Oliver Wichert - Research

My research focuses on the stationarity properties of large panels, with a particular focus on high-dimensional factor models. We have studied the implications of heterogeneous alternatives to the unit-root hypothesis, demonstrated the equivalence of two common factor specifications and derived asymptotically uniformly most powerful tests in both setups. In my job market paper, I show how additional stationary covariates can be used to obtain considerably more powerful unit-root tests for unobserved common factors.

Working Papers

Wichert, O. (2020). Using Stationary Covariates to Test for Common Stochastic Trends in High-Dimensional Panels.

Werker, B.J.M. and O. Wichert. (2020). Panel Unit-Root Tests Under Cross-Sectional Cointegration.

Wichert, O., I.G. Becheri, F.C. Drost, and R. van den Akker (2019). Local Asymptotic Equivalence of the Bai and Ng (2004) and Moon and Perron (2004) Frameworks for Panel Unit Root Testing. Submitted.

Publications

Becheri, I.G., F.C. Drost, R. van den Akker, and O. Wichert (2016). The power envelope of panel unit root tests in case stationary alternatives offset explosive ones. Statistics & Probability Letters, Vol. 108, pp. 1–8.

Covariate paper.pdf

Using Stationary Covariates to Test for Common Stochastic Trends in High-Dimensional Panels

This paper considers panel unit-root tests in the presence of stationary covariates and cross-sectional dependence. Our starting point is the popular PANIC framework and we analyze the potential power gains due to observing additional stationary covariates, focusing on unit-root tests that are robust to cross-sectional cointegration, i.e., tests for a unit root in the common unobserved factors. The stationary, observed covariates are assumed to be unit-specific but allowed to be cross-sectionally correlated. We differentiate two-cases: one in which the contribution of the factor of interest to the covariance structure of the covariate can be perfectly identified, and a more general one, where the contribution of the factor innovations in the covariate equation is perturbed by another unobserved common shock.

In the former case, the inclusion of stationary covariates leads to vastly more powerful tests, entailing a faster convergence rate. We first analyze the problem for an observed factor, and show that the statistical experiment is locally asymptotically mixed normal (LAMN). This implies that no UMP test exists, but we obtain an asymptotically optimal invariant test. We demonstrate how to conduct valid inference also based on estimated factors. The improved rate allows us to compare different factor estimation schemes in terms of resulting asymptotic power. When implemented well, the asymptotic power of estimated factor based tests is relatively close to the observed-factor power envelope.

In the second case, the statistical problem is closely related to that of univariate unit-root tests with stationary factors that have been studied in Hansen (1995) and Elliott and Jansson (2003). We demonstrate that the original time-series experiment is locally, asymptotically Brownian Functional (LABF) but converges to the better understood LAMN case as the contribution of the covariate grows to 1. Moreover, we show that the CADF test of Hansen (1995) becomes optimal invariant as the share of the variation explained by the covariate converges to unity. This explains why the tests of Hansen (1995) are competitive in terms of power to those of Elliott and Jansson (2003), in particular when the covariate is more important. We show that both the CADF tests and the point-optimal tests can also be implemented in a panel setting with unobserved common factors and that their optimality properties carry over to the panel setup.

FactorTests.pdf

Panel Unit-Root Tests Under Cross-Sectional Cointegration
(with B.J.M. Werker)

We study unit-root tests for unobserved common factors in large panels. Recent panel unit-root tests typically allow for cross-sectional correlation due to common unobserved factors. As originally proposed in Bai and Ng (2004) ("PANIC"), unit-root tests are applied separately to the common factors and idiosyncratic deviations. While the testing problem for the idiosyncratic parts is in many cases well-understood, the testing problem for the factors has received much less attention. Bai and Ng (2004) show that using principal component estimates in ADF tests does not change their properties. We generalize this result to other unit-root tests and other factor estimates, which can lead to higher finite sample powers. In particular, we show that a Kalman smoother imposing the null hypothesis to estimate the factors often has a simple closed-form solution that avoids the computational issues usually associated with such methods.

We also discuss the implications of including deterministic trends in the factor equation, i.e., having factors with non-zero mean innovations. This specification can be considered as an alternative to including individual deterministic trends for each unit. Although this leads to nontrivial powers closer to the unit root, we can again attain these powers based on estimated factors. In particular, we propose tests based on simple cross-sectional averages that are asymptotically uniformly most powerful. We derive the prop erties of these unit ro ot tests in the presence of multiple potentially cointegrated factors and show that they can be interpreted as unit-root tests for the observations. The cross-sectional averaging ap- proach can lead to higher powers than cointegration-rank based tests and does not require pre-estimation of the total number of factors.

WichertEtAl2019.pdf

Local Asymptotic Equivalence of the Bai and Ng (2004) and Moon and Perron (2004) Frameworks for Panel Unit Root Testing
(with I.G. Becheri, F.C. Drost, and R. van den Akker)

This paper considers unit-root tests in large n and large T heterogeneous panels with cross-sectional dependence generated by unobserved factors. We reconsider the two prevalent approaches in the literature, that of Moon and Perron (2004) and the PANIC setup proposed in Bai and Ng (2004). While these have been considered as completely different setups, we show that, in case of Gaussian innovations, the frameworks are asymptotically equivalent in the sense that both experiments are locally asymptotically normal (LAN) with the same central sequence. Using Le Cam’s theory of statistical ex- periments we determine the local asymptotic power envelope and derive an optimal test jointly in both setups. We show that the popular Moon and Perron (2004) and Bai and Ng (2010) tests only attain the power envelope in case there is no heterogeneity in the long-run variance of the idiosyn- cratic components. The new test is asymptotically uniformly most powerful irrespective of possible heterogeneity. Moreover, it turns out that for any test, satisfying a mild regularity condition, the size and local asymptotic power are the same under both data generating processes. Thus, applied researchers do not need to decide on one of the two frameworks to conduct unit root tests. Monte-Carlo simulations corroborate our asymptotic results and document significant gains in finite-sample power if the variances of the idiosyncratic shocks differ substantially among the cross sectional units.

BecheriEtAl2016.pdf

The power envelope of panel unit root tests in case stationary alternatives offset explosive ones
(with I.G. Becheri, F.C. Drost, and R. van den Akker)

We derive the power envelope for panel unit root tests where heterogeneous alternatives are modeled via zero-expectation random perturbations. We obtain an asymptotically UMP test and discuss how to proceed when one is agnostic about the expectation of the perturbations.

Working Papers

Publications

Using Stationary Covariates to Test for Common Stochastic Trends in High-Dimensional Panels

Panel Unit-Root Tests Under Cross-Sectional Cointegration (with B.J.M. Werker)

Local Asymptotic Equivalence of the Bai and Ng (2004) and Moon and Perron (2004) Frameworks for Panel Unit Root Testing (with I.G. Becheri, F.C. Drost, and R. van den Akker)

The power envelope of panel unit root tests in case stationary alternatives offset explosive ones (with I.G. Becheri, F.C. Drost, and R. van den Akker)

Panel Unit-Root Tests Under Cross-Sectional Cointegration
(with B.J.M. Werker)

Local Asymptotic Equivalence of the Bai and Ng (2004) and Moon and Perron (2004) Frameworks for Panel Unit Root Testing
(with I.G. Becheri, F.C. Drost, and R. van den Akker)

The power envelope of panel unit root tests in case stationary alternatives offset explosive ones
(with I.G. Becheri, F.C. Drost, and R. van den Akker)