The Effect of Tax-Based Savings 

Incentives on the Self-Employed 

by 

Laura Power * and Mark Rider**

*U.S. Treasury Dept. and **Kennesaw State Univ.

OTA Paper 84 July 1999

OTA Papers is an occasional series of reports on the research, models, and data sets developed to 

inform and improve Treasury’s tax policy analysis. The papers are works in progress and subject 

to revision. Views and opinions expressed are those of the authors and do not necessarily 

represent official Treasury positions or policy. OTA papers are distributed to document OTA 

analytic methods and data and to invite discussions and suggestions for revision and improvement. 

Comments are welcome and should be directed to the authors. 

Office of Tax Analysis

U.S. Department of the Treasury

Washington, D.C. 20220

We would like to thank Jim Cilke, William Gentry, Doug Holtz-Eakin, Luc Noiset, Karl Scholz, 

Mary Beth Walker, Steve Woodbury and members of the ASSA individual taxation session for 

helpful comments. Thanks also to Bob Gillette for help constructing the data set. The views 

expressed in this paper are solely those of the authors and, in particular, do not represent those of 

the U.S. Department of the Treasury. 

please direct correspondence to Laura Power, ph (202) 622-0238, fax (202) 622-0236, 

laura.power@do.treas.gov. 
Abstract 

The U.S. individual income tax allows employers to make tax-preferred contributions to qualified 

pension plans for their employees and, in the case of the self-employed, on their own-behalf. We 

examine the effect of this tax preference on the self-employed’s preferred compensation mix 

between taxable income and tax-preferred savings. We use a panel of sole proprietors constructed 

from the Statistics of Income individual income tax files for tax years 1985, 1989 and 1993. We 

find that taxes have a substantial effect on the preferred compensation mix of the self-employed. 

This finding is surprisingly robust to a number of alternative specifications. The study has several 

advantages over previous studies. For example, by focusing on the self-employed there is less 

ambiguity about whose utility is being maximized. 
1. Introduction 

There is growing concern among policy-makers about the ability of the U.S. pension 

system to meet the demands that the impending retirement of the baby-boom population will place 

on it. To help ensure that Americans have adequate retirement savings the U.S. federal income tax 

allows employers to make tax-preferred contributions to qualified pension plans for their 

employees and, in the case of the self-employed, on their own-behalf. By lowering the after-tax 

price of retirement savings with respect to taxable compensation, this tax preference encourages 

employees, including the self-employed, to accept a greater share of total compensation in the 

form of pension savings.1 

In this study we attempt to gauge the effect of this tax preference on the self-employed’s 

contributions to qualified retirement plans. Following Woodbury and Hamermesh (1992), we 

estimate a regression equation derived from individual utility maximization. We estimate this 

equation using data obtained from a sample of federal income tax returns spanning three major tax 

reforms in 1986, 1990 and 1993. We find that taxes have a substantial effect on the selfemployed’s preferred compensation mix. Furthermore, this result is surprisingly robust to a 

number of alternative specifications. 

1

Since compensation in the form of contributions to tax-preferred savings plans are not 

taxable, the net-of-tax price of a one dollar contribution, relative to ordinary taxable wage income 

is (1-t), where t is the marginal tax rate on ordinary income. An increase in the tax rate, holding all 

other things constant, decreases the price of contributions relative to ordinary income. The 

resulting change in relative prices encourages individuals to accept a higher share of compensation 

in the form of tax preferred savings. The income effect from the tax rate increase discourages 

making such contributions. In other words, there are two offsetting effects from a change in the 

tax rate. The evidence suggests that the substitution effect dominates the income effect in which 

case the ordinary price effect is negative. In our discussion below, we assume the price effect is 

negative, however, the reader should be aware that the price effect could be positive or negative 

depending upon which effect is greater. 
There are a number of advantages to focusing on the self-employed in this context. First, 

there are about 10.5 million sole proprietors in the U.S., however, little is known about the effect 

of tax-based savings incentives on them.2 Focusing on the self-employed may also provide a 

useful way to gauge the general efficacy of tax-based savings incentives. Since self-employment 

presumably offers greater autonomy in decision-making and higher than average income, the selfemployed may have a greater ability to achieve their preferred compensation mix than the typical 

salaried employee.3

 Hence their behavioral response may provide an upper bound estimate of the 

potential effect of tax incentives on retirement savings. Furthermore, by comparing estimated 

elasticities obtained from our sample of sole proprietors with and without employees, we may be 

able to gauge the effect of non-discrimination rules. Non-discrimination rules are designed to 

ensure that the employer does not treat themselves or their highly compensated employees more 

generously than their rank and file employees. 

In addition, individual tax data have distinct advantages over those used in previous 

studies. Previous studies, of which Woodbury and Hamermesh (1992) is an excellent example, by 

necessity rely upon establishment level data to measure the effect of taxes on the preferred mix of 

compensation. These data require assumptions about the collective choice process and the 

appropriate measures of certain variables, particularly the tax-price and income. In the case of the 

self-employed, however, there is less ambiguity about whose utility is being maximized and, as a 

2

 See the Statistical Abstract of the United States, 1998. 

3

1996 Statistics of Income tax return data indicate that the average income of the self 

employed (where the self employed are defined to be those taxpayers who file a self employment 

tax schedule [Schedule SE] with their 1040), was $61,534, while the average income of the rest 

of the population was $34,753. 

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result, the appropriate income and marginal tax rate measures to employ. Furthermore, tax data 

include information on other important sources of income, particularly income from capital, that 

are not typically available in conventional data sets. Thus tax data allow us to precisely calculate 

the individual’s marginal tax rate using detailed tax calculators as well as after-tax income. Finally, 

these data straddle several major tax reforms which provide the necessary exogenous variation in 

the after-tax price of contributions to qualified retirement plans. 

The paper proceeds as follows. In Section 2, we provide a brief description of the federal 

income tax treatment of retirement savings by the self-employed and the tax law changes during 

the sample period. In Section 3, we describe the econometric model, the data and the construction 

of the variables used in our analysis. We discuss our empirical results in Section 4 and Section 5 

concludes with a summary of our results. 

2. Background 

In this section, we briefly review the literature on tax-based savings incentives. Then, we 

review the laws and institutions governing contributions to tax-preferred savings plans by the selfemployed. Then we summarize relevant aspects of the three major tax bills enacted during the 

period spanned by our data. We conclude this section with a discussion of recent trends in taxpreferred pension savings. 

A Brief Review of the Literature 

There is a rather extensive literature on tax-based savings incentives. This literature 

addresses three issues: (1) the net effect of tax-based savings incentives on private and national 

savings; (2) the substitutability of assets in tax-based savings plans and ordinary savings; and (3) 

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the effect of these incentives on government revenue. Based upon their review of this literature, 

Engen, Gale and Scholz (1996) conclude that tax-based savings incentives have not had a 

substantial effect on private or national savings. They reach this conclusion, at least in part, 

because the evidence indicates that people perceive IRA’s and other tax-preferred plans as good 

substitutes for ordinary savings. Hence, they conclude that contributions to tax-preferred savings 

plans are less likely to be new savings. Finally, the evidence is mixed on the government revenue 

effect of tax-based savings incentives. The effect depends upon whether tax-based savings 

incentives induce sufficient new savings, and investment, to grow the economy by an amount 

sufficient to make up the lost revenue from providing the incentives. 

A related literature [Long and Scott, 1982; Woodbury and Bettinger, 1990; Woodbury 

and Hamermesh, 1992; and Barth, Cordes and Friedland, 1985] tries to account for historical 

trends in fringe benefits as a share of total compensation. Employer contributions to employee 

pensions comprise a large proportion of fringe benefits. Although our study may be relevant to 

issues (2) and (3) above, our empirical strategy has more in common with the approach taken in 

the fringe benefits literature. 

In the post-war period fringe benefits were a growing share of total compensation. The 

growth in benefits is attributed to rising incomes, changing tax laws, unions, scale economies and 

other sources.4

 In the 1980's, however, this trend was reversed and fringe benefits as a share of 

total compensation began to decline. In a seminal study, Woodbury and Hamermesh (1992) 

estimate an almost ideal demand (AID) equation for the share of benefits in total compensation 

using establishment level data on faculty salaries. Their data exploit the natural experiment 

4

 Woodbury and Hamermesh (1992) provide a review of this literature. 

