IN STEADY-STATE SAVING AND EFFICIENCY GAINS FROM REPLACING INCOME TAXES WITH A

FLAT-RATE CONSUMPTION TAX=

lntratemporal Elasticity of Substitution Intertemporal Elasticity of Substitution

(Labor-Supply Elasticity) E, = 0.15 E, = 0.50 E, = 0.70

E, = 0.10 (q = 0.008) + 1.8% + 15.7% + 19.8% - 0.03, - 0.26 0.63,4.7 0.88, 6.4

E, = 0.50 (q = 0.11) +3.0% + 17.2% +21.5% 0.17, 1.3 0.97, 7.5 1.2, 8.9

E, = 0.90 (Tj = 0.40) + 5.5% +21.3% + 26.3% 0.47, 3.8 1.4, 12.3 1.7, 14.7

‘The top line of each row indicates change in steady-state saving as percent of benchmark steady-state saving. The bottom line of each row shows present-value of equivalent variation relative to present-value of lifetime income and relative to present-value of income-tax revenue.

441

bar/consumption tax base relative to an income base. The simulated tax change involves both a flattening of tax rates (de- creased progressivity) and a switch to a consumption base; it is thus possible that a higher labor-supply elasticity could increase or decrease the level of efficiency gains. Thus, the simulated positive relationship between the labor-supply elasticity and efficiency gains, shown in Table 1, suggests that the gains from flatness are more affected by the labor-supply elasticity than are the losses from the increased labor-supply distortion. Note also that the welfare gains appear to be more sensitive to the intertemporal elasticity than to the labor-supply elasticity, which is also consistent with the offsetting effects associated with an increased value of the latter.

Uncertainty about the Saving and the Labor-Supply Parameters

Our sensitivity analysis is the standard way that uncertainty about the underlying parameters is discussed in policy simulation studies. Understanding how and why the simulatiori results vary when the parameters are changed can improve understanding of the economics underlying the model. However, the sensitivity results do not easily translate into simple statements of uncertainty about the policy forecasts.

One way to represent the uncertainty systematically would be to use Monte Carlo simulations. lJnder this approach, the an- alysts would choose subjective probability distributions to characterize uncertainty about each unknown parameter. A straightforward Monte Carlo analysis would then be to use the subjective distributions to randomly chclose parameter values at which to conduct the simulations. After a large number of simulations, statistical methods could then be applied to make statements about the probability distribution of the forecasts implied by the subJective probability distri-

butions of the parameters. A serious problem with this straightforward Monte Carlo approach, howevpr, is that it may require an infeasibly lar e number of simulations, even if the ex

”

eriment is designed to study the im lications of uncertainty about only a couple of parameters.

Harrison and Vinod (19e2) show how the Monte Carlo approach Ian be made more efficient by using ‘what are essentially opttmal survey dedign techniques to more systematically cho/ose the parameter values at which to conduct the simulations. Their method, however, still can require too many simulations. In their appli- cation, for example, thqy perform over 15,000 simulations. Th$ would not be feasible lor large CGE models.

Bernheim, Scholz, and $hoven (199’1) take an alternative approach. They specify uncertainty about the parameters in terms of standard errorb. This approach is very natural, for example, when a parameter has been estimated from an econometric model and the qodeler wishes to use statistical standard krrors of the estimates to calculate the itnplied statistical standard errors of the fprecasts. The authors use the fact that Ihe policy forecasts from a CGE model can Abe expressed as an implicit function of qhe underlying parameters. They then callculate numerical derivatives of the implidit forecast function with respect to each parameter by varying the parameters! one at a time, and observing how the forecast changes. The derivatives are the0 combined with the standard errors of tlhe parameters to calculate an approximation to the standard error of the forecast. By increasing the sizes of the underly~ing standard errors, they can show how higher levels of uncertainty about the parameters increase the uncertainty about the forecast.

