Accounting for Economic Growth in Taiwan and Mainland China: A Comparative Analysis

Journal of Comparative Economics 30, 507–530 (2002)doi:10.1006/jcec.2002.1786

Accounting for Economic Growth in Taiwan and MainlandChina: A Comparative Analysis1

Gregory Chow

Princeton University, Princeton, New Jersey 08544E-mail: [email protected]

and

An-loh Lin

Chung-Hua Institution for Economic Research, Taipei, TaiwanE-mail: [email protected]

Received April 29, 2002

Chow, Gregory, and Lin, An-loh—Accounting for Economic Growth in Taiwan andMainland China: A Comparative Analysis

Aggregate economic growth is studied using Cobb–Douglas production functions. ForTaiwan, new capital stock and human capital data are constructed. We find a constant laborexponent of about 0.7, assuming constant returns; a constant rate of increase in total factorproductivity (TFP) of about 0.03 from 1951 to 1999; and a smaller exponential rate ofgrowth of real GDP of about 0.065 since 1987 than the 1951 to 1999 average of 0.081,mainly due to a slower growth of the labor input. For mainland China, we find a constantlabor exponent of about 0.35 from 1952 to 1998, a rate of TFP increase of about 0.027beginning only after 1979, and a more stable increase in the labor input than in Taiwanresulting in a smaller reduction in future growth rate. J. Comp. Econ., September 2002,30(3), pp. 507–530. Princeton University, Princeton, New Jersey 08544; and Chung-HuaInstitution for Economic Research, Taipei, Taiwan. C© 2002 Association for Comparative Economic

Studies. Published by Elsevier Science (USA). All rights reserved.

Key Words: aggregate production function; comparative economic growth; total factorproductivity.

Journal of Economic Literature Classification Numbers: D24, E23, O47, O57, P52.

1 The authors thank Win-Lin Chou and a referee for helpful comments. The first author acknowledgesfinancial support from the Center for Economic Policy Study and the Gregory C. Chow EconometricResearch Program at Princeton University in the preparation of this article.

5070147-5967/02 $35.00C© 2002 Association for Comparative Economic StudiesPublished by Elsevier Science (USA)All rights reserved.

508 CHOW AND LIN

1. INTRODUCTION

In the second half of the 20th century, Taiwan and mainland China experienceddifferent economic histories. They started with different initial conditions andadopted different development strategies during the first three decades of this pe-riod when the mainland government practiced central planning. Economic reformtoward a market economy started in the mainland in 1978. By the end of the 20thcentury, both economies succeeded in achieving rapid development by fosteringmarket institutions and the use of high-quality Chinese human capital, with themainland’s rapid growth occurring about two decades later than that in Taiwan.

This essay provides a statistical summary of the growth histories of these twoeconomies from an comparative perspective. The analytical framework adoptedis the familiar growth accounting using a common Cobb–Douglas production toaccount for, and to compare, output growth and the sources of growth for the twoeconomies over the last fifty years, in terms of the growths in labor, capital, and totalfactor productivity. Institutional details are omitted in such a framework, but themajor historical trends together with their input components are clearly revealed.Readers interested in institutional changes can observe their consequences in termsof aggregate growth rates. The statistical summary is also useful for prediction ifthe aggregate relation between output and inputs can be expected to continue.

Building on the work of Dessus (1999) for Taiwan, we provide new estimates ofthe physical capital stock and of human capital as in Section 2, which also containsan analysis of growth trends in Taiwan. Section 3 provides estimates of productionfunctions for Taiwan using different measures of physical and human capital andarrives at four major conclusions concerning Taiwan’s growth history at the end. Acomparative analysis with mainland China is made in Section 4, after a productionfunction is estimated by updating the work of Chow (1993). Major conclusionsconcerning the mainland’s growth history are presented at the end of Section 4 forcomparison. Section 5 concludes the article.

2. DATA FOR TAIWAN

Data for real GDP and its components are available in Statistical Yearbook ofthe Republic of China 1999 (English edition, pp. 151–153) and Quarterly NationalEconomic Trends, ROC (February 2000, pp. 22–23). For labor force we use twoseries. One is H , the number of hours worked during a year, which includesdomestic and foreign workers and can be found in Yearbook of Manpower Statisticsand Bulletin of Labor Statistics. Foreign workers have been employed since 1991and their work hours are longer than those of domestic workers. These have beentaken into account in our derivation of H . The second is H∗, which is the numberof hours worked adjusted for the quality of human capital by using the distributionof schooling weighted by a base-year relative earnings structure of schooling. Asin Collins and Bosworth (1996), our measure of the quality of human capital S isgiven by the sum of the percentage of the j th schooling in the civilian population

GROWTH IN TAIWAN AND MAINLAND CHINA 509

of age 15 or over multiplied by the relative earnings scale of the j th schoolingprevailed in 1991 with the average earnings of primary and below taken as 100,which equals 722.4 per month in U.S. dollars. The year 1991 is chosen because itis also the base year of real GDP and other national income statistics. The relativescale of earnings is 102.38 for junior high, 105.17 for vocational, 114.00 for highschool, 139.77 for junior college, and 176.94 for college and above. These relativescales are fixed throughout our sample period 1951 to 1999 while the distributionof schooling varies through time. H∗ is the product of H and S.

An alternative measure of H∗ is the number of hours worked adjusted by usingthe average number of years of schooling of the working population. According tothe well-known Mincer equation with the log of wages as the dependent variable,an important independent variable is the number of years of schooling. For Taiwan,based on a study by Wu (1988), we can assume the coefficient of the number ofyears s to be 0.1 and adjust H (t) in year t to form H∗(t) by the following equation:

ln H∗(t) = ln H (t) + 0.1[s(t) − s(1951)].

Such an adjustment may overstate the improvement in the amount of human capitalas measured by its marginal product or wage to the extent that education at theprimary school level may not have as much effect as 0.1. Therefore, we choosethe first measure rather than the alternative measure.

Estimation of capital stock presents two problems. One is to estimate deprecia-tion in real terms. The second is to estimate the initial stock in 1951. Depreciationfigures that result from dividing official nominal depreciation by the implicit de-flator of gross fixed investment would underestimate real depreciation if priceshave risen because nominal depreciation is based on historical prices. On the otherhand, accounting depreciation tends to overestimate the true depreciation for tax-saving purposes. Although these two factors offset each other to some extent, thereal depreciation figures as obtained above tend to be overestimated. Many works,such as Nehru and Dhareshwar (1993), Collins and Bosworth (1996) and Dessus(1999), have chosen a much lower depreciation rate (4% per year) than the de-preciation rate estimated from deflating official nominal depreciation as describedabove. We will adopt a depreciation rate of 4%.

We apply the equation Kt = (1 − d)Kt−1 + It to estimate capital stock, where Iis real gross fixed investment and d is the rate of depreciation, assumed to be 4%.To estimate the initial capital stock in 1951, we have found the following threepieces of key information on fixed capital stock, inventory stock, and land in theearly 1950’s.

On fixed capital stock and land in the nonagricultural sectors, we utilize thefirst census of industrial and commercial industries in Taiwan for the year 1954prepared by the Committee on Industrial and Commercial Censuses (1956). Thecensus gives a value of NT$18,869.2 million as total gross fixed assets for allindustrial and commercial firms. Total gross fixed assets are in nominal book value

510 CHOW AND LIN

and consist of land, plant, and other construction; machinery and other equipment;transport equipment; and unfinished construction. The book value of gross fixedassets is inclusive of cumulative depreciation, which is an offsetting item in thebalance sheet and will be reduced when an asset is disposed of. Thus we mustexclude value of land and cumulative depreciation from total gross fixed assets toobtain a net value for nonland fixed assets. The value of land was 5.13% of totalgross fixed assets in the industries of mining, manufacturing, construction, power,gas, and trade, whose main gross fixed assets was about 46.8% of all industrialand commercial gross fixed assets. Since the data for the remaining industries arenot available and the 1961 Census indicated that the land ratio of these industrieswas higher, 6% of total gross fixed assets is assumed for land in all industries. Theresulting value of land is thus estimated as 1,132.2 million. This yields an amountof 17,737 million for nonland gross fixed assets in 1954.

Gross fixed assets are assumed to be the sum of the book values of all assetsacquired and not depreciated until they are scraped after t years. In order to convertgross fixed assets into net fixed assets, we take out cumulative depreciation, whichis the depreciation of all the assets included, namely the following:

D(t) = It d + It−1(1 − d)d + It−2(1 − d)2d + · · · + I1(1 − d)t−1d

= I1d[(1 + g)t−1 + (1 + g)t−2(1 − d) + · · · + (1 − d)t−1].

