16 Uzawa-Lucas and Solow-Swan-Models

The Uzawa-Lucas model (1988) grew out of criticism of the AK model, in which capital is considered independently of its expression. Lucas leaned it on a model by Uzawa (1965) :

    (16.1).

Here one tries to compute the importance of human capital H. Now human capital is always a part of the production Y, which can be represented byas a share of GDP. The functionmay of course be any arbitrarily complicated function that represents this proportion as correctly as possible. By simple algebraic conversion, we now get:

    (16.2)

which the Uzawa-Lucas model also identifies as a specific AK-model. The same goes for the older Solow-Swan model (1956), which is based on the approach

    (16.3).

here means the labor, which of course can also been represented as a partof GDP, and thus also is an AK-model with

    (16.4).

These facts led historically to the fact that the mathematical theory of economic growth, pushed by an emphatic post-war phase, to the end of the last century got into the background. The fundamental impossibility³⁵ of forming a self-consistent theory had not been detected directly, but one rejected the virtually no useful results mostly. The IMF 2005 model is in principle after all still the best of the current classical models, as it, if one chooses different and realistic, at least points to some extent in the right direction. However, the growth of the capital coefficient is significantly underestimated, and the capital productivity greatly overestimated.

The IMF, therefore, summarized in his 2005 report:

„The investment equation is less successful than the saving equation in tracking recent developments. This result is similar to other recent studies, which have found that traditional econometric models of investment have difficulty explaining recent trends. The equation overpredicts investment in both the industrial and emerging market regions, in some cases by large margins. For instance, while the equation predicts that investment should have increased in industrial countries - largely as a result of the decline in the cost of capital - investment in several key industrial countries, including Japan and the Large Euro countries fell. Similarly, the equation fails to explain the drop in investment in emerging markets, particularly in the east Asian countries. The equation suggests that the investment accelerator - whereby investment rates and output growth move in the same direction - has not worked as strongly as expected in recent years in these countries, most likely because corporates have focused on reducing debt and strengthening balance sheets, rather than on investing in capital.“.

In an actual working paper [Arcand, Berkes, Panizza, 2012] of the IMF titled “Too Much Finance?” the International Monetary Fund agrees by statistical means with the conception, that to much assets will stall the economy.