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provided by TRA ‘86 to estimate the effects of taxes on the preferred compensation mix. They 

find that taxes have a substantial effect on the form of compensation. Based on their analysis of 

faculty salaries, they conclude that the positive effect on fringe benefits of rising incomes in the 

1980's was offset by the negative effect of the increase in the after-tax relative price due to 

declining marginal tax rates.5 

As previously noted, however, estimates obtained with establishment level data are 

vulnerable to criticism for three reasons. First, they require an assumption about the collective 

choice mechanism. This assumption raises uncertainty about the appropriate measures of income 

and the tax rate. Second, such data often lack information on non-wage income, particularly from 

interest, dividends and capital gains. Third, they may lack the necessary information on other 

income, filing status, number of dependents, and itemized deductions to precisely estimate 

effective marginal tax rates. 

Tax-Preferred Pension Plans 

In general, there are two types of retirement plans for the self-employed, Keogh plans and 

Simplified Employee Pension Plans (SEP’s). Like traditional employer provided plans, Keogh 

plans can be structured as either defined benefit plans (DB) or defined contribution plans (DC). 

SEP's are generally considered DC plans. DB plans specify the yearly benefit level which the 

participant will receive upon retirement. Subject to certain limitations, the employer then 

5

 Other potential explanations for the decline of fringe benefit coverage in the 1980's are 

the increasing proportion of females and minorities in the labor force, the decline of unionization 

and the shift of employment to the Sunbelt. See, for example, Woodbury and Bettinger (1990) for 

a discussion of the decline in fringe benefit coverage in the 1980's. 

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contributes the amount necessary to achieve that level of benefit.6

 A DC plan can be either a profit 

sharing plan or money purchase plan. In either case, the employer contributes a limited percentage 

of the employee’s compensation, up to a fixed dollar amount. The cumulative stock of money in 

the plan is then available to the participant upon retirement.7

 The self-employed taxpayer is 

treated as an employee of himself for purposes of the plan. The self-employed can have more than 

one type of plan; however, contributions to all plans cannot exceed the overall limitations. 

Tax Legislation Enacted from 1985 through 1993 

During the period spanned by our sample (1985-1993), the laws governing retirement 

plans for the self-employed and the contribution incentives facing the self-employed changed 

several times and in opposite directions. 

The Tax Reform Act of 1986 (TRA ‘86) decreased the top marginal tax rate from 50 

percent to 33 percent. This rate reduction significantly increased the price of tax-preferred 

pension plans. It also tightened the IRA eligibility rules. Furthermore, TRA ‘86 also established 

and tightened a host of non-discrimination rules which are designed to ensure that employers, 

including the self-employed, do not treat themselves or their highly compensated employees more 

favorably than rank and file employees. Non-discrimination rules include a variety of specified 

6

 In 1985, the employer was limited to contribute the lessor of $90,000 or 100 percent of 

the employee’s total compensation. The maximum contribution cap is indexed. 

7

 Individuals, and sole proprietors, are also subject to various federal “penalty” excise 

taxes which apply to qualified retirement plans, including a 10 percent tax on early distributions, 

and a 50 percent tax on excess accumulations in qualified retirement plans. During the period 

under study, they were also subject to a 15 percent tax on excess distributions from qualified 

retirement plans to an individual during the calendar year. However, this tax was repealed in the 

Tax Reform Act of 1997. See Shoven and Wise (1996) for an interesting discussion of how these 

“penalty” excise taxes interact with the federal income and estate and gift taxes and the behavioral 

consequences thereof. 

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tests (e.g., ratio percentage test, average benefit test and percentage coverage test) which must be 

applied when determining qualification for, and coverage under, a qualified retirement savings 

plan. In an attempt to level the playing field, TRA ‘86 established a cap of $200,000 on the 

amount of compensation which can be considered in determining benefit amounts; an excise 

penalty of 10 percent on excess contributions; and limits on allowable IRA contributions for 

taxpayers participating in qualified retirement plans. 

The Omnibus Budget Reconciliation Act of 1990 (OBRA ‘90) increased the marginal tax 

rate on ordinary income from 28 percent to 31 percent for taxpayers with taxable incomes over 

$100,000 or $190,000, depending upon their filing status. In addition, the 33 percent rate, or 

“bubble,” was eliminated for taxpayers with taxable incomes between $60,000 and $190,000, 

depending upon their filing status.8

 However, it created two new bubbles due to the phase-out of 

personal exemptions and itemized deductions. 

The Omnibus Budget Reconciliation Act of 1993 (OBRA ‘93) imposed a 36 percent rate 

on taxable incomes over $70,000 or $150,000, depending upon filing status. In addition, OBRA 

‘93 imposed a 10 percent surtax on individuals with taxable incomes in excess of $250,000 and 

raised the taxable maximum for hospital insurance contributions to infinity. In summary, TRA’86 

increased the tax-price of pension contributions for high income individuals; OBRA’90 decreased 

8

 OBRA ‘90 also increased the “penalty” excise tax on employer reversions of qualified 

plan assets to employers from 15 percent to 20 percent, or 50 percent if the employer does not 

maintain or establish a qualified replacement plan. This Act also increased the flat-rate perparticipant premium from $16 to $19, payable with respect to each single-employer defined 

benefit retirement plan covered under title IV of the Employee Retirement Income Security Act 

(ERISA). 

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the tax-price for some and increased it for others; and OBRA’93 decreased the tax- price for high 

income individuals. 

Trends in Pension Savings 

In addition to national trends, Table 1 provides information on the share of tax-preferred 

pension contributions in after-tax compensation for our sample of sole proprietors measured in 

three different ways. Column 2 shows the share based on Keogh contributions; column 3 shows 

the share based on the Keogh Contribution and the Self Employment Tax (SECA) contribution; 

and column 4 shows the share based on Keogh, SECA and own and spouse's IRA contributions. 

All four series exhibit the same pattern. In 1989 the share of contributions is less than that 

observed in 1985, while the share in 1993 is greater than in 1989. 

The down-then-up pattern in Table 1 is consist with changes in the price of contributions 

due to enacted tax legislation during this period. After a tax hike (cut) the price of tax-preferred 

savings decreases (increases). Therefore, everything else held constant, the individual should 

prefer a greater (smaller) share of total compensation in the form of tax-preferred savings after a 

tax increase (decrease). Since TRA ‘86 decreased the top marginal rate, the price of contributions 

increased between 1985 and 1989, at least for high income individuals, and, as shown in Table 1, 

the share of contributions in total compensation decreased. And vice versa, between 1989 and 

1993 the price decreased as a result of tax rate increases due to OBRA ‘90 and ‘93 and the share 

increased. Although this pattern is suggestive, we turn to our multivariate analysis to shed further 

light on this issue. 

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3. The Estimation Strategy 

This section begins with a description of our econometric model. Then we proceed with a 

description of the data used to estimate the model and the construction of the variables. 

The Econometric Model 

The econometric specification is derived from individual utility maximization. The sole 

proprietor's utility is assumed to be a function of total after-tax business income, which includes 

taxable income and tax-preferred contributions to qualified retirement plans. Thus the observed 

mix of taxable and tax-preferred income depends on the individual's relative costs of providing 

ordinary taxable income and tax-preferred retirement savings and certain individual 

characteristics, including preferences and income. 

Following Woodbury and Hamermesh (1992), this optimization problem gives rise to a 

system of share equations which define demand for income and retirement savings as follows: 

Sit ' !it % #i ln[Ct /Pt] % 'i ln[pit /pjt] % AiXt % uit 

where the i and j index the types of compensation (income and retirement savings in our context); 

t indexes the year (t = 1985, 1989 and 1993); Si

 is the ith form of compensation in net (after-tax) 

compensation, C; and pi is the price of the ith form of compensation. The price index P is 

approximated by ln[Pt ] . 3 i Si ln[pi ]. The vector X includes age, age-squared, marital status, 

number of dependents, industry and year.9 These are included to help control for heterogenous 

9 We would like to be able to control for the age of the business because new 

entrepreneurs may prefer to invest a higher share of earnings in their new enterprise to “get the 

business going.” Since we do not have information on the age of business, we hope that the 

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tastes as well as potential life-cycle and business cycle effects. Finally, we assume uit is a normally 

distributed error term.10 

Two potential problems arise when estimating this specification. First, if there is 

unobserved heterogeneity in the choice of compensation mix across individuals, there may be 

serial correlation in the error term as well as correlation between the error term and the 

independent variables. As a result, the parameter estimates may be biased. In order to remove any 

unobserved individual fixed effect in the rate of pension contributions, we estimate the model in 

first differences. Specifically, we estimate 

)Sit ' !i % #i )ln[Ct /Pt] % 'i )ln[pit /pjt] % AiXt % )uit 

where ) indicates the first difference of the succeeding variable. 

