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Growth and multiple forms of human capital in an augmented Solow model: a panel data investigation
Economics Letters 74 (2002) 271–276 www.elsevier.com / locate / econbase
Growth and multiple forms of human capital in an augmented Solow model: a panel data investigation Scott McDonald a,b , Jennifer Roberts a,b , * a
b
Department of Economics, 9 Mappin Street, University of Sheffield, Sheffield, UK Sheffield Health Economics Group, ScHARR University of Sheffield, Regent Court, Sheffield S1 4 DA, UK Received 28 March 2000; received in revised form 30 April 2001; accepted 24 July 2001
Abstract The empirical analyses reported in this paper test the argument that human capital is a complex input that consists of more than knowledge capital. The results indicate that omitting health capital from augmented Solow growth models produces misspecification biases, and that health capital has a significant impact upon economic growth rates. 2002 Elsevier Science B.V. All rights reserved. Keywords: Growth; Health; Human capital; Panel data JEL classification: O47; I12; O15; C23
1. Introduction A substantial part of the empirical literature on economic growth has been dedicated to quantifying the contribution of human capital (Mankiw et al., 1992; Barro and Lee, 1993; Benhabib and Spiegel, 1994). Mankiw et al. (1992), hereafter MRW, justify the inclusion of human capital by noting that if multiple forms of capital exist then ‘‘omitting human-capital accumulation biases the estimated coefficients’’ (1992, p. 408). However, it has long been argued that human capital is a complex input that consists of more than knowledge capital, and, in particular, that attention should be given to health capital (Schultz, 1961; Mushkin, 1962; Knowles and Owen, 1995). If health is an important dimension of human capital its omission will result in a model with misspecification bias. Furthermore, the limitations of the cross-country cross-section method have been recognised in recent panel data studies (Islam, 1995; Lee et al., 1997; McDonald and Roberts, 1999). In this paper an augmented Solow model is developed that incorporates both health and education * Corresponding author. Tel.: 144-114-222-0801; fax: 144-114-272-4095. E-mail address: [email protected] (J. Roberts). 0165-1765 / 02 / $ – see front matter PII: S0165-1765( 01 )00539-0
2002 Elsevier Science B.V. All rights reserved.
S. McDonald, J. Roberts / Economics Letters 74 (2002) 271 – 276
272
capital in a dynamic panel data model. The next section reports the derivation of the estimating equation and discusses panel data methods. The data and results are presented in Section 3. Section 4 contains concluding comments.
2. Health, growth and convergence in an augmented Solow model
2.1. An augmented Solow model Augmenting a Solow model with both education capital and health capital is straightforward. Assuming constant returns to scale and labour augmenting technical progress, an aggregate Cobb– Douglas production function with three forms of capital can be written as Yit 5 [A it Lit ] 12 a 2 b 2 c K ait E bit H cit
(1)
