Note: SMETR(L), MMETR(L), HMETR(L) are METRs on earned income for single households, married households and heads of household, respectively.

The METRs faced by married households differ substantially from those faced by single households and heads of household (Figure 1 and 2). Low-income married households do not face particularly high METRs, primarily because their marginal transfer effects are fairly low. For the most part, the METRs increase linearly with a slightly positive slope.

Households in decile eight (with a mean gross income of $57,629) face the highest METR on earned income, 44 percent, mostly because of high marginal tax rates. Payroll taxes are not levied on the highest income categories, however, so the marginal tax rates and hence METRs decline for deciles nine and ten. For unearned income, the first decile (with a mean gross income of $7,969) faces the highest METR, 42 percent, only slightly more than that faced by the tenth decile. Middle-income households, with gross incomes between $22,000 and $45,701, face METRs on earned income between 30 and 40 percent. The corresponding numbers for unearned income are generally between 20 and 30 percent.

Note: SMETR(K), MMETR(K), HMETR(K) are METRs on earned income for single households, married households and heads of household, respectively.

rate for married households, 29 percent, is slightly higher than the lowest rate for single households, 24 percent.

The METR schedules look similar across the different filing statuses whether households are grouped using deciles or pooled status deciles (Figure 3 and 4), with the exception that married households in the income range $0 to $2,417 face an METR on their earned income of 147 percent. While this number is surprisingly high, it must be remembered that few married households, less than 2 percent, actually face this situation. Indeed, the 134 percent faced by low-income heads of household is perhaps more worrisome because it applies to more than 30 percent of heads of household.

Figure 4 compares METRs on unearned income. The shape of METR schedules for unearned income for the different household types is also similar when the households are grouped into pooled status deciles, though the levels differ. Again, METRs on unearned income are extremely high for heads of household.

My METR estimates are substantially higher than previous estimates. It is hard to compare numbers between this study and earlier studies, however, because of substantial differences in the approaches employed and the benefits considered. My estimates are generally more comprehensive than estimates from earlier studies, though when aggregated across income and filing statuses they are fairly similar to Browning and Johnson’s.

2.6 Conclusions

In this paper, I estimate METRs on earned and unearned income across the income distribution for heads of household, single households, married households, and all households pooled together in the U.S. These METRs measure how fiscal policy affects households’ incentives to work and accumulate capital. The higher they are, the lower are the incentives.

Alarmingly, I find that many low-income heads of household face METRs that are close or even greater than one hundred percent. In fact, 30 percent of all heads of household face METRs of over 100 percent on earned income. For unearned income, 30 percent face a rate over 600 percent.

The reductions in METRs for low-income heads of household required to provide work incentives for the poor, a goal of many current welfare reforms, are enormous and practically unlikely. Indeed, these results may go a long way toward explaining why the labor supply of low-income household heads is so remarkably inelastic and has not changed over time, despite changes to the welfare system and tax laws which have effectively lowered METRs. It seems likely, then, that welfare recipients can perhaps only be compelled to enter the labor force by linking welfare eligibility to work directly. Alternatives should be explored, however, that can provide for the poorest households without creating such extreme disincentives to future self-sufficiency. This is especially urgent because society is becoming increasingly dissatisfied with the functioning of the current welfare system. The Earned Income Tax Credit helps to bring down the high METRs at the very end of the income distribution, but is not enough and its effect tapers off quickly.

References

Appendix A

Note: All values reflect decile means. Earned, unearned income and transfers refer

Household Statistics for Single Households

Household Statistics for Married Households

Appendix B

Fraction of Average Annual Expenditures Spent on Various

Consumption Goods of Pre-tax Income, by Quintiles

1. I conduct sensitivity analyses by re-estimating the model using different gross values for the recipient. The different values are chosen by reducing, one at a time, the various component transfers by 50 percent, an arbitrary though rather extreme value.

I begin with public housing. When the gross value of public housing is reduced by 50 percent, the marginal transfer effect declines are the largest for the first decile of heads of households, 21 percentage points (3 percent) on unearned income and 9 percentage points (6 percent) on earned income. A 50 percent reduction in rent subsidy leads to a decline of at most 13 percentage points (2 percent) on unearned income and at most 4 percentage points (3 percent) on earned income. A 50 percent reduction in Energy Assistance lowers the marginal transfer effect by at most 3 percentage points (0.5 percent) on unearned income and 0.2 percentage points (0.1 percent) on earned income.

I conduct sensitivity analyses on Medicaid transfers using two different values. First, a 50 percent reduction leads to declines in marginal transfer effects of at most 21 percentage points (3 percent) on unearned income and 2 percentage points (1.6 percent) on earned income for the same first decile of heads of household. Second, the effect of using the higher mean Medicaid outlay per beneficiary ($1,242), i.e., under the hypothesis that all recipients value Medicaid benefits equally, the marginal transfer effects increased most for the first decile of heads of household, 48 percentage points (7 percent) on unearned income, and most for first decile of single households, 32 percentage points (22 percent) on earned income.

Finally, I examine the effect of reducing the value of public housing, rent subsidy, Energy Assistance, and Medicaid together. This reduces the marginal transfer effects for the first decile of heads of household by 62 percentage points (9 percent) on unearned income and by 7 percentage points (5 percent) on earned income. This suggests that these transfer programs play a less important role in the determination of the marginal transfer effects than, for example, AFDC and Food Stamps. My assumptions about the value of public housing, rent subsidies, Energy Assistance, and Medicaid transfers, thus, have little bearing on the results.

2. Re-estimating the model with quadratic earned and unearned income terms does not change the results significantly. There is no statistical difference between this regression and the base regression model. For unearned income, however, the fit may be slightly better with the inclusion of the quadratic term for decile one. Including interaction terms for state of residence and income does not improve the model. A simple F-test suggests that the interaction terms do not belong in the model.

3. Because I estimate state personal income taxes based only on the four most populous states in the sample, I may under- or over-estimate the tax obligations for individuals in other States. Excluding state personal income taxes affects neither marginal transfer effects nor METRs for the first deciles of all filing statutes and decreases METRs by at most 7 percentage points (15 percent) for the highest deciles. My results, thus, are unaffected at the lower end of the income distribution by assumptions about state taxes, and moderately sensitive at the higher end.

4. Social security payroll taxes can alternatively be treated as a form of forced saving for retirement. Excluding social security taxes altogether causes the marginal tax rate to decline by 6 percentage points (17.2 percent) for middle-income households, but by a lot less at the lower and higher ends of the income distribution.

5. Indirect tax rates affect METRs on earned income in two ways. A decline in the indirect tax rate first lowers the marginal tax rate on earned income directly, and then increases the net value of transfers and hence the marginal transfer effect. METRs on unearned income are unaffected by indirect taxes.

If t_i is zero the marginal tax rate declines by nearly 3 percentage points for the first two deciles of heads of household (21.3 percent), and the marginal transfer effect increases by 9 percentage points (7 percent) on earned income for the lowest decile of heads of household. Taken together, this means that a change in the indirect tax rate can lower or increase the overall METRs. For the first deciles of heads of household the marginal transfer effect dominates and overall METRs on earned income increase by at most 3 percentage points (2 percent). For remaining deciles and filing statuses, overall METRs are reduced by at most 5 percentage points (about 12 percent).

6. I censor negative capital and self-employment incomes at zero. If negative capital and self-employment incomes are included, the results change notably at the lower end of the income distribution. For instance, the first decile of heads of household is no longer the decile receiving most transfers.

3.1 Introduction

High welfare costs have made welfare reform a hot topic in many developed countries in recent years. In the U.S., for instance, welfare reform became a top priority on the political agenda in the 1990s (Keane[1995]), and it remains a major campaign issue in the 2000 presidential election. The wide range of countries that have recently discussed the need of welfare reforms includes countries from Northern Europe, for instance Sweden (Lindbeck et al. [1994], Socialdepartementet [1999]) and Denmark (Torfing [1999]); Central and Southern Europe, for instance the U.K. (Jessop [1995]) and Italy (Morley-Fletcher [1998]); and even the former Eastern Block (Kornai [1999]).

One of the key problems with many welfare systems is that welfare recipients face high "effective" marginal tax rates, thus making their economic returns to working very low. Even though the statutory tax rates paid in this income range are often low, means-testing of benefits can boost the marginal effective tax rate to 100 percent or more. In Sweden, for example, a welfare recipient who earns income loses welfare benefits on a one-for-one basis. The result of these high marginal effective tax rates is that many safety nets, rather than providing temporary relief, effectively trap participants into welfare dependency.

A common thread of recent welfare programs is the goal of increasing the economic incentives for recipients to join the labor force. The earned-income tax credit in the U.S., for instance, is a negative income tax that directly lowers the marginal effective tax rates faced by the working poor. Nevertheless, for a variety of reasons, the results of welfare reform have generally been mixed (see e.g., Haveman and Scholz [1994], Gueron [1996], Blank [1997], Torfing [1999]).

