Heterogeneous life-cycle profiles, income risk and consumption inequality

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Abstract

Was the increase in income inequality in the US due to permanent shocks or merely to an increase in the variance of transitory shocks? The implications for consumption and welfare depend crucially on the answer to this question. We use Consumer Expenditure Survey (CEX) repeated cross-section data on consumption and income to decompose idiosyncratic changes in income into predictable life-cycle changes, transitory and permanent shocks and estimate the contribution of each to total inequality. Our model fits the joint evolution of consumption and income inequality well and delivers two main results. First, we find that permanent changes in income explain all of the increase in inequality in the 1980s and 1990s. Second, we reconcile this finding with the fact that consumption inequality did not increase much over this period. Our results support the view that many permanent changes in income are predictable for consumers, even if they look unpredictable to the econometrician, consistent with models of heterogeneous income profiles.

Introduction

This paper evaluates the nature of increased income inequality in the US over the 1980–2000 period. This is important because income inequality originating from different sources may have different implications for consumption inequality and welfare. For example, under standard models of consumption smoothing, households do not adjust their consumption much in response to transitory shocks to their income. Hence, increases in income inequality generated by transitory shocks will have only very small effects on consumption inequality and welfare. Similarly, consumption does not respond to permanent changes in income that are insured or foreseen in advance. On the other hand, unexpected and uninsurable permanent income shocks will translate almost one-for-one into changes in consumption and will, therefore, have strong welfare effects.

We use repeated cross-section data on income and consumption from the Consumer Expenditure Survey (CEX) to estimate the extent to which different types of income shocks have contributed to the evolution of inequality. In order to extract this information, we need to put some structure on the data. More precisely, we make assumptions on the form of the stochastic process governing the evolution of individual income and postulate a model of consumption choice. These assumptions allow us to map cross-sectional variances of income and consumption within a cohort (inequality) into variances of permanent and transitory shocks (risk).

In our model, income follows an exogenous stochastic process driven by permanent and transitory shocks. We assume that consumers can self-insure against transitory shocks. In addition, we allow for permanent changes in income that do not translate into changes in consumption. We model these permanent income ‘shocks’ that do not affect consumption as heterogeneity: changes in income over the life-cycle that are predictable to the consumer. If in reality there are other reasons why changes in consumption do not reflect permanent changes in income, then we will overestimate the contribution of heterogeneity to inequality. We discuss this issue, in particular the possibility that there exist insurance markets that allow for risk sharing between consumers, and argue that there is a role for heterogeneity over and above risk sharing.

Our study delivers two main results. First, essentially all of the increase in income inequality over the sample period is due to an increase in the cross-sectional variance of permanent shocks to income. Second, most of these permanent income shocks were not of the kind that gets transmitted to consumption. Therefore, our estimates point to heterogeneity as a major source of the increase in inequality in the 1980s. The variance of transitory and unpredictable permanent shocks to income also increased in the early 1980s, but the increase was small compared to the total increase in inequality and got reversed by the end of the 1990s.

The intuition behind these results is straightforward. The trends in the data can be characterized by three salient features: (i) individual income is highly persistent over the whole sample period, (ii) income inequality rose substantially in the 1990s and, particularly, in the 1980s but (iii) over the same period consumption inequality did not increase much. If the evolution of income inequality were driven by transitory shocks, we should see much lower autocorrelation in individual income processes. If unexpected and uninsurable permanent shocks were the driving force, we would expect a rise in consumption inequality accompanying the increase in income inequality. This leaves only the third candidate, heterogeneity, able to explain all aspects of the data.

We are not the first to notice that consumption does not respond to permanent income shocks as much as standard models would predict. This finding is typically interpreted as evidence that consumers have access to markets that allow them to share risks with other consumers, insuring some or all of their idiosyncratic shocks (Krueger and Perri, 2006; Storesletten et al., 2004b; Primiceri and Van Rens, 2004; Pistaferri et al., forthcoming; Heathcote et al., 2006).1 In this paper, we offer an alternative explanation. If there is heterogeneity in life-cycles across consumers, as Lillard and Weiss (1979) and more recently Guvenen, 2005, Guvenen, 2007 have argued, then consumption may not reflect changes in income, even if they are permanent, because these changes are predictable to the household in advance.

Partial risk sharing and heterogeneity are observationally equivalent in our model. Nevertheless, we argue that it is unlikely that risk sharing is the sole mechanism responsible for the muted response of consumption to permanent shocks. First, the degree of risk sharing necessary to match the data would have to be substantially higher than what other studies have found (Attanasio and Davis, 1996). Second, we test a number of predictions of the risk sharing hypothesis (some risk sharing happens through government taxes and transfers or through markets for financial assets) and do not find convincing evidence for any of these. Finally, our interpretation that heterogeneity is an important driver of inequality is consistent with a number of recent papers decomposing inequality in heterogeneity and uncertainty, using schooling choices (Cunha et al., 2005; Cunha and Heckman, 2006; Huggett et al., 2006). The identifying assumption in these papers as well as in ours is that heterogeneity, even if unobservable to econometrician, is forecastable to the consumer and therefore affects her choices. Then, using an observable outcome of those choices, one can identify heterogeneity from risk. The main difference is that in our case the observable is not the individual's education level but her consumption choice. The fact that both ‘instruments’ yield similar conclusions about the sources of inequality provides additional support for our interpretation.