where Y is output, A is technology, L is the stock of labour, K, E and H are, respectively, the stocks of physical, education and health capital. a, b and c are the elasticities of output with respect to the capital terms, and the subscripts denote country (i) and time (t). If the labour forces grow at country-specific constant rates n i , technology advances at periodspecific constant rates gt , and the physical, education and human capital stocks depreciate at the same constant rate, d, then an expression for the (augmented) steady state output per capita for country i at time t, y *it , can be derived in terms of the parameters of the production function and the shares of income invested in the accumulation of physical, human and health capital, s ki , s Ei and S Hi , respectively. Since data on the shares of income invested in the accumulation of human and health capital are not readily available it is convenient to specify the relationship in terms of steady state levels of human and health capital per capita, e *it and h it* , respectively. An estimating equation with a ‘speed of convergence parameter’ can be obtained, following MRW, by linearising the growth equation around the steady-state level of income per capita. The resultant equation is a dynamic panel data model with two-way fixed effects, i.e.,
Oux 4
z *it 5 g z *i 0 1
j
j it
1 ht 1 mi 1 nit
j51
where z *it 5 ln y *it
g 5 e 2lt z *i 0 5 ln y *i 0
f 5 (1 2 e 2 l t )
fb u3 5 ]]] (1 2 a ) 3 x it 5 ln e *it fc u4 5 ]]] (1 2 a ) x it4 5 ln h *it
fa u1 5 2 u2 5 ]]] ht 5 gt t (1 2 a ) x 1it 5 ln(n i 1 gt 1 d ) mi 5 f ln A i 0 x 2it 5 ln s ki
(2)
S. McDonald, J. Roberts / Economics Letters 74 (2002) 271 – 276
273
Eq. (2) is the basis for the econometric estimates reported in this paper. Country-specific effects are captured by variations in initial states of technology, ln A i 0 , and time-specific technology effects are captured by variations in the growth rates of technology, gt . Cross-section studies typically assume common initial states of technology and constant rates of technical progress (see MRW). If these assumptions are not valid then doubts must be cast upon the results from empirical research dependent on these assumptions. Solow (1994), among others, has cast doubt upon the validity of the assumption that the parameters of the production function were common across countries with only the variables subject to differences. And Islam (1995) has used panel data methods to estimate the augmented Solow model with fixed-effects to allow for parameter heterogeneity.1
3. Analysis
3.1. Data The main source of data is the Penn World Tables version 5.6 (PWT) (Summers and Heston, 1991). The data used are real GDP per worker (YW), share of real GDP invested (I), and working population (POPW). It is assumed that the s ki are measured by the rate of investment in real GDP (per worker), and these savings are used solely for physical capital accumulation. The education stock data are the mean years of total education (HKT) from Nehru et al. (1995). The two proxies for health capital are from World Data (World Bank, 1997). Infant mortality (INF) is defined as the number of infant deaths before 1 year of age per 1000 live births. And life expectancy at birth is defined as the shortfall of life expectancy relative to a nominal benchmark, i.e., LE5 2ln(80–life expectancy).2 Although these proxies have been criticised as crude (Knowles and Owen, 1995, p. 102), they have been strongly defended in the macroeconomic context of developing countries (see Sen, 1998). All the variables are in logarithms. There are four samples. The full sample of 77 countries, which is defined by the intersection of the MRW 98 non-oil producing country sample with the human capital data series. There are three sub-samples, a 22-country OECD sample, a 55-country sample of LDCs (defined as the full sample less the OECD sample), and a 39-country LDC2 sample (defined as the LDC sample less the Latin American countries). Full details of the samples are given in Table 1.