Second, an increase in tax-preferred savings reduces taxable income which may, in turn, 

effect the price of tax preferred savings. Consequently, the tax price may be endogenous (see, for 

example, Feenberg, 1987) which could bias the estimates. In order to account for the potential 

endogeneity of the tax price and compensation, we estimate the model using Two Stage Least 

Squares (TSLS). In order to estimate TSLS, however, it is necessary to have an instrument for 

proprietor’s age serves as a partial control, albeit imperfect. 

10 This model adapts Deaton and Muellbauer's (1980) almost ideal demand system to the 

decision problem of the self-employed individual. This system of equations is derived directly 

from the theory of utility maximization, but the generality of the associated expenditure function 

allows substantial flexibility in the functional form of the estimating equation. Finally, the system 

can be estimated using Ordinary Least Squares (OLS) and the parameters of the income and price 

variables can be transformed to provide income and price elasticities, respectively. 

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the potentially endogenous variable. A valid instrument must be correlated with the potentially 

endogenous variable and uncorrelated with the error term. 

We construct an instrumental variable for the tax price that takes advantage of the most 

prominent feature of our data: the exogenous change in tax rates due to tax legislation enacted 

during this period.11 First, we compute each individual’s tax price in 1989 (1993) using the data 

and tax law for 1989 (1993). Next we compute each individual’s marginal tax rate using the data 

for 1985 (1989), inflated to 1989 (1993) levels, but employing the tax law for 1989 (1993). 

Clearly, the change between the 1985 (1989) and 1989 (1993) tax rates computed in this fashion 

is due entirely to modifications in the tax code. Essentially, this procedure removes the 

endogenous component of tax rate movements from )ln(TAXPRICE), leaving only the part due 

to the exogenous change in the tax law associated with TRA ‘86, OBRA ‘90 and OBRA ‘93. 

Furthermore, since tax-based savings incentives permit the self-employed to achieve a 

given level of after-tax income with a lower amount of total net-business income, income may be 

endogenous too. Therefore, we use after-tax capital income as our measure of income. For this 

purpose capital income is defined as the sum of taxable and tax exempt interest, dividends, net 

long-term capital gains and net S-Corporation and rental income. We calculate the tax liability 

attributable to capital income by taking the product of total tax liability and the proportion of 

taxable capital income in total taxable income. The construction of these instruments is discussed 

11 Several studies on the behavioral effects of individual income taxes have used the Tax 

Reform Act of 1986 to identify the tax-price. See, for example, Woodbury and Hamermesh 

(1992), Feldstein (1993), Auten and Carroll (1995), Eissa (1995) and Carroll et al. (1996). See 

Feenberg (1987) for a discussion of the issues involved in the identification of tax price models. 

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in greater detail in Appendix I. Prior to estimating the regressions with instrumental variables, 

however, we implement a Hausman-Wu test to assess whether endogeneity is indeed a problem.12 

Construction of the Sample and the Variables 

Our sample consists of data from the Statistics of Income (SOI) individual tax files for 

1985, 1989 and 1993. The resulting panel consists of 15,468 returns of individual filers who 

report non-zero Schedule C business income in all three years.13 The data contain detailed 

information on a taxpayer’s income and deductions, as reported on IRS Form 1040 and many of 

the associated schedules. We use this information to construct the variables used in this analysis, 

in particular the share of tax-preferred retirement savings in total after tax compensation 

)[SHAREt

]; the change in the log of real income )[ln(INCOMEt) ]; and the change in the log of 

the relative price of tax-preferred savings )[ln(TAXPRICEt)]. 

Following Woodbury and Hamermesh (1992), we construct two versions of the dependent 

variable; one treatment assumes SECA is a tax and the other an actuarially fair benefit. In the 

SECA-as-a-benefit treatment the numerator of SHAREt

 includes contributions to Keogh, SEP, 

and own and spousal IRA’s as well as Social Security contributions. The denominator is the sum 

of earned income (i.e., wages, sole proprietorship income, farm income and partnership income) 

12 See Wu (1973). 

13 We should point out two caveats which should be kept in mind when intrepreting the 

results. First, some aspects of the Statistics of Income sampling criteria (e.g., higher income 

individuals are sampled with greater probability), as well as our own restrictions (e.g., taxpayers 

must have positive business income in all three years) might imply that our results cannot be 

generalized to the self employed population as a whole. Second, that despite the benefits of panel 

estimation, there are some inherent problems with panels based on SOI data. For example, the 

young and high income taxpayers have a higher probability of being sampled in consecutive 

periods. Furthermore, it is difficult to interpret changes in income, deductions and tax rates for 

those getting married or divorced during the period spanned by the panel. 

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and the employer’s Social Security contribution for wages less the tax attributable to earned 

income. In contrast, the SECA-as-a-tax treatment does not include Social Security contributions 

in the numerator, and the denominator is reduced by Social Security contributions. We compute 

last dollar marginal tax rates using detailed tax calculators that include the tax rate schedule and 

the many implicit rates induced by the phase-outs of certain deductions and credits. Since 

contributions to tax-preferred savings plans by the self-employed are not deductible for purposes 

of calculating the SECA tax, the marginal tax rates are identical in both treatments. 

There are a number of sample exclusions which also should be noted. First, the structure 

of )[SHARE] and )ln(INCOME) require that we exclude 4,778 observations with incomes less 

than or equal to zero. Second, we exclude 1,292 returns subject to the alternative minimum tax 

(AMT),14 Third, we exclude 122 returns with anomalous observations of SHARE; those less than 

zero or greater than one. Finally, we exclude 229 returns in which the primary filer is over 71 

because they are required by law to begin making withdrawals. The resulting sample consists of 

9,047 returns. 

Table 2 reports the means and standard deviations for two samples: SECA as a tax 

(column 1) and SECA as a benefit (column 2). Note there is a difference in the number of 

observations between the two treatments of SECA. The denominator of SECA as a tax is reduced 

14 The alternative minimum tax (AMT) is a parallel tax which some taxpayers are subject 

to for a variety of reasons. The AMT essentially has its own tax base and tax rate schedule. 

Although the tax calculators for each individual year can capture the impact of the AMT on the 

tax price for fringe benefits, it is not clear how to accurately construct a tax-price instrument for 

the subset of taxpayers who switch on and off the AMT (i.e., those who are subject to the AMT 

in some years but not in others). Thus, we exclude AMT taxpayers from our sample. However, 

we re-estimated our canonical specifications using our sample augmented by observations which 

are subject to the AMT in every year. In other words, we only eliminate observations that switch 

on and off the AMT. Our basic results are unchanged. 

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relative to the value for SECA as a benefit by employer and employee contributions to FICA and 

SECA (see Appendix I). Further, the numerator is reduced by both FICA and SECA 

contributions. As a result 3,582 additional returns are excluded because the share variable is nonpositive. The resulting sample consists of 5,465 returns. 

Examining Table 2, we see that the average age in the SECA-as-a-tax sample is 

approximately 47 years old; 90 percent are married; and the average number of dependents is 

approximately 1.23. In contrast, the SECA-as-a-benefit sample is, on average, slightly younger; 

they are slightly less likely to be married; and have, on average, fewer dependents. Likewise the 

distributions by principle business activity is generally the same in both samples. Although the 

first-differences of share, the log of real income and the log of the tax-price are difficult to 

interpret, they are provided in Table 2 for the reader’s convenience. Again, in the SECA-as-abenefit sample the mean values of these three variables are somewhat lower than in the SECA-asa-tax sample. 

4. The Empirical Results 

We focus on the model estimated in first differences because we believe that it has a 

number of attractive features. As previously noted, estimating the model in first-differences 

removes the mean value of each variable between any two years which helps to eliminate potential 

bias from unobserved heterogeneity. First differences also permits us to construct a suitable 

instrument for the potentially endogenous tax-price. 

