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.

On DSGE Models

This 2018 Journal of Economic Perspectives essay by Lawrence Christiano, Martin Eichenbaum, and Mathias Trabandt is a perspective/survey defense of dynamic stochastic general equilibrium (DSGE) modeling rather than an empirical study: it traces how the DSGE research program evolved from real business cycle (RBC) models through New Keynesian DSGE to post-crisis models with financial frictions, argues that the transparency of these models’ microfoundations is a virtue because it exposes suspicious assumptions to scrutiny against micro data, explains why the pre-crisis vintage of these models failed to predict the 2008 financial crisis, and closes with a point-by-point rebuttal of Joseph Stiglitz’s (2017) critique of the DSGE program. The authors argue RBC models (Kydland-Prescott 1982; Long-Plosser 1983) “crumbled” under three forces – micro evidence against frictionless labor markets, failure to match aggregate facts such as hours volatility and the equity premium, and the absence of any role for money – and that the New Keynesian DSGE models that followed can reproduce the hump-shaped consumption, investment, and output responses to a monetary policy shock (estimated under recursive/Cholesky identification on US data, 1951Q1-2008Q4, a pattern the authors report as robust across lag lengths of one to five quarters and multiple sample start dates) only by combining habit formation in consumption, investment adjustment costs, and Calvo (1983) nominal price/wage rigidities with features that keep marginal cost nearly acyclical. In the Christiano-Eichenbaum-Trabandt (2016) Bayesian re-estimation of the Christiano-Eichenbaum-Evans (2005) model that the essay treats as its illustrative case, the posterior mode implies firms reprice roughly once every 2.3 quarters, households reset wages about once a year, the habit-formation coefficient is 0.75, and the elasticity of investment to a one percent temporary rise in the price of installed capital is 0.16, with the fit to the hump-shaped facts depending critically on sticky nominal wages – a flexible-wage counterfactual “deteriorates drastically.” On the crisis, the authors concede that DSGE models’ failure to signal the buildup of shadow-banking vulnerability “is correct” as a criticism, but frame it as a failure of the broader economics profession rather than something specific to DSGE, and defend the relative absence of large financial frictions in pre-crisis models by noting that postwar US recessions were not historically tied to financial disturbances and that the financial accelerator mechanism (Bernanke-Gertler-Gilchrist 1999) that some models did include had only “a modest quantitative effect” on estimated dynamics. The essay then surveys post-crisis extensions – rollover-crisis and fire-sale models of financial intermediaries (Gertler-Kiyotaki), risk-shock models in which time-varying cross-sectional dispersion of firm returns (Christiano-Motto-Rostagno 2014) is reported to account for about 60 percent of the variance of US business cycles versus roughly 13 percent for technology shocks, zero-lower-bound (ZLB) and nonlinear models attributing much of the Great Recession to financial frictions interacting with a binding ZLB, a government-spending multiplier the authors describe as “much larger than one” at the ZLB and “substantially below one” away from it, the “forward guidance puzzle” (standard models make forward guidance implausibly powerful), and heterogeneous-agent (HANK) models – before rebutting Stiglitz (2017) on four specific fronts: that modern DSGE estimation does not rely on HP-filtered data, that pre-crisis DSGE models did incorporate financial frictions, that interest-rate spreads do appear as central endogenous variables in some models, and that household heterogeneity is an active DSGE research frontier (HANK). The authors judge Stiglitz’s criticisms “not informed” while explicitly acknowledging that DSGE models will not reliably predict the next crisis and that the modeling program is “an organic process” of ongoing interaction between data and theory.

Mathias Trabandt | Macro Paper Warehouse

DSGE Models for Monetary Policy Analysis

On DSGE Models