Testing for Weak Instruments in Linear IV Regression

Weak instruments can produce biased IV estimators and hypothesis tests with large size distortions. But what, precisely, are weak instruments, and how does one detect them in practice? This paper proposes quantitative definitions of weak instruments based on the maximum IV estimator bias, or the maximum Wald test size distortion, when there are multiple endogenous regressors. We tabulate critical values that enable using the first-stage F-statistic (or, when there are multiple endogenous regressors, the Cragg-Donald (1993) statistic) to test whether given instruments are weak. A technical contribution is to justify sequential asymptotic approximations for IV statistics with many weak instruments.

The Use of Monetary Aggregate to Target Nominal GDP

This paper studies the possibility of using the broad monetary aggregate M2 to target the quarterly rate of growth of nominal GDP. Our findings indicate that the Federal Reserve could probably guide M2 in a way that reduces not only the long-term average rate of inflation but also the variance of the annual rate of growth of nominal GDP. An optimal M2 rule, derived from a simple VAR, reduces the mean ten-year standard deviation of annual GDP growth by over 20 percent. Although there is uncertainty about this value because of both parameter uncertainty and stochastic shocks to the economy, we estimate that the probability that the annual variance would be reduced over a ten year period exceeds 85 percent. A much simpler policy based on a single equation linking M2 and GDP is shown to be almost as successful in reducing this annual GDP variance. Additional statistical tests indicate that M2 is a useful predictor of nominal GDP. Moreover, a battery of recently developed tests for parameter stability fails to reject the hypothesis that the M2 - GDP link is stable, but the MI - GDP and monetary base - GDP relations are found to be highly unstable. This evidence contradicts those who have argued that the M2 - GDP relation is so unstable in the short run that it cannot be used to reduce the variance of nominal GDP growth.

Measuring Money Growth When Financial Markets Are Changing

This paper examines the problem of measuring the growth of a monetary aggregate in the presence of innovations in financial markets and changes in the relationship between individual assets and output. We propose constructing a monetary aggregate so that it is a good leading indicator of nominal GDP; in general the weights on its components vary over time. We investigate two specific procedures: one in which subaggregates discretely switch in and out, and one in which the growth of the aggregate is a time-varying weighted average of the growth of the subaggregates, where the weights follow a random walk. These procedures are used to construct aggregates which potentially augment M2 with stock and/or bond mutual funds. Over 1960-1991, the time-varying aggregates look much like M2, but during 1992-93 the time-varying aggregates outperform M2.

Inference with Weak Instruments

This paper reviews recent developments in methods for dealing with weak instruments (IVs) in IV regression models. The focus is more on tests (and confidence intervals derived from tests) than estimators. The paper also presents new testing results under "many weak IV asymptotics," which are relevant when the number of IVs is large and the coefficients on the IVs are relatively small. Asymptotic power envelopes for invariant tests are established. Power comparisons of the conditional likelihood ratio (CLR), Anderson-Rubin, and Lagrange multiplier tests are made. Numerical results show that the CLR test is on the asymptotic power envelope. This holds no matter what the relative magnitude of the IV strength to the number of IVs.Conditional likelihood ratio test, instrumental variables, many instrumental variables, power envelope, weak instruments

Has the Business Cycle Changed and Why?

From 1960-1983, the standard deviation of annual growth rates in real GDP in the United States was 2.7%. From 1984-2001, the corresponding standard deviation was 1.6%. This paper investigates this large drop in the cyclical volatility OF real economic.activity. The paper has two objectives. The first is to provide a comprehensive characterization of the decline in volatility using a large number of U.S. economic time series and a variety of methods designed to describe time-varying time series processes. In so doing, the paper reviews the literature on the moderation and attempts to resolve some of its disagreements and discrepancies. The second objective is to provide new evidence on the quantitative importance of various explanations for this 'great moderation.' Taken together, we estimate that the moderation in volatility is attributable to a combination of improved policy (20-30%), identifiable good luck in the form of productivity and commodity price shocks (20-30%), and other unknown forms of good luck that manifest themselves as smaller reduced-form forecast errors (40-60%).

A Relationship Between Regression Tests and Volatility Tests of Market ncy

Volatility tests are an alternative to regression tests for evaluating the joint null hypothesis of market efficiency and risk neutrality. Acomparison of the power of the two kinds of tests depends on what the alternative hypothesis is taken to be. By considering tests based on conditional volatility bounds, we show that if the alternative is that one could"beat the market" using a linear combination of known variables, then the regression tests are at least as powerful as the conditional volatility tests.If the application is to spot and forward markets, then the most powerful conditional volatility test turns out to be equivalent to the analogous regression test in terms of asymptotic power. In other applications,the volatility test will be less powerful than regression tests against our chosen alternative. However, these results are not inconsistent with the observation that volatility tests may be more powerful against other alternative hypoth-eses, such as that risk-averse investors are rationally maximizing the present discounted utility of future consumption,with a time-varying discount rate.

Understanding Changes in International Business Cycle Dynamics

The volatility of economic activity in most G7 economies has moderated over the past forty years. Also, despite large increases in trade and openness, G7 business cycles have not become more synchronized. After documenting these twin facts, we interpret G7 output data using a structural VAR that separately identifies common international shocks, the domestic effects of spillovers from foreign idiosyncratic shocks, and the effects of domestic idiosyncratic shocks. This analysis suggests that, with the exception of Japan, the widespread reduction in volatility is in large part associated with a reduction in the magnitude of the common international shocks. Had the common international shocks in the 1980s and 1990s been as large as they were in the 1960s and 1970s, G7 business cycles would have been substantially more volatile and more highly synchronized than they actually were.