In this chapter, we go beyond the two-period model and begin our investigation of the determinants of long-run economic growth in economies that exist for a large number of periods.
In fact, we focus on economies with an infinite horizon and examine the relationship between savings, investment, capital accumulation, and economic growth.
The starting point for the analysis of this process is the Solow [1956] model.
This is a model of an infinite-horizon economy. It is based on a neoclassical production function, such as the one postulated in chapter 2, but instead of optimizing households, it is based on the assumption that the savings rate is exogenous and constant. Given that in a closed economy, aggregate savings are always equal to investment, the process of capital accumulation depends on the savings rate, which in equilibrium determines the investment rate.1In this model, capital accumulation per employee continues until savings per employee is equated with the depreciation and the additional investment per employee required to maintain a constant ratio of capital to labor. The growth rate of population and the growth rate of the number of employees is assumed to be exogenous in this model.
The model also allows for exogenous technical progress, which raises the efficiency of labor continuously. In this case, capital accumulation per efficiency unit of labor continues until savings per efficiency unit of labor is equated to depreciation plus the additional investment required to provide for population growth and technical progress.
In the long-run equilibrium of this infinite-horizon model, alternatively referred to as the steady state or the balanced growth path, economic growth is exogenous and equal to the rate of population growth plus the rate of technical progress. Essentially, on the balanced growth path, per capita output grows at the exogenous rate of technical progress.
During the adjustment process toward the balanced growth path, an economy that has an initial capital stock lower than its steady state value experiences a growth rate that is higher than its long-run growth rate.
Capital accumulates at a rate that exceeds the sum of the rate of growth of population and the rate of technical progress, and so does output. For an economy that has an initial capital stock that is higher than its steady state value, the growth rate during the transition is below the long-run growth rate, as capital accumulates at a rate that falls short of the sum of the rate of population growth and the rate of technical progress.This model predicts that economies converge to a unique balanced growth path. A “poor” economy and a “rich” one (in terms of initial capital stock) converge to the same balanced growth path, provided that they are characterized by the same savings rate and the same technological and demographic parameters.
However, if two economies have different savings rates, total factor productivity, initial labor efficiency, rates of population growth or depreciation rate of capital, they will converge to different balanced growth paths. Convergence in this model is thus conditional. The balanced growth path depends on the structural characteristics of economies, such as their savings and investment rates, total factor productivity, the rate of population growth, and the rate of technical progress.
This model predicts that an economy with a higher savings (and investment) rate will be characterized by higher steady state capital and output per worker. Furthermore, it predicts a positive impact on capital and output per worker from higher total factor productivity and initial labor efficiency, and a negative impact from the rate of population growth, the rate of technical progress, and the depreciation rate of capital.
The Solow model is a key model and an important reference point for the theory of economic growth. Although it is not an intertemporal model in which households determine savings and investment optimally, and although the basic model has other theoretical and empirical weaknesses, this model provides a very useful, simple, and flexible framework for the analysis of the growth process, and it has stood the test of time well.
From the point of view of modern intertemporal macroeconomics, it has two main weaknesses. First, the assumption of an exogenous savings rate. This weakness is addressed by extensions of the model to optimizing models in which households choose savings in an individually optimal fashion. The representative household model of chapter 4 and the overlapping generations models of chapter 5 are such optimizing dynamic general equilibrium models, which retain most of the characteristics of the Solow model.
The second weakness is that the accumulation of physical capital, which is the main engine of economic growth in the Solow model, cannot fully explain either the long-term growth of output per worker and per capita income that has been observed in developed economies, or the large differences in labor productivity and living standards per head between developed and less developed economies. Only a small part of these differences can be explained by the accumulation of physical capital. Most of it is accounted for by differences in total factor productivity and technical progress, which in the Solow model are considered exogenous parameters. In this sense, the Solow model, like all models that rely on similar assumptions about technology and technical progress, shows us how to overcome its weaknesses, first, by introducing human as well as physical capital, and second, by trying to explain technical progress endogenously. Such extensions are introduced in chapter 8.
3.1