Bayesian comparison of production function-based and time-series GDP models

A purely Bayesian vector autoregression (VAR) framework is proposed to formulate and compare tri-variate models for the logs of the economy-wide aggregates of output and inputs (physical capital and labour). The framework is derived based on the theory of the aggregate production function, but at the same time, accounts for the dynamic properties of macroeconomic data, which makes it particularly appealing for modelling GDP. Next, using the proposed framework we confront a-theoretical time-series models with those that are based on aggregate production function-type relations. The common knowledge about capital and labour elasticities of output as well as on their sum is used in order to formulate prior distribution for each tri-variate model, favouring the linearly homogenous Cobb–Douglas production function-type relation. In spite of this, production function-based co-integration models fail empirical comparisons with simple VAR structures, which describe the three aggregates by three stochastic trends.