Hence, the value of gross assets is as follows:

I (t) = It + It−1 + · · · + I1

= I1[(1 + g)t−1 + (1 + g)t−2 + · · · + 1],

under the assumption that investment grows at an annual rate g. Assuming t = 8,d = 4%, and g = 27% (the rate observed from 1951 to 1954 for national in-come of all industries excluding agriculture), the ratio D(t)/I (t) equals 12.3%.If we changed t from 8 to 15, the ratio would be 15.3%. In view of large in-creases in new assets during the years after 1945, we apply a 12% ratio to thevalue 17,737 million of gross fixed assets to obtain net fixed assets equal to15,608.6 million for all nonagriculture industries. This nominal figure is convertedto 99,417.8 million in 1991 constant dollars for the year 1954 based on the averageof the implicit deflators of nonagricultural gross fixed investment for 1951–1954(1991 = 100).

Solving the equation Kt = 0.96Kt−1 + It backward using data on the nona-gricultural real gross fixed investment from the national income account for theperiod 1952 to 1954, the real net fixed capital stock in 1951 is estimated as 77,862million for nonagriculture industries. The estimated 1954 nominal land value,1,132.2 million as given above, is converted to 11,682 million at 1991 constantprices for 1951 by assuming a 8.73% growth rate of land value between 1951 and


1954 (the rate of increase for 1953 to 1954 for those industries as provided by theCensus), and using the GDP price index as the deflator.

The second piece of information consists of the estimates of land and nonlandfixed capital for the agricultural sector found in a report on Relationships betweenAgricultural and Industrial Development in Taiwan during 1950–1959 preparedby the late Professor Mo-huan Hsing (1960). In Table 2.8 of the report (p. 18),Professor Hsing provided estimates of farm land and total nonland fixed capital(including cattle and fixed equipment) in millions of 1953 constant New Taiwandollars for the period 1950 to 1958. The estimate of total nonland fixed capital,2,044 million for 1954, is converted to 17,758 million in 1991 constant dollarsbased on the implicit deflator of gross fixed investment in agriculture, which isfurther moved backward to obtain a value of 4,834.9 million for 1951 by usingequation Kt = 0.96Kt−1 + It and the estimates of real gross fixed investment of theagricultural industry in the national income account for the period 1952 to 1954.Hsing’s estimate of land value in 1951 is 19,131 million in 1953 constant dollarsand is 166,791 million in 1991 constant dollars based the 1953 GDP deflator with1991 = 100. Thus the estimates of the agricultural land and nonland fixed capitalare 166,792 million and 4,835 million, respectively, for 1951 in 1991 constantdollars.

The third piece of information is on the estimates of inventory stock from aspecial study prepared by the Committee on Industrial and Commercial Censuses(1978). The inventory stock of all industries in 1951 was estimated at 9,081 millionin 1971 constant dollars and is converted to 22,241 million in 1991 constant dollarsby the 1971 deflator of inventory investment with 1991 = 100.

To summarize, for the year 1951 and in 1991 constant dollars, our estimateis 82,697 million (77,862 + 4,835) for nonland fixed capital, 22,241 million forinventory, and 178,474 million (11,682 + 166,792) for land for all industries. Theirtotal is 283,412 million, with 29.2% for nonland fixed capital, 7.9% for inventorystock, and 63% for land, which is more than double the nonland fixed capital invalue. In 1951 Taiwan was largely an agrarian economy whose dominant factor ofproduction was land. In the above estimation for nonagricultural industries, if theratio of land value to total gross fixed asset were 8% and the ratio of cumulativedepreciation to gross assets were 15%, instead of the 6 and 12% figures that weemployed, the estimate would be 6,140 million, or 7.4%, smaller for nonland fixedcapital but 3,892 million, or 2.2%, larger for land. The difference between the twosets of estimates is not large.

We use our 1951 estimates of nonland fixed capital (K 1) and K 1 plus inventory(K 2), namely 82,697 and 104,938, as the initial stocks to construct K 1 and K 2 forthe period 1951 to 1999 based on two equations: K 1t = 0.96K 1t−1 + It , where Iis real gross fixed investment, and K 2t = K 1t + Vt , where V is initial inventoryplus cumulative real inventory investment. Another possible measure of capital isthe sum of K 2 and land, which will not be used because we have not found dataon the changes of land use during the sample period. Based on our estimates of

512 CHOW AND LIN

capital, the capital/output ratio in 1951 with real GDP serving as output is foundto be 0.5058 for K 1, 0.6418 for K 2, and 1.7333 for K 2 plus land. The low valuefor nonland fixed capital is due to the facts that a large fraction, about 37.4%, ofGDP in Taiwan in 1951 was from agriculture and land is excluded from the K 1and that industry after World War II was mainly labor-intensive manufacturing andhandicraft, which required a small amount of capital. As the economy became moreindustrialized, the K 1/output (or K 2/output) ratio gradually increased to 1.4614(or 1.7047) in 1975 and to 2.2919 (or 2.4797) in 1999. Even after industrializationtook place, much manufacturing in Taiwan was accounted for by small firms thatemployed less sophisticated tools and thus a small amount of fixed capital.

For comparison purposes and in order to check the sensitivity of our estimatesof production function parameters, we also add to our K 1 and K 2 a measure ofnonland fixed capital created according to the steps taken by Dessus (1999) in hisestimation of Taiwan’s production function. The steps involve first estimating the1962 level of capital stock based on the assumption that capital stock and real GDPgrew at the same rate at a steady state from 1960 to 1964 and then constructing thecapital stock series based on the equation Kt = 0.96Kt−1 + It . Under the aboveassumption, net investment I − d K = gK , or K = I/(d + g), where the growthrate g of capital stock is estimated by the growth rate of real GDP. This methodgives an estimate of 331,576 million 1991 constant dollars for K in 1962 and anestimate of 134,307 million for K in 1951, to be designated K 3. K 3 in 1951 ismuch higher than K 1. K 3 may be an overestimate because, from 1960 to 1964,the growth of capital stock had not yet reached a steady state and was larger thanthe rate of growth of real GDP (as the data on K 1 in Table 1 reveal). Using anunderestimate of g by the growth rate of GDP leads to an overestimate of K . TheK 3/output ratio is 0.8214 in 1951 and 2.2928 in 1999, which comes very close to2.2919 for K 1.

The annual data on real GDP, H , H∗, K 1, K 2, and K 3 are presented in Table 1for the period 1951 to 1999. The average exponential rates of growth for eachvariable are summarized at the bottom of the table for five periods: 1951–1999,1951–1975, 1975–1999, 1975–1987, and 1987–1999. The two subperiods 1951–1975 and 1975–1999 represent the first half and second half of the sample period.The other two subperiods, 1975–1987 and 1987–1999, represent the first half andsecond half of the 1975–1999 period. The year 1987 happened to be the year whenthe Taiwan economy reached its pinnacle and its economic conditions began todeteriorate.

As the bottom of Table 1 indicates, the growth of GDP was faster on averageduring the first half than the second half of the period 1951 to 1999. The averagegrowth rate was 0.08515 exponentially or 8.89% per year for the period 1951–1975 and was 0.07637 or 7.94% per year for the period 1975–1999, yielding anexponential rate of 0.08076 or a growth rate of 8.41% per year for the entireperiod. The average annual growth rate actually attained 9.22% over the subperiod1975–1987 but fell considerably to 6.67% over the subperiod 1987–1999.


TABLE 1Data on Outputs and Inputs for Taiwan

(in Millions of 1991 Constant NT Dollars or Hours)

