Total factor productivity So far we have studied technical progress from various conceptual angles. It is also important to think about how
we can measure such progress. In this section, we introduce the concept of total factor productivity as a measure of technical progress and explain why an accurate measure of this concept is useful in practice.
To begin with, it is useful to go back to the simplest specification of a production function. In symbolic notation, we write this as
Y(t) = F(K(t), P(t), E(t)),
where Y(t) is output at date t, K(t) is capital at date t, P(t) denotes the labor force at date t, and E(t) is some measure of knowledge at date t. The notation F(K, P, E) simply means that output is a function of all three variables.
Published data yield estimates of Y, K, and P, even though with each one there are important problems of measurement. The variable E is a more nebulous object, representing the state of knowledge, and cannot be directly measured. Hence, obtaining an estimate of E, or at least the growth in output attributable to E, requires a trick. To see how the argument goes, imagine first that there is no increase in E over time, so that output is essentially a function of capital and labor alone. Now let us track the growth of output.
e use the notation X(t) to denote the change in some variable X over periods t and t 1 thus X(t) ≡ Xt + 1− X(t). It is easy to see that as a first approximation, the equation
must hold, where MPK denotes the marginal product of capital and MPL denotes the marginal product of labor around the date t. The intuition behind this equation is very simple. Because we assume for the moment that there is no technical progress, the total increase in output between any two dates must be made up of the total increase in all inputs, weighted by their marginal contribution to total output.19
Now divide through by Y(t) in equation (4.11), and multiply and divide by K(t) and P(t) in their corresponding terms to get
Look at the terms (MPK · K(t))/(Y)(t)) and (MPL · P(t))/(Y(t)). Under the assumptions of constant returns to scale and perfect competition, introductory economics tells us that all factors are paid their marginal products. If this is indeed so, then MPK and MPL are simply the payments to a single unit of capital and labor, respectively. Multiplying these by the total amounts of capital and labor, and then dividing by aggregate output gives us the share of national income accruing to these factors of production. Therefore, if we define k(t) ≡ ( K(t))/(Y(t)) and P(t) ≡ ( P(t))/(Y(t)), our equation becomes
where k(t) and (t) are the income shares of capital and labor, which are observable from the data. We now have 89
P a situation where both sides of the equation are observable. What if we insert the actual data and the equation does not “add up,” with the left-hand side equalling the right-hand side? Well, then, our initial assumption that E is unchanged must be wrong and there must have been some technical progress (or regress). The extent of progress can then be measured by the difference between the left-hand and right-hand side of the equation. This difference is often referred to as growth in total factor productivity (or TFP growth). Thus TFP growth is positive when output is increasing faster than predicted by the growth of inputs, and this is a way to quantify technical progress. We summarize all this in the equation
where TFPG(t) stands for TFP growth over the periods t and t + 1. Note once again that everything in equation (4.12) except the term TFPG is measured by looking at the data; TFP growth is then calculated as the “residual” from this equation.
There are several points to note about this methodology.
(1) The concept of total factor productivity level, as opposed to its growth, is not important. The level carries no information at all, because it can be chosen arbitrarily. What matters is how the level changes over time, and this is what is calculated in equation (4.12).
(2) Be careful measuring increases in P(t), which stands for the labor force. One standard method is simply to proxy this by the rate of population growth. Such a proxy may be all right in some cases and highly misleading in others, as we will see. The error is especially pronounced in countries where the participation rate in the labor force has significantly altered over time.
(3) The concept of an aggregate capital stock, and indeed of an aggregate labor force, may be useful in a theoretical exposition, but in practice we may need to aggregate stocks of capital that are growing at different rates. This can be done by expressing aggregate capital growth as the weighted sum of different subgroups of capital, much in the same way that we express aggregate output growth as the weighted sum of capital and labor. Concentrating, as we have already, on the importance of human capital accumulation, we can easily see how important it is to correct for changes in the quality of the labor force when we measure the growth of labor input. Correction can be done if we have some idea of the proportions of the population at various stages of education.20
(4) Finally, the methodology runs into problems if either factors of production are not paid their marginal product or if the production function is not constant returns to scale. In either of these cases, we cannot use the observed shares of a factor (such as labor) in national income to proxy for the variables P or K. We lose the ability to measure these variables, and once this happens, we can no longer get a handle on TFP growth.21
4.5. Total factor productivity and the East Asian miracle We already mentioned the spectacular rates of economic growth enjoyed by East Asia since 1965. Over the period 1965-90, the region grew faster than any other region in the history of the world. Most of this growth was due to stellar performances by eight economies: Japan, Hong Kong, Korea, Taiwan, and Singapore in the East, and three Southeast Asian countries, Indonesia, Thailand, and Malaysia. Economists have turned to these countries for clues that might explain their success—clues that perhaps can be transplanted elsewhere with a similar effect.