Earlier investigations of the sources of increase in income inequality have followed either of two alternative approaches. Carroll (1992), Gottschalk and Moffitt (1994) and Moffitt and Gottschalk, 1995, Moffitt and Gottschalk, 2002 use only data on income, thus avoiding having to model consumer behavior and arguing that the autocovariance structure of income growth is informative about the relative importance of permanent and transitory shocks. In particular, Gottschalk and Moffitt (1994) exploit the long panel dimension of the Michigan PSID. They emphasizes the contribution of transitory inequality, but nevertheless conclude that approximately two-thirds of the increase in inequality between the 1970–1978 and 1979–1987 periods was due to permanent shocks and only one-third to transitory shocks. Moreover, Moffitt and Gottschalk (2002) find that transitory shocks contributed negatively to the overall evolution of income inequality in the 1990s.

On the other hand, Blundell and Preston (1998) investigate a similar issue using consumption data and a simple model of consumption behavior. Their identifying assumption is the permanent income hypothesis (PIH) in its pure form, which implies that consumption responds to permanent but not to transitory shocks to income. Since consumption inequality did not increase (much) over the sample period, Blundell and Preston conclude that the increase in income inequality must have been mainly due to transitory shocks.

In this paper, we use the information in both the autocovariance structure of income and the comovement between consumption and income inequality. As documented by Gottschalk and Moffitt on the one hand and Blundell and Preston on the other, these two pieces of information seem to contradict each other.2 In order to reconcile them, we need to allow for income shocks that are permanent, but are not transmitted to changes in consumption. Predictable permanent changes in income, capturing heterogeneity in life-cycle profiles, deliver this property.

The paper most closely related to ours is Pistaferri et al. (forthcoming), who use individual income and consumption data to estimate the extent to which households are able to insure against income shocks. Pistaferri et al. (forthcoming) use income data from the PSID and adopt an imputation procedure to construct a measure of total non-durable consumption for households in the PSID, given food expenditure data and a demand function for food, estimated from the CEX. One advantage of our approach is that we measure consumption and income for the same household and do not need to worry about potential weaknesses of the imputation procedure. Consistent with our estimates, Pistaferri et al. (forthcoming) find that consumption is insulated from most income shocks, but they interpret this result as evidence for a substantial degree of risk sharing. We show that heterogeneity can explain the same patterns in the data as partial risk sharing and argue in favor of the former interpretation.

In this respect, our paper is related to the work of Guvenen, 2005, Guvenen, 2007, who shows that heterogeneity in income profiles accounts for a large part of the increase in income inequality for a given cohort with age. The predictable and unpredictable shocks in Guvenen's work have different statistical properties, which allows for their identification using income data only. In this paper, identification relies on the comovement of consumption with income. It is therefore reassuring that our results are broadly consistent.

This paper is organized as follows. In the next section, we describe the structure we impose on the stochastic process for income. We also set out a simple model of consumption and discuss how this model can be used to decompose income changes into predictable life-cycle shocks and permanent and transitory income risk. Section 3 describes the dataset and discusses the evolution of income and consumption inequality in the raw data. In Section 4, we discuss how we use the information in these data to estimate our model and describe the estimation procedure. Finally, in Section 5 we provide some evidence that the estimated model gives an accurate description of the joint evolution of income and consumption inequality and present our results. Section 6 concludes.

Section snippets

Model

In this section, we discuss the model that we employ to relate the evolution of income and consumption inequality to income risk. Consider a stochastic process for log income yit of an individual consumer i of age a at time t, where we omit the cohort index a for simplicity. Income consists of a permanent and a transitory component and is subject to three types of shocks,yit=yitp+uityitp=yit-1p+vit+αitwhere uit is a transitory shock and vit and αit are permanent shocks. The shocks uit and vit

Data

For our empirical analysis, we use data on US household income and consumption from the CEX (US Department of Labor, Bureau of Labor Statistics, 1999). This survey is conducted on an annual basis from 1980. Notice that although the CEX data on income are not of the best quality, the CEX is the only US dataset that has acceptable consumption as well as income data for the same individuals.6

Empirical approach

The raw data are very noisy due to the relatively small number of households in a cohort-year cell. In this section, we discuss our estimation procedure, which is designed to extract slow moving trends from these noisy data. First, we present a set of moment conditions that represent the information available in the data. Then, we discuss a likelihood based, Bayesian procedure that treats the time-varying variances of the idiosyncratic shocks as unobservable components. Because this procedure

Results

Fig. 4 plots the actual data (thin solid line) and the fitted values of our model (thick solid line) for the evolution of inequality over the sample period. The upper panel displays income inequality, the lower panel consumption inequality. The model captures the overall trend in both income and consumption inequality very well, as well as some of the high frequency fluctuations in the data. The random walk assumption on the law of motions for the time-varying variances imposes some smoothness

Conclusions

In this paper, we used repeated cross-section data on income and consumption from the CEX to evaluate the nature of the increase in income inequality in the US over the last two decades. The stochastic process for income that we assume includes predictable life-cycle changes and unexpected permanent and transitory shocks. We estimate the contribution of each of these three shocks to total inequality. The model fits the joint evolution of income and consumption inequality well. Almost all of the

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    This paper was prepared for the April 2008 Carnegie-Rochester Conference on Public Policy. We are grateful to Pierre-Olivier Gourinchas and Jonathan Parker for many helpful discussions and to Richard Blundell, Chris Carroll, Guido Lorenzoni, Alberto Martin, Claudio Michelacci, Josep Pijoan-Mas, Chris Telmer, our discussants Miklós Koren, Michele Pellizzari and especially Jonathan Heathcote, and the editor Mark Bils for helpful suggestions. Thijs van Rens gratefully acknowledges financial support from the Spanish Ministry of Education and Science (Grants Juán de la Cierva, SEJ2005-01124 and SEJ2006-02235); the Generalitat de Catalunya, DURSI (Grants Beatriu de Pinós and 2005SGR00490) and the Barcelona GSE Research Network.

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