This paper introduces novel threshold factor-augmented vector autoregressive (FAVAR) models which extend the conventional FAVAR model to allow for the threshold effect. We develop economically sensible identification conditions and propose a method for estimating threshold values, latent factors and regime-dependent parameters. We also study the estimation of impulse response functions using external instruments and provide a bootstrap procedure to compute their confidence intervals. Asymptotic theories are established. Monte Carlo experiments show good finite sample performance. In empirical applications, we investigate the performance of a threshold FAVAR which employs industrial production growth to determine boom and recession regimes. It outperforms the alternative models in forecasting, and suggests that the monetary policy shocks identified using orthogonalized monetary policy surprises have significantly weaker effects in recessions, on certain macroeconomic variables especially the real ones.
In this study, we address the problem of testing for structural changes in time series models that allow for time-varying distributions of regressors. We propose a novel stochastic process within a nonparametric framework, which combines the CUSUM method with Fourier-transformed data, and based on this process, develop a Cram & eacute;r-von Mises (CvM) type statistic. We show that the constructed process weakly converges to a centered complex-valued Gaussian process and derive the asymptotic distribution of the test under the null hypothesis, while also examining its properties under alternative hypotheses. The test is consistent against a wide range of global alternatives and can detect Pitman sequences of local alternatives at the parametric rate T-1/2 , outperforming most existing nonparametric tests. Due to the nonstandard asymptotic distribution of the test statistic, we propose a bootstrap method to obtain critical values and establish its validity. Monte Carlo simulations and an empirical application to major Chinese stock indices demonstrate that the proposed test achieves accurate size and strong power in finite samples, while the empirical results reveal recurrent structural breaks with strong co-movement across indices, highlighting the role of common market-wide factors in driving regime shifts.
In this review, we provide practical guidance on some of the main machine learning tools used in portfolio weight formation. This is not an exhaustive list, but a fraction of the ones used and have some statistical analysis behind it. All this research is essentially tied to precision matrix of excess asset returns. Our main point is that the techniques should be used in conjunction with outlined objective functions. In other words, there should be joint analysis of Machine Learning (ML) technique with the possible portfolio choice-objective functions in terms of test period Sharpe Ratio or returns. The ML method with the best objective function should provide the weight for portfolio formation. Empirically we analyze five time periods of interest, that are out-sample and show performance of some ML-Artificial Intelligence (AI) methods. We see that nodewise regression with Global Minimum Variance portfolio based weights deliver very good Sharpe Ratio and returns across five time periods in this century we analyze. We cover three downturns, and 2 long term investment spans.
We develop testable implications for the identifying assumptions of Tobit and IV-Tobit models: linear index, (joint) normality of errors, treatment (instrument) exogeneity, and relevance. The new testable equalities can detect all possible observable violations of the identifying conditions. The proposed test procedure for the model's validity uses existing inference methods for intersection bounds. Simulations suggest adequate test size and power in detecting exogeneity and error structure violations. We review and propose alternatives to partially identify the parameters of interest under less restrictive assumptions. We revisit a study of married women's labor supply in Lee (1995) to demonstrate the test's practical implementation. We qualitatively replicate their original findings, but our validity test rejects the IV-Tobit model. Estimating our proposed robust lower bound, we find that an additional $ 1,000 in other household income cannot reduce female labor supply by more than 4.2 hours annually, but cannot rule out that the effect is zero.
In this paper, we propose a deep pooled estimator, motivated by the universal approximation property of neural networks, to capture nonlinear relationships between predictors and targets when modeling and forecasting with panel data. The approach is flexible, accommodating different penalty functions and potentially high-dimensional predictors. It allows for nonlinear cross-sectional dependencies. To evidence the utility of the proposed estimator when forecasting, we apply it in two different applications. First, we forecast the progression of new COVID-19 cases across G7 countries. Second, we forecast inflation in the G7. In both applications, our method delivers significant forecasting gains over both linear panel and nonlinear time-series (unit-specific) models that do not pool data across countries. These results highlight the importance when forecasting of pooling cross-country information via a flexible nonlinear model. Examining partial derivatives from our model provides interpretable insights: school closures and workplace restrictions show declining effectiveness as COVID-19 immunity strengthened, while the inflation-unemployment relationship proves highly unstable across both countries and time periods, particularly during the post-pandemic inflation surge.
