Jonathan H. Wright

A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments

Weak instruments arise when the instruments in linear instrumental variables (IV) regression are weakly correlated with the included endogenous variables. In generalized method of moments (GMM), more generally, weak instruments correspond to weak identification of some or all of the unknown parameters. Weak identification leads to GMM statistics with nonnormal distributions, even in large samples, so that conventional IV or GMM inferences are misleading. Fortunately, various procedures are now available for detecting and handling weak instruments in the linear IV model and, to a lesser degree, in nonlinear GMM.

GMM with Weak Identification

This paper develops asymptotic distribution theory for GMM estimators and test statistics when some or all of the parameters are weakly identified. General results are obtained and are specialized to two important cases: linear instrumental variables regression and Euler equations estimation of the CCAPM. Numerical results for the CCAPM demonstrate that weak-identification asymptotics explains the breakdown of conventional GMM procedures documented in previous Monte Carlo studies. Confidence sets immune to weak identification are proposed. We use these results to inform an empirical investigation of various CCAPM specifications; the substantive conclusions reached differ from those obtained using conventional methods.

Alternative Variance-Ratio Tests Using Ranks and Signs

This article proposes using variance-ratio tests based on the ranks and signs of a time series to test the null that the series is a martingale difference sequence. Unlike conventional variance-ratio tests, these tests can be exact. In Monte Carlo simulations, I find that they can also be more powerful than conventional variance-ratio tests. I apply the proposed tests to five exchange-rate series and find that they are capable of detecting violations of the martingale hypothesis for all five series, whereas conventional variance-ratio tests yield ambiguous results.

An arbitrage-free three-factor term structure model and the recent behavior of long-term yields and distant-horizon forward rates

This paper reviews a simple three-factor arbitrage-free term structure model estimated by Federal Reserve Board staff and reports results obtained from fitting this model to U.S. Treasury yields since 1990. The model ascribes a large portion of the decline in long-term yields and distant-horizon forward rates since the middle of 2004 to a fall in term premiums. A variant of the model that incorporates inflation data indicates that about two-thirds of the decline in nominal term premiums owes to a fall in real term premiums, but estimated compensation for inflation risk has diminished as well.

The TIPS Yield Curve and Inflation Compensation

For over ten years, the U.S. Treasury has issued index-linked debt. Federal Reserve Board staff have fitted a yield curve to these indexed securities at the daily frequency from the start of 1999 to the present. This paper describes the methodology that is used and makes the estimates public. Comparison with the corresponding nominal yield curve allows measures of inflation compensation (or breakeven inflation rates) to be computed. We discuss the interpretation of inflation compensation and its relationship to inflation expectations and uncertainty, offering some empirical evidence that these measures are affected by an inflation risk premium that varies considerably at high frequency. In addition, we also find evidence that inflation compensation was held down in the early years of the sample by a premium associated with the illiquidity of TIPS at the time. We hope that the TIPS yield curve and inflation compensation data, which are posted here and will be updated periodically, will provide a useful tool to applied economists.

Bayesian Model Averaging and Exchange Rate Forecasts

Exchange rate forecasting is hard and the seminal result of Meese and Rogoff (1983) that the exchange rate is well approximated by a driftless random walk, at least for prediction purposes, has never really been overturned despite much effort at constructing other forecasting models. However, in several other macro and financial forecasting applications, researchers in recent years have considered methods for forecasting that combine the information in a large number of time series. One method that has been found to be remarkably useful for out-of-sample prediction is simple averaging of the forecasts of different models. This often seems to work better than the forecasts from any one model. Bayesian Model Averaging is a closely related method that has also been found to be useful for out-of-sample prediction. This starts out with many possible models and prior beliefs about the probability that each model is the true one. It then involves computing the posterior probability that each model is the true one, and averages the forecasts from the different models, weighting them by these posterior probabilities. This is effectively a shrinkage methodology, but with shrinkage over models not just over parameters. I apply this Bayesian Model Averaging approach to pseudo-out-of-sample exchange rate forecasting over the last ten years. I find that it compares quite favorably to a driftless random walk forecast. Depending on the currency-horizon pair, the Bayesian Model Averaging forecasts sometimes do quite a bit better than the random walk benchmark (in terms of mean square prediction error), while they never do much worse. The forecasts generated by this model averaging methodology are however very close to (but not identical to) those from the random walk forecast.

News and Noise in G-7 GDP Announcements

Revisions to GDP announcements are known to be quite large in all G-7 countries: many revisions in quarterly GDP growth are over a full percentage point at an annualized rate. In this paper, we examine the predictability of these data revisions. Previous work suggests that U.S. GDP revisions are largely unpredictable, as would be the case if the revisions reflect news not available at the time that the preliminary number is produced. We find that the degree of predictability varies throughout the G-7. For the U.S., the revisions are very slightly predictable, but for Italy, Japan and the UK, about half the variability of subsequent revisions can be accounted for by information available at the time of the preliminary announcement. For these countries, it appears that revisions reflect, to a significant degree, the removal of noise from the preliminary numbers, rather than the arrival of news.

Identifying VARs Based on High Frequency Futures Data

Using the prices of federal funds futures contracts, we measure the impact of the surprise component of Federal Reserve policy decisions on the expected future trajectory of interest rates. We show how this information can be used to identify the effects of a monetary policy shock in a standard monetary policy VAR. This constitutes an alternative approach to identification that is quite different, and, we would argue, more plausible, than the conventional short-run restrictions. We find that the usual recursive identification of the model is rejected, but we nevertheless agree with the literatures conclusion that only a small fraction of the variance of output can be attributed to monetary policy shocks.

Comparing Greenbook and Reduced Form Forecasts Using a Large Realtime Dataset

Many recent articles have found that atheoretical forecasting methods using many predictors give better predictions for key macroeconomic variables than various small-model methods. The practical relevance of these results is open to question, however, because these articles generally use ex post revised data not available to forecasters and because no comparison is made to best actual practice. We provide some evidence on both of these points using a new large dataset of vintage data synchronized with the Fed’s Greenbook forecast. This dataset consist of a large number of variables as observed at the time of each Greenbook forecast since 1979. We compare realtime, large dataset predictions to both simple univariate methods and to the Greenbook forecast. For inflation we find that univariate methods are dominated by the best atheoretical large dataset methods and that these, in turn, are dominated by Greenbook. For GDP growth, in contrast, we find that once one takes account of Greenbook’s advantage in evaluating the current state of the economy, neither large dataset methods, nor the Greenbook process offers much advantage over a univariate autoregressive forecast.

Uncovered Interest Parity: It Works, But Not For Long

The failure of uncovered interest parity can be ascribed to the existence of a risk premium. The size of this risk premium may shrink to zero over sufficiently small intervals of time. In contrast, because no interest is paid on intradaily positions and interest is instead paid discretely at the point when a position is rolled over from one day to the next, the size of the interest differential remains fixed over any interval that covers the time of the discrete interest payment. This is true no matter how short that interval is. Using a large dataset of high frequency exchange rate data, we run uncovered interest parity regressions over different time intervals. We replicate the rejection of the uncovered interest parity hypothesis with daily data, but find results that are consistently much more supportive of the uncovered interest parity hypothesis over short windows of intradaily data that span the time of the discrete interest payment.