Abstract
This Selected Issues paper highlights that the authorities in the Republic of Korea recognize the pension policy challenges ahead, and a first wave of reforms has already been launched. Despite the reforms to date, much remains to be done. Without further reforms, the public pension systems in Korea are not financially sustainable. This paper considers options for moving to a funded first-pillar pension system. The main results show that a sustainable, funded pension system can be achieved in Korea with reasonably modest changes to key parameters and extra financing.
III. Long-Run Economic Growth in Korea1
A. Introduction
1. Whether a miracle or a case of “plain vanilla” factor accumulation, Korea’s economic growth performance has been impressive. Average annual GDP growth in Korea was 7.1 percent in the last three decades, well above the OECD average of about 3 percent and that of many developing countries. As a result, Korea’s GDP per capita (in PPP terms) is now nearly half that of the United States, compared to about one-seventh in 1970. Korea’s per capita GDP has surpassed that of Argentina, Brazil, and Turkey and now ranks between Chile and Portugal. This impressive growth record together with that of the other Asian “tiger” economies has attracted much attention from researchers and policy makers. Many papers have investigated the factors driving GDP growth in these economies.2 The general conclusion from this literature is that growth in the Asian tiger economies has largely reflected rapid capital accumulation and increases in labor—both a reflection of their low starting point in the 1960s—with only moderate increases in total factor productivity (TFP). This suggests that the high historical growth rates of the tiger economies cannot be sustained unless productivity growth increases substantially. If this does not happen, economic growth is bound to descend to more mundane levels as capital-labor ratios approach those of the more advanced economies.
2. This chapter goes one step beyond the traditional growth accounting exercise in that it tries to unravel the long-run relations between the factors of production. Although growth accounting is useful as a mechanical decomposition of GDP growth into various inputs, it does not uncover the fundamental sources of growth. For example, is rapid capital accumulation the result of a big gap between the current capital-labor ratio and the long-run equilibrium ratio, or is it driven by increases in educational attainment of the labor force or technological progress? To answer this question it is necessary to determine the long-run equilibrium relation between the factors of production, both tangible (capital and labor) and intangible (technological progress). In doing so, this chapter seeks to contribute to a better understanding of the growth process in Korea’s economy and to provide policy suggestions for sustaining high growth in the future.
3. The main policy implication is that for Korea to achieve annual GDP growth of about 5-6 percent over the medium term it needs a higher rate of technological progress. Some of the factors that have contributed to rapid GDP growth in the past, in particular the increase in educational attainment of the work force, will be exhausted over the medium term. To ensure continuous high GDP growth alternative sources of growth need to be more fully exploited. In particular, growth in human capital will have to become more intensive in knowledge accumulation rather than in further increases in the number of years of schooling of the average worker. This could be achieved through greater openness to foreign trade and investment and through devoting more resources to research and development. Structural reforms can play an important role in this context by raising efficiency, so that alternative sources of economic growth can be better exploited.
B. A Dissection of Korea’s GDP Growth: 1980–2002
4. Investment in Korea was high by international standards during 1980-2002. Gross fixed capital formation increased from 30 percent of GDP in the 1980s to 37 percent in the 1990s prior to the Asian financial crisis. After the crisis, the investment ratio fell to just below the level of the early 1980s, but remained high compared to the OECD average of about 22 percent. Machinery and construction (excluding residential buildings) have been the main components of gross fixed capital formation (Figure III.1). Capital stocks have been estimated for non-residential buildings, other construction, land improvements, machinery, and transport equipment using the perpetual-inventory method. An aggregate capital stock that allows for quality changes was then constructed by weighting each of the five capital stocks by their relative rental rates.3 The capital stock that allows for quality changes increases at a slightly faster rate than the unadjusted capital stock, because machinery and transportation equipment—the two fastest growing investment categories—receive more than proportional weights (Figure III.2).
Investment Categories 1/
(in percent of GDP).
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
1/ Public and private investment, excluding residential construction.Investment Categories 1/
(in percent of GDP).
