The welfare cost of business cycles revisited: Finite lives and cyclical variation in idiosyncratic risk
Introduction
The notion that an important macroeconomic policy objective should be the mitigation of business cycles is a familiar one, both in academic and non-academic circles. In his influential monograph, Lucas (1987) challenged this orthodoxy by demonstrating, in a representative agent environment, that the welfare gains associated with eliminating variation in aggregate consumption are miniscule. Subsequent work has challenged Lucas’ finding on a number of grounds, ranging from statistical assumptions regarding aggregate consumption, to assumptions about preferences, to the basic assumptions underlying the representative agent paradigm. Our paper follows along this latter tack. The main idea is that there are important distributional effects associated with aggregate variation and that these distributional effects lie at the heart of why individuals care about business cycles. The primary effects we focus on are cyclicality in the cross-sectional variance of idiosyncratic risk – the idea that individual-specific shocks become more volatile during aggregate downturns – and how this interacts with life-cycle consumption and savings decisions. What we mean by a ‘business cycle’, therefore, goes beyond aggregate productivity shocks to include shocks to the cross-sectional distribution.
We find large welfare gains from eliminating business cycles – approximately an order of magnitude larger than what Lucas (1987) found. About a half of the overall welfare gain is attributable to how much agents value the removal of countercyclical heteroskedasticity in the idiosyncratic shocks they face. The remainder is due to the removal of aggregate productivity shocks. The costs associated with these shocks are significantly amplified by the presence of the cyclical variation in idiosyncratic shocks and rise non-linearly with risk aversion.
The specifics of our analysis are as follows. We begin by providing evidence that the focal point of our study – persistent idiosyncratic risk in the labor market, distinguished by countercyclical heteroskedasticity – is a robust feature of U.S. data. Borrowing from previous work, we provide both qualitative evidence as well as quantitative estimates of a specific time-series process. Next, we embed these estimates in an overlapping generations (OLG) model in which agents face both aggregate and idiosyncratic sources of uncertainty. The latter arises in the form of persistent shocks to individual labor market productivity. The model's financial market structure, in conjunction with the stochastic process for idiosyncratic shocks and the fact that lives are finite, limits the extent to which agents can collectively pool idiosyncratic risk. As a result, the cyclical component in each individual's earnings process – an increase in volatility during aggregate downturns – is manifested in their consumption process, thereby leading to potential welfare benefits associated with the elimination of business cycles.
The methodology with which we measure welfare effects, and the quantitative results we find, are as follows. Our welfare calculations explicitly incorporate the transition from a world with business cycles to a world without business cycles. Such calculations are important because they ensure that the welfare results are not driven by the new economy's lower-steady-state level of capital stock. Our baseline model is an economy with both aggregate productivity shocks as well cyclical variation in the variance of idiosyncratic shocks. To begin with we eliminate only the aggregate productivity shocks. The welfare effects of doing so are large, being equivalent to a 1.44% increase in an agent's consumption. Next, we eliminate the variation in the variance of the idiosyncratic shocks, reformulating the process so that it has the same unconditional variance as in our baseline economy. The welfare costs in this case are also large, especially in light of previous work. We find that an unborn agent is better off by 5.09% and that, on average, the population is better off by 1.03%. Finally, we ask to what extent ‘general equilibrium effects’ – changes in market clearing prices due to changes in aggregate savings – are the driving force. By conducting experiments in which prices are not allowed to change we conclude that the bulk of our results are not attributable to these general equilibrium effects.
Two channels are the key for the sizable welfare gains we find. First, idiosyncratic earnings shocks and aggregate productivity shocks interact in a way that amplifies the costs associated with cyclical variation in idiosyncratic risks. Experiencing larger idiosyncratic risks during downturns in aggregate productivity – a key feature of our economy – is effectively much more costly than experiencing the same cyclical variability in idiosyncratic risks absent any aggregate productivity shocks. Thus the welfare benefits of removing aggregate shocks are larger than the sum of the welfare gains of removing aggregate fluctuations in an economy without idiosyncratic shocks plus the welfare gains of removing the cyclical variation in idiosyncratic shocks in an economy without aggregate productivity shocks. This feature of our economy – ‘when it rains it pours’ – captures the notion that agents who already face larger idiosyncratic risks during downturns really dislike having things magnified by a decline in aggregate output.