Table 3 provides the OLS and TSLS coefficients and associated standard errors for both 

treatments of SECA. We begin by discussing the OLS estimates treating SECA as a tax which are 

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reported in column 1 of Table 3. Focusing on the economic variables, the income and tax price 

have the expected signs and are statistically significant. More specifically, the estimated coefficient 

for )ln(INCOME) is equal to 0.002 with a standard error equal to 0.38*10-3. The estimate for 

)ln(TAXPRICE) is equal to -0.012 (S.E. = 0.009). Turning to the taste variables, the number of 

dependents and marital status have a negative and statistically significant effect, while age is 

positive and statistically significant. The estimated coefficient on age-squared is negative and 

statistically significant, indicating that the effect of age is non-linear. Finally, the year dummy 

variable is negative and statistically significant, while the industry dummy variables are statistically 

insignificant. 

The OLS estimates treating SECA as a benefit, which are reported in column 3, are rather 

disappointing, in particular, most of the estimated coefficients are statistically insignificant. But, as 

previously noted, )ln(INCOME) and )ln(TAXPRICE) are potentially endogenous. In order to 

check for endogeneity we implement a Hausman-Wu test. In both equations the joint test rejects 

exogeneity of )ln(INCOME) and )ln(TAXPRICE) at the 1 percent level. Specifically, the chisquare statistic is equal to 110.32 for the specification treating SECA as a tax and 326.12 treating 

SECA as a benefit. Consequently, we re-estimate both equations using TSLS. 

Column 2 of Table 3 reports the TSLS estimates, treating SECA as a tax. As before, the 

estimated coefficient for )ln(INCOME) is positive and statistically significant. In fact, the 

magnitude of the estimate is virtually unchanged compared to its OLS counterpart. Similarly, the 

estimated coefficient for )ln(TAXPRICE) is negative and statistically significant, but more than 

twice its OLS counterpart in absolute value. In contrast to their OLS counterparts, the TSLS 

estimates treating SECA as a benefit, reported in column 4, have the expected signs and are 

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statistically significant. More specifically, the estimated coefficients for )ln(INCOME) and 

)ln(TAXPRICE) are 0.001 (S.E.=0.26*10-3) and -0.061 (S.E.=0.008), respectively. Both 

equations exhibit similar patterns for the remaining variables as well. 

Now we examine the economic significance of our estimates. Accordingly, we transform 

the estimated regression coefficients reported in Table 3 into elasticities.15 These elasticities and 

their associated standard errors are reported in Table 4 for all four specifications. Since there is 

evidence of endogeneity of the tax-price and income, we believe the TSLS estimates are superior. 

Furthermore, in our opinion it is more likely that the self-employed perceive SECA to be a tax 

than a benefit. Therefore, we focus the discussion on the TSLS estimates obtained by treating 

SECA as a tax. Nevertheless, Table 4 provides the OLS and TSLS estimates treating SECA as a 

benefit. 

Examining the TSLS estimates treating SECA as a tax, which are reported in column 3, 

we see that the own-price elasticity of demand for tax-preferred compensation (0f,f) is equal to 

-1.454 (S.E.=0.272). This implies that a 1 percent increase in the price of contributions results in a 

1.454 percent decrease in tax-preferred compensation. The income elasticity of demand for taxpreferred compensation (0f,y) is 1.037 (S.E.=0.015). Similarly, the income elasticity of demand for 

taxable compensation (0w,y) is equal to 0.998 (S.E. = 0.4*10-3). Based on these estimates, a 1 

percent increase in income, for all practical purposes, leads to a 1 percent increase in each form of 

compensation. 

15 See Woodbury and Hamermesh (1992) for a description of the formulas used to 

compute the elasticities and associated standard errors. 

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The cross-price elasticity of demand for taxable income with respect to the price of 

contributions (0w,f) is equal to 0.028 (S.E. = 0.013). This suggests a 1 percent increase in the price 

of tax-preferred compensation results in a 0.028 percent increase in the demand for wage 

compensation. Finally, the marginal rate of substitution between these two forms of compensation 

(Fw,f) is equal to approximately 1.479 (S.E.=0.262). A value greater than one indicates that these 

two forms of compensation are easy substitutes. 

Alternative Specifications 

In order further to test the robustness of our results, we also tried a number of alternative 

specifications. First, TRA ‘86 tightened the rules on deductibility of contributions to IRA’s. To 

ensure that our elasticity estimates are not simply an artifact of the new IRA regime, we excluded 

IRA contributions from the numerator of share and re-estimated all four specifications. These 

estimates have the expected signs and are statistically significant. For example, treating SECA as 

a tax, the TSLS estimates of the marginal rate of substitution is equal to 2.61 (S.E. = 0.566); the 

own-price elasticity equals -2.487 (S.E. = 0.579); and both income elasticities are approximately 

equal to 1.0 and statistically significant. 

In an attempt to account for the fact that the tax-price of contributions should include any 

future taxes when distributions are taken, we re-calculate the tax price assuming that taxpayers 

discount the value of future distributions to their net-after-tax present value. This calculation 

requires assumptions about the age of retirement; the average annual rate of return on 

-19-
contributions; the discount rate; and the expected future marginal tax rate on distributions. We

find that these estimates have the expected sign and are statistically significant.16

Some Issues Related to the Sample

Before concluding, we should note some important issues related to our sample. First, in 

order to ensure that changes in marital status due to marriage or divorce are not substantially 

affecting the results, we re-estimate all four specification on the subsample of taxpayers who do 

not change filing status throughout the period. The resulting subsamples consist of 5,060 returns 

for SECA as a tax and 8,294 returns for SECA as a benefit. The magnitude of the results are 

essentially unchanged, although the standard errors of some of the estimated coefficients are 

larger, particularly in the SECA-as-a-tax regressions. 

Second, many of the returns in our sample receive wage income, thus we can not exclude 

the possibility that they or their spouse participate in an employer provided tax-preferred 

retirement plan Clearly, participation in such a plan could affect their willingness to establish and 

contribute to a Keogh or SEP plan. Estimating the model in first differences may help alleviate 

16 Clearly, these estimates require a number of rather heroic assumptions regarding the rate 

of return, discount rate, tax rate on distributions, etc. Also, alterations in these assumptions could 

obviously affect the estimates. For example, taxpayers that believe their future tax rates will be 

higher upon retirement than their current rate would contribute a lower rate than those one 

anticipate a lower rate. Furthermore, there is likely to be considerable unobserved variation 

among individuals in the appropriate rate of return, age of retirement, etc. In order to address 

these potential concerns, we also estimate a specification in which we simply interact the 

conventional change in the log of the tax-price with the age of the primary filer. Again, the 

estimated elasticities in all four specifications have the expected signs and are statistically 

significant. Finally, we also include state dummy variables in our canonical specifications reported 

in Table 3 to control for state taxes, different rates of unionism, etc. Our results are essentially 

unchanged. 

-20-
this concern. Nevertheless, the fact that many of the self-employed receive wage income is a 

source of legitimate concern. 

Thus, we re-estimate all four models on the subsample of 767 (1,473) returns, treating 

SECA as a tax (benefit), that do not report wage income on IRS Form 1040. The estimated 

elasticities are reported in rows 1 and 2 in the upper and lower panels of Table 5. For 

comparison’s sake, we also provide Woodbury and Hamermesh’s (1992) estimated elasticities in 

the column labeled W&H in the upper panel of Table 5. Examining the TSLS estimates treating 

SECA as a tax, which are reported in row 2 of the upper panel, we find that our basic results are 

unchanged. For example, both income elasticities are approximately equal to 1.0; the own-price 

elasticity of demand is negative and significant; and the marginal rate of substitution is greater 

than 1.0 and statistically significant. But, the substitution and own-price elasticity estimates are 

substantially larger than our previous estimates, specifically 3.569 (S.E. = 1.331) and -3.333 

(S.E.=0.528), respectively. 

Similarly, estimates treating SECA as a benefit obtained from the no-wage subsample, 

which are reported in row 2 of the lower panel, have the expected signs and are statistically 

significant. They are also larger than their Table 4 counterparts, however, the increase is not 

nearly as dramatic as in the SECA-as-a-tax case described above. 

