Macroeconomic Fluctuations with HANK & SAM: an Analytical Approach

This is a HANK model built to be solved on paper rather than on a computer. The motivation is stated as a gap in the literature: HANK models “have had a considerable impact on macroeconomics,” but “due to the complexity of such models, the literature has focused on numerically solved models and therefore little is known about their general properties.” The construction grafts Diamond-Mortensen-Pissarides search and matching frictions onto a monopolistically competitive economy with Rotemberg price adjustment costs, so that job prospects are uncertain and households can only self-insure. Tractability comes from three assumptions — no shorting equity and borrowing only by the employed, heterogeneity in both labour productivity and equity access, and exactly two household types — which together imply that “firms are owned by capitalists who drop out of bond and labor markets, while workers hold no equity and are either employed or unemployed,” everyone consumes their income period by period, and the real interest rate satisfies the employed workers’ Euler equation. The result is an economy with “inequality in outcomes but the wealth distribution is degenerate,” which is what makes it analytically solvable. The new object is an endogenous earnings risk wedge in the employed workers’ Euler equation, pinned down by labour market tightness because tightness determines both transition rates and wages. Because those two forces oppose each other — a tighter market means less unemployment risk but a larger income loss if the job is lost — the wedge can be countercyclical or procyclical, and every result turns on which. The authors argue countercyclicality is empirically plausible on three grounds: Storesletten, Telmer and Yaron’s finding that idiosyncratic risk is strongly countercyclical, Guvenen, Ozkan and Song’s finding that it comes from increased left-skewness in recessions rather than countercyclical variance, and a direct evaluation of the wedge using a 25.2 percent monthly job finding rate and 2 percent monthly job loss rate from CPS data (January 1990 to August 2019), a 20 percent consumption drop on job loss following Karabarbounis and Chodorow-Reich, and a wage semi-elasticity of −0.16 for job stayers from Gertler, Huckfeldt and Trigari. On that evaluation “the countercyclical effect of unemployment risk clearly dominates,” failing only when a 5 percent consumption drop is combined with a wage elasticity of −1.5. Four results follow. The economy may have three steady states rather than two, including an unemployment trap with a zero job finding rate and inflation between the intended steady state’s and the liquidity trap’s, which “cannot exist if prices are flexible, if markets are complete, or, if prices are sticky, when the endogenous earnings risk is either acyclical or procyclical.” The Taylor principle no longer suffices for local determinacy of the intended steady state, because “expectations of higher inflation may be self-fulfilling even if the central bank were to stabilize the direct impact of inflation on the real interest rate since demand (and thus inflation) is also stimulated by a decline in unemployment risk.” Nominal rigidities and market incompleteness become complements, so stickier prices can amplify productivity shocks and positive productivity shocks can be inflationary — which the authors support with a local projection of CPI inflation on Fernald TFP growth from 1980, where “higher TFP either leaves inflation unchanged or gives rise to higher inflation.” And the long-run real interest rate depends on policy parameters, while a liquidity trap need not be deflationary. The scope condition is theirs: “while our analysis rests on the analytical convenience produced by the simplifying assumptions that we make, we believe that the insights are general and apply to models with a non-degenerate wealth distribution and with more complicated asset structures” — a belief, supported by a numerical extension with capital accumulation, not a demonstration.

Vincent Sterk | Macro Paper Warehouse

Macroeconomic Fluctuations with HANK & SAM: an Analytical Approach