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Previous literature demonstrates that in a standard life cycle model the optimal tax on capital is large. This paper highlights that after changing two assumptions in the standard model the optimal tax drops by almost half. First, the utility function is altered such that it implies that an agent's Frisch labor supply elasticity is constant over his lifetime. Second, the government is allowed to tax accidental bequests and ordinary capital income at separate rates. Quantifying the effect of these assumptions is important because the first has limited empirical evidence and the second confounds a motive for taxing capital and accidental bequests.

Receipts from taxes on individuals’ capital income (capital gains and dividends) in 2005 were approximately $140 billion, or 15% of total personal income tax receipts.2 Based on the sizable tax receipts from capital income in the U.S. economy and savings disincentives created by a capital tax, considerable research has been devoted to determining whether a non-zero tax on capital income is optimal.3 In the seminal works on this topic, Chamley (1986) and Judd (1985) conclude that it is not optimal to tax capital in a model with infinitely lived agents who face no idiosyncratic risk. Atkeson et al. (1999) show that the optimal tax on capital is still zero in a two-period overlapping generations model when the government is allowed to condition the labor income tax on age. Other works, such as Aiyagari (1995), Hubbard and Judd (1986), İmrohorogˇlu (1998), Erosa and Gervais (2002), Conesa et al. (2009), Garriga (2003), Jones et al. (1997) and Correia (1996), identify theoretical conditions under which it is optimal to tax capital. When determining the optimal tax on capital, the policymaker must weigh the relevant benefits versus the distortions imposed by the tax. Since a tax on capital discourages saving, it is important to analyze the tax in an overlapping generations (OLG) model that includes the life cycle factors that motivate saving. One such study, Conesa et al. (2009), uses a calibrated life cycle model and finds that the optimal tax policy consists of flat tax rates on capital and labor income of 34% and 14%, respectively.4 Additional studies such as Gervais (2012), Garriga (2003), Peterman (2012), Smyth (2006), and İmrohorogˇlu (1998) find that a non-zero tax on capital is optimal in an OLG model. Given the computational complexities of these OLG models, it is helpful to determine the economic factors driving these results. Studies that quantify the optimal tax on capital weigh the trade-off between realism and computational intensity when choosing simplifying assumptions. This paper quantifies the relative importance of two of the key modelling assumptions that motivate a positive tax on capital in a canonical OLG model. Understanding the effect of these assumptions is relevant in order to more accurately determine the optimal tax on capital. I start by solving for optimal tax policy in a benchmark model similar to the model in Conesa et al. (2009). Next, in order to measure the assumptions effects on optimal tax policy, I solve for the optimal tax policy in an altered model in which I eliminate two commonly adopted assumptions that generate a non-zero tax on capital. First I eliminate the assumption that the Frisch elasticity varies over the life cycle.5 Second I relax several restrictions in the benchmark model regarding how the government is allowed to tax accidental bequests. I test the effect of a varying Frisch elasticity since there is limited empirical evidence on whether the Frisch labor supply elasticity varies over the lifetime.6 Therefore, it is important to understand the impact of this assumption on optimal tax policy. The restrictions regarding taxing accidental bequests are used to make the model more tractable, but these restrictions confound a motive for taxing ordinary capital with a motive to tax accidental bequests and are not consistent with actual policy. The main finding of this paper is that these two assumptions are responsible for almost half of the positive optimal tax on capital in the benchmark OLG model. When these two assumptions are removed from the model the optimal tax on capital is reduced from approximately 30% to 16%. Additionally, I find that welfare losses are equivalent to 0.35% of total consumption if I implement the optimal tax policy from the benchmark model in the altered model. Altering just one of either two assumptions causes the optimal tax on capital to drop by approximately one-third. Therefore, the simplifying restrictions on the tax function regarding accidental bequests should not be included when determining optimal tax policy. These results also indicate that to more precisely determine the optimal tax on capital, one needs to empirically determine if the Frisch elasticity varies over the life cycle. A varying Frisch elasticity over the life cycle motivates a positive optimal tax on capital because it causes the government to want to condition labor income taxes on age. If the government is disallowed from using age-dependent taxes, then a non-zero tax on capital can be used to mimic age-dependent taxes since a capital tax implicitly taxes younger labor income at a relatively higher rate. In a related work, Gervais (2012) demonstrates that a progressive labor income tax can also be used in tandem with a tax on capital to mimic an age-dependent tax policy.7 The benchmark utility function in Conesa et al. (2009) is non-homothetic in labor, which implies that the Frisch elasticity varies over the life cycle with hours worked.8 Therefore, in order to test the impact of this assumption, I determine the effect on optimal tax policy of changing the utility function such that it is homothetic in labor, which implies that the Frisch elasticity does not vary.9 Restricting how the government can tax accidental bequests confound a motive for a non-zero tax on ordinary capital income. In the benchmark model, it is assumed that the government cannot distinguish accidental bequests from ordinary capital, which implies that the government has to tax the returns from both sources at the same rate. Additionally, the government is restricted to taxing only the return on the accidental bequests and not the principal. Since accidental bequests are inelastic income, the government would like to fully tax them. If they cannot distinguish between the two incomes, the optimal tax on capital is a mix of the optimal tax on ordinary capital income and the optimal tax on accidental bequests. I test the effect of relaxing these tax restrictions by allowing the government to separately tax accidental bequests and ordinary capital income. Given that these two assumptions motivate approximately half of the optimal tax on capital in the benchmark model, it becomes relevant to quantify the individual effect of all the modelling features that could motivate a non-zero tax on capital within a common framework. Four common features in an OLG model that motivate a non-zero optimal tax on capital are: (i) a varying lifetime Frisch labor supply elasticity, (ii) restrictions on how the government can tax accidental bequests, (iii) the inability of individuals to borrow, and (iv) the inability of the government to