Journal of the European Economic Association | Macro Paper Warehouse

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.”

Country Portfolios in Open Economy Macro-Models

This paper develops a simple, general approximation method for computing equilibrium country portfolios – the composition of gross foreign asset and liability holdings – in dynamic stochastic general equilibrium (DSGE) open-economy macro models. The problem it solves is a genuine gap in standard solution technique: the usual approach of taking a first-order approximation around the non-stochastic steady state cannot pin down portfolio holdings at all, because in both the non-stochastic steady state and a first-order approximation all assets earn (expected) returns that make them perfect substitutes, so any portfolio is consistent with equilibrium. The authors’ solution is to combine a second-order approximation of just the portfolio first-order conditions – which captures the covariance between asset excess returns and the marginal utility of consumption, and hence each asset’s value as a hedge against consumption risk – with an ordinary first-order approximation of the rest of the model, yielding a simple closed-form formula for the constant (“zero-order”) component of the equilibrium portfolio. The method applies to any number of assets, to complete or incomplete asset markets, and to any DSGE model otherwise solvable by standard perturbation methods; the paper illustrates it first in a tractable two-country, two-asset endowment economy, where it shows analytically that home investors’ equity home bias is governed by the covariance between domestic capital income and domestic labor income, and then generalizes the method to an n-asset, general-structure open-economy model, including an extension with traded nominal bonds in which monetary shocks affect the optimal hedging portfolio. A final section sketches, without full derivation, how the same logic extends (via a third-order approximation of the portfolio conditions) to solving for the time-varying, first-order-accurate dynamics of portfolios themselves, with the full derivation left to a companion paper (Devereux and Sutherland, 2007).

Macroeconomic Fluctuations with HANK & SAM: an Analytical Approach

This is a HANK model built to be solved on paper rather than on a computer. The motivation is stated as a gap in the literature: HANK models “have had a considerable impact on macroeconomics,” but “due to the complexity of such models, the literature has focused on numerically solved models and therefore little is known about their general properties.” The construction grafts Diamond-Mortensen-Pissarides search and matching frictions onto a monopolistically competitive economy with Rotemberg price adjustment costs, so that job prospects are uncertain and households can only self-insure. Tractability comes from three assumptions — no shorting equity and borrowing only by the employed, heterogeneity in both labour productivity and equity access, and exactly two household types — which together imply that “firms are owned by capitalists who drop out of bond and labor markets, while workers hold no equity and are either employed or unemployed,” everyone consumes their income period by period, and the real interest rate satisfies the employed workers’ Euler equation. The result is an economy with “inequality in outcomes but the wealth distribution is degenerate,” which is what makes it analytically solvable. The new object is an endogenous earnings risk wedge in the employed workers’ Euler equation, pinned down by labour market tightness because tightness determines both transition rates and wages. Because those two forces oppose each other — a tighter market means less unemployment risk but a larger income loss if the job is lost — the wedge can be countercyclical or procyclical, and every result turns on which. The authors argue countercyclicality is empirically plausible on three grounds: Storesletten, Telmer and Yaron’s finding that idiosyncratic risk is strongly countercyclical, Guvenen, Ozkan and Song’s finding that it comes from increased left-skewness in recessions rather than countercyclical variance, and a direct evaluation of the wedge using a 25.2 percent monthly job finding rate and 2 percent monthly job loss rate from CPS data (January 1990 to August 2019), a 20 percent consumption drop on job loss following Karabarbounis and Chodorow-Reich, and a wage semi-elasticity of −0.16 for job stayers from Gertler, Huckfeldt and Trigari. On that evaluation “the countercyclical effect of unemployment risk clearly dominates,” failing only when a 5 percent consumption drop is combined with a wage elasticity of −1.5. Four results follow. The economy may have three steady states rather than two, including an unemployment trap with a zero job finding rate and inflation between the intended steady state’s and the liquidity trap’s, which “cannot exist if prices are flexible, if markets are complete, or, if prices are sticky, when the endogenous earnings risk is either acyclical or procyclical.” The Taylor principle no longer suffices for local determinacy of the intended steady state, because “expectations of higher inflation may be self-fulfilling even if the central bank were to stabilize the direct impact of inflation on the real interest rate since demand (and thus inflation) is also stimulated by a decline in unemployment risk.” Nominal rigidities and market incompleteness become complements, so stickier prices can amplify productivity shocks and positive productivity shocks can be inflationary — which the authors support with a local projection of CPI inflation on Fernald TFP growth from 1980, where “higher TFP either leaves inflation unchanged or gives rise to higher inflation.” And the long-run real interest rate depends on policy parameters, while a liquidity trap need not be deflationary. The scope condition is theirs: “while our analysis rests on the analytical convenience produced by the simplifying assumptions that we make, we believe that the insights are general and apply to models with a non-degenerate wealth distribution and with more complicated asset structures” — a belief, supported by a numerical extension with capital accumulation, not a demonstration.