A third issue with the full sample is that the self-employed may have employees. As 

previously noted, non-discrimination rules effectively require that an employer making 

contributions to a qualified plan on his own-behalf offer a comparable plan to his employees. Thus 

non-discrimination rules may influence the self-employed’s decision to establish and contribute to 

-21-
a Keogh or SEP plan. Furthermore, it raises the issue of collective choice and whose utility is 

being maximized. 

In order to address this concern, we re-estimate all four specifications on the subsample of 

3,608 (6,227) returns treating SECA as a tax (benefit) which do not report a wagebill deduction 

on their Schedule C. These estimates are reported in rows 3 and 4 of the upper and lower panels 

of Table 5. Again, focusing on the TSLS estimates treating SECA as a tax, which are reported in 

row 4 of the upper panel, we observe the same pattern. Now, however, the estimated elasticities 

are more in line with their Table 4 counterparts. For example, as before, both income elasticities 

are approximately equal to 1.0; the own-price elasticity of demand is approximately equal to -1.5; 

and the marginal rate of substitution is equal to about 1.5. The SECA-as-a-benefit estimates, 

reported in rows 4 and 5 of the lower panel, by and large exhibit the same patterns and 

magnitudes. 

Finally, we re-estimate all four specifications on the subsample of 386 (849) returns 

without wages or employees and report these results in rows 5 and 6 of Table 5. In short, these 

estimates have the expected signs and are statistically significant. But, the magnitudes are similar 

to those obtained in the no-wage subsample. For example, in row 6 of the upper panel, we see 

that the TSLS estimate of own-price elasticity treating SECA as a tax is equal to -3.207 

(S.E.=0.698) and 3.450 (S.E. = 1.471) for the elasticity of substitution. 

Some comments follow from the results reported in Table 5. First, given that the selfemployed, particularly those without employees and therefore not subject to non-discrimination 

rules, have greater autonomy in their decision making, one would expect that the self-employed 

could more readily adjust their compensation mix in response to changing tax incentives than the 

-22-
typical institution with many employees. For this and other reasons, it is interesting to compare 

our estimates with those obtained with establishment level data. 

Thus, comparing our TSLS estimates treating SECA-as-a-tax obtained from the no-wage 

and no-employee sub-sample with those obtained by Woodbury and Hamermesh (1992), we find 

that our estimates of the marginal rate of substitution, the own-price elasticity of tax-preferred 

compensation, and income elasticity of demand for taxable compensation are somewhat larger, in 

absolute value, than theirs. These higher estimates support the notion that the greater autonomy 

enjoyed by the self-employed provides them with more flexibility in adjusting their compensation 

to changing tax incentives. 

One must be cautious, however, not to over interpret such results. In particular, with the 

exception of the above mentioned elasticities, our estimated elasticities are generally lower than 

theirs. Most notably, their income elasticity for tax-preferred compensation is more than double 

ours. When we exclude observations with wages, however, this pattern is largely reversed. Thus, 

rigid comparison of the two sets of estimates is complicated, since our estimates vary somewhat 

among our sub-samples. Further, Woodbury and Hamermesh’s (1982) estimates may be subject 

to measurement error in the independent variables, particularly the price and income variables, for 

the reasons previously noted. Finally, it should be noted that Woodbury and Hamermesh (1982) 

include contributions to health insurance in their measure of tax-preferred compensation, while we 

do not.17 

17 Since contributions to health insurance do not appear to be as readily substitutable for 

wage income as pension contributions, some differences in our estimates may be understated. See 

Woodbury and Huang (1991) for further discussion of the substitutability of health insurance, 

wages, and pension contributions. 

-23-
Overall, the two sets of estimates are fairly similar. In our opinion, this lends support to 

Woodbury and Hamermesh’s conclusion that a substantial amount of the decline in the share of 

fringe benefits in total compensation in the 1980's is attributable to the Reagan era tax cuts. 

It also interesting to compare the TSLS estimates from the no-wage sample with those 

from the no-wage and no-employees sample. Any difference in the estimates between these two 

samples could be attributable to the effect of non-discrimination rules. In other words, sole 

proprietors with employees, and therefore subject to non-discrimination rules, may not be able to 

adjust their compensation mix in response to changing tax incentives as readily as those without 

employees. Nevertheless, the estimates are remarkably similar. This offers some suggestive 

evidence that the non-discrimination rules do not seem to unduly influence the preferred 

compensation mix of the self-employed.18 Perhaps the self-employed are able to use own and 

spousal IRA’s to achieve their tax-preferred retirement savings goals or the rules are not that 

onerous at least for the sole proprietors in our sample. Alternatively, employees may influence the 

decision to establish a plan but not the level of contribution once the decision to establish a plan 

has been taken. Measuring the effect of non-discrimination rules, if any, is a very interesting issue 

and certainly worthy of further research. 

18We tried a number of alternative specifications in order to identify an effect from 

nondiscrimination rules on the sole proprietor’s contribution rate. For example, we included an a 

dummy variable for sole proprietor’s with employees in the pooled sample as well as interacting 

the dummy variable with the tax rate. Nevertheless, we are not able to demonstrate a statistically 

significant effect. 

-24-
5. A Summary of Our Findings 

In this paper, we focus on the effect of federal income taxes on the sole proprietor’s 

preferred mix of compensation among ordinary taxable income and tax-preferred contributions to 

qualified retirement plans. We use tax return data for a sample of sole proprietors for the period 

1985 through 1993. This period spans several changes in federal tax law, affecting individual rates 

and thus the after-tax price of retirement savings. These exogenous changes in rates help us 

identify the tax-price. Furthermore, individual tax data allow us to measure the after-tax price of 

contributions and after-tax income more precisely. Having the necessary exogenous variation and 

precise measures of income and tax rates is crucial for obtaining consistent estimates of the 

desired income, own- and cross-price elasticities. 

We find that taxes have a substantial effect on the preferred mix of compensation. 

Controlling for endogeneity of income and the tax-price, our findings are surprisingly robust to a 

number of alternative specifications. In fact, the magnitudes of our estimated elasticities are 

generally consistent with those obtained by Woodbury and Hamermesh (1992), particularly for 

the no-wage sample. Thus our findings support their conclusion that tax reductions in the 1980's 

account for a substantial amount of the decline in the share of fringe benefits in total 

compensation. 

Unfortunately, this study does not have any direct bearing on whether tax-based savings 

incentives create new savings. But, if Engen et al. (1996) are correct and assets in tax-preferred 

savings plans are good substitutes for other savings, then these incentives may not induce much, if 

any, new savings. Rather, they simply provoke portfolio re-allocations. Absent significant new 

savings, high own-price and substitution elasticities of the order of magnitude obtained here 

-25-
suggest that the government may lose a significant amount of revenue as individuals re-shuffle 

existing savings in response to tax incentives without the benefit of stimulating additional savings, 

investment, economic growth and the resulting growth in government revenues. 

-26-
APPENDIX I 

Variable Construction 

We estimate the jth share equation for individual i in time period t using the following difference 

equation: 

)Sjit = Aj + Bj)ln[Cjit / Pjit] + ' )ln[pjit /pkit]+ AjXjit + )ujit 

where j indicates tax favored pension contributions, k indicates other compensation; ) indicates 

the first difference of the succeeding variable; and the letters A, B, ', and A are parameters to be 

estimated. The population we are examining are taxpayers with positive schedule c business 

income (BIL) in all three years of the sample (1985,1989,1993). The construction of the variables 

are described below. 

The Dependent Variable 

1. Social Security Contributions Treated as Taxes 19 

Sjit = (PENit ) / (TATCit) 

where: Sjit is individual i’s share of tax-preferred contributions to qualified pension plans, 

or PENit, in total after tax compensation, TATCit. 

PENit = [KEOGHit + SEPit + IRAit,own + IRAit,spouse ] 

19In addition to the standard income tax, most workers are required to make payments, 

based on their wages, to the Social Security Trust Fund, up to an indexed maximum dollar 

amount, or cap. These Social Security contributions are made to three separate accounts: the Old 

Age Survivors Insurance (OASI) Trust Fund, the Disability Insurance (DI) Trust Fund, and the 

Hospital Insurance, (HI) Trust Fund. Employers are also required to contribute on behalf of the 

employee. In an analogous manner, the self-employed are required to pay a certain percent of net 

income (where net income is defined to be income from sole proprietorships, farm income, and 

Schedule K partnership income) to the Social Security Trust Fund. Since the self employed 

individual essentially acts as both the employer and employee, he is required to pay both an 

employee and employer contribution to the Social Security Trust Funds. 

