An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area

The paper develops and estimates a stochastic dynamic general equilibrium model of the euro area in which prices and wages are both set in staggered Calvo contracts with partial indexation to past inflation, consumption is subject to external habit formation, capital utilisation is variable with a utilisation cost expressed in consumption goods, and capital adjustment costs are a function of the change in investment rather than its level – a structure assembled from Christiano, Eichenbaum and Evans (2001), Kollmann (1997), Erceg, Henderson and Levin (2000), Greenwood, Hercowitz and Huffman (1988) and King and Rebelo (2000). What distinguishes it from that lineage is the estimation: ten orthogonal structural shocks (two supply, three demand, three cost-push and two monetary policy) are introduced so that the model can be confronted with seven euro area macroeconomic series – real GDP, consumption, investment, the GDP deflator, real wages, employment and the nominal short-term interest rate – over 1970:1-1999:4, with the likelihood computed by the Kalman filter and the posterior explored by a Metropolis-Hastings algorithm. Because euro area hours worked are unavailable, employment enters instead, with only a fixed fraction of firms able to adjust employment each period and unobserved hours per employee absorbing the remainder. A small set of parameters is fixed rather than estimated – the discount factor at 0.99 (a 4 percent annual steady-state real rate), quarterly depreciation at 0.025, the capital share at 0.3, consumption and investment shares of output at 0.6 and 0.22, and the wage mark-up parameter at 0.5 because it is not identified – leaving 34 estimated parameters. On marginal likelihood the estimated model beats standard VARs of lag order one to three and is nearly matched by the best Bayesian VAR with a Minnesota prior, the BVAR(3), over 1980:2-1999:4. The parameter estimates imply considerable nominal stickiness, with average price contract duration of about two and a half years against about one year for wages – an ordering the authors call counterintuitive but robust, and attribute partly to their assumption of a flat marginal cost curve in the intermediate goods sector. Price indexation is estimated at 0.4, implying a weight on lagged inflation of only 0.28; external habit is about 55 percent of past consumption; the labour supply elasticity is estimated to be relatively high but imprecisely; and the estimated policy rule satisfies the Taylor principle with substantial interest rate smoothing. In the variance decomposition, three shocks – preference, labour supply and monetary policy – explain significant fractions of output, inflation and interest rates at medium to long horizons, with the price mark-up shock important for inflation but not output and productivity accounting for at most about 12 percent of output forecast error variance. Using the model to construct potential output, defined as the flexible-price-and-wage level in the absence of mark-up shocks, the authors obtain a path very different from a smoothed output trend, with a sharp fall in potential from 1973 to 1975; but they emphasise that the confidence bands are wide, and that the real interest rate gap “is hardly significant over the sample period,” suggesting it “may be a poor guide for monetary policy.”

Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach

The paper estimates an extended New Neoclassical Synthesis model on US data covering 1966:1-2004:4 using Bayesian likelihood methods, with seven observable series – real GDP, hours worked, consumption, investment, real wages, prices and the short-term nominal interest rate – and seven orthogonal structural shocks: total factor productivity, risk premium, investment-specific technology, wage mark-up, price mark-up, exogenous spending and monetary policy. The model carries sticky Calvo price and wage setting with backward indexation, habit formation in consumption, investment adjustment costs, variable capital utilisation and fixed costs in production. Three questions organise the paper. First, does the model describe the data? Compared against unrestricted VARs and a Sims-Zha Bayesian VAR over the full sample (with 1956:1-1965:4 as a training sample to standardise priors), the tightly parameterised model beats the unrestricted VARs decisively and is matched by the best BVAR(4) on marginal likelihood; in a rolling out-of-sample RMSE exercise over 1990:1-2004:4 the two are comparable one quarter ahead but the structural model “does considerably better than both the VAR(1) and BVAR(4) model” over horizons up to three years, with the improvement “quite uniform across the seven macro variables.” Second, which frictions earn their place? Cutting the Calvo probability for prices or for wages to 0.10 each costs about 50 in log marginal likelihood; removing investment adjustment costs costs about 160; reducing habit formation is costly but much less so; shutting off variable capital utilisation “comes at no cost”; and restricting price indexation to 0.01 actually improves the marginal likelihood. Third, what drives the US business cycle? Within a year, output is dominated by the exogenous spending, risk premium and investment-specific shocks, which together account for more than 50 percent of forecast error variance; beyond two years the productivity and wage mark-up shocks account for more than half, with the wage mark-up dominant in the long run, while monetary policy shocks “contribute only a small fraction of the forecast variance of output at all horizons.” Inflation is driven by price mark-ups in the short run and wage mark-ups in the medium to long run, which the authors attribute to a very small estimated slope of the New Keynesian Phillips curve and to an aggressive estimated policy response. A positive productivity shock reduces hours worked immediately and significantly, turning positive only after two years, and does so even under flexible prices and wages, which the authors trace to habit persistence and capital adjustment costs. Finally, sub-sample estimates for the “Great Inflation” (1966:2-1979:2) and the “Great Moderation” (1984:1-2004:4) show most structural parameters stable, the standard deviations of productivity, monetary policy and price mark-up shocks lower in the second period, the policy response to the output gap level halved and no longer significant, and a counterfactual exercise attributing the fall in volatility mainly to milder shocks rather than to policy or structural change.

Frank Smets | Macro Paper Warehouse

An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area

Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach