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Economic efficiency of multi-product structure: the evidence from Korean housebuilding firms
JOURNAL OF
Journal of Housing Economics 12 (2003) 337–355
HOUSING ECONOMICS www.elsevier.com/locate/jhe
Economic efficiency of multi-product structure: the evidence from Korean housebuilding firmsq Youngha Cho* Department of Land Economy, Cambridge Centre for Housing and Planning Research, University of Cambridge, 19 Silver Street, Cambridge CB3 9EP, UK Received 13 June 2002
Abstract The Korean housebuilding industry has been subject to structural changes since the 1980s. One of the key features is that housebuilding firms have become diversified into a range of businesses and as a result display multi-product structure. This paper examines the efficiency of the multi-product structure of Korean housebuilding firms. For the analysis, translog cost functions were estimated using data for 201 building firms for the 3 years 1993–1995. The empirical results indicate that medium-size building firms enjoy increasing returns to scale, whereas large firms experience constant returns to scale. Korean building firms exhibit significant economies of scope in their diversification activities. Large firms have the greatest economies of scope. These results are consistent with cost efficiency for the multi-product structure of Korean housebuilding firms. The estimated optimum scale suggests that many large firms should expand only through diversification. Ó 2003 Elsevier Inc. All rights reserved. JEL classification: D21; L23; L74 Keywords: Multi-product structure; Economies of scale; Economies of scope; Optimum scale of business; Housebuilding industry
q I thank Christine Whitehead, Diane Reyniers, and two anonymous referees for comments on an earlier version. I have greatly benefited from the helpful suggestions of the editor Henry Pollakowski. * Fax: +1223-330863. E-mail address: [email protected] (Y. Cho).
1051-1377/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.jhe.2003.09.003
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1. Introduction The Korean housebuilding industry has undergone steady growth concurrently with general economic development since the 1970s. The industry has grown particularly rapidly since the mid-1980s and has experienced significant structural changes. Approximately 70% of new construction has been built by the private sector since the mid-1980s. Most of the private output has been produced by large-scale firms that the Korean government certified, and not by small-scale housebuilders which had dominated the industry before the 1980s. In addition, apartment houses comprise 70–80% of total new construction, whereas the single detached house was the most popular type until the beginning of the 1980s. Another important feature is that housebuilding firms have diversified by extending into a range of businesses unrelated to their own industry (Kim and Park, 1996). Even small firms which have recently entered the business are involved in various other businesses. The emergence of large firms in the housebuilding industry since the 1970s is not confined to Korea and is found in other countries as well (Ball, 1996; Ball et al., 1988; Cough, 1988; Grebler, 1973; Lambert, 1990). Housebuilding firms in industrialised countries have begun to involve themselves in various businesses through the diversification strategy since the 1970s (Ball, 1983, 1988; Gillies and Mittelbach, 1962; Hasegawa and Shimizu Group, 1988; Hillebrandt and Cannon, 1990). Kim and Park (1996) observe that most of the active housebuilding firms are carrying out more than one business besides housebuilding. Their main business is either housebuilding or other construction, but they are also involved in other businesses such as land development, property management (rental and sale), and other unrelated business (such as shopping centre development and rental, and restaurant business). There are distinctive differences among different sized firms. Large firms are mainly those that started business in other construction and have emerged into housebuilding business since the 1980s. They are very large scale in terms of numbers of employees, total sales, and capital. Typically, medium and small firms are those which started their business in housebuilding as speculative housebuilders. Cho (2000) found that when we consider only direct production costs, housebuilding is more profitable than the ‘‘other construction’’ activities. However, large firms return relatively higher profits than small- and medium-sized firms, which are more involved in the profitable housebuilding business. One possible reason is that small firms incur relatively higher overhead costs, including interest and other financial costs. This suggests that large firms may be achieving economic efficiency from the large-scale, multi-activity nature of their business. This paper examines the economic efficiency of the diversified product structure of Korean housebuilding firms. The plan of this paper is as follows: Section 2 reviews the implications of the economies of scale and economies of scope in the housebuilding industry. Section 3 introduces the form of the model for estimating the cost function of multi-product firms. Economies of scale and economies of scope are derived from the function. Section 4 outlines the variables to be included in the model, data sources, number of observations, and the estimation method. Section 5 contains the estimation results which address whether or not the multi-product structure is
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economically efficient. Optimum scales of firmsÕ business are also derived from the results. Section 6 contains a summary and discussion.
2. Economies of scale and economies of scope: the implications The relationship between average costs and output can be explained by the relation between physical quantities of inputs and outputs summarised in the production function. At given factor prices, some firms use more inputs, whereas others use fewer inputs per unit of output, as output rises. This is a function of the technology and production techniques employed. We assume that economies of scale exist when long-run average costs decrease as output rises in the fixed product mix. In this definition, scale refers to the size of the business as measured by its output. If a specific industry is observed as having increasing returns to scale, firms can increase cost efficiency through the extension of the businessÕs size. In addition to economies of scale, cost savings may result from simultaneous production of several different outputs in a single firm. We observe that Korean housebuilding firms rarely engage in extreme specialisation. Instead, firms in different size categories appear to specialise in different output compositions. Diversification into new products is generally explained to be the main engine of corporate growth (Teece, 1982). In order to grow faster than the rate of growth of the markets in which a firm has established itself, it must carry out further successful diversification. However, there are obviously significant costs attached to diversification that can reduce rate of return on capital. How then does diversification arise successfully? One way of reducing diversification costs is the sharing of inputs (Mester, 1987; Teece, 1980). The extent to which housebuilding technology is relevant to the production of alternate businesses (other construction activity or property management) may be an example of the joint utilisation of inputs. In housebuilding, common utilisation of existing human resources and building facilities such as building equipment, knowledge of the contracting system used in the construction business, and market and customer information are important sources that can lower the average costs of the multi-product firms. Hence, the relevant question is whether lower operating costs result from joint production of an output bundle for a large firm, whose output bundle is representative for its size category, compared with specialised production of the same total output bundle by two smaller firms. This is an issue of economies of scope as well as economies of scale.
