Popper and production: Testing parametric restrictions in systems under nonstationarity

This study tests symmetry and homogeneity restrictions on a system of facto r demand equations for central and western Canadian agriculture under the a ssumption that the variables are integrated processes and the demands repre sent cointegrating relationships. It is well known that the distribution of f-statistics derived from ordinary least squares estimates in such systems are not distributed as the ratio of two independent chi(2) random variables normalized by their degrees of freedom even asymptotically. Indeed, the us e of traditional critical values of F-statistics in such cases will severel y underestimate the tote critical values and therefore use of traditional c ritical values would tend to overreject symmetry and homogeneity restrictio ns. Bootstrapping techniques are employed to generate the true distribution of the F-statistic so that the proper critical values call be compared wit h the calculated F-statistic on symmetry and ho,homogeneity. For both regio ns, the calculated F-statistic is not rejected using the proper critical va lues but would have been strongly rejected using standard critical values. Results are consistent with the argument that the regularity of rejection o f the parametric restrictions of symmetry and homogeneity found by Fox and Kivanda may be due to inappropriate assumptions regarding the time series p roperties of the data rather than a rejection of neoclassical production th eory. This interpretation is consistent with arguments made by Clark and Co yle in their comments on Fox and Kivanda.