One issue is understanding the sources of growth in these countries. Based on the many theories that we have studied, we can trace high growth to one or more of several contributing factors: among these, the most important are capital accumulation, both physical and human, and the pace of technical progress.
These eight economies have taken huge strides in the accumulation of physical and human capital. Rates of savings in these countries (excluding Japan) were lower than those in Latin America in 1965, but in 1990 the excess over Latin America was nearly 20 percentage points. Investment rates are higher than average in the world economy but not remarkably so, although private investment is significantly higher. These countries are net exporters of capital, in contrast to most other developing economies. Human capital levels, by all indications, are very high relative to per capita income levels. By 1965, Hong Kong, Korea, and Singapore had already achieved universal primary education, and soon secondary enrollment rates began to climb. In 1987, Korea had a secondary education enrollment rate of 88% (up from 35% in 1965), and that of Indonesia was 46%, well above the average for countries at that level of per capita income. (Thailand was below the predicted average, however.) Real
expenditures per pupil have risen significantly as well.22
How about growth in TFP? Did this account for a significant fraction of the phenomenal growth rates that we observe? The East Asian Miracle, published by the World Bank, argues that it did indeed. In fact, the study coined the phrase “productivity-based catching up” for this rapid TFP growth and pushed the notion that such growth was largely the outcome of openness: specifically, openness to international trade allowed the world’s technological frontier to be rapidly absorbed by the East Asian economies. Thus the prescription (see World Bank ):
“Most explanations of the link between TFP growth and exports emphasize such static factors as economies of scale and capacity utilization. While these may account for an initial surge of productivity soon after the start of an export push, they are insufficient to explain continuing high TFP growth rates. Rather, the relationship between exports and productivity growth may arise from exports’ role in helping economies adopt and master international best-practice technologies. High levels of labor force cognitive skills permit better firm-level adoption, adaptation, and mastery of technology. Thus, exports and human capital interact to provide a particularly rapid phase of productivity-based catching up.
Now, it is important for practical policy makers to know just what lies at the heart of the East Asian miracle. If the bulk of growth came from the accumulation of physical and human capital, then we are led to one sort of conclusion: that policies aimed at these variables can have enormous effects on growth. On the other hand, if TFP growth lies at the core of the overall growth spurt, then we are led to a set of policies that favor sectors conducive to technology assimilation. If the foregoing quotation is taken seriously, the trade sector is surely in this class. If this is the case, then countries can benefit most from having economies that are open to trade, and a trade policy aimed at openness becomes of critical significance. Of course, no one is arguing that it’s one or the other. Like most things that we have studied so far, it’s probably a bit of everything. Nevertheless, some idea of the quantitative magnitudes certainly helps.
This is precisely why TFP accounting, as developed in the previous section, can be of immense use. By decomposing overall growth into several components, it helps us understand what drives growth and therefore pushes policy in the right direction.
According to the World Bank study that we have mentioned, approximately two-thirds of the observed growth in these economies can be attributed to the accumulation of physical and human capital, and primary education is the single largest contributor among these factors. The remaining growth comes from TFP growth. This is particularly held to be the case for Japan, Korea, Hong Kong, Thailand, and Taiwan. Make no mistake: the study does not argue that TFP growth is the dominant factor in growth, but relative to other developing economies, the contribution of productivity change appears to be very high indeed. Because of this seeming anomaly, the World Bank study devotes much thought to the sources of TFP growth. One of the main conclusions is summarized in the foregoing quotation.
Now, careful TFP accounting is needed to conclusively establish that productivity growth has indeed been high in these countries, so that we can then go on to evaluate the export argument as a basis for technological catching- up. Young  does just this. His study is exemplary in that it really makes an effort to control properly for all changes in inputs of production. Recall the warnings of the previous section: it is important to properly measure input growth. This means that one has to account properly for rising participation rates, transfers of labor between agriculture and industry (if one is looking only at the nonagricultural sector of the economy, where TFP growth was supposedly concentrated), and certainly the changes in education levels as well as the rapid pace of capital accumulation. Remember that TFP growth is the residual after these inputs have taken their crack at explaining overall growth. Young’s careful study shows that “all of the influences noted above. . . serve to chip away at the productivity performance of [Hong Kong, Singapore, South Korea, and Taiwan], drawing them from the top of Mount Olympus down to the plains of Thessaly.” For the period 1966–90, it turns out that in manufacturing, productivity growth varied from a low of negative 1.0% in Singapore to a respectable, but not astronomically high, 3.0% in South Korea. Singapore was a particularly bad performer (as far as TFP growth goes), and the other three countries were respectable, but not strikingly above average. Tables 4.1 and 4.2 detail Young’s findings and list TFP growth in several other countries for the sake of comparison.
Table 4.1. Average TFP growth, 1966-90.a
Source: Young . aNA denotes not available. bYears are 1970–90 for Singapore. cAgriculture excluded in the case of Korea and Taiwan.
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