3. Estimating the cost function of multi-product firms It is necessary to estimate the production function in order to analyse the efficiency of production behaviour in a specific firm or industry. In an empirical analysis, however, it is difficult to estimate the production function because our data do
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not permit estimates of prices or their proxies calculated as revenue divided by the number of units of output (Mullineaux, 1978). Consequently, under the hypothesis that the production function is homogeneous, the cost function is estimated instead, using Samuelson–Shephard Duality Theorem (Diewert, 1971). The cost function shows the relationship between input prices and output assuming that firms produce a single product. Multi-product cost theory has been developed by Baumol et al. (1982). The estimation of economies of scale and economies of scope that they have developed have been widely used in the study of the efficiency of multi-product firms. 3.1. General form of translog cost function In a multi-product environment, the single product scale economy measure has an analogous measure in the concept of ray scale economies. Ray scale economies are defined as the proportional effect on cost of a scale expansion along a ray in multi-product-cost space, holding constant the relative proportions of the outputs (Goldberg et al., 1991). To analyse the efficiency of the production structure, we can use Cobb–Douglas, CES or translog cost functions. Although Cobb–Douglas and CES functions are convenient specifications for the purposes of modelling and estimation, they are incapable of generating anything other than smooth, monotonically increasing or decreasing average cost curves. Returns to scale are forced to remain constant across all output levels and may therefore present an inaccurate picture of the production/cost relationships. The translog cost function avoids such pitfalls, as it allows us to enter the various outputs as separate variables, and does not force the assumptions of homogeneity and constant elasticity of substitution (Murray and White, 1983). In its most general form, the translog function provides a second-order approximation to any twice-differentiable function. The production technology of a multiproduct housebuilding firm can therefore be modelled with maximum flexibility, giving explicit recognition to each of the outputs. Provided certain regularity conditions and behavioural assumptions are met, one can obtain a complete representation of the underlying technology simply by analysing the structure of the related cost function. The optimised cost function is defined with output quantity and input factor prices. This function, especially, shows the proportional effect of the relationship between various input prices and outputs on total cost, according to output expansion. On the basis of a homogeneous production function, the translog cost function is essentially a Taylor series expansion in output quantities and input prices (Diewert, 1971). The function can be written as follows: logTC ¼ a0 þ
n X i¼1
ai ðlog yi Þ þ
n X n n X 1X hi;k ðlog yi Þðlog yk Þ þ bj ðlog wj Þ 2 i k j¼1
m X m n X m X 1X cj;h ðlog wj Þðlog wh Þ þ di;j ðlog yi Þðlog wj Þ; þ 2 j h i j
ð1Þ
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where TC is the total cost, yi is the output of ith product, i ¼ 1; 2; 3; . . . ; n, and wj is the price of jth input factor j ¼ 1; 2; 3; . . . ; m. Basic assumptions of the cost function, in Eq. (1), are first, the function should be linearly homogeneous in all input prices; second, it should be concave in price of input factors (wj ); and third, output (yi ) and price of input factors (wj .) should increase. The linearly homogeneity condition is satisfied when: (i)
n X
bj ¼ 1;
j¼1
(ii)
m X
cj;h ¼ 0
j ¼ 1; . . . ; m;
h¼1
(iii)
m X
di;j ¼ 0 i ¼ 1; . . . ; n;
j¼1
and symmetry conditions are as follows: (iv) hi;k ¼ hk;i cj;h ¼ ch;j
i; k ¼ 1; 2; . . . ; n; j; k ¼ 1; 2; . . . ; m:
Eq. (1) is quadratic in logarithms and linear in the unknown parameters, permitting ease of estimation. This cost function may be estimated alone; alternatively, factor share equations can be derived using ShephardÕs lemma, and the system of equations can be estimated simultaneously (Murray and White, 1983). When we estimate Eq. (1) alone under the restrictions of the OLS method, OLS provides a simple means of deriving unbiased estimates. However, it fails to incorporate extra information which might be extracted from a restricted system of cost equations (Goldberg et al., 1991). For this reason, it is deemed desirable to estimate the single cost equation and a set of cost share equations simultaneously. A system of cost share equations can be derived directly from the translog cost function by differentiating Eq. (1) with respect to wj . SHj ¼
m n X X logTC ¼ bj þ cj;h ðlog Wh Þ þ dij ðlog yi Þ; log Wj h¼1 i¼1
ð2Þ
where SHj is the cost share on the jth input factor in total cost. Because of the restriction of linear homogeneity in input prices, the factor share equations must sum to one to avoid singularity problems. One of the share equations must be excluded from the estimation process. Christensen et al. (1973) explain that the parameter estimates are invariant with respect to which equation is excluded from the estimated system. By estimating the cost function and the derived cost share equations together as a multivariate regression system, we gain additional degrees of freedom. It is known that the system estimates should be more efficient than the single equation estimates generated by the cost function alone, since the cost share equations do not
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introduce any additional unknown parameters into the estimation (SAS Institute, 1985). 3.2. Modelling for estimation The specific equations to be estimated are described as follows. Eq. (3) includes the total cost variable (TC), output variables (yi ) and input factor prices (wj ). Korean building firms produce three outputs: other construction (y1 ), housebuilding (y2 ), and other business (y3 ). Input factorsÕ prices are used for materials (w1 ), labour (w2 ), subcontracting (w3 ), and overhead (w4 ) (capital). The equation to be estimated consists of a total of 36 coefficients and can be expressed as follows: 1 2 logTC ¼ a0 þ a1 log y1 þ a2 log y2 þ a3 log y3 þ h11 ðlog y1 Þ þ h12 log y1 log y2 2 1 1 2 2 þ h13 log y1 log y3 þ h22 ðlog y2 Þ þ h23 log y2 log y3 þ h33 ðlog y3 Þ 2 2 1 2 þ b1 log w1 þ b2 log w2 þ b3 log w3 þ b4 log w4 þ c11 ðlog w1 Þ 2 þ c12 log w1 log w2 þ c13 log w1 log w3 þ c14 log w1 log w4 1 1 2 2 þ c22 ðlog w2 Þ þ c23 log w2 log w3 þ c24 log w2 log w4 þ c33 ðlog w3 Þ 2 2 1 2 þ c34 log w3 log w4 þ c44 ðlog w4 Þ þ d11 log y1 log w1 2 þ d12 log y1 log w2 þ d13 log y1 log w3 þ d14 log y1 log w4 þ d21 log y2 log w1 þ d22 log y2 log w2 þ d23 log y2 log w3 þ d24 log y2 log w4 þ d31 log y3 log w1 þ d32 log y3 log w2 þ d33 log y3 log w3 þ d34 log y3 log w4 :
ð3Þ
Cost share equations to be estimated are expressed as follows: SH1 ¼ b1 þ c11 log w1 þ c12 log w2 þ c13 log w3 þ c14 log w4 þ d11 log y1 þ d21 log y2 þ d31 log y3 ; SH2 ¼ b2 þ c21 log w1 þ c22 log w2 þ c23 log w3 þ c24 log w4 þ d12 log y1 þ d22 log y2 þ d32 log y3 ;
ð4Þ
SH3 ¼ b3 þ c31 log w1 þ c32 log w2 þ c33 log w3 þ c34 log w4 þ d13 log y1 þ d23 þ log y2 þ d33 log y3 ; SH4 ¼ 1 ðSH1 þ SH2 þ SH3 Þ: As one of the share equations has to be excluded in the estimation process, the single cost function equation and three cost share equations are to be estimated simultaneously.
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The restrictions given to the cost function are expressed as follows: b1 þ b2 þ b3 þ b4 ¼ 1; c11 þ c21 þ c31 þ c41 ¼ 0; c12 þ c22 þ c32 þ c42 ¼ 0; c13 þ c23 þ c33 þ c43 ¼ 0; c14 þ c24 þ c34 þ c44 ¼ 0; d11 þ d12 þ d13 þ d14 ¼ 0; d21 þ d22 þ d23 þ d24 ¼ 0; d31 þ d32 þ d33 þ d34 ¼ 0; d41 þ d42 þ d43 þ d44 ¼ 0: 3.3. Estimation of economies of scale and economies of scope Once the translog cost function is estimated using the above Eqs. (3) and (4), we can derive various efficiency measures. 3.3.1. Economies of scale Economies of scale are obtained by differentiating Eq. (3) with respect to all yi (Murray and White, 1983). Se ¼ ¼
n n X oCðyi Þ yi X o logCðyÞ ¼ o logyi oyi CðyÞ i¼1 i¼1 n X i¼1
ai þ
n X n X i¼1
k¼1
hi;k ðlog yk Þ þ
n X m X i
di;j ðlog wj Þ:
ð5Þ
j
If Se is greater than one, firms will experience decreasing returns to scale, as costs rise proportionately more than output. When Se equals one, this indicates constant returns to scale. When Se is less than one, this indicates increasing returns to scale. 3.3.2. Economies of scope Panzar and Willig (1977) have shown that a multi-product cost function exhibits economies of scope as follows: Pn Cðyi Þ CðyÞ ; ð6Þ SCe ¼ i¼1 CðyÞ where Eq. (6) is calculated using the estimated value from the cost function in Eq. (3). Cðyi Þ denotes the cost incurred when a firm produces only yi . CðyÞ refers to the cost incurred when the firm produces all products. Eq. (6) can be rewritten specifically when the firms produce three outputs as follows:
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SCe ¼
ðcðy1; 0; 0Þ þ cð0; y2 ; 0Þ þ cð0; 0; y3 Þ cðy1 ; y2 ; y3 ÞÞ : cðy1 ; y2 ; y3 Þ
If the estimated value is less than zero, firms experience diseconomies of scope, whereas, if it is greater than zero, firms experience economies of scope. That is, output combinations satisfying Eq. (6) > 0 enjoy cost complementarities or jointness in their production. Even though the translog cost function is the most frequently used one due to ease of estimation and reliability of the estimated results, this function has a weakness in that it cannot explain the case where the value of output is zero (Christensen et al., 1973; Denny and Pinto, 1978). Therefore, we need an approximation in estimating the SCei; that is, when we calculate SCie , the smallest output in each sample is used instead of zero, following Goldberg et al. (1991).
