Discussion Paper

No. 2013-21 | March 04, 2013
Age-specific Rise of Income and Consumption Inequality


Based on Panel Study of Income Dynamics (PSID) and Consumer Expenditure Survey (CEX), the author presents evidence that the rise of income/consumption inequality over the past decades is more significant among younger households. This is consistent with the theory that the secular rise of inequality is due to increasing heterogeneity in earning ability. The author further shows that such age-specificity implies significant changes to the previously documented life-cycle profiles of inequality which are the basis of many important economic inferences.

Data Set

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The data set for this article can be found at: http://hdl.handle.net/1902.1/20442

JEL Classification

C81 E21 J31

Cite As

Guozhong Zhu (2013). Age-specific Rise of Income and Consumption Inequality. Economics Discussion Papers, No 2013-21, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2013-21


Comments and Questions

Anonymous - Referee Report 1
March 26, 2013 - 09:03

see attached file

Guozhong Zhu - Response to referee 1
April 08, 2013 - 19:05

I appreciate the candid comments from the referee. However I think some misunderstanding exists. So I would like to further clarify the main contribution and main point of the paper.

The main contribution of my paper is that it documents the age-specificity of the secular rise of inequality of ...[more]

... income and consumption. The referee cited Lemieux (2000) (it is should be Lemieux 2001 QJE, as I cited in my paper) to argue that my finding is nothing new. However, as I noted in footnote 1. The existing studies have only documented the age-specificity of college-highschool wage gap. My finding is more general in two ways. First, I use variance of logarithm of income, so it is both within-group and between-group inequality; while college-highschool wage gap is only between-group inequality. Second, in addition to income inequality, I further show the age-specificity of the rise of consumption inequality.

The referee also cited Lemieux (2006), arguing that it also documented similar findings. However, Lemieux (2006) does not show that rise of within-group inequality is stronger for younger individuals. From Table 1A and Table 1B, actually the rise of inequality is not stronger among less the experienced. And again, no age-specificity of consumption inequality is studied.

One of the main points of my paper is that many macro models (implicitly) assume that age effect is time-invariant. This is true in virtually all the papers I cited, including the one by Storesletten, elmer, and Yaron titled "Consumption and risk sharing over the life cycle" ,JME2004 (Cited as Storesletten et al. (2000) by the referee). Given time-invariant age effect, my simple regression shows that the secular rise of inequality is stronger among the younger. Therefore this is not a reiteration of the life-cycle profile of income and consumption inequality as discussed in Heathcote et al. (2010), because life-cycle profiles is already controlled for by the age dummies.

In summary, my empirical findings have not been well-documented before.

Regarding the model specification test. It is true that different specifications represent different ways to look at the data. However when no theory clearly points to a preferred way, we might want to let the data speak. In this sense, I think Table 4 adds values to our understanding.

The assumption of time-invariant age effect is also related to the fundamental problem of disentangling age, cohort and time effects, as pointed out by the referee. Given this assumption, it is reasonable to let year dummies interact with age, because this linear age is meant to capture how year effect is age-specific, rather than to capture the age-profile.

Anonymous - Invited Reader Comment
April 08, 2013 - 09:26

see attached file

Guozhong Zhu - About family income
April 08, 2013 - 19:16

Many thanks to the referee for helpful comments. I shall revise my paper according to these comments. Here I quickly respond to two issues.

The first issue is about why I use family income, but not income per person. I'm sure income per person is a good measure of ...[more]

... disposable income. However in this paper, as in some other paper in the literature, I need to compare income inequality and consumption inequality. It is very difficult to measure consumption at the individual level, and family consumption is closely related to family income. Therefore I decided to use family income.

Regarding Figure 1, the lines in the figure is a mixture of age, year and cohort effect. While it is not possible to disentangle the three, I controlled for age effect in the regression, and estimate year effect that is age-specific. Figure 1 is meant to show that for some age group, the age-specificity of year effect is so strong that it is clearly seeable. I have picked two age groups with most noticeable age-specific year effects.

Anonymous - Referee Report 2
May 13, 2013 - 10:35

This paper does three things. First, it documents an interesting fact: the rise in income and consumption inequality in the US in the 1980s varies by age and is more pronounced for younger households. Second, the paper offers a potential explanation for this fact: skill-biased technological change made investments in ...[more]

... human capital more attractive and this effect was stronger for younger households, who have more of their life ahead of them to reap the benefits of this investment. Finally, the paper argues that controlling for age-specific time effects in inequality changes the estimated life-cycle profile of inequality, which could potentially change our thinking about several results in the literature.

The fact that the rise in inequality is age-specific is interesting. The explanation offered for the fact is plausible. However, offering a plausible explanation is not enough. A good paper should provide evidence that the proposed explanation is in fact true. To do this, the usual procedure would be to model the proposed explanation, then generate testable predictions (over-identifying restrictions) from the model and finally show that these predictions are supported by the data. A different procedure would be fine too, but currently the paper makes no attempt to provide any empirical support for the explanation it proposes.

If controlling for age-specific time trends in inequality changes the estimated age profiles, then that would be an important contribution. However, unfortunately, I do not believe this result. In a review of an earlier version of this paper, which I attach, I explained this is more detail.

Minor comment: There is something wrong with the table references. All tables are referred to as Table 5.

Guozhong Zhu - Response to Referee Report 2
June 03, 2013 - 19:13

I appreciate the nice comments from the referee who already provided helpful suggestions to an earlier version of my paper.

I agree with the referee that it would be more interesting/convincing to write a model of human capital accumulation with skill-biased technological change, then test the implications from ...[more]

... such a model. However, this would make a different paper. I prefer to leave this work to the future.

The referee believes the paper would be an important contribution if I make the main results more convincing. Namely, controlling for age-specific time trend changes the age profile. Below I try to clarify my main points.

The key issues here is, it is not possible to distinguish between age-specific time effect and time-specific age effect. They are mathematically equivalent as shown by the referee. Thus it boils down to which view makes more economic sense. I think it makes more sense to take the "age-specific year effect view" . Underlying time effect are random shocks, institutional changes and structural changes from the market, each can have systemically different impact on different age groups. On the other hand, the rise of inequality with age is driven by ex ante heterogeneity (Guvenen 2007) or ex post random shocks (Storesletten et.al 2004). It is hard to imagine these factors can change from one year to another in a systematic way.

in recognition of the referee's insights, I also study age profiles of income and consumption inequality on the premise of "year-specific age effect". As shown in the figure below, this implies age-profiles that varies substantially over years. Especially for income inequality, the profile becomes much flatter over time. This would be a headache for much of macro research based on lifecycle profiles. Of course one can take the average of these profiles, as shown by the circled line. Then we fall back to the traditional year effect model, ignoring any age-specificity.

Overall I think the empirical findings in my paper help people better understand the changes of income and consumption inequality. It also provokes researchers to think more about lifecycle profiles. It has many shortcomings. Some are fixable which I'd make every effort to do. Others are beyond my capability or the scope of this paper, which I'd love to admit in the paper.


Guvenen, Fatih, "Learning Your Earning: Are Labor Income Shocks Really Very Persistent?," American Economic Review, 2007, 97 (3), 687-712.

Storesletten, Kjetil, Christopher I. Telmer, and Amir Yaron, "Consumption and risk sharing over the life cycle," Journal of Monetary Economics, 2004,
51 (3), 609-633.

Figure available in the attached file