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
1/ Public and private investment, excluding residential construction.Investment Categories 1/
(in percent of GDP).
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
1/ Public and private investment, excluding residential construction.
Measures of the Capital Stock
(in logarithms)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Measures of the Capital Stock
(in logarithms)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Measures of the Capital Stock
(in logarithms)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Investment Ratios
(in percent of GDP)
Unweighted average.
Investment Ratios
(in percent of GDP)
| 1980-89 | 1990-97 | 1998-99 | 1999-2002 | |
|---|---|---|---|---|
| Korea | 29.7 | 36.8 | 28.8 | 27.4 |
| Japan | 29.3 | 29.5 | 26.5 | 25.5 |
| United States | 20.1 | 18.0 | 20.1 | 19.6 |
| OECD 1/ | 23.4 | 21.9 | 22.5 | 21.9 |
Unweighted average.
Investment Ratios
(in percent of GDP)
| 1980-89 | 1990-97 | 1998-99 | 1999-2002 | |
|---|---|---|---|---|
| Korea | 29.7 | 36.8 | 28.8 | 27.4 |
| Japan | 29.3 | 29.5 | 26.5 | 25.5 |
| United States | 20.1 | 18.0 | 20.1 | 19.6 |
| OECD 1/ | 23.4 | 21.9 | 22.5 | 21.9 |
Unweighted average.
5. Labor force growth during 1980–2002 was largely driven by increases in the working age population of about 1.9 percent a year on average. The labor force participation rate increased only slightly from 59.0 percent in 1980 to 62.2 percent in 1997, after which it fell to 61.3 percent in 2002. Korea’s participation rate is low compared with other OECD economies, which averaged 71 percent in 2002. This is largely the result of the traditionally low participation rate of women, which in 2002 was 49.1 percent compared with 74.1 percent among men. Employment, rather than the labor force, is needed to calculate the contribution of labor input to GDP growth, and, as with the capital stock, it is important to allow for quality changes.4 This has been done by disaggregating employed persons by their level of educational attainment—middle school and below, high school, and college and above—and then weighting them by their relative wage levels. Employment allowing for quality changes increased faster than raw employment, because of increases in the educational attainment of the average Korean worker during 1980–2002.
Educational Attainment of Labor Force
(in million persons)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Educational Attainment of Labor Force
(in million persons)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Educational Attainment of Labor Force
(in million persons)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Measures of Employment
(in logarithms)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Measures of Employment
(in logarithms)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Measures of Employment
(in logarithms)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
6. TFP growth is defined as the growth rate of GDP minus the weighted sum of the growth rates of quality adjusted capital and labor. Under the assumption of perfect competition the weights are the income shares of capital and labor in GDP. The labor share was derived from the national accounts and, assuming constant returns to scale, the capital share was calculated as one minus the labor share.
7. Korean TFP growth estimated in this way was 1.9 percent a year during 1980–2002. This is not very different from the TFP growth rates typical of other OECD countries. Although the time period and coverage differ, the estimated TFP growth rate for Korea is within the range of estimates in other studies (Iwata, Khan, and Murao, 2002; Ma, 2001; Pyo and others, 1993; Young, 1995). Young (1995), for example, estimates average annual TFP growth for the economy excluding agriculture to be 1.7 percent in 1966–90. For 1980–90, Young estimates TFP growth of 2.5 percent a year whereas this study, which includes the agricultural sector, suggests average annual TFP growth of 2 percent. The contribution of TFP to Korea’s GDP growth has not been constant over time. The trend in TFP fell from about 3 percent a year in the early 1980s to 1.3 percent in the early 1990s and then picked up after the Asian financial crisis (note the different scales in the figure).