4. Research method 4.1. Data sources and number of observations The equation we need to estimate includes the total cost variable (TC), output variables (yi ), and input factor prices (wj ). The data are taken from the ÔAnnual Business ReportÕ of each building firm formally published by the Korea Stock Exchange. All building firms registered to the Korea Stock Exchange have an obligation to report their business performance every year using a standard form that covers details of annual business.1 Even though housebuilding is classified within the construction business category according to the Korea Standardised Industry Classification, building firms usually tabulate the housebuilding output separately from the other construction output. The 3-year period 1993–95 for which all variables can be constructed was a stable one. Housebuilding during the period was about 600,000 dwellings per year, following the unstable mass construction period 1988–92 when ‘‘the construction programme for two million dwellings’’ occurred. The governmentÕs investment level in housing held constant at 7% during 1993–95. Housing prices also stabilised during 1993–95. Korea had experienced housing speculation in the late 1980s, with house prices decreasing after the beginning of the 1990s and then stabilising during the period of analysis. The 3-year period is not long enough to reflect all business conditions of building firms. Nonetheless, the period is regarded as a stable one relative to preceding years. Table 1 summarises the classification and number of firms in each size group. Sample firms used in this analysis are limited to those registered on the Korea Stock
1 The report includes company profile, capital increase, share ownership, officers and employees, major business, sales of major business, income statement, cost of goods produced, cash flow statement, statement of appropriation of retained earnings, stock price, key securities analysis and investment indices, financial analysis, and CPAÕs assessment.
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Table 1 Number of firms used for estimation of cost function Size of firms
Group
Classification
Small firms
Group I and Group II firms
Medium firms
Group III firms
Large firms
Group IV firms
Total sales < 45,577 million won 45,577 million won 6 Total sales < 126,000 million won 126,000 million won 6 Total sales < 300,000 million won 300,000 million won 6 Total sales
Number of firms
Total
55
71 75 201
Exchange. A pooled time-series/cross-sectional data was constructed. The total number of firms was originally 318. The sample of firms was initially divided into four groups based on average total sales quartile values. Due to missing variables for Groups I and II firms, especially in input factor prices, these two groups are combined into one group, representing small firms. Groups III and IV firms are classified as medium- and large-size firms, respectively. Consequently, 201 firms are included in the regression analysis. 4.2. Operational definitions of variables Table 2 summarises the operational definitions of the variables required for the estimation. Total cost (TC) includes all labour and real capital expenses, as well as the interest and financial expenses. Apart from housebuilding business, most of the Korean building firms are involved in other construction activities and other unrelated business. Outputs are categorised into three groups: ‘‘other construction,’’ housebuilding, and other business. As discussed above, building firmsÕ main business is either housebuilding or other construction, but they are also involved in other businesses. Some of them are Table 2 Operational definitions of variables Variables
Operational definition
Dependent variable
Total cost (TC)
All expenses allocated to output which has accrued in each year (all labour and real capital expenses as well as the interest and financial cost)
Output variables
y1: other construction y2: housebuilding y3: other business
Sales from other construction business Sales from housebuilding business Sales from other business
Input factor variables
w1: material factor price w2: labour factor price
Material expenses/total sales Labour expenses/number of full time employees Subcontracting expenses/total sales Other expenses/total sales
w3: subcontracting factor price w4: overhead factor price
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Y. Cho / Journal of Housing Economics 12 (2003) 337–355
involved in land development and sales, property management (rental and sale), while others are involved in unrelated business such as shopping centre development and rental, and restaurant business. These other activities are categorised as ‘‘other business.’’ We assume that economic output is best measured by the monetary value of revenues. Following other previous research (Murray and White, 1983; Sealey and Lindley, 1977), sales (revenue) for each product is used as a measure of output. Factor prices for four inputs are used: materials, labour, subcontracting, and other overhead. As shown in Table 2, input factor prices are obtained by dividing total input expense by number of full time employees for labour price, and by total sales for the other three input prices. Material and labour expenses are straightforward. Subcontracting is important: subcontracting expenses compose on average 30 and 50% of total expenses per housebuilding project (Cho, 2000). Overhead expense includes overhead expenditure in both the main office and building site, expenditure for leasing construction machinery or facilities, and expenditures such as interest and financial costs. The use of sales (revenue) as a measure of output could be problematic if market prices of input factors are systematically related to measures of output of building firms. However, this is not a problem since input prices are constructed by dividing by total sales or employment (Goldberg et al., 1991; Mitchell and Onvural, 1996; Murray and White, 1983; Sealey and Lindley, 1977). Table 3 gives summary statistics for the total cost, outputs, and input prices. All monetary values are discounted with the GNP deflator index (base 1993). 4.3. Estimation methods The translog cost function is estimated simultaneously with the cost share equations as a multiple regression system. In this case, current endogenous variables in Eq. (3) are used as regressors in other cost share equations (4). The seemingly unrelated regressions (SURs) method is used to estimate the system of equations since this method is useful when error terms are contemporaneously correlated across equations. The SUR estimation method uses the estimates of the covariance of residuals across equations in an attempt to improve the efficiency of estimates (Goldberg et al., 1991). Furthermore, we gain additional degrees of freedom by estimating the cost function and the derived cost share equations together as a multiple regression system, because the cost share equations do not introduce any additional unknown parameters into the estimation (SAS Institute, 1985). The system estimation method is more efficient than the single equation estimates generated by the cost function alone. The ÔSyslinÕ procedure in the SAS statistical programme was used.
