Knowledge that Transforms

Structural vector autoregressions (SVARs) are widely used for policy analysis and to provide stylized facts for dynamic stochastic general equilibrium (DSGE) models; yet no workable rank conditions to ascertain whether an SVAR is globally identified have been established. Moreover, when nonlinear identifying restrictions are used, no efficient algorithms exist for small-sample estimation and inference. This paper makes four contributions towards filling these important gaps in the literature. First, we establish general rank conditions for global identification of both identified and exactly identified models. These rank conditions are sufficient for general identification and are necessary and sufficient for exact identification. Second, we show that these conditions can be easily implemented and that they apply to a wide class of identifying restrictions, including linear and certain nonlinear restrictions. Third, we show that the rank condition for exactly identified models amounts to a straightforward counting exercise. Fourth, we develop efficient algorithms for small-sample estimation and inference, especially for SVARs with nonlinear restrictions.

The paper investigates inference in non-linear and non-Gaussian models with moderately time-varying parameters. We show that for many decision problems, the sample information about the parameter path can be summarized by an artificial linear and Gaussian model, at least asymptotically. The approximation allows for computationally convenient path estimators and parameter stability tests. Also, in contrast to standard Bayesian techniques, the artificial model can be robustified so that in misspecified models, decisions about the path of the (pseudo-true) parameter remain as good as in a corresponding correctly specified model.

We analyse a Bewley-Huggett-Aiyagari incomplete-markets model with labour-market frictions. Consumers are subject to idiosyncratic employment shocks against which they cannot insure directly. The labour market has a Diamond-Mortensen-Pissarides structure: firms enter by posting vacancies and match with workers bilaterally, with match probabilities given by an aggregate matching function. Wages are determined through Nash bargaining. We also consider aggregate productivity shocks and a complete set of contingent claims conditional on this risk. We use the model to evaluate a tax-financed unemployment insurance scheme. Higher insurance is beneficial for consumption smoothing, but because it raises workers' outside option value, it discourages firm entry. We find that the latter effect is more potent for welfare outcomes; we tabulate the effects quantitatively for different kinds of consumers. We also demonstrate that productivity changes in the model—in steady state as well as stochastic ones—generate rather limited unemployment effects, unless workers are close to indifferent between working and not working; thus, recent findings are corroborated in our more general setting.

We present a novel structural estimation procedure for models of intertemporal allocation. This is based on modelling expectations errors directly; we refer to it as synthetic residual estimation (SRE). The flexibility of SRE allows us to account for measurement error in consumption and for heterogeneity in intertemporal allocation parameters. An investigation of the small sample properties of the SRE estimator indicates that it dominates generalized method of moments (GMM) estimation of both exact and approximate Euler equations in the case when we have short panels and noisy consumption data. We apply SRE to two panels drawn from the Panel Study of Income Dynamics (PSID) and estimate the joint distribution of the discount factor and the elasticity of intertemporal substitution. We reject strongly homogeneity of the discount factor and the elasticity of intertemporal substitution. We find that, on average, the more educated are more patient and less willing to substitute intertemporally than the less educated. Within education strata, patience and willingness to substitute are positively correlated.