Firm-specific capital, nominal rigidities and the business cycle

Macroeconomic data show inertial inflation, and the standard way of accounting for it inside New Keynesian models is to assume firms re-optimise prices only once every six quarters or, without indexation to lagged inflation, once every two years or more – an assumption that clashes directly with micro evidence that firms change prices more often than once every two quarters. This paper formulates and estimates a three-shock US business cycle model that reproduces inflation inertia while firms re-optimise prices on average once every 1.8 quarters, and traces the difference to a single modelling assumption: capital is firm-specific rather than homogeneous and traded in economy-wide rental markets. With a predetermined firm-level capital stock, a firm’s short-run marginal cost curve slopes up in its own output, so a contemplated price rise – which cuts the firm’s demand and output – also cuts its marginal cost, working against the price rise. The authors work with two versions of the Christiano-Eichenbaum-Evans (2005) model that differ only in this respect, and show that the log-linearised equilibrium equations differ only in the mapping from structural parameters to the reduced-form coefficient linking the change in inflation to average real marginal cost. Parameterised in terms of that coefficient the two models are observationally equivalent for aggregate data, which means macro evidence cannot adjudicate between them and the case must be made on micro implications. Estimation follows the CEE limited-information strategy, matching model impulse responses to those from a ten-variable identified VAR on quarterly US data for 1982:1-2008:3, with long-run restrictions identifying neutral and capital-embodied technology shocks and a recursive-timing restriction identifying the monetary policy shock; the three shocks together account for roughly 60 percent of the cyclical variance of aggregate output, with capital-embodied technology the largest single contributor and, notably, about 30 percent of the cyclical variation in the real wage. The point estimate of the inflation-marginal cost coefficient is 0.014, implying that a temporary one percent change in marginal cost moves the aggregate price level by only about 0.02 percent; under homogeneous capital this implies price re-optimisation once every 9.36 quarters, while under firm-specific capital it implies once every 1.8 quarters. Wage contracts are re-optimised on average once every 4.5 quarters, the habit parameter is 0.76, and the estimated cost of varying capital utilisation is higher than in CEE. The decisive micro comparison concerns the cross-firm distribution of production after a monetary policy shock: under homogeneous capital roughly 70 percent of firms produce essentially all of the economy’s output four periods after the shock while the rest effectively shut down, an implication the firm-specific capital model does not share. The authors conclude they “strongly prefer the firm-specific capital model,” while leaving open that other propagation mechanisms – firm-specific labour, sectoral heterogeneity in price-change frequency, intermediate inputs, rational inattention and sticky information – “may be at least as important.”

David Altig | Macro Paper Warehouse

Firm-specific capital, nominal rigidities and the business cycle