RELATIVE EFFICIENCY IN CHINESE URBAN CONSTRUCTION: A COMPARISON OF STATE-OWNED AND COLLECTIVE ENTERPRISES ARER REFORM Elliott Parker ABSTRACT: This paper estimates the relative efficiency of locally-controlled urban collective and pro- vincially-controlled state-owned enterprises in the Chinese construction industry between 1985 and 1988, a period following significant economic reforms. A generalized restricted translog cost function approach is used which allows for both fixed and variable factor choices to deviate from profit-maximizing out- comes. Results indicate that collectives were less efficient in this sample than state-owned enterprises in the use of variable inputs, and this gap was not closing by 1988. State-owned enterprises were, however, much less efficient in the use of capital, even when the measure of capital is adjusted for a relatively higher percentage of nonproductive investment. For both sectors of Chinese construction, the growth rate of total factor productivity (or average technical efficiency) rose to approximately four percent per year by 1988, but this improvement did not extend to more cost-efficient combinations of inputs. JEL Numbers: P21, P31, C30, 024. INTRODUCTION Does the form of socialist enterprise ownership have a significant effect on efficiency? Whether or not collectively-owned enterprises tend to be more efficient in their use of resources than their more traditional state-owned counterparts has important implications for economic reform in the socialist economy. If collectives are, or are becoming, relatively more efficient, then one implication is that greater intensive growth can be promoted through changes in the institutional structure controlling management. If, on the other hand, collectives are not becoming more efficient, then the institutional structure may not much matter, and privatization may therefore be the only hope for a significant and sustained improvement in living standards. In China, the collective sector has grown much faster than the state sector since the first wave of economic reform began in 1978, though it is not entirely clear whether this was due to intensive growth due to improvements in factor productivity, or extensive growth from the reduction of once-chronic shortages and marshalling of additional resources once devoted to agriculture. Using a 1984 cross-section of Chinese industry and a two-factor value-added production function, Jefferson (1989) compared state-owned enterprises Direct all correspondence to: Elliott Parker, Department of Economics /030, University of Nevada, Reno, NV 89557-0016. China Economic Review, Volume 5, Number 2, 1994, pages 161-178 Copyright 0 1994 by JAI Press, Inc. All rights of reproduction in any form reserved. ISSN: 1043-951X.
Transcript
RELATIVE EFFICIENCY IN
CHINESE URBAN CONSTRUCTION:
A COMPARISON OF STATE-OWNED AND
COLLECTIVE ENTERPRISES ARER REFORM
Elliott Parker
ABSTRACT: This paper estimates the relative efficiency of locally-controlled urban collective and pro-
vincially-controlled state-owned enterprises in the Chinese construction industry between 1985 and 1988,
a period following significant economic reforms. A generalized restricted translog cost function approach
is used which allows for both fixed and variable factor choices to deviate from profit-maximizing out-
comes. Results indicate that collectives were less efficient in this sample than state-owned enterprises in
the use of variable inputs, and this gap was not closing by 1988. State-owned enterprises were, however,
much less efficient in the use of capital, even when the measure of capital is adjusted for a relatively higher
percentage of nonproductive investment. For both sectors of Chinese construction, the growth rate of total
factor productivity (or average technical efficiency) rose to approximately four percent per year by 1988,
but this improvement did not extend to more cost-efficient combinations of inputs. JEL Numbers: P21,
P31, C30, 024.
INTRODUCTION
Does the form of socialist enterprise ownership have a significant effect on efficiency?
Whether or not collectively-owned enterprises tend to be more efficient in their use of
resources than their more traditional state-owned counterparts has important implications
for economic reform in the socialist economy. If collectives are, or are becoming, relatively
more efficient, then one implication is that greater intensive growth can be promoted through changes in the institutional structure controlling management. If, on the other hand,
collectives are not becoming more efficient, then the institutional structure may not much
matter, and privatization may therefore be the only hope for a significant and sustained
improvement in living standards. In China, the collective sector has grown much faster than the state sector since the first
wave of economic reform began in 1978, though it is not entirely clear whether this was
due to intensive growth due to improvements in factor productivity, or extensive growth
from the reduction of once-chronic shortages and marshalling of additional resources once
devoted to agriculture. Using a 1984 cross-section of Chinese industry and a two-factor value-added production function, Jefferson (1989) compared state-owned enterprises
Direct all correspondence to: Elliott Parker, Department of Economics /030, University of Nevada, Reno, NV
89557-0016.
China Economic Review, Volume 5, Number 2, 1994, pages 161-178 Copyright 0 1994 by JAI Press, Inc. All rights of reproduction in any form reserved. ISSN: 1043-951X.
