So far in this chapter we have introduced exogenous technological progress into the Solow model to explain sustained growth in standards of living. Let’s now discuss what happens when the theory is forced to confront the facts. Since the Solow model is intended to describe a closed economy, and since the United States is the most important developed Western economy that trades a relatively small percentage of its GDP with the rest of the world, it is customary to evaluate the Solow model by comparing its predictions to outcomes in the United States.

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According to the Solow model, technological progress causes the values of many variables to rise together in the steady state. This property, called balanced growth, does a good job of describing the long-run data for the U.S. economy.

Consider first output per worker Y/L and the capital stock per worker K/L. According to the Solow model, in the steady state, both of these variables grow at g, the rate of technological progress. U.S. data for the past half century show that output per worker and the capital stock per worker have in fact grown at approximately the same rate—about 2 percent per year. To put it another way, the capital-output ratio has remained approximately constant over time.

Technological progress also affects factor prices. Problem 3(d) at the end of the chapter asks you to show that, in the steady state, the real wage is predicted to grow at the rate of technological progress. The real rental price of capital, however, is predicted to stay constant over time. Again, these predictions hold true for the United States. Over the past 50 years, the real wage has increased about 2 percent per year; it has increased by about the same amount as real GDP per worker. Yet the real rental price of capital (measured as real capital income divided by the capital stock) has remained about the same.

The Solow model’s prediction about factor prices—and the success of this prediction—is especially noteworthy when contrasted with Karl Marx’s theory of the development of capitalist economies. Marx predicted that the return to capital would decline over time and that this would lead to economic and political crisis. Economic history has not supported Marx’s prediction, which partly explains why we now study Solow’s theory of growth rather than Marx’s.

If you travel around the world, you will see tremendous variation in living standards. The world’s poor countries have average levels of income per person that are less than one-tenth the average levels in the world’s rich countries. These differences in income are reflected in almost every measure of the quality of life—from the number of televisions and telephones per household to the infant mortality rate and life expectancy.

Much research has been devoted to the question of whether economies converge over time to one another. In particular, do economies that start off poor subsequently grow faster than economies that start off rich? If they do, then the world’s poor economies will tend to catch up with the world’s rich economies. This property of catch-up is called convergence. If convergence does not occur, then countries that start off behind are likely to remain poor.

The Solow model makes clear predictions about when convergence should occur. According to the model, whether two economies will converge depends on why they differ in the first place. On the one hand, suppose two economies happen by historical accident to start off with different capital stocks, but they have the same steady state, as determined by their saving rates, population growth rates, and the efficiency of labour. In this case, we should expect the two economies to converge; the poorer economy with the smaller capital stock will naturally grow more quickly to reach the steady state. (In a case study in Chapter 7, we applied this logic to explain rapid growth in Germany and Japan after World War II.) On the other hand, if two economies have different steady states, perhaps because the economies have different rates of saving, then we should not expect convergence. Instead, each economy will approach its own steady state.

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Experience is consistent with this analysis. In samples of economies with similar cultures and policies, studies find that economies converge to one another at a rate of about 2 percent per year. That is, the gap between rich and poor economies closes by about 2 percent each year. An example is the economies of individual American states. For historical reasons, such as the U.S. Civil War of the 1860s, income levels varied greatly among states a century ago. Yet these differences have slowly disappeared over time.

In international data, a more complex picture emerges. When researchers examine only data on income per person, they find little evidence of convergence: countries that start off poor do not grow faster on average than countries that start off rich. This finding suggests that different countries have different steady states. If statistical techniques are used to control for some of the determinants of the steady state, such as saving rates, population growth rates, and accumulation of human capital (education), then once again the data show convergence at a rate of about 2 percent per year. In other words, the economies of the world exhibit conditional convergence: they appear to be converging to their own steady states, which in turn are determined by such variables as saving, population growth, and human capital.²

As a matter of accounting, international differences in income per person can be attributed to either (1) differences in the factors of production, such as the quantities of physical and human capital, or (2) differences in the efficiency with which economies use their factors of production. That is, workers in a poor country may be poor because they lack tools and skills or because the tools and skills they have are not being put to the best use. To describe this issue in terms of the Solow model, the question is whether the large gap between rich and poor is explained by differences in capital accumulation (including human capital) or differences in the production function.

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Much research has attempted to estimate the relative importance of these two sources of income disparities. The exact answer varies from study to study, but both factor accumulation and production efficiency appear important. Moreover, a common finding is that they are positively correlated: nations with high levels of physical and human capital also tend to use those factors efficiently.³

There are several ways to interpret this positive correlation. One hypothesis is that an efficient economy may encourage capital accumulation. For example, a person in a well functioning economy may have greater resources and incentive to stay in school and accumulate human capital. Another hypothesis is that capital accumulation may induce greater efficiency. If there are positive externalities to physical and human capital, then countries that save and invest more will appear to have better production functions (unless the research study accounts for these externalities, which is hard to do). Thus, greater production efficiency may cause greater factor accumulation, or the other way around.

A final hypothesis is that both factor accumulation and production efficiency are driven by a common third variable. Perhaps the common third variable is the quality of the nation’s institutions, including the government’s policymaking process. As one economist put it, when governments screw up, they screw up big time. Multiple bad policies, such as high inflation, excessive budget deficits, widespread market interference, and rampant corruption, often go hand in hand. We should not be surprised that economies exhibiting these maladies both accumulate less capital and fail to use the capital they have as efficiently as they might.