5. Estimation results Estimation is carried out for the entire sample and by firm size category. The results are reported in Table 4. The model is fairly precisely estimated. About
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Table 3 Summary of major variables (unit: million won) Variables
Large
Medium
Small
Total
Dependent variable
Total cost
Mean Std. Deviation Maximum Minimum
839465.66 673616.14 3903057 283846
189194.39 49090.29 305280 110283
55723.37 37298.41 140378 926
243817.63 405696.91 3348763 61
Output variable
Other construction sales
Mean Std. Deviation Maximum Minimum Mean Std. Deviation Maximum Minimum Mean Std. Deviation Maximum Minimum
510959.63 550240.90 3527995 36163 225546.03 171938.94 829068 6723 94262.39 161295.20 885003 401
110271.71 53445.29 244930 1757 67112.39 47699.84 180179 320 12850.81 24726.76 121601 19
30934.50 31162.12 122532 201 21722.37 22619.10 100479 186 2369.46 6276.69 41286 37
171405.10 341416.06 3527995 201 84274.90 123510.63 829068 186 28091.03 90268.18 885003 19
Mean Std. Deviation Maximum Minimum Labour Mean expenses Std. Deviation Maximum Minimum Subcontracting Mean expenses Std. Deviation Maximum Minimum Overhead Mean expenses Std. Deviation Maximum Minimum
237500.52 217973.43 937642 45677 66333.34 62073.65 304112 16992 285820.92 243091.59 1558640 78940 86549.61 79151.84 341271 18711
51153.47 27884.89 146056 19690 16674.97 7726.43 41448 4176 71603.58 19513.04 116487 29508 20526.20 9716.57 57793 4348
17965.33 23494.13 193094 53 6481.78 5329.44 26087 25 23503.28 20317.23 133188 0 6793.11 7144.11 42930 51
90489.88 151965.74 937642 53 26564.45 42394.39 304112 25 112450.23 172924.65 1558640 0 33595.35 54973.50 341271 51
0.2747 0.1058 0.6647 0.0958 52.23 120.87 981.01 6.56 0.3588 0.0880 0.5356 0.1111 0.1035 0.0420 0.2992 0.0288
0.2659 0.1228 0.7608 0.1285 33.81 17.59 136.00 5.51 0.3869 0.0887 0.5515 0.2007 0.1059 0.0355 0.2310 0.0305
0.3157 0.3041 2.9166 0.0290 41.34 38.16 286.15 1.09 0.3835 0.1752 1.3202 0.0000 0.1090 0.0760 0.5463 0.0148
0.2904 0.2196 2.9166 0.0290 42.45 70.41 981.01 1.09 0.3773 0.1338 1.3202 0.0000 0.1066 0.0581 0.5463 0.0148
Housebuilding sales
Other business sales
Input factor variable
Material expenses
Unit price of Material unit input factor price
Mean Std. Deviation Maximum Minimum Labour unit Mean price Std. Deviation Maximum Minimum Subcontracting Mean unit price Std. Deviation Maximum Minimum Overhead unit Mean price Std. Deviation Maximum Minimum
a1 (other construction) a2 (housebuilding) a3 (other business)
h11 h12 h13 h22 h23 h33
Output
Cross product of output
Cross product of input factor prices
c11 c12 c13 c14 c22 c23 c24
(materials) (labour) (subcontracting) (overhead)
a0
Constant
Input factor prices b1 b2 b3 b4
Parameters
Variables
Table 4 Estimation translog cost functions
1.050 11.207 9.738 )3.684 35.534 )34.993 0.657 23.029 2.410 4.363 17.481 7.347 12.448 11.642 63.337 )4.204 )25.793 )40.716 2.036 0.988 )0.663
0.499 0.566 0.684 )0.112 0.168 )0.176 0.001 0.155 0.006 0.007 0.292 0.218 0.260 0.231 0.170 )0.011 )0.067 )0.093 0.009 0.003 )0.002
0.179 )0.003 )0.071 )0.104 0.009 0.006 )0.011
0.218 0.266 0.309 0.207
51.347 )0.947 )22.224 )35.121 1.761 1.653 )3.268
5.010 4.522 7.524 5.245
17.672 )10.439 )0.950 10.864 0.045 0.506
)1.557 2.396 0.884
)0.371 0.586 0.078 0.218 )0.145 )0.005 0.135 0.000 0.002
2.303
6.120
Parameter T value estimates
Parameter estimates
T value
Large firms
Total firms
0.171 0.003 )0.060 )0.113 )0.009 0.008 )0.001
0.461 )0.013 0.393 0.159
0.096 )0.195 )0.003 0.073 )0.011 0.007
43.109 0.609 )14.295 )30.750 )0.979 1.401 )0.261
11.051 )0.159 8.253 2.906
7.222 )9.456 )0.699 5.152 )2.446 3.431
4.312 5.377 1.379
)2.781
)10.702 1.477 1.855 0.129
T value
Parameter estimates
Medium firms
0.162 )0.014 )0.068 )0.081 )0.009 0.009 0.013
0.331 0.531 0.091 0.048
0.127 )0.199 )0.006 0.161 0.002 0.003
1.257 0.930 0.035
)4.969
Parameter estimates
Small firms
31.590 )2.799 )14.871 )18.801 )0.865 1.398 1.980
6.154 5.239 1.402 0.659
6.310 )11.964 )0.754 6.788 0.168 0.514
4.506 2.856 0.276
)1.781
T value
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0.002 0.014
)5.123 0.295 2.601 )1.972 )0.038 9.127 )7.688
)0.013 0.001 0.004 )0.001 0.000 0.008 )0.007
Adjusted R2
d31 (other business/ materials) d32 (other business/labour) d33 (other business/ subcontracting) d34 (other business/ overhead) 0.98
)0.006
5.395
0.008
d21 (housebuilding/ materials) d22 (housebuilding/labour) d23 (housebuilding/ subcontracting) d24 (housebuilding/ overhead)
)0.010
0.007
)0.012 )0.001
0.97
)9.481
1.352 12.661
)4.900
3.208
)3.506 )0.340
2.135
4.678
0.011
4.766 0.005
2.632 )1.633 )5.010
0.007 )0.006 )0.012
)2.868 0.131 )2.364
d11 (construction/materials) )0.004 0.000 d12 (construction/labour) d13 (construction/ )0.004 subcontracting) d14 (construction/overhead) 0.007
27.821 )19.426 37.552
Statistically significant from zero at the 5% level of significance on a two-tailed test. Statistically significant from zero at the 1% level of significance on a two-tailed test.
**
*
Cross products of output and input factor prices
0.147 )0.081 0.196
37.829 )34.364 54.728
0.159 )0.096 0.191
c33 c34 c44
)0.004
0.001 0.005
)0.002
0.007
)0.008 )0.001
0.002
0.007
)0.015 0.021 )0.013
0.154 )0.102 0.217
0.96
)3.542
0.803 5.447
)2.990
2.661
)2.025 )0.305
0.862
1.927
)4.996 3.515 )4.132
19.692 )22.005 39.663
)0.003
)0.006 0.008
0.001
0.013
)0.028 0.006
0.009
0.010
)0.010 )0.006 0.007
0.168 )0.110 0.177
0.96
)1.207
)1.930 3.667
0.776
2.486
)3.748 1.178
2.272
2.516
)3.422 )1.166 1.945
24.753 )23.220 26.955
Y. Cho / Journal of Housing Economics 12 (2003) 337–355 349
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Table 5 AllenÕs own substitution elasticities of each input factor
Material factor Labour factor Subcontracting factor Overhead factor
Total firms
Large firms
Medium firms
Small firms
)0.0989 )0.8037 )0.1160 )0.1105
)0.0747 )0.8126 )0.1692 )0.1018
)0.0868 )0.9662 )0.1264 )0.0501
)0.1322 )0.9580 )0.0935 )0.1438
two-thirds of the 36 coefficient estimates are statistically significant at the 0.01 level, and adjusted R2 values are high. In order to examine whether the estimated cost function shows an adequate cost structure or not, we investigated AllenÕs own substitution elasticities (Diewert and Wales, 1987; Guilkey et al., 1983). The elasticities can be calculated as below: rii ¼ cii =SHi 1; where cii is the estimated coefficient of ith input price and SHi is the average share ratio of ith factor in the cost function. The elasticities must be estimated as negative to satisfy the condition. The substitution elasticities by group shown in Table 5 are negative for all groups. Therefore, we may consider that the cost functions are estimated adequately and can use the coefficients of this cost function to derive the efficiency measures. 5.1. Economies of scale Based on the coefficients estimated from Eq. (3), economies of scale can be obtained as expressed in Eq. (5). Table 6 summarises the results. In all cases, the estimated standard errors are very small, indicating precise coefficient estimates. For the total sample, the measure of economies of scale is 0.98. As this value is close to one, we can interpret it as constant returns to scale. However, firms in the total sample vary greatly in size, creating interest in separate estimation for the three size groups. In fact, this estimation yields results that vary by firm size class. As shown in Table 6, medium-size firms, with an economies of scale measure of 0.86, appear to enjoy increasing returns to scale. Large- and small-size firms have values of 0.97 and 0.94, respectively, leaving them closer to constant returns to scale. This suggests that Table 6 Economies of scale and economies of scope
Number of firms Average total sales (million won) Economies of scale (Se ) Economies of scope (SCe )
Total firms
Large firms
Medium firms
Small Firms
201 267,452
71 788,505
75 179,075
55 51,426
0.98 (0.002) 1.49 (0.005)
0.97 (0.006) 1.71 (0.005)
0.86 (0.014) 1.30 (0.007)
0.94 (0.013) 1.33 (0.009)
( ), standard error; Se < 1, increasing returns to scale; Se ¼ 1, constant returns to scale; Se > 1, decreasing returns to scale; SCe < 0, diseconomies of scope; SCe > 0, economies of scope.
