Received May 1973, revised version received December 1973 | C.W.J. GRANGER and P. NEWBOLD
The paper by C.W.J. Granger and P. Newbold addresses the issue of spurious regression in econometrics, where time series regression equations show a high degree of fit (as measured by the coefficient of multiple correlation \( R^2 \) or the corrected coefficient \( \bar{R}^2 \)) but have extremely low Durbin-Watson statistics. Despite warnings in econometric textbooks about the dangers of autocorrelated errors, such cases are frequently observed in applied research. The authors highlight three major consequences of autocorrelated errors: inefficient estimates of regression coefficients, sub-optimal forecasts, and invalid significance tests. They focus on the third point, examining the potential for 'discovering' spurious relationships in current econometric methodology.
The paper begins by summarizing relevant results in time series analysis, including the mixed autoregressive moving average (ARIMA) process and the importance of differencing to achieve stationarity. It then discusses how nonsense regressions can arise when the independent variables are non-stationary or highly autocorrelated, leading to inappropriate test procedures. The authors conduct simulation experiments to illustrate these points, showing that high \( R^2 \) values and low \( d \) values do not necessarily indicate a true relationship.
In the discussion and conclusion, Granger and Newbold emphasize the importance of considering the time series properties of variables and recommend taking first differences of highly autocorrelated variables. They suggest building models with both levels and changes to improve interpretability and reduce the risk of spurious relationships. The authors also discuss the relevance of their findings to the structural model-reduced form controversy, arguing that a good theory should provide a structure where residuals are white noises and can be forecast from other economic variables.The paper by C.W.J. Granger and P. Newbold addresses the issue of spurious regression in econometrics, where time series regression equations show a high degree of fit (as measured by the coefficient of multiple correlation \( R^2 \) or the corrected coefficient \( \bar{R}^2 \)) but have extremely low Durbin-Watson statistics. Despite warnings in econometric textbooks about the dangers of autocorrelated errors, such cases are frequently observed in applied research. The authors highlight three major consequences of autocorrelated errors: inefficient estimates of regression coefficients, sub-optimal forecasts, and invalid significance tests. They focus on the third point, examining the potential for 'discovering' spurious relationships in current econometric methodology.
The paper begins by summarizing relevant results in time series analysis, including the mixed autoregressive moving average (ARIMA) process and the importance of differencing to achieve stationarity. It then discusses how nonsense regressions can arise when the independent variables are non-stationary or highly autocorrelated, leading to inappropriate test procedures. The authors conduct simulation experiments to illustrate these points, showing that high \( R^2 \) values and low \( d \) values do not necessarily indicate a true relationship.
In the discussion and conclusion, Granger and Newbold emphasize the importance of considering the time series properties of variables and recommend taking first differences of highly autocorrelated variables. They suggest building models with both levels and changes to improve interpretability and reduce the risk of spurious relationships. The authors also discuss the relevance of their findings to the structural model-reduced form controversy, arguing that a good theory should provide a structure where residuals are white noises and can be forecast from other economic variables.