3.2. Results Cross-section regressions confirm the key results of Knowles and Owen (1995).3 For all three samples, including either LE or INF to account for health capital produces coefficients with the expected sign and substantially reduces the marginal significance level of the coefficient on education. The model is estimated using a 5-yearly panel, to preserve the time series information present in the data, and the results are reported in Table 1. The dependent variable in each case is the level of income per capita at the end of each 5-year period (z it ). Time effects are included where the coefficients are significant at t 0.10 . The Breusch–Pagan tests indicate that country-specific effects are 1
Lee et al. (1997) have argued for an alternative approach. This transformation is typical of the Human Development Reports (e.g., UN, 1998). 3 These results are available from the authors. 2
S. McDonald, J. Roberts / Economics Letters 74 (2002) 271 – 276
274
Table 1 Five-yearly panel models Full (n577) I (n1g1d ) HKT
0.222 (0.027) 20.313 (0.047) 0.010 (0.032)
LE YW(21) Y3 Y4
0.640 (0.030) 0.051 (0.013) 0.029 (0.013)
LDC (n555) 0.229 (0.027) 20.291 (0.045) 20.005 (0.031) 0.120 (0.040) 0.557 (0.044) 0.060 (0.014) 0.038 (0.013)
0.226 (0.030) 20.317 (0.057) 0.025 (0.032)
0.599 (0.043) 0.058 (0.019) 0.049 (0.019)
0.229 (0.030) 20.308 (0.057) 20.005 (0.035) 0.106 (0.069) 0.549 (0.054) 0.064 (0.020) 0.054 (0.019)
LDC2 (n539)
OECD* (n522)
0.244 (0.036) –0.374 (0.062) 0.036 (0.035)
0.173 (0.037) 20.225 (0.053) 0.067 (0.024)
0.622 (0.051)
0.257 (0.036) 20.348 (0.061) 0.017 (0.037) 0.331 (0.100) 0.468 (0.068)
Y5 ]2 R BP H
0.68 41.33 [0.000] 112.18 [0.000]
0.69
Structural parameter estimates l 0.09 0.12 a 0.40 0.35 b 0.00 20.01 c h(LE) 0.18 Wald (F) 2.87 1.36 [0.091] [0.245]
0.836 (0.016) 0.049 (0.016)
0.175 (0.038) 20.228 (0.054) 0.069 (0.026) 20.006 (0.022) 0.840 (0.020) 0.048 (0.017)
20.066 (0.016)
20.065 (0.016)
0.64 29.77 [0.000] 80.38 [0.000]
0.64
0.93 17.55 [0.000] 62.20 [0.000]
0.89
0.97 2.64 [0.104]
0.97
0.10 0.37 0.02
0.12 0.34 20.00 0.16 1.45 [0.230]
0.10 0.41 0.04
0.16 0.33 20.03 0.42 1.60 [0.208]
0.03 0.53 0.19
0.03 0.54 0.20 20.02 0.05 [0.833]
1.97 [0.162]
3.10 [0.080]
0.03 [0.865]
All estimation carried out using STATA v7.0 Dependent variable is ZYW (z *it ). Y3, Y4 and Y5 are time dummies for 1970–74, 1975–79 and 1980–84. White’s heteroscedasticity consistent standard errors in parentheses. Wald (F), Breusch–Pagan (BP) and Hausman (H) tests reported. Panel estimation based on 5-yearly averages 1960–1989 (i.e., t51,2, . . . ,6) The full sample contains all 77 countries listed here. The OECD sample countries are marked by (o), the LDC sample contains the remaining countries, the LDC2 sample is the LDC sample less Latin American countries, which are marked by (l). Algeria, Angola, Argentina(l), Australia(o), Austria(o), Bangladesh, Belgium(o), Bolivia(l), Brazil(l), Cameroon, Canada(o), Chile(l), Colombia(l), Costa Rica(l), Denmark(o), Ecuador(l), Egypt, El Salvador(l), Ethiopia, Finland(o), France(o), Germany(o), Ghana, Great Britain(o), Greece(o), Guatemala(l), Haiti, Honduras(l), Iceland, India, Ireland(o), Israel, Italy(o), Ivory Coast, Jamaica, Japan(o), Kenya, Korea, Madagascar, Malawi, Malaysia, Mali, Mauritius, Mexico(l), Morocco, Mozambique, Myanmar, The Netherlands(o), New Zealand(o), Nigeria, Norway(o), Pakistan, Panama(l), Paraguay(l), Peru(l), Philippines, Portugal(o), Rwanda, Senegal, Sierra Leone, Singapore, Spain(o), Sri Lanka, Sudan, Sweden(o), Switzerland(o), Tanzania, Thailand, Tunisia, Turkey(o), Uganda, United States(o), Uruguay(l), Venezuela(l), Zaire, Zambia, Zimbabwe. * Pooled data model.