162 CHINA ECONOMIC REVIEW VOLUME 512) 1994
(SOEs) to urban collectively-owned enterprises (COEs), and found that COEs exhibited a significantly higher marginal product for capital, a lower marginal product for labor, and less than 40 percent of the state sector’s total factor productivity (TFP). Part, but not all, of the first two results was due to an increase in capital’s estimated output elasticity, from 3 1 percent for SOEs to 72 percent for COEs. This stndy was extended by Jefferson, Rawski, and Zheng (1992) to cover two years, 1984 and 1987. By estimating a gross-output produc- tion function which allowed for substitution between capital, labor, and intermediate inputs, the output elasticity, or technical share, of capital between the two sectors was sta- bilized. By estimating parameter values with the two years of cross-sectional data, then extending this to aggregate national series, growth was decomposed over the 1980-1988 period. Correcting for the state sector’s relatively lower percentage of productive invest- ment, they still found that industrial COEs were not only growing at a much faster rate than SOEs, but also that their TFP growth rate of 4.6 percent per year almost doubled that of SOEs. They estimated that most of the output growth, however, was due to the increased use of intermediate inputs.
Why should collectively-owned enterprises be so different? Prior to economic reform, urban COEs typically existed within the plan but were of smaller scale than SOEs, and con- trolled by lower levels of government (a state bureau, city governments, local wards, or even an SOE). Intended as a means to combat urban unemployment and organize the infor- mal periphery of the urban economy in order to produce handicrafts and other goods for urban consumption, collectives were originally formed in the 1950s from “petty capital- ists,” small peddlers and repair workers (Tang & Ma, 1985). Many of the more efficient collectives grew up into full-scale factories, losing any semblance of independence (Walder, 1986, p. 46); these tended to be absorbed into the state sector, particularly during the Cultural Revolution. Even after economic reform, managers of COEs still tend to be chosen by the state rather than the workers, and party interference in decisions is still wide- spread. Yet local governments may lack the deep pockets and access to scarce materials of the state, and so may tend to be more concerned with local incomes, tax revenues, and employment levels more ,than the expansion drive and investment hunger described by Komai (1992). Collective employment has certainly been less valued from the point of view of workers, as an “earthen rice bowl” rather than the iron one of state employment. If the budget constraint is harder, this would lead to a prediction of greater efficiency for COEs. The lower level of control should imply that COEs are more dyn~cally efficient than SOEs, since they are better able to respond to changing conditions.
The evidence that COEs are quickly becoming more efficient is not entirely consistent. McGuckin & Nguyen (1993) examine Chinese state-owned, collective, and private enter- prises in 22 manufacturing sectors and 11 non-manufacturing sectors. Consistent with the above discussion, they find that the specification of output had a major impact on TFP growth estimates, while a restriction that technical shares equal cost shares (an assumption of price efficiency) had less effect. They further find that the non-manufacturing sectors overall had negative growth in TFP, especially before reform, while the manufacturing sec- tors significantly increased the annual growth rate of TFP after reform. Most importantly, they find that the boost in TFP was most significant in the emerging private enterprises; COEs experienced high rates of output growth due to their rapid growth of inputs, while their TFP growth was found to be very similar to that of the state sector.
In order to determine the characteristics of both price and technical inefficiency in the Chinese constrnction sector, and to test whether collectives are either more efficient than
RELATIVE EFFICIENCY IN CHINESE CONSTRUCTION 163
state-owned enterprises or becoming so, this paper uses a generalized restricted cost func-
tion approach that is described in the next section. This approach has not yet been applied to Chinese data, though its applications comparing public to private enterprises in regu- lated U.S. markets are becoming more numerous. It assumes that decision-makers are min-
imizing costs subject to shadow prices, which due to shortages or non-profit motives may systematically deviate from observed prices. Following that description, the third section describes the data, and the fourth section contains the description of the actual estimation
and results. Prior to the conclusion, an alternative specification of the cost function is described and estimated.
A GENERALIZED RESTRICTED COST FUNCTION MODEL
Empirical studies of efficiency in the Chinese economy have tended to rely on the produc- tion function methodology, since output maximization given fixed inputs is a behavioral assumption somewhat easier to justify in a socialist economy than profit maximization. These studies, however, tend to overlook the fact that efficiency implies not only output
maximization but also cost minimization. The mix of inputs is as important as the level of output. In this section, I specify a cost function model which deviates from standard cost minimization in two respects: first, capital inputs are assumed fixed, at least in the short- run; and second, input shadow prices may deviate systematically from those observed from the outside.
