Resumen. En este artículo se presenta un modelo de crecimiento donde la función de producción es del tipo Leontief (1941), la tasa de ahorro es endógena y el crecimiento de largo plazo es explicado por cambio tecnológico sesgado. En este entorno se obtienen dos resultados: (i) si la participación de los factores reproducibles en el producto es suficientemente alta, en el largo plazo la economía presenta una senda de crecimiento balanceado; (ii) si, en cambio, la participación de los factores reproducibles es baja, en el largo plazo no hay crecimiento y la economía se comporta al estilo Harrod-Domar.
Palabras clave: crecimiento endógeno, cambio tecnológico sesgado.
Clasificación JEL: 011, 031, 033.
Abstract. This paper presents an endogenous growth model where the aggregate production function is a Leontief (1941) and long run growth is completely explained through biased technological change. Under this framework we get two results: (i) if the income share of reproducible factors is high enough, in the long run the economy presents a positive balanced growth path; (11) if the income share of reproducible factors is low, in the long run the economy behaves as a Harrod-Domar economy without long run growth.
Key words: endogenous growth, capital using and labor saving technological change.
JEL classification: 011, 031, 033.
In the early years of capitalism, a new way of production emerged where the capital income share was substantially higher than in the feudal production system. The institutional framework under which this phenomenon took place determined to a great extent the economic success of countries. Social organizations that let capitalists retain a greater share of the output enjoyed faster capital accumulation and, as a result, higher rate of technological growth. (1) Along with the changes in the functional distribution of income a process of biased technological change took place, and these facts together lead to the industrial revolution and the subsequent industrialization of the economies. (2)
In this article we provide a growth model that can account for these facts. We modify the Harrod-Domar model (3) endogenizing the savings rate and allowing capital using and labor saving technological change. The model is one of biased innovations where factor income shares are determined politically or institutionally, that is, they are independent of market forces. Under this framework we get two results: (1) if the income share of reproducible factors is high enough, in the long run the economy presents a positive balanced growth path; (11) if the income share of reproducible factors is low, in the long run the economy behaves as a Harrod-Domar economy.
In order to achieve long run growth, the income share of factors like land and unskilled labor should be low and the income share of reproducible factors like physical and human capital should be high. A similar result was obtained by Bertola (1993) who relates the growth rate of the economy to the functional distribution of income in an endogenous growth model. However, in his paper, the production function is AK and the technology is constant (there are no innovations), so the model cannot support a neoclassical steady state.
The set-up of the model is simple: every economy starts with a Leontief production function, which combines the fixed factor (L) and the reproducible factor (K), namely, Y = A min(K, [beta]L) where A and [beta] are technological parameters. Therefore, a change in A is a neutral technological change while a change in [beta] is a biased technological change. For concreteness, we refer to the reproducible factor as capital. Once the stock of capital is equal to [beta]L, capital productivity starts to decrease as well as the capital income share. For this reason, the economy cannot grow in the long run. Note that, under this framework, increasing total factor productivity increases output but does not generate incentives to accumulate capital. Therefore, technological innovations most be factor saving.
Nowadays, the Leotief production function is almost out of use and modern growth theorists do not give much importance to the Harrod-Domar model. Two main reasons may explain this fact: on the one hand, some undesirable predictions of the original model (perpetual growth of unemployment or perpetual growth of idle machinery) and, on the other hand, assumptions about the savings rate and about the behavior of the marginal productivity of factors. However, with the extensions we make, the so called undesirable elements of the original model are eliminated and, depending on the parameters of the economy, in the long run the economy may behave as if the production function were AK.
Since the incentives to save depend crucially on capital income share, the speed of capital accumulation is higher for economies where the capital income share is bigger. Similarly, technological change is costly, therefore the net income share of capital is smaller when technology is improving. For this reason, in economies where capital income share is small there are no incentives to make technological innovations; these economies are trapped in a steady state. This result has two implications. First, the bigger the income share of reproducible factors, the bigger the incentives to innovate. (4) This implication is consistent with the institutional view of the industrial revolution; according to which, a critical factor to explain the economic performance in seventeenth-century England was the ability of the government to commit to private property rights and exchange instead of producing rules that benefit a small elite of land-owners (see North and Weingast, 1989). Second, labor is not a reproducible factor, so technologies in rich economies are likely to be less labor intensive than technologies in poor economies. Therefore, when technology is transferred from rich to poor economies (FDI), these countries are likely to experiment an increase in marginal productivity of capital and a decrease in labor demand. This implication is consistent with the increase in FDI and the subsequent behavior of wages and unemployment in many Latin-American countries from the second half of the 90's until now.
Our approach combines two strands of the literature: biased innovations and transition from stagnation to sustained growth.
In models of biased innovations, technological progress takes place through the adoption of new activities that demand less fixed factors per unit of output (Kennedy, 1964; Zeira, 1998; Boldrin and Levine, 2002; and Zuleta, 2006). The relevance of the biased innovations theory is supported by the evidence provided by researchers in economic history who show that during the industrial revolution there was capital using and labor saving technological change (Cain and Paterson, 1981). Economic literature also provides evidence that during the last few decades there has been human capital using and raw labor saving technological change (Krusell et al., 1997). Moreover, in both cases, the technological change was preceded by a change in factor abundance. The story behind these two facts is a story of biased technological change triggered by changes in factor abundance. (5)
To our knowledge, this is the first model of biased innovation that explains the transition from stagnation to sustained growth through the functional distribution of income.
The literature on transition from stagnation to growth is wide. The first unified theories view the transition from stagnation to growth as primarily driven by technological change (Galor and Weil, 2000; Hansen and Prescott 2002; and Doepke, 2004). A second set of theories point to institutions as a determinant of the quality of institutions and long run development success (Acemoglu, Johnson, and Robinson, 2000, among others). There is also a third approach which reconciles the previous theories: economic institutions affect economic incentives but also respond to changes in the economic environment (Engerman and Sokoloff, 2003). Our theory is in line with the third approach. In this paper, the ultimate mechanism that triggers the transition from stagnation to sustained growth is the functional distribution of income. However, we take factor shares as given, that is, we do not model the institutional or political changes. Nevertheless, our story is perfectly consistent with the institutional view. Indeed, one of the main consequences of the institutional changes was a change in the distribution of income.
Our paper differs from the previous literature...