S. McDonald, J. Roberts / Economics Letters 74 (2002) 271 – 276
275
appropriate for the Full, LDC and LDC2 sample, but marginal for the OECD sample. Hence the reported results for the OECD are from pooled data. The Hausman tests indicate that where individual effects are needed these should be fixed, rather than random. For all the samples the coefficients on investment (I) and ‘work force growth’ (n1g1d ) have the expected signs and are significant, and the coefficients on investment decline as the average income of the samples decline. The lagged income terms all return the expected positive and significant coefficients. There are positive time dummies for three samples for 1970–74 and two samples for 1975–79, with negative and significant time dummies for the OECD for 1980–84, which casts doubts on an assumption of a constant rate of growth of technology over time. For the two largest samples the explanatory power is about two-thirds and this increases to above 90% for the LDC2 and OECD samples. The tests for country-specific effects indicates that the assumption of common initial technologies, which is implicit to cross-section studies, is inappropriate for the Full, LDC and LDC2 samples, but appropriate for the OECD, a conclusion that is consistent with expectations. The most interesting results are for human capital, and in particular the contrasts between the LDC and OECD samples and between the LDC and LDC2 samples. The coefficients on education capital are insignificantly different from zero in both LDC samples but positive and significant for the OECD, whereas the coefficients on health capital are positive and significant for the LDC samples but insignificant for the OECD.4 Further investigation of the data indicated that the characteristics of the Latin American countries in the full sample were more similar to the OECD than LDC samples. The differences between the coefficients for the LDC and LDC2 samples particularly demonstrate this through the tripling of the coefficient on life expectancy. The structural parameters reported at the bottom of Table 1 were derived from a restricted version of Eq. (2), where u1 5 2 u2 is imposed. The Wald test suggests that this restriction is valid in each case. As expected the estimated rates of convergence ( l) increase if the health capital coefficients are significant, and are appreciably larger than those of Islam (1995). The implied shares of the product for each form of capital differ appreciably across the sample. The elasticity of output of physical capital (a ) declines, as expected, whenever the health capital coefficients are significant. The implied values for b are small when the coefficients on education capital are insignificant, but substantial when the coefficients are significant. The opposite applies for c. Hence, the inclusion of health capital substantially alters the elasticities of output for the education, which is the expected finding if there is a misspecification problem, with health and education stock correlated.
4. Concluding comments These results support the view that education capital alone is a potentially inadequate proxy for human capital as a factor in the determination of growth, while the importance of country- and time-specific fixed effects challenge the assumptions of common initial states of technology and constant rates of technical progress. Moreover they indicate that the roles of different forms of capital in the growth process change as incomes rise. The coefficients on investment are inversely related to the average incomes of the samples, with health capital seemingly more important at low incomes and 4
Only the life expectancy results are reported, but in all samples the infant mortality variables returned the expected opposite sign to life expectancy and the significances were the same.
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S. McDonald, J. Roberts / Economics Letters 74 (2002) 271 – 276
education capital more important at high incomes. Consequently the results lend support to Sen’s (1998) argument that infant mortality rates and life expectancy are meaningful in a macroeconomic context. As such the analyses reported in this paper substantially reinforce the conclusions of Knowles and Owen (1995) and Islam (1995).
Acknowledgements The research reported in this paper was supported by a research grant from ScHARR, University of Sheffield. The authors gratefully acknowledge research assistance by Jon Harper, and comments by an anonymous referee that induced substantial improvements in the analyses, but retain sole responsibility for all errors in the arguments and conclusions reported in this paper.