The cost function may be considered equivalent to a profit function restricted to an exogenous output level. The further restriction that capital inputs are also exogenous in the short-run implies that producers minimize variable costs. These restrictions allow capital inputs and output to deviate from their profit-maximizing levels. The resulting
variable cost function is specified as a translog functional form, which is a second-order approximation to any arbitrary function (Christensen, Jorgensen, & Lau, 1973). This function is:
4 2 4 4
lnVC* = lnf(Y,Z) = InA,+ Cai lnYi+ C 6,Z,+iC CPijlnYilnYj i=l m=l i=l j=l
+ i i i yimlnYiZm+ i i i O,,Z,Z,.
(1)
i=l m=l m=l n=l
The minimum variable cost function (VC*) is assumed to depend on the prices of mate-
rial (PM) and labor (PL ) inputs, output (Qj, capital stock (X,), an annual time variable (T), and a dummy variable for collective ownership (C). The six independent variables are sep- arated into two groups, Y = [PL, PM, Q, X,] and Z = [I: c], because the latter two may be equal to zero and the log of zero is undefined. As will be explained below, prices are assumed to be shadow prices which may not be directly observed, and this minimum vari- able cost function is therefore assumed to be shadow variable cost.
A number of restrictions should be imposed on the above cost function:
164 CHINA ECONOMIC REVIEW VOLUME 512) 1994
1) the cost function is necessarily linearly homogeneous in factor prices; 2) by Young’s theorem, symmetry is required for all second order parameters; and 3) since C is a dummy variable, its square cannot be separately identified.
These requirements are imposed with the following 14 restrictions:
(1) am = 1 - aL; ymM = -ymLQm; PiM = --P,vi
(2) pij = pjitli,j; emn = enmQm, n
(3) ccc = 0.
G-9
Constant returns to scale (CRTS) is imposed on the underlying production technology, since the interpretation of returns to scale is questionable when using aggregated data. Since capital stock is not independent of scale, CRTS is easier to impose if X, is replaced in the translog function with the capital-output ratio (K = XK/QJ This transformation does not alter the translog function, but only rearranges the coefficients for output. Allowing a tilde to represent the original coefficients in equation (l), the new coefficients are defined as:
(3)
With this redefinition, CRTS requires six simple additional restrictions beyond those imposed above:
aQ = l,ymQ = 0 Vm, pie = 0 Vi. (4)
Price indices reflect changes over time, but may not accurately reflect interprovincial price differences, even though adjustment has been made for floor space under construc- tion, since quality differences in output may vary across provinces. Interprovincial differ- ences in average cost are therefore not separable from average differences in quality. These differences are assumed to be constant across ownership types, so the intercept term A0 is defined as exponential function of provincial dummy variables (D) only:
30
InA, = ao+ x AiDi. (5) i=2
RELATNE EFFICIENCY IN CHINESE CONSTRUCTION 165
The cost-minimizing factor demands (x* = L, M), in share form (S*), can be derived with an application of Shephard’s lemma:
Pixi* alnvc* 3 4
si* E vc* =alnpi=
ai + C rmiZm + C j3,1nYi, Vi = L, M. m=l j=l
(6)
The VC* must be both increasing and concave in factor prices (implying positive share equations and a negative semidefinite Hessian matrix), and increasing in output. This is not costlessly imposed on the translog (Diewert & Wales, 1987), but can be checked by calculating the expressions for necessary first and second partial derivatives using mean parameter estimates, then checking the percentage of observations which violate one or more of the sign conditions. Expressions for the estimated second partial price derivatives are:
a*vti = *(s,’ (ii* - 1) + pii)Vi
ai$ if (7)
The problem with the above specification of the cost function is that the true shadow prices producers face may in fact deviate from those observed, because of unobserved monetary or nomnonetary costs or subsidies which are nonetheless real to the decision- maker. Capital loans may not need to be repaid, implying a subsidy; materials may be in chronic shortage, implying an additional cost of shortage; and the excess hiring of labor may bring nonmonetary rewards to the manager. The cost function generalized to the case of shadow prices which deviate systematically from observed prices is a non-minimum cost function in which minimizing behavior is still implicit.’ Since input shadow prices known to the enterprise may differ from observed prices for a number of reasons, direct estimation of the above system of variable cost and share equations may be n-&specified unless the difference between observed and shadow prices is accounted for.
