This comment addresses a point raised in Russell Cooper and Jonathan Willis (2003, 2004), which discusses whether the “gap approach” is appropriate to describe the adjustment of production factors. They show that this approach to labor adjustment as applied in Ricardo J. Caballero, Eduardo Engel, and John C. Haltiwanger (1997) and Caballero and Engel (1993) can falsely generate evidence in favor of nonconvex adjustment costs, even if costs are quadratic. Simulating a dynamic model of firm-level employment decisions with quadratic adjustment costs and estimating a gap model from the simulated data, they identify two factors producing this spurious evidence: approximating dynamic adjustment targets by static ones, and estimating the static targets themselves. This comment reassesses whether the first factor indeed leads to spurious evidence in favor of fixed adjustment costs. We show that the numerical approximation of the productivity process is pivotal for Cooper and Willis's finding. With more precise approximations of the productivity process, it becomes rare to falsely reject the quadratic adjustment cost model due to the approximation of dynamic targets by static ones.

The cross-sectional dispersion of firm-level investment rates is procyclical. This makes investment rates different from productivity, output, and employment growth, which have countercyclical dispersions. A calibrated heterogeneous-firm business cycle model with nonconvex capital adjustment costs and countercyclical dispersion of firm-level productivity shocks replicates these facts and produces a correlation between investment dispersion and aggregate output of 0.53, close to 0.45 in the data. We find that small shocks to the dispersion of productivity, which in the model constitutes firm risk, suffice to generate the mildly procyclical investment dispersion in the data but do not produce serious business cycles.

We show how a heterogeneous agent New Keynesian (HANK) model with incomplete markets and portfolio choice can be estimated in state space using a Bayesian approach. To render estimation feasible, the structure of the economy can be exploited and the dimensionality of the model automatically reduced based on the Bayesian priors. We apply this approach to analyze how much inequality matters for the business cycle and vice versa. Even when the model is estimated on aggregate data alone and with a set of shocks and frictions designed to match aggregate data, it broadly reproduces observed US inequality dynamics.