One potential drawback of lowering the marginal effective tax rates faced by welfare recipients is that doing so could generally be costly for the government. In order to reduce the marginal effective tax rates, either or both of the components that make up the marginal effective tax rates – that is, the marginal tax rate and the benefit-reduction rate – must be reduced. Reducing the marginal tax rate – defined as the increase in tax payments resulting from a unit rise in gross earned income – can be costly because it reduces the taxes paid by all income earners, not just welfare recipients. Similarly, reducing the benefit-reduction rate – defined as the reduction in transfers received resulting from a unit rise in gross earned income – is also costly. Making benefits independent of income, for example, would dramatically increase government outlays.

Decreases in the marginal effective tax rate paid by welfare recipients must be offset by increases in the marginal tax rate paid by higher-income individuals if the budget is to balance. From a general equilibrium perspective, it is not obvious that the distortions of an increase in tax rates faced by higher-income individuals are smaller than the distortions high marginal effective tax rates cause faced by welfare recipients. Indeed, little is known empirically about how they actually compare.

In this paper, we develop a model for deriving the optimal benefit-reduction rate based on Sheshinski’s [1972] model of optimal income taxation. Unfortunately, our framework does not permit an analytic solution without assumptions about functional form. Rather than making these assumptions, however, we derive mathematical bounds around the optimal benefit-reduction rate based on a number of labor supply elasticities.

We find that the optimal benefit-reduction rate depends negatively on the optimal marginal tax rate on labor income, and either negatively on the average labor supply elasticity with respect to changes in net income of welfare recipients or positively on welfare non-recipients’ labor supply with respect to changes in the benefit-reduction rate. The optimal benefit-reduction rate can even be negative if welfare recipients are very elastic in their labor supply and the optimal marginal tax rate on labor income is high. A negative optimal benefit-reduction rate implies that welfare recipients should be given a subsidy for working and an example is the Earned Income Tax Credit in the U.S.

By inserting estimates from the literature of labor supply elasticities into the analytical results, we compute numerical values of the upper bounds of the optimal benefit-reduction rate. These values can then be compared to actual rates. We find that actual rates in some countries are in excess of bounds derived in the optimal income taxation model.

3.2 General Approach

The theory of optimal income taxation, first developed by Mirrlees [1971], provides tools that are well-suited to exploring the welfare dependency problem. The essential elements in Mirrlees’ model are: the social welfare function, an ability distribution, households’ utility functions (labor supply elasticities), and a fiscal side where the government levies taxes to fund government expenditures. In particular, the social welfare function is a maximand and can be used as a yardstick for comparing tax-related distortions for one group against distortions for other groups. The ability distribution allows individuals to differ in their ability to earn wages. Individual utility functions capture individual preferences, for instance labor supply elasticities, which are key inputs in measuring the magnitude of the distortions that marginal tax rates create. Finally, the existence of a fiscal side allows for redistribution. The government chooses a tax function and thereby the level of redistribution.

Without assuming a specific utility function or ability distribution, Mirrlees was limited to a few analytical conclusions. Subsequent work showed that the assumptions made about the functional form are critical (e.g., Atkinson [1973], Stern [1976], and Tuomala [1984])).

Sheshinski [1972] placed linearity restrictions on Mirrlees’ model, which enabled him to draw more analytical conclusions. He found that when labor supply is a non-decreasing function of net wage, the optimal linear tax is characterized by a negative lump-sum tax (a subsidy) at zero income. Moreover, the marginal tax rate is less than one and bounded from above by a function of labor supply elasticities that decreases with the minimum elasticity of the labor supply.

We extend Sheshinski’s [1972] work by introducing the benefit-reduction rate to the model. That is, we generalize Sheshinski’s model from a linear tax to a tax schedule that is kinked with two linear segments. One segment is for welfare recipients who face both marginal tax and marginal benefit-reduction rates. The other segment is for welfare non-recipients who face only a marginal tax rate.

3.3 The Model

The optimal marginal tax rate on labor income and the optimal benefit-reduction rate are chosen so that social welfare is maximized subject to two constraints. The first constraint guarantees that individuals maximize their utility by choosing the optimal bundle of consumption and leisure given the tax rates. The second constraint ensures that the tax rates lead to an outcome that meets the government’s revenue requirements. The government sets the tax rates – the marginal tax rate on labor income and the benefit-reduction rate – thereby fixing the guarantee level. Individuals, in turn, take marginal tax rates as given and maximize utility by choosing optimal amounts of leisure and consumption.

Individuals are assumed to have identical preferences that depend on consumption, c, and leisure, l,

(1)

where u is a continuously differentiable and strictly concave function with positive marginal utility of consumption and leisure. Leisure is defined as l = d -L, where d is hours available and L is hours worked. We assume that individuals differ in their ability to supply labor, their marginal product of labor, and hence have different wage rates, n. Gross earning, nL, thus, depends on ability.

Whether individuals receive welfare or not depends on their earned income. Individuals with zero earned income receive a guarantee level. This guarantee level is then diminished at the benefit-reduction rate, assumed to be linear, when individuals’ income increases. The income level at which individuals cease to receive welfare payments is referred to as the cut-off income, B, and is assumed to be set by the government. In addition, individuals who earn income pay income taxes. The income tax rate is assumed to be linear. We refer to individuals with income below the cut-off income as welfare recipients, denoted by the superscript wr, and individuals with income equal to or greater than this level as welfare non-recipients, denoted by wnr.

Disposable income for welfare recipients, wr, and welfare non-recipients, wnr, is given by

(2)

and

(3)

respectively. c is disposable income, T₀ is the guarantee level given to individuals with zero earned income, t_i is the marginal tax rate on labor income, t_b is the benefit-reduction rate, n is wage rate, and L is labor supplied. Figure 1 shows how disposable income depends on gross earned income.

Individuals choose amounts of consumption and leisure to maximize their utility subject to their budget constraint. The first-order conditions for welfare recipients and welfare non-recipients are, respectively,

when nL < B, and (4)

where b = (1 - t_i – t_b) and a = (1 - t_i) are the net returns to a unit increase in earned income. Solving the first-order conditions, the optimal amounts of leisure and consumption are

(5)

for welfare recipients and

(6)

for welfare non-recipients.

Wages in the population are distributed according to the density function f(n). The corresponding cumulative distribution function is F(n), where dF(n)/dn = f(n). The wage rate distribution is assumed to be continuous, where f(n) > 0 for 0 £ n < ¥ .

The social welfare function, W, integrates the utilities across individuals.

(7)

The maximization problem consists of finding the constants T₀, b , and a that maximize W subject to satisfying the government budget constraint. The guarantee level, T₀, is treated as a negative lump-sum tax. Net tax payments, TR, for welfare recipients and welfare non-recipients are then

and (8)

respectively.

Total net tax receipts are calculated as the integral of individual tax payments across all of the individuals. The government budget constraint is thus

(9)

where b is the ability level associated with the cut-off income level B. Rewriting the equality in equation (9) yields

(10)

where

To solve the government’s optimization problem, we set up the Lagrangian

(11)

where l is the shadow price of the government’s budget constraint. The first-order conditions of £ with respect to T₀, b , and a are

(12)

(13)

and

(14)

To obtain explicit solutions of the optimal benefit-reduction rate and the optimal marginal tax rate on labor income, specific functional forms of individual and social utility functions as well as assumptions about the wage distribution are required. It is possible to say something about the bounds of the optimal benefit-reduction rate and the optimal marginal tax rate without assuming specific functional forms, however, which is the topic of section 4.

3.4 Analytical Interpretation of the Tax Rates

We can interpret the tax rates analytically if we are willing to make assumptions about how the amounts of labor supplied by welfare and welfare non-recipients are affected by changes in T₀, b , and a . This can be done by differentiating the first-order conditions from the individuals’ utility maximization problem with respect to T₀, b , and a . (The calculations are presented in the appendix).

The optimal income taxation literature has demonstrated that the optimal tax rate should be less than unity (Mirrlees [1971]), otherwise L = 0 and c = 0. In our framework this corresponds to (t_i + t_b) < 1, which implies b > 0, for welfare recipients and a > 0 for welfare non-recipients.

If we substitute (1 - t_i – t_b) for b and (1 - t_i) for a , and rewrite equations (13) and (14) using labor supply elasticities with respect to net wage, equations (12) to (14) become

(12')

(13')

and

(14')

where

and

in accordance with equation (A6) to (A8) and because a and b are greater than zero.

The first term in equations (12’) to (14’), the integral of the marginal utility of consumption, is positive because the marginal utility of consumption should always be positive, as are n and L(n).

It is relatively easy to show that l must be positive, that is, the marginal utility of relaxing the government budget is positive. First, it is clear that l cannot be zero. Similarly, a negative value of l can be ruled out because it cannot simultaneously satisfy all the equations. For instance, from equation (12’) a negative l requires that (t_i + t_b) < 0. However, equations (A7) and (13’) cannot hold when both l and (t_i + t_b) are negative.

It is clear from equation (13’) that at least one of the last two terms has to be negative for the whole expression to equal zero. If the absolute value of the third term is greater than the absolute value of the last term, that is

(15)

then the third term must be negative. There are several instances under which (15) may hold. Inequality of (15) may hold, for example, if there are many individuals with an income substantially larger than the cut-off income, that is B/nL is small. It may also hold if e _b^wnr and e _b^wr are very small, or if t_b is negative and e _b^wr is large. If equation (15) is satisfied, equation (13’) implies that

(16)

where is the weighted conditional average labor supply elasticity for welfare recipients,

(17)

The optimal benefit-reduction rate, t_b, is then bounded from above by the average labor supply elasticity of welfare recipients with respect to net income and the optimal marginal tax rate on labor income. That is, the optimal benefit-reduction rate depends negatively on both the labor supply elasticity of welfare recipients and the optimal marginal tax rate on labor income. Thus, the more elastic the labor supply elasticity of welfare recipients the lower is the upper bound of the optimal benefit-reduction rate, and the higher the optimal marginal tax rate on labor income the lower is the optimal benefit-reduction rate.