Both the VC* and S* functions depend on shadow prices which affect the behavior of decision makers but may be unobserved by the econometrician. Following Atkinson and Halvorsen (1984), these prices (P) are specified as the observed input price (W) times some systematic proportion k:
Pi = kiwi. (8)
The non-minimum observed variable cost function (VC) is expressed in terms of the minimum (shadow) variable cost function and the cost-minimizing (shadow) shares:
1nVC = lnVC* + In t I .$ ’
(9)
166 CHINA ECONOMIC REVIEW VOLUME 542) 1994
and the resulting observed share equations (S) are:
yi wi* xi* si* sis “c E--jy- = - k, c 1 c, y -l* t j=L,M J
(10)
If k=I for all inputs, the ratio of VC* to VC collapses to unity and the enterprise may be said to be “price efficient.” The assumption of shadow variable cost ~~~zation implies that apparent price inefficiency does not in fact exist from the decision maker’s point of view, except as au error (Stigler, 1976); yet we can still use this measure to gauge the extent to which estimated incentives deviate from observed prices. Because the cost function is linearly homogeneous in prices, only relative “price efficiency” may be estimated, and absolute price efficiency is indistinguishable from technical efficiency. The shadow price ratio is identical to the ratio of the marginal rate of technical substitution between labor and materials divided by their observed factor price ratio. Because it is necessarily positive, this is specified as a log-linear function of the Z variables, as well as output level Q:
(11)
Since capital is assumed fixed, direct estimation of capital’s shadow price ratio is not specified. We may, however, still approximate the degree to which the level of capital devi- ates from its long-run optimum. We do this by first defining the elasticity of variable cost with respect to the capital-output ratio:
4 dlnVF
+=-= aInK i=l
(12)
The hypothesis that capital is in static equilib~um implies that total shadow cost is mini- mized, so:
a (vc* + PKXK) vc* EK
3% = -+P
XK K= 0; (13)
where PK equals tire return to capital on the margin. Since the marginal return to capital investment can be calculated as the marginal decrease in variable costs, this may be rear- ranged to estimate the variable-cost savings, or return, to marginal capital:
PK Vc*&,
=-- XK ’ (14)
RELATIVE EFFICIENCY IN CHINESE CONSTRUCTION 167
Capital’s shadow price ratio, its return divided by its cost, is therefore equal to the nega- tive of capital elasticity, divided by the ratio of capital’s fixed cost to variable cost, times the ratio of VC* to VC. A hat symbol is used to denote that this shadow price ratio is calcu- lated from variables derived from estimates:
The data used in this estimation includes aggregates for 29 provinces, for both state- owned construction enterprises and urban collectives, from 1985 to 1988.2 It is largely taken from the construction yearbooks (CSSB, 1988a; 1986a), though some data is avail- able in the Chinese statistical yearbooks (CSSB, 1989; 1988b; 1987; 1986b). This data includes both gross and net output values, both original and net value of fixed assets, both year-end and average number of staff and workers, the number of enterprises, wages, con- tributions to welfare funds, after-tax profits, square meters under construction, and both output and material price indices. While many statistics are available for other years, indi- ces of material and output price inflation are available only through 1988, and gross output, wages, and profitsare only available beginning in 1985.
Output Q is defined as gross output value divided by the output price index Pp Material inputs X, are defined as the difference between gross and net output value, divided by the material price deflator WM Labor inputs X, are defined as the average number of staff and workers, and average wages WL include base wages, piece-rate payments, overtime, above-quota payments, bonuses, and contributions to welfare funds, but not subsidies or benefits-in-kind. Total cost is defined as gross output value less after-tax profits, and observed variable cost VC is defined as the combined cost of both material and labor inputs. Prior to estimation, all physical and cost quantities are calculated for the average enterprise in each observation, then normalized.
Output price indices are adjusted to account for average interprovincial differences in gross output value per square meter of building under construction, and material prices are similarly adjusted for average interprovincial differences in the weighted prices of timber, cement, and steel, construction’s three largest inputs. It is assumed that SOEs and COEs face identical output and material prices in each province.3 An alternative assumption, which uses the number of building square meters under construction as a measure or year- to-year changes in real output, fails to account for changing quality and completion rates between the two sectors; such an assumption would bias real COE output downwards over time.
Following the general approach of Chen, Jefferson, Rawski, Wang, and Zheng (1988), the nominal value of fixed assets is adjusted into real capital stock by decomposing the enterprise averages in each year, from 1980 on, into gross and net investment and calculat- ing depreciation rates. Each province’s average enterprise series is then depreciated, deflated by a national price index for equipment, adjusted for the ratio of productive invest- ment, and recomposed into a year-end capital series. Finally, productive capital inputs X,
168 CHINA ECONOMIC REVIEW VOLUME S(2) 1994
‘liable 1 Summary Statistics for Chinese Provincial-Level Construction Enterprises
Notes: All annual growth rates calculated with differences in natural logarithms + In millions of Renminbi
for the average enterprise are defined as the average of current-year and previous-year deflated and depreciated year-end productive capital.