Contributions to GDP Growth
(average annual percent changes)
Contributions to GDP Growth
(average annual percent changes)
| 1980-2002 | 1980-90 | 1990-2002 | 1990-96 | 1996-2002 | |
|---|---|---|---|---|---|
| GDP | 6.8 | 8.2 | 5.7 | 7.1 | 4.4 |
| Capital accumulation | 2.0 | 2.0 | 2.1 | 2.4 | 1.5 |
| Employment | 2.8 | 4.1 | 1.9 | 2.9 | 1.0 |
| TFP | 1.9 | 2.0 | 1.9 | 1.8 | 1.8 |
Contributions to GDP Growth
(average annual percent changes)
| 1980-2002 | 1980-90 | 1990-2002 | 1990-96 | 1996-2002 | |
|---|---|---|---|---|---|
| GDP | 6.8 | 8.2 | 5.7 | 7.1 | 4.4 |
| Capital accumulation | 2.0 | 2.0 | 2.1 | 2.4 | 1.5 |
| Employment | 2.8 | 4.1 | 1.9 | 2.9 | 1.0 |
| TFP | 1.9 | 2.0 | 1.9 | 1.8 | 1.8 |
TFP Growth
(annual percent changes)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
1/ HP-filtered.TFP Growth
(annual percent changes)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
1/ HP-filtered.TFP Growth
(annual percent changes)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
1/ HP-filtered.8. Growth in employment and the capital stock accounted for most of Korea’s GDP growth during 1980–2002. The largest contribution came from growth in quality adjusted employment. In particular, increases in educational attainment were an important source of growth in labor input throughout 1980–2002, although its contribution diminished in the 1990s. This declining contribution is likely to continue given the limits on further increases in educational attainment. The contribution of capital accumulation to GDP growth rose in 1990–96 and then fell sharply after the Asian financial crisis. The pick up in TFP growth after the crisis suggests that structural reforms may have improved the allocation of resources and thus the efficiency of the Korean economy.
C. Sources of Output Growth
9. The growth accounting exercise indicates that increases in capital and labor accounted for most of Korea’s GDP growth. As in other studies, the analysis uncovered a relatively modest contribution from TFP growth. However, this does not mean that TFP growth is a less significant source of growth than capital accumulation and employment growth. In the long run, TFP growth may be the only source of growth. For example, in the neoclassical growth model developed by Solow (1956), per capita GDP growth in the steady state is entirely driven by exogenous technological progress. Without this technological progress GDP growth and capital accumulation only take place as the economy converges to its long-run steady state. Once the economy arrives at the steady state, growth comes to a halt. The speed at which the economy moves to its steady state is a function of the structural parameters of the model. In the neoclassical growth model these are the rate of intertemporal substitution of households, the parameters of the production function, the depreciation rate, the growth rate of the labor force, and the rate of exogenous technological progress.
10. To obtain a better understanding of the sources of GDP growth, rather than the contributions from different factors of production, it is necessary to analyze the growth process that generates the time series data for GDP, capital, labor, and TFP. This process was analyzed using cointegration techniques to study the long-run relationship between real GDP, quality adjusted fixed capital, quality adjusted employment, TFP, and a measure of trade, the latter included to capture the potential impact of trade on TFP as suggested by the literature on endogenous growth (Grossman and Helpman, 1991).5
11. The long-run relationship between GDP, capital, labor, and TFP in Korea can be interpreted in terms of a two-sector growth model with physical and human capital. Cointegration analysis was carried out for two sets of variables. The results for the first set, including GDP, quality adjusted capital K, quality adjusted labor L, and trade XM (defined as exports plus imports) are reported in the table. All variables are expressed in logarithms, so the estimated coefficients represent elasticities. The number of cointegrating vectors was determined with a Johansen cointegration test.