Year GDP H H∗ K 1 K 2 K 3

1951 163,509 7,481 7,582 82,697 104,938 134,3071952 183,090 7,426 7,532 94,821 120,815 144,3671953 200,175 7,118 7,228 111,066 139,427 158,6301954 219,272 7,307 7,428 128,291 159,675 173,9521955 237,045 7,734 7,871 141,911 175,463 185,7461956 250,091 7,963 8,108 157,049 193,501 199,1301957 268,500 8,126 8,288 171,209 211,087 211,6071958 286,518 8,416 8,597 188,533 230,643 227,3151959 308,438 8,658 8,854 211,091 256,674 248,3221960 327,896 8,731 8,939 239,494 291,267 275,2361961 350,450 8,780 9,001 268,401 326,743 302,7121962 378,147 8,838 9,069 298,637 362,119 331,5761963 413,520 8,970 9,213 335,371 405,166 366,9931964 463,967 9,175 9,393 373,583 453,221 403,9401965 515,628 9,393 9,640 421,390 516,887 450,5331966 561,583 9,649 9,938 482,314 584,349 510,2911967 621,737 10,160 10,489 559,541 675,598 586,3991968 678,758 10,609 11,019 653,918 782,439 679,7021969 739,495 10,864 11,271 757,230 896,966 781,9831970 823,581 11,406 11,834 873,845 1,034,964 897,6071971 929,784 11,806 12,266 1,019,527 1,199,989 1,042,3391972 1,053,607 12,373 12,901 1,190,592 1,385,064 1,212,4911973 1,188,812 13,369 14,019 1,377,387 1,605,980 1,398,4101974 1,202,625 13,581 14,218 1,586,216 1,899,295 1,606,3981975 1,261,896 13,798 14,546 1,844,184 2,151,154 1,863,5601976 1,436,804 14,235 15,096 2,103,250 2,439,828 2,121,8501977 1,583,209 15,038 15,975 2,371,924 2,736,506 2,389,7801978 1,798,427 15,668 16,737 2,679,492 3,077,285 2,696,6341979 1,945,430 16,374 17,548 3,026,414 3,492,365 3,042,8711980 2,087,472 16,501 17,810 3,426,185 3,938,527 3,441,9831981 2,216,116 16,801 18,159 3,830,707 4,374,944 3,845,8731982 2,294,815 16,822 18,210 4,220,704 4,753,746 4,235,2631983 2,488,657 17,312 18,787 4,584,422 5,130,361 4,598,3991984 2,752,443 17,878 19,466 4,957,216 5,523,991 4,970,6341985 2,888,758 18,105 19,744 5,289,117 5,859,791 5,301,9991986 3,225,062 18,852 20,622 5,662,069 6,215,677 5,674,4351987 3,635,979 20,136 22,125 6,126,214 6,725,795 6,138,0851988 3,921,060 20,120 22,196 6,671,767 7,374,313 6,683,1641989 4,243,891 20,337 22,505 7,313,031 8,070,351 7,323,9711990 4,472,848 20,388 22,686 7,997,578 8,785,068 8,008,0801991 4,810,727 20,649 22,997 8,744,879 9,586,104 8,754,9621992 5,170,928 21,166 23,683 9,659,510 10,574,924 9,669,1901993 5,533,607 21,534 24,245 10,688,849 11,665,874 10,698,1411994 5,926,938 21,559 24,314 11,781,779 12,810,688 11,790,7001995 6,307,686 22,431 25,405 12,942,094 13,995,543 12,950,658

514 CHOW AND LIN

TABLE 1—Continued

Year GDP H H∗ K 1 K 2 K 3

1996 6,692,595 22,338 25,450 14,083,106 15,189,357 14,091,3271997 7,139,450 22,729 26,045 15,355,114 16,581,388 15,363,0061998 7,465,751 22,757 26,212 16,723,272 18,073,191 16,730,8491999 7,889,155 23,092 26,766 18,081,131 19,562,794 18,088,405

Average Annual Exponential Rate of Growth

1951–1999 0.08076 0.02348 0.02628 0.11224 0.10892 0.102141951–1975 0.08515 0.02551 0.02715 0.12936 0.12585 0.109591975–1999 0.07637 0.02146 0.02541 0.09512 0.09198 0.094701975–1987 0.08819 0.03150 0.03495 0.10005 0.09500 0.099341987–1999 0.06455 0.01141 0.01587 0.09019 0.08897 0.09006

Note. GDP is real gross domestic product, H is employment in annual work hours, H∗ is H adjustedfor quality, K 1 is nonland fixed capital as calculated from K 1t = 0.96K 1t−1 + I , K 2 is K 1 plusinventory, K 3 is nonland fixed capital based on Dessus’s method.

The growth trend of GDP had the same pattern as that of labor input. As canbe seen from Table 1, the average annual growth rate of unadjusted labor (H ) was2.58% for the period 1951–1975, rose to 3.20% during the period 1975–1987, andthen dropped sharply to 1.15% over the period 1987–1999. The growth rates ofadjusted labor (H∗) for the three periods are 2.75, 3.56, and 1.60%, higher than thecorresponding rates for unadjusted labor, but both have the same growth pattern.

For the capital input, the average annual growth rate of nonland fixed capitalstock (K 1) was 13.8% for the period 1951–1975, dropped to 10.5% during theperiod 1975–1987, and fell further to 9.30% over the period 1987–1999, a growthpattern similar to those of K 2 and K 3 but dissimilar to that of labor. Thus, duringthe subperiod 1975–1987, the reduced growth of capital input acted to moderate thestimulating effect of the higher growth in labor but during the subperiod 1987–1999it acted to accentuate the depressing effect of the lower growth in labor, causinga substantial drop of the average annual growth of GDP from 9.22% to 6.67%between the two subperiods. This shows that labor input has played a significantrole in reducing the rate of Taiwan’s economic growth during the past decade.

We now present two estimated series of total factor productivity (TFP) basedon K 1 with H or H∗. The equation is as follows:

TFP = GDP/[(K KS)(H LS)],

where K = K 1, H is labor without or with adjustment for quality, LS is laborshare, and KS is the capital share, which we assume to be 1 minus the labor share.The labor share includes the official share of paid-employee compensation andthe imputed share of unpaid worker compensation. The official share is computedbased on the national income account. Estimation of the imputed share of those


unpaid workers, which include employers, own-account workers and unpaid familyworkers, is based on the input/output tables and the national income account. Theseries of the official share of paid-employee compensation and the official andimputed shares are shown by PLS and LS, respectively, in Table 2. The index oftotal input, which is the denominator of TFP, is shown by TFI with H and TFI∗

with H∗ in the same table. The computed TFP and TFP∗ are also given in thesame table. As can be seen on the bottom of the table, TFP has increased 0.0268exponentially or 2.72% per year based on the unadjusted labor input (H ) for theentire period 1951 to 1999 and it has increased 0.0252 exponentially or 2.56% peryear based on the labor input adjusted for labor quality over the sample period.The slope of the exponential linear trend is estimated as 0.0324 with H and 0.0306with H∗, respectively.

As for the subperiods, both TFP and TFP∗ grew faster for the first subperiod,1951–1975, which are 3.56 and 3.45% per year, respectively, than the secondsubperiod 1975–1999, which are 1.89 and 1.65% per year. The growth of TFPwas slightly higher for the latest subperiod 1987–1999 at an annual rate of 1.99%with H and 1.72% with H∗ than the corresponding rates of 1.78 and 1.58% forthe subperiod 1975–1987.

3. ACCOUNTING FOR TAIWAN’S GROWTHBY PRODUCTION FUNCTIONS

The data analysis of the last section provides a general picture of the growth ofTaiwan’s economy since 1951. We now consider growth accounting by estimatinga Cobb–Douglas production function. The calculation of total factor productivityin the last section is based on the conceptual framework that the rate of growthof real GDP can be decomposed into the contributions from changes in capital,labor, and a remainder, which is designated to be total factor productivity under theassumption of constant returns to scale. Using the same framework, we estimateproduction functions with alternative measures of capital stock series and laborhours H and H∗, with the latter adjusted for the quality of human capital. In viewof the problem of multicollinearity, we adopt the assumptions of constant returns,a constant exponent of capital (and thus of labor hour), and a constant exponentialgrowth rate of total factor productivity (as an approximation). Data on the laborshare as given in the column under LS in Table 2 suggest that a constant exponentof capital is a reasonable assumption. The production functions estimated shouldbe interpreted as short-hand means of summarizing the data under the above-maintained assumptions.

Since we interpret the estimated Cobb–Douglas production functions as long-run relations among the output and input variables, we first perform a set of unitroot and cointegration tests for the variables. The tests confirm that the individualvariables are integrated of order 1 and a linear relation between the output andinput variables is stationary. White’s (1997) SHAZAM provides two sets of unit