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under the current cost structure, extending business size is most cost efficient for medium-size firms whose total sales fall in the 126,000–300,000 million won range. The advantage of expansion for large firms appears to be negligible. 5.2. Economies of scope Table 6 also shows that the results for economies of scope. For every group of firms, economies of scope are estimated as being greater than zero. Economies of scope for total firms is estimated to be 1.49. Economies of scope are somewhat lower for small- (1.33) and medium-size firms (1.30). However, large firms show higher scope economies (1.71). Diversifying into other businesses-related or unrelated- is cost efficient for all size categories of building firms in the current cost structure, and especially so for large firms. If Korean building firms operate more than one business besides housebuilding, the total cost is lower than that when individual firms operate businesses, i.e., housebuilding, other construction, and other business, separately. A single firm can operate the three groups of different businesses at a lower cost than the aggregated cost of other firms which specialised and attempted to operate the businesses individually. 5.3. Optimum size of business The estimated economies of scale differ by firm size category. Medium-size firms exhibit the greatest increasing returns to scale, whereas large firms are very close to constant returns to scale. This suggests that there may be an optimum range of firm size where economies of scale are enjoyed but diminish as firm size increases. Figs. 1–3 provide further detail on patterns in economies of scale and economies of scope by size of firm. For small firms, increasing returns to scale do not become apparent until total sales reach about 50,000 million won (Fig. 1). This is a reasonable result: firms typically need to reach a certain critical size before significant increasing returns occur. A firm with sales less than 50,000 million won is quite small. For medium-size firms, increasing returns generally continue, with the most pronounced increasing returns occurring for firms with sales of more than 175,000 million won (Fig. 2). Large firms (300,000+ million won), constant returns to scale have come to dominate (Fig. 3). Thus, the firm-size benefits in terms of economies of scale are largely exhausted by the time firms reach total sales of 300,000 million won—the low end of our large firm category. With respect to economies of scope, Figs. 1–3 reflect the firm-size category results presented above. Economies of scope are fairly constant for the small- and mediumsize firms, and considerably higher for the large firms. It has been shown that there is no specific relationship between economies of scale and economies of scope, and that scale and scope economies can exist independently or simultaneously (Panzar and Willig, 1981). In Figs. 1–3, we observe the existence of economies of scope at all firm sizes, with larger economies of scope accruing to the larger firms. Increasing returns to scale, however, are found mainly in the sales range
352
Y. Cho / Journal of Housing Economics 12 (2003) 337–355
Fig. 1. Scale and scope economies in small firms.
Fig. 2. Scale and scope economies in medium firms.
of 50,000 to 300,000 million won. At roughly 300,000 million won, the advantages of scale economies disappear, while economies of scope become distinctly greater. In comparing economies of scale with economies of scope, it is the medium-size group of firms that deserves the most attention because they do well by both measures. Even though scope economies of the large firms are higher than those of the medium firms, the results suggest that the medium group of firms is operating the multi-product business rather efficiently.
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Fig. 3. Scale and scope economies in large firms.
6. Findings and discussion Research on diversification has been actively carried out since the 1970s, as diversified business groups increasingly dominated private-sector industrial and service activity in many of the worldÕs economies. Much research has focused on the nature and efficiency of diversification at business group level. In Korea, several studies have examined the efficiency of diversified business groups since the mid-1980s. However, there has been little investigation of the efficiency of the multi-product structure at the firm level. The present study is the first to investigate whether or not building firmsÕ multi-product structure that evolved during the rapid growth period is cost efficient. The empirical results presented here are consistent with cost efficiency, and we conclude that Korean housebuilding firms can achieve cost efficiency from the multi-product structure. Korean firms exhibit increasing returns to scale over an important range of firm sizes. However, economies of scale do not provide a sufficient raison d0^etre for diversified building firms. We suggest that one factor driving the diversification of Korean building firms into other business is economies of scope. If positive scope economies did not exist, the multi-product building firms would do better if broken up into several specialised firms without any increase in cost. The economies of scope provide the incentive for firms to expand the range of their businesses. The sharing of industry technological knowledge across building work would appear to be a strong motive for diversification between housebuilding and other construction activities. The estimated scope economies may be used as information for firmsÕ decisions to further diversify.
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The estimates have important implications. First, the Korean governmentÕs policy to encourage large construction firms to participate in the housebuilding industry is well founded. Cost efficiency may have contributed to the high and rapid growth of the housebuilding industry in the 1980s and 1990s. Second, taking into consideration the fact that most of the Korean building firms are diversified into various related and unrelated businesses, these results suggest that the diversification of Korean housebuilding firms is a cost efficient strategy. Third, the results presented here suggest that a very large scale is not necessarily optimal. The medium-size firms achieve significant scale economies as well as scope economies, while the large firms do not enjoy increasing returns to scale even though they are achieving greater economies of scope. These results also suggest that the medium-size firms have some efficiency advantages over the large firms. The large firms exhibit quite a substantial difference in business scale from that of the medium and small firms. The average size of the large firms (790,000 million won) is about four times greater than that of medium-size firms (180,000 million won). The results suggest that the current scale of Korean housebuilding firms may be larger than is optimal. More clearly, they also suggest that the large firms should consider other approaches rather than simply further expansion of business scale. The Korean housebuilding industry has recently experienced another re-structuring process, as part of the Korean economyÕs experience of tremendous structural change along with the Asian Financial Crisis at the end 1990s (Ministry of Construction and Transportation, 1995). Several large building firms went bankrupt, some of which survived and have since grown further. Further research is needed on these successful building firms in terms of their nature, business scale, and strategy.
References Ball, M., 1983. Housing Policy and Economic Power: The Political Economy of Owner Occupation. Methuen, London. Ball, M., 1988. Rebuilding Construction: Economic Change and British Construction Industry. Routledge, London. Ball, M., 1996. Investing in New Housing: Lessons for the Future. The Policy Press, Bristol. Ball, M., Harloe, M., Martens, M., 1988. Housing and Social Change in Europe and the USA. Routledge, London. Baumol, W.J., Panzar, J.C., Willig, R.D., 1982. Contestable Markets and the Theory of Industry Structure. Harcourt Brace Jovanovich, New York. Cho, Y., 2000. The Korean Housebuilding Industry: Aspects of Growth, Efficiency and Diversification, 1980–1995. LSE Ph.D. Dissertation. Christensen, L.R., Jorgensen, D.W., Lau, L.J., 1973. Transcendental logarithmic production frontiers. Rev. Econ. Statist. 55, 28–45. Cough, C., 1988. Aspect of structural change in speculative housing production: a case study in merseyside. Environ. Planning A 20 (10), 1385–1396. Denny, M., Pinto, C., 1978. An aggregate model with multi-product technologies. In: Fuss, M., MacFadden, D., (Eds.), Production Economies: A Dual Approach to Theory and Applications. North Holland, Amsterdam.
