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.

This paper studies the role of fluctuations in the aggregate consumption–wealth ratio for predicting stock returns. Using U.S. quarterly stock market data, we find that these fluctuations in the consumption–wealth ratio are strong predictors of both real stock returns and excess returns over a Treasury bill rate. We also find that this variable is a better forecaster of future returns at short and intermediate horizons than is the dividend yield, the dividend payout ratio, and several other popular forecasting variables. Why should the consumption–wealth ratio forecast asset returns? We show that a wide class of optimal models of consumer behavior imply that the log consumption–aggregate wealth ~human capital plus asset holdings! ratio summarizes expected returns on aggregate wealth, or the market portfolio. Although this ratio is not observable, we provide assumptions under which its important predictive components for future asset returns may be expressed in terms of observable variables, namely in terms of consumption, asset holdings and labor income. The framework implies that these variables are cointegrated, and

This paper employs response surface regressions based on simulation experiments to calculate asymptotic distribution functions for the Johansen-type likelihood ratio tests for cointegration. These are carried out in the context of the models recently proposed by Pesaran, Shin, and Smith (1997) that allow for the possibility of exogenous variables integrated of order one. The paper calculates critical values that are very much more accurate than those available previously. The principal contributions of the paper are a set of data files that contain estimated asymptotic quantiles obtained from response surface estimation and a computer program for utilizing them. This program, which is freely available via the Internet, can be used to calculate both asymptotic critical values and P values. JEL Classification Number: C22 Keywords: cointegration tests, Johansen tests, vector autoregressions, exogenous variables, response surfaces, critical values, approximate

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We study market microstructure noise in high-frequency data and analyze its implications for the real-ized variance (RV) under a general specification for the noise. We show that kernel-based estimators can unearth important characteristics of market microstructure noise and that a simple kernel-based estimator dominates the RV for the estimation of integrated variance (IV). An empirical analysis of the Dow Jones Industrial Average stocks reveals that market microstructure noise is time-dependent and correlated with increments in the efficient price. This has important implications for volatility estimation based on high-frequency data. Finally, we apply cointegration techniques to decompose transaction prices and bid–ask quotes into an estimate of the efficient price and noise. This framework enables us to study the dynamic effects on transaction prices and quotes caused by changes in the efficient price.

Are business cycles mainly the result of permanent shocks to productivity? This paper uses a long-run restriction implied by a large class of real-business-cycle models-identifying permanent productivity shocks as shocks to the common stochastic trend in output, consumption, and investment-to provide new evidence on this question. Econometric tests indicate that this common-stochastic-trend / cointegration implication is consistent with postwar U.S. data. However, in systems with nominal variables, the estimates of this common stochastic trend indicate that permanent productivity shocks typically explain less than half of the business-cycle variability in output, consumption, and investment. (JEL E32, C32) A central, surprising, and controversial result of some current research on real business cycles is the claim that a common stochastic trend-the cumulative effect of permanent shocks to productivity-underlies the bulk of economic fluctuations. If confirmed, this finding would imply that many other forces have been relatively unimportant over historical business cycles, including the monetary and fiscal policy shocks stressed in traditional macroeconomic analysis. This paper shows that the hypothesis of a common stochastic productivity trend has a set of econometric implications that allows us to test for its presence, measure its importance, and extract estimates of its realized value. Applying these procedures to consumption, investment, and output for the postwar United States, we find results that both support and contradict this claim in the real-businesscycle literature. The U.S. data are consis-

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amples in this text rely on a small data sample with 49 observations that can be used with the Student Version of MATLAB. The collection of around 450 functions and demonstration programs are organized into libraries, with approximately 30 spatial econometrics library functions described in this text. For those interested in other econometric functions or in adding programs to the spatial econometrics library, see the manual for the Econometrics Toolbox. The 350 page manual provides many details regarding programming techniques used to construct the functions and examples of adding new functions to the Econometrics Toolbox. This text does not focus on programming methods. The emphasis here is on applying the existing spatial econometric estimation functions to modeling spatial data sets. A consistent design was implemented that provides documentation, example programs, and functions to produce printed as well as graphical presentation of estimation results for all of the econometric functions. This

Both textbook economics and common sense teach us that the value of household wealth should be related to consumer spending. Early academic work by Franco Modigliani (1971) suggested that a dollar increase in wealth (holding � xed labor income) leads to an increase in consumer spending of about � ve cents. Since then, the so-called “wealth effect ” on consumption has increasingly crept into both mainstream and policy discussions of the macroeconomy. 1 Today, it is commonly presumed that signi �-cant movements in wealth will be associated with movements in consumer spending, either contemporaneously or subsequently. Quantitative estimates of roughly the magnitude reported by Modigliani are routinely cited in

This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of non-stationarity in the data. We refer to it as PANIC – a ‘Panel Analysis of Non-stationarity in Idiosyncratic and Common components’. PANIC consists of univariate and panel tests with a number of novel features. It can detect whether the nonstationarity is pervasive, or variable-specific, or both. It tests the components of the data instead of the observed series. Inference is therefore more accurate when the components have different orders of integration. PANIC also permits the construction of valid panel tests even when cross-section correlation invalidates pooling of statistics constructed using the observed data. The key to PANIC is consistent estimation of the components even when the regressions are individually spurious. We provide a rigorous theory for estimation and inference. In Monte Carlo simulations, the tests have very good size and power. PANIC is applied to a panel of inflation series.