Consensus professional stock return forecasts are three times more volatile than those of non-professionals and econometricians. We show that this difference reflects professionals’ strong countercyclical responses to macro shocks, which explain 20–40% of forecast variation and are consistent with rational asset pricing models in which discount rates rise in bad times. We use macro shocks to identify the discount-rate component of professional forecasts and find that it closely matches realized returns. We conclude that professionals’ assessment of the discount-rate impact of macro shocks distinguishes them from other forecasts, challenging existing models of expectation formation.
This paper develops a test for coefficient variability in spatial regressions. The test is designed to have good power for a wide range of persistent patterns of coefficient variation, be applicable in a wide range of spatial designs, and accommodate spatial correlation in regressors and regression errors. The test approximates the locally best invariant test for coefficient stability in a Gaussian regression model with martingale-like coefficient variation under the alternative, and is thus a spatial generalization of the Nyblom (1989) test of coefficient stability in time series regressions.
This paper proposes a novel time-varying model averaging (TVMA) approach to enhancing forecast accuracy for multivariate time series subject to structural changes. The TVMA method averages predictions from a set of time-varying vector autoregressive models using optimal time-varying combination weights selected by minimizing a penalized local criterion. This allows the relative importance of different models to adaptively evolve over time in response to structural shifts. We establish an asymptotic optimality for the proposed TVMA approach in achieving the lowest possible quadratic forecast errors. The convergence rate of the selected time-varying weights to the optimal weights minimizing expected quadratic errors is derived. Moreover, we show that when one or more correctly specified models exist, our method consistently assigns full weight to them, and an asymptotic normality for the TVMA estimators under some regularity conditions can be established. Furthermore, the proposed approach encompasses special cases including time-varying VAR models with exogenous predictors, as well as time-varying factor augmented VAR (FAVAR) models. Simulations and empirical applications illustrate the proposed TVMA method outperforms some commonly used model averaging and selection methods in the presence of structural changes.
Accurately estimating the Phillips curve remains a significant methodological challenge. Recent panel data approaches reveal substantial cross-sectional heterogeneity, raising doubts about pooled estimates. This paper develops a novel group-based approach that systematically accounts for unobserved heterogeneity in the regional Phillips curve. We identify two distinct groups of U.S. states: one with a steep, significant Phillips curve, and another with a flat, insignificant relationship. Our results show that regional heterogeneity persists across regimes, with parameter nonlinearity emerging during recessions. Much of the flattening of the Phillips curve is region-specific, indicating the importance of both heterogeneity and nonlinearity in Phillips curve dynamics.
This paper considers identification and estimation of distributional effect parameters that depend on the joint distribution of an outcome and another variable of interest ("treatment") in a setting with "two-sided" measurement error-that is, where both variables are possibly measured with error. Examples of these parameters in the context of intergenerational income mobility include transition matrices, rank-rank correlations, and the poverty rate of children as a function of their parents' income, among others. Building on recent work on quantile regression (QR) with measurement error in the outcome (particularly, Hausman et al. (2021)), we show that, given (i) two linear QR models separately for the outcome and treatment conditional on other observed covariates and (ii) assumptions about the measurement error for each variable, one can recover the joint distribution of the outcome and the treatment. Besides these conditions, our approach does not require an instrument, repeated measurements, or distributional assumptions about the measurement error. Using recent data from the 1997 National Longitudinal Study of Youth, we find that accounting for measurement error notably reduces several estimates of intergenerational mobility parameters.