The data is summarized in Table 1 for both sectors and all four years. The typical SOE in 1985 produced almost 11.213 million Renminbi (RMB) of gross output, compared to 2.583 million RMB for the typical COE. Nominal output from COEs grew much more rap- idly than SOEs, but this was largely accounted for by an increasing number of enterprises; over the sample, real output per COE actually fell. Real capital stock per enterprise, once adjusted for inflation and depreciation, grew at approximately 8.6 percent per year for COEs and 5.3 percent per year for SOEs, while the average staff fell over time in both sec- tors and the share of material inputs held relative&steady. Consistent with the lack of wage discipline predicted by Komai (1992) under reform, wages grew faster than inflation for both sectors in all years, and COEs typically paid more than a third extra to their employees than COEs. Consistent with the observations of Naughton (1992), profits fell for both sec- tors over time as competition increased, though they were generally somewhat higher to begin with for SOEs.
ESTIMATION AND RESULTS
After imposing conditions (2) through (5) on the minimum variable cost fVC*) function in equation (1) it can be normalized to the following function of the shadow prices of labor and materials (PL PM ), output {Qj, the capital-output ratio (K), year (7’), and collective ownership (C):
30
In vc* = InP, + lnpQ + a0 x A,D, + a,ln (FL/PM) + aKInK + S,T + S,C
+ y&n ( PL/PM) T + y&n (P,/P,) C + y,,lnKT + y&nKC
The non-minimum variable cost function estimated is shown in equation (9), and is a function of the minimum variable cost function above, the shadow variable cost shares shown in equation (6), and the shadow price ratio in equation (11). The log non-minimum variable cost equation is simultaneously estimated with the observed variable cost share shown in equation (lo), each with normal error terms appended. Because the share equa- tions for labor and material inputs sum to unity, only the first is includede4 In both equa- tions, the relative shadow price for labor (PL) is the observed price (WL) times the shadow price ratio (k~w]~ and the relative shadow price for materials is the observed price of mate- rials.
The model is estimated using the iterative nonlinear seemingly unrelated regression technique, which in convergence approximates maximum likelihood (ML) estimation by ~ni~zing the dete~n~t of the residual Vance-cov~ance matrix. In order to increase
170 CHINA ECONOMIC REVIEW VOLUME 5(2) 1994
able 2 Results of Model Estimation
Parameter Estimate Standard Error Parameter Estimate Siam&& Error
% -0.4109
EL 0.0611
a, -0.1009
8T 0.0479
6C -0.1381
0l.L 0.0096
bK 0.0013
&KK -0.0448
YLT -0.0001
YLC -0.0069
YKT 0.0166
YKC -0.0554
err -0.0160
OTC 0.0108
50 -1.8155
ST 0.0072
SC -0.2131
scr -0.0097
CQ 0.1674
R2 WC) 0.9989
R2 (Sz) 0.9820
(0.0865)”
(0.0360)*
(0.0743)
(0.0142)**
(0.0657)**
(0.0060)
(0.0011)
(0.03 12)
(0.0010)
(0.0098)
(0.0047)**
(0.0236)**
(0.0038)**
(0.0065)*
(0.7960)**
(0.0340)
(0.2199)
(0.0320)
(0.0206)**
A2 0.4224
A3 0.2560
A4 0.0206
A5 0.3991
A6 0.3195
A7 0.3950
At7 0.4289
4 0.2807
Alo 0.3730
All 0.0382
A12 -0.0054
A13 -0.4066
A14 -0.3375
A15 -0.0105
A16 -0.3047
A17 0.0299
A18 -0.0740
A19 -0.3198
A20 -0.1370
A21 -0.2417
A22 -0.0750
A23 -0.2527
A24 0.1958
A25 0.5565
A26 -0.0688
A27 0.2657
A2a 0.5283
A29 0.4212
Log-Likelihood: 1054.95 A30 0.2008
(0.0268)**
(0.0266)**
(0.0292)
(0.0301)**
(0.0292)**
(0.0299)**
(0.0303)**
(0.0289)**
(0.0300)**
(0.0282)
(0.0272)
(0.0277)**
(0.0274)**
(0.0296)
(0.0255)**
(0.0269)
(0.0276)**
(0.0227)**
(0.0283)‘;
(0.0307)**
(0.0258)**
(0.0262)**
(0.0291)**
(0.0297)**
(0.0288)**
(0.0290)**
(0.0308):’
(0.0306)**
(0.0292)**
Notes: ** ‘Ih-tailed t-statistic significant at tive percent * Two-tailed t-statistic significant at 10 percent
the likelihood of finding the global maximum, initial parameter values are derived in steps, beginning with a system of linear equations then adding estimation of nonlinear compo-
nents. The ML parameter estimates and their asymptotic standard errors are reported in
Table 2. Given the reported mean parameter estimates, the shadow price ratio for capital is
derived from equation (15) and reported along with the shadow price ratio between labor
and materials for both the state-owned and urban collective construction sectors, for all
years in the sample. Further information regarding efficiency and the underlying technol-
RELATIVE EFFICIENCY IN CHINESE CONSTRUCTION 171
ogy is also derived, and shown in Table 3. The first of these, the Allen-Uzawa short-run
elasticity of substitution (AUES) between labor and materials, is?