References Barro, R.J., Lee, J., 1993. International comparisons of educational attainment. Journal of Monetary Economics 32, 363–394. Benhabib, J., Spiegel, M.M., 1994. The role of human capital in economic development: evidence form aggregate cross-country data. Journal of Monetary Economics 34, 143–173. Islam, N., 1995. Growth empirics: a panel data approach. Quarterly Journal of Economics 110, 1127–1170. Knowles, S., Owen, P.D., 1995. Health capital and cross-country variation in income per capita in the Mankiw-Romer-Weil model. Economics Letters 48, 99–106. Lee, K., Pesaran, M.H., Smith, R., 1997. Growth and convergence in a multi-country empirical stochastic Solow model. Journal of Applied Econometrics 12, 357–392. Mankiw, N.G., Romer, D., Weil, D.N., 1992. A contribution to the empirics of economic growth. Quarterly Journal of Economics 107, 407–437. McDonald, S., Roberts, J., 1999. Testing growth models: should cross-section growth studies be used to inform policy? South African Journal of Economics 67, 441–462. Mushkin, S.J., 1962. Health as an investment. Journal of Political Economy 70, 129–157. Nehru, V., Swanson, E., Dubey, A., 1995. A new database on human capital stock in developing and industrial countries: sources, methodology and results. Journal of Development Economics 46, 379–401. Schultz, T.W., 1961. Investment in human capital. American Economic Review 51, 1–17. Sen, A., 1998. Mortality as an indicator of economic success and failure. Economic Journal 108, 1–25. Solow, R.M., 1994. Perspectives on growth theory. Journal of Economic Perspectives 8, 45–54. Summers, R., Heston, A., 1991. The Penn World Table (Mark 5): an expanded set of international comparisons, 1950–1988. Quarterly Journal of Economics 106, 327–368. UN, 1998. In: Human Development Report. Oxford University Press, Oxford. World Bank, 1997. In: World Development Indicators 1997. World Bank, Washington.
Growth and multiple forms of human capital in an augmented Solow model: a panel data investigation Scott McDonald a,b , Jennifer Roberts a,b , * a
b
Department of Economics, 9 Mappin Street, University of Sheffield, Sheffield, UK Sheffield Health Economics Group, ScHARR University of Sheffield, Regent Court, Sheffield S1 4 DA, UK Received 28 March 2000; received in revised form 30 April 2001; accepted 24 July 2001
Abstract The empirical analyses reported in this paper test the argument that human capital is a complex input that consists of more than knowledge capital. The results indicate that omitting health capital from augmented Solow growth models produces misspecification biases, and that health capital has a significant impact upon economic growth rates. 2002 Elsevier Science B.V. All rights reserved. Keywords: Growth; Health; Human capital; Panel data JEL classification: O47; I12; O15; C23
1. Introduction A substantial part of the empirical literature on economic growth has been dedicated to quantifying the contribution of human capital (Mankiw et al., 1992; Barro and Lee, 1993; Benhabib and Spiegel, 1994). Mankiw et al. (1992), hereafter MRW, justify the inclusion of human capital by noting that if multiple forms of capital exist then ‘‘omitting human-capital accumulation biases the estimated coefficients’’ (1992, p. 408). However, it has long been argued that human capital is a complex input that consists of more than knowledge capital, and, in particular, that attention should be given to health capital (Schultz, 1961; Mushkin, 1962; Knowles and Owen, 1995). If health is an important dimension of human capital its omission will result in a model with misspecification bias. Furthermore, the limitations of the cross-country cross-section method have been recognised in recent panel data studies (Islam, 1995; Lee et al., 1997; McDonald and Roberts, 1999). In this paper an augmented Solow model is developed that incorporates both health and education * Corresponding author. Tel.: 144-114-222-0801; fax: 144-114-272-4095. E-mail address: [email protected] (J. Roberts). 0165-1765 / 02 / $ – see front matter PII: S0165-1765( 01 )00539-0
2002 Elsevier Science B.V. All rights reserved.
S. McDonald, J. Roberts / Economics Letters 74 (2002) 271 – 276
272
capital in a dynamic panel data model. The next section reports the derivation of the estimating equation and discusses panel data methods. The data and results are presented in Section 3. Section 4 contains concluding comments.