If (15) is not satisfied, the optimal benefit-reduction rate is bounded by

(18)

where

(19)

This allows the benefit-reduction rate to be larger since is negative. The optimal benefit-reduction rate can be negative if equation (15) is satisfied and . This may happen if welfare recipients are elastic in their labor supply and the optimal marginal tax rate on labor income is high. A negative benefit-reduction rate implies that welfare recipients receive a subsidy when working.

From equation (14'), it follows

(20)

where is the weighted conditional average labor supply elasticity for welfare non-recipients,

(21)

if

(22)

This condition holds when t_b > 0 and and If t_b < 0 and is not sufficiently larger than so that the above condition is validated, then,

(23)

where

(24)

The optimal marginal tax rate on labor income, t_i, depends on the sign of the optimal benefit-reduction rate and on the magnitude of the labor supply elasticities with respect to net labor income for welfare and welfare non-recipients, respectively.

If t_b is positive and welfare recipients are more elastic in their labor supply than welfare non-recipients, then the optimal marginal tax rate on labor income is bounded from above by the average labor supply elasticity of welfare non-recipients. The more elastic the labor supply of welfare non-recipients, the lower is the optimal marginal tax rate on labor income.

If t_b is negative and , however, the upper bound of the optimal marginal tax rate is higher. When the optimal benefit-reduction rate is negative, the upper bounds of the optimal marginal tax rate on labor income depend on the elasticities of welfare recipients as well as the magnitude of the optimal benefit-reduction rate. The bounds of the optimal marginal tax rate on labor income are allowed to be higher when the optimal benefit-reduction rate is negative and/or welfare non-recipients are more elastic than welfare recipients. When the optimal benefit-reduction rate is negative, more tax revenues are required to finance welfare recipients' subsidy for working. The optimal marginal tax rate on labor income must be higher, thus, for the budget to balance.

The optimal guarantee level is positive when the optimal benefit-reduction rate is positive or as long as . The optimal guarantee level depends on the optimal levels of the tax rates and the labor supply elasticities. The guarantee level depends positively on the optimal benefit-reduction rate as long as the labor supply elasticity of welfare recipients with respect to a change in the benefit-reduction rate is low enough that an increase in the benefit-reduction rate is not completely offset by a decrease in the amount of labor supplied by welfare recipients. The guarantee level depends positively on the optimal marginal tax rate on labor income if welfare non-recipients' labor supply elasticity is low enough that an increase in the tax rate is not offset by a decrease in labor supplied. In addition, the optimal guarantee level depends on the cut-off income. An increase in the cut-off income will affect the amount of labor supplied by welfare non-recipients, so the total effect depends on how sensitive welfare non-recipients' labor supply is to changes in the cut-off income. If welfare non-recipients are relatively insensitive, an increase in the cut-off income when t_b is positive will increase the guarantee level, while an increase in the cut-off income when t_b is negative will lower the guarantee level.

3.5 Discussion

Many studies have estimated labor supply elasticities, but no real consensus on their magnitude has emerged (Killingsworth [1983]). Typically, labor supply elasticities have been estimated for the entire labor force, or for male and female labor forces separately, but seldom for welfare and welfare non-recipients separately or for different income levels. In addition, elasticities typically measure how labor supplied is affected by changes in net wages; few studies have examined the effect of changes in alternative sources of incomes. It is very hard to find elasticities that measure, for example, how sensitive welfare recipient and welfare non-recipient labor supply decisions are to changes in benefit levels.

An estimate based on uncompensated labor supply elasticity for males and females, estimated by taking the median elasticities across a large number of studies from the 1970s and early 1980s and weighing together median male and female elasticities using relative male and female income shares as weights, is 0.10 (Hansson and Stuart [1985]). An estimate derived in the same way but based on relatively more recent and sophisticated estimates is 0.44 (Hansson and Stuart [1993]). If , t_i should be no greater than 0.69 given that condition (22) holds. If t_i is equal to 0.69, then t_b can not exceed 0.31.

Other studies of labor supply elasticities have found different results, however. In fact, Theeuwes [1988], in a survey of eight empirical studies, found that uncompensated elasticities in the Netherlands range from -0.25 to 0.27 for males (mean =0.07) and from 0.20 to 3.23 for females (mean =1.39). Blomquist and Hansson-Brusewitz [1990] found uncompensated elasticities for males in Sweden between 0.08 and 0.13, and elasticities for females between 0.1 and 0.79.

Since labor supply elasticities vary across both countries and individuals, as well as across different studies, we plot the upper bounds of the optimal benefit-reduction rate and marginal tax rate on labor income as functions of labor supply elasticities.

Figure A plots the upper bounds of the optimal benefit-reduction rate for welfare recipients as a function of labor supply elasticities of welfare recipients at

various optimal marginal tax rates on labor income when equation (15) is satisfied. The higher the optimal marginal tax rate on labor income, the lower is the upper

From Figure A, it is apparent that the optimal benefit-reduction rate can be negative. At what point the upper bound of the optimal benefit-reduction rate is negative depends on the labor supply elasticity as well as the optimal marginal tax rate on labor income.

Finally, the upper bounds of the optimal marginal tax rate on labor income are plotted in Figure D for the case when equation (22) does not hold. Note that the

upper bounds of the optimal marginal tax rate depend on labor supply elasticities with respect to changes in labor income of welfare recipients. The upper bounds are higher when the optimal benefit-reduction rate is negative. For example, if we assume that the labor supply elasticities of welfare recipients and welfare non-recipients with respect to net labor income are the same, 0.4, then the upper bound of the marginal tax rate on labor income when t_b is positive is 0.71. The upper bound is 0.72 when t_b = -0.01 and larger when t_b is more negative.

Marginal tax rates vary widely between countries. If actual marginal tax rates reflect optimal conditions, the large variation in marginal tax rates on labor income

across countries may suggest a wide range in labor supply elasticities across the various countries. For instance, it may be the case that taxpayers in Sweden, a high tax country, are less elastic in their labor supply than taxpayers in the U.S., a lower tax country.

worker over 1972-1992 was 0.73 (Hansson and Stuart [1998]). (Again, remember that actual tax rates may be far from optimal tax rates). An optimal marginal tax rate of 0.73 corresponds relatively closely to the lowest of the bounds in Figure A and Figure B, which implies that the upper bound of the optimal benefit-reduction rate is fairly low regardless of welfare recipients' and welfare non-recipients' labor supply elasticities with respect to changes in the benefit-reduction rate. Clearly, the actual benefit-reduction rate of 100 percent in Sweden (Socialdepartementet [1999]) is not supported in this optimal income-tax model.

The U.S., on the other hand, is a low-tax country where the average production worker faces a marginal tax rate of 0.37 (Hansson and Stuart [1998]). An optimal marginal tax rate of 0.37 implies that the upper bound of the benefit-reduction rate is higher than in Sweden, ceteris paribus.

The average production worker in the U.K. faces a marginal tax rate of 0.52 (Hansson and Stuart [1998]), a tax rate that lies between what an average production worker faces in Sweden and the U.S. An optimal marginal tax rate of 0.52 corresponds to the second lowest bound in Figure A and Figure B. Thus, the upper bound of the optimal benefit-reduction rate would lie between the optimal benefit-reduction rates in Sweden and the U.S. if the labor supply elasticity for welfare and welfare non-recipients were the same in the three countries.

Several limitations to the approach used in this paper should be acknowledged. First, a linear income tax does not allow for different marginal income tax rates. In many countries, actual income tax schedules are characterized by increasing marginal tax rates. Often, there are two or more income brackets. Similarly, benefit-reduction rates may also be non-linear. The benefit-reduction rate likely depends on income, and allowing for non-linearity in the benefit-reduction rate may allow us to develop a more realistic structure.

3.6 Conclusions

We derive upper bounds of the optimal benefit-reduction rate using a modified version of Sheshinski's [1972] model of optimal income taxation. Specifically, we add a term for the rate at which welfare recipients lose welfare when their gross earned income increases by a unit. We find that the optimal income-tax problem is characterized by a guarantee level at zero income that is reduced at the benefit-reduction rate when welfare recipients earn income. The upper bound of the benefit-reduction rate depends negatively on the magnitude of the optimal marginal tax rate on labor income, and either negatively on the average labor supply elasticity with respect to changes in net income of welfare recipients or positively on the average labor supply elasticity with respect to changes in the benefit-reduction rate of welfare non-recipients. The optimal benefit-reduction rate can be negative, in which case welfare recipients should be given a subsidy for working. The optimal marginal tax rate on labor income is positive and depends on the sign of the optimal benefit-reduction rate and on the average elasticities of labor supply with respect to changes in labor income of welfare and welfare non-recipients.

