24 FLEISHER AND CHEN x, is a measure of investment in housing(to correct for the inclusion of expenditure on new housing in total investment ), and is negative, x2 is a measure of the vintage of the physical capital stock, and egative, xs is a measure of investment in human capital, and is positive xa is a measure of infrastructure(highways, railways, and waterways) and is positive, xs is foreign direct investment(FDI) as a share of total investment, an Is positive, C is a dummy variable I for coastal provinces and Beijing t is the year of observation(1979=1..1993= 15), and U is an i.i.d. error term. We follow Wolff (1991)in including lagged TFP, Ti-l, in Eq. (4). Full definitions and sources of the variables are included in the Appendix 7 The rationale for including vintage as a contributing factor to TFP and TFP growth is neatly summarized by Wolff (1991). Although Wolff uses the rate of change of the capital stock as a proxy for vintage, we have chosen to define variable x2 as a weighted average of the age of existing capital, specifi I(y2i-I Iuxt-j+ 1)l, where I is real accumulation of fixed assets 8 The contribution of human capital to production is by now part of received knowledge. It would be appropriate to include investment in human capital in conjunction with physical-capital investment in Eq (3) We do not do this because data on the actual magnitude of human-capital (1988) stock data have been purged of housing and other nonproductive capital. Jefferson et al.(1992) use corrected data for state and collective industry. It would be ideal for such net capital stock data for each province, but constructing such data is a task that is far beyond our urrent resources. In order to solve the problem that annual data for this variable are not available 1978 to 1993, we use an instrument for housing in estimating Eq.(4). The instrument is obtained by regressing a measure of housing area(square meters) per capita on per capita real income. The predicted level of per capita housing is then used as the measure of variable x Unfortunately, variables x(infrastructure)and xs(FDI) are not available annually from 1978 to 1993. Therefore in our empirical work we have treated them nvironmental variables Details are contained in the notes to table 2 Data for accumulation of fixed assets is available after 1952 for all provinces in our sample. We deflate using a price index obtained from series on construction both in nominal prices and in]fixed Chen et al. (June, 1988)assert that the data on construction in fixed prices are unreliable. However, our alternative is to use the provincial national income deflator that can be obtained by comparing national income and national income at fixed prices. We chose to use the construction deflator on the assumption that it provides an index closer to the correct one for accumulation than any alternative. We also used the same data to construct a variable(AK/ K)=(n2-o Iy), which is conceptually similar to the variable used by Wolff. The empirical results are not very sensitive to which of these variables is used to estimate Eq (4)224 FLEISHER AND CHEN x1 is a measure of investment in housing (to correct for the inclusion of expenditure on new housing in total investment), and is negative,6 x2 is a measure of the vintage of the physical capital stock, and is negative, x3 is a measure of investment in human capital, and is positive, x4 is a measure of infrastructure (highways, railways, and waterways), and is positive, x5 is foreign direct investment (FDI) as a share of total investment, and is positive, C is a dummy variable Å 1 for coastal provinces and Beijing, t is the year of observation (1979 Å 1 rrr 1993 Å 15), and £i,t is an i.i.d. error term. We follow Wolff (1991) in including lagged TFP, tt01 , in Eq. (4). Full definitions and sources of the variables are included in the Appendix.7 The rationale for including vintage as a contributing factor to TFP and TFP growth is neatly summarized by Wolff (1991). Although Wolff uses the rate of change of the capital stock as a proxy for vintage, we have chosen to define variable x2 as a weighted average of the age of existing capital, specifi- cally, Vi,t Å (t jÅ1 [(Ii,j/(t jÅ1 Ii,j)(t 0 j / 1)], where Ij is real accumulation of fixed assets.8 The contribution of human capital to production is by now part of received knowledge. It would be appropriate to include investment in human capital in conjunction with physical-capital investment in Eq. (3). We do not do this because data on the actual magnitude of human-capital 6 Chen et al. (1988) report estimates of production functions for state industry in which capital￾stock data have been purged of housing and other nonproductive capital. Jefferson et al. (1992) use corrected data for state and collective industry. It would be ideal for us to use such net capital stock data for each province, but constructing such data is a task that is far beyond our current resources. In order to solve the problem that annual data for this variable are not available for 1978 to 1993, we use an instrument for housing in estimating Eq. (4). The instrument is obtained by regressing a measure of housing area (square meters) per capita on per capita real income. The predicted level of per capita housing is then used as the measure of variable x1 . 7 Unfortunately, variables x4 (infrastructure) and x5 (FDI) are not available annually from 1978 to 1993. Therefore in our empirical work we have treated them as ‘‘environmental’’ variables. Details are contained in the notes to Table 2. 8 Data for accumulation of fixed assets is available after 1952 for all provinces in our sample. We deflate using a price index obtained from series on construction both in nominal prices and in fixed prices. Chen et al. (June, 1988) assert that the data on construction in fixed prices are unreliable. However, our alternative is to use the provincial national income deflator that can be obtained by comparing national income and national income at fixed prices. We chose to use the construction deflator on the assumption that it provides an index closer to the correct one for accumulation than any alternative. We also used the same data to construct a variable (DK/ K)i,t Å (Ii,t/(t jÅ0 Ii,j), which is conceptually similar to the variable used by Wolff. The empirical results are not very sensitive to which of these variables is used to estimate Eq. (4). AID JCE 1462 / 6w10$$$122 09-30-97 14:16:24 cea