Macroeconomics and Household Heterogeneity

Households at the bottom of the 2006 wealth distribution cut their consumption growth far more sharply between 2006 and 2010 than their (comparatively modest) income slowdown would predict, and this behavior is not simple hand-to-mouth consumption but an increase in saving. In 2006, the bottom two net-worth quintiles held essentially no wealth yet accounted for “11.3% + 12.4% = 23.7% of total consumption expenditures” (Section 2.2, p. 10). Decomposing the change in consumption growth into an income-growth term and an expenditure-rate term, the authors find that overall “households reduce their expenditure growth significantly more than the slowdown in their disposable income alone would suggest (-6.9% v/s -2.9%),” and for the bottom wealth quintile specifically, the rise in the saving rate accounts for “over two-thirds (69%) of the consumption growth decline” (Section 2.3, p. 13). This, they argue, “suggests that the decline in consumption at the bottom of the wealth distribution is not simply explained by standard hand-to-mouth behavior…but primarily by changes in consumption behavior through a decline in expenditure rates” (p. 13).

The benchmark model is a real business cycle economy with aggregate technology shocks, in which households face idiosyncratic unemployment and (conditional on employment) persistent labor-productivity risk, save in a single, non-negative asset, and are additionally heterogeneous in a fixed time-discount factor; it also includes a simple two-stage life cycle (working and retired) with social security, and a government-run unemployment insurance system with a replacement rate calibrated to U.S. data (Section 3, pp. 14-19). Relative to the original Krusell-Smith economy – which has homogeneous discounting, no life cycle, and only a token unemployment insurance system (ρ = 1%) – the benchmark adds preference heterogeneity and a substantially more generous UI system (ρ = 50%) specifically because “as documented above, [it] provides a model wealth distribution that matches its empirical counterpart very well” (Section 6.1, p. 41).

The original KS model cannot match the empirical wealth distribution at either end: “the very wealthy are not nearly wealthy enough, and the poor hold far too much wealth relative to the data” (Introduction, p. 3). Because it is specifically the discrepancy at the bottom of the distribution that matters, the KS economy places “almost no mass on households with very little net worth, exactly the households with the largest consumption declines” (Section 6.2, p. 44), so that even though individual consumption drops for a given wealth level are larger in the KS economy than in the benchmark, the aggregate consumption response ends up smaller. As a result, the authors show, “the aggregate consumption and investment behavior over the business cycle in the KS economy approximates an economy with representative agents (RA) very well” (Section 6.1, p. 41) – the KS consumption decline of 1.9% for a one-time shock compares to 1.78% in a matched representative-agent economy.

Highly persistent idiosyncratic earnings shocks and preference heterogeneity are the two ingredients that matter most, while adding the life-cycle structure alone has only a modest effect on the aggregate consumption response. Adding persistent income risk on top of unemployment risk “significantly amplifies the aggregate consumption response above that of the original KS model,” in fact generating a larger response than the full benchmark (Section 6.2, p. 45). Preference heterogeneity is separately important because it creates “a share of highly impatient households at the bottom of the wealth distribution” who consume at a high rate and hold little wealth in normal times, and who, facing a persistent recession, “start to save more for precautionary reasons” once unemployment risk rises for the “foreseeable future” (Section 6.2, p. 48). The authors also show, using a variant with only 1% of the population holding a distinct discount factor, that it is “the lack of wealth at the bottom, as opposed to significant concentration at the very top, that is crucial for explaining aggregate consumption dynamics” (Section 6.2, p. 50).

The authors directly compare the benchmark economy to a version in which the bottom 40% of the wealth distribution mechanically consumes its current income and unemployment benefits every period, finding the mechanical hand-to-mouth model generates a smaller aggregate consumption decline (2% versus 2.4% in the benchmark for a one-period recession) (Section 6.2.1, pp. 50-51). The gap arises because in the benchmark, “households at the bottom of the wealth distribution on average (and especially those not currently unemployed) find it optimal to reduce consumption rates for precautionary reasons,” anticipating a long recession and building a buffer against future job loss – a response “absent among households that follow a mechanical hand-to-mouth consumption rule” (p. 51). This gap widens further under less generous unemployment insurance, since the precautionary motive becomes stronger as UI becomes less generous (Section 6.3.1, p. 57).

