arXiv subjects

Siddhartha Chib

Publications and source records attributed to Siddhartha Chib.

9 recordsLinked to original sources

arXiv2026

Dynamic Factor Stochastic Volatility-in-Mean VAR for Large Macroeconomic Panels

We develop a dynamic factor stochastic volatility-in-mean (SVM) specification for vector autoregressions (VARs) that embeds an SVM component within a dynamic factor stochastic volatility structure. A small number of latent volatility factors capture common movements in conditional variances, while volatility enters the conditional mean of the VAR. This specification allows time-varying uncertainty to influence macroeconomic dynamics through both second moments and expected outcomes while preserving tractability in large panels. We construct an efficient Markov chain Monte Carlo algorithm for estimation in this high-dimensional, non-Gaussian setting. Using quarterly data on twenty variables from the FRED-QD database, we compare predictive performance with the benchmark stochastic volatility VAR model. The dynamic factor SVM specification delivers superior forecasts for more variables during major macroeconomic disruptions such as the 2008 global financial crisis. The results indicate that allowing volatility to enter the mean captures an important transmission channel in macroeconomic dynamics.

stat.ME↗

arXiv2026

Testing for Endogeneity: A Moment-Based Bayesian Approach

A standard assumption in the Bayesian estimation of linear regression models is that the regressors are exogenous in the sense that they are uncorrelated with the model error term. In practice, however, this assumption can be invalid. In this paper, using the exponentially tilted empirical likelihood framework, we develop a Bayes factor test for endogeneity that compares a base model that is correctly specified under exogeneity but misspecified under endogeneity against an extended model that is correctly specified in either case. We provide a comprehensive study of the log-marginal exponentially tilted empirical likelihood. We demonstrate that our testing procedure is consistent from a frequentist point of view: as the sample grows, it almost surely selects the base model if and only if the regressors are exogenous, and the extended model if and only if the regressors are endogenous. The methods are illustrated with simulated data, and problems concerning the causal effect of automobile prices on automobile demand and the causal effect of potentially endogenous airplane ticket prices on passenger volume.

econ.EM↗

arXiv2025

Learning the Macroeconomic Language

We show how state-of-the-art large language models (LLMs) can be trained effectively on limited historical data for macroeconomic forecasting. We estimate a dynamic stochastic general equilibrium (DSGE) model with stochastic volatility and Student-t shocks on an initial segment of the data to obtain a posterior distribution over structural parameters. We sample from this posterior to generate millions of theory-consistent synthetic panels that, when mixed with macroeconomic data, form the training corpus for a deep learning transformer. Rather than using the DSGE model as a direct forecasting device, we use it as a structural simulator that regularizes transformer training in a small-sample environment. Our results show that this hybrid forecaster, which combines the theoretical coherence of DSGE models with the representational power of modern LLMs, learns key features of the macroeconomic language. Relative to a conventional vector autoregression benchmark, the transformer achieves comparable or stronger predictive performance in both token accuracy and predictive likelihood. These gains are strongest under a theory-heavy training mix and remain broadly robust to finer tokenization and deeper network architecture.

econ.EM↗

arXiv2025

Bayesian Estimation of Cohort-Time-Stratum Specific Effects in Staggered Difference-in-Differences

Difference-in-Differences designs with staggered treatment adoption are widely used to study heterogeneous treatment effects across cohorts and time periods. We develop a probabilistic framework for estimating potentially high-dimensional ATT arrays that vary across cohorts, periods, and strata defined by baseline covariates. The framework jointly estimates subgroup-specific treatment effects through a unified likelihood-based model, stabilizing inference in sparse cohort-by-time-by-stratum settings. We establish a Bernstein-von Mises theorem for the ATT array, implying asymptotically valid frequentist coverage of posterior credible intervals. Simulations and an application to minimum wage increases and teen employment demonstrate meaningful finite-sample improvements and important subgroup heterogeneity.

econ.EM↗

arXiv2024

Stochastic Volatility in Mean: Efficient Analysis by a Generalized Mixture Sampler

In this paper we consider the simulation-based Bayesian analysis of stochastic volatility in mean (SVM) models. Extending the highly efficient Markov chain Monte Carlo mixture sampler for the SV model proposed in Kim et al. (1998) and Omori et al. (2007), we develop an accurate approximation of the non-central chi-squared distribution as a mixture of thirty normal distributions. Under this mixture representation, we sample the parameters and latent volatilities in one block. We also detail a correction of the small approximation error by using additional Metropolis-Hastings steps. The proposed method is extended to the SVM model with leverage. The methodology and models are applied to excess holding yields and S&P500 returns in empirical studies, and the SVM models are shown to outperform other volatility models based on marginal likelihoods.