A number of economic models produce testable implications in the form of inequalities involving conditional functionals of the distribution of an outcome variable Y conditional on X, a vector of observable covariates. In applications where X includes a large collection of predictors, researchers may wish to pursue dimension reduction and aggregate X into a lower-dimensional, parameterized function g(X,theta), indexed by a finite-dimensional parameter theta, and proceed to test the functional inequalities conditional on g(X,theta) instead of X, where theta is a first-step estimator. Motivated by this, we introduce tests for functional inequalities conditional on estimated, aggregate functions of X. Our tests are based on one-sided Cram & eacute;r-von Mises (CvM) statistics where violations to the inequalities are measured through a tuning parameter converging to zero. Our proposed test-statistics adapt to the properties of the contact sets (the set of values of conditioning variables where the inequalities are binding) and have asymptotically pivotal properties. In Monte Carlo experiments, our procedure displays good power properties, capable of detecting violations to the inequalities that occur with very small probability.
This paper suggests bootstrap resampling for detecting weak instruments in the instrumental variable regression. When instruments are not weak, the bootstrap distribution of the standardized Two-Stage-Least-Squares estimator is close to the standard normal distribution. In contrast, a substantial difference between these two distributions indicates the existence of weak instruments. A bootstrap-based test for evaluating the strength of instruments is developed. Monte Carlo simulations show that the test has good size and power. The test is illustrated by an application taken from Card, where the return to schooling is significantly positive under a strong instrument, but insignificant under a weak one.
Accounting for multiway clustering is essential for valid statistical inference. This paper develops a new Kolmogorov-Smirnov test for stochastic dominance that accommodates multiway clustered sampling, where separate exchangeability holds and non-overlapping cells are independent. The proposed test controls the size well asymptotically and is consistent against fixed alternatives. More importantly, our test remains valid whether or not clustering is present, and if so, irrespective of its form. Simulation results support the theoretical findings in that the proposed test maintains excellent size control and has good power under multiway clustering across various settings, while remaining conservative in degenerate and i.i.d. cases. Applied to income distribution data, the results are consistent with the hypothesis that male income stochastically dominates female income among workers with children, while no clear dominance relationship is observed among childless workers. Moreover, the evidence provides support for the dominance of fathers' income distribution over that of childless men, whereas no such relationship is supported among female workers.
We propose non-nested hypotheses tests in multivariate regressions. Our approach relies on regression augmentation, and allows for multiple alternatives. Tests are bootstrap-based, and exact under Gaussian disturbances. Simulations document good size and power properties for single and multiple alternatives. Tests are applied to asset pricing models with the Fama and French factors as the null hypothesis, and consumption-based and liquidity-augmented factors as the alternatives. Results reveal intermittent rejections over relatively short sub-samples at the quarterly frequency. The null model is rejected as a long run stable specification. Overall, the liquidity factor emerges as a key driver of such rejections.
This paper evaluates a set of widely used methodologies for determining the number of latent factors in large-dimensional factor models. Its contribution is a comprehensive and systematic comparison of their performance. We assess these estimators not only under the data-generating processes for which they were originally designed, but also across a broader set of environments. Our analysis encompasses static, dynamic, and generalized dynamic factor models, considering factor strength that ranges from strong to semi-strong and semi-weak. Our results show that with strong factors, most estimators across all three classes deliver near-perfect identification when both the cross-section n and time dimension T are large, providing practitioners with a wide set of reliable choices. As factor strength weakens, performance diverges: only a few estimators remain comparatively robust, while other estimators tend to underestimate the true number of factors or shocks, particularly when the idiosyncratic components are not i.i.d. Overall, no single estimator dominates across all settings. Our findings provide practical guidance for applied work and highlight the advantages and limitations of existing methodologies.