CJ L&f = l+&. (17)
The average annual rate of technical progress (or improvement in technical efficiency not due to bidding) can be approximated as:
(18)
The estimated effect of collective ownership on average costs is not constant, but can be derived as:
4 alnvc*
g,= ac= 6~ + z qciln Yi + i&T. (19) i= 1
Farrell (1957) indices of technical efficiency and short-run price efficiency may be easily derived. Using estimated parameters, we calculate a measure of variable cost which leaves out the effect of Z variables by setting all 6, ‘y, and 8 parameters to zero?
4 4 4
1nfC = In&+ C &ilnYi + i x C bijlnYilnYj + In i= 1 i=l j=l
c cw
i=L,M
The index of technical efficiency, normalized so that the maximum observed efficiency is unity, may then be calculated as:
(21)
For short-run price ineffkiency, the appropriate index is the ratio of shadow to actual variable costs, once relative technical inefficiency is separated out. This index is unity if km=l.
172 CHINA ECONOMIC REVIEW VOLUME 5(2) 1994
(22)
Finally, an aggregate short-run efficiency index (q) is derived which is the product of
both technical and price efficiency:
This aggregate index is perhaps the most useful, since the price efficiency index accounts for only relative price inefficiency. If more than one shadow price ratio differs from unity,
the cost function’s linear homogeneity makes price inefficiency indistinguishable from
technical inefficiency. Judging from the t-statistics in Table 2, the hypotheses that a large number of the param-
eter estimates are individually equal to zero cannot be rejected, even at 10 percent; how- ever, the relevant joint hypotheses are all rejected. The hypothesis that COEs are identical
to SOEs yields a Wald x2 statistic of 19.59, with six degrees of freedom (d.o.f.); and the
hypothesis that the only difference between the two sectors are the parameters &-, &-, and kcT yields a Wald statistic of 7.88, with three d.o.f. The hypothesis that the elasticity of
capital is zero is rejected with a Wald statistic of 19.34, with five d.o.f., and the hy~thesis
that time had no effect on the underlying technology was rejected with a statistic of 57.05,
also with five d.o.f.. The hypothesis of relative price efficiency is rejected with a Wald sta-
tistic of 145.04 (or a likelihood ratio test x2 statistic of 147.13), with five d.o.f.; for COEs
this statistic was 100.60, and for SOEs 85.38, both with three d.o.f..7 The results suggest that both types of enterprises exhibited significant relative price inef-
ficiency which did not improve over time. In Table 3, the estimated shadow price ratio kM
is approximately 11 percent for COEs and 17 percent for SOEs, suggesting the overuse of
labor relative to materials. The calculated shadow price ratio kK begins low and becomes negative for COEs, and becomes increasingly negative for SOEs; this suggests that invest-
ment continued to take place even though the marginal product of capital was nonpositive. Judging by the calculated effect of time on average costs, technical efficiency was improv-
ing at an increasing pace. By 1988, the marginal annual reduction in average costs due to
changing TFP had increased to 3.7 percent for COEs and 3.8 percent for SOEs. Overall, SOEs appeared to be somewhat more efficient, and the gap did not significantly decrease
over time. The mean short-run elasticity of substitution between materials and labor was slightly
less elastic than unity, but the t-statistic for this hypothesis, that l3, (= -13~ = l3,,> = 0,
cannot be rejected even at 10 percent significance. The estimated shadow cost function is concave and monotonic in the shadow prices of variable inputs for 100 percent of the observations, but the expectation that it is monotonically decreasing in capital inputs is vio-
lated for a significant portion of observations, increasingly over time and especially for
SOEs. Urban collectives, then, do not appear to have been more efficient in the late 1980s than
state-owned enterprises in the const~ction sector, at least not in variable inputs, nor are they threatening to be. This result is in spite of the assumption that they face the same set
of output and material prices as SOEs; if the price were assumed to change consistent with the growth of nominal output per square meter of building space under construction, the resulting faster-growing output price for COEs would have exaggerated this effect. COEs do appear to have been more efficient in the use of capital inputs, even though SOE invest- ment was adjusted downwards due to their higher rate of nonproductive investment. Capi- tal’s marginal product continued to decline, however, as investment proceeded rapidly.