Our results suggest that rates in some countries exceed the bounds derived in the optimal income taxation theory. With a benefit-reduction rate of 100 percent and an inclusive marginal tax rate on labor income around 70 percent welfare recipients in Sweden lack economic incentives to break their welfare dependency. These rates are clearly in excess of optimal bounds.

We consider estimation of bounds on the optimal benefit-reduction rate to be a positive step at a critical moment in policy formation globally. At the same time, we hope it will spawn future modeling efforts to improve correspondence with reality. For example, the model used in this paper is admittedly crude and would likely benefit from relaxing the linearity restriction and by including capital.

References

Killingsworth, M., 1983, Labor Supply, Cambridge: Cambridge University Press.

Pigou, C.A., 1947, "A Study in Public Finance," MacMillan, 3^rd edition, London.

—, 1987, "Studies in the Theory of Optimal Income Taxation, Helsinki

Appendix

To obtain the derivatives of the supply function with respect to T₀, a , and b as an expression of derivatives of the utility function, we differentiate the first-order conditions. Namely,

. (A1)

Leisure is assumed to be a normal good; that is,

(A2)

The higher the guarantee level an individual receives, the more leisure the individual will consume. The assumption that leisure is a normal good requires that

(A3)

From this it follows that the labor supplied depends negatively on the guarantee level, that is

(A4)

We also assume that leisure (labor supply) is a decreasing (increasing) function of the net wage rate; that is

(A5)

or

(A6)

Accordingly,

when nL < B, (A7)

and

when nL ³ B. (A8)

Intuitively, when welfare recipients are allowed to keep more of their earned income, welfare non-recipients have fewer incentives to work.

4.1 Introduction

Government grew dramatically in size during the 20^th century in nearly all developed countries. In Sweden, the U.K., and the U.S., for example, general government expenditures grew from 10, 13, and 8 percent of GDP, respectively, in 1913 to 66, 43, and 33 percent in 1995 (Tanzi and Schuknecht [1997(a)]). This growth in government expenditures was nearly uninterrupted for a century, with the exception of the post- World War II period in Germany and Japan and a period in the 1980s in several OECD countries. The growth in government size was remarkably rapid during the 1960s, 1970s, and 1980s.

As the large share of developed economies currently commanded by the public sector may have important consequences for economic performance, this buildup in government activity has alarmed many observers (Lindbeck [1986], Tanzi and Schuknecht [1997(b)]). For instance, a large government sector may induce inefficiencies in the economic system due to various disincentive effects, crowd out the private sector, and impoverish the economy in the long run.

Alternatively, a large government sector could be a catalyst for economic prosperity, particularly if most activity occurs in areas thought especially likely to promote economic activity. For instance, the provision of a legal framework and well-defined property rights is critical to economic development, as are law and order and an efficient infrastructure (North [1990], Hall and Jones [1997], Tornell and Lane [1999]).

Not surprisingly, the relationship between large government and economic performance (commonly measured as the growth rate) has been widely studied (Levine and Renelt [1992], Durlauf and Quah [1998], Temple [1999]). Despite widespread interest, however, researchers have to date been generally unsuccessful in attempts to settle the issue (Slemrod [1995], Temple [1999]). Some studies have found evidence of a negative relationship between the size of government and the growth rate (e.g., Landau [1983], Barro [1989], Barro[1991]) and others evidence of a positive relationship (e.g., Ram [1986] Devarajan et al. [1996]), though many studies have been unable to demonstrate a statistically significant correlation between the two variables (e.g., Kormendi and Meguire [1985], Levine and Renelt [1992], Easterly and Rebelo[1993]).

Differences in the data and statistical approaches used can explain much of the heterogeneity of results in this branch of the economic growth literature. For instance, even the studied countries vary widely among previous studies, ranging from just developed nations (e.g., Barth and Bradley [1987], Fölster and Henrekson [1999]) to both developed and developing nations (e.g., Kormendi and Meguire [1985], Barro [1991], Easterly and Rebelo [1993]) to only developing nations (e.g., Devarajan et al. [1996] Dowrick [1996]). Interestingly, there is more often evidence of a negative relationship between the size of government and the growth rate in wealthy countries and more often evidence of a positive relationship in poor countries (Landau [1983], Ram [1986], Grier and Tullock [1987]).

Similarly, there is little agreement among the measures of government size used in previous studies. Many studies have used government consumption expenditures as a share of gross domestic product (GDP) to measure government size (e.g., Landau [1983], Ram [1986] Karras [1997]), though a number of them have adjusted the values in various ways to improve the fit. For instance, Barro [1991] and Easterly and Rebello [1993] net out expenditures on defense and education as these relate more to public investment than public consumption. Kormendi and Meguire [1985] and Grier and Tullock [1987], in contrast, use the growth in total government expenditures, though they exclude fixed capital formation and transfer payments. Nevertheless, many of these studies suggest that the total government impact (including regulations) would be a better measure (Landau [1983], Kormendi and Meguire [1985], Grier and Tullock [1987]), though they use less inclusive measures for lack of data.

There is also substantial heterogeneity in the independent control variables included alongside government size, which is not surprising given that theory offers no clear guidelines as to what factors influence economic growth (Agell et al. [1997]). Levine and Renelt [1992] suspected that these differences in the conditioning variables explained much of the conflict seen among results in the economic growth literature, and conducted extensive sensitivity testing using extreme bounds analysis (EBA). Specifically, by systematically altering the set of conditioning variables and observing changes in the resulting coefficient estimates, they found that many fiscal policy indications - either individually or in groups - were correlated with growth but that the relationship for any particular indicator or group of indicators was sensitive to the set of included variables. Sala-i-Martin [1997] criticized this approach as too extreme and re-examined the data by looking at the entire distribution of coefficient estimates rather than just the two extreme bounds. Nevertheless, he also failed to find a measure of government spending that was consistently statistically significant.

While statistical modeling is undeniably important, there is too little heterogeneity in the approaches used in this literature to explain the diversity of results. Indeed, most empirical studies of this relationship have used cross-sectional estimators to estimate the relationship, applying them either to cross-section data sets (one observation per country) or to repeated cross-section (panel) data sets (multiple observations per country over time), with mixed results. A smaller number of studies have estimated the relationship using time series methods for individual countries (Grossman [1988], Aschauer [1989], and Peden [1991]) with likewise mixed results. Though these studies have the advantage that more than one observation per country is used, time series estimation is known to be especially sensitive to model specification issues (Leamer [1974], Leamer [1978]).

Several recent papers cast doubt on the suitability of cross-sectional estimators for estimating this relationship, however. Dowrick [1996], for instance, found that the positive relationship between government and GDP growth found in such studies as Ram [1986] could be attributed to endogeneity. Controlling for time-invariant factors with fixed effects and reverse causality by using lagged endogenous variables as instruments and two-stage least square estimation, he found that the significantly positive relationship, found by Ram [1986], became insignificant. Devarajan et al. [1996] similarly found that government expenditures changed from being a positive to a negative determinant of economic growth when country-specific factors were taken into account, though the coefficient did not attain statistical significance in either specification. Finally, Fölster and Henrekson [1999] find that the relationship between growth and the public sector is more robustly negative when using fixed effect estimation than cross-sectional estimation.

In this paper, we attempt to shed light on the relationship in industrialized countries between government size and economic performance as measured by the growth rate. Specifically, we estimate the relationship using an econometric approach that controls for country- and time-specific fixed factors and a unique measure of government size that more closely captures the true impact of government. Moreover, we additionally estimate the relationship using individual government components, for instance transfers and public goods, both separately and together to examine whether particular government activities have more favorable or less favorable consequences for economic growth.

We also conduct sensitivity testing of the relationship to determine the robustness of model results. For instance, we estimate the model using two cross-section estimators in order to evaluate the importance of the estimators that have been used extensively in previous analyses. Moreover, we also estimate the model using conventional government consumption expenditures as a share of GDP as a measure of government size.

We find that government size is a negative and statistically significant determinant of the economic growth rate. Moreover, the magnitude implies that a 1 percentage point increase in government size leads to a 0.23 percentage point decline in the growth rate, which translates to an elasticity of -2.4 at the means. In contrast, both cross-section estimates are statistically insignificant and considerably smaller. We also find substantial differences in the contributions of different types of government expenditures. For instance, the coefficients for pecuniary transfers - that is spending on education, health, housing and community amenities - and interest payments are negative and statistically significant. Cash transfers are also negatively correlated with the growth rate, but the coefficient is statistically insignificant. In contrast, public goods are positively related to growth. Finally, replacing our measure of government size with the more conventional government consumption measure resulted in virtually unchanged coefficient estimates, but substantially reduced statistical significance.

The paper is organized as follows. Section 4.2 describes the data, focusing especially on our measure of government size. Section 4.3 presents our estimation strategy. Section 4.4 contains the main results and section 4.5 follows up with results from the sensitivity analysis. Finally, section 4.6 concludes the paper.