-27-
where: KEOGHit is the individual’s reported contribution to a Keogh account; 

SEPit is the reported contribution to a self-employed pension (SEP) account; 

IRAit,own is the primary taxpayer’s reported contribution to an individual 

account; and 

IRAit,spouse is the reported contribution to the spouse’s individual retirement 

account. 

TATCit = WASit + FILit + BILit + SCHKit - ETAXit - EESECAit - ERSECAit - EEFICAit,e 

where: WASit is reported wages and salaries; 

BILit is reported net Schedule C income; 

FILit is reported net Schedule F income; 

SCHKit is partnership and S-corporation income; 

ETAXit is the reported federal individual income tax liability associated with 

earned income; 

ERSECAit is the employer portion of the SECA contribution; 

EESECAit is the employee’s portion of the SECA contribution; 

EEFICAit is the employee’s contribution to FICA; and 

ERFICAit is the employer's contribution to FICA. 

The taxpayer’s reported wages and net-income from Schedules C, F, and K are obtained directly 

from the taxpayer’s Form 1040 and the associated schedules. The other variables used to 

construct TATCit are constructed as follows. 

-28-
In 1985 and 1989: 

If CAPOASDHI 

t

 > WASit , then ERFICAit = EEFICAit = 

[1/2 × OASDIt × WASit ] + [1/2 × HIt × WASit ], 

if CAPOASDHI 

t # WASit , then ERFICAit = EEFICAit = 

[1/2 × OASDIt ×CAPOASDHI 

t

 ] + [1/2 × HIt ×CAPOASDHI 

t

 ], 

and 0 otherwise. 

In 1993: 

If CAPOASDI > WASit , then ERFICAit = EEFICAit = 

[1/2 × OASDIt × WASit ] + [1/2 × HIt × WASit ], 

if CAPOASDI # WASit #CAPHI , then ERFICAit = EEFICAit = 

[1/2 × OASDHIt × CAPOASDI ] + [1/2 × HIt × (WASit - CAPOASDI) ], 

if WASit > CAPHI, then ERFICAit = EEFICAit = 

[1/2 × OASDHIt ×CAPOASDI] + [1/2 × HIt × (CAPHI - CAPOASDI) ]. 

In 1985 and 1989: 

If CAPOASDHI 

t > WASit + SECINCit, then ERSECAit = EESECAit = 

[1/2 × (OASDIt - CREDt) × max{0, SECINCit}] + 

[1/2 × HIt × max{0, SECINCit}] 

if CAPOASDHI 

t # WASit + SECINCit , then ERSECAit = EESECAit = 

[1/2 × (OASDIt - CREDt ) × max{0, (CAPOASDHI 

t - WASt

)}] + 

[1/2 × HIt × max{0, (CAPOASDHI - WASt )}] 

and 0 otherwise. 

-29-
In 1993: 

If CAPOASDI 

t > WASit + SECINCit , then EeSECAt

 = ErSECAit = 

[1/2 × OASDIt × max{0,SECINCit )] + [1/2 × HIt × max{0, SECINCit)] 

if CAPHI 

t $ WASit + SECINCit $ CAPOASDIt , then EeSECAt

 = ErSECAit = 

[1/2 × (OASDIt ) × max{0, (CAPOASDI

t

 - WASit )}] + 

[1/2 × HIt × max{0, SECINCit }] 

if CAPHI 

t < WASit + SECINCit , then EESECAt

 = ERSECAit = 

[1/2×(OASDIt )×max{0,(CAPOASDI

t

 - WASit)}] + 

[1/2 × HIt × max{0, (CAPHI

t

 - WASit)}]. 

where: OASDIt is the combined employer and employee Old Age Survivor’s and 

t

when t = 1985, 1989, and 1993, respectively; 

Disability Insurance tax rate in year t; or OASDI = 0.114, 0.1212, or 0.124 

HIt is the combined employer and employee Hospital Insurance tax rate in year t; 

or Hi = 0.027, 0.029, or 0.029 when t = 1985, 1989, or 1993, respectively; t

CREDt is the sole proprietor SECA credit, or CREDt

t = 1985 and 1989, respectively. 

= 0.023 or 0.02, when 

CAPOASDI 

t is the OASDI taxable maximum amount in year t; or $39,600, $48,000, 

or $57,600 when t = 1985, 1989, and 1993, respectively; 

CAPHI

t is the HI taxable maximum amount in year t, or $39,600, $48,000, and 

$135,000, when t = 1985, 1989, and 1993, respectively; and 

SECINCit = BILit + FILit + PARTit , where PARTit is partnership income. 

Note 4: Employers make a FICA contribution on behalf of their employees. Throughout the 

analysis, we assume that employees bear the burden of the employer’s contributions in the 

form of lower wages. That is, the employee bears the burden of both the employer and 

employee portions of the FICA tax. However, for the calculation of total after tax 

compensation (treating Social Security payments as taxes), the employee’s contribution to 

FICA, but not the employer’s contribution, must be subtracted from total compensation, 

since reported wages (WASit) include the employee contribution to FICA but do not 

include the employer contribution to FICA. 

ETAXit = PCNTEit × TAXit 

-30-
If TOTINCit > EARNEDit > 0, then PCNTEit = EARNEDit / TOTINCit, and 

if EARNEDit =>TOTINCit, then PCNTEit = 1, and otherwise 

PCNTEit = 0. 

where: TAXit is the total federal income tax liability reported on IRS Form 1040; 

EARNEDit = (WASit + FILit + BILit + SCHKit ); and 

TOTINCit is the sum of wages (WASit ), net Schedule C income (BILit), net Schedule F 

income (FILit), taxable interest, (INTSTit ) reported on Form 1040, dividends (DBEt ) 

reported on Form 1040, net long-term capital gains or losses (NLTGLit ) reported on the 

Form 1040, and Schedule E income reported on Form 1040 (SCHEit ). SCHEit includes 

rental income, royalty income, and partnership and S-corporation income. 

Note 6: PCNTEit is not computed for observations in which TOTINC

zero. 

it is less than or equal to 

2. Social Security Contributions Treated as Benefits 

Sjit = (PENit + SECAjit + FICAjit ) / (TATCjit ) 

PENit = [KEOGHit + SEPit + IRAit,own + IRAit,spouse ] 

TATCjit = WASt + FILt + BILt + SCHKt + ERFICAit - ETAXt 

where: SECA and FICA represent the sum of the employer and employee contributions 

for FICA and SECA, as defined above. 

Note 7: The employer FICA contribution must be added into total compensation, since employer 

and employer SECA, and employee FICA, are already included in WASit and BILit .20 

Note 8: When constructing the independent variables, the differenced variables, and the 

instruments in “the Social Security Contributions as Taxes” versus “Social Security 

Contributions as Benefits”analyses, the relevant specifications of the share variable and 

after tax compensation are utilized. 

20Recall that the employer's FICA contribution is already excluded from wages. 

-31-
The Independent Variables 

Xit is a vector of demographic variables, including the age of the primary filer 

(AGE), age-squared (AGE-SQUARED), the number of dependents 

(DEPENDENTS), and dummy variables for marital status (MARRIED), year 

(YEAR), and industrial sector. 

Cit /Pit is defined as real after-tax capital income, 

where: Cit is capital income (CAPINCit

tax liability attributable to capital income (CAPTAX

) less the amount of total reported 

it). 

CAPINCit is equal to the sum of taxable interest (INTSTit), tax exempt interest 

(TXINTSTit) reported on Form 1040, dividends (DBEit), net long-term capital 

gains (NLTGLit), and reported Schedule E income net of partnership and Scorporation income (SCHEit - SCHKit ), 

CAPTAXit = (TAXit - ETAXit ) 

lnPit is the weighted average tax price of total compensation, in log form, 

or lnPit = 3Sjit ×ln(pjit ). Note: pjit = 1 - LMTRt

 , as defined below. 

pjit /pkit is the relative tax-price of contributing to a tax-favored retirement account. 

where: pkit is the price of taxable compensation, which serves as the numeraire in our 

analysis. Accordingly, we set this equal to 1. 

pjit is the tax price of contributing to a Keogh, SEP, or IRA; or, 

jit p , jit = 1 - LMTR

where: LMTRjit is the last dollar ordinary federal individual marginal income tax rate, 

computed as follows. Using detailed tax calculators developed at the U.S. 