2. Health, growth and convergence in an augmented Solow model
2.1. An augmented Solow model Augmenting a Solow model with both education capital and health capital is straightforward. Assuming constant returns to scale and labour augmenting technical progress, an aggregate Cobb– Douglas production function with three forms of capital can be written as Yit 5 [A it Lit ] 12 a 2 b 2 c K ait E bit H cit
(1)
where Y is output, A is technology, L is the stock of labour, K, E and H are, respectively, the stocks of physical, education and health capital. a, b and c are the elasticities of output with respect to the capital terms, and the subscripts denote country (i) and time (t). If the labour forces grow at country-specific constant rates n i , technology advances at periodspecific constant rates gt , and the physical, education and human capital stocks depreciate at the same constant rate, d, then an expression for the (augmented) steady state output per capita for country i at time t, y *it , can be derived in terms of the parameters of the production function and the shares of income invested in the accumulation of physical, human and health capital, s ki , s Ei and S Hi , respectively. Since data on the shares of income invested in the accumulation of human and health capital are not readily available it is convenient to specify the relationship in terms of steady state levels of human and health capital per capita, e *it and h it* , respectively. An estimating equation with a ‘speed of convergence parameter’ can be obtained, following MRW, by linearising the growth equation around the steady-state level of income per capita. The resultant equation is a dynamic panel data model with two-way fixed effects, i.e.,
Oux 4
z *it 5 g z *i 0 1
j
j it
1 ht 1 mi 1 nit
j51
where z *it 5 ln y *it
g 5 e 2lt z *i 0 5 ln y *i 0
f 5 (1 2 e 2 l t )
fb u3 5 ]]] (1 2 a ) 3 x it 5 ln e *it fc u4 5 ]]] (1 2 a ) x it4 5 ln h *it
fa u1 5 2 u2 5 ]]] ht 5 gt t (1 2 a ) x 1it 5 ln(n i 1 gt 1 d ) mi 5 f ln A i 0 x 2it 5 ln s ki
(2)
S. McDonald, J. Roberts / Economics Letters 74 (2002) 271 – 276
273
Eq. (2) is the basis for the econometric estimates reported in this paper. Country-specific effects are captured by variations in initial states of technology, ln A i 0 , and time-specific technology effects are captured by variations in the growth rates of technology, gt . Cross-section studies typically assume common initial states of technology and constant rates of technical progress (see MRW). If these assumptions are not valid then doubts must be cast upon the results from empirical research dependent on these assumptions. Solow (1994), among others, has cast doubt upon the validity of the assumption that the parameters of the production function were common across countries with only the variables subject to differences. And Islam (1995) has used panel data methods to estimate the augmented Solow model with fixed-effects to allow for parameter heterogeneity.1
3. Analysis
3.1. Data The main source of data is the Penn World Tables version 5.6 (PWT) (Summers and Heston, 1991). The data used are real GDP per worker (YW), share of real GDP invested (I), and working population (POPW). It is assumed that the s ki are measured by the rate of investment in real GDP (per worker), and these savings are used solely for physical capital accumulation. The education stock data are the mean years of total education (HKT) from Nehru et al. (1995). The two proxies for health capital are from World Data (World Bank, 1997). Infant mortality (INF) is defined as the number of infant deaths before 1 year of age per 1000 live births. And life expectancy at birth is defined as the shortfall of life expectancy relative to a nominal benchmark, i.e., LE5 2ln(80–life expectancy).2 Although these proxies have been criticised as crude (Knowles and Owen, 1995, p. 102), they have been strongly defended in the macroeconomic context of developing countries (see Sen, 1998). All the variables are in logarithms. There are four samples. The full sample of 77 countries, which is defined by the intersection of the MRW 98 non-oil producing country sample with the human capital data series. There are three sub-samples, a 22-country OECD sample, a 55-country sample of LDCs (defined as the full sample less the OECD sample), and a 39-country LDC2 sample (defined as the LDC sample less the Latin American countries). Full details of the samples are given in Table 1.