Their method has an advantage over other methods because it can be used to produce useful statements about uncer-

442

I IMPLICATIONS FOR TAX POLICY

tainty after performing a limited number of model simulations. The required number of simulations increases only propor- tionally with the number of uncertain parameters, whereas the straightforward Monte Carlo approach requires a number of simulations that increases exponen- tially. A disadvantage of the approach taken by Bernheim, Scholz, and Shoven (1991) is that standard errors are not easily converted into readily understood information for many policy makers. Fur- ther, unless more is known about the probability distribution of the policy predictions, the standard errors do not provide much information about the likelihoods of alternative forecasts.

Our method for expressing uncertainty is less general, but it is more practical and yields results that should be easier for most policy makers to interpret. First, we only wish to account for uncertainty about a couple of parameters, the intertemporal and intratemporal substitution elasticities. Second, the simulation outcomes we are interested in, for example, efficiency gain as a percentage of lifetime income, appear to be smooth functions of the two unknown elasticities. In contrast to the simple Monte Carlo approach, which requires one simulation for each of many randomly selected combinations of parameter values, we conduct simulations only at three regularly spaced values of each parameter, nine actual simulations. By using polynomial interpolation (and extrapolation), we approximate what the simulation outcomes would be at other values of the parameters. Combining the nine actual simulations with interpolation, we apply the Monte Carlo approach directly by doing one interpolation for each of many (10,000) randomly chosen values of the parameter. Assuming that the numerical interpolations and extrapolations are reliable, we then use the outcomes of the Monte Carlo experiment to approximate

percentiles of the distribution of uncertain policy forecasts.

Our method is practical because it only requires a small number of actual simulations. Too many simulations would be required if we wished to express the uncertainty about a large number of parameters, but a few more parameters could be added to the analysis without much trouble. Because we only account for uncertainty about two parameters, our results are likely to understate the total forecast uncertainty implied by uncertainty about all other parameters and aspects of the CGE model. However, our results provide more information, and in a more concise fashion, than a point forecast and an informal array of sensitivity experiments.

We have chosen our subjective (prior) distributions somewhat informally, based on our review of the empirical literature. It is difficult to think of a formal method by which to derive these distributions, given that much of the uncertainty about the parameter estimates is qualitative. Some of our uncertainty is simply statistical, as summarized by the standard errors of estimates produced by different studies. If this accounted for all uncertainty, we could simply average the results from alternative studies and calculate a standard error. However, because we have doubts about some of the underlying assumptions of many of the studies, and are aware that many potentially important aspects of inter-temporal substitution and labor supply have not even been explored empirically, much of our uncertainty can not be formally derived from the studies. Though we choose the distributions somewhat arbitrarily, we find the choice less arbitrary than choosing a single parameter value from within the range of possible alternatives, as is typically done for CGE simulation.

As a subjective distribution of the intertemporal elasticity of substitution, we use

443

a distribution that is uniform between zero and 0.5. This range reasonably cov- lers the range of results from available studies. As a subjective distribution of the uncompensated labor-supply elasticity, ‘we use a distribution that is uniform between -0.1 and 0.3.

Table 2 shows the distributions of efficiency gains and savings effects, as implied by the subjective distributions of estimates for the intertemporal and intratemporal elasticities of substitution. We calculate that there is a 50 percent probability that the efficiency gains from a switch to a proportional consumption tax are at least 2.2 percent of revenue and 0.32 percent of lifetime income. There is more than a 20 percent chance, however, that the efficiency gain is negative. Moreover, there is less than a 10 percent probability that the efficiency gain exceeds 1 percent of lifetime income.

As we described in the sensitivity analysis, the efficiency gain from a switch to a proportional consumption tax appears to be positively related to both the intertemporal and intratemporal elasticities, at least for positive values for these elastici-

ties. However, the gains are much more sensitive to the interte poral elasticity.

