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| Q1: What is Growth Accounting? What is Total Factor Productivity? (Hayami 2001) |
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InputDate: 7/9/2006 |
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| Reference: Hayami, Yujiro. 2001. Development Economics, From the Poverty to the Wealth of Nations, Second Edition, Oxford University Press. p140-142 | |||
| A: Grouth accounting assumes an aggregate production function relating an economy's output to the inputs of labor and capital. Using this production function, contribution of increase inputs to output growth are measured, and any residual not explained by input increases is considered a measure of growtth in the productivity of factor inputs. This residual, called growth in 'total factor productivity' (abbreviated as TFP), is a measure of technological progress broadly defined as output growth when input are being held constant. |  |
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Simple production function |
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The simplest and most commomly used equation for growth accounting can be derives from an aggregate prodiction function of the following form: Y=AF(L,K) (1) where national product (Y) is produced from labour (L) and capital (K). (this specification assumes neutral technological change in Hick's definition) |
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Growth rate of income will be the sum of labor and capital contribution plus technological change |
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In addition, another simplifying assumption of linear homogeneity or constant return to scale is adopted. Then, taking total derivatives of equation (1) with respect to time (t) and dividing all term by Y yields: G(Y)=G(A)+aG(L)+bG(K) (2) where G() represents the growth rate of any variable specified inside the parentheses, and a and b are production elasticities of labor and capital respectively, which are expressed by a=(dY/dL)/(Y/L) and b=(dY/dK)/(Y/K) which present percentage increase in output relative to 1 percent increase in labor and capital respectively. Under the assumption of linear homogeneity, the sum of elasticities is equal to one (a+b=1). |
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Estimating TFP growth |
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| Since G(L) and G(K) are the growth rate of labor and capital, multiplying them by a and b estimates the contributions of increases in L and K to growth in Y. If time series data are available for Y, L, and K, the growth rate of TFP represented by G(A) can be calculated by subtracting measured aG(L) and BG(K) from the measured G(Y) according to the relation of equation (2). | |||
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a and b can be estimated as labor and capital share in totla income |
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Statistical estimation of production elasticities from input-outpu data are possible but subject to major technical difficulties. A widely used convention is to regard the income shares of labor and capital as equivalent with a and b under the assumption of competitive equilibrium in factor markets. Under this assumption wage rate (w) and the profit rate (r) should be equal to marginal productivity of labor and capital; dY/dL and dY/dK, Therefore, a=(dY/dL)/(Y/L)=wL/Y b=(dY/dK)/(Y/K)=rK/Y These wL/Y and rK/Y represents labor and capital share in the totla income Y. |
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Previous Item| Q2: How Growth Accounting has been developed? |
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InputDate: 1/24/2007 |
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| Reference: FAGERBERG, JAN. 1994. "Technology and International Differences in Growth Rates". Journal of Economic Literature Vol. XXXII (September 1994), pp. 1147-1175 | |||
| A: From the late 1950s onwards empirical research on factors affecting long run growth grew steadily. Much in the same way as the postwar work on national accounts decomposed GDP into its constituent parts, the empirical research on growth attempted to decompose growth of GDP (so-called "growth accounting"). Although some of this work actually preceded the formal models, Solow's growth theory gave a natural theoretical framework for these exercises. |  |
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Solow's growth model is the basis of growth accounting |
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The Solow model predicts that apart from technological progress, GDP growth (y) will be a weighted sum of the growth in physical capital (k) and the growth of the labor force (n), with the shares of capital and labor in national income (a and b) as weights: y = ak + bn If the functional distribution of income, the growth of the capital stock, and the growth of the labor force are known, equation (1) can be used to calculate the contributions to economic growth from factor growth. |
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Abramovitz (1956) studied U. S. growth |
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| One of the first analyses of this kind was carried out by Abramovitz (1956) in a historical study of U. S. growth. His results indicated that only a small part of U. S. productivity growth could be explained by factor growth. Thus, the major part of U: S. productivity growth had to be classified as unidentified total factor productivity growth (the residual). | |||
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Abramovitz s comment was: |
