A Pretest to Differentiate Between Weak and Nearly-Weak Instrument Asymptotics

We propose a pretest, bootstrap Kolmogorov-Smirnov test, to differentiate between weak and nearly-weak asymptotics. This is based on bootstrapping Wald Continuous Updating Estimator (CUE) based test. Since Wald CUE test has different limits under weak and nearly-weak cases this can be used in a pretest. We also conduct some simulations and show that some of the asset pricing models conform to nearly-weak asymptotics.Bootstrap, Kolmogorov-Smirnov Test

Oracle Inequalities for Convex Loss Functions with Non-Linear Targets

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target is linear this inequality also provides an upper bound of the estimation error of the estimated parameter vector. These are new results and they generalize the econometrics and statistics literature. Next, we use the non-asymptotic results to show that the excess loss of our estimator is asymptotically of the same order as that of the oracle. If the target is linear we give sufficient conditions for consistency of the estimated parameter vector. Next, we briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions covered by our framework and show how penalized nonparametric series estimation is contained as a special case and provide a finite sample upper bound on the mean square error of the elastic net series estimator.Comment: 44 page

Size distortions of tests of the null hypothesis of stationarity: Evidence and implications for applied work

It is common in applied econometrics to test the null hypothesis of a level-stationary process against the alternative of a unit root process. We show that the use of conventional asymptotic critical values for the stationarity tests of Kwiatkowski et al. (1992) and Leybourne and McCabe (1994) may cause extreme size distortions, if the model under the null hypothesis is highly persistent. The existence of such size distortions has not been recognized in the previous literature. We illustrate the practical importance of these distortions for the problem of testing for long-run purchasing power parity under the recent float. Size distortions of tests of the unit root null hypothesis may be overcome by the use of finite-sample or bootstrap critical values. We show that such corrections are not possible for tests of the null hypothesis of stationarity. Our results suggest that the common practice of viewing tests of stationarity as complementary to tests of the unit root null will tend to result in contradictions or in spurious acceptances of the unit root hypothesis. We conclude that tests of the null hypothesis of stationarity cannot be recommended for applied work unless the sample size is very large. --I(0) null hypothesis,finite-sample critical values,size,Monte Carlo simulation

A New Paradigm: A Joint Test of Structural and Correlation Parameters in Instrumental Variables Regression When Perfect Exogeneity is Violated

The instrumental variables strategy is commonly employed in empirical research. For correct inference using this econometric technique, the instruments must be perfectly exogenous and relevant. In fact, the standard t-ratio test statistic used in this context yields unreliable and often inaccurate results even when there is only a slight violation of the exclusion restriction. It is crucial to realize that to make reliable inferences on the structural parameters we need to know the true correlation between the structural error and the instruments. The main innovation in this paper is to identify an appropriate test in this context: a joint null hypothesis of the structural parameters with the correlation between the instruments and the structural error term. Since correlation cannot be estimated, we propose a test statistic involving a grid search over correlation values. To address inference under violations of exogeneity, significant contributions have been made in the recent literature by assuming some degree of non-exogeneity. We introduce a new approach by deriving a modified t-statistic that corrects for the bias associated with non-exogeneity of the instrument. A key advantage of our approach over that of the previous literature is that we do not need to make any assumptions about the degree of violation of exogeneity either as possible values or prior distributions. In particular, our method is not a form of sensitivity analysis. Since our modified test statistic is continuous and monotonic in correlation it is easy to conduct inference by a simple grid search. Even though the joint null may seem to be limiting in interpreting rejection, we can still make accurate inferences on the structural parameters because of a feature of the grid search over correlation values. The procedure for calculating the modified coefficients and statistics is illustrated with two empirical examples.Violation of exogeneity; Instrumental variables regression: Joint test

When do sudden stops really hurt?

This paper analyzes the drivers and consequences of sudden stops of capital flows. It focuses on the impact of external vulnerability on the depth and length of sudden stop crises. The authors analyze 43 developing and developed countries between 1993 and 2006. They find evidence that external vulnerability not only significantly impacts the probability of a sudden stop crisis, but also prolongs the time it takes for growth to revert to its long-term trend once a sudden stop occurs. Interestingly, external vulnerability does not significantly impact the size of the instantaneous output effect in case of a sudden stop but prompts a cumulative output effect through significantly diminishing the speed of adjustment of output to its trend. This finding implies that countries financing a large part of their absorption externally do not suffer more ferocious output losses in a sudden stop crisis, but take longer to adapt afterward and are hence expected to suffer more protracted crises periods. Compared with previous literature, this paper makes three contributions: (i) it extends the country and time coverage relative to datasets that have previously been used to analyze related topics; (ii) it specifically accounts for time-series autocorrelation; and (iii) it provides an analysis of the adjustment path of economic growth after a sudden stop.Currencies and Exchange Rates,Debt Markets,Achieving Shared Growth,Emerging Markets,Economic Theory&Research

Deep Learning Based Residuals in Non-linear Factor Models: Precision Matrix Estimation of Returns with Low Signal-to-Noise Ratio

This paper introduces a consistent estimator and rate of convergence for the precision matrix of asset returns in large portfolios using a non-linear factor model within the deep learning framework. Our estimator remains valid even in low signal-to-noise ratio environments typical for financial markets and is compatible with weak factors. Our theoretical analysis establishes uniform bounds on expected estimation risk based on deep neural networks for an expanding number of assets. Additionally, we provide a new consistent data-dependent estimator of error covariance in deep neural networks. Our models demonstrate superior accuracy in extensive simulations and the empirics