4.2 Data

We have compiled data for 21 industrialized countries for the period 1973 to 1992 based in large part on data from the OECD and Summers and Heston's Penn World Table (PWT 5.6). See Table A in the appendix. Specifically, we include each of the OECD member countries that reported information over this time period, except for Greece and Iceland which were excluded due to frequently missing data. We divide the data into four five-year periods (cross-sections), so there are 84 observations in total. Relative to much of the existing literature, our data offers two important advantages. First, by limiting the data to the industrialized OECD countries, we can reduce the problems of trying to fit a model to data from unduly dissimilar nations (Grier and Tullock [1987], Devarajan et al. [1996]). Moreover, limiting the data to OECD members increases the comparability and reliability of the data as, while the data are far from perfect, the OECD has gone through great pains to standardize definitions and encourage accuracy in collection. Second, the panel nature of the data enables us to model unobservable time- and country-specific fixed factors, for instance national culture. National culture has been found to be an important determinant for the growth rate (Clark [1987], Abrams and Lewis [1997]. Culture is, however, often omitted in growth regressions because it is hard to observe and measure.

All financial variables are measured in constant U.S. dollars. We define economic growth as the average of the annual per capita GDP growth rates over each five-year interval. While one can measure economic growth in numerous ways, this specification is one of the most widely used and thus offers better comparability with the results of other studies. To assess the sensitivity to this measure, however, we also estimate the model using economic growth defined as the growth in per capita GDP over the five-year interval.

In contrast to previous studies, most of which have used government consumption to proxy for government size, our measure includes all government expenditures plus interest on pre-existing debt. Interest payments are a fairly large component of government spending. This more inclusive measure, thus, better reflects the scope of government activity, and hence may better model the potential overall influence on economic growth (Landau [1983] and Kormendi and Meguire [1985]). Interest payments may crowd out other public consumption, not to mention private investment through changes in the interest rate.

We define government size (S) as government spending on transfers (T), spending on public goods (G), and the interest on pre-existing debt (r b). Specifically,

(1)

We consider the effect of individual spending categories separately in the second part of the analysis, so it is necessary to point out that we depart from convention in defining these categories. In much of the literature, spending categories have been defined based on the anticipated effect of the expenditures on economic growth, i.e., negative or positive. In contrast, we define spending categories based on the attributes of the expenditures themselves. Specifically, we treat general public services, defense, public order and safety, and economic services as public goods (G) because the marginal cost of another consumer is zero (or nearly zero) and it is costly to exclude consumers. We include spending on education, health, and housing and community amenities under pecuniary transfers (T_#) because they can easily be provided privately, and in many countries they are. Finally, we consider spending on social security and welfare expenditures to be cash transfers (T_$), so that total transfers can be written as:

(2)

Two areas fit poorly into the above categories: recreational, cultural, and religious affairs and the residual "other". Both contain a mixture of public goods and pecuniary transfers. We divide these categories equally between G and T_#.

The data on public good expenditures and transfers comes predominantly from OECD data (OECD [1991]), though it reflects International Monetary Fund (IMF) and United Nations (UN) data in some cases. Government interest payments (r b) equal the nominal interest paid minus interest received for consolidated government for each country except Japan and New Zealand, for which net-interest reflects only the budget of the central government. The interest payments come primarily from U.N. data, though it was necessary to use IMF data in a couple of cases.

The other regressors are initial income (i.e., income at the start of each 5-year period), population growth over the interval, average investment as a share of GDP over the five years, and average number of total years of schooling of the total population. Some comments are in order. First, data on real GDP per capita and investment for Germany, Portugal, and New Zealand were missing for the last two years, so data from OECD [1992] were used instead. In addition, data on population for the Netherlands for the whole period, and for the last two years for Germany, Portugal, and New Zealand are from OECD [1991]. Second, the education data are based on quinquennial educational attainment from 1960 to 1985 as reported by Barro and Lee [1993]. We extrapolated figures for 1990 using linear regression on the data from 1960 to 1985. Education data was absent for Luxembourg, so we estimated it as a linear combination of the values seen for Belgium, Germany, and the Netherlands. While our estimation may seem crude, the education data did not influence model results noticeably and, hence, the crudeness of these estimations is most likely negligible.

4.3 Estimation

We estimate the effect of government size on economic growth using fixed effects regression, an approach capable of accounting for many of the unobservable factors that may be confounded with the functioning of government. By controlling explicitly for country- and time-specific fixed factors, this approach may mitigate omitted variable bias due to such unobservable and poorly measurable quantities as national culture (Clark [1987], Abrams and Lewis [1995]), legal-political institutional infrastructure (North [1990]), government efficiency, and the degree of urbanization. To the extent that these factors are correlated with government size, the OLS and OLS-type estimators used so widely in this literature will mistakenly allocate the effect of these omitted factors to government size (as well as perhaps to some of the other included regressors).

The fixed effects estimator may remedy the problem of omitted variable bias. It exploits the repetition across observational units in panel data to separate the effect of persistent unmeasurable factors from the relationship of interest. Specifically, a separate dummy variable is included for each observational unit so, in consequence, only within movements in the dependent variable and the regressors are used to estimate the parameters. If the unobservables that are correlated with government size do not vary over time, the fixed effects estimator solves the omitted variable problem. For instance, if factors reflecting institutional infrastructure are omitted, the fixed effects estimates will be unbiased as long as these institutions are constant over time. Since it takes a long time for institutions to change, this may not be a totally unrealistic assumption.

Our regression model can be written as:

(3)

The dependent variable, g_it, denotes the average 5-year per capita growth rate for country i at time period t. X_it is a vector of measures of government size that in various regressions includes such variables as total government size, transfers, public goods spending, and interest payments on debt. Z_it is a vector of explanatory variables including the variables investment, initial income, annual average population growth, and human capital.

The m _i terms are fixed country effects (i.e., unmeasured shocks). These terms account for time-invariant determinants of economic growth that vary among the countries in our sample. If m _i were correlated with X_it in equation (3), then estimators that failed to include the country-specific fixed effects would yield inconsistent estimates of the effect of government size on economic growth.

The d _t terms are sample-wide period effects. These terms account for trends that affect the economic growth in each of the countries similarly, such as business cycles and the oil shocks in the 1970s. Because government size increased during this period, a model that failed to account for such trends would confound those trends with the effects of increased government size.

The terms b and g are parameters to be estimated. The e _it terms are idiosyncratic disturbance terms that vary by country and time period, and are assumed to be independently and identically distributed with mean zero and variance s e ². t indexes each 5-year time period.

To illustrate the effect that the choice of econometric approach has on the results, we also report estimates based on two cross-sectional estimators chosen to correspond generally with the results of the majority of studies in the literature. Specifically, we estimate the model using the full panel data but no country-specific fixed effects (time dummies were included, however). We refer to this as the pooled cross-section estimator. We also estimate the model with OLS using a modified data set consisting of country-specific averages of the data over the four time periods. We refer to this as the between estimator. Neither the pooled cross-section estimator nor the between estimator accounts for country-specific unobserved factors that are correlated with both economic growth and government size, and hence both are susceptible to omitted variable bias.

We also estimate the basic model using random effects estimation. In contrast to the fixed effects estimator described above, the random effects model does not address the issue of omitted variable bias (i.e., correlation between the disturbance term and the included regressors). It is a generalized least squares (GLS) estimator, however, and hence is efficient in its class. If country- and time-specific fixed factors are statistically unwarranted, the random effects specification will provide a better opportunity to identify the true relationship. We use Hausman’s test (Hausman [1978]) to discriminate between the two econometric estimators.

We include a final set of regressions to assess the goodness of fit of our fixed effects estimates. Specifically, there is no reason a priori to expect a linear relationship between government size and economic growth, so we consider a quadratic specification for government size, one that would allow for a U-shaped or inverted U-shaped relationship, as well as a cubic and logarithmic specification. Neither do we have a strong reason to believe that the relationship is additive; i.e., that the growth rate should be measured in levels. We, thus, estimate the model first using a log-linear specification and subsequently based on a Box-Cox transformation of the dependent variable (see Greene [1993], chapter 11). Unfortunately, since growth rates are not restricted to being positive, we lose 8 observations because the Box-Cox transformation is not defined for negative values. We then re-estimated the fixed effects model using the restricted sample, but the results changed little.

Studies on government size and growth may suffer from several other statistical problems as well. One of them is the endogeneity problem. Several of the explanatory variables, like government size and investment, may both influence the growth rate and be influenced by it. To deal with this one wants to find instruments that are correlated with the endogenous variable but not with the disturbance term. The studies in the literature that have accounted for this have typically used lagged variables of the endogenous variables as instruments. As already mentioned, Dowrick [1996] showed – using 2SLS and lagged variables on government size, investment, and prices as instruments – that the correlation between government size and growth is caused by reverse causality. Before one draws too many conclusions from this result, however, one needs to evaluate the quality of the instruments. We find in our data that lagged investment and lagged government size are poor instruments for investment and government size, and hence 2SLS estimates using lagged investment and lagged government size are fruitless.

Table 1 reports the results of three different regression models of the relationship between economic growth and government size. The first column reports the results of fixed effects regression. The second and third columns report the results of pooled cross-section and cross-section regression, respectively. Statistical significance refers to the 5 percent significance level unless otherwise stated.

All variables included in the fixed effects model, besides government size, have the expected signs. Initial income is highly significant and negatively correlated with the growth rate, which gives support for the convergence hypothesis. Investment is positively correlated with economic growth, though statistical significance is not attained even at the 10 percent level. Population growth is negatively and significantly correlated with the growth rate and

explains a substantial part of the variation in growth rates. Education, however, is positively though insignificantly correlated with the growth rate. In addition, total size of government is negatively correlated with the growth rate and strongly significant. A one-percentage point increase in the size of government is associated with a decline of 0.23 percentage points in the annual average growth rate.