AN ALTERNATIVE SPECIFICATION OF THE VARIABLE COST FUNCTION
In order to examine whether or not the specification of the provincial-level dummy vari- ables had any significant impact on the results of this study, the cost function in equation (9) was re-estimated in log-difference form:
The thirty parameters in ZnAo cancel out, along with 6c, so the log-difference minimum shadow variable cost function is:
Table 4 Results of Model Estimation for Log-Difference Model
Log-Difference Model Secondary Estimates
Parameter Estimate Standand Error Parameter Eshate Standard Ermr
sT
4t.L &K BKK
en eTC
& ST 4c kT SQ
0.0713 (0.0289)**
0.0076 (0.0921)
0.0287 (0.0207)
0.0143 (0.~70)**
-0.0013 (0.0019)
-0.0128 (0.0382)
0.0029 (0.0032)
-0.0098 (0.0114)
0.0088 (0.0077)
-0.0890 (o.O483)*
-0.0161 (0.0039)**
0.0146 (0.0110)
-1 s437 (0.5702)**
0.0764 (0.0650)
-0.1859 (0.2966)
0.025 1 (0.0398)
0.1955 (0.03 12)**
0.9989
0.9822
%I -0.2598
AC -0.2340
A2 0.4621
A3 0.2891
A4 0.0620
AS 0.4456
hi 0.3715
67 0.4494
A8 0.4786
A9 0.3217
A10 0.4172
AlI 0.0846
A12 0.0382
A13 -0.3642
A14 -0.2975
Al5 o.a401
A16 -0.2704
A17 0.0766
Al8 -0.0302
A19 -0.2844
A20 -0.0858
A21 -0.1803
A22 -0.0348
AZ.23 -0.2169
A24 0.2381
A25 0.5786
A26 -0.0203
A27 0.3068
62% 0.5580
A29 0.4625
Log-Likelihood: 1030.21’ A30 0.2417
(0.0116)**
(0.0042)**
(0.4245)
(0.8509)
(0.9043)
(0.9555)
(0.9373)
(0.7655)
(0.9244)
(0.5837)
(0.8982)
(0.9019)
(0.7164)
(0.5542)
(0.9339)
(0.7948)
(0.8~8)
(0.8944)
(0.9629)
(0.8154)
(0.9300)
(0.6598)
(0.8960)
(0.8882)
(0.9387)
(0.5539)
(0.9073)
(0.9157)
(0.7939)
(0.8786)
(0.7351)
Notes: ** Two-tailed r-statistic significant at five percent * ?\vo-tailed r-statistic significant at 10 percent
Appending a normal error, equation (24) was estimated together with the observed share equation (9) for 1986 through 1988, since the initial year was necessarily dropped due to differencing. For purposes of comparability, once the parameters in this estimation were derived, a second estimation was made with the undifferenced observed variable cost func- tion for 1985 through 1988, in order to derive estimates of the intercepts and provincial dummy variables. The conditional results are reported in Table 4, and the mean effkiency and tec~ologic~ indices are reported in Table 5.
The results are not exactly identical to the previous estimation. Estimating the log-differ- ence cost function results in a decrease of significance in the t-statistics for 8, ‘yKli yKc, and flTC, and an increased significance for tag and 8,. The joint hypothesis that capital’s elas-
RELATIVE EFFICIENCY IN CHINESE CONSTRUCTION 175
Table 5 Mean Effkiency and Technological Indices for Log-Difference Model
Urban Collectives State-owned Enterprises
Statistic 1985 1986 1987 1988 1985 1986 1987 1988
0.706 0.717 0.723 0.731 0.757 9
TIT VP bt k s,* %f* %v gT
gc &K
0.670
0.758
0.884
0.146
0.695
0.064
0.936
0.759
0.010
0.065
-0.039
100%
0.674
0.753
0.895
0.159
0.608
0.066
0.934
0.767
-0.005
0.064
-0.032
100%
0.684
0.755
0.906
0.175
0.377
0.068
0.932
0.775
-0.020
0.075
-0.024
100%
0.77 1 0.773 0.773 0.776 0.798
0.916 0.928 0.935 0.942 0.949
0.194 0.230 0.247 0.267 0.289
0.237 -0.701 -0.885 -0.797 -0.831
0.072 0.076 0.080 0.082 0.085
0.928 0.924 0.920 0.918 0.915
0.785 0.797 0.805 0.810 0.816
-0.035 0.003 -0.012 -0.028 -0.043
0.083 0.002 0.010 0.018 0.026
-0.016 0.041 0.049 0.057 0.065
100% 100% 100% 100% 100%
Monotonicity:
s,*>o
S,‘>O
&K<O
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
100%
0%
100%
100%
0%
100%
100%
0%
100%
100%
0%
ticity is zero is not rejected at 10 percent significance (the Wald x2 statistic is 8.32, with five d.o.f.), as is the hypothesis that there is no technological difference between COEs and SOEs (with a Wald statistic of 4.80, with three d.o.f.). In estimating the provincial-level intercepts, given the prior estimates from the above equation (24), all provincial dummy variables become singly and jointly insignificant (the conditional Wald statistic is 2.11, with 18 d.o.f.).
