Research

Abstract:

This paper is concerned with the estimation of aggregate relationships among a potentially very large number of panel data variables in the presence of unobserved heterogeneity in the form of interactive effects, an empirically very relevant scenario that has not been considered before. One of our findings is that if the regressors load on the same set of latent factors as the dependent variable, which seems a priori likely since many variables are co-moving, the aggregation automatically accounts for the unobserved heterogeneity. In order to also account for the many regressors, the aggregate model is estimated using LASSO, leading to the ``Cross-sectionally Averaged aDAptive LASSO'' (CADA-LASSO). It is shown that under suitable regulatory conditions, the new estimator is oracle efficient and selection consistent, properties that are verified in small samples using Monte Carlo simulations. The empirical usefulness of the estimator is illustrated using as an example the gravity equation of trade.

Abstract:

We reconcile dense and sparse modeling by exploiting the positive aspects of both. We employ a high-dimensional, approximate static factor model and assume the idiosyncratic term follows a sparse vector autoregressive model (VAR). The estimation is articulated in two steps: (i) factors and loadings are estimated via principal component analysis (PCA); (ii) a sparse VAR is estimated via the lasso on the estimated idiosyncratic components from (i). Step (ii) allows to model cross-sectional and time dependence left after the factors estimation. We prove the consistency of this approach as the time and cross-sectional dimensions diverge. In (ii), sparsity is allowed to be very general: approximate, row-wise and growing with the sample size. However, the estimation error of (i) needs to be accounted for. Instead of simply plugging-in the standard rates derived for the PCA estimation of the factors in (i), we derive a refined expression of the error which enables to derive tighter rates for the lasso in (ii). We discuss applications on forecasting \& factor augmented regression and present an empirical application on macroeconomic forecasting using the Federal Reserve Economic Data - Monthly Database (FRED-MD). 

Abstract:

The least squares estimator can be cast as depending only on the precision matrix of the data, similar to the weights of a global minimum variance portfolio. We give conditions under which any plug-in precision matrix estimator produces an unbiased and consistent least squares estimator for stationary time series regressions, in both low- and high-dimensional settings. Such conditions define a class of “Precision Least Squares” (PrLS) estimators, which are shown to be approximately Gaussian, efficient, and to provide automatic family-wise error control in large samples. For estimating high-dimensional sparse regression models, we propose a LASSO Cholesky estimator of the plug-in precision matrix. We show its consistency and how to properly bias correct it, thereby obtaining a LASSO Cholesky-based PrLS (LC-PrLS) estimator. LC-PrLS performs well in finite samples and better than state-of-the-art high-dimensional estimators. We employ LC-PrLS to investigate the dynamic network of predictive connections among a large set of global bank stock returns. We find that crisis years correspond to a collapse of predictive linkages. 

Abstract:

In the interactive effects panel data literature information criteria are commonly used to consistently determine which of the estimated principal components factors to include. The present paper shows that the same approach can be applied to factors estimated by taking the cross-sectional averages of the observables, as prescribed by the popular common correlated effects (CCE) approach. This should be useful to practitioners, because at the moment there is no other theory that justifies the use of information criteria in CCE.

Abstract:

We develop an LM test for Granger causality in high-dimensional VAR models based on penalized least squares estimations. To obtain a test retaining the appropriate size after the variable selection done by the lasso, we propose a post-double-selection procedure to partial out effects of nuisance variables and establish its uniform asymptotic validity. We conduct an extensive set of Monte-Carlo simulations that show our tests perform well under different data generating processes, even without sparsity. We apply our testing procedure to find networks of volatility spillovers and we find evidence that causal relationships become clearer in high-dimensional compared to standard low-dimensional VARs.