Semiparametric estimation and inference using doubly robust moment conditions

We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step. The key difference is that we do not impose any parametric restriction on the nuisance functions that are estimated in a first stage, but retain a fully nonparametric model instead. We call these estimators semiparametric doubly robust estimators (SDREs), and show that they possess superior theoretical and practical properties compared to generic semiparametric two-step estimators. In particular, our estimators have substantially smaller first-order bias, allow for a wider range of nonparametric first-stage estimates, rate-optimal choices of smoothing parameters and data-driven estimates thereof, and their stochastic behavior can be well-approximated by classical first-order asymptotics. SDREs exist for a wide range of parameters of interest, particularly in semiparametric missing data and causal inference models. We illustrate our method with a simulation exercise.

Purchasing power parity and the unit root tests: a robust analysis

Empirical evidence suggests that real exchange rate is characterized by the presence of near-unity and additive outliers. Recent studeis have found evidence on favor PPP reversion by using the quasi-differencing (Elliott et al., 1996) unit root tests (ERS), which is more efficient against local alternatives but is still based on least squares estimation. Unit root tests basead on least saquares method usually tend to bias inference towards stationarity when additive out liers are present. In this paper, we incorporate quasi-differencing into M-estimation to construct a unit root test that is robust not only against near-unity root but also against nonGaussian behavior provoked by assitive outliers. We re-visit the PPP hypothesis and found less evidemce in favor PPP reversion when non-Gaussian behavior in real exchange rates is taken into account.

A unit root test based on partially adaptive estimation

This paper constructs a unit root test baseei on partially adaptive estimation, which is shown to be robust against non-Gaussian innovations. We show that the limiting distribution of the t-statistic is a convex combination of standard normal and DF distribution. Convergence to the DF distribution is obtaineel when the innovations are Gaussian, implying that the traditional ADF test is a special case of the proposed testo Monte Carlo Experiments indicate that, if innovation has heavy tail distribution or are contaminated by outliers, then the proposed test is more powerful than the traditional ADF testo Nominal interest rates (different maturities) are shown to be stationary according to the robust test but not stationary according to the nonrobust ADF testo This result seems to suggest that the failure of rejecting the null of unit root in nominal interest rate may be due to the use of estimation and hypothesis testing procedures that do not consider the absence of Gaussianity in the data.Our results validate practical restrictions on the behavior of the nominal interest rate imposed by CCAPM, optimal monetary policy and option pricing models.

Robust statistical modeling of portfolios

Atypical points in the data may result in meaningless e±cient frontiers. This follows since portfolios constructed using classical estimates may re°ect neither the usual nor the unusual days patterns. On the other hand, portfolios constructed using robust approaches are able to capture just the dynamics of the usual days, which constitute the majority of the business days. In this paper we propose an statistical model and a robust estimation procedure to obtain an e±cient frontier which would take into account the behavior of both the usual and most of the atypical days. We show, using real data and simulations, that portfolios constructed in this way require less frequent rebalancing, and may yield higher expected returns for any risk level.