Lawrence J. Christiano | Macro Paper Warehouse

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.

Expectation Traps and Monetary Policy

Embedding the Kydland-Prescott/Barro-Gordon time-inconsistency logic into a standard sticky-price, cash-credit-goods general equilibrium model, this paper shows the resulting model generically has either two Markov equilibria – a high-inflation and a low-inflation one – or none at all, with no trigger strategies (repeated-game punishments) required to sustain the multiplicity. In the model, monopolistically competitive firms produce inefficiently low output; some firms preset prices before the monetary authority chooses the money growth rate, so unanticipated monetary expansion raises output and, because output is inefficiently low to begin with, can raise welfare. Households simultaneously choose, before the money growth rate is set, how much to purchase with previously accumulated cash (costly in forgone interest) versus credit (costly in labor time); realized inflation forces substitution away from cash goods, which lowers welfare. The paper’s key insight is that both sticky-price firms and cash-using households take defensive actions that depend on their expectations of inflation: if either expects high inflation, their optimal defensive response (high preset prices, or lower cash use) lowers the marginal cost to a benevolent monetary authority of actually delivering high inflation, making validation optimal; the reverse defensive choices under low-inflation expectations sustain low inflation instead. The paper proves formally that the model has at least two Markov equilibria whenever it has at least one, labels the resulting persistent multiplicity an “expectation trap,” and shows the two equilibria have starkly different comparative statics: the interest rate’s response to a technology shock switches sign between them, implying the output-interest-rate correlation should be systematically more negative in high-inflation regimes. Examining cross-country and within-country data from the IMF’s International Financial Statistics, the paper finds support for this prediction (correlations of roughly −0.45 versus −0.08 within high-inflation countries’ high- and low-inflation episodes, and −0.33 versus −0.20 across high- and low-inflation countries) as well as for the model’s prediction of higher nominal-variable volatility under high inflation.

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.”

Monetary policy shocks: What have we learned and to what end?

This chapter in the 1999 Handbook of Macroeconomics (Volume 1) by Lawrence Christiano, Martin Eichenbaum, and Charles Evans surveys and unifies the VAR-based literature on identifying monetary policy shocks and tracing their dynamic effects on the U.S. economy, comparing multiple identification schemes within a common recursive framework. Using quarterly U.S. data (1965:Q3-1995:Q2) and three benchmark recursive identification schemes — treating the federal funds rate, nonborrowed reserves, or the ratio of nonborrowed to total reserves as the policy instrument — the authors find a robust set of qualitative facts following a contractionary monetary policy shock: the federal funds rate rises persistently, monetary aggregates decline (some with a delay), the price level responds very little for roughly a year before declining, and real GDP falls in a hump-shaped pattern with its maximal decline about one to one-and-a-half years after the shock. They also document and help resolve the “price puzzle” — the anomalous finding that a contractionary shock appears to raise prices — showing it arises from omitting commodity prices (a leading indicator of inflation available to the Fed) from the policy reaction function’s information set, and that including them typically eliminates the puzzle. Comparing the recursive approach against a fully simultaneous (Sims-Zha) identification and against narrative-based measures of policy shocks (Romer-Romer episodes), the chapter concludes that “qualitative inference about the effects of a monetary policy shock is quite robust to the different shock measures,” even though quantitative estimates — particularly the fraction of output variance attributable to policy shocks (ranging from about 7% to 44% at the 4-to-8-quarter horizon depending on the shock measure) — are considerably more sensitive to the specific identification chosen.

Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy

This 2005 Journal of Political Economy paper by Christiano, Eichenbaum, and Evans (CEE) builds and estimates a general-equilibrium model to answer a specific question: what combination of frictions lets a DSGE model reproduce two features economists had already documented in the data - an inertial response of inflation and a persistent, hump-shaped response of output - after a shock to monetary policy? Rather than picking parameters to match a few moments, CEE identify the monetary policy shock as the seventh element (ordered after prices, output, consumption, investment, the real wage, and labor productivity, but before profits and M2 growth) of the Cholesky-orthogonalized innovations to a nine-variable recursive VAR estimated on quarterly U.S. data from 1965Q3 to 1995Q3, then estimate a subset of the model’s structural parameters by minimum-distance matching of the model’s impulse responses to the first 25 periods of the VAR-implied impulse responses. The model combines Calvo price contracts with lagged-inflation indexation for firms that cannot reoptimize, Calvo wage contracts with analogous lagged-inflation indexation for households, habit formation in consumption, convex costs of adjusting the flow of investment, variable capital utilization, and a working-capital channel through which firms borrow to finance their wage bill in advance, so that the nominal interest rate enters marginal cost directly. The estimated benchmark model puts the average price contract at about 2.5 quarters (Calvo parameter 0.60) and the average wage contract at about 2.8 quarters (0.64), with habit parameter 0.65 and an investment-adjustment-cost parameter implying a temporary 1 percent increase in the price of capital raises investment by 0.40 percent; the capital-utilization curvature parameter is driven to its lower bound of 0.01, indicating a highly elastic supply of capital services. With these parameters, the model’s impulse responses lie within the two-standard-deviation confidence bands of the VAR-estimated responses for most variables: inflation shows no noticeable rise until roughly three years after an expansionary shock, output rises for nine quarters with a cumulative response of 3.14 percent, of which more than 78 percent occurs after the typical wage and price contract in effect at the time of the shock has been reoptimized (a “contract multiplier” of 3.7). Counterfactual re-estimations show sticky wages, not sticky prices, are the crucial nominal friction - setting price stickiness to zero barely affects the estimated wage-contract length or the model’s qualitative fit, while setting wage stickiness to zero forces price stickiness to an extreme (contracts averaging over three years, which the authors call inconsistent with microeconomic evidence) and destroys the hump-shaped output response - and that variable capital utilization is the crucial real friction, since removing it roughly halves the output response and again forces implausibly long price contracts when re-estimated. The paper is explicit that its results are estimated on a single U.S. sample ending in 1995Q3, that Calvo pricing is treated as a reduced-form device for nominal sluggishness rather than a literal description of contracting, and that the model is disciplined only against monetary-policy-shock responses, leaving its performance against other shocks as a separate, only preliminarily addressed question.

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.

Time to Plan and Aggregate Fluctuations

Studies of major capital projects report two facts about investment gestation: projects take longer than a quarter to complete, and they open with a lengthy planning phase – drawing plans, arranging finance, obtaining permits – during which the direct resource cost is small relative to the project total. Kydland and Prescott’s Time to Build built the first fact into a macro model; this paper argues the second is the one that matters quantitatively, and that the first “per se has relatively modest implications for business cycle dynamics.” The authors take Christiano and Eichenbaum’s divisible-labour model with technology and government consumption shocks and compare three investment technologies: one-period completion; Kydland and Prescott’s four-period gestation with resource weights of 0.25 in each quarter (time to build); and the same four-period gestation reweighted to 0.01, 0.33, 0.33, 0.33 so that the first quarter consumes almost nothing (time to plan). The empirical basis is explicit – in Mayer’s (1960) data projects took 22 months on average with the first 7 months a preconstruction planning phase, and Krainer (1968) finds that in all 25 projects he studies less than 5 percent of total cost was incurred in the first three months, and in 18 of them less than 2.5 percent. The mechanism the planning phase supplies is a delay in the response of hours worked. In a standard model a positive technology shock makes households work harder to accumulate the investable resources needed to exploit the higher return on investment; with a planning phase there is little to do with those resources in the period of the shock, so hours worked actually falls a little, investment barely moves, and much of the extra output is simply consumed. That delay in hours translates into a delay in output, and produces three matches to U.S. quarterly data for 1947:1-1995:1. First, persistence: the first-order autocorrelation of U.S. GDP growth is 0.37 (standard error 0.07), the one-period and four-period even-weight models produce essentially zero even though the exogenous technology growth rate is serially uncorrelated, and the time-to-plan model produces 0.36. Second, the timing of productivity and hours: because hours are damped on impact while productivity jumps, productivity comes to lead hours worked, and the contemporaneous hours-productivity correlation falls from roughly 0.90 in the other two models to 0.28 – the U.S. figure being near zero with a significantly positive correlation between productivity and future hours. Third, investment now lags output, which is counterfactual for aggregate investment but matches the behaviour of business investment in structures and equipment, the components for which a planning period is most plausible. The authors are careful about what does not work: consumption leads the cycle and is far too volatile in the time-to-plan model, both counterfactual, and they attribute this to the level of aggregation rather than to the mechanism, conjecturing that a model separating business structures from residential investment and household durables would fix it. Adding government consumption shocks – which in their specification are temporary – cuts persistence rather than raising it, because with no investment margin available hours must rise sharply to absorb the shock; it also reduces the excess volatility of consumption, and contributes almost nothing to output volatility. They describe the work as “primarily as preliminary and, we hope, suggestive.”