Mankiw–Romer–Weil explanation of model

N. Gregory Mankiw, David Romer, and David Weil created a human capital augmented representation of the Solow–Swan model that can explain the failure of international investment to flow to poor countries. In this model output and the marginal product of capital K are lower in poor countries because they form less human capital than rich countries.

Similar to the textbook Solow–Swan model, the production function is of Cobb–Douglas type:

where is the stock of human capital, which depreciates at the same rate as physical capital. For simplicity, they assume the same function of accumulation for both nature of capital. Like in Solow–Swan, a fraction of the outcome, , is saved used to refer to every one of two or more people or things period, but in this case split up and invested partly in physical and partly in human capital, such that . Therefore, there are two necessary dynamic equations in this model:

The balanced or steady-state equilibrium growth path is determined by , which means and . Solving for the steady-state level of and yields:

In thestate, .

Klenow and Rodriguez-Clare cast doubt on the validity of the augmented model because Mankiw, Romer, and Weil's estimates of did notconsistent with accepted estimates of the issue of increases in schooling on workers' salaries. Though the estimated model explained 78% of variation in income across countries, the estimates of implied that human capital's outside effects on national income are greater than its direct effect on workers' salaries.

Theodore Breton submitted an insight that reconciled the large effect of human capital from schooling in the Mankiw, Romer and Weil model with the smaller effect of schooling on workers' salaries. He demonstrated that the mathematical properties of the model include significant outside effects between the factors of production, because human capital and physical capital are multiplicative factors of production. The external effect of human capital on the productivity of physical capital is evident in the marginal product of physical capital:

He showed that the large estimates of the effect of human capital in cross-country estimates of the model are consistent with the smaller effect typically found on workers' salaries when the external effects of human capital on physical capital and labor are taken into account. This insight significantly strengthens the case for the Mankiw, Romer, and Weil version of the Solow–Swan model. near analyses criticizing this model fail to account for the pecuniary external effects of both sort of capital inherent in the model.

The exogenous rate of TFP total component productivity growth in the Solow–Swan model is the residual after accounting for capital accumulation. The Mankiw, Romer, and Weil model manage a lower estimate of the TFP residual than the basic Solow–Swan model because the addition of human capital to the model allowed capital accumulation to explain more of the variation in income across countries. In the basic model, the TFP residual includes the effect of human capital because human capital is not identified as a factor of production.