This paper builds on the composite likelihood concept of Lindsay (1988) to develop a framework for parameter identification, estimation, inference, and forecasting in dynamic stochastic general equilibrium (DSGE) models allowing for stochastic singularity. The framework consists of four components. First, it provides a necessary and sufficient condition for parameter identification, where the identifying information is provided by the first- and second-order properties of nonsingular submodels. Second, it provides a procedure based on Markov Chain Monte Carlo for parameter estimation. Third, it delivers confidence sets for structural parameters and impulse responses that allow for model misspecification. Fourth, it generates forecasts for all the observed endogenous variables, irrespective of the number of shocks in the model. The framework encompasses the conventional likelihood analysis as a special case when the model is nonsingular. It enables the researcher to start with a basic model and then gradually incorporate more shocks and other features, meanwhile confronting all the models with the data to assess their implications. The methodology is illustrated using both small- and medium-scale DSGE models. These models have numbers of shocks ranging between 1 and 7.

Abstract Markov regime-switching models are very common in economics and finance. Despite persisting interest in them, the asymptotic distributions of likelihood ratio-based tests for detecting regime switching remain unknown. This study examines such tests and establishes their asymptotic distributions in the context of nonlinear models, allowing multiple parameters to be affected by regime switching. The analysis addresses three difficulties: (i) some nuisance parameters are unidentified under the null hypothesis, (ii) the null hypothesis yields a local optimum, and (iii) the conditional regime probabilities follow stochastic processes that can only be represented recursively. Addressing these issues permits substantial power gains in empirically relevant settings. This study also presents the following results: (1) a characterization of the conditional regime probabilities and their derivatives with respect to the model’s parameters, (2) a high-order approximation to the log-likelihood ratio, (3) a refinement of the asymptotic distribution, and (4) a unified algorithm to simulate the critical values. For models that are linear under the null hypothesis, the elements needed for the algorithm can all be computed analytically. Furthermore, the above results explain why some bootstrap procedures can be inconsistent, and why standard information criteria can be sensitive to the hypothesis and the model structure. When applied to US quarterly real gross domestic product (GDP) growth rate data, the methods detect relatively strong evidence favouring the regime-switching specification. Lastly, we apply the methods in the context of dynamic stochastic equilibrium models and obtain similar results as the GDP case.

This paper considers issues related to estimation, inference, and computation with multiple structural changes that occur at unknown dates in a system of equations. Changes can occur in the regression coefficients and/or the covariance matrix of the errors. We also allow arbitrary restrictions on these parameters, which permits the analysis of partial structural change models, common breaks that occur in all equations, breaks that occur in a subset of equations, and so forth. The method of estimation is quasi-maximum likelihood based on Normal errors. The limiting distributions are obtained under more general assumptions than previous studies. For testing, we propose likelihood ratio type statistics to test the null hypothesis of no structural change and to select the number of changes. Structural change tests with restrictions on the parameters can be constructed to achieve higher power when prior information is present. For computation, an algorithm for an efficient procedure is proposed to construct the estimates and test statistics. We also introduce a novel locally ordered breaks model, which allows the breaks in different equations to be related yet not occurring at the same dates.

This article presents a framework for analysing global identification in log linearized Dynamic Stochastic General Equilibrium (DSGE) models that encompasses both determinacy and indeterminacy. First, it considers a frequency domain expression for the Kullback–Leibler distance between two DSGE models and shows that global identification fails if and only if the minimized distance equals 0. This result has three features: (1) it can be applied across DSGE models with different structures; (2) it permits checking whether a subset of frequencies can deliver identification; (3) it delivers parameter values that yield observational equivalence if there is identification failure. Next, the article proposes a measure for the empirical closeness between two DSGE models for a further understanding of the strength of identification. The measure gauges the feasibility of distinguishing one model from another based on a finite number of observations generated by the two models. It is shown to represent the highest possible power under Gaussianity when considering local alternatives. The above theory is illustrated using two small-scale and one medium-scale DSGE models. The results document that certain parameters can be identified under indeterminacy but not determinacy, that different monetary policy rules can be (nearly) observationally equivalent, and that identification properties can differ substantially between small and medium-scale models. For implementation, two procedures are developed and made available, both of which can be used to obtain and thus to cross validate the findings reported in the empirical applications. Although the article focuses on DSGE models, the results are also applicable to other vector linear processes with well-defined spectra, such as the (factor-augmented) vector autoregression.

Abstract We propose methods to estimate and make inferences on conditional quantile processes for models with both nonparametric and (locally or globally) linear components. We derive their asymptotic properties, optimal bandwidths, and uniform confidence bands over quantiles allowing for robust bias correction. Our framework covers the sharp regression discontinuity design, which is used to study the effects of unemployment insurance benefits extensions, focusing on heterogeneity over quantiles and covariates. We show economically strong effects in the tails of the outcome distribution. They reduce the within-group inequality, but can be viewed as enhancing between-group inequality, although they help to bridge the gender gap.