The pooled cross-section estimator yields quite different estimates. All variables have the same sign as in the fixed effects model but generally explain less of the variation in the growth rate and are less statistically significant. The only variables that are significant at a 5 percent significance level are initial income and population growth. Total government size is negatively though insignificantly correlated with the growth rate. The magnitude of the government size coefficient is only about one-tenth of that estimated with fixed effects.

The between estimates explain even less of the variation in the growth rate and are even less significant. In fact, none of the variables are statistically significant at even the 10 percent significance level. The government size coefficient remains negative but falls in absolute magnitude to only one-hundredth of that estimated with fixed effects, and is insignificant.

The results of the three estimation models differ importantly in not only the significance level but also in the magnitude of the coefficients, which suggests that omitted variables are present and the pooled cross-section and between estimators are biased. The coefficient for government size is more negative in the fixed effects model than in the other two estimation models, which suggests that important omitted factors are correlated with both the disturbance term and the regressors. These omitted factors either have positive coefficients and positive correlation with included variables or have negative coefficients and negative correlation. Suppose, for instance, that factors determining the efficiency of government activities are omitted. Then, if these factors are positively correlated with the size of government and have a positive impact on the growth rate, the government size coefficients in the between and pooled cross-section models will have the less negative magnitude observed. That the coefficient for government size in the between model is smaller in magnitude than in the pooled cross-section model suggests that time-specific effects may matter as well. Innovations over time that have a positive impact on growth and are positively correlated with government size can explain this.

Consistently, the F tests support the inclusion of the country-specific fixed effects, m _i, in the regressions and hence support the conjecture that the growth rate varies in important unmeasured ways across countries. With a critical value of about 1.97 at 95 percent confidence, the test statistic for including country fixed effects (given that time-specific fixed effects are included) is 4.68. Likewise, the F tests support the inclusion of time-specific fixed effects, d _t, in the regression (given that country fixed effects are included), which supports the conjecture that the growth rate varies in important unmeasured ways across time. With a critical value of about 2.79 at 95 percent confidence, the test statistic is 13.0 in the fixed effects model. In the pooled cross-section regression the test statistic is 7.54 and the critical value 3.10 at a 95 percent confidence level.

We also estimate the same model using a random effects estimation technique. Using Hausman’s specification test, however, we find evidence to strongly reject the random effects specification both for country- and time- specific effects. The test statistic has a value of 18.58 and a p-value of 0.0023.

In addition, we test for the existence of other non-linear relationships between government size and its various components and the growth rate, using the fixed effects specification. We do not, however, find much support for non-linear relationships between the total size of government and the growth rate, nor between the various components of government spending and the growth rate. We test for a quadratic, cubic and logarithmic relationship between both total government size and its components and the growth rate. None of these relationships are found to be significant, however.

Since we have no strong prior indication regarding the correct functional form of the model, we re-estimated the model using first a log-linear specification and then a Box-Cox specification. As mentioned above, the growth rate is not constrained to be positive so we lose 8 observations. To provide a benchmark, we re-estimated the fixed effects model using the restricted sample. Table 2 shows these results for the linear, log-linear, and Box-Cox specification models.

The results are generally similar in the three models and government size is negatively and significantly correlated with the growth rate in each specification. l is the dependent variable in the Box-Cox specification estimated by grid search. l = 1 corresponds to a linear specification, whereas l = 0 corresponds to the log-linear specification. The test for log-linear specification is soundly rejected, and the linear specification is also rejected at a 5 percent significance level. Nevertheless, the Box-Cox estimates do not support generally different conclusions from those of linear specification.

Finally, estimating the model with 2SLS and lagged government size as instrument alters the coefficient from –0.259 to –0.322 and the t-statistic from –2.36 to –1.58. The result is still negative though less significant. The validity of this estimation, however, depends crucially on how good an instrument lagged government size is. We abstain from drawing any further conclusions from this result, however, due to the dubious validity of the instrument.

It seems reasonable to expect that the various components of government spending may affect the growth rate to different degrees and in different directions. We test for this by dividing government size into its components. These components are then included in the base line fixed effects regression. The components are included first all together and then one at a time. Again, we use Hausman's test to discriminate between the fixed- and random effects estimates. Table 3 reports results from these regressions.

Including all the components together or one at a time changes the results only slightly. The magnitude of the coefficients and the significance level differ little and the R² values are slightly lower when components are included one at a time. All variables have the expected sign, though not all are statistically significant. The only component that is positively correlated with

the growth rate is public good spending (regressions 1, 2, and 4). Because it is

insignificant, it is hard to draw any conclusions from this result, but it may

suggest that the provision of "true" public goods has a positive effect on the growth rate, at least up to some level.

Interest payments on pre-existing debt seem to discourage growth (regressions 1, 2, and 5). A one-percentage point increase in interest payments is associated with about a 0.3 percentage point decline in the growth rate. This could be explained by the crowding out effect that interest payments have on other more productive public spending, and by the negative impact large public deficits may have on private investment. This is consistent with the findings of Aschauer (1989). He finds that public-sector deficits may be an important determinant for the level of real interest rates, private investment decisions, and the economy’s dynamic performance.

In two cases, regressions 4 and 7, the Hausman test statistic of whether fixed or random effects estimation is preferable is just below the critical value at the 5 percent significance level, weakly suggesting that random effects specification may provide better estimates. The random effects estimation of regression 4 results in a larger and statistically significant estimate for public goods. The random effects coefficient is 0.225 and the t-statistic is 2.35. The random effects coefficient (-0.138) for cash transfers in regression 7 is less negative than the fixed effects coefficient (-0.236), though it is statistically more significant. The t-statistic is -1.15 instead of -0.51.

4.5 Multicollinearity and Other Sensitivity Analyses

Another issue in studies of government size and growth is multicollinearity. That is, some of the right-hand side variables may be overly correlated, for example initial income and the size of government. This is less serious than the question of endogeneity, however, since it is not a statistical problem that biases the estimates but rather an issue with the data. The problem arises because it is hard to discern where the effect is actually coming from (initial income or government size), and may result in statistically insignificant estimates even if the estimator provides unbiased estimates of the true effect. A remedy for this is to drop variables. The only variables that are not significant in our fixed effects model are investment and education. Dropping these two variables has no significant impact on the results.

To further test the robustness of our results, we alter the conditioning set of included variables. The result of this is presented in Table 4. Levine and Renelt [1992] show that only by selecting a very particular conditioning set of variables can a significant correlation between government consumption expenditures and the growth rate be identified in a linear regression model. Alterations to that conditioning set lead to an insignificant correlation. They find, for instance, that including a trade variable makes the correlation insignificant.

Changes in the data set do not alter the result noticeably. For example, including the available years for Turkey (1975 to 1992) and excluding the last period for Germany (because of the unification) does not change the results much.

Using Summers and Heston’s data on the government consumption share instead of our measure of government size does change the results modestly. The coefficient changes from –0.258 to –0.275, and the t-statistic decreases in absolute magnitude from –3.15 to –1.81.

Changes in the growth rate measure have small impacts on the overall results. For instance, changing the growth rate variable to growth rate over 5 years instead of the average annual growth rate over a 5-year period does not change the results noticeably.

Using the growth in government size instead of the level results in a negative, while insignificant, correlation. A one-percentage point increase in the growth rate of the government size is associated with a 7.6 percent decrease in the growth rate (t- statistic of 1.50).

We have estimated the relationship between government size and economic growth in a number of OECD countries using an estimator that controls for omitted country- and time-specific factors. Consistent with Fölster and Henrekson [1999], we find a strong negative correlation between the size of government and the growth rate. When compared to a pair of cross-section estimates based on the same data set, the fixed effects results are statistically significant and substantially larger in absolute magnitude, suggesting that omitted variable bias may be an important problem. Indeed, this could help explain why the results of earlier studies are so diverse.

We have also estimated the model using data on individual government activities. We find that interest payments on pre-existing debt and the provision of pecuniary transfers are strongly negatively correlated with the growth rate. Social security and welfare payments are negatively correlated with the growth rate, though the coefficient is statistically insignificant. The provision of public goods, in contrast, has a positive, though insignificant in the fixed effects specification, impact on the growth rate.

The results of this study have practical implications for public policy; for example, they can provide some guidance on how public resources can best be spent. With increased unification in Europe, public policy may be one of the few remaining determinants of the growth rate that individual governments can modify.

Finally, we wish to point out that we make no claims that our results accurately reflect the true relationship between government size and growth. There are a number of serious econometric issues involved. Our results suggest we have overcome some of the problems common in earlier literature. However, many still remain. For example, studies have been generally unsuccessful in properly accounting for endogeneity. The instruments used have often been inappropriate, and the search to find more suitable instruments should continue. Moreover, extending the time dimension to pick up long-run effects may also be fruitful.

Levine, R. and D. Renelt, 1992, "A Sensitivity Analysis of Cross- Country Growth Regressions," American Economic Review, 84(4), 942-963.

5.1 Introduction

earlier. Moreover, the countries with the greatest peak spending and transfers tended to have the greatest declines from the peaks to 1992.