516 CHOW AND LIN

TABLE 2Input Shares and Total Factor Productivity in Taiwan

Year PLS LS KS TFI TFI∗ TFP TFP∗

1951 0.3841 0.4733 0.5267 26,521 26,690 6.1653 6.12631952 0.4040 0.4956 0.5044 26,835 27,024 6.8229 6.77501953 0.3843 0.4696 0.5304 30,566 30,788 6.5489 6.50171954 0.4363 0.5301 0.4699 28,087 28,333 7.8068 7.73901955 0.4333 0.5227 0.4773 31,012 31,297 7.6437 7.57391956 0.4426 0.5321 0.4679 32,136 32,446 7.7824 7.70801957 0.4316 0.5161 0.4839 35,513 35,876 7.5606 7.48411958 0.4364 0.5185 0.4815 37,607 38,024 7.6188 7.53521959 0.4246 0.5024 0.4976 42,424 42,903 7.2703 7.18911960 0.4283 0.5058 0.4942 44,858 45,395 7.3097 7.22321961 0.4339 0.5111 0.4889 46,736 47,334 7.4985 7.40371962 0.4468 0.5255 0.4745 46,964 47,604 8.0519 7.94361963 0.4414 0.5179 0.4821 51,405 52,122 8.0443 7.93371964 0.4440 0.5193 0.4807 54,504 55,174 8.5125 8.40921965 0.4535 0.5533 0.4467 51,369 52,112 10.0378 9.89461966 0.4662 0.5628 0.4372 53,360 54,255 10.5244 10.35071967 0.4727 0.5663 0.4337 57,801 58,855 10.7564 10.56391968 0.4868 0.5767 0.4233 60,718 62,059 11.1789 10.93731969 0.4917 0.6006 0.3994 59,181 60,504 12.4956 12.22231970 0.4935 0.5936 0.4064 66,514 67,984 12.3821 12.11441971 0.5107 0.6069 0.3931 68,118 69,718 13.6496 13.33641972 0.5004 0.5863 0.4137 81,839 83,870 12.8741 12.56231973 0.4869 0.5670 0.4330 99,474 102,187 11.9510 11.63371974 0.5152 0.6013 0.3987 90,618 93,151 13.2713 12.91061975 0.5366 0.6207 0.3793 88,349 91,292 14.2830 13.82271976 0.5282 0.6007 0.3993 104,629 108,387 13.7324 13.25631977 0.5319 0.6016 0.3984 112,937 117,119 14.0185 13.51791978 0.5354 0.6028 0.3972 120,775 125,675 14.8907 14.31021979 0.5460 0.6108 0.3892 124,848 130,242 15.5823 14.93701980 0.5512 0.6147 0.3853 128,934 135,126 16.1903 15.44831981 0.5650 0.6336 0.3664 122,825 129,023 18.0429 17.17611982 0.5720 0.6399 0.3601 123,010 129,411 18.6555 17.73281983 0.5636 0.6313 0.3687 135,420 142,594 18.3773 17.45271984 0.5669 0.6332 0.3668 140,728 148,517 19.5586 18.53281985 0.5666 0.6339 0.3661 144,694 152,862 19.9647 18.89781986 0.5500 0.6117 0.3883 172,749 182,498 18.6690 17.67171987 0.5423 0.5933 0.4067 206,015 217,859 17.6491 16.68961988 0.5532 0.6043 0.3957 200,002 212,232 19.6051 18.47541989 0.5753 0.6276 0.3724 182,000 193,945 23.3181 21.88191990 0.5894 0.6426 0.3574 172,314 184,554 25.9575 24.23601991 0.5885 0.6378 0.3622 184,649 197,776 26.0534 24.32411992 0.5910 0.6419 0.3581 189,644 203,826 27.2664 25.36941993 0.5844 0.6324 0.3676 210,913 227,338 26.2365 24.34091994 0.5833 0.6330 0.3670 217,932 235,171 27.1963 25.20261995 0.5812 0.6365 0.3635 226,219 244,877 27.8831 25.7586


TABLE 2—Continued

Year PLS LS KS TFI TFI∗ TFP TFP∗

1996 0.5664 0.6261 0.3739 248,791 269,958 26.9005 24.79131997 0.5454 0.6010 0.3990 305,928 332,022 23.3370 21.50291998 0.5478 0.6020 0.3980 314,677 342,621 23.7251 21.79011999 0.5378 0.5908 0.4092 352,850 385,010 22.3584 20.4908

Average Annual Exponential Rate of Growth

1951–1999 0.0070 0.0046 −0.0053 0.0539 0.0556 0.0268 0.02521951–1975 0.0139 0.0113 −0.0137 0.0501 0.0512 0.0350 0.03391975–1999 0.0001 −0.0021 0.0032 0.0577 0.0600 0.0187 0.01641975–1987 0.0009 −0.0038 0.0058 0.0706 0.0725 0.0176 0.01571987–1999 −0.0007 −0.0004 0.0005 0.0448 0.0475 0.0197 0.0171

Note. PLS is labor share of paid employees, LS is PLS plus imputed share of unpaid employees,TFI (using H ) and TFI∗ (using H∗) are total factor input, TFP and TFP∗ are their factor productivityin level.

root tests, namely augmented Dickey–Fuller (ADF) tests and Phillips–Perron (PP)tests. They have the same critical values but the PP method uses a nonparametriccorrection for serial correlation instead of lag terms. Based on both tests, the nullhypothesis of unit roots is not rejected for ln(GDP), ln(H ), ln(H∗), ln(K 1), ln(K 2),and ln(K 3). Their t statistics with constant term and linear trend from the ADFtests, for example, equal −0.5923 for ln(GDP), −0.9974 for ln(H ), −1.5362 forln(H∗), −0.7642 for ln(K 1), −0.8227 for ln(K 2), and −2.6145 for ln(K 3) whilethe 10% asymptotic critical value is −3.13. Similarly, the null hypothesis is also notrejected using the same tests (ADF with constant and trend) for per-hour variablessuch as ln(GDP/H ) with t = −3.0841, ln(GDP/H∗) with t = −2.6934, ln(K 1/H )with t = −1.2326, ln(K 1/H∗) with t = −1.1249, ln(K 2/H ) with t = −1.2148,ln(K 2/H∗) with t = −1.1038, ln(K 3/H ) with t = −1.7373, and ln(K 3/H∗) witht = −1.5594. In fact, all of these variables, except ln(GDP/H ), are shown to be adifference stationary process.2

Our tests for cointegration are confined to the regressions reported in Table 3.Due to the presence of a linear time trend used to measure total factor productivityin each regression, we adopt a two-step test procedure. We run each regressionto obtain a series of estimated residuals and then test each series for the pres-ence of unit roots. The absence of unit roots supports treating these relations ascointegration relations. Since the OLS regressions are found to have very low

2 The equation �Yt = a0 + a1Yt−1 + a2t + lag in terms of �Y + ut , a1 = a2 = 0 implies that Yis a difference stationary process. This null is not rejected for ln(GDP) with F value = 1.05, ln(H )with F = 0.57, ln(H∗) with F = 1.18, ln(K 1) with F = 0.92, ln(K 2) with F = 0.91, ln(K 3) withF = 4.04, ln(GDP/H∗) with F = 4.02, ln(K 1/H ) with 1.89, ln(K 1/H∗) with F = 2.04, ln(K 2/H )with F = 1.66, ln(K 2/H∗) with F = 1.82, ln(K 3/H ) with F = 1.53, and ln(K 3/H∗) with F = 1.30but is rejected for ln(GDP/H ) with F = 6.19 at the 10% significance level with the asymptotic criticalF value = 5.34.

518 CHOW AND LIN

TAB

LE

3R

egre

ssio

nE

quat

ions

with

AR

(1)

Err

ors

for

Taiw

an

Dep

ende

ntva

riab

leln

(K,

K/

H,

(in

bold

)or

K/

H∗ )

ln(H

orH

∗ )t

t2C

R2/s

DW

ρp

valu

ePP

ln(G

DP

)(1

)K

1&H

0.26

210.

5394

0.03

874.

2115

0.99

97/

1.38

290.

7378

0.10

40−5

.160

8(0

.068

5)(0

.139

5)(0

.007

0)(1

.102

0)0.

0203

(0.0

964)

(2)

K2&

H0.

2539

0.55

150.

0402

4.13

740.

9997

/1.

3882

0.73

130.

1123

5.21

31(0

.068

8)(0

.137

6)(0

.068

0)(1

.109

0)0.

0205

(0.0

974)

(3)

K3&

H0.

1820

0.55

440.

0490

4.93

020.

9996

/1.

4660

0.82

770.

0694

−6.3

196

(0.1

076)

(0.1

661)

(0.0

100)

(1.3

660)

0.02

20(0

.080

2)

ln(G

DP

)(4

)K

1&H

∗0.

2892

0.50

930.

0350

4.17

320.

9997

/1.

3632

0.75

230.

1095

−5.1

472

(0.0

684)

(0.1

336)

(0.0

074)

(1.1

520)

0.02

04(0

.094

1)(5

)K

2&H

∗0.

2822

0.51

980.

0365

4.09

250.

9997

/1.

3649

0.74

750.

1184

−5.1

927

(0.0

689)

(0.1

343)

(0.0

073)

(1.1

650)

0.02

07(0

.094

9)(6

)K

3&H

∗0.

1838

0.51

120.

0485

5.28

870.

9996

/1.

4566

0.86

900.

0477

−6.2

896

(0.1

162)

(0.1

649)

(0.0

111)

(1.4

880)

0.02

22(0

.070

7)

ln(G

DP

/H)

(7)

K1/

H0.

2825

0.03

172.

4046

0.99

93/

1.41

620.

7775

−5.3

455

(0.0

750)

(0.0

067)

(1.1

874)

0.02

08(0

.089

9)(8

)K

2/H

0.26

960.

0338

2.37

330.

9993

/1.

4243

0.76

34−5

.432

0(0

.074

4)(0

.064

0)(0

.203

6)0.

0210

(0.0

923)

(9)

K3/

H0.

2138

0.03

962.

5081

0.99

92/

1.50

230.

8280

−6.7

381

(0.1

097)

(0.0

089)

(0.3

059)

0.02

27(0

.081

)

GROWTH IN TAIWAN AND MAINLAND CHINA 519ln

(GD

P/H

∗ )(1

0)K

1/H

∗0.

