DSGE Models for Monetary Policy Analysis

This 2011 Handbook of Monetary Economics chapter by Lawrence Christiano, Mathias Trabandt, and Karl Walentin is a selective survey and original empirical estimation of medium-scale New Keynesian (NK) DSGE models for monetary policy analysis. The chapter first works through a simple NK model modified in two ways relative to the textbook Calvo-pricing setup of Clarida-Gali-Gertler and Woodford: a “working capital channel,” in which firms must borrow to finance a share ψ of their wage and materials bill, so that a rise in the nominal interest rate directly raises marginal cost and enters the Phillips curve; and a “materials inputs” channel (following Basu 1995), in which a share (1-γ) of intermediate-good production is materials rather than labor, so the aggregate price index itself becomes a cost input. Using this modified model, the chapter shows that when the working capital channel is strong and the materials share is realistic, the Taylor principle (raising the policy rate more than one-for-one with expected inflation) can become a source of equilibrium indeterminacy rather than a guarantee of stability, because a rate hike itself raises firms’ financing costs and can validate the higher inflation expectations that provoked it. Further simple-model sections examine an unemployment extension (Christiano-Trabandt-Walentin 2010a) in which unemployment carries information about the output gap and can be used to estimate the gap as a latent variable, and examine conditions under which the HP filter is (or is not) a good estimator of the model-implied output gap, concluding this depends sensitively on model details. The chapter’s central empirical contribution is a two-step Bayesian impulse-response-matching estimation of a medium-sized DSGE model on quarterly US data, 1951:Q1-2008:Q4: a 14-variable VAR is used to estimate impulse responses of nine macro variables to a monetary policy shock (identified by a contemporaneous-only restriction on the federal funds rate), a neutral technology shock, and an investment-specific technology shock (both identified by long-run restrictions), yielding 397 stacked responses; DSGE structural parameters are then chosen via a Bayesian procedure (random-walk Metropolis, 600,000 draws, 100,000 burn-in, 27% acceptance rate) to match those VAR responses using a Newey-West-corrected, bootstrap-estimated weighting matrix (10,000 bootstrap draws). The posterior estimates imply moderate price stickiness (Calvo parameter 0.62, implying reoptimization roughly every three quarters), substantial interest-rate smoothing (0.87), a Taylor inflation coefficient of 1.43, high habit persistence in consumption (0.77), and a very high implied labor supply elasticity (about 8) that the authors interpret under an “indivisible labor” reading rather than a representative-agent one. At the posterior mean, the model reproduces the empirically observed slow, hump-shaped, roughly two-year-peak inflation response to a monetary policy shock, plus an initial “price puzzle,” using only modest price and wage stickiness — a resolution the authors attribute to the working capital channel plus the elimination (relative to Altig-Christiano-Eichenbaum-Linde 2005) of full lagged-inflation price indexation, which simultaneously lets the model match the rapid inflation decline following a technology shock. The chapter reports the VAR-based responses are reasonably robust to varying the estimation window (1951:Q1 through starts as late as 1985:Q4) and the lag length (1 to 5 lags), and that a Laplace approximation to the posterior closely matches the full Metropolis-Hastings estimates. It closes by flagging open issues: the model understates the rise in capacity utilization after a monetary shock, the underlying Euler equation faces the classic Hansen-Singleton statistical rejection even though the impulse-response-matching exercise fits well, and the survey does not cover financial frictions or open-economy extensions in detail.

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DSGE Models for Monetary Policy Analysis