Full-Information Estimation of Heterogeneous Agent Models Using Macro and Micro Data

We develop a generally applicable full-information inference method for heterogeneous agent models, combining aggregate time series data and repeated cross sections of micro data. To handle unobserved aggregate state variables that affect cross-sectional distributions, we compute a numerically unbiased estimate of the model-implied likelihood function. Employing the likelihood estimate in a Markov Chain Monte Carlo algorithm, we obtain fully efficient and valid Bayesian inference. Evaluation of the micro part of the likelihood lends itself naturally to parallel computing. Numerical illustrations in models with heterogeneous households or firms demonstrate that the proposed full-information method substantially sharpens inference relative to using only macro data, and for some parameters micro data is essential for identification

Standard Errors for Calibrated Parameters

Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate of the correlation structure of the empirical moments, which is often unavailable in practice. Instead, the variances of the individual empirical moments are usually readily estimable. Using only these variances, we derive conservative standard errors and confidence intervals for the structural parameters that are valid even under the worst-case correlation structure. In the over-identified case, we show that the moment weighting scheme that minimizes the worst-case estimator variance amounts to a moment selection problem with a simple solution. Finally, we develop tests of over-identifying or parameter restrictions. We apply our methods empirically to a model of menu cost pricing for multi-product firms and to a heterogeneous agent New Keynesian model

Instrumental Variable Identification of Dynamic Variance Decompositions

Macroeconomists increasingly use external sources of exogenous variation for causal inference. However, unless such external instruments (proxies) capture the underlying shock without measurement error, existing methods are silent on the importance of that shock for macroeconomic fluctuations. We show that, in a general moving average model with external instruments, variance decompositions for the instrumented shock are interval-identified, with informative bounds. Various additional restrictions guarantee point identification of both variance and historical decompositions. Unlike SVAR analysis, our methods do not require invertibility. Applied to U.S. data, they give a tight upper bound on the importance of monetary shocks for inflation dynamics

Robust Empirical Bayes Confidence Intervals

We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The intervals are centered at the usual linear empirical Bayes estimator, but use a critical value accounting for shrinkage. Parametric EBCIs that assume a normal distribution for the means (Morris, 1983b) may substantially undercover when this assumption is violated. In contrast, our EBCIs control coverage regardless of the means distribution, while remaining close in length to the parametric EBCIs when the means are indeed Gaussian. If the means are treated as fixed, our EBCIs have an average coverage guarantee: the coverage probability is at least $1 - \alpha$ on average across the $n$ EBCIs for each of the means. Our empirical application considers the effects of U.S. neighborhoods on intergenerational mobility.Comment: 45 pages and a 25-page supplemental appendi

When is growth at risk?

This paper empirically evaluates the potentially nonlinear nexus between financial indicators and the distribution of future GDP growth, using a rich set of macroeconomic and financial variables covering thirteen advanced economies. We evaluate the out-of-sample forecast performance of financial variables for GDP growth, including a fully real-time exercise based on a flexible nonparametric model. We also use a parametric model to estimate the moments of the time-varying distribution of GDP and evaluate their in-sample estimation uncertainty. Our overall conclusion is pessimistic: moments other than the conditional mean are poorly estimated, and no predictors we consider provide robust and precise advance warnings of tail risks or indeed about any features of the GDP growth distribution other than the mean. In particular, financial variables contribute little to such distributional forecasts, beyond the information contained in real indicators

Bayesian inference on structural impulse response functions

Copyright © 2019 The Author. I propose to estimate structural impulse responses from macroeconomic time series by doing Bayesian inference on the Structural Vector Moving Average representation of the data. This approach has two advantages over Structural Vector Autoregressions. First, it imposes prior information directly on the impulse responses in a flexible and transparent manner. Second, it can handle noninvertible impulse response functions, which are often encountered in applications. Rapid simulation of the posterior distribution of the impulse responses is possible using an algorithm that exploits the Whittle likelihood. The impulse responses are partially identified, and I derive the frequentist asymptotics of the Bayesian procedure to show which features of the prior information are updated by the data. The procedure is used to estimate the effects of technological news shocks on the U.S. business cycle

Discussion of “Narrative Restrictions and Proxies” by Raffaella Giacomini, Toru Kitagawa, and Matthew Read

Discussion of “Narrative Restrictions and Proxies” by Raffaella Giacomini, Toru Kitagawa, and Matthew Rea

Local Projections vs. VARs: Lessons From Thousands of DGPs

We conduct a simulation study of Local Projection (LP) and Vector Autoregression (VAR) estimators of structural impulse responses across thousands of data generating processes, designed to mimic the properties of the universe of U.S. macroeconomic data. Our analysis considers various identification schemes and several variants of LP and VAR estimators. A clear bias-variance trade-off emerges: LP estimators have lower bias than VAR estimators but substantially higher variance at intermediate and long horizons. Consequently, unless researchers are overwhelmingly concerned with bias, shrinkage via Bayesian VARs or penalized LPs is attractive

Consistent Factor Estimation in Dynamic Factor Models with Structural Instability

This paper considers the estimation of approximate dynamic factor models when there is temporal instability in the factor loadings. We characterize the type and magnitude of instabilities under which the principal components estimator of the factors is consistent, and find that these instabilities can be larger than earlier theoretical calculations suggest. We further characterize the rate of convergence of the estimated factors as a function of the magnitude of the time variation in the factor loadings for general types of parameter instability, and provide numerical evidence that this consistency rate is tight in the special case of random walk parameter variation. We also discuss implications of these results for the robustness of regressions based on the estimated factors and of estimates of the number of factors in the presence of parameter instability.Economic