3190

0.02

662.

3164

0.99

92/

1.38

920.

7953

−5.3

299

(0.0

746)

(0.0

064)

(0.1

869)

0.02

09(0

.086

6)(1

1)K

2/H

∗0.

3089

0.02

862.

2688

0.99

92/

1.39

310.

7849

−5.4

041

(0.0

743)

(0.0

062)

(0.2

038)

0.02

11(0

.088

5)(1

2)K

3/H

∗0.

2503

0.03

482.

3998

0.99

90/

1.48

800.

8779

−6.6

997

(0.1

167)

(0.0

091)

(0.3

277)

0.02

31(0

.068

4)

ln(G

DP

/H)

(13)

K1/

H0.

2772

0.03

25−0

.000

005

2.41

570.

9993

/1.

4151

0.77

73−5

.327

8(0

.104

8)(0

.012

2)(0

.000

075)

(0.2

422)

0.02

080

(0.0

899)

(14)

K2/

H0.

2509

0.03

63−0

.000

019

2.41

720.

9993

/1.

4213

0.76

33−5

.368

8(0

.103

9)(0

.011

7)(0

.000

073)

(0.2

649)

0.02

100

(0.0

923)

(15)

K3/

H0.

1497

0.05

09−0

.000

127

2.64

460.

9992

/1.

4375

0.75

94−5

.629

2(0

.097

5)(0

.008

8)(0

.000

054)

(0.2

676)

0.02

169

(0.0

930)

Not

e.D

epen

dent

vari

able

isln

(GD

P),l

n(G

DP/

H),

orln

(GD

P/H

∗ )as

indi

cate

d.E

quat

ions

are

estim

ated

byth

eM

Lm

etho

d.Fi

gure

sin

pare

nthe

ses

are

stan

dard

erro

rsof

estim

ates

;H

∗is

H(e

mpl

oym

enth

ours

)ad

just

edfo

rla

bor

qual

ity;

K1

toK

3ar

eva

riou

sve

rsio

nsof

capi

tals

tock

,sam

ple

peri

od=

1951

–199

9,sa

mpl

esi

ze=

49;C

=co

nsta

ntte

rm;

R2=

adju

sted

R2;s

=st

anda

rder

ror

ofth

ere

gres

sion

;DW

=D

urbi

n–W

atso

nst

atis

tic;ρ

=es

timat

edau

toco

rrel

atio

nco

effic

ient

;p

valu

e=

prob

abili

tyva

lue

for

the

test

ofco

nsta

ntre

turn

sto

scal

e;an

dPP

=t

stat

istic

from

the

Phill

ips–

Perr

onun

itro

otte

stw

ithco

nsta

ntan

dno

tren

d[c

ritic

alva

lue

bein

g−3

.982

9(o

r−4

.352

1)fo

rfo

ur(o

rfiv

e)va

riab

les

inth

ere

gres

sion

and

n=

49at

the

10%

leve

l].

520 CHOW AND LIN

Durbin–Watsom statistics ranging from 0.3830 to 0.5770, we adopt the Beach–MacKinnon AR(1) maximum likelihood method to account for first-order serialcorrelation and obtain the estimated equations as shown in Table 3. The resultingDW statistics range from 1.3632 to 1.5023. We then test the null of unit root foreach estimated AR(1) series based on the PP test. The t statistics with constantand no trend, given in Table 3 under the heading of PP, range from −5.1472 to−6.7381. These are all smaller (or larger in absolute term) than the critical valueof −4.3283 (−3.9826) or −4.7057 (4.3521) for four or five variables in the regres-sion with 49 sample observations at the 5(10)% significance level as tabulated byMacKinnon (1991, Table 1, p. 275) and all fall within the rejection region. Sincein equation ut = ρut−1 + et , the estimated coefficient of serial correlation (ρ) inTable 3 is significantly below unity at the level of less than 5%3 and the null ofunit root for et is rejected for each regression as explained above, the null is alsorejected for ut . Therefore we conclude that the regressions presented in Table 3are all stationary cointegrated relations.

Turning to the regression results in Table 3, we first note that the variable H∗ isthe product of H and S. One may treat H∗ as one variable or consider S and H asseparate variables. Our preliminary regressions suggest that the effects of S andH should be combined in H∗ as one variable because using a separate ln(S) yieldsunstable and sometimes negative coefficients. The dependent variable is the log ofreal GDP as given in Table 1. As explained above, because of the presence of serialcorrelation in the residuals, we have used the Beach–MacKinnon AR(1) procedureto account for first-order serial correlation. In Table 3, the standard errors (not tstatistics) are in parentheses placed below the estimated coefficients, R2 is adjusted,s is the standard error of the regression, DW is the Durbin–Watson statistic, andρ is the estimated coefficient of serial correlation. We test the assumption thatthe capital and labor exponents sum to 1 and report the p value for rejecting thishypothesis. We also report the t statistic of the cointegration test based on thePhillips–Perron procedure under the heading labeled PP.

Equation 1 is based on K 1 and H . The estimated output elasticity of capital is0.2621 and that of labor is 0.5394. The estimated coefficient for t is 0.0387. Thenull hypothesis that the coefficients of ln K and ln H sum to 1 is rejected only atthe 10.4% level. Under the assumption of constant returns, the estimates are givenin Eq. (7). The coefficient of capital increases from 0.2621 to 0.2825 and that oft decreases to 0.0317 from 0.0387. The coefficients of t in Eqs. (1) and (7) havethe same order of magnitude as those reported by Kuo (1983) for the period 1961to 1971. The results using the quality-adjusted hours H∗ are given in Eqs. (4) and

3 Under the null hypothesis of ρ = 1, we obtain t values equal to 2.72 for K 1 and H , 2.76 for K 2and H , 2.15 for K 3 and H , 2.63 for K 1 and H∗, 2.66 for K 2 and H∗, 1.85 for K 3 and H∗, 2.48 forK 1/H , 2.56 for K 2/H , 2.12 for K 3/H , 2.36 for K 1/H∗, 2.43 for K 2/H∗, 1.79 for K 3/H∗, 2.48for K 1/H with t2, 2.56 for K 2/H with t2, and 2.59 for K 3/H with t2. The critical values at the 5,2.5, and 1% significance levels for n = 49 are about 1.68, 2.01, and 2.41, respectively. Thus the null isrejected in each case at a significance level of less than 5%.


(10) [corresponding to Eqs. (1) and (7)]. The hypothesis of constant returns underH∗ can be rejected only at the 11.0% level. While the coefficients in Eqs. (4) and(10) are similar to those in Eqs. (1) and (7), the variable H∗ is not an improvementover the unadjusted variable H as judged by the standard error of the regressions, which turns out to be only slightly larger in each regression using H∗.

The estimated coefficients and the fit using K 2 (K 1 plus inventory) are veryclose to those using K 1 in all cases. No additional comments are required. By thesize of the standard error of the regression s, the fit using K 1 is only slightly betterthan that using K 2 in every case.

To find out the effects on our results of the choice of capital stock, we presentresults based on nonland capital K 3 constructed by following Dessus’s method.These are Eqs. (3), (6), (9), and (12). Using K 3, the coefficients of log capitalare lower and of t higher as compared with results using K 1 or K 2. The hypoth-esis of constant returns is rejected at the 6.9 and 4.8% level under H and H∗,respectively.

Based on the standard errors of the regressions, we have two conclusions. First,K 1 is only slightly better than K 2 and both are better than K 3. Second, H is onlyslightly better than H∗ in every corresponding case, suggesting that our measureof human capital H∗ is not an improvement over the quality-unadjusted laborH . The capital coefficients estimated from using K 3 are below 0.3 and appearunreasonable from the data analysis of factor share under Section 2. This confirmsK 3 to be an inferior capital stock variable. TFP growth rates obtained under K 3are also much higher than those obtained by Kim and Lau (1994), Young (1995),and Collins and Bosworth (1996). Our conclusion that K 3 is an inferior measureof capital does not imply a criticism of Dessus (1999). His measure of output isin U.S. dollars based on the work of Summers and Heston (1991) and his sampleperiod is shorter. His estimation of a Cobb–Douglas production function for theperiod 1951 to 1990 yielded a sum of the estimated coefficients of capital andlabor equal to 0.867 and an exponential growth rate of TFP equal to 0.024 by OLS[Eq. (1) of Table 9.1, p. 194]. Using official GDP data, we have obtained somewhatdifferent estimates employing our K 3 for the period 1951 to 1999 or 1951 to 1990.Although K 3 is inferior to K 1 and K 2, it will be employed for comparison.

