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. (Formerly circulated under the title "An
Alternative Sense of Asymptotic Efficiency".)
The paper
studies the asymptotic
efficiency and robustness of hypothesis tests when models of interest
are defined in terms of a weak convergence property. The null and local
alternatives induce different limiting distributions for a random
element, and a test is considered robust if it controls asymptotic size
for all data generating processes for which the random element has the
null limiting distribution. Under weak regularity conditions,
asymptotically robust and efficient tests are then simply given by
efficient tests of the limiting problem--that is, with the limiting
random element assumed observed--evaluated at sample analogues. These
tests typically coincide with suitably robustified versions of optimal
tests in canonical parametric versions of the model. This paper thus
establishes an alternative and broader sense of asymptotic efficiency
for many previously derived tests in econometrics, such as tests for
unit roots, parameter stability tests and tests about regression
coefficients under weak instruments.
Efficient
Estimation of the Parameter Path in Unstable Time Series Models.
Accepted for publication in the Review
of
Economic Studies. Supplement. (Joint with PHILIPPE-EMMANUEL
PETALAS.)
t-statistic
Based Correlation and
Heterogeneity Robust Inference. Accepted for publication in the Journal of Business &
Economic Statistics. Supplement. Alternative proof of small sample
conservativeness. (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.)