Clive W. J. Granger

Investigating Causal Relations by Econometric Models and Cross-Spectral Methods

There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.

Co-integration and Error Correction: Representation, Estimation, and Testing

The relationship between cointegration and error correction models, first suggested by Granger, is here extended and used to develop estimation procedures, tests, and empirical examples. A vector of time series is said to be cointegrated with cointegrating vector a if each element is stationary only after differencing while linear combinations a8xt are themselves stationary. A representation theorem connects the moving average , autoregressive, and error correction representations for cointegrated systems. A simple but asymptotically efficient two-step estimator is proposed and applied. Tests for cointegration are suggested and examined by Monte Carlo simulation. A series of examples are presented. Copyright 1987 by The Econometric Society.

Spurious regressions in econometrics

It is very common to see reported in applied econometric literature time series regression equations with an apparently high degree of fit, as measured by the coefficient of multiple correlation R2 or the corrected coefficient R2, but with an extremely low value for the Durbin-Watson statistic. We find it very curious that whereas virtually every textbook on econometric methodology contains explicit warnings of the dangers of autocorrelated errors, this phenomenon crops up so frequently in well-respected applied work. Numerous examples could be cited, but doubtless the reader has met sufficient cases to accept our point. It would, for example, be easy to quote published equations for which R2 = 0.997 and the Durbin-Watson statistic (d) is 0.53. The most extreme example we have met is an equation for which R2 = 0.99 and d = 0.093. I-Iowever, we shall suggest that cases with much less extreme values may well be entirely spurious. The recent experience of one of us [see Box and Newbold (1971)] has indicated just how easily one can be led to produce a spurious model if sufficient care is not taken over an appropriate formulation for the autocorrelation structure of the errors from the regression equation. We felt, then, that we should undertake a more detailed enquiry seeking to determine what, if anything, could be inferred from those regression equations having the properties just described. There are, in fact, as is well-known, three major consequences of autocorrelated errors in regression analysis :

A long memory property of stock market returns and a new model

Abstract A ‘long memory’ property of stock market returns is investigated in this paper. It is found that not only there is substantially more correlation between absolute returns than returns themselves, but the power transformation of the absolute return ¦rt¦d also has quite high autocorrelation for long lags. It is possible to characterize ¦rt¦d to be ‘long memory’ and this property is strongest when d is around 1. This result appears to argue against ARCH type specifications based upon squared returns. But our Monte-Carlo study shows that both ARCH type models based on squared returns and those based on absolute return can produce this property. A new general class of models is proposed which allows the power δ of the heteroskedasticity equation to be estimated from the data.

Some recent development in a concept of causality

Abstract The paper considers three separate but related topics. (i) What is the relationship between causation and co-integration? If a pair of I(1) series are co-integration, there must be causation in at least one direction. An implication is that some tests of causation based on different series may have missed one source of causation. (ii) Is there a need for a definition of ‘instantaneous causation’ in a decision science? It is argued that no such definition is required. (iii) Can causality tests be used for policy evaluation? It is suggested that these tests are useful, but that they should be evaluated with care.

The combination of forecasts

Two separate sets of forecasts of airline passenger data have been combined to form a composite set of forecasts. The main conclusion is that the composite set of forecasts can yield lower mean-square error than either of the original forecasts. Past errors of each of the original forecasts are used to determine the weights to attach to these two original forecasts in forming the combined forecasts, and different methods of deriving these weights are examined.

Some properties of time series data and their use in econometric model specification

It is well known that time-series analysts have a rather different approach to the analysis of economic data than does the remainder of the econometric profession. One aspect of this difference is that we admit more readily to looking at the data before finally specifying a model, in fact we greatly encourage looking at the data. Although econometricians trained in a more traditional manner are still very much inhibited in the use of summary statistics derived from the data to help model selection, or identification, it could be to their advantage to change some of these attitudes. In fact, I have heard rumors that econometricians do data-mine in the privacy of their own offices and I am merely suggesting that some aspects, at least, of this practice should be brought out into the open. The type of equations to be considered are generating equations, so that a simulation of the explanatory side should produce the major properties of the variable being explained. If an equation has this property, it will be said to be consistent, reverting to the original meaning of this term. As a simple example of a generally non-consistent model, suppose that one has

Testing for causality: A personal viewpoint

Abstract A general definition of causality is introduced and then specialized to become operational. By considering simple examples a number of advantages, and also difficulties, with the definition are discussed. Tests based on the definitions are then considered and the use of post-sample data emphasized, rather than relying on the same data to fit a model and use it to test causality. It is suggested that a Bayesian viewpoint should be taken in interpreting the results of these tests. Finally, the results of a study relating advertising and consumption are briefly presented.

Estimation of Common Long-Memory Components in Cointegrated Systems

The study of cointegration in large systems requires a reduction of their dimensionality. To achieve this, we propose to obtain the I(1) common factors in every subsystem and then analyze cointegration among them. In this article, a new way of estimating common long-memory components of a cointegrated system is proposed. The identification of these I(1) common factors is achieved by imposing that they be linear combinations of the original variables Xt , and that the error-correction terms do not cause the common factors at low frequencies. Estimation is done from a fully specified error-correction model, which makes it possible to test hypotheses on the common factors using standard chi-squared tests. Several empirical examples illustrate the procedure.

Semiparametric Estimates of the Relation between Weather and Electricity Sales

Abstract A nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data. This accommodates introduction of covariates, timing adjustments due to the actual billing schedules, and serial correlation. The procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross-validation criterion introduced by Craven and Wahba (1979). Estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines.