Effects of Demand Share Patterns on GDP, Okun's Law, Beveridge Curves, and Sector Sizes

Using a simple stochastic multi-sector model we show patterns of demand shares on sectors with different productivity coefficients have some expected and some unexpected effects on GDP, sector sizes, the magnitudes of the Okun's law coefficients, and Beveridge curves shifts. The basic stochastic multi-sector model is as in Aoki (2002, Sec.8.6) augmented with a scheme for firing and hiring workers. We distinguish pools of unemployed by some characteristics such as past job experiences, and introduce distances between different pools by use of ultrametric distance. We do not use the usual matching function device. When larger demand shares are allocated to less productive sectors, the sizes of these sectors become large. When demand patterns are changed before the model reaches some stochastic equilibrium, and less demand shares are allocated to less productive sectors, we show that the process of these sectors shrinking in size may overpower the process of size increases by more productive sectors and GDP may shrink in magnitude rather than increase as one would expect. Our simple model can also exhibit increase in the coefficient of the Okun's law, and shift of Beveridge curves.