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Diewert, W.E., 1971. An application of Shephard duality theorem: a generalized Leontief production function. J. Polit. Economy 79, 481–507. Diewert, W.E., Wales, T.J., 1987. Flexible functional forms and global curvative conditions. Econometrica 55, 43–68. Gillies, J., Mittelbach, F., 1962. Management in the Construction Industry: A Study of Contractors in Southern California. University of California Press, Berkeley and Los Angeles. Goldberg, G., Hanweck, A., Keenan, M., Young, A., 1991. Economies of scale and scope in the securities industry. J. Banking Finance 15, 91–107. Grebler, L., 1973. Large Scale Housing and Real Estate Firms. Praeger, New York. Guilkey, D.K., Lovell, C.A.K., Sickles, R.C., 1983. A comparison of the performance of three flexible functional forms. Int. Econ. Rev. 24, 591–616. Hasegawa, F., Shimizu Group, 1988. Built by Japan: Competitive Strategies of the Japanese Construction Industry. Wiley, New York. Kim, J., Park, J., 1996. A Study on the Korean Housebuilding Industry, Seoul, Korea. Korea Research Institute for Human Settlement. Lambert, C., 1990. New Housebuilding and the Development Industry in the Bristol Area, Working Paper 86, School for Advanced Urban Studies, University of Bristol, Bristol. Hillebrandt, P., Cannon, J. (Eds.), 1990. Modern Construction Firms. Macmillan Press, London. Mester, L.J., 1987. Efficient production of financial services: scale and scope economies, Federal Reserve Bank of Philadelphia. Bus. Rev. (Jan/Feb), 15–25. Ministry of Construction and Transportation, 1995. An Assessment of Korea Housing Policy and Future Policy Direction, Seoul, Korea. Mitchell, K., Onvural, N., 1996. Economies of scale and scope at large commercial banks evidence from the fourier flexible functional form. J. Money, Credit, Banking 28 (2), 178–199. Mullineaux, D.J., 1978. Economies of scale and organizational efficiency in banking: a profit function approach. J. Finance 33, 317–330. Murray, J.D., White, R.W., 1983. Economies of scale and economies of scope in multi product financial institutions: a study of British Columbia credit unions. J. Finance 38, 887–902. Panzar, J.C., Willig, R.D., 1977. Economies of scale in multi-output production. Quart. J. Econ. (Aug), 481–493. Panzar, J.C., Willig, R.D., 1981. Economies of scope. Amer. Econ. Rev. 7 (2), 268–272. SAS Institute Inc., 1985. SAS/STAT Guide for Personal Computers, Version 6 Edition. Sealey, C., Lindley, J., 1977. Input, outputs, and a theory of production and cost at depository financial institution. J. Finance 32, 1256–1266. Teece, D., 1980. Economics of scope and the scope of the enterprise. J. Econ. Behav. Organ. 1, 223–247. Teece, D., 1982. Towards an economic theory of the multiproduct firm. J. Econ. Behav. Organ. 3, 39–63.
Journal of Housing Economics 12 (2003) 337–355
HOUSING ECONOMICS www.elsevier.com/locate/jhe
Economic efficiency of multi-product structure: the evidence from Korean housebuilding firmsq Youngha Cho* Department of Land Economy, Cambridge Centre for Housing and Planning Research, University of Cambridge, 19 Silver Street, Cambridge CB3 9EP, UK Received 13 June 2002
Abstract The Korean housebuilding industry has been subject to structural changes since the 1980s. One of the key features is that housebuilding firms have become diversified into a range of businesses and as a result display multi-product structure. This paper examines the efficiency of the multi-product structure of Korean housebuilding firms. For the analysis, translog cost functions were estimated using data for 201 building firms for the 3 years 1993–1995. The empirical results indicate that medium-size building firms enjoy increasing returns to scale, whereas large firms experience constant returns to scale. Korean building firms exhibit significant economies of scope in their diversification activities. Large firms have the greatest economies of scope. These results are consistent with cost efficiency for the multi-product structure of Korean housebuilding firms. The estimated optimum scale suggests that many large firms should expand only through diversification. Ó 2003 Elsevier Inc. All rights reserved. JEL classification: D21; L23; L74 Keywords: Multi-product structure; Economies of scale; Economies of scope; Optimum scale of business; Housebuilding industry
q I thank Christine Whitehead, Diane Reyniers, and two anonymous referees for comments on an earlier version. I have greatly benefited from the helpful suggestions of the editor Henry Pollakowski. * Fax: +1223-330863. E-mail address: [email protected] (Y. Cho).
1051-1377/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.jhe.2003.09.003
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Y. Cho / Journal of Housing Economics 12 (2003) 337–355
1. Introduction The Korean housebuilding industry has undergone steady growth concurrently with general economic development since the 1970s. The industry has grown particularly rapidly since the mid-1980s and has experienced significant structural changes. Approximately 70% of new construction has been built by the private sector since the mid-1980s. Most of the private output has been produced by large-scale firms that the Korean government certified, and not by small-scale housebuilders which had dominated the industry before the 1980s. In addition, apartment houses comprise 70–80% of total new construction, whereas the single detached house was the most popular type until the beginning of the 1980s. Another important feature is that housebuilding firms have diversified by extending into a range of businesses unrelated to their own industry (Kim and Park, 1996). Even small firms which have recently entered the business are involved in various other businesses. The emergence of large firms in the housebuilding industry since the 1970s is not confined to Korea and is found in other countries as well (Ball, 1996; Ball et al., 1988; Cough, 1988; Grebler, 1973; Lambert, 1990). Housebuilding firms in industrialised countries have begun to involve themselves in various businesses through the diversification strategy since the 1970s (Ball, 1983, 1988; Gillies and Mittelbach, 1962; Hasegawa and Shimizu Group, 1988; Hillebrandt and Cannon, 1990). Kim and Park (1996) observe that most of the active housebuilding firms are carrying out more than one business besides housebuilding. Their main business is either housebuilding or other construction, but they are also involved in other businesses such as land development, property management (rental and sale), and other unrelated business (such as shopping centre development and rental, and restaurant business). There are distinctive differences among different sized firms. Large firms are mainly those that started business in other construction and have emerged into housebuilding business since the 1980s. They are very large scale in terms of numbers of employees, total sales, and capital. Typically, medium and small firms are those which started their business in housebuilding as speculative housebuilders. Cho (2000) found that when we consider only direct production costs, housebuilding is more profitable than the ‘‘other construction’’ activities. However, large firms return relatively higher profits than small- and medium-sized firms, which are more involved in the profitable housebuilding business. One possible reason is that small firms incur relatively higher overhead costs, including interest and other financial costs. This suggests that large firms may be achieving economic efficiency from the large-scale, multi-activity nature of their business. This paper examines the economic efficiency of the diversified product structure of Korean housebuilding firms. The plan of this paper is as follows: Section 2 reviews the implications of the economies of scale and economies of scope in the housebuilding industry. Section 3 introduces the form of the model for estimating the cost function of multi-product firms. Economies of scale and economies of scope are derived from the function. Section 4 outlines the variables to be included in the model, data sources, number of observations, and the estimation method. Section 5 contains the estimation results which address whether or not the multi-product structure is
Y. Cho / Journal of Housing Economics 12 (2003) 337–355
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economically efficient. Optimum scales of firmsÕ business are also derived from the results. Section 6 contains a summary and discussion.