3.2. Results Cross-section regressions confirm the key results of Knowles and Owen (1995).3 For all three samples, including either LE or INF to account for health capital produces coefficients with the expected sign and substantially reduces the marginal significance level of the coefficient on education. The model is estimated using a 5-yearly panel, to preserve the time series information present in the data, and the results are reported in Table 1. The dependent variable in each case is the level of income per capita at the end of each 5-year period (z it ). Time effects are included where the coefficients are significant at t 0.10 . The Breusch–Pagan tests indicate that country-specific effects are 1
Lee et al. (1997) have argued for an alternative approach. This transformation is typical of the Human Development Reports (e.g., UN, 1998). 3 These results are available from the authors. 2
S. McDonald, J. Roberts / Economics Letters 74 (2002) 271 – 276
274
Table 1 Five-yearly panel models Full (n577) I (n1g1d ) HKT
0.222 (0.027) 20.313 (0.047) 0.010 (0.032)
LE YW(21) Y3 Y4
0.640 (0.030) 0.051 (0.013) 0.029 (0.013)
LDC (n555) 0.229 (0.027) 20.291 (0.045) 20.005 (0.031) 0.120 (0.040) 0.557 (0.044) 0.060 (0.014) 0.038 (0.013)
0.226 (0.030) 20.317 (0.057) 0.025 (0.032)
0.599 (0.043) 0.058 (0.019) 0.049 (0.019)
0.229 (0.030) 20.308 (0.057) 20.005 (0.035) 0.106 (0.069) 0.549 (0.054) 0.064 (0.020) 0.054 (0.019)
LDC2 (n539)
OECD* (n522)
0.244 (0.036) –0.374 (0.062) 0.036 (0.035)
0.173 (0.037) 20.225 (0.053) 0.067 (0.024)
0.622 (0.051)
0.257 (0.036) 20.348 (0.061) 0.017 (0.037) 0.331 (0.100) 0.468 (0.068)
Y5 ]2 R BP H
0.68 41.33 [0.000] 112.18 [0.000]
0.69
Structural parameter estimates l 0.09 0.12 a 0.40 0.35 b 0.00 20.01 c h(LE) 0.18 Wald (F) 2.87 1.36 [0.091] [0.245]
0.836 (0.016) 0.049 (0.016)
0.175 (0.038) 20.228 (0.054) 0.069 (0.026) 20.006 (0.022) 0.840 (0.020) 0.048 (0.017)
20.066 (0.016)
20.065 (0.016)
0.64 29.77 [0.000] 80.38 [0.000]
0.64
0.93 17.55 [0.000] 62.20 [0.000]
0.89
0.97 2.64 [0.104]
0.97
0.10 0.37 0.02
0.12 0.34 20.00 0.16 1.45 [0.230]
0.10 0.41 0.04
0.16 0.33 20.03 0.42 1.60 [0.208]
0.03 0.53 0.19
0.03 0.54 0.20 20.02 0.05 [0.833]
1.97 [0.162]
3.10 [0.080]
0.03 [0.865]
All estimation carried out using STATA v7.0 Dependent variable is ZYW (z *it ). Y3, Y4 and Y5 are time dummies for 1970–74, 1975–79 and 1980–84. White’s heteroscedasticity consistent standard errors in parentheses. Wald (F), Breusch–Pagan (BP) and Hausman (H) tests reported. Panel estimation based on 5-yearly averages 1960–1989 (i.e., t51,2, . . . ,6) The full sample contains all 77 countries listed here. The OECD sample countries are marked by (o), the LDC sample contains the remaining countries, the LDC2 sample is the LDC sample less Latin American countries, which are marked by (l). Algeria, Angola, Argentina(l), Australia(o), Austria(o), Bangladesh, Belgium(o), Bolivia(l), Brazil(l), Cameroon, Canada(o), Chile(l), Colombia(l), Costa Rica(l), Denmark(o), Ecuador(l), Egypt, El Salvador(l), Ethiopia, Finland(o), France(o), Germany(o), Ghana, Great Britain(o), Greece(o), Guatemala(l), Haiti, Honduras(l), Iceland, India, Ireland(o), Israel, Italy(o), Ivory Coast, Jamaica, Japan(o), Kenya, Korea, Madagascar, Malawi, Malaysia, Mali, Mauritius, Mexico(l), Morocco, Mozambique, Myanmar, The Netherlands(o), New Zealand(o), Nigeria, Norway(o), Pakistan, Panama(l), Paraguay(l), Peru(l), Philippines, Portugal(o), Rwanda, Senegal, Sierra Leone, Singapore, Spain(o), Sri Lanka, Sudan, Sweden(o), Switzerland(o), Tanzania, Thailand, Tunisia, Turkey(o), Uganda, United States(o), Uruguay(l), Venezuela(l), Zaire, Zambia, Zimbabwe. * Pooled data model.