The results are still qualitatively similar to those in Tables 2 and 3 above. Certainly the basic patterns hold. SOEs are somewhat more efficient than COEs overall, except in the use of capital. Relative to material inputs, labor is overallocated, and this is more true for COEs because labor’s output elasticity is slightly smaller. Total factor productivity appears to be improving slightly faster for SOEs. Relative price efficiency is significantly rejected (with Wald test statistics of 74.79 for both sectors, 49.34 for SOEs, and 65.37 for COEs), though the estimated kLM rises somewhat. Overall technical and price efficiency follows the same general pattern, though the superiority of SOEs is less pronounced. The hypothe- sis that time does not affect the shadow cost function is rejected with a Wald statistic of 32.31 (with five d.o.f.), and the marginal growth rate of total factor productivity is again close to four percent per year by 1988. For all observations, the shadow cost function is concave and monotonic in variable shadow prices; additional capital decreases variable cost for all COE observations and none of the SOE observations.
CONCLUSION
This paper began by asking whether or not the form of socialist ownership mattered. If col- lectively-owned enterprises tend to be more efficient, or are improving their total factor pro- ductivity at a faster rate than larger state-owned enterprises which are likely to have a softer
176 CHINA ECONOMIC REVIEW VOLUME 5(2) 1994
budget constraint then continued economic reforms, will likely lead to the demise of the
more formal state sector. To answer this question, this paper applied a generalized restricted translog cost function approach which allows input choices to depart from cost-minimizing
choices. This paper represents the first application of this approach to a Chinese production dataset in the literature, and enables the testing of hypotheses regarding the relative degree
of input price inefficiency. While Jefferson et al. (1992) answered in the affirmative, at least regarding the higher
intensive growth rate of industrial collectives, this study finds that this result does not hold for the Chinese construction sector in the late 1980s. Urban collectives are less efficient in
the use of variable inputs, with a lower shadow price ratio (the marginal product of a factor relative to its wage) for labor relative to materials, though they were less inefficient in their overuse of capital than their state-owned counterparts. Both sectors were improving total factor productivity (average technical efficiency) at a significant pace, but this did not
extend to improving price efficiency in the mixture of inputs. Though the conclusions are significant and consistent, their generality should not be
extended too far. The construction sector is different from other sectors insofar as its output is not marketed directly to the final consumer and competition among producers is still lim-
ited. The impact of economic reforms on differential growth rates and price efficiency may not have occurred during this sample of years. Whether or not collectives are becoming more efficient than state-owned enterprises is a matter for future research into other years
or other sectors of the Chinese economy.
NOTES
1. The non-minimum generalized cost (or non-maximum profit) function approach was first
developed by Lau and Yotopoulos (1971) and extended by Yotopoulos and Lau (1973), Toda (1976), Love11 and Sickles (1983), Atkinson and Halvorsen (1980, 1984), and Kumbhakar (1992).
2. Beginning in 1988, separate dam is available for Hainan island. Prior to that, Hainan Island was considered part of Guangdong and the estimation of capital deflators, etc., is adjusted
accordingly. There are therefore 2x(3x29+30) = 234 observations. 3. A specification which included the ratio of the free-market to state-list price index as an
explanatory variable of the shadow price ratio for collectives was found to be statistically insignificant.
4. The results are invariant to the particular share equation dropped (Greene, 1980). 5. The Morishima elasticity of estimation, Mu = P&i/C+ - PjCii/Ci, is generally superior to the
AUES in measuring the ease of substitution (Blackorby & Russell, 1989). The AUES, how- ever, is still used here because it provides a single symmetric statistic which, to the extent that it differs from unity, can be interpreted as the deviation of the translog form from the Cobb- Douglas form. Furthermore, in the case of only two inputs, the AUES “reduces to the original
Hicksian concept” (Blackorby & Russell, 1989, p. 882). 6. Other parameters in equation (20) are from the original estimation, and are not reestimated in
a restricted model. 7. In order to check stability of the estimate, price efficiency was imposed. This is equivalent to
setting shadow shares equal to observed shares. In this restricted model, the constant and dummy coefficients were not changed significantly. All other coefftcients, with the exception of yLn exhibited statistical significance at the five percent level. However, the basic results comparing SOEs to COEs, as described by n, gn and gc, were not significantly affected.
RESTIVE ~FF~~~EN~Y fN CHINESE ~ONSTR~CT~ON 177
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