More generous unemployment insurance both changes households’ consumption response to a given wealth level and reshapes the equilibrium wealth distribution itself, and these two channels pull in opposite directions for the aggregate consumption response. Holding the pre-recession wealth distribution fixed, cutting the UI replacement rate from 50% to 10% roughly doubles the aggregate consumption decline (from 2.4% to 4.6%), driven overwhelmingly by the small group of newly and already unemployed households, who make up 8.4% of the population but 17.6%-24.3% of the consumption drop depending on the UI regime (Section 6.3, pp. 52-55). But because generous UI also reduces households’ incentive to accumulate precautionary buffers, it leaves “a sizeable mass of households [with] little or no wealth” in the long-run ergodic distribution; when the wealth distribution is allowed to adjust endogenously to lower UI, “the endogenous shift in the wealth distribution to the right…partially offsets the larger individual consumption declines in the no-benefits economy,” so the two economies’ aggregate consumption responses end up “broadly consistent” (2.7% versus 2.4%) even though the underlying group-level dynamics differ starkly (Section 6.3, p. 56).

Only once output is allowed to be partially demand-determined, via an aggregate-demand externality in which total factor productivity depends positively on aggregate consumption (Z = ZC^ω with ω > 0), does the wealth distribution affect the size of the output decline itself rather than merely how the same output decline splits between consumption and investment* (Section 7, pp. 58-60). In the baseline model (ω = 0), capital is predetermined in the short run so wealth inequality reallocates the output decline between consumption and investment but barely changes output; with the demand externality (ω = 0.3) calibrated so that the externality economy matches the benchmark’s output volatility, the benchmark (high-inequality) economy generates a larger output decline than the KS (low-inequality) economy with the same exogenous TFP process – 5.0% versus 4.8% on impact, and 8.8% versus 8.0% at the end of a typical severe recession (Section 7.2.2, Table 15, p. 63).

Because a fall in aggregate consumption now feeds back into lower total factor productivity and thus lower output, a social insurance program that stabilizes the consumption of adversely affected households “might not only be beneficial in providing public insurance, but can also serve a potentially positive role for stabilizing aggregate output” (Section 7, p. 59). Quantitatively, the authors find that “the output decline with an unemployment insurance benefit replacement rate of 50% to a Great Recession-like shock is 1 percentage point smaller on impact than in an economy with a replacement rate of 10%” (Introduction, p. 4), and this stabilizing effect is described as “quite persistent” because of the added endogenous persistence the demand externality introduces into the model (Section 7.2.3, p. 60).

The model captures several qualitative features well but has notable quantitative shortcomings, especially in matching expenditure rates. On the positive side, the model reproduces the positive correlation of net worth with earnings, income, and consumption, and it generates a bottom-two-wealth-quintile consumption share of 17.9% against 23.7% in the data (Section 5, p. 33). However, the wealth-poor consume too little in the model relative to the data, and the wealth-rich (top quintile) consume too much – 42% of the model’s aggregate consumption against 37.2% in the data – so that “the correlation between net worth and consumption expenditures is positive in the model, as it is in the data, but is much larger than it is in the PSID” (Section 5.2, p. 33). The retirement/life-cycle structure is “absolutely crucial” for this result: without it, expenditure rates average roughly 100% across wealth quintiles and are counterfactually U-shaped in net worth (p. 33). The model also understates the observed decline in expenditure rates during the actual Great Recession, generating rising rather than falling consumption rates for most wealth groups in the downturn (Section 5.3.2, p. 37).

A substantial share of the aggregate consumption decline comes from households who have not (yet) lost their jobs but cut consumption anyway because future unemployment risk has risen. Comparing the low- and high-UI economies holding the wealth distribution fixed, the authors find that employed households – who make up 91.6% of the population – “cut their consumption much more significantly in the (surprise) low-benefit economy” even though “these groups in both economies start with the same wealth distribution…and experience the same income loss coming from a modest decline in aggregate wages” (Section 6.3, p. 55). The explanation is that “future unemployment risk has gone up for these households as the economy falls into the highly persistent recession, and the potential future income losses from unemployment are larger in the economy with low unemployment insurance,” so this group’s extra saving is “an important contributor to the overall larger decline of aggregate consumption in the low UI economy” (p. 55).

The chapter’s conclusion names three extensions: richer dimensions of household heterogeneity to better match the joint distribution of wealth, income and expenditure; a richer labor market with elastic labor supply and other frictions, to better link consumption and output dynamics (which the current model connects only “in a very reduced form way”); and the explicit introduction of aggregate financial shocks to household net worth, since the current one-asset model cannot capture “large changes in the net worth of households” that the PSID data show occurred during the Great Recession (Section 8, “Conclusion,” pp. 67-68). More broadly, the authors describe the confluence of “new rich household and firm-level data sets” with “continuous theoretical and computational advances” as making quantitative heterogeneous-agent macroeconomics “an exciting area for future inquiry” (p. 68).