12. The first vector in the table shows that in the long-run steady state, quality adjusted capital is positively related to quality adjusted employment and trade. This is consistent with the prediction of the growth model with human and physical capital that is described in Appendix II. A one percent increase in L and XM would raise the steady-state level of K by 1.3 percent, absent any feed back effects from K to L and XM. The second vector can be interpreted as a production function with constant returns to scale, which was imposed by restricting the sum of the coefficients on K and L to be equal to one. The coefficients on capital and labor are close to the average income shares from the national accounts, which are respectively 0.24 and 0.76. TFP calculated in the previous section cannot be included as a right-hand variable in the production function. Instead, XM was included as a potential explanatory variable of TFP. By construction, the elasticity of GDP with respect to TFP is equal to one. Hence, the coefficient on XM in the second cointegrating vector is also the elasticity of TFP with respect to XM. It is possible, though, that this elasticity is biased because the elasticities of GDP with respect to capital and labor are assumed to be fixed over time. TFP can be interpreted as Aα, where A is a measure of labor augmenting technological progress and α is the elasticity of GDP with respect to labor. In that case, the elasticity of A with respect to XM is 0.1308/0.7167 = 0.1925.
Cointegrating Relations with GDP
(standard errors in parentheses)
Cointegrating Relations with GDP
(standard errors in parentheses)
| Vector 1 | Vector 2 | |
| K | 1 | -0.2833 |
| (0.0526) | ||
| L | -0.8269 | -0.7167 |
| (0.1864) | (0.0526) | |
| GDP | 0 | 1 |
| XM | -0.4700 | -0.1308 |
| (0.0705) | (0.0240) | |
| Constant | 1,3804 | 0.2299 |
| LR test for binding restrictions (rank =2) | ||
| Chi-square(5) | 2.3309 | |
| Probability | 0.8017 | |
Cointegrating Relations with GDP
(standard errors in parentheses)
| Vector 1 | Vector 2 | |
| K | 1 | -0.2833 |
| (0.0526) | ||
| L | -0.8269 | -0.7167 |
| (0.1864) | (0.0526) | |
| GDP | 0 | 1 |
| XM | -0.4700 | -0.1308 |
| (0.0705) | (0.0240) | |
| Constant | 1,3804 | 0.2299 |
| LR test for binding restrictions (rank =2) | ||
| Chi-square(5) | 2.3309 | |
| Probability | 0.8017 | |
Cointegrating Relations with TFP
(standard errors in parentheses)
Cointegrating Relations with TFP
(standard errors in parentheses)
| Vector 1 | Vector 2 | |
| K | 1 | 0 |
| L | -0.9564 | 0 |
| (0.0896) | ||
| TFP | -0.9564 | 1 |
| (0.0896) | ||
| XM | -0.2271 | -0.1531 |
| (0.0623) | (0.0462) | |
| Constant | 1,7754 | -0.0967 |
| LR test for binding restrictions (rank =2) | ||
| Chi-square(5) | 2.0697 | |
| Probability | 0.8394 | |
Cointegrating Relations with TFP
(standard errors in parentheses)
| Vector 1 | Vector 2 | |
| K | 1 | 0 |
| L | -0.9564 | 0 |
| (0.0896) | ||
| TFP | -0.9564 | 1 |
| (0.0896) | ||
| XM | -0.2271 | -0.1531 |
| (0.0623) | (0.0462) | |
| Constant | 1,7754 | -0.0967 |
| LR test for binding restrictions (rank =2) | ||
| Chi-square(5) | 2.0697 | |
| Probability | 0.8394 | |
13. To test the validity of the above results, cointegration analysis of a second set of variables, including quality adjusted capital, quality adjusted employment, TFP, and trade, was carried out. Because of how TFP is calculated, both cointegration analyses would yield similar results if the income shares in the national accounts, which were used to derive TFP, had been constant over time. Hence, the cointegration analysis with the second set of variables is similar to the analysis of the first set with the addition of time varying coefficients for capital and labor in the production function. Ln(TFP(t)) is divided by α(t) so that it reflects the logarithm of labor augmenting technological progress In(A(t)). The results of both analyses are broadly similar. To start with the second vector, in the long run A is only a function of XM. Specifications that included either K or L in the second cointegrating vector were insignificant. The elasticity of A with respect to XM is about the same order of magnitude as in the specification with constant factor shares. In the first cointegrating vector, the coefficients on L and A are restricted to be equal, so that In(L) plus In(A) can be interpreted as a measure of human capital that has a counter part in the growth model in Appendix II. These results further indicate that trade has a positive effect on capital accumulation in the long run over and above its indirect effect through A, which could be interpreted as efficiency gains from greater access to a wider variety of intermediate goods.