To study whether the rate of growth of total factor productivity implied by aproduction function with constant returns has declined, we supplement the analysisgiven in the bottom of Table 2 under TFP and TFP∗ by estimating a quadratic trendfunction in Eqs. (7), (8), and (9). The results are Eqs. (13), (14), and (15) in Table 3.They indicate that linear trends are valid for K 1 and K 2, but the quadratic termis significant for K 3. As seen from Eq. 15, adding a t2 term lowers the capitalelasticity from 0.2138 to 0.1497 and confirms the variable K 3 to be less reliable.

As pointed out in Section 2, Taiwan’s GDP growth rates have slowed downduring the second half of the period 1951 to 1999. The average exponential growthrate fell from 0.08515, or 8.89%, per year in 1951–1975 to 0.07637, or 7.94%, peryear in 1975–1999. In particular, the average exponential rate was only 0.06455,

522 CHOW AND LIN

or 6.67%, per year during 1987–1999. The figures in Tables 1 and 2 also showdeclining rates for capital, labor, and the TFP in the corresponding periods. Wenow use the exponential growth rates of these input variables in Table 1 and theestimated restricted equations in Table 3 to account for the exponential growth ratesof actual real GDP. The results are presented in Table 4 for each of the Eqs. (7) to(12) and (15) in Table 3.

In Table 4, we consider the four periods, 1951–1975, 1975–1987, 1987–1999,and 1951–1999 and show the following decomposition of the GDP growth rate asfollows:

Estimated gGDP = 0.2825∗gK 1 + 0.7175∗gH + 0.0317 or(1)

S = K + H + t,

where the g’s are the exponential growth rates as given in Table 1 for variousvariables and the coefficients are the estimates in Table 3. We use Eq. (1) to accountfor the changes in GDP growth rates in the specified sample periods. In Table 4,the actual GDP exponential growth rates are given in column A. Columns K andH give the products of the estimated coefficients in Table 3 and the exponentialgrowth rates in Table 1 and t is given by the estimated coefficient for the time trendin Table 3. As seen from the top three rows of the table, the decline of the growthrate in real GDP during the period 1975 to 1999 resulted from decreases in thegrowth of capital and labor, in fact more due to capital in 1975–1987 and more tolabor in 1987–1999. The predicted growth rates from Eq. (1) are given in columnS (for the sum of the three components) and the ratios of the predicted to actualrates in column S/A. The values of S/A are close to 1 except for the period 1975–1987. For the entire period 1951 to 1999 and based on Eq. (7), the main sources ofGDP growth came from the growth in capital and in total factor productivity, eachcontributing about 39.3% (columns K and t under “Contributions to Growth”).

Contributions to growth by the three sources as estimated by the other equationscan be read similarly from Table 4. In the case of Eq. (15) including t and t2, theexponential growth rates of TFP for various sample periods are given by the averagevalues calculated from the equation: 0.05094 − 0.000254t . Several observationsfrom Table 4 may be noted. First, the rates of growth due to capital had decreasedfor all equations over the two periods 1975–1987 and 1987–1999 because therates of growth of capital itself as shown in Table 1 had decreased. Second, thegrowth due to either measure of labor increased in the period 1975–1987 butdecreased very substantially during 1987–1999 in all equations because the laborvariable itself behaved in this way in Table 1. The data may suggest a shortage oflabor since 1987. Third, the contribution of increase in TFP to economic growthgenerally exceeded the contribution of increase in capital except for the cases ofK 1/H∗ and K 2/H∗. The addition of t2 in the equation using K 3/H has raisedthe contribution of TFP and lowered that of capital substantially. Fourth, figures in

GROWTH IN TAIWAN AND MAINLAND CHINA 523TA

BL

E4

Sour

ces

ofan

dC

ontr

ibut

ions

toG

DP

Gro

wth

for

Var

ious

Sam

ple

Peri

ods

Sour

ces

ofgr

owth

(Exp

onen

tialr

ates

exce

ptS/

A)

Con

trib

utio

nsto

grow

th(%

)E

quat

ion

Sam

ple

unde

rpe

riod

KH

tS

AS/

AK

Ht

R

(7)

K1/

H19

51–7

50.

0365

50.

0183

00.

0317

50.

0866

00.

0851

51.

0170

142

.921

.537

.3−1

.719

75–8

70.

0282

70.

0226

00.

0317

50.

0826

20.

0881

90.

9367

932

.125

.636

.06.

319

87–9

90.

0254

80.

0081

90.

0317

50.

0654

20.

0645

51.

0134

139

.512

.749

.2−1

.319

51–9

90.

0317

10.

0168

50.

0317

50.

0803

10.

0807

60.

9943

739

.320

.939

.30.

6(8

)K

2/H

1951

–75

0.03

393

0.01

863

0.03

381

0.08

637

0.08

515

1.01

436

39.9

21.9

39.7

−1.4

1975

–87

0.02

561

0.02

301

0.03

381

0.08

243

0.08

819

0.93

468

29.0

26.1

38.3

6.5

1987

–99

0.02

399

0.00

833

0.03

381

0.06

613

0.06

455

1.02

448

37.2

12.9

52.4

−2.4

1951

–99

0.02

937

0.01

715

0.03

381

0.08

033

0.08

076

0.99

462

36.4

21.2

41.9

0.5

(9)

K3/

H19

51–7

50.

0234

30.

0200

60.

0396

00.

0830

80.

0851

50.

9757

327

.523

.646

.52.

419

75–8

70.

0212

40.

0247

70.

0396

00.

0856

00.

0881

90.

9706

624

.128

.144

.92.

919

87–9

90.

0192

50.

0089

70.

0396

00.

0678

20.

0645

51.

0507

129

.813

.961

.3−5

.119

51–9

90.

0218

30.

0184

60.

0396

00.

0799

00.

0807

60.

9892

927

.022

.949

.01.

1(1

0)K

1/H

∗19

51–7

50.

0412

70.

0184

90.

0266

40.

0864

00.

0851

51.

0146

648

.521

.731

.3−1

.519

75–8

70.

0319

20.

0238

00.

0266

40.

0823

60.

0881

90.

9338

936

.227

.030

.26.

619

87–9

90.

0287

70.

0108

10.

0266

40.

0662

20.

0645

51.

0258

844

.616

.741

.3−2

.619

51–9

90.

0358

10.

0179

00.

0266

40.

0803

40.

0807

60.

9948

544

.322

.233

.00.

5(1

1)K

2/H

∗19

51–7

50.

0388

80.

0187

60.

0285

60.

0862

00.

0851

51.

0123

645

.722

.033

.5−1

.219

75–8

70.

0293

50.

0241

50.

0285

60.

0820

60.

0881

90.

9305

233

.327

.432

.46.

919

87–9

90.

0274

80.

0109

70.

0285

60.

0670

10.

0645

51.

0381

742

.617

.044

.2−3

.819

51–9

90.

0336

50.

0181

60.

0285

60.

0803

70.

0807

60.

9951

941

.722

.535

.40.

5(1

2)K

3/H

∗19

51–7

50.

0274

30.

0203

60.

0347

60.

0825

40.

0851

50.

9693

532

.223

.940

.83.

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524 CHOW AND LIN

the R column under “Contributions to Growth” are residuals (in percentage terms)in our explanation of the growth in real GDP. They are small for various sampleperiods except the period 1975–1987 using K 1/H , K 2/H , K 1/H∗, and K 2/H∗

and the period 1987–1999 using K 3/H and K 3/H∗.We end this section with conclusions concerning economic growth of Taiwan

from 1951 to 1999. First, one production function with a constant exponent forcapital (and thus of labor under constant returns) and a constant rate of increaseof TFP suffices to explain the growth of real GDP in Taiwan for the entire period.Second, the exponent of capital is about 0.3 and the rate of increase of TFP is about0.03 [see Eqs. (7), (8), (10), and (11) of Table 3] no matter whether the capitalstock includes inventory or whether labor incorporates a quality adjustment. Third,for the entire period, capital contributes about 40% (because of the rapid rate ofcapital accumulation), labor only 20%, and TFP 40% to the exponential rate ofgrowth of GDP (see Table 4 under K 1/H ), which averaged 0.08 annually. Fourth,the period 1987 to 1999 experienced a slower exponential growth rate of about0.065, resulting mainly from the slower growth in labor force (see columns H andH∗ in the bottom of Table 1).

4. COMPARATIVE ANALYSIS WITH MAINLAND CHINA

How do the above conclusions compare with findings about mainland Chinain the period 1952 to 1998 for which official data are available? China StatisticalYearbook 1999 (CSY99) provides data on nominal GDP 1952 to 1998 (p. 55), realGDP 1978 to 1998 (p. 58), labor force (p. 134), and nominal gross capital formation1978–1998 (p. 68). Since this section is an extension of Chow (1993), data on GDP,labor, and capital are taken from Chow up to 1980 and then constructed for theyears thereafter based on the sources cited above. For the period before 1980,we rely on Chow (1993), which indicates K = 2213 (nonland fixed capital plusinventory = 1493 and land = 720, Table VI, p. 822) at the end of 1952. To updateChow (1993), we keep land = 720 (which is a constant included in capital stock)and accumulate nonland net capital formation. From 1953 to 1980, official dataon accumulation (in Table III of Chow 1993, p. 815) include net fixed investmentand inventory changes and are the sums of accumulations of total assets by threetypes of enterprises and individuals (Table IV of Chow 1993, p. 818), all in 1952prices or 1978 prices, which are assumed to be identical.