Treasury, we recompute each taxpayer's federal individual income tax liability 

(TAXit,BIL+100) by adding $100 to reported net business income (BILit ). Then we 

subtract the reported federal tax liability (TAXit) from this recalculated amount, 

and divide the quantity by 100; or, LMTRjit = [(TAXit,BIL+100 - TAXit)/100]. 

Intuitively, this is the change in the income tax rate resulting from a small change in Schedule C 

income, or the marginal income tax rate associated with Schedule C income. 

DIFFERENCED VARIABLES 

-32-
The difference of the variables defined above, regardless of whether SECA is treated as a tax or 

benefit, are computed as follows: 

C )Sjit = [Sjit - Sji(t-4)], for t = 1989 and 1993; 

C )ln[pjit /pkit] = ln[1-LMTRjit ] - ln[1-LMTRji(t-4) ], for t = 1989 and 1993; and 

C )ln[Cit /Pit ] = ln[Cit /Pit ] - ln[Cit-4 /Pit-4], for t = 1989 and 1993. 

INSTRUMENTS 

The last dollar marginal tax rate is potentially endogenous. Therefore, we construct instruments 

for the last dollar marginal tax rates for both treatments of SECA. We construct an instrumental 

variable that takes advantage of the most prominent features of our data: the exogenous changes 

in marginal tax rates due to changes in federal tax law. 

The instrument for the last dollar marginal tax rate is computed as follows. After adjusting 1985 

income to conform with 1989 tax law, we use the CPI-U to inflate the taxpayer’s 1985 attributes 

to 1989 levels, and calculate their tax liability using 1989 tax law. Then, we add $100 to their 

1985 reported net Schedule C income in 1989 dollars, and re-compute their tax liability. Then we 

compute a “synthetic” 1989 marginal tax rate for each observation by taking the difference 

between these two measures of tax liability and dividing by $100 (ie. in a manner analogous to the 

computation of the last dollar marginal tax rate described above) . The “synthetic” 1993 marginal 

tax rate is computed in a similar manner, except 1989 attributes are inflated, using the CPI-U, to 

1993 levels. 

Because the 1985 (1989) data reflect the behavior and incentive structure present in 1985 (1989), 

the marginal tax rates computed using 1985 (1989) data but 1989 (1993) law reflect only the 

exogenous, statutory changes in the tax rate, rather than the endogenous changes in the marginal 

tax rate (resulting from the behavioral response to the changes in the law; that is, his behavioral 

response to the statutory tax rate changes effect the level of his taxable income and deductions, 

and which can effect his marginal tax rate). 

Let XMTRit stand for the “synthetic” 1989 (1993) marginal tax rate. We compute the instrument 

for )ln[pjit /pkit], called )ln[ITPjit ] , as follows: 

)ln[ITPjit ] = ln[1 - XMTRit] - ln[1 - MTRit-4], for t=1989 and 1993. 

Thus, this procedure removes the endogenous, behavioral component of tax rate movements from 

] , leaving the exogenous component which is due to the change in the tax law 

associated with TRA ‘86, OBRA ‘90, and OBRA ‘93. 

)ln[ITPjit 

-33-
The instrument for the variable )ln[Cit /Pit ], called ln(ICPit), is computed as follows. 

ln(ICPit ) = ln[Cit /(IPit ) ] - ln[Cit-4/Pit-4

t ] = 3Sjit *ln( 1-XMTRjit) 

], for all t=1989,1993 

where: ln[IPit ] is computed as ln[IP

-34-
References 

Adamache, Killard W. and Frank A. Sloan, “Fringe Benefits: To Tax or Not to Tax?,” 

National Tax Journal, March 1985. 

Auten, Jerry and Robert Carroll, The Effect of Income Taxes on Household Behavior,” Review 

of Economics and Statistics, forthcoming. 

Barth, James R., Joseph J. Cordes and Robert B. Friedland, “Taxes and the Share of Fringe 

Benefits in Total Compensation: Preliminary Evidence from Micro-Cross Section Data,” 

working paper, 1985. 

Carroll, Robert, Douglas Holtz-Eakin, Mark Rider and Harvey S. Rosen, “Income Taxes and 

Entrepreneurs’ Use of Labor,”Journal of Labor Economics, forthcoming. 

Deaton, Angus, and John Muellbauer, “An Almost Ideal Demand System,” American 

Economic Review, 70, 1980, pp. 312-326. 

Eissa, Nada, “Taxation and Labor Supply of Married Women: the Tax Reform Act of 1986 as a 

Natural Experiment,” NBER working paper no. 5023, 1995. 

Engen, Eric M., William G. Gale, and John Karl Scholz, “Effects of Tax-Based Saving 

Incentives on Saving and Wealth,” NBER working paper no. 5759, 1996. 

Feenberg, Daniel, “Are Tax Price Models Really Identified: The Case of Charitable Giving,” 

National Tax Journal, 40, no. 4, December 1987, pp. 629-633. 

Feldstein, Martin, “The Effect of Marginal Tax Rates on Taxable Income; A Panel Study of the 

1986 Tax Reform Act,” NBER working paper no. 4496, 1993. 

Long, James and Frank Scott, “The Income Tax and Non-wage Compensation,” The Review of 

Economics and Statistics, 64, 1982, pp. 211-19. 

Organization for Economic Cooperation and Development, Economic Outlook, Historical 

Statistics, 1989. 

The Complete Internal Revenue Code, New York: Research Institute of America, 1996. 

U.S. Department of Commerce, Statistical Abstract of the United States, The National Data 

Book, Bureau of the Census, Washington, D.C.: U.S. Government Printing Office, 1998. 

Turner, Robert W., “Fringe Benefits: Should We Milk This Sacred Cow?,” National Tax 

Journal, 42, no. 3, pp. 293-300. 

-35-
Woodbury, Stephen A., “Substitution Between Wage and Non-wage Benefits,” American 

Economic Review, 73, March, 1983, pp. 166-182. 

Woodbury, Stephen A. and Douglas R. Bettinger, “The Decline of Fringe Benefit Coverage in 

the 1980's,” Structural Changes in U.S. Labor Markets, ed. Randall Eberts and Erica 

Groshen, (Armonk, New York:M.E. Sharpe, 1991, pp.105-138). 

Woodbury, Stephen A. and Daniel S. Hamermesh, “Taxes, Fringe Benefits, and Faculty,” 

Review of Economics and Statistics, 74 (2), May, 1992, pp. 287-296. 

Woodbury, Stephen A. and Wei-Jang Huang, The Tax Treatment of Fringe Benefits, 

(Kalamazoo, MI:W.E. Upjohn Institute for Employment Research, 1991) 

Wu, D., “Alternative Tests of Independence Between Stochastic Regressors and Disturbances,” 

Econometrica, 41, 1973, pp. 733-750. 

-36-
Table 1

The Share of Fringe Benefits in Total Compensation

National Totals Share of Keogh 

Contribution 

Only 

Share of Keogh 

and SECA 

Contribution 

Share of Keogh, 

SECA,Own, 

and Spouse's IRA 

Contributions 

Share of Fringe Benefits in 

Total Compensation: 1985 16.64% 6.50% 15.27% 18.70% 

Share of Fringe Benefits in 

Total Compensation: 1989 16.57% 3.35% 13.08% 15.07% 

Share of Fringe Benefits in 

Total Compensation: 1993 17.98% 4.25% 15.20% 17.16% 

Source: Department of Commerce, Bureau of Economic Analysis. 

Note: The national share of fringe benefits in total compensation 

also includes employer contributions to health insurance. 

