Quantitative Macroeconomics with Heterogeneous Households

The SIM model combines an income fluctuation problem facing individual households with general equilibrium, so that a continuum of agents draw idiosyncratic productivity realizations, choose consumption and saving (and in some versions labor supply) independently, and their aggregated choices determine capital, effective labor, and equilibrium prices (Section 2, pp. 6-8). The model was “a natural starting point for introducing heterogeneity into macroeconomics” because it embeds Friedman’s permanent income hypothesis income-fluctuation problem in a multi-agent general equilibrium setting while fitting naturally with the stochastic growth model that already dominated business cycle theory, the only difference being that shocks hit the individual level rather than (or in addition to) the aggregate level (p. 6). Under conditions ensuring a “monotone mixing condition” for social mobility, the model delivers a unique invariant cross-sectional distribution of income, consumption, and wealth, in contrast to the indeterminate wealth distribution of the complete-markets benchmark (p. 8).

Complete markets are “soundly rejected by the data”: earnings changes pass through to consumption (Attanasio and Davis 1996), and there is empirical consumption mobility that complete markets (with identical preferences) rule out entirely (pp. 3-4). The authors quote Lucas (1992): “If the children of Noah had been able and willing to pool risks, Arrow-Debreu style, among themselves and their descendants, then the vast inequality we see today, within and across societies, would not exist” (p. 3) – a model preserving the initial ranking of individuals forever would badly limit any research program aimed at understanding the dynamics of inequality.

The “model what you can see” approach (the SIM tradition) simply models the actually observed markets, institutions, and borrowing limits, which maps cleanly onto data but leaves open why agents cannot find better ways to insure each other; the “model what you can microfound” approach instead derives the scope for risk sharing endogenously from deep informational or enforcement frictions (pp. 4-5). The microfounded approach is more robust to policy experiments – avoiding a version of the Lucas critique, since public insurance changes are recognized to alter incentives for private insurance (p. 5, citing Attanasio and Ríos-Rull 2000) – but “these models have an important limitation. They often imply substantial state-contingent transfers between agents for which there is no obvious empirical counterpart” (p. 5). The authors note the two approaches can be combined, as in models where the traded-asset menu is exogenous but borrowing costs are endogenously default-determined (p. 5, citing Chatterjee et al. 2007).

The evidence is genuinely split: Keane and Wolpin (1997) attribute 90% of lifetime earnings dispersion to factors predetermined before labor-market entry, while Storesletten et al. (2004a), estimating a fixed effect alongside a persistent shock component from panel data, find fixed effects account for “slightly less than half” of cross-sectional variation in lifetime earnings, with the rest coming from very persistent shocks that cumulate over time (pp. 13-14). Guvenen (forthcoming) argues the two views – a pure permanent-transitory shock process versus ex ante heterogeneous income profiles with less-persistent shocks – are “statistically hard to distinguish” in typical panel data (p. 14). Attempts to use consumption-dispersion evidence to discriminate between the models are complicated because the empirical facts on life-cycle consumption dispersion have themselves shifted across studies (from a “thirty log point increase” in Deaton and Paxson 1994 to “only five log points” in Heathcote et al. 2005) and because insurance in both models is sensitive to seemingly minor assumptions, such as shock persistence (p. 14-15).

Because a foreseen earnings change has very different implications than a true shock, the literature exploits the co-movement of consumption and future income growth: Blundell et al. (forthcoming) find that future earnings growth at date t+k is not significantly correlated with current consumption growth at date t, which is inconsistent with an “advance information” story, though the authors caution that “the large amount of measurement error in the data…makes this a weak test” (p. 16). An alternative strategy exploits survey questions asking households to report a probability distribution over next-year earnings changes (Jappelli and Pistaferri 2000, on Italian data), and a growing literature uses labor supply, consumption, and education choices jointly to separate risk from predictable income change (p. 16). The authors stress that “the issue of predictability versus shocks is intimately linked to the issue of availability of insurance” (p. 16), since what looks uninsured could either be a genuine shock or a foreseen change that simply was not insured.

The review discusses four endogenous channels: labor supply, job search, human capital accumulation, and self-selection into risk-bearing occupations. With flexible labor supply, “uninsurable idiosyncratic risk is transferred from earnings to hourly wages,” and whether flexible hours amplify or dampen earnings volatility depends on whether shocks are mostly permanent (large income effects, dampening) or transitory (small income effects, amplifying) (p. 17). Search-and-matching models such as Postel-Vinay and Turon (2008) show earnings dynamics can look highly persistent even when underlying productivity shocks are uncorrelated over time, “offer[ing] a structural microfoundation for commonly used ARIMA-type processes” (p. 18). In human-capital models such as Huggett et al. (2006), a wage decline can reflect either a shock or a choice to invest in skills, complicating identification of the exogenous shock process (p. 18-19). Finally, agents self-select into riskier income streams – Quadrini (2000) models entrepreneurs choosing riskier but higher-expected-payoff “projects,” and Schulhofer-Wohl (forthcoming) documents that less risk-averse individuals experience wider earnings fluctuations, consistent with preference heterogeneity driving occupational risk-taking (p. 19).

