Chapter 8. Alternative Theories of Endogenous Growth. Instructor: Dmytro Hryshko

Transcription

1 Chapter 8. Alternative Theories of Endogenous Growth Instructor: Dmytro Hryshko

2 Endogenous growth models Models we studied thus far: government policies, such as subsidies to R&D or investment taxes, have level eects but no growth eects. This chapter: develop models in which policies can have permanent growth eects. Implication: the observed growth rate dierences across countries reect underlying permanent growth dierences. Is this true?

3 The \AK" model A Assume that _ = 0, A = 1, and L _ = 0. For simplicity, L normalize L to 1 so that all aggregates are also per capita aggregates. Aggregate production function is Y = AK, where A is some positive constant. The law of motion of capital: _K = sy K = sak K. For this model, if sa >, the growth in per capita output and capital, even though there is no technological progress, is never _K ending: = sy K K = sa ; Y _ = K _ = sa. Y K The key to this result: constant returns to capital accumulation. Permanent increases in investment rate, s, lead to permanent growth rates in capital and output. Intuitively, for close to 1, transition dynamics never stops, and the growth rate in per capita income is ensured without exogenous technological growth rate. Hence, the AK model is an endogenous growth model.

4 Intuition and other endogenous growth models The AK model generates endogenous growth due to linearity in the capital accumulation equation. If < 1, _K = sak K there are diminishing returns to capital K accumulation, and _ = K sak 1 = sa : the growth K 1 rate of capital declines the more capital is accumulated. Consider another linear dierential equation: A _ = ga permanent changes in g induce permanent growth. The Lucas (1988) model. Production function: Y = K (hl) 1, where h is human capital per person. Human capital evolves as: h _ = (1 u)h, where u is time spent working and (1 u) time spent accumulating human capital. h enters the production function just like labor-augmenting technological progress and the growth rate in Y, in the very long-run, will be L equal to the growth rate in h, or (1 u). Thus, any policy that raises time accumulating human capital will permanently raise the long-run growth of income per capita.

5 Externalities and AK models Under perfect competition, no income would remain to compensate for creation of ideas; we introduced imperfect competition. Maintain the assumption of perfect competition and increasing returns but assume that accumulation of ideas is a by-product of other activity, that is, accumulation of knowledge is an externality. Let production function of an individual rm be Y (t) = B(t)K(t) L(t) 1. If B is accumulated endogenously, production function is increasing returns to scale. Assume B is taken by the rm as given but the stock of B is related to the stock of accumulated capital as B(t) = AK(t) 1, where A is some constant.

6 Externalities and AK models, contd. Individual rm does not recognize that its use of capital improves the technology in the economy since the rm is small relative to the economy. Utilizing the functional relationship for B, Y (t) = AK(t) 1 K(t) L(t) 1 = AK(t)L(t) 1. If L(t) is normalized to 1, production function is of the AK variety. Recall that in Chapter 5 we relied on externalities in knowledge creation. Assuming that = 1, A _ = dl A A. If > 0, the average productivity of researchers increases with A. The extent of increasing returns is 1 +. Individuals take A as given, and are not compensated for enlarging A with their own idea, which improves productivity of others in the economy.

7 Evaluating endogenous growth models Do policies change growth rates permanently? In particular, do subsidies to research, education, ivestment have growth eects or only level eects in the very long run? Some arguments in favor of the growth eects only: Dierential equations are not linear: the share of capital income in total income is not equal to one. Recall Chapter 5: _A = da L _A A. If = 0, and = 1, = dla. In the A last century, labor engaged in R&D increased but the growth rate of output per capita in the U.S. has not accelerated. Thus, this observation motivates imposing < 1. Within the U.S., over the last century, education improved, the share of labor in R&D increased, ivestment rates increased, yet the growth rate was about the same as from 1870 to There are countries with similar growth rates (e.g., the U.S., Bolivia, Malawi) that dier substantially in their policies. These dierences are reected in the levels of income per capita.