-37-
Table 2

Means and Standard Deviations

Variable 

Full Sample 

SECA as a Tax SECA as a Benefit 

)Share -0.02 

[0.11] 

-0.57*10-3 

[0.09] 

)ln(Income) 0.64 

[3.77] 

0.47 

[3.66] 

)ln(TaxPrice) 0.05 

[0.19] 

0.04 

[0.18] 

Age 47.04 

[10.34] 

45.76 

[11.02] 

Age Squared 2319.3 

[992.42] 

2215.8 

[1,036.80] 

Dependents 1.23 

[1.23] 

1.21 

[1.24] 

Marriage Indicator 0.9 

[0.29] 

0.86 

[0.34] 

Mining 0.06 

[0.23] 

0.05 

[0.21] 

Construction 0.05 

[0.22] 

0.09 

[0.28] 

Manufacturing 0.02 

[0.15] 

0.03 

[0.16] 

Transportation 0.02 

[0.15] 

0.03 

[0.17] 

Wholesale Trade 0.02 

[0.14] 

0.02 

[0.13] 

Retail Trade 0. 09 

[0.29] 

0.11 

[0.31] 

Finance 0.12 

[0.32] 

0.1 

[0.30] 

Service 0. 52 

[0.50] 

0.48 

[0.50] 

Other 0. 01 

[0.11] 

0.01 

[0.11] 

Year 0.5 

[0.50] 

0.51 

[0.50] 

Number of observations 5,465 9,047 

Standard deviations are provided in square brackets. 

-38-
Table 3

Regression Coefficients 

First-Differences of the AID Equation for Share of Pension Contributions 

(Full Sample)

Coefficient 

SECA as a Tax SECA as a Benefit 

OLS TSLS OLS TSLS 

Constant -0.021 

[0.027] 

-0.026 

[0.027] 

0.023 

[0.015] 

0.004 

[0.015] 

) ln(Income) 0.002 

[0.38*10-3] 

0.002 

[0.38*10-3] 

0.001 

[0.26*10-3] 

0.001 

[0.26*10-3] 

) ln(TaxPrice) -0.012 

[0.009] 

-0.026 

[0.012] 

0.002 

[0.006] 

-0.061 

[0.008] 

Age 0.003 

[0.001] 

0.003 

[0.001] 

0.2*10-3 

[0.001] 

0.001 

[0.001] 

Age Squared -0.37*10-4 

[0.12*10-4] 

-0.38*10-4 

[0.12*10-4] 

0.26*10-5 

[0.71*10-5] 

0.67*10-5 

[0.71*10-5] 

Dependents -0.002 

[0.001] 

-0.002 

[0.001] 

-0.001 

[0.001] 

-0.001 

[0.001] 

Marriage Indicator -0.027 

[0.005] 

-0.027 

[0.005] 

-0.014 

[0.003] 

-0.014 

[0.003] 

Mining 0.008 

[0.008] 

0.009 

[0.008] 

-0.003 

[0.006] 

0.003 

[0.006] 

Construction 0.012 

[0.008] 

0.012 

[0.008] 

0.012 

[0.005] 

0.013 

[0.005] 

Manufacturing 0.005 

[0.010] 

0.006 

[0.010] 

-0.008 

[0.007] 

-0.006 

[0.007] 

Transportation 0.003 

[0.011] 

0.004 

[0.011] 

0.010 

[0.006] 

0.012 

[0.006] 

Wholesale Trade -0.010 

[0.011] 

-0.009 

[0.011] 

-0.010 

[0.008] 

-0.007 

[0.008] 

Retail Trade 0.011 

[0.007] 

0.011 

[0.007] 

0.010 

[0.004] 

0.012 

[0.004] 

Finance -0.008 

[0.006] 

-0.007 

[0.006] 

-0.005 

[0.004] 

-0.001 

[0.004] 

Service 0.002 

[0.005] 

0.003 

[0.005] 

-0.001 

[0.004] 

0.002 

[0.004] 

Other -0.009 

[0.014] 

-0.008 

[0.014] 

-0.007 

[0.009] 

-0.004 

[0.009] 

Year -0.032 

[0.004] 

-0.029 

[0.004] 

-0.032 

[0.002] 

-0.021 

[0.002] 

Number of observations 5,465 5,465 9,047 9,047 

Standard errors are provided in square brackets. 

-39-
Table 4

Estimates of Substitution, Uncompensated Price, and Income Elasticities 

First-Differences of the AID Equation for Share of Pension Contributions

Elasticity* SECA as a Tax SECA as a Benefit 

OLS TSLS OLS TSLS 

Fw,f 1.222 

[0.167] 

1.479 

[0.262] 

0.984 

[0.039] 

1.527 

[0.085] 

0f,f -1.211 

[0.175] 

-1.454 

[0.272] 

-0.988 

[0.045] 

-1.458 

[0.062] 

0w,f 0.013 

[0.010] 

0.028 

[0.013] 

-0.002 

[0.007] 

0.071 

[0.010] 

0w,y 0.998 

[0.4*10-3] 

0.998 

[0.4*10-3] 

0.998 

[0.000] 

0.998 

[0.000] 

0f,y 1.036 

[0.015] 

1.037 

[0.015] 

1.010 

[0.002] 

1.010 

[0.002] 

Number of obs 5,465 5,465 9,047 9,047 

Standard errors are provided in square brackets. 

* Definitions of the notation used to indicate estimated elasticities reported 

in Tables 4 and 5 are as follows: 

Fw,f marginal rate of substitution between taxable and tax-preferred compensation. 

0f,f own-price elasticity of demand for tax-preferred compensation. 

0w,f cross-price elasticity of demand for taxable compensation with respect to 

the price of tax-preferred compensation. 

0w,y income elasticity of demand for taxable compensation. 

0f,y income elasticity of demand for tax-preferred compensation. 

-40-
Table 5 

Estimates of Substitution, Uncompensated Price, and Income Elasticities 

on Alternative Samples 

Elasticity 

SECA as a Tax 

W & H* 

No Wages No Wagebill No Wages/No Wagebill 

OLS TSLS OLS TSLS OLS TSLS 

Fw,f 2.641 

[0.351] 

2.336 

[0.606] 

3.569 

[1.331] 

0.977 

[0.228] 

1.465 

[0.344] 

1.913 

[0.649] 

3.450 

[1.471] 

0f,f -2.651 

[0.359] 

-2.216 

[0.628] 

-3.333 

[1.362] 

-0.980 

[0.239] 

-1.445 

[0.357] 

-1.826 

[0.695] 

-3.207 

[1.517] 

0w,f 0.318 

[0.034] 

0.125 

[0.036] 

0.241 

[0.056] 

-0.001 

[0.012] 

0.023 

[0.016] 

0.093 

[0.062] 

0.247 

[0.080] 

0wy 0.672 

[0.020] 

0.995 

[0.002] 

0.996 

[0.002] 

0.998 

[0.001] 

0.998 

[0.001] 

0.994 

[0.003] 

0.995 

[0.003] 

0f,y 2.701 

[0.431] 

1.045 

[0.025] 

1.041 

[0.028] 

1.047 

[0.022] 

1.047 

[0.022] 

1.052 

[0.037] 

1.043 

[0.037] 

Number of obs 1,477 767 767 3,608 3,608 386 386 

Elasticity 

SECA as a Benefit 

No Wages No Wagebill No Wages/No Wagebill 

OLS TSLS OLS TSLS OLS TSLS 

Fw,f 1.537 

[0.108] 

2.169 

[0.237] 

0.991 

[0.050] 

1.554 

[0.095] 

1.581 

[0.148] 

2.408 

[0.316] 

0f,f -1.456 

[0.122] 

-1.991 

[0.258] 

-0.994 

[0.057] 

-1.484 

[0.103] 

-1.490 

[0.171] 

-2.186 

[0.347] 

0w,f 0.083 

[0.019] 

0.180 

[0.031] 

-0.001 

[0.009] 

0.072 

[0.011] 

0.093 

[0.029] 

0.224 

[0.045] 

0w,y 0.998 

[0.001] 

0.998 

[0.001] 

0.999 

[0.4*10-3] 

0.998 

[0.4*10-3] 

0.998 

[0.001] 

0.999 

[0.001] 

0f,y 1.012 

[0.005] 

1.009 

[0.005] 

1.010 

[0.003] 

1.010 

[0.003] 

1.011 

[0.007] 

1.007 

[0.007] 

Number of obs 1,473 1,473 6,227 6,227 849 849 

Standard errors are provided in square brackets. 

* Column 6 of Table 4 in Woodbury and Hamermesh (1992). 

-41-