14. Changes in the physical capital stock can be attributed to two factors: convergence toward its steady state, and changes in the variables that determined the steady-state level of physical capital. As the analysis above showed, these variables are human capital and the efficiency gains resulting from international trade. To illustrate how this decomposition works, suppose that K0 = 10 and that K0–a1H0–a2XM0 = – 2 where H = L + A and a1 and a2 are the estimated coefficients in the previous table (all variables are in logarithms). Further, suppose that in the next period K1 = 11 and that K1 – a1H1—a2XM1 = –1.5. If the growth rate of K would have been equal to the weighted growth rates of H and XM, the gap between K and its long-run equilibrium level would have remained the same, – 2 in this example. This is defined to be the change in K accounted for by changes in H and XM. However, in this example K grows faster than the weighted average of H and XM, as the gap declines by 0.5—this is convergence. If, on the other hand, the gap widens to say – 2.5, this would be considered a negative shock as K moved away from its long-run equilibrium. This decomposition only holds over suitably long time horizons as K cannot immediately catch up with increases in H and XM.
Gap Between Current and Steady-State Capital Stock
(in logarithms)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Gap Between Current and Steady-State Capital Stock
(in logarithms)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Gap Between Current and Steady-State Capital Stock
(in logarithms)
Citation: IMF Staff Country Reports 2003, 080; 10.5089/9781451822137.002.A003
Sources of Long-Run Capital Accumulation
(average annual percent changes)
Sources of Long-Run Capital Accumulation
(average annual percent changes)
| 1980-90 | 1985-95 | 1990-2001 | 1995-2001 | ||
|---|---|---|---|---|---|
| Captital accumulation | 9.7 | 10.0 | 8.3 | 7.5 | |
| Human capital accumulation | 8.6 | 6.8 | 5.5 | 5.0 | |
| Efficiency increases | 2.4 | 3.1 | 2.6 | 2.2 | |
| Convergence | -1.3 | 0.1 | 0.3 | 0.4 | |
Sources of Long-Run Capital Accumulation
(average annual percent changes)
| 1980-90 | 1985-95 | 1990-2001 | 1995-2001 | ||
|---|---|---|---|---|---|
| Captital accumulation | 9.7 | 10.0 | 8.3 | 7.5 | |
| Human capital accumulation | 8.6 | 6.8 | 5.5 | 5.0 | |
| Efficiency increases | 2.4 | 3.1 | 2.6 | 2.2 | |
| Convergence | -1.3 | 0.1 | 0.3 | 0.4 | |
15. Increases in human capital and efficiency were key factors in sustaining rapid capital accumulation in Korea in 1980–2001. Convergence towards the long-run steady state can only explain a small portion of Korea’s high rate of capital accumulation in 1980–2001. Instead, human capital accumulation and increases in efficiency kept the rate of return to investment from falling to its steady-state level, thereby sustaining economic growth. Convergence in 1980–90 was negative, because K was above its long-run equilibrium level in the early 1980s, as shown in the table. However, the negative impact of convergence was more than offset by increases in human capital and efficiency gains from international trade. The slowdown in physical capital accumulation in the second half of the 1990s is in part explained by a deceleration of human capital accumulation. Human capital has been defined as the product of the level of labor augmenting technological progress and quality adjusted employment. Growth of the latter slowed and is bound to slow further as population growth and increases in the educational attainment of the work force slow. Ultimately labor augmenting technological progress will be the main source of human capital growth.
D. Conclusion
16. GDP growth in Korea in 1980–2002 was impressive at 6.8 percent a year. Growth accounting showed that increases in capital and labor, both adjusted for quality improvements, were the main contributors to Korea’s growth. TFP growth was only modest and similar to that in other OECD countries.
