Functional form, multicollinearity and the common equity valuation models

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1979
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Abstract

During the past three decades there have been a large number of research studies conducted in the area of share pricing models. The methodology typically used for estimation of the share pricing model has been the ordinary least squares regression analysis (OLS). The OLS technique is usually applied to cross-sectional data sets comprising financial variables such as dividends, expected growth in dividends, financial risk and business risk in order to estimate the regression coefficients (parameters). The parameter estimates should help investors to determine what relative weights the market places on various characteristics of common stock in setting share prices. A knowledge of this process can be used for the guidance of corporate financial policy. In most of the previous studies, the nature of the functional relationship between share price and its determinants has been assumed to be either linear or of the log-log type. However, there is no a priori economic rationale for the choice of either of these two functional forms. Previous studies have shown that the use of an inappropriate functional relationship can lead to incorrect parameter estimates. If the assumptions of the linear or log-log type of functional relationship between share price and its determinants are invalid, then the results of previous valuation studies could be in error. To search for the appropriate functional form, the generalized functional form technique (GFF), as originally developed by Box and Cox, was applied. Another problem area in previous valuation studies is the possible presence of multicollinearity in the data set. When a severe degree of multicollinearity Is present in the data, the OLS regression estimates can be both too large in magnitude and incorrect with respect to sign. There are several methods for obtaining more reliable parameter estimates when multicollinearity is a problem. One such method employed in this study is the ridge regression technique. The ridge regression technique is a biased estimation procedure that generally provides coefficient estimates with lower variances than OLS, when multicollinearity is present in the data set. A sample of 183 films from 26 different industry classifications was obtained from the COMPUSTAT files and regrouped to form six major industry subsamples, viz., food, wood, machinery, auto parts, chemical, and building materials. Preliminary OLS regressions were estimated for four annual cross-sections, 1967, 1969, 1971, and 1973, for each of the six industry groups to choose from alternate variable definitions on the basis of goodness of fit. Using the selected variable definitions, OLS regressions were estimated on ten annual industry cross-sections, 1965-1974. The loglog functional framework provided higher values of the coefficient of determination compared to the linear specification for all the industry groups except the chemical industry. This was further substantiated by the results of the OFF analysis on the data sets. In most cases, the appropriate functional form between the share price and its determinants was found not to be different form the log-log framework at the 5% level of significance. Using the Haitovsky test, the cross-sectional data sets with a high degree of multicollinearity were identified. Ridge regressions were estimated on these cross-sections, and the results indicated that the OLS parameters were inaccurate due to the presence of multicollinearity in the data set. When ridge regression was applied, the OLS regression coefficients on the dividend and growth variables appeared to be grossly overestimated while the sign on the total risk variable coefficient was contrary to expectations in some cases. Suggestions were made for further research.

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