The review highlights health shocks, family shocks, and capital-income risk as increasingly important extensions. Health shocks affect both the budget constraint and the utility function directly – Palumbo (1999) estimates a negative health shock significantly reduces the marginal utility of nonmedical consumption, and Attanasio et al. (2008) find a deterioration from “good” to “bad” self-reported health cuts hourly wages by an average of 15% (p. 20). French and Jones (2004) model medical expenditure shocks as including a “with probability 0.1% per year” catastrophic event exceeding $100,000 in present value (p. 20). Family composition risk – marriage, divorce, births, deaths – is found by Cubeddu and Ríos-Rull (2003) to be “a larger source of precautionary saving than earnings risk” (p. 21). Capital income risk, especially from private equity and housing, “remains relatively underexplored within this class of models” (p. 22), even though private equity risk directly becomes income risk for the self-employed and housing carries a large geographically idiosyncratic component (Davis and Heathcote 2007) that is hard to diversify because rental markets function poorly (p. 22).

The review organizes insurance channels into financial markets, labor supply, the family, and government. Within financial markets, unsecured credit with default (Athreya 2002; Livshits et al. 2007; Chatterjee et al. 2007) lets households make repayment state-contingent, but harsher bankruptcy treatment trades off easier precautionary saving in equilibrium against a lower likelihood that debtors actually exercise the default option, “in the limit, debt is effectively noncontingent” (p. 23-24). Housing offers self-insurance but also hinders early-life-cycle consumption smoothing because of down-payment requirements (p. 24). Within-family insurance – spousal labor-supply adjustment, intergenerational transfers, and the option to live with parents – is empirically important but poorly pinned down because “there is as yet no consensus on what is the right way to model the family” (p. 27); the standard unitary household model is “typically rejected” empirically (p. 27), yet fully dynamic collective models imply perfect ex post risk-sharing within the family that Mazzocco (2007) also rejects. Government insurance operates through social security, unemployment insurance, and especially public education and health care, but Hubbard et al. (1995) show means-tested programs can crowd out private precautionary saving (p. 28).

Krusell and Smith (1997, 1998) solved the problem that market-clearing prices in a heterogeneous-agent economy depend on the entire (infinite-dimensional) cross-sectional distribution by having agents forecast prices using only a small number of moments of that distribution (e.g., its mean), checking that resulting forecast errors are small ex post (p. 31). Their central empirical finding, “approximate aggregation,” is that “in equilibrium all aggregate variables […] can be almost perfectly described as a function of two simple statistics: the mean of the wealth distribution and the aggregate productivity shock,” and simulated aggregate time series from the incomplete-markets economy were “almost indistinguishable” from a representative-agent economy with the same preferences (p. 32). The authors caution this does not mean a representative-agent economy always exists that reproduces the same dynamics: Heathcote’s (2005) tax-timing experiment shows approximate aggregation can hold in the Krusell-Smith sense while still generating large real effects that Ricardian equivalence would rule out in any representative-agent economy (p. 32).

Not automatically: if individual and aggregate risk are independent and aggregate shocks are transitory, idiosyncratic risk turns out to be irrelevant to the welfare cost of aggregate fluctuations under CRRA preferences (Constantinides and Duffie 1996; De Santis 2007) (p. 33). Two modifications do raise the cost above Lucas’s near-zero benchmark: making the variance of persistent idiosyncratic shocks countercyclical, for which Storesletten et al. (2004b) find PSID evidence, and treating both idiosyncratic and aggregate shocks as permanent rather than transitory, under which De Santis (2007) shows aggregate fluctuations become more costly because “lifetime utility declines increasingly quickly” as permanent-shock variance grows (p. 34). Krusell et al. (forthcoming) additionally find this heterogeneity is quantitatively large – “low-wealth agents enjoy a utility gain of up to 4% of lifetime consumption” from eliminating aggregate fluctuations, echoing an earlier finding of large gains for young households in Storesletten et al. (2001) (p. 34).

When idiosyncratic and aggregate risk are independent, individual risk turns out to be irrelevant to the price of aggregate risk (Mankiw 1986; Constantinides and Duffie 1996; Krueger and Lustig 2006), so heterogeneity alone does not resolve Mehra and Prescott’s (1985) puzzle (p. 35-36). Two channels can move the needle: countercyclical idiosyncratic risk raises the equity premium (Mankiw 1986; Storesletten et al. 2007 find individual risk “can account for up to one-quarter of the empirical equity premium”), and concentrating aggregate risk on a minority of stockholders – as in Guvenen’s (2006) model where only 20% of agents hold equity – can account “remarkably well” for the equity premium and related asset-pricing moments, though the concentration this requires “is difficult to detect empirically” (pp. 36-37). The authors’ summary judgment is that “incomplete markets and heterogeneity have significant implications for asset pricing, but…these features alone cannot fully resolve the equity premium puzzle” (p. 37).

The authors argue that future research should move beyond treating aggregate and idiosyncratic risk as merely statistically correlated and instead develop “economic microfoundations relating aggregate and idiosyncratic risk” (Concluding remarks, pp. 38-39). They point to candidate mechanisms – technological change and trade openness potentially raising both average productivity and earnings dispersion simultaneously, asymmetric-information models in which the quality of public versus private signals moves both means and variances, and search-and-matching models in which aggregate productivity shocks generate waves of match creation and destruction – as promising but underdeveloped directions (p. 39). The stated payoff is squarely practical: a deeper theory of this interaction is what would let the field deliver on “the promise held out by Lucas (2003)” of jointly evaluating aggregate stabilization policy and social insurance policy within a single, unified framework (p. 39).