REFEREE REPORT FOR
“HETEROGENEOUS LABOR SKILLS,
THE MEDIAN VOTER, AND LABOR TAXES”
(This report is written on the presumption that the paper is submitted to the Journal of Economic
Theory.) This paper discusses theoretically the determination of labor income taxes in a neoclassical real business cycle model with workers heterogeneous in their skills, and the sequences of
policies be decided at period 0 through majority voting. The authors first showed that in this environment, the Median Voter Theorem holds in the sense that the equilibrium policy is the one preferred by the agent with the median skill. They then characterized the properties of the equilibrium
policy. In particular, the equilibrium taxes are increasing in the distance between the median and
mean skills, and are also increasing in the aggregate labor supply. The existence of a median voter
is proved by showing that the indirect utilities of the agents satisfy single cross condition, which
comes from the monotonicity of the indirect utility on the agents’ innate skills. The equilibrium
taxes are shaped by the balance of the benefits and costs from redistribution, and the distortions in
efficiency that come along. Redistribution is more beneficial if the distribution of income is more
skewed, in the meanwhile, it is also more costly in periods with lower labor supply. Both channels
are consistent with the literature (Meltzer and Richard (1981) and Chari, Christiano, and Kehoe
(1994)). Calibrated versions of the model are used to explore the cyclical properties of the model
quantitatively.
Overall, I think the paper answers an interesting research question. The methodology adopted in
the paper is appropriate. The insights drawn from this paper contribute to the discussions of optimal
taxation in theory and are potentially important in explaining long-run changes or some crosscountry comparisons of tax policies. However, there are still rooms for the paper to be improved in
my opinion. Some of these are related to the content of the paper, while others are concerning the
exposition of the paper. Section I summarizes those relate to the content of the paper, and section
II lists those relate to the exposition of the paper. Section III concludes.
I
C ONTENT
First and foremost, I think the paper could be more focused. The authors presented a lot of interesting results in the paper, however, some of them are not in direct support of the main subject. As
a result, instead of strengthening the main points, the messages conveyed by the paper are blurred
by too many loosely related results. The paper could either focus on theoretical insights from the
characterization of the optimal labor income taxes, or could go further positively by emphasizing
the ability of the model to explain observed patterns from the data. Since the paper appears to be
marching further over the theoretical contributions, most of the rest comments are aiming at highlighting the theoretical contributions of this paper. If the authors choose to go the other way round,
some of my suggestions are explained at the end of this section.
1
1. Highlighting the Theoretical Contributions.—As is stated by the authors, this paper is an
extension of the work by Bassetto and Benhabib (2006). More specifically, Bassetto and
Benhabib (2006) discussed the determination of capital income taxes in a similar environment where workers are homogeneous, and the only heterogeneity is on the initial capital
endowment. This paper extends the analysis by introducing heterogeneous skills and labor
income taxes. I think it would be nice to highlight the difference between the channels introduced by initial capital and skills heterogeneity, and those introduced by capital income taxes
and labor income taxes. My understand is that in Bassetto and Benhabib (2006), the capital
taxes have a Bang-bang property because finite periods high capital taxes with lump-sum
transfers could completely achieve the redistribution purpose of the median voter, leaving
only the efficiency consideration at work in later periods, which leads to zero capital income
taxes. The difference here is that since skills heterogeneity generates persistent inequality in
income stream, a Bang-bang labor income taxes will never correct all inequality perceived
by the median voter. As a result, the labor income taxes are always positive, so long as the
median skill is less than the mean.
Regarding the intuitions in the previous paragraph, I wish to make three remarks. First, I
think the authors could emphasize this intuition explicitly in the paper to help readers both
understand the general logic of the paper better, and to connect with the literature closer.
Second, I am not sure why the authors need to keep the heterogeneity in initial wealth and
capital income taxes in their analysis. Having both taxes simultaneously is important in the
optimal taxation literature (Chamley-Judd) because the insight there relies on the comparison of capital income taxes and labor income taxes. However, it does not seem to me that
the interactions between the labor income taxes and capital income taxes will lead to different qualitative properties of the equilibrium labor income taxes, especially since a strong
structure—affine to skills—is imposed on the heterogeneity in the initial capital. Also since
in all the quantitative experiments, zero initial capital is assumed, I do not think quantitatively, the capital taxes matter for the purpose of this paper either. In fact, I think what is
under explored here is the role played by leisure. While it is clear from Proposition 3 that
the elastic labor supply is key to bound the labor income taxes from unity, what is less explored is how the consumption-leisure choices affect the redistribution/efficiency motives of
the median voter.