This special issue brings together 21 papers that reflect the expanding scope and methodological evolution of Bayesian econometrics. We introduce a new organizing taxonomy that distinguishes between Traditional Bayesian Approaches - rooted in conjugate priors, standard likelihood-based estimation, and established Markov Chain Monte Carlo (MCMC) techniques - and Contemporary Bayesian Frontiers, characterized by nonparametric methods, variational inference, highdimensional shrinkage, and integration with machine learning. We further classify contributions across two broad domains covering applications in Economics (focusing on macroeconomics, microeconomics, and climate econometrics) and Finance (focusing on asset pricing, volatility, and bank business models). Across these fields, four cross-cutting themes emerge: (1) highdimensionality, volatility, and time-varying dynamics; (2) structural identification and model uncertainty; (3) semiparametric and nonparametric flexibility; and (4) data quality, granularity, and novel data structures. This survey synthesizes the methodological and empirical contributions of the special issue, proposes a unifying framework for organizing recent advances in Bayesian econometrics, and identifies unresolved challenges and promising directions for future research.
This paper develops inference tools for the number of common latent factors across two large cross-sectional panels observed over a short time span (large n, small T). Our approach builds on a general test for determining the dimension of the intersection of two matrix column spaces, where each matrix is estimated with noise. The proposed test statistics are based on canonical correlations, and their asymptotic distributions are derived via perturbation methods. An empirical application to large cross-sections of monthly US stock returns and corporate bond returns finds that, on average, five latent factors influence both asset classes over an 18-month period. Our results suggest that a plausible candidate for a common factor is a stock portfolio with weights sorted on book leverage. Overall, the common factors between the two asset classes behave more like stock characteristic portfolios than bond characteristic portfolios, both in terms of pricing performance and time series dynamics.
Mutual fund managers’ skills, measured by risk-adjusted alphas, are predictable using fund characteristics identified by machine learning (e.g., Kaniel et al., 2023, JFE; DeMiguel et al., 2023, JFE). However, alpha’s predictive power varies across funds and periods, with most funds exhibiting negligible alphas. To model this heterogeneous predictability, this paper introduces Sparse Clustering GMM, a nonparametric approach for identifying latent fund groups. SCGMM clusters funds using estimated alphas and identifies group-specific parameters tied to market predictors. The method accounts for heterogeneity in cross-sectional grouping and time-varying mechanisms across predictors, without requiring prior cluster information or time-varying specifications. We establish consistency for group recovery and time-varying parameter estimation. Empirically, using monthly U.S. mutual fund data, we find that predictable alpha is concentrated in a small subset of funds, with the majority of funds exhibiting near-zero, weakly predictable alphas. The skilled clusters also exhibit lower benchmark R2, moderate expense ratios, and longer manager tenure.
We consider structural vector autoregressions that are identified through stochastic volatility under Bayesian estimation. Three contributions emerge from our exercise. First, we show that a non-centred parameterization of stochastic volatility yields a marginal prior for the conditional variances of structural shocks that is centred on homoskedasticity, with strong shrinkage and heavy tails-unlike the common centred parameterization. This feature makes it well suited for assessing partial identification of any shock of interest. Second, Monte Carlo experiments on small and large systems indicate that the non-centred setup estimates structural parameters more precisely and normalizes conditional variances efficiently. Third, revisiting prominent fiscal structural vector autoregressions, we show how the non-centred approach identifies tax shocks that are consistent with estimates reported in the literature.
The modal factor model represents a novel statistical framework for dimension reduction in high dimensional panel data analysis. It is specifically designed to capture modal factors which exert a significant influence on the conditional mode of the distribution of the observables. Statistical inference for this model is developed based on a newly proposed modal component analysis, where modal factors and their corresponding loadings are estimated through maximizing a kernel-type objective function. Two computationally efficient and easy-to-implement algorithms-minorization-maximization and alternating maximization-are devised for the numerical computation of these estimators. Furthermore, two model selection criteria are proposed to determine the optimal number of modal factors. Under mild regularity conditions that accommodate both cross-sectional and time-series dependence, the asymptotic properties of the proposed estimators are established. Additionally, the limiting distributions of parameter estimators and forecasts derived from factor-augmented regressions incorporating estimated modal factors are rigorously derived. Simulation studies demonstrate that the proposed estimators exhibit favorable finite-sample performance, even in the presence of heavy-tailed, skewed, multimodal, and heteroskedastic error distributions. Finally, an application to inflation and industrial production index forecasting validates the practical merits and superior predictive power of modal factors in real-world macroeconomic scenarios.