This paper introduces extremile regression (ER) as an alternative to quantile regression (QR) in the predictive regression framework under various persistence regimes. We establish the theoretical properties of ER estimators, which, in contrast to their QR counterparts, admit closed-form expressions and facilitate a more tractable asymptotic analysis. To address distortions in ordinary ER estimation under local-to-unity and unit-root settings, we integrate IVX filtering into predictive ER modeling. The resulting IVX-ER estimators converge to (mixture) normal distributions across all persistence levels. We further develop an IVX-ER test statistic for predictability and derive its null limiting distribution. Monte Carlo simulations confirm the finite-sample accuracy of the ER estimators and demonstrate the robustness and efficiency of the IVX-ER framework under diverse persistence patterns and heavy-tailed innovations. In an empirical application to long-horizon stock returns, the results reveal a fundamental shift in market dynamics, where the broad-based predictive power of valuation, corporate-finance, and bond-yield measures in the historical period gives way to a more specialized, interaction-driven regime in the modern era, with certain variable combinations emerging as robust predictors across the entire return distribution while others become specialized indicators for downside risk.
This article presents a method for selecting variables and determining parameter heterogeneity in Bayesian hierarchical panel data models. Mixture distributions are used as priors for the mean and the variance of the individuals' parameters. Selection indicators determine the best-fitting component of each mixture distribution and indicate whether the mean parameter is non zero and whether the parameters are heterogeneous. The method is applied to two panel data sets. The first is on inflation of US CPI sub-indices, and the results suggest that a heterogeneous panel AR model with a lagged, first principal component is the preferred model. A second application to house price inflation across US metropolitan statistical areas shows that the model includes either the autoregressive component or the lagged spatial components, but not both at the same time.
This article studies binary choice games with complete information and proposes a test for the null hypothesis of collusion / cooperation, where players coordinate their actions to maximize the weighted sum of all players' payoffs. Consider an arbitrary game, referred to as the original game. With data on players' actual choices and under weak regularity conditions, I show that the collusive model of the original game is observationally equivalent to an equilibrium model of a transformed game with an alternative payoff structure. Notably, this equivalent equilibrium model must satisfy two key restrictions: one on each player's strategic effect and the other on the equilibrium selection mechanism. This observational equivalence transforms the test for collusion / cooperation into a test on structural functions estimated under an equilibrium framework-one that need not be the true model but nonetheless yields informative implications for testing collusive behaviors. In particular, it amounts to a joint test of the strategic effects and the equilibrium selection mechanism. I illustrate the implementation of this test by revisiting the entry game between Wal-Mart and Kmart, as studied by Jia (2008). The estimation results strongly reject the hypothesis that these two chains coordinate their entry decisions to maximize the weighted sum of their profits.
This article considers the break point detection and parameter estimation problem in the high-dimensional structural break vector autoregressive models that have banded autoregressive coefficient matrices. The banded structure portrays a type of sparsity in the high-dimensional time series modeling and indicates explicit dependence on neighboring component series, which is often convenient and, more importantly, practically meaningful for empirical analysis. The bandwidth parameter is first assumed to be known, under which scenario the breakpoint detection problem is reformulated as a high-dimensional variable selection one solved by a group Lasso-based procedure. Then a Bayesian information criterion is proposed to determine the bandwidth, and finally, the autoregressive matrices are estimated within each segment separated by the estimated break points. Theoretical properties of the proposed estimators are established, with data-driven choices of tuning parameters in the procedure. The finite sample performance of the procedure is nicely illustrated through several simulated and real data examples. Our empirical analysis shows that the proposed procedure successfully detects structural breaks in the constituent stock return series and delivers more accurate forecasts than existing methods.
This article introduces a methodology for selecting large portfolios in the presence of asymmetries in asset returns and risk attitudes. Within this framework, the optimal portfolio depends on inverting the covariance matrix of returns. However, traditional estimators of this matrix become nearly singular when the number of assets is significantly larger than the sample size. This results in a selected portfolio that deviates substantially from the optimal one. To address this challenge, we propose four regularization techniques aimed at stabilizing the inverse of the covariance matrix: Ridge, Spectral Cut-Off, Landweber-Fridman, and Lasso for Nodewise Regression. These regularization techniques involve a tuning parameter that requires careful selection. To tackle this, we introduce a data-driven approach for choosing the optimal tuning parameter. Through extensive simulation exercise, we demonstrate the superior performance of the regularized optimal portfolio over several benchmark portfolios. Finally, we provide two empirical applications to illustrate the practical relevance of the proposed methods. In these applications, the results consistently show that incorporating asymmetries in returns and regularizing the inverse of the covariance matrix significantly improves the performance of the optimal portfolio. Specifically, our approach achieves higher Sharpe and Generalized Sharpe ratios, lower turnover, and greater stability compared to benchmark strategies.