After 1980 we adopt the following method to convert nominal into real grosscapital formation in order to construct the capital stock. First, comparing nominaland real GDP provides a GDP deflator that we use to deflate the sum of nominalconsumption and gross capital formation to obtain real domestic final expenditures.Second, we convert nominal into real consumption by using the general consumerprice index (CSY99 , p. 294), which is linked with the general retail price in-dex (p. 294) for the period 1981 to 1985. Third, we subtract real consumptionfrom real domestic final expenditures to obtain real gross investment I (including


inventory investment). We then construct our capital series K for the period 1981to 1998 based on the equation: K (t) = (1 − d)[K (t) − 720] + I (t) + 720, whereK (t = 1952) = 2213 and land = 720. The depreciation rate d equals 0.04, whichis slightly lower than the average depreciation rate of nonland fixed capital 0.045found in China Report: Social and Economic Development 1949–1989, publishedby China Statistical Information and Consultancy Service Center, 1990. We use aslightly lower depreciation rate because K includes inventory. Thus, we have allthe data to update the production function of Chow (1993).

The data on real GDP in 1978 prices, labor input in 10 thousand persons, andcapital stock in 1978 prices are presented in Table 5 for the period 1952 to 1998.The average exponential rates of growth for each variable are summarized at thebottom of the table for three periods: 1952–1998, 1952–1978, and 1978–1998. Thetwo subperiods are the periods before and after the economic reform. As can be

TABLE 5Data on Mainland China

Year GDP L K t Year GDP L K t

1952 799 20,729 2,213 0 1978 3,624 40,152 14,112 01953 911 21,364 2,381 0 1979 3,900 41,024 15,273 11954 964 21,832 2,576 0 1980 4,204 42,361 16,438 21955 1,026 22,328 2,761 0 1981 4,425 43,725 17,268 31956 1,170 23,018 2,978 0 1982 4,824 45,295 18,297 41957 1,223 23,771 3,211 0 1983 5,349 46,436 19,515 51958 1,492 26,600 3,590 0 1984 6,161 48,197 20,928 61959 1,615 26,173 4,148 0 1985 6,991 49,873 22,755 71960 1,591 25,880 4,649 0 1986 7,611 51,282 24,822 81961 1,119 25,590 4,844 0 1987 8,491 52,783 27,123 91962 1,046 25,910 4,943 0 1988 9,448 54,334 30,085 101963 1,158 26,640 5,126 0 1989 9,832 55,329 33,445 111964 1,349 27,736 5,389 0 1990 10,209 63,909 36,565 121965 1,578 28,670 5,754 0 1991 11,148 64,799 39,776 131966 1,846 29,805 6,224 0 1992 12,735 65,554 43,589 141967 1,713 30,814 6,528 0 1993 14,453 66,373 48,994 151968 1,601 31,915 6,826 0 1994 16,283 67,199 55,006 161969 1,910 33,225 7,183 0 1995 17,994 67,947 61,856 171970 2,355 34,432 7,801 0 1996 19,719 68,850 69,304 181971 2,520 35,620 8,485 0 1997 21,455 69,600 77,218 191972 2,592 35,854 9,133 0 1998 23,129 69,957 85,692 201973 2,807 36,652 9,874 0 Average Annual Exponential Rate of Growth1974 2,839 37,369 10,615 0

1952–1998 0.07316 0.02644 0.079491975 3,075 38,168 11,445 01952–1978 0.05815 0.02543 0.071261976 2,993 38,834 12,193 01978–1998 0.09268 0.02776 0.090191977 3,227 39,377 13,025 0

Note. GDP = real GDP in 1978 prices; L = labor in 10,000 persons; K = capital in 1978 prices;t = time.

526 CHOW AND LIN

seen from the table, GDP growth rates are much higher in the second period, whenaverage exponential growth rate is 0.09268 or 9.7% per year compared with the0.05815 exponential growth rate or 6.0% per year in the first period, yielding anaverage exponential growth rate of 0.07316 or 7.6% per year for the entire period.The average exponential growth rates of labor and capital are 0.02776 (2.8%) and0.09019 (9.4%), respectively, for the second period as compared with the ratesof 0.02543 (2.6%) and 0.07126 (7.4%) for the first period. Thus the growth ratesof labor and capital are also higher in the second period but only moderately,supplementing the significant contribution of increasing total factor productivityto GDP growth during this period. Note that there is a substantial increase in theofficial estimate of labor force in 1990, which was the result of a new census, butwe chose not to make any smoothing of the data since this study is concerned withlong-term trends that are hardly affected by this census result.

Following the procedure taken for Taiwan, we first test the variables ln(GDP),ln(L) and ln(K ) with data given in Table 5 and the derived variables ln(GDP/L)and ln(K/L) for the presence of unit roots. The null of unit root is not rejectedbased on either the ADF test or the PP test with constant and trend. Based on theformer, for example, the t statistic is −1.2155 for ln(GDP), −2.4568 for ln(L),0.6995 for ln(K ), −1.2775 for ln(GDP/L), and −0.4930 for ln(K/L) while theasymptotic critical value at 10% level is −3.13. These variables are all shown tobe a difference stationary process (see footnote 2). Our tests of cointegration areconfined to the three regressions reported in Table 6.

We use AR(1) residuals instead of OLS residuals. The DW statistic is only0.6651 for K &L , 0.6482 for K/L , and 0.7906 for K/L with t2 for OLS residualsbut equal to 1.7118, 1.6270, and 1.6314 for AR(1) residuals. The estimates ofserial correlation coefficient under AR(1) are equal to 0.7653, 0.6796, and 0.6040as shown in Table 6. They deviate significantly from 1 with a t value equal to 2.16,2.58, and 2.94, respectively, while the critical value is 2.03 (or 2.44) at 2.5 (or 1)%level with n = 35. Furthermore, the null of a unit root for AR(1) residuals is rejectedfor each of the three regressions in Table 6 based on the PP test with constant and notrend at the significance level of 5% or less from MacKinnon’s tabulation. Thus, asthe case for Taiwan, we conclude that the above three regressions are all stationarycointegrated relations.

We now turn to the regression results in Table 6. Since Chow (1993) found noincrease in TFP before 1980, we estimate a Cobb–Douglas production functionwith or without the restriction of constant returns by introducing a trend begin-ning with t = 1 in 1979, the year after economic reform started (see the positivedeviations of log output from the estimates by a production function after 1979in Table VIII of Chow 1993, p. 825). As explained in Chow (1993), the years1958 to 1969 are considered and shown to be abnormal years to be excluded inall regressions. Table 6 presents three estimated equations for the period 1952 to1998. Equation 1 is the unrestricted estimation. The coefficient is 0.7741 for ln(K )and 0.0020, subject to a large error, for ln(L) as compared with 0.6353 and 0.3584,


TABLE 6Regression Equations with AR(1) Errors for Mainland China

Dependent ln(K orvariable K/L) ln(L) t t2 C R2/s DW ρ p value PP

ln(GDP)(1) K &L 0.7741 0.0020 0.0255 0.7890 0.9986/ 1.7118 0.7653 0.1261 −5.7210

(0.0960) (0.2354) (0.0050) (0.6017) 0.0338 (0.1088)

ln(GDP/L)(2) K/L 0.6467 0.0268 −0.1096 0.9964/ 1.6270 0.6796 −5.3536

(0.0412) (0.0043) (0.1274) 0.0349 (0.1240)(3) K/L 0.6377 0.0380 −0.00059 −0.0925 0.9965/ 1.6314 0.6040 −5.3355

(0.0360) (0.0077) (0.00036) (0.1108) 0.0338 (0.1347)

Note. Dependent variable is ln(GDP) or ln(GDP/L) as indicated. Equations are estimated bythe ML method. Figures in parentheses are standard errors of estimates. L = labor; K = capitalstock; C = constant term, sample period = 1952–1998, sample size = 35 (1958–1969 omitted);R2 = adjusted; s = standard error of the regression; DW = Durbin–Watson statistic; ρ = estimatedautocorrelation coefficient; p value = probability value for the test of constant returns to scale; PP = tstatistic from the Phillips–Perron unit root test with constant and no trend (critical value being −5.2923(or −4.8255) for four (or five) variables and n = 35 at 1 (or 5)% level.