We ask whether some of this apparent leveling or peaking of sizes of government may be a result of limits to taxation. The "limit to taxation" might be defined in several ways. For instance, a well-informed electorate that desires an extensive safety net may rationally keep transfers and spending below maximum feasible levels because efficiency losses per marginal unit of tax revenue could be infinite at maximum revenue (Atkinson and Stern [1974], Browning [1976], Meltzer and Richard [1981], and Svensson [1990]). On the other hand, the political-economy analysis of Brennan and Buchanan [1977] posits that government maximizes revenue in long-run equilibrium, and Buchanan and Lee [1982] model a simple political process that leads to an equilibrium tax rate greater than the rate that maximizes long-run revenue.

We compute theoretical spending and transfer maxima calculated in a model of the long-run Laffer curve and compare these maxima to observed levels of spending and transfers. The model differs primarily from those in the literature in that the focus is on the size of government - for example, spending, transfers, and revenue - rather than on the tax rates that maximize revenue. Although the model is simplified by treating capital as constant, the tax rates that maximize revenue in the model are comparable to the rates that maximize revenue in other models of the long-run Laffer curve (e.g., Fullerton [1982]).

In the model, government provides public goods and private goods, and transfers are defined as the net claims to private goods that result directly from government fiscal decisions about budgeted spending and its funding. This definition differs from the accounting definition underlying Table 1, in which transfers are simply amounts recorded on public budgets when governments make payments to provide private goods. To compare transfers calculated in our theoretical model with actual data, the first step is to measure transfers as we define them in our theoretical model. Because accounting practices vary from country to country, using a measure of transfers that is consistent with our theoretical model can also make comparisons across countries and time more informative than comparisons based on traditional measures from public budgets.

We find that tendencies toward flat or falling spending and transfer percentages are somewhat more marked with measures corresponding to our definition of transfers than the accounting-based relationship observed in Table 1. The pattern that countries with the greatest peak fiscal sizes usually experienced the greatest declines in fiscal sizes is also more marked with our measures. We find, moreover, that calculated long-run limits under reasonable assumptions are less than observed peak ratios of spending, transfers, and revenue to GNP in several OECD countries.

Because the greatest observed fiscal sizes exceed calculated long-run maximum fiscal sizes, and because the countries with the greatest peak fiscal sizes also had the greatest declines in fiscal sizes, we cannot reject the idea that fiscal sizes in some developed countries have bumped up against limits to taxation. Put differently, political processes in a number of developed countries may for a period of time have led to spending and transfers greater than the maximum levels that can be supported in a theoretical long-run equilibrium.

In section 5.2 we calculate maximum spending, transfers, and tax revenue that can be supported in a theoretical long-run general equilibrium. Section 5.3 begins with a description of the approach used to derive internally consistent measures of fiscal size of government, then presents measures of fiscal size established with actual data, and finally compares these numbers to numbers derived in section 5.2. Section 5.4 concludes this paper.

5.2 A Theoretical Limit to the Fiscal Size of Government

The well-known Laffer hypothesis (Laffer [1979]) posits a maximum sustainable size of government. It is not generally known, however, how close actual spending and transfer patterns are to these theoretical maxima. We address this issue by comparing observed levels of spending, transfers, and tax revenue to limits derived in a theoretical model.

We categorize government spending as either transfers (T), spending on public goods (G), or interest on preexisting debt (r b). Note that G includes only public provision of public goods, which is usually a small part of total government spending. We categorize the sources of government revenue as either tax revenues (R), non-tax payments from households to government (N) (e.g., fines, fees, forfeitures, penalties, and sales), non-tax revenue in the form of financial returns from government enterprises (F), or the government's budget deficits (D b), which equals the increase in the household's holding of government debt. The government budget is written as

(1)

According to the Laffer hypothesis one tax rate, or a vector of tax rates, maximizes equilibrium tax revenue. Similarly, there are associated maximum levels of spending and transfers for given levels of public goods (G), interest on the debt (r b), non-tax revenue (N + F), and the deficit (D b). Such maximum levels of spending, transfers, and tax revenue may be thought of as theoretical limits to the fiscal size of government.

We compute rough technical limits by embedding the government and household budgets (described below) into a general-equilibrium model in which the aggregate household receives utility from net income (y), leisure, and public spending. We simplify the model by not allowing capital to vary. While including capital distortions would permit a more accurate representation of the economy, it introduces a number of important complications such as whether to model the economy as open or closed (Feldstein and Horioka [1989], Mendoza and Tesar [1995]), whether to use a naive or optimization model of investment (Bernanke, Bohn, and Reiss [1988]), and what values to assume for the elasticity of intertemporal substitution (Judd [1987], Hansen and Singleton [1983], Mankiw and Zeldes [1991], and Engen and Gale [1997]). In the end, we limit our analysis to labor distortions because, averaged across OECD countries over 1972-1992, labor income was 63 percent of total income.

The aggregate household receives income from labor, capital, and holdings of government bonds (debt), and pays taxes to government on each type of income. The household also receives transfers from government and makes payments to government to cover nontax liabilities and to augment holdings of government bonds.

The aggregate household’s total income, net of all payments to government,

is written as

(2)

where t_l, t_k, t_b, are the marginal tax rates faced by the aggregate household on labor income, capital income, interest income from government bonds; w and r are gross returns to labor and capital; r is the interest rate on government debt; l is labor supplied by the household; k is capital owned by the household including capital owned indirectly through firms; b is the net level of (preexisting) government debt; and T is transfers. The corresponding tax revenues are thus R º t_lwl + t_krk + t_br b. All variables are defined over a given accounting period, taken below to be a year, and time subscripts are suppressed.

The model is parameterized to fit a stylized "average OECD economy" in a calibration allocation described in appendix C, with labor supply elasticities in empirically reasonable ranges. Because most differences in spending reflect differences in transfers (see Table 1), we compute equilibria at different values of the tax rate on labor income (t_l) when T adjusts to keep the government budget (1) in balance. In these calculations, G, t_k, t_b, N, and F are held constant, government meets interest obligations on preexisting debt at a given interest rate, and primary deficits (deficits net of interest payments) equal zero, which approximates actual average primary deficits over our sample. By comparing equilibria, we find the value of t_l at which spending, transfers, and tax revenue attain maxima, and divide by the associated level of GNP to compare with observed fiscal sizes reported above.^,

We assume initially that GNP is a Cobb-Douglas function, a₀K^al⁽1-a), where a is a parameter equal to capital’s share of GNP and K is the sum of private capital (k) plus government capital (k’). Without loss of generality, we choose units so a₀ = 1, K=1, and, in the calibration allocation, l = 1. Under competition, gross returns to labor and capital are then

(3)

and

(4)

Factor payments exhaust GNP (wl + rk + F = K^al⁽1-a)), so (3) and (4) imply that returns on private and government capital are equal (F = rk’).

An equilibrium is an allocation such that (1), (2), (3), and (4) hold, and the household maximizes utility by choice of l subject to the budget (2), taking t_l, w, t_k, r, k, t_b, r , b, T, N, D b, and G as given. Utility is assumed to be a Stone-Geary-modified CES function:

(5)

where a , w , and d parameters and V is a function that captures utility effects of G and utility effects of T not operating through consumption of net income (y). The form of V does not affect the results.

The parameters a , w , and d are chosen such that: (i) the uncompensated labor supply elasticity equals a given value in the calibration allocation; (ii) the compensated labor supply

elasticity equals a given value in the calibration allocation; and (iii) the calibration allocation is an equilibrium. To reflect the uncertainty that exists about labor supply elasticities, we consider two pairs of uncompensated and compensated elasticities: 0.1 and 0.25; and 0.44 and 0.52.

When the uncompensated and compensated elasticities are assumed to be small (0.1 and 0.25, respectively), maximum spending, transfers, and tax revenue occur when the marginal labor tax rate is 81 percent, at which point spending is 72 percent of GNP, transfers are 58 percent of GNP, and tax revenue is 68 percent of GNP. When large uncompensated and compensated elasticities are assumed (0.44 and 0.52, respectively), maximum fiscal size occurs when the labor tax rate is 64 percent, at which point spending is 61 percent of GNP, transfers are 48 percent of GNP, and tax revenue is 57 percent of GNP. The revenue-maximizing tax rates in these two cases are quantitatively similar to those in Fullerton [1982], who used a more detailed model with variable capital.

Sensitivity analysis in appendix A indicates that computed limits to the fiscal size of government are not particularly sensitive to reasonable alternative assumptions about the initial level of government debt, labor’s share, the elasticity of substitution in the aggregate production function, the interest rate on government debt, or the level of taxes on labor at which the model is calibrated. Results are somewhat sensitive, however, to the values of t_k and t_b, primarily because the assumptions of constant capital and given debt make taxes on capital and debt lump-sum taxes in the model. Computed limits are obviously sensitive to assumed labor supply elasticities, and presumably would also be sensitive to assumptions that would be made if the analysis were broadened to treat capital and debt as endogenous (see appendix A for a brief analysis).