econ.EM↗

arXiv2023

Scalable Estimation of Multinomial Response Models with Random Consideration Sets

A common assumption in the fitting of unordered multinomial response models for $J$ mutually exclusive categories is that the responses arise from the same set of $J$ categories across subjects. However, when responses measure a choice made by the subject, it is more appropriate to condition the distribution of multinomial responses on a subject-specific consideration set, drawn from the power set of $\{1,2,\ldots,J\}$. This leads to a mixture of multinomial response models governed by a probability distribution over the $J^{\ast} = 2^J -1$ consideration sets. We introduce a novel method for estimating such generalized multinomial response models based on the fundamental result that any mass distribution over $J^{\ast}$ consideration sets can be represented as a mixture of products of $J$ component-specific inclusion-exclusion probabilities. Moreover, under time-invariant consideration sets, the conditional posterior distribution of consideration sets is sparse. These features enable a scalable MCMC algorithm for sampling the posterior distribution of parameters, random effects, and consideration sets. Under regularity conditions, the posterior distributions of the marginal response probabilities and the model parameters satisfy consistency. The methodology is demonstrated in a longitudinal data set on weekly cereal purchases that cover $J = 101$ brands, a dimension substantially beyond the reach of existing methods.

stat.ME↗

arXiv2021

Bayesian Estimation and Comparison of Conditional Moment Models

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed to satisfy a sequence of unconditional moments based on an increasing (in sample size) vector of approximating functions (such as tensor splines based on the splines of each conditioning variable). For any given sample size, results are robust to the number of expanded moments. We derive Bernstein-von Mises theorems for the behavior of the posterior distribution under both correct and incorrect specification of the conditional moments, subject to growth rate conditions (slower under misspecification) on the number of approximating functions. A large-sample theory for comparing different conditional moment models is also developed. The central result is that the marginal likelihood criterion selects the model that is less misspecified. We also introduce sparsity-based model search for high-dimensional conditioning variables, and provide efficient MCMC computations for high-dimensional parameters. Along with clarifying examples, the framework is illustrated with real-data applications to risk-factor determination in finance, and causal inference under conditional ignorability.

math.ST↗

arXiv2017

Bayesian Estimation and Comparison of Moment Condition Models

In this paper we consider the problem of inference in statistical models characterized by moment restrictions by casting the problem within the Exponentially Tilted Empirical Likelihood (ETEL) framework. Because the ETEL function has a well defined probabilistic interpretation and plays the role of a nonparametric likelihood, a fully Bayesian semiparametric framework can be developed. We establish a number of powerful results surrounding the Bayesian ETEL framework in such models. One major concern driving our work is the possibility of misspecification. To accommodate this possibility, we show how the moment conditions can be reexpressed in terms of additional nuisance parameters and that, even under misspecification, the Bayesian ETEL posterior distribution satisfies a Bernstein-von Mises result. A second key contribution of the paper is the development of a framework based on marginal likelihoods and Bayes factors to compare models defined by different moment conditions. Computation of the marginal likelihoods is by the method of Chib (1995) as extended to Metropolis-Hastings samplers in Chib and Jeliazkov (2001). We establish the model selection consistency of the marginal likelihood and show that the marginal likelihood favors the model with the minimum number of parameters and the maximum number of valid moment restrictions. When the models are misspecified, the marginal likelihood model selection procedure selects the model that is closer to the (unknown) true data generating process in terms of the Kullback-Leibler divergence. The ideas and results in this paper provide a further broadening of the theoretical underpinning and value of the Bayesian ETEL framework with likely far-reaching practical consequences. The discussion is illuminated through several examples.

stat.ME↗

arXiv2016

Bayes factor consistency

Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent surge of attention in the literature. We thoroughly review existing results. As there exists such a wide variety of settings to be considered, e.g. parametric vs. nonparametric, nested vs. non-nested, etc., we adopt the view that a unified framework has didactic value. Using the basic marginal likelihood identity of Chib (1995), we study Bayes factor asymptotics by decomposing the natural logarithm of the ratio of marginal likelihoods into three components. These are, respectively, log ratios of likelihoods, prior densities, and posterior densities. This yields an interpretation of the log ratio of posteriors as a penalty term, and emphasizes that to understand Bayes factor consistency, the prior support conditions driving posterior consistency in each respective model under comparison should be contrasted in terms of the rates of posterior contraction they imply.

math.ST↗