7 Thus, at very low value 7

for both elasticities, the efficiency gains become negative because the gain from the removal of the intertemporal distortion’ is sharply re- duced, while at small values for the labor- supply elasticity, the gailn from proportionality of the rates (which is positively related to the labor-supbly elasticity) is re- duced less than is the loss from the nar- rowing of the base (wh ch is also positively related to the lab 4 r-supply elasticity). More simply, iwhen elasticities are very low, the effects of the labor-supply distortion are more bronounced than are the effects of the intertemporal distortion.

Similarly, the effects onsavings are not always positive; we calciulate that there is at least a 20 percent chance that steady- state savings will decrease. A decrease in saving occurs at low vallues of the intertemporal elasticity because a low elasticity implies very little substitution effect, and makes it more likely tha~t the income effect from the removal of capital taxation (which implies a decrease in saving) dominates. While Table 2 indicates that there

PERCENT11 TABLE 2

.E DISTRIBUTIONS OF EFFICIENCY AND SAVINGS EFFECTS, SIMULATEP SWITCH FROM PROGRESSIVE INCOME TAX TO A FLAT CONSUMPTION TAX”

Percentile of Distribution

5 10 20 30 40 50 (median) 60 70 80 90

~ - _ - . - . I

Efficiency Change as a Percen age Change Percentage of t in ,Savings

-- Revenue Lifetime Income Initial Period In Steady State

-- . -

-2.2 -0.31 - - 31 -4.4

-1.8 -0.22 -- 13 -2.9 -0.91 -0.078 22 -0.038

0.10 0.057 55 2.7 1.1 0.19 89 5.2 2.2 0.32 120 7.5 3.5 0.46 150 9.7 4.8 0.62 190 12 6.3 0.79 220 14 8.1 0.98 260 16

95 9.2 1.1 290 17 --- .-

aThese distributions represent the uncertainty implied by uncertainty about the inter-temporal el sticity of substitution and the uncompensated labor-supply elasticity. The subjective prior distribution of the intertemporal 1 lasticity of substitution is uniform between 0.0 and 0.5. The subjective prior distribution of the uncompensated labor supply elasticity is uniform between - 0.1 and 0.3.

444


is a 50 percent probability that initial-period savings will increase by at least 120 percent, this initial-period increase is largely due to the transitional transfers from the old (dissavers) to the young (savers). At the 50th percentile, the expected steady-state change in savings is only 7.5 percent.

In general, the distributions of efficiency gains and savings effects shown in Table 2 appear rather modest. Moreover, these effects are based on the replacement of progressive income taxes with a proportional, flat-rate consumption tax. Because some of these gains are due to the flattening of the rate structure, they tend to overstate the gains that would result from a switch to a progressive consumption tax alone.

Conclusion

While there is much disagreement among economists about the values of many behavioral parameters, rarely is this uncertainty conveyed accurately in the economic analyses of proposed tax policies. In this paper we have surveyed the literature on parameters that are important in tax analysis-the elasticities of intertemporal substitution and labor supply-and have found that a large amount of uncertainty remains about the sizes of these parameters. We then showed how it is possible to translate these ranges of values into probability statements concern- ing the economic effects of a change in tax policy. Using the Fullerton and Rogers (1993) model, we simulated the effects of replacing a stylized income tax with a flat- rate, proportional consumption tax. Based on subjective distributions of the intertemporal and labor-supply elasticities suggested by our survey, we conclude that the switch is likely to produce efficiency gains, although the gains are never large and are sometimes negative. Our presentation does not capture all uncertainty about the model and its predictions. Our

presentation is, however, more honest than point predictions alone, and it is more informative and potentially less con- fusing than the standard ways of present- ing a sensitivity analysis.

ENDNOTES

Any views expressed in this paper are those of the authors and do not necessarily reflect the views of the Congressional Budget Of- fice. See for example, Auerbach and Kotlikoff (1987) and Fullerton and Rogers (1993). See, for example, Ballard et al. (1985). See Chapter 2 in Fullerton and Rogers (1993) for additional detail about the model. The sizes of predicted efficiency gains are consistent with those found by Gravelle (1991), who also used a life-cycle CGE model for simulation.

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