5.3 Comparing Observed Fiscal Sizes of Government in OECD Countries to Theoretical Limits

We make two adjustments to the accounting definition of transfers used by the OECD in order to increase the comparability of our theoretical peak levels with the observed data. First, we add tax expenditures, that is subsidies given through tax exclusions, deductions, and credits. Whereas a cash transfer is a payment from government, a tax expenditure is a reduction in payments to government. Second, we subtract indirect taxes paid by recipients of cash or equivalent transfers. Taken together, these two adjustments greatly improve the consistency of the raw data with our definition of transfers, namely that transfers are net claims to private goods that result directly from government fiscal decisions about budgeted spending and its funding.

To put the first adjustment into perspective, consider two countries that are identical except that the government in country A provides cash payments to a group or activity and records this as an expenditure on its budget, while the government in country A¢ provides the same size of subsidy to the same group or activity in the form of tax expenditure which shows up on budget as a reduction in tax revenue. The two governments use different accounting practices but provide households with the same net claims to private goods or transfers. One way to account for this discrepancy is to count tax expenditures as transfers.

The traditional approach to measuring tax expenditures is to list a set of exclusions, deductions, and credits; calculate the values of each of these for each taxpayer at the taxpayer’s own marginal rate; and sum to obtain total tax expenditures (see e.g., Surrey and McDaniel [1985]). Forming the list of exclusions, deductions, and credits in turn requires a large number of decisions about how to treat each aspect of the tax code. The approach we develop avoids this difficulty. We recover inclusive measures of tax expenditures as well as government spending, transfers, and tax revenue from data on marginal tax rates and other variables using a form of the government budget constraint written in terms of marginal tax rates that are taken to be constants, as in linear-tax models and as is implicit in traditional calculations of tax expenditures.

The second adjustment is useful because transfers paid in cash or the equivalent are typically subject to indirect taxes such as sales and value-added taxes, so transfers recorded on official budgets - that is the gross amounts paid to governments - overstate the net claims to private goods provided by government. Netting out indirect taxes from calculated transfers better reflects the actual benefits conferred.

Implementing these adjustments empirically is a complicated matter. We put them into practice and describe some important features in what follows.

We begin by assuming that each national economy can be characterized to contain an aggregate or representative household. This assumption greatly reduces data requirements but is not required generally for the approach. In appendix B, we show how the approach can be generalized to calculate tax expenditures, transfers, spending, and revenue from data on a large number of households in an economy, each of which faces its own marginal tax rates. The appendix also contains a numerical example showing that calculations based on disaggregate data could yield results essentially similar to results based on aggregate data.

Because tax revenue R º t_lwl + t_krk + t_br b, and because we wish to distinguish R from tax revenue as measured on official budgets (R⁰), we refer to R as full tax revenue. We establish below that S and T are also inclusive measures, including tax expenditures as well as on-budget spending, so these might similarly be termed full government spending and full transfers. For brevity, however, we suppress "full" in referring to S and T.

Because it is useful to distinguish between transfers that are not subject to indirect taxes (t_i), in-kind transfers (T_#), and transfers that are subject to indirect taxes, cash transfers or the equivalent (T_$), we break transfer into two components, where T º T_# + (1-t_i) T_$. We refer to transfers that are subject to indirect taxes as pecuniary transfers.

We use (1') to measure S, T, and R over time in OECD countries. Specifically, we use data on t_l, wl, t_k, rk, t_b, and r b for a given year and country to find the value of R, and then add N, F, and D b to find the value of S. Thereafter we subtract G and r b to find the value of T. We also break transfers into in-kind and pecuniary components by solving T º T_# + (1-t_i) T_$ for T_$ and inserting data on T_# and t_i to find the value of T_$.

A central property of this approach is that transfers include tax expenditures; specifically, pecuniary transfers equal on-budget cash transfers plus tax expenditures. To see this, let x_l, x_k, and x_b denote income excluded from labor-income, capital-income and debt-interest taxation, let d_l, d_k, and d_b denote deductions permitted against labor income, capital income, and debt-interest income, and let c denote total tax credits. Then on-budget tax revenue is

(6)

Similarly, on-budget transfers consist of in-kind transfers plus cash transfers (denoted T_$$), and equal total on-budget sources of funds (R⁰ + N + F + D b) less on-budget spending on public goods and interest (G + r b), or

(7)

Finally, tax expenditures (E) are the loss in revenue from all exclusions, deductions, and credits. The exclusion of one currency unit of income that otherwise would be taxed at rate t results in a loss of revenue of t currency units. A deduction of one currency unit similarly results in a revenue loss of t currency units. A tax credit of one currency unit, on the other hand, costs the government one currency unit in revenue. Thus tax expenditures are

(8)

An immediate consequence of the definition of full tax revenue, (6) and (8) is that tax expenditures are the difference between full tax revenue and on-budget tax revenue, with an adjustment because on-budget tax revenue includes revenue from taxation of pecuniary transfers but full tax revenue does not:

(9)

Note that t_iT_$ is netted from gross transfers of T_# + T_$ on the spending side of the government budget (1) and hence is not included in full tax revenue on the sources-of-funds side. Below, we

report values of tax expenditures calculated using (9). Instead of beginning with an explicit list of all tax preferences, these calculations start with full tax revenue and recover tax expenditures indirectly as a revenue difference.

From (1), (7), and (9):

(10)

This "transfer identity" says that gross transfers, T_# + T_$ = T + t_iT_$, are identically equal to on-budget transfers plus tax expenditures. The transfer identity, (10), and the definition T = T_# +

(1- t_i)T_$ then imply that

(11)

which establishes that pecuniary transfers equal cash transfers plus tax expenditures.

It should be clear that E is a broad notion that captures the values of all reasons why on-budget tax revenue is less than full tax revenue plus revenue from indirect taxation of pecuniary transfers, including all explicit and implicit exclusions, deductions, and tax credits. The inclusive

treatments of tax expenditures and transfers parallel the inclusive notion of full tax revenue.

A feature of tax expenditures calculated using (9) is that our tax expenditures have a progressive nature. Because the approach here treats the marginal tax rates t_l, t_k, and t_b as constants, any progressivity in the rate structures of actual tax systems shows up not in t_l, t_k, and t_b but rather as exclusions, deductions, and credits. Specifically, a progressive rate structure means that some infra-marginal labor income is taxed at rates below t_l. A household is better off if infra-marginal income is taxed at rates below t_l than if that income is taxed at rate t_l. Under the approach here, the household is viewed as taxed at t_l on each unit of labor income, and government is then viewed as providing a lump-sum transfer to the household equal to the benefit of lower rates on infra-marginal income. The resulting progressivity tax expenditure reflects the net claims to private goods that government provides by applying lower tax rates at lower income levels.

Because we treat each economy as containing an aggregate household, progressivity tax expenditures reported below are the sums of both positive and negative components. Thus, the aggregate household in a country represents the household sector in the country, so the marginal tax rates t_l, t_k, and t_b are measured below as the rates that apply to an "average" household in the country. In actual economies with progressive rate structures, this means not only that some income is taxed at rates below t_l, t_k, and t_b, but also that some higher-income households face marginal rates above t_l, t_k, and t_b. Income taxed at rates below t_l, t_k, and t_b results in positive progressivity tax expenditures, whereas income taxed at rates above t_l, t_k, and t_b results in negative progressivity tax expenditures. That is, households with income taxed at rates greater than t_l, t_k, and t_b are viewed as paying lump-sum transfers to government, and such payments reduce the calculated value of E. An implication is that, under the aggregate-household assumption, the progressivity tax expenditure could in principle be negative; this could occur in a tax system with marginal tax rates that are relatively constant up to the income at which rates t_l, t_k, and t_b apply, and strongly progressive at higher incomes.

Although aggregate tax expenditures calculated below using (9) can be larger or smaller than tax expenditures calculated using the traditional "list-and-sum" approach, there are two reasons why (6) might give larger numbers. First, traditional data generally exist for national governments only, and miss tax expenditures by subnational governments. Second, the list of exclusions, deductions, and credits underlying the traditional approach may not be inclusive. For example, traditional calculations typically do not include a progressive tax expenditure. Another example is that the approach here counts as tax expenditures the tax savings to households that arise because personal income taxes are eliminated or postponed when corporations retain capital income.

A potential downside of including tax expenditures as transfers, however, is that it can distort cross-country comparisons of government size. For instance, a country that has high marginal tax rates but generous tax credits will appear to have a larger government than an otherwise identical country that has lower marginal tax rates but tax credits just low enough that the households in the two countries are equally well off. Nevertheless, this is not necessarily a weakness. There is, indeed, clearly greater government involvement in the first country despite an equal net result.

A description of data used to implement the approach is given in appendix C.

Table 2 reports summary statistics for fiscal sizes as percentages of GNP for the 22 countries in the sample averaged across the years 1972-1992. Spending, transfers, and full tax revenue varied by a factor of about two, where the U.S. had the smallest and Sweden the largest values during the period. A clear geographical pattern is that countries with relatively greater fiscal sizes of government lie in northern and, to a lesser extent, central Europe, home to, for instance, all countries with spending above 56 percent of GNP, transfers above 47 percent of GNP, or full tax revenue above 54 percent of GNP except Italy and Canada.

The difference between our measure and measures reported in official budgets is substantial. Formally, we measure government spending as S = T + G + r b, whereas government spending measured on official budgets is S⁰ º T⁰ + G +r b. From the definition T = T_# + (1- t_i)T_$, (7), and (11), the difference is

(12)