facilitate a social security program.10 I solve for the optimal tax policy in four other models with one of the four features that motivate a non-zero optimal tax on capital changed in order to determine the effect of each feature. Additionally, I solve for the optimal tax policy with an exogenously determined level of government debt or savings in order to ascertain its effect on optimal tax policy.11 In addition to the non-constant Frisch elasticity and the government not being able to separately tax accidental bequests, I find that individual liquidity constraints also motivates a positive tax on capital but to a lesser extent. I find that assuming that the government holds savings or debts has a dramatic effect on the optimal tax on capital. When I assume that the government holds savings (debt), the optimal tax on capital decreases (increases) a significant amount. There are only small changes to the optimal tax policy when I exclude the reduced-form social security program from the benchmark model; however, the life cycle profiles look less realistic. I find that the welfare cost of implementing the benchmark model's optimal tax policy in each of these alternative models ranges from 0.08% to 2.53% of total lifetime consumption. These results demonstrate that for some models there are large welfare consequences from adopting the optimal tax policy derived from a different model. Finally, this paper analyzes how the effect of the features changes when the model is calibrated to match different targets for the Frisch elasticity since there is a large variance in the empirical estimates of this value. Generally, I find that these five features have a larger effect on the optimal tax on capital when the model is calibrated to match a medium or low Frisch elasticity as opposed to a high value. This exercise is related to Conesa et al. (2009), however it includes three important differences. First, I exclude inter-cohort heterogeneity as a possible motive for a positive tax on capital. I abstract from this type of heterogeneity because Conesa et al. (2009) demonstrate that it does not affect the level of the optimal tax on capital.12 Second, I examine how relaxing the restrictions on taxing accidental bequest affects optimal tax policy. The effects of these restrictions are not studied in Conesa et al. (2009). Third, I take an alternative approach to discern the effect of a varying Frisch elasticity. Conesa et al. (2009), similar to my benchmark model, use a utility specification in which the agent's Frisch labor supply elasticity is negatively related to hours worked. To determine the effect of a varying Frisch elasticity on optimal tax policy, the authors eliminate the variance by holding the labor supply exogenously constant. Using this approach eliminates any general equilibrium effects of endogenously determined labor supply on optimal tax policy. Instead, in this paper, I eliminate the variation in the Frisch elasticity by using a utility specification that implies that the Frisch labor supply elasticity is constant.13 The advantage of this approach is that it isolates the effect of a constant Frisch while including general equilibrium effects from endogenously determined labor supply. In another related exercise, Garriga (2003) examines the effect on optimal tax policy of altering the social discount factor in a model where the government endogenously determines the level of savings or debt it holds. He finds that as the government decreases their discount rate, the optimal tax on capital increases. In contrast, this paper follows (Conesa et al., 2009) and focuses on the relative effect of the five other common features on optimal tax policy when the government maximizes ex-ante welfare of a newborn in the steady state in a model where the level of government debt is exogenously determined. This paper is organized as follows: Section 2 examines a simplified version of the model in order to provide analytical insights into the effect of the two channels eliminated in the alternative specification. I introduce the computational model and present the competitive equilibrium in Section 3. Section 4 describes the functional forms and calibration parameters. Section 5 sets up the computational experiment, and Section 6 reports the results of the computational experiment. Section 7 examines the sensitivity of the results with respect to the target that the Frisch elasticity is calibrated to match. Finally, Section 8 summarizes the paper's findings.

Through an analysis of the optimal tax on capital in a standard life cycle model, this paper concludes that if one alters the utility function such that the Frisch elasticity profile is constant and allows the government to tax accidental bequests at a separate rate from ordinary capital income, then the optimal tax on capital falls from 29.3% to 16.4%. It is important to quantify the effect of these two model features because there is not a consensus on whether the labor supply elasticity profile is upward sloping and prohibiting the government from taxing accidental bequests at a different rate from ordinary capital income confounds the government's desire to confiscate the bequests with a positive optimal tax on capital. Although the optimal tax on capital is not zero in the model without these features, it is no longer large. Comparing steady states under the baseline-fitted U.S. tax policy and the optimal tax policy, the CEV is 0.73% and 0.95% for the benchmark and alternative models, respectively. In the case of the benchmark model, over the transition, I find that adopting the optimal tax policy causes welfare to decrease for agents who are already living at the time of the tax policy change. In contrast, I find that in the alternative specification adopting the new tax policy increases the welfare of living individuals. I also find that if the government holds savings (debt), then the optimal tax on capital decreases (increases). Removing individual liquidity constraints cause the optimal tax on capital to fall. I show that it is important to include at least a reduced-form social security program in a life cycle analysis of optimal tax policy, otherwise the life cycle profiles will be unrealistic. Overall, I find that in the various models, the welfare loss from adopting the optimal tax policy determined in the benchmark model as opposed to the actual optimal tax policy for that specific model range from 0.08% to 2.53% of total lifetime consumption. Finally, I find that generally as the models are calibrated to match a lower Frisch elasticity, the effect of changing the various features is larger. When modelling certain aspects of the economy, economists try to balance realism and tractability. I demonstrate that some of these simplifying assumptions have a sizable effect on optimal tax policy. For example, assuming that the government cannot distinguish between ordinary capital and accidental bequests has large implications for optimal tax policy. Therefore, further research should focus on modelling this feature more realistically. Additionally, the shape of the Frisch labor supply elasticity profile has a large effect on the optimal tax policy. Since little empirical evidence addresses whether the Frisch elasticity varies, it is an important question for economists to examine.