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appropriate for the Full, LDC and LDC2 sample, but marginal for the OECD sample. Hence the reported results for the OECD are from pooled data. The Hausman tests indicate that where individual effects are needed these should be fixed, rather than random. For all the samples the coefficients on investment (I) and ‘work force growth’ (n1g1d ) have the expected signs and are significant, and the coefficients on investment decline as the average income of the samples decline. The lagged income terms all return the expected positive and significant coefficients. There are positive time dummies for three samples for 1970–74 and two samples for 1975–79, with negative and significant time dummies for the OECD for 1980–84, which casts doubts on an assumption of a constant rate of growth of technology over time. For the two largest samples the explanatory power is about two-thirds and this increases to above 90% for the LDC2 and OECD samples. The tests for country-specific effects indicates that the assumption of common initial technologies, which is implicit to cross-section studies, is inappropriate for the Full, LDC and LDC2 samples, but appropriate for the OECD, a conclusion that is consistent with expectations. The most interesting results are for human capital, and in particular the contrasts between the LDC and OECD samples and between the LDC and LDC2 samples. The coefficients on education capital are insignificantly different from zero in both LDC samples but positive and significant for the OECD, whereas the coefficients on health capital are positive and significant for the LDC samples but insignificant for the OECD.4 Further investigation of the data indicated that the characteristics of the Latin American countries in the full sample were more similar to the OECD than LDC samples. The differences between the coefficients for the LDC and LDC2 samples particularly demonstrate this through the tripling of the coefficient on life expectancy. The structural parameters reported at the bottom of Table 1 were derived from a restricted version of Eq. (2), where u1 5 2 u2 is imposed. The Wald test suggests that this restriction is valid in each case. As expected the estimated rates of convergence ( l) increase if the health capital coefficients are significant, and are appreciably larger than those of Islam (1995). The implied shares of the product for each form of capital differ appreciably across the sample. The elasticity of output of physical capital (a ) declines, as expected, whenever the health capital coefficients are significant. The implied values for b are small when the coefficients on education capital are insignificant, but substantial when the coefficients are significant. The opposite applies for c. Hence, the inclusion of health capital substantially alters the elasticities of output for the education, which is the expected finding if there is a misspecification problem, with health and education stock correlated.
4. Concluding comments These results support the view that education capital alone is a potentially inadequate proxy for human capital as a factor in the determination of growth, while the importance of country- and time-specific fixed effects challenge the assumptions of common initial states of technology and constant rates of technical progress. Moreover they indicate that the roles of different forms of capital in the growth process change as incomes rise. The coefficients on investment are inversely related to the average incomes of the samples, with health capital seemingly more important at low incomes and 4
Only the life expectancy results are reported, but in all samples the infant mortality variables returned the expected opposite sign to life expectancy and the significances were the same.
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education capital more important at high incomes. Consequently the results lend support to Sen’s (1998) argument that infant mortality rates and life expectancy are meaningful in a macroeconomic context. As such the analyses reported in this paper substantially reinforce the conclusions of Knowles and Owen (1995) and Islam (1995).
Acknowledgements The research reported in this paper was supported by a research grant from ScHARR, University of Sheffield. The authors gratefully acknowledge research assistance by Jon Harper, and comments by an anonymous referee that induced substantial improvements in the analyses, but retain sole responsibility for all errors in the arguments and conclusions reported in this paper.
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