respectively, obtained by Chow (1993, p. 882) for the period 1952 to 1980. Bothestimates of the coefficient for labor are subject to large errors but the data forthe period up to 1980 and for the entire period 1952 to 1998 both support theassumption that the sum of the coefficients of ln K and ln L equals 1. For the entiresample, this hypothesis can be rejected only at the 0.126 level of significance.Thus, we impose this restriction to find the capital exponent to be about 0.647and the exponential trend coefficient to be about 0.027, as given by Eq. (2) inTable 6. The first coefficient is in agreement with the result given in Table VII ofChow (1993, p. 823) using old official national income data (revised in 1994) foroutput and a sample period of 1952 to 1980, excluding 1958 to 1969. To examinewhether the output elasticity of capital has remained unchanged throughout theentire sample period 1952 to 1998, we add a variable dd × ln(K/L) to Eq. (2) inTable 6, where dd is a dummy taking the value of 1 for the period 1979 to 1998 andzero otherwise. This variable measures the incremental coefficient of ln(K/L) forthe period 1979 to 1998. The estimated coefficient is 0.0035 (s = 0.0099) and isstatistically insignificant. The coefficients of ln(K/L) and t are 0.6433 and 0.0262,respectively, remaining almost the same as in the absence of the added dummyvariable. In addition, we also estimate Eq. (2) with the square of ln(K/L) as anadditional variable and find it insignificant, with a coefficient of −0.0352 and itsstandard error being 0.0426. The data are thus consistent with a constant outputelasticity of capital throughout the entire sample period 1952 to 1998. To examinewhether the rate of growth of total factor productivity implied by a productionfunction with constant returns has declined, we estimate a quadratic trend functionas given in Eq. (3). We find the coefficient of t2 significant only at the 0.096 level.

528 CHOW AND LIN

TABLE 7Sources of and Contributions to GDP Growth for Various Sample Periods

Contributions toSources of growth growth (%)

Equation 2 Sampleof Table 6 period K L t S A S/A K L t R

(2) K/L 1952–1978 0.04609 0.00898 0.00000 0.05507 0.05815 0.94703 79.3 15.4 0.0 5.31978–1998 0.05833 0.00981 0.02675 0.09489 0.09268 1.02382 62.9 10.6 28.9 −2.41952–1998 0.05141 0.00934 0.01163 0.07238 0.07316 0.98934 70.3 12.8 15.9 1.1

Note. Equation number is same as in Table 6. K = capital; L = labor; t = time; S = sum of estimates;A = actual GDP exponential growth rate; R = 100 – percentage contributions of K , L , and t .

Table 7 presents the decomposition of the rate of GDP growth into its factorcomponents, similar to Table 4. In the period 1952 to 1978 when there was noincrease in TFP, capital contributed 0.046 and labor 0.009 to the rate 0.058 ofexponential growth of GDP. In the period 1978 to 1998, capital contributed 0.058,labor 0.010, and increase in TFP 0.027 to the rate 0.093 of exponential growth ofGDP. For the entire period 1952 to 1998, capital contributed 0.051, labor 0.009, andincrease in TFP 0.012, which is 20/46 of 0.027, to the rate of 0.073 of exponentialgrowth of GDP. The sum of the estimated contributions for each period is notfar from the actual GDP growth rate as shown by the S/A ratios in Table 7. Inpercentage terms, these amount to 70, 13, and 16 from 1952 to 1998 as comparedwith approximately 39, 21, and 40 for Taiwan from 1951 to 1999.

One very important difference between the two economies is the relatively smallexponent of labor in the production function for the mainland. The accuracy ofthis small estimate was carefully examined in Chow (1993) where factor sharesduring the market economies of 1953 and the 1920’s were cited to support such alow estimate. Low labor exponents were also found in Table XII of Chow (1993,p. 833) for production functions of the three sectors of industry, construction, andtransportation. The rationale for the low estimate is that the elasticity of outputwith respect to labor is low because labor is in abundance in the mainland. In theextreme case, such surplus labor may yield almost zero marginal output. Sincethe Cobb–Douglas production function is an approximation to the input–outputrelation with constant elasticities, the small marginal output of labor is reflectedin its small exponent. As the economy grows, the ratio of capital to labor willincrease and labor will not be in such abundance. Hence, the labor exponent willincrease gradually as suggested by the labor shares given in columns PLS and LS inTable 2 for Taiwan. Our examination of the Chinese mainland data indicates thatthe abundance of labor has persisted after two decades of rapid growth since 1978.This finding is consistent with the existence of very poor regions in Western Chinaand the low wage rates of workers in those regions.

We end this section by stating conclusions concerning economic growth ofmainland China from 1952 to 1998 for comparison with the conclusions concerning


Taiwan stated at the end of Section 3. First, ignoring the interruptions in the period1958 to 1969 resulting from the Great Leap and the Cultural Revolution, GDPgrowth in mainland China can be characterized by a constant exponent for capital(and thus of labor under the empirically supported assumption of constant returns),no increase in TFP up to 1978, and a constant rate of increase in TFP from 1979 to1998. Second, the exponent of capital is about 0.65 and the rate of increase of TFPafter 1979 is about 0.027. Third, in the period 1978 to 1998, capital contributesabout 62% (because of the large capital exponent and the rapid rate of capitalaccumulation), labor only 10%, and TFP 28% to the average exponential rate0.093 of GDP growth. Fourth, there is no obvious sign of decline in the growthrate of GDP since 1978 as there has been no decline in the rate of growth of laborin the last decade similar to the decline in Taiwan and the contribution of labor togrowth is small. A factor which may have a small impact on the future growth rateis the anticipated decline in the growth of labor force in the mainland.

5. CONCLUSIONS

Having constructed capital stock data for Taiwan and mainland China and es-timated Cobb–Douglas production functions we have reached the following con-clusions. First, one production function with constant returns, constant capital andlabor exponents, and constant exponential rate of increase in TFP can explain thedata on GDP growth in Taiwan from 1951 to 1999. The same is true for mainlandChina from 1952 to 1998, except that TFP remains constant in 1952 to 1978 andbegins to increase at an approximately constant rate since 1978. Second, the capitalexponent is about 0.3 and the trend coefficient about 0.03 in Taiwan. The capitalexponent is about 0.6 and the trend coefficient beginning 1979 is about 0.03 in themainland. Third, for the entire period 1951 to 1999, capital contributes about 40%,labor 20%, and TFP 40% to the 0.08 exponential rate of GDP growth in Taiwan.For the period 1978 to 1998, capital contributes about 62%, labor 10%, and TFP28% to the 0.093 exponential rate of GDP growth in the mainland. Fourth, in thelast decade of the sample period Taiwan’s GDP growth rate decreased to about0.065 mainly as a result of the slower increase in labor input and the large exponentof labor in the production. No such phenomenon is observed for the mainland, butfuture growth might be slightly slower because of the anticipated slower growthrate of labor force, which has only a small effect on output. Fifth, a significantfinding is the small exponent of about 0.4 for labor in the mainland, which canbe interpreted as resulting from the very large supply of labor relative to capitalstock. Approximating the input–output relation by a function with a constant elas-ticity with respect to labor yields a low estimate of this elasticity. The elasticityis expected to increase gradually as the economy accumulates more capital, butthere is no evidence up to this point of a substantial increase, suggesting that laboris still in abundance in the mainland. Sixth, capital accumulation has been themost important factor for increasing output in both economies, contributing 40%

530 CHOW AND LIN

to the growth in Taiwan in 1951–1999 and about 70% in the mainland in 1952 to1998. Both are the result of a large rate of gross investment relative to GDP, whichamounts to about 25% in Taiwan and over 30% in the mainland in the past decade.

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Dessus, Sebastien, “Total Factor Productivity and Outward Orientation in Taiwan: What is the Nature ofthe Relationship?” In Tsu-Tan Fu, C. J. Huang and C. A. Knox Lovell (Eds.), Economic Efficiencyand Productivity Growth in the Asia-Pacific Region, pp. 191–213. Northampton, MA: EdwardElgar, 1999.

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Kuo, Shirley W. Y., The Taiwan Economy in Transition. Boulder, CO: Westview Press, 1983.MacKinnon, James G., “Critical Values for Cointegration Tests.” In R. F. Engle and C. W. J. Granger

(Eds.), Long-run Economic Relationships: Readings in Cointegration: 267–276. Oxford, UK:Oxford Univ. Press, 1991.

Mincer, Jacob, Schooling, Experience and Earnings. New York: Columbia Univ. Press, 1974.Nehru, Vikram, and Dhareshwar, Ashok, “A New Database on Physical Capital Stock: Sources, Method-

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User’s Reference Manual, Version 8.0. New York: McGraw–Hill, 1997.Wu, Hui-lin, “Labor Earnings Determinants of College Graduates: The Case of Taiwan.” Taiwan Econ.

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Documents

Accounting for Economic Growth in Taiwan and Mainland China: A Comparative Analysis