2. Economies of scale and economies of scope: the implications The relationship between average costs and output can be explained by the relation between physical quantities of inputs and outputs summarised in the production function. At given factor prices, some firms use more inputs, whereas others use fewer inputs per unit of output, as output rises. This is a function of the technology and production techniques employed. We assume that economies of scale exist when long-run average costs decrease as output rises in the fixed product mix. In this definition, scale refers to the size of the business as measured by its output. If a specific industry is observed as having increasing returns to scale, firms can increase cost efficiency through the extension of the businessÕs size. In addition to economies of scale, cost savings may result from simultaneous production of several different outputs in a single firm. We observe that Korean housebuilding firms rarely engage in extreme specialisation. Instead, firms in different size categories appear to specialise in different output compositions. Diversification into new products is generally explained to be the main engine of corporate growth (Teece, 1982). In order to grow faster than the rate of growth of the markets in which a firm has established itself, it must carry out further successful diversification. However, there are obviously significant costs attached to diversification that can reduce rate of return on capital. How then does diversification arise successfully? One way of reducing diversification costs is the sharing of inputs (Mester, 1987; Teece, 1980). The extent to which housebuilding technology is relevant to the production of alternate businesses (other construction activity or property management) may be an example of the joint utilisation of inputs. In housebuilding, common utilisation of existing human resources and building facilities such as building equipment, knowledge of the contracting system used in the construction business, and market and customer information are important sources that can lower the average costs of the multi-product firms. Hence, the relevant question is whether lower operating costs result from joint production of an output bundle for a large firm, whose output bundle is representative for its size category, compared with specialised production of the same total output bundle by two smaller firms. This is an issue of economies of scope as well as economies of scale.
3. Estimating the cost function of multi-product firms It is necessary to estimate the production function in order to analyse the efficiency of production behaviour in a specific firm or industry. In an empirical analysis, however, it is difficult to estimate the production function because our data do
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not permit estimates of prices or their proxies calculated as revenue divided by the number of units of output (Mullineaux, 1978). Consequently, under the hypothesis that the production function is homogeneous, the cost function is estimated instead, using Samuelson–Shephard Duality Theorem (Diewert, 1971). The cost function shows the relationship between input prices and output assuming that firms produce a single product. Multi-product cost theory has been developed by Baumol et al. (1982). The estimation of economies of scale and economies of scope that they have developed have been widely used in the study of the efficiency of multi-product firms. 3.1. General form of translog cost function In a multi-product environment, the single product scale economy measure has an analogous measure in the concept of ray scale economies. Ray scale economies are defined as the proportional effect on cost of a scale expansion along a ray in multi-product-cost space, holding constant the relative proportions of the outputs (Goldberg et al., 1991). To analyse the efficiency of the production structure, we can use Cobb–Douglas, CES or translog cost functions. Although Cobb–Douglas and CES functions are convenient specifications for the purposes of modelling and estimation, they are incapable of generating anything other than smooth, monotonically increasing or decreasing average cost curves. Returns to scale are forced to remain constant across all output levels and may therefore present an inaccurate picture of the production/cost relationships. The translog cost function avoids such pitfalls, as it allows us to enter the various outputs as separate variables, and does not force the assumptions of homogeneity and constant elasticity of substitution (Murray and White, 1983). In its most general form, the translog function provides a second-order approximation to any twice-differentiable function. The production technology of a multiproduct housebuilding firm can therefore be modelled with maximum flexibility, giving explicit recognition to each of the outputs. Provided certain regularity conditions and behavioural assumptions are met, one can obtain a complete representation of the underlying technology simply by analysing the structure of the related cost function. The optimised cost function is defined with output quantity and input factor prices. This function, especially, shows the proportional effect of the relationship between various input prices and outputs on total cost, according to output expansion. On the basis of a homogeneous production function, the translog cost function is essentially a Taylor series expansion in output quantities and input prices (Diewert, 1971). The function can be written as follows: logTC ¼ a0 þ
n X i¼1
ai ðlog yi Þ þ
n X n n X 1X hi;k ðlog yi Þðlog yk Þ þ bj ðlog wj Þ 2 i k j¼1
m X m n X m X 1X cj;h ðlog wj Þðlog wh Þ þ di;j ðlog yi Þðlog wj Þ; þ 2 j h i j
ð1Þ
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341
where TC is the total cost, yi is the output of ith product, i ¼ 1; 2; 3; . . . ; n, and wj is the price of jth input factor j ¼ 1; 2; 3; . . . ; m. Basic assumptions of the cost function, in Eq. (1), are first, the function should be linearly homogeneous in all input prices; second, it should be concave in price of input factors (wj ); and third, output (yi ) and price of input factors (wj .) should increase. The linearly homogeneity condition is satisfied when: (i)
n X
bj ¼ 1;
j¼1
(ii)
m X
cj;h ¼ 0
j ¼ 1; . . . ; m;
h¼1
(iii)
m X
di;j ¼ 0 i ¼ 1; . . . ; n;
j¼1
and symmetry conditions are as follows: (iv) hi;k ¼ hk;i cj;h ¼ ch;j
i; k ¼ 1; 2; . . . ; n; j; k ¼ 1; 2; . . . ; m:
Eq. (1) is quadratic in logarithms and linear in the unknown parameters, permitting ease of estimation. This cost function may be estimated alone; alternatively, factor share equations can be derived using ShephardÕs lemma, and the system of equations can be estimated simultaneously (Murray and White, 1983). When we estimate Eq. (1) alone under the restrictions of the OLS method, OLS provides a simple means of deriving unbiased estimates. However, it fails to incorporate extra information which might be extracted from a restricted system of cost equations (Goldberg et al., 1991). For this reason, it is deemed desirable to estimate the single cost equation and a set of cost share equations simultaneously. A system of cost share equations can be derived directly from the translog cost function by differentiating Eq. (1) with respect to wj . SHj ¼
m n X X logTC ¼ bj þ cj;h ðlog Wh Þ þ dij ðlog yi Þ; log Wj h¼1 i¼1
ð2Þ
where SHj is the cost share on the jth input factor in total cost. Because of the restriction of linear homogeneity in input prices, the factor share equations must sum to one to avoid singularity problems. One of the share equations must be excluded from the estimation process. Christensen et al. (1973) explain that the parameter estimates are invariant with respect to which equation is excluded from the estimated system. By estimating the cost function and the derived cost share equations together as a multivariate regression system, we gain additional degrees of freedom. It is known that the system estimates should be more efficient than the single equation estimates generated by the cost function alone, since the cost share equations do not
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introduce any additional unknown parameters into the estimation (SAS Institute, 1985). 3.2. Modelling for estimation The specific equations to be estimated are described as follows. Eq. (3) includes the total cost variable (TC), output variables (yi ) and input factor prices (wj ). Korean building firms produce three outputs: other construction (y1 ), housebuilding (y2 ), and other business (y3 ). Input factorsÕ prices are used for materials (w1 ), labour (w2 ), subcontracting (w3 ), and overhead (w4 ) (capital). The equation to be estimated consists of a total of 36 coefficients and can be expressed as follows: 1 2 logTC ¼ a0 þ a1 log y1 þ a2 log y2 þ a3 log y3 þ h11 ðlog y1 Þ þ h12 log y1 log y2 2 1 1 2 2 þ h13 log y1 log y3 þ h22 ðlog y2 Þ þ h23 log y2 log y3 þ h33 ðlog y3 Þ 2 2 1 2 þ b1 log w1 þ b2 log w2 þ b3 log w3 þ b4 log w4 þ c11 ðlog w1 Þ 2 þ c12 log w1 log w2 þ c13 log w1 log w3 þ c14 log w1 log w4 1 1 2 2 þ c22 ðlog w2 Þ þ c23 log w2 log w3 þ c24 log w2 log w4 þ c33 ðlog w3 Þ 2 2 1 2 þ c34 log w3 log w4 þ c44 ðlog w4 Þ þ d11 log y1 log w1 2 þ d12 log y1 log w2 þ d13 log y1 log w3 þ d14 log y1 log w4 þ d21 log y2 log w1 þ d22 log y2 log w2 þ d23 log y2 log w3 þ d24 log y2 log w4 þ d31 log y3 log w1 þ d32 log y3 log w2 þ d33 log y3 log w3 þ d34 log y3 log w4 :
ð3Þ
Cost share equations to be estimated are expressed as follows: SH1 ¼ b1 þ c11 log w1 þ c12 log w2 þ c13 log w3 þ c14 log w4 þ d11 log y1 þ d21 log y2 þ d31 log y3 ; SH2 ¼ b2 þ c21 log w1 þ c22 log w2 þ c23 log w3 þ c24 log w4 þ d12 log y1 þ d22 log y2 þ d32 log y3 ;
ð4Þ
SH3 ¼ b3 þ c31 log w1 þ c32 log w2 þ c33 log w3 þ c34 log w4 þ d13 log y1 þ d23 þ log y2 þ d33 log y3 ; SH4 ¼ 1 ðSH1 þ SH2 þ SH3 Þ: As one of the share equations has to be excluded in the estimation process, the single cost function equation and three cost share equations are to be estimated simultaneously.