17. Analysis of Korea’s growth process revealed that human capital accumulation was an important source of economic growth. It contributed to GDP growth directly as a factor input and indirectly by boosting physical capital accumulation. In the absence of rapid human capital accumulation the rate of return to investment would have declined much faster and growth would have slowed. Indeed, the deceleration in physical capital accumulation in the second half of the 1990s is in part explained by slower growth of human capital. Looking ahead, it is likely that increases in the educational attainment of the labor force, one of the components of human capital, will become smaller as increases in the years of schooling of the average worker slow. Nevertheless, there is still scope for further increases in the educational attainment of the work force, as new entrants are on average better trained than retiring workers, but the contribution of these increases to growth of quality adjusted labor will also decline. It is also projected that labor force growth will slow along with population growth. A higher participation rate of women might mitigate this projected trend.
18. To achieve annual GDP growth of 5–6 percent over the medium term Korea has to increase its rate of technological progress. This can be achieved by devoting more resources to scientific research and commercial R&D, as well as by importing more foreign knowledge through international trade and foreign direct investment. Structural reforms will be important in this respect, as they improve the efficient allocation of resources and thereby increase the scope for greater exploitation of alternative sources of economic growth.
References
Barro, Robert J. and Xavier Sala-i-Martin, 1995, Economic Growth (New York: McGraw-Hill).
Collins, Susan M. and Barry P. Bosworth, 1996, “Economic Growth in East Asia: Accumulation versus Assimilation,” Brookings Papers on Economic Activity, No. 2, pp. 135–191.
Grossman, Gene M., and Elhanan Helpman, 1991, Innovation and Growth (Cambridge, Massachusetts: MIT Press).
Iwata, Shigeru, Moshin S. Khan, and Hiroshi Murao, 2002, “Sources of Economic Growth in East Asia: A Nonparametric Assessment,” IMF Working Paper 02/13 (Washington, D.C.: International Monetary Fund).
Ma, Henry, 2001, “Potential Output, the Output Gap, and Inflation in Korea,” in Korea: Selected Issues, IMF Country Report 01/101 (Washington, D.C.: International Monetary Fund).
Lucas, Robert E., Jr., 1988, On the Mechanics of Development Planning,” Journal of Monetary Economics, Vol. 22, no. 1, pp. 3–42.
Pyo, Hak-kil, Byung-ho Kong, Ho-young Kwon, and Eun-ja Kim, 1993, An Analysis of the Causes of Growth and Productivity by Industry for the Republic of Korea, 1970—1990 (Seoul: Korean Economics Research Institute).
Solow, Robert M., 1956, “A Contribution to the Theory of Economic Growth,” Quarterly Journal of Economics, Vol. 70, no. 1, pp. 65–94.
Uzawa, Hirofumi, 1965, Optimal Technical Change in an Aggregative Model of Economic Growth,” International Economic Review, Vol. 6, pp. 18–31.
Young, Alwyn, 1992, “A Tale of Two Cities: Factor Accumulation and Technical Change in Hong Kong and Singapore,” in S. Fisher and O. Blanchard (eds.), NBER Macroeconomics Annual 1992 (Cambridge, Massachusetts: MIT Press).
Young, Alwyn, 1995, “The Tyranny of Numbers: Confronting the Statistical Realities of the East Asian Growth Experience,” Quarterly Journal of Economics, Vol. 110, pp. 641–680.
ANNEX I Construction of Relative Rental Rates of Capital
With geometric depreciation and perfect foresight the rental price of a capital good Kj in period t is given by:
where pij(t) denotes the investment price of capital good j in period t, r(t) is the economy-wide nominal rate of return between periods t and t – 1, and δj is the depreciation rate of capital good j. The above arbitrage equation says that the return on investing PIJ in capital good j, which is the rental rate plus any valuation changes minus depreciation, is equal to the opportunity cost of investing the same amount in an asset with known return r.
Investment series for each type of capital good in current and constant prices were used to obtain investment prices. The price series were smoothed by taking four period averages. Depreciation rates are taken from Young (1992).