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| This result is surprising ... Since we know little about the causes of productivity increase, the indicated importance of this element may be taken to be some sort of measure of our ignorance about the causes of economic growth. (Abramovitz 1956, p. 11) | |||
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Embody technological progress into the factors |
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| This result was soon corroborated by other studies (Solow 1957; John Kendrick 1961; and Denison 1962). Two avenues were followed for "squeezing down the residual" as Nelson (1981) puts it. One has been to embody, as much as possible, technological progress into the factors themselves by adjusting for shifts in quality, composition, etc. (Denison 1962; Dale Jorgenson and Zvi Griliches 1967; see also Angus Maddison 1987). Most growth accounting exercises do this to some extent, but the most prominent advocates of this view were Jorgenson and Griliches. Initially, they argued that the residual could be eliminated altogether (Jorgenson and Griliches 1967), but after being criticized by Denison (1969), they retreated from that position (Jorgenson and Griliches 1972a, 1972b; Denison 1972). | |||
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Denison (1962) add other explanatory variables |
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| Another approach in this literature, originally developed by Denison (1962), has been to add other possible explanatory variables, such as structural change, economies of scale, etc. The list may in some cases be quite long. The reader is referred to the survey by Maddison (1987) for a more detailed account. By far the most influential studies of "Why Growth Rates Differ" across countries have been those of Denison (Denison 1967; Denison and William Chung 1976). The 1967 study considers the growth of ten capitalist economies between 1950 and 1962, the 1976 study extends the country coverage to Japan (and more recentt data). The methods are the same in both. First, the contributions of factor growth (capital, labor, and land) are deducted. The contribution from the growth of the labor force is adjusted to take into account changes in unemployment, hours worked, composition (sex, age) and education, the latter having by far the greatest impact. What remains when the contributions from factor growth are deducted-so called total factor productivity growth-is then further reduced by taking into account the contribution to growth from structural changes in the employment mix (from low-productivity to high-productivity activities), from better utilization of economies of scale (through growth of markets and reduced barriers to trade) and other (less important) factors. The final residual is then divided into two parts, assumed to reflect technological progress and catch-up, respectively. | |||
| Reference: | |||
| ABRAMOVITZ, MOSES. "Resource and Output Trends in the United States since 1870," Amer. Econ. Rev., May 1956, 46(2), pp. 5-23. | |||
| SOLOW, ROBERT M. "Technical Change and the Aggregate Production Function," Rev. Econ. Statist., Aug. 1957, 39(3), pp. 312-20. | |||
| KENDRICK, JOHN W. Productivity trends in the United States. New York: NBER; Princeton: Princeton U. Press, 1961. | |||
| DENISON, EDWARD F. "The Sources of Economic Growth in the United States and the Alternatives Before Us." Committee for Economic Development, New York, 1962. | |||
| NELSON, RICHARD R. "Research on Productivity Growth and Productivity Differences: Dead Ends and New Departures," J. Econ. Lit., Sept. 1981, 19(3), pp. 1029-64. | |||
| JORGENSON, DALE W. AND GRILICHES, ZVL "The Explanation of Productivity Change," Rev. Econ. Stud., July 1967, 34(3), pp. 249-83. | |||
| Maddison, Angus. ."Growth and Slowdown in Advanced Capitalist Economies," J. Econ. Lit., June 1987, 25(2), pp. 649-98. | |||
| DENISON, EDWARD F. Why growth rates differ. Washington, DC: Brookings Institution, 1967. | |||
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| Q3: Why growth accounting concept does not explain the reality? (Nelson 1996) |
:3 FAQID:686 |
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InputDate: 7/26/2006 |
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| Reference: Nelson, R. Richard. 1996. The sources of Economic Growth. Harvard University Press. Cambridgw Massachusetts. p8 | |||
| A: In the late 1950s neoclassical growth theory was formulated and, in a sense, rationalized many of the calculations made by the empirical workers, but otherwise did not add much to the empirical research enterprise.in any case,during this period,there was a considerable amount of research on the source of growth.What was learned then hasby and large stood the test of time. I indicated at least three respect where I believe that analysis was problematic. |  |
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Divide up the sources of growth is not appropriate |
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| One was its proclivity to "divide up the sources of growth", when in factthere was powerful evidence that they were strong complements. | |||
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Continuing dis-equilibrium |
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| The second was tendency to treat economic growth as a process involving moving, continuing equilibrium, whereas evidence of continuing disequilibrium was very powerful. | |||
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Neglect of institutional complexity |
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| Third, much of the institutional complexity of modern capitalism was repressed. | |||
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