Nearly Optimal Tests when a Nuisance Parameter is Present Under the Null Hypothesis.
(Joint with GRAHAM ELLIOTT and MARK
WATSON.)
This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish a bound on the weighted average power of all valid tests, and develop a numerical algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regression coefficient when the sign of a control coefficient is known; small sample inference about the difference in means from two independent Gaussian samples from populations with potentially different variances; inference about the break date in structural break models with moderate break magnitude; predictability tests when the regressor is highly persistent; inference about an interval identified parameter; and inference about a linear regression coefficient when the necessity of a control is in doubt.
Forecasts in a Slightly Misspecified Finite Order VAR.
(Joint with JAMES STOCK.)
We propose a Bayesian procedure for exploiting small, possibly long-lag linear predictability in the innovations of a finite order autoregression. We model the innovations as having a log-spectral density that is a continuous mean-zero Gaussian process of order 1/sqrt(T). This local embedding makes the problem asymptotically a normal-normal Bayes problem, resulting in closed-form solutions for the best forecast. When applied to data on 132 U.S. monthly macroeconomic time series, the method is found to improve upon autoregressive forecasts by an amount consistent with the theoretical and Monte Carlo calculations.
Measuring Prior Sensitivity and Prior Informativeness in Large Bayesian Models.
The paper derives measures of prior sensitivity and prior informativeness for posterior results in large Bayesian models that account for the high dimensional interaction between prior and likelihood information. The basis for both measures is the derivative matrix of the posterior mean with respect to the prior mean, which is easily obtained from Markov Chain Monte Carlo output. We illustrate the approach by examining posterior results in the unobserved factor model of Kose, Otrok and Whiteman (2003), the three equation dynamic stochastic general equilibirum model of Lubik and Schorfheide (2004), and Smets and Wouters' (2007) larger scale dynamic stochastic general equilibrium model.
Risk of Bayesian Inference in
Misspecified Models, and the Sandwich Covariance Matrix.
It is well known that in misspecified parametric models, the maximum likelihood estimator (MLE) is consistent for the pseudo-true value and has an asymptotically normal sampling distribution with "sandwich" covariance matrix. Also, posteriors are asymptotically centered at the MLE, normal and of asymptotic variance that is in general different than the sandwich matrix. It is shown that due to this discrepancy, Bayesian inference about the pseudo-true parameter value is in general of lower asymptotic risk when the original posterior is substituted by an artificial normal posterior centered at the MLE with sandwich covariance matrix. An algorithm is suggested that allows the implementation of this artificial posterior also in models with high dimensional nuisance parameters which cannot reasonably be estimated by maximizing the likelihood.
Pre and Post Break Parameter Inference. (Joint
with GRAHAM ELLIOTT.)
This paper provides a method for conducting inference about the pre and post break value of a scalar parameter in GMM time series models with a single break at an unknown date. We show that treating the break date estimated by least squares as the true break date leads to substantially oversized tests and confidence intervals unless the break is large. We develop an alternative test that controls size uniformly and that is approximately efficient in a well defined sense.
Low-Frequency Robust Cointegration Testing. (Joint
with MARK
WATSON.)
Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1) model for the common stochastic trends, which may not accurately describe the data's persistence. This paper discusses efficient low-frequency inference about cointegrating vectors that is robust to this potential misspecification. A simple test motivated by the analysis in Wright (2000) is developed and shown to be approximately optimal in the case of a single cointegrating vector.
Efficient Tests under a Weak Convergence
Assumption, Econometrica 79 (2011), 395 – 435. (Formerly circulated under the title "An
Alternative Sense of Asymptotic Efficiency".)
Efficient
Estimation of the Parameter Path in Unstable Time Series Models, Review
of
Economic Studies 77 (2010), 1508 – 1539. Supplement. Correction. (Joint with PHILIPPE-EMMANUEL
PETALAS.)
t-statistic
Based Correlation and
Heterogeneity Robust Inference, Journal of Business &
Economic Statistics 28 (2010), 453 – 468. Supplement. (Joint with RUSTAM IBRAGIMOV.)
Valid Inference in Partially Unstable
GMM
Models, Review
of
Economic Studies 76 (2009), 343 – 365. (Joint
with HONG LI.)
Comment on
"Unit Root Testing in Practice: Dealing with Uncertainty over the Trend
and Initial Condition" by D. I. Harvey, S. J. Leybourne and A. M. R.
Taylor, Econometric
Theory 25 (2009), 643 –
648.
Testing Models of Low-Frequency
Variability, Econometrica
76 (2008), 979 – 1016. (Joint with MARK
WATSON.)
The Impossibility of Consistent
Discrimination between I(0) and I(1) Processes, Econometric Theory
24 (2008), 616 – 630.
A Theory of
Robust Long-Run Variance Estimation, Journal of
Econometrics 141 (2007), 1331 – 1352. (Substantially
different 2004 working paper).
Confidence Sets for the Date
of a Single
Break in Linear Time Series Regressions, Journal of
Econometrics 141 (2007), 1196 – 1218.
(Joint with GRAHAM
ELLIOTT.)
Minimizing the Impact of the
Initial Condition on Testing for Unit Roots, Journal of
Econometrics 135 (2006), 285 – 310. (Joint with
GRAHAM ELLIOTT.)
Efficient Tests for General
Persistent Time Variation in
Regression
Coefficients, Review
of
Economic Studies 73 (2006), 907 – 940. Formerly
circulated under the title “Optimally Testing General
Breaking
Processes in Linear Time Series Models”. (Joint
with GRAHAM
ELLIOTT.)
Are
Forecasters Reluctant to Revise their Predictions? Some German
Evidence, Journal of
Forecasting 25 (2006), 401 – 413. (Joint with
GEBHARD KIRCHGÄSSNER.)
Size and Power of Tests for
Stationarity in Highly
Autocorrelated Time
Series, Journal
of
Econometrics 128 (2005), 195 – 213.
Tests for Unit Roots and the
Initial Condition, Econometrica
71
(2003), 1269 – 1286. (Joint with GRAHAM
ELLIOTT.)
Ecological Tax Reform and
Involuntary Unemployment: Simulation Results for Switzerland,
Schweizerische
Zeitschrift für Volkswirtschaft und Statistik 134
(1998), 329 – 359. (Joint with GEBHARD
KIRCHGÄSSNER and MARCEL
SAVIOZ.)