Mark W. Watson

A simple estimator of cointegrating vectors in higher order integrated systems

Efficient estimators of cointegrating vectors are presented for systems involving deterministic components and variables of differing, higher orders of integration. The estimators are computed using GLS or OLS, and Wald Statistics constructed from these estimators have asymptotic x2 distributions. These and previously proposed estimators of cointegrating vectors are used to study long-run U.S. money (Ml) demand. Ml demand is found to be stable over 1900-1989; the 95% confidence intervals for the income elasticity and interest rate semielasticity are (.88,1.06) and (-.13, -.08), respectively. Estimates based on the postwar data alone, however, are unstable, with variances which indicate substantial sampling uncertainty.

Testing for Common Trends

Abstract Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are often modeled as having a unit root in their autoregressive representation, or (equivalently) as containing a stochastic trend. But both casual observation and economic theory suggest that many series might contain the same stochastic trends so that they are cointegrated. If each of n series is integrated of order 1 but can be jointly characterized by k > n stochastic trends, then the vector representation of these series has k unit roots and n — k distinct stationary linear combinations. Our proposed tests can be viewed alterna...

Macroeconomic Forecasting Using Diffusion Indexes

This article studies forecasting a macroeconomic time series variable using a large number of predictors. The predictors are summarized using a small number of indexes constructed by principal component analysis. An approximate dynamic factor model serves as the statistical framework for the estimation of the indexes and construction of the forecasts. The method is used to construct 6-, 12-, and 24-monthahead forecasts for eight monthly U.S. macroeconomic time series using 215 predictors in simulated real time from 1970 through 1998. During this sample period these new forecasts outperformed univariate autoregressions, small vector autoregressions, and leading indicator models.

Forecasting Using Principal Components From a Large Number of Predictors

This article considers forecasting a single time series when there are many predictors (N) and time series observations (T). When the data follow an approximate factor model, the predictors can be summarized by a small number of indexes, which we estimate using principal components. Feasible forecasts are shown to be asymptotically efficient in the sense that the difference between the feasible forecasts and the infeasible forecasts constructed using the actual values of the factors converges in probability to 0 as both N and T grow large. The estimated factors are shown to be consistent, even in the presence of time variation in the factor model.

Forecasting Output and Inflation: The Role of Asset Prices

This paper examines old and new evidence on the predictive performance of asset prices for inflation and real output growth. We first review the large literature on this topic, focusing on the past dozen years. We then undertake an empirical analysis of quarterly data on up to 38 candidate indicators (mainly asset prices) for seven OECD countries for a span of up to 41 years (1959 1999). The conclusions from the literature review and the empirical analysis are the same. Some asset prices predict either inflation or output growth in some countries in some periods. Which series predicts what, when and where is, however, itself difficult to predict: good forecasting performance by an indicator in one period seems to be unrelated to whether it is a useful predictor in a later period. Intriguingly, forecasts produced by combining these unstable individual forecasts appear to improve reliably upon univariate benchmarks.

Systematic Monetary Policy and the Effects of Oil Price Shocks

Macroeconomic shocks such as wil price increases induce a systematic (endogenous) response of monetary policy. We develop a VAR-based technique for decomposing the total economic effects of a given exogenous shock into the portion attributable directly to the shock and the part arising from the policy response to the shock.

Sources of Business Cycle Fluctuations

What shocks account for the business cycle frequency and long-run movements of output and prices? This paper addresses this question using the identifying assumption that only supply shocks, such as shocks to technology, oil prices, and labor supply affect output in the long-run. Real and monetary aggregate demand shocks can affect output, but only in the short-run. This assumption sufficiently restricts the reduced form of key macroeconomic variables to allow estimation of the shocks and their effect on output and price at all frequencies. Aggregate demand shocks account for about 20 percent to 30 percent of output fluctuations at business cycle frequencies. Technological shocks account for about 1/4 of cyclical fluctuations, and about 1/3 of outputs variance at low frequencies. Shocks to oil prices are important in explaining episodes in the 1970s and 1980s. Shocks that permanently affect labor input account for the balance of fluctuations in output, namely, about half of its variance at all frequencies.

Univariate detrending methods with stochastic trends

Abstract This paper discusses detrending economic time series, when the trend is modelled as a stochastic process. It considers unobserved components models in which the observed series is decomposed into a trend (a random walk with drift) and a residual stationary component. Optimal detrending methods are discussed, as well as problems associated with using these detrended data in regression models. The methods are applied to three time series: GNP, disposable income, and consumption expenditures. The detrended data are used to test a version of the Life Cycle consumption model.

Evidence on Structural Instability in Macroeconomic Time Series Relations

An experiment is performed to assess the prevalence of instability in univariate and bivariate macroeconomic time series relations and to ascertain whether various adaptive forecasting techniques successfully handle any such instability. Formal tests for instability and out-of-sample forecasts from sixteen different models are computed using a sample of 76 representative U.S. monthly postwar macroeconomic time series, constituting 5700 bivariate forecasting relations. The tests indicate widespread instability in univariate and bivariate autoregressive models. However, adaptive forecasting models, in particular time varying parameter models, have limited success in exploiting this instability to improve upon fixed-parameter or recursive autoregressive forecasts.

Interpreting the evidence on money-income causality☆

Previous authors have reached puzzlingly different conclusions about the usefulness of money for forecasting real output based on closely related regression-based tests. An examination of this and additional new evidence reveals that innovations in M1 have statistically significant marginal predictive value for industrial production, both in a bivariate model and in a multivariate setting including a price index and an interest rate. This conclusion follows from focusing on the trend properties of the data, both stochastic and deterministic, and from drawing inferences using asymptotic theory that explicitly addresses the implications of these trends for the distributions of the various test statistics.