Under constant returns to scale, the following equality holds:
where the left-hand side is the share of aggregate capital income in GDP and the right-hand side is the sum of the rental incomes of the five types of capital goods. This equality can be exploited to calculate the rental rates of the different capital goods. This is done by varying r(t) until the sum of rental payments to individual capital goods is equal to the share of aggregate capital income in GDP.
ANNEX II A Two-sector Model with Physical and Human Capital
The model in this appendix closely follows those developed by Uzawa (1965) and Lucas (1988). It has two sectors and two factors of production, human capital H and physical capital K. Sector 1 uses both inputs to produce consumption goods and capital goods, which have the same relative price:
where Y1 is output of sector 1,
where Y2 is output of sector 2 and B2 is a constant. Human capital employed in both sectors cannot exceed the available stock: H ≥ H1 + H2. GDP is the sum of output in sectors 1 and 2: GDP = Y1+ pY2, with p the relative price of H.
A crucial assumption in the Lucas’ model is that H is produced with constant returns to scale (β = 1), which, as can be shown, yields a long-run equilibrium in which K, H, and GDP all grow at the same rate.6 When the economy is in this equilibrium it is said to be on its balanced growth path (BGP). Along this path K/H is constant. In the case with β < 1, a BGP does not exist and the economy converges to a steady state in which growth comes to a halt in the absence of exogenous increases in H, just as in the neoclassical growth model (Solow, 1956). The case with β > 1 is not very interesting as it implies accelerating growth over the long-run, which is normally not observed over long time horizons.
The model has transitional dynamics. Because it takes time to accumulate K and H, an economy with an initial endowment K0/H0 that is different from the long-run ratio K*/H* cannot jump instantaneously to its BGP or steady state. For K0/H0 < K*/H*, K/H will gradually increase while the economy moves toward its long-run equilibrium, vice versa for K0/H0 > K*/H*.
Now let H be defined as the product of years of schooling s, raw labor LR, and the state of knowledge in the economy A:
The above relation shows the sources of human capital accumulation. In the long-run, however, only LR and A can be sources of growth in human capital, because educational attainment is bounded by the maximum number of years a person can spend in school. The state of knowledge increases through research and development, scientific research, learning-by-doing, and adoption and adaptation of foreign technologies. Learning-by-doing can be the by-product of investment, which can extend beyond the firm that makes the investment. Foreign technologies can be introduced into an economy through trade and foreign direct investment and possibly other channels.
Dividing equation (A2.2) by H it can be rewritten as:
where (1–u) = H2/H
If TFP is interpreted as Aα, then the product of TFP1/α and quality adjusted labor is a measure of human capital similar to that in equation (A2.3). The Uzawa-Lucas model then predicts that K/(sLRTFP1/α) is constant in the long-run. In logarithms this is:
where L = sLR is quality adjusted labor and θ0 is a constant. TFP is assumed to be a function of learning-by-doing through capital accumulation and foreign knowledge imported through trade XM:
Substituting equation (A2.5) into equation (A2.4) yields:
Equations (A2.4)-(A2.6) along with a logarithmic aggregate production function are tested in the cointegration analysis in the main text.
This paper, which was prepared by Harm Zebregs (APD), reports preliminary results for a forthcoming IMF working paper.
Bosworth and Collins (1996), Iwata, Khan, and Murao (2002), Ma (2001), and Young (1995) are some of the more recent papers that include Korea.
See Appendix I for details.
The measure of labor input could be refined further by taking into account actual hours worked. These data are available on a quarterly basis from 1980 onward, but they appear to suffer from measurement errors in the early 1980s.
This literature suggests that productivity rises with increases in specialization in the production process. Specialization is proxied by the number of intermediate inputs incorporated in a unit of final output. Trade raises productivity because it gives producers access to a larger variety of intermediate inputs.
See Barro and Sala-i-Martin (1995) for a more detailed description of the Uzawa-Lucas model.