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The restrictions given to the cost function are expressed as follows: b1 þ b2 þ b3 þ b4 ¼ 1; c11 þ c21 þ c31 þ c41 ¼ 0; c12 þ c22 þ c32 þ c42 ¼ 0; c13 þ c23 þ c33 þ c43 ¼ 0; c14 þ c24 þ c34 þ c44 ¼ 0; d11 þ d12 þ d13 þ d14 ¼ 0; d21 þ d22 þ d23 þ d24 ¼ 0; d31 þ d32 þ d33 þ d34 ¼ 0; d41 þ d42 þ d43 þ d44 ¼ 0: 3.3. Estimation of economies of scale and economies of scope Once the translog cost function is estimated using the above Eqs. (3) and (4), we can derive various efficiency measures. 3.3.1. Economies of scale Economies of scale are obtained by differentiating Eq. (3) with respect to all yi (Murray and White, 1983). Se ¼ ¼
n n X oCðyi Þ yi X o logCðyÞ ¼ o logyi oyi CðyÞ i¼1 i¼1 n X i¼1
ai þ
n X n X i¼1
k¼1
hi;k ðlog yk Þ þ
n X m X i
di;j ðlog wj Þ:
ð5Þ
j
If Se is greater than one, firms will experience decreasing returns to scale, as costs rise proportionately more than output. When Se equals one, this indicates constant returns to scale. When Se is less than one, this indicates increasing returns to scale. 3.3.2. Economies of scope Panzar and Willig (1977) have shown that a multi-product cost function exhibits economies of scope as follows: Pn Cðyi Þ CðyÞ ; ð6Þ SCe ¼ i¼1 CðyÞ where Eq. (6) is calculated using the estimated value from the cost function in Eq. (3). Cðyi Þ denotes the cost incurred when a firm produces only yi . CðyÞ refers to the cost incurred when the firm produces all products. Eq. (6) can be rewritten specifically when the firms produce three outputs as follows:
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SCe ¼
ðcðy1; 0; 0Þ þ cð0; y2 ; 0Þ þ cð0; 0; y3 Þ cðy1 ; y2 ; y3 ÞÞ : cðy1 ; y2 ; y3 Þ
If the estimated value is less than zero, firms experience diseconomies of scope, whereas, if it is greater than zero, firms experience economies of scope. That is, output combinations satisfying Eq. (6) > 0 enjoy cost complementarities or jointness in their production. Even though the translog cost function is the most frequently used one due to ease of estimation and reliability of the estimated results, this function has a weakness in that it cannot explain the case where the value of output is zero (Christensen et al., 1973; Denny and Pinto, 1978). Therefore, we need an approximation in estimating the SCei; that is, when we calculate SCie , the smallest output in each sample is used instead of zero, following Goldberg et al. (1991).
4. Research method 4.1. Data sources and number of observations The equation we need to estimate includes the total cost variable (TC), output variables (yi ), and input factor prices (wj ). The data are taken from the ÔAnnual Business ReportÕ of each building firm formally published by the Korea Stock Exchange. All building firms registered to the Korea Stock Exchange have an obligation to report their business performance every year using a standard form that covers details of annual business.1 Even though housebuilding is classified within the construction business category according to the Korea Standardised Industry Classification, building firms usually tabulate the housebuilding output separately from the other construction output. The 3-year period 1993–95 for which all variables can be constructed was a stable one. Housebuilding during the period was about 600,000 dwellings per year, following the unstable mass construction period 1988–92 when ‘‘the construction programme for two million dwellings’’ occurred. The governmentÕs investment level in housing held constant at 7% during 1993–95. Housing prices also stabilised during 1993–95. Korea had experienced housing speculation in the late 1980s, with house prices decreasing after the beginning of the 1990s and then stabilising during the period of analysis. The 3-year period is not long enough to reflect all business conditions of building firms. Nonetheless, the period is regarded as a stable one relative to preceding years. Table 1 summarises the classification and number of firms in each size group. Sample firms used in this analysis are limited to those registered on the Korea Stock
1 The report includes company profile, capital increase, share ownership, officers and employees, major business, sales of major business, income statement, cost of goods produced, cash flow statement, statement of appropriation of retained earnings, stock price, key securities analysis and investment indices, financial analysis, and CPAÕs assessment.
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Table 1 Number of firms used for estimation of cost function Size of firms
Group
Classification
Small firms
Group I and Group II firms
Medium firms
Group III firms
Large firms
Group IV firms
Total sales < 45,577 million won 45,577 million won 6 Total sales < 126,000 million won 126,000 million won 6 Total sales < 300,000 million won 300,000 million won 6 Total sales
Number of firms
Total
55
71 75 201
Exchange. A pooled time-series/cross-sectional data was constructed. The total number of firms was originally 318. The sample of firms was initially divided into four groups based on average total sales quartile values. Due to missing variables for Groups I and II firms, especially in input factor prices, these two groups are combined into one group, representing small firms. Groups III and IV firms are classified as medium- and large-size firms, respectively. Consequently, 201 firms are included in the regression analysis. 4.2. Operational definitions of variables Table 2 summarises the operational definitions of the variables required for the estimation. Total cost (TC) includes all labour and real capital expenses, as well as the interest and financial expenses. Apart from housebuilding business, most of the Korean building firms are involved in other construction activities and other unrelated business. Outputs are categorised into three groups: ‘‘other construction,’’ housebuilding, and other business. As discussed above, building firmsÕ main business is either housebuilding or other construction, but they are also involved in other businesses. Some of them are Table 2 Operational definitions of variables Variables
Operational definition
Dependent variable
Total cost (TC)
All expenses allocated to output which has accrued in each year (all labour and real capital expenses as well as the interest and financial cost)
Output variables
y1: other construction y2: housebuilding y3: other business
Sales from other construction business Sales from housebuilding business Sales from other business
Input factor variables
w1: material factor price w2: labour factor price
Material expenses/total sales Labour expenses/number of full time employees Subcontracting expenses/total sales Other expenses/total sales
w3: subcontracting factor price w4: overhead factor price
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involved in land development and sales, property management (rental and sale), while others are involved in unrelated business such as shopping centre development and rental, and restaurant business. These other activities are categorised as ‘‘other business.’’ We assume that economic output is best measured by the monetary value of revenues. Following other previous research (Murray and White, 1983; Sealey and Lindley, 1977), sales (revenue) for each product is used as a measure of output. Factor prices for four inputs are used: materials, labour, subcontracting, and other overhead. As shown in Table 2, input factor prices are obtained by dividing total input expense by number of full time employees for labour price, and by total sales for the other three input prices. Material and labour expenses are straightforward. Subcontracting is important: subcontracting expenses compose on average 30 and 50% of total expenses per