We introduce general estimation and inference methods for threshold spatial panel regression with two-way fixed effects in a diminishing-threshold-effects framework. A valid objective function is obtained through a simple adjustment on the concentrated quasi loglikelihood with fixed effects being concentrated out, which leads to a consistent estimation of all common parameters. We show that the estimation of threshold parameter has a negligible effect on the asymptotic distribution of the main parameter estimators and thereby regular inference methods apply, though a bias correction may be necessary. The limiting distribution of the threshold parameter estimator is shown to be non-regular and infeasible, and for inference, a likelihood ratio test procedure is proposed. The test for the non-existence of threshold effects faces an identification issue at the null. To overcome this difficulty, we propose a sup-Wald test and a bootstrap method for its critical values. Monte Carlo results show that the proposed methods perform well in finite samples. An empirical application is presented on age-of-leader effects on political competitions across Chinese cities.
This paper considers the estimation of a censored partial linear quantile regression model with endogeneity. Our method extends those for partial linear quantile regression (Lee, 2003, Qu et al. 2024), nonparametric quantile regression (Qu and Yoon, 2015, Belloni et al., 2019), and censored linear quantile regression with endogeneity (Chen, 2018). Our estimation method involves a tractable sequential-multiple-step procedure. We establish the uniform consistency, the uniform representation and the asymptotic normality for the proposed estimators. We further extend our analysis to allow for sample selection. A set of Monte Carlo experiments show that our estimators have a good finite sample performance and an empirical application is given to show the usefulness of our estimators.
We study nonparametric distance-based (isotropic) local polynomial methods for estimating the boundary average treatment effect curve, a causal functional that captures treatment effect heterogeneity in boundary discontinuity designs. We establish identification, estimation, and inference results both pointwise and uniformly along the treatment assignment boundary. We show that the geometric regularity of the boundary, a one-dimensional manifold, plays a central role in determining feasible convergence rates and valid inference procedures. Our theoretical contributions are threefold. First, we derive uniform lower and upper bounds on the convergence rate of the misspecification bias of isotropic local polynomial estimators. Second, we obtain uniform distributional approximations that justify boundary-robust inference. Third, we establish minimax lower bounds for a broad class of nonparametric isotropic regression estimators. These results yield practical guidance for empirical implementation, including new bandwidth selection rules that adapt to local irregularities of the treatment-assignment boundary. We illustrate the proposed methods using simulation evidence and an empirical application, and provide companion general-purpose software.
This paper considers time domain estimation of possibly non-fundamental (that is, non-causal and/or non-invertible) non-Gaussian linear ARMA models with martingale difference innovations that may display conditional heteroskedasticity of unknown form. Instead of explicitly parametrizing the underlying volatility process (the higher order dependence) and employing maximum likelihood procedures, we propose a time domain minimum distance objective function based on innovations predictability using second and third powers of past innovations. Using the proposed efficient GMM estimator, which is consistent and asymptotically normal, we estimate possibly non-fundamental ARMA models to inflation data from 29 OECD countries and find widespread evidence on non-fundamentalness.
This paper develops methods for the empirical analysis of singular processes, particularly in macroeconomics. A strong rationale, a well-developed theoretical framework and, as we show, empirical support exist for multivariate time series with a singular spectral density. A singular spectral density is consistent with economic theory underlying, for example, DSGE models in which the number of variables is greater than the number of structural shocks. This assumption guarantees the existence of a finite order VAR representation but there does not exist a unique probability density function with respect to the Lebesgue measure. We therefore define a density on a compact linear submanifold with respect to the Hausdorff measure and, in a Bayesian framework, develop an HMC algorithm that jointly samples coefficients, lag length, and the number of shocks. We use the proposed framework to carry out structural analysis on the US macroeconomy with fewer shocks than variables.
