Using nonlinear testing procedures to specify the right hand side of an aggregate production function containing financial variables in the period 1967–2011

Starting with Sinai and Stokes (1972), a number of papers that followed included various measures of the financial sector (real balances) in an aggregate production function. Sinai and Stokes (1972) and many, but not all, of the studies used the Christensen and Jorgenson (1969, 1970) data on output, labor and capital for the period 1929–1967. While generalized least squares, GLS, was used to remove serial correlation, Fisher (1974) and others, including Sinai and Stokes (1972), were concerned about increasing returns to scale that were observed, even in the cases where the financial variable was omitted from the model. Stokes (2013) chose the four original datasets (annual data 1929–1967, nonfinancial quarterly data 1953:1 to 1977:3, annual data 1930–1978 and annual data 1959–1985) and used various nonlinear estimation techniques to test whether the estimated increasing returns might be due to an inappropriate functional forms rather than variable mismeasurement. In that paper, the finding of significant nonlinearities suggested that the choice of functional form might indeed be the cause of increasing returns. For a proper test of the source of the problem, however, other data and periods need to be investigated to rule out the possibility that data mismeasurement might have given a false indication of nonlinearity. If the estimated increasing returns could be removed and nonlinearity was not detected in models with alternative data, that finding would be consistent with the hypothesis that the original research was marred by data mismeasurement rather than function misspecification. The current paper uses a new annual dataset 1967–2011 and experiments with Divisia real monetary aggregates, in contrast to work which used the original real financial variables which were based on the usual simple sum M2 data. In addition an improved labor variable using hours was found to be superior, with the result that increasing returns is removed and no measured nonlinearity remains.