The second channel is due to the stochastic properties of the regime shifting process for idiosyncratic shocks. Our estimates for the magnitude for the increase in idiosyncratic risk during downturns are quite large and imply an unconditional distribution of idiosyncratic shocks that is leptokurtic (i.e., the regime shifting nature of the conditional distribution leads to a fat-tailed unconditional distribution). Because agents in our economy dislike kurtosis, and because the elimination of business cycles leads to normally distributed idiosyncratic shocks, this represents an avenue for welfare gains. Finally, it is important to note that, in contrast to Lucas's welfare measure which rises linearly in agents’ risk aversion, both of the channels described above depend in a highly non-linear fashion on risk aversion, thereby generating quite large welfare gains even for moderate levels of risk aversion.
Our study follows a long line of papers on the welfare costs of business cycles. Most closely related are studies which focus on the interaction between business cycles, heterogeneous agents and uninsurable labor market risk, including Atkeson and Phelan (1994), Beaudry and Pages (1999), İmrohoroğlu (1989), and Krusell and Smith (1999). What distinguishes us is an OLG framework and the way in which we model and calibrate the process which drives heterogeneity. We focus on earnings as opposed to unemployment, and calibrate our model using microeconomic data from the Panel Study on Income Dynamics (PSID). The latter leads to substantially more volatile and persistent idiosyncratic shocks with a greater dependence on aggregate variation. Finally, our approach is similar in spirit to İmrohoroğlu (1989), but departs from the approach of Atkeson and Phelan (1994) and Krusell and Smith (1999), who assume that the cyclical distribution of idiosyncratic risk is impervious to changes in the aggregate technological process. The dependence between aggregate and idiosyncratic shocks in our framework leads to the distinct result that the welfare gains we identify are due to the elimination of both of these shocks.
The paper continues as follows. In Section 2 we present empirical evidence on idiosyncratic risks and how it varies over business cycles. Section 3 presents our model and Section 4 describes our calibration strategy. Section 5 presents quantitative results and Section 6 provides some concluding remarks.
Section snippets
Evidence
Our question is inherently one about how income and consumption variation across households is related to aggregate, time-series variation. In order for this question to have empirical content, we require that the cross-sectional distribution of labor income exhibit the following three properties. First, there must be an interesting cross-sectional distribution to begin with. In our framework this translates to the requirement that individual-specific income must contain an idiosyncratic
Theory
We now embed the evidence of the previous section into a stationary overlapping generations (OLG) model. The motivation for a life-cycle framework arises from previous work where we have argued that finite lives and a life-cycle pattern in idiosyncratic risk are important for understanding the mapping between income and consumption. The main idea is that the infinite horizon abstraction affords theoretical agents far greater ability to use financial markets to self-insure against idiosyncratic
Calibration
We interpret one period in our model as corresponding to 1 year of calendar time. The aggregate production technology is Cobb–Douglas:We set θ equal to 0.4 (which corresponds to capital's share of national income being 40%, cf. Cooley and Prescott (1995)) and allow for a 7.8% annual depreciation rate on the aggregate capital stock. The average growth rate in GNP per capita is chosen to be . The technology shocks, Z, follow a first-order Markov chain with parameter values
Quantitative results
We start by describing the basic features of our baseline economy. We then describe how we compute welfare gains: ‘How much will individuals be willing to pay in order to move to an alternative economy?’ Finally, we describe our welfare results as well as various experiments designed to isolate some of the economics underlying our results.
Our baseline economy is broadly consistent with several key features of the aggregate U.S. economy. Consumption is roughly 70% of the magnitude of output
Conclusions
Our main finding is that agents value the elimination of business cycles by a significant amount. The primary forces driving these welfare gains are (i) the direct elimination of aggregate productivity shocks and the way in which these shocks interact with variation in the variance of idiosyncratic shocks, and (ii) the elimination of cyclical fluctuations in the distribution of idiosyncratic risk. Both of these channels are different than alternative explanations put forth in the literature. In
Acknowledgements
For helpful discussions we thank Marianne Baxter, Michael Brandt, Chris Geczy, Joao Gomes, Per Krusell, José Victor Rı́os-Rull, Tony Smith, Stan Zin and especially Rao Aiyagari who originally suggested using our framework to assess the welfare costs of business cycles. This work has benefited from the support of NSF grant SES-9987602 and the Rodney White Center at Wharton.
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