Tests for Specification Errors in Classical Linear Least-Squares Regression Analysis

Abstract

Summary The effects on the distribution of least‐squares residuals of a series of model mis‐specifications are considered. It is shown that for a variety of specification errors the distributions of the least‐squares residuals are normal, but with non‐zero means. An alternative predictor of the disturbance vector is used in developing four procedures for testing for the presence of specification error. The specification errors considered are omitted variables, incorrect functional form, simultaneous equation problems and heteroskedasticity.

House prices and regional labor markets

“…The diagnostics which we report in these tables are the t statistics on the coefficients, the coefficient of determination, the Durbin-Watson test for serial correlation, the F form of the second order RESET test of functional form due to Ramsey (1969), the F form of the second order ARCH test for heteroscedasticity devised by Engle (1982) and the chi-squared Jarque and Bera (1980) test for the normality of residuals.…”

An analysis of price formation in the Dutch mussel industry

“…The equation was Initially estimated on a monthly basis, using OLS over the time period 1988 to 1991 Quantities and prices of imports were thought probably to have some effect on Dutch prices and these variables were all tested for Prices of imports were not found to be slgmficant The best fit was found with the quantity of imports, speofically those from Germany Imports from Germany form the bulk of Dutch imports and are the most responsive to shortfalls on the Dutch market (Table 3) Because quantities for export are firstly traded at Yerseke, it was not surprising to find a high correlation between the quantity of exports and the total quantity of mussels traded at the auction market, as the quantity of exports is a subtotal of total quantity traded Therefore the quantity of exports was not included as a separate variable m the estimation The price of exports was found to have a significant and positive effect on the price at Yerseke However, causality is unclear Both Dutch wholesale and export prices are determined at the Yerseke auction market Therefore they may not be independent of each other It is as likely that Dutch wholesale prices influence export prices as vice versa Inclusion of the export price variable led the estimation to fall the RESET test for functional form (Ramsey, 1969) This variable was therefore excluded from the estimation Various alternative functional forms (linear, log-hnear, semdog) were examined and a linear format was found to give the best results Several criteria were considered m choosing the final model The first was consistency of expected signs and magnitudes for the coefficients of the explanatory variables The goodness of fit of the regression equation was evaluated by examining the r 2 and the F-statistic that test the lolnt hypothesis that all coefficients are zero Also the standard diagnostic tests of parameter restrictions and mls-speclfiCatlons were camed out, including the Durbln-Watson test of residual autocorrelatlon (Durbln and Watson, 1951), tests for heteroscedastlclty, parameter stabihty and simultaneity…”

Foreign dependence of individual stock prices: The role of aggregate product market developments

“…Since the presence of a specification error would imply biased estimates, we performed a regression specification error test (RESET) (see Ramsey 1969, Thursby 1981 …”