2. Log-Utility.—Throughout the main body of the paper, the authors stick to the special case
of log-utility as opposed to the more general case. I understand that a log-utility simplifies
significantly the algebra, and makes the economic intuition much more transparent. However,
if the authors would like to emphasize on the theoretical contributions of this paper, I think it
would be nice to state all the main results in the more general case, and later use the log-utility
as illustrating examples. According to Table 4, the intertemporal elasticity of substitution σ
seems to have a significant impact on the quantitative performance of the model. Therefore,
I think it worths the efforts to check whether some economic insights could be found in
this more general treatment, especially given the recent contribution by Werning and Straub
2
(2015), where σ assumes a central role.1
3. Normative or Positive?—This is closely related to how the paper could be motivated, and how
the quantitative results of the model should be interpreted. The way that the authors currently
motivate the paper seems to suggest that they would like the theory presented here to serve as
a candidate to explain (1) the simultaneous rise of labor income inequality and labor income
taxes in the U.S in the last several decades, and (2) the procyclical fiscal policies observed in
some developing countries. Although the model has the ability to deliver the empirical facts,
to claim the theory explains these facts requires more work. More specifically, I think the
empirical evidence as is in the paper now could shed light on the first fact, however, more
efforts on empirical evidence are needed if the second fact is to be explained using the theory
here.
To state that the rising wage inequality drives the increase in labor income taxes, in the context of this paper, is equivalent to saying that the increasing redistribution motives causes the
corresponding increase in the taxes. I think it is a reasonable statement, if put in a relatively long period of time like several decades. By a comparison of the equilibrium tax rates
between two steady states which only differ in the wage inequality, the size of the increase
in labor income taxes driven by the increase in inequality through the channel of majority
voting could be isolated. This is essentially the results in Table 3 of the paper. However, I
am not sure how much can be taken out of the results in Figure 2. Given the way the ρs are
measured, and the way the upper and lower bounds are calculated, it is not clear to me how
to interpret the fact that the actual tax path lies with in the two bounds, and what is the extra
insight that we are gaining beyond the steady-state comparison. Somewhat related, since the
job and wage polarization, and the inequality that follows are being intensively examined
by labor economists recently, I think a connection to that literature will help the motivation
of the paper. See for example the series of work by David Autor, Autor, Levy, and Murnane (2003), Autor, Katz, and Kearney (2008), Acemoglu and Autor (2011), Autor and Dorn
(2013), and related work by Jaimovich and Siu (2015).2
The implications of the model over the business cycles in my opinion, should be interpreted
with much more caution. While I think few people will argue that over a longer horizon, wage
inequality has an important role in shaping the labor income tax policy, it is less apparent to
me why over the business cycle—which usually happens in horizon measured by quarters—
this is the case. It is important to show at least some anecdotal evidence which indicates
deliberate changes in labor income taxes at the cyclical frequency. The work cited in this
paper (McDaniel (2007)) in my opinion is not enough to justify this causal relationship. To
see this, consider the following example. The way McDaniel (2007) imputed the average
labor income tax rate is by dividing the tax revenue that comes from the labor income by the
total labor income in the economy. Suppose that the tax rate does not change at all over the
business cycles. Since the United States adopts a progressive labor income tax in reality, if we
1
A fair point though is that at 2009, Werning and Straub (2015) is yet to come.
Again, I am not sure whether Jaimovich and Siu (2015) exists dates back to 2009, but the other papers certainly
have been circulated back then.
2
3
assume that poor people are hit harder during recessions (Elsby, Hobijn, and Sahin (2010)),
the population that has taxable labor income will turn out to earn relatively higher wages
and hence are subject to higher average tax rate in recessions. Therefore, in this hypothetical
example, although the actual tax rates do not change at all, the measured tax rate according
to McDaniel (2007) will show up as counter-cyclical, simply due to the mechanical change
of the composition of the population.3 If the above example is actually true, it would be risky
to claim that the cyclical variation of income inequality is the driving force of the cyclical
variation of the measured average income taxes. Even if empirical evidence could be found
on the causal relationship over the business cycle, caveats must be taken with the structural
assumption of the evolution of θ. If the relationship of θi (st ) = γ(st ) + ρ(st )θ0i is in fact
mis-specified, how the implied statistical property of the model should be interpreted is not
very clear to me.
It is for the reasons above that I would suggest the author to concentrate on the theoretical
contributions of the paper with numerical implications on the long-run taxes change. I think
it would require some extensive amount of efforts empirically to credibly justify that over the
business cycles, the redistribution-efficiency trade-off works as the driving force to shape the
labor income tax rates. The section of the paper that describes how the model is calibrated
(Section 7.1), however, should definitely be written in a clearer manner regardless of what
the quantitative exercises in the future will be. I find it, for example, confusing of how the
transition matrix is estimated. Issues like what are the filters being used, what are the criteria
that A and ρ are categorized as high and low should definitely be clearly and explicitly stated,
in order that the quantitative results be interpreted correctly.
II
E XPOSITION
Overall I think the exposition of the paper is quite clear, in this section I will state some suggestions
on minor issues that I think will improve the flow of the paper.
1. Conciseness.—As is explained in the last section, I think the paper could be sharper and more
concise than it is at this moment by either dropping some of the results or leaving them in
a separate appendix. First, if my understanding about the weak relationship between the
capital income taxes and labor income taxes are correct, I think results on capital income
taxes could be dropped from the main body of the paper (with a suitable modification of the
model). This includes Assumption 1, Lemma 4, Lemma 5, and Corollary 1. The spaces
that are saved could then be devoted to more explanation on the theoretical insights arisen
from heterogeneous skills and labor income taxes. Second, I am not sure the numerical
example of the cyclical properties of the model with stochastic labor skills (section 6.1) is
needed, because the discussions on the directions of the each functioning channel is clear
already in the preceding section. To further show that the overall effect of two channels
working on opposite directions could go either way using a hypothetical numerical example
seems redundant to me. In fact, given the concerns over the applicability of the model to
3
More on the recent development of the composition of the unemployed population, see Mueller (2012).
4
cyclical facts, I am not even sure about whether a quantitative investigation of the model with
stochastic labor skills is needed (the second experiment in Section 7.1 and Section 7.2).
2. Related Literature.—The literature review of the paper should be considered again. The way
the literature review is written at this moment contains too much description of the papers,
but too little explanations on how the current paper is connected to those papers. As a result,
it is somewhat difficult to locate the paper in the literature, and to understand the contribution
of this paper to which strand of literature and by how much. I think this should be jointly
considered with the authors’ decision about on which direction to push the paper, and how to
motivate the paper.
3. Typos.—Here omitted.
III
C ONCLUSIONS
To summarize, I think the paper studies an interesting research question with an appropriate method.
The general structure the analysis is developed and delivered is clear and easy to follow. However,
because the economic mechanism at work, and hence the theoretical insights that can be drawn are
not very different from that in Meltzer and Richard (1981), I do not think the paper fits the scope of
this journal, which targets the general audience in all fields. However, given the close relationship
of this paper with Bassetto and Benhabib (2006), I think it is a very nice follow-up work for the
Review of Economic Dynamics. I think the paper also fits theoretical journals that have a more
targeted audience, for example the Theoretical Economics.
R EFERENCE
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and Earnings,” in Handbood of Labor Economics, ed. by D. Card, and O. Ashenfelter, vol. 4b, chap. 12,
pp. 1043–1171. Elsevier. 3
AUTOR , D. H., AND D. D ORN (2013): “The Growth of Low Skill Service Jobs and the Polarization of the
U.S. Labor Market,” American Economic Review, 103(5), 1553–1597. 3
AUTOR , D. H., L. F. K ATZ , AND M. S. K EARNEY (2008): “Trends in U.S. Wage Inequality: Revising the
Revisionists,” The Review of Economics and Statistics, 90(2), pp. 300–323. 3
AUTOR , D. H., F. L EVY, AND R. J. M URNANE (2003): “The Skill Content of Recent Technological
Change: An Empirical Exploration,” The Quarterly Journal of Economics, 118(4), 1279–1333. 3
BASSETTO , M., AND J. B ENHABIB (2006): “Redistribution, Taxes, and the Median Voter,” Review of
Economic Dynamics, 9(2), 211–223. 2, 5
C HARI , V. V., L. J. C HRISTIANO , AND P. J. K EHOE (1994): “Optimal Fiscal Policy in a Business Cycle
Model,” Journal of Political Economy, 102(4), 617–652. 1
E LSBY, M. W. L., B. H OBIJN , AND A. S AHIN (2010): “The Labor Market in the Great Recession,” Brookings Papers on Economic Activity, Spring, 1–69. 4
JAIMOVICH , N., AND H. E. S IU (2015): “The Trend is the Cycle: Job Polarization and Jobless Recoveries,”
Manuscript. 3
5
M C DANIEL , C. (2007): “Average Tax Rates on Consumption, Investment, Labor and Capital in the OECD
1950-2003,” Manuscript. 3, 4
M ELTZER , A. H., AND S. F. R ICHARD (1981): “A Rational Theory of the Size of Government,” The Journal
of Political Economy, 89(5), 914–927. 1, 5
M UELLER , A. I. (2012): “Separation, Sorting and Cyclical Unemployment,” Manuscript. 4
W ERNING , I., AND L. S TRAUB (2015): “Positive Long Run Capital Taxation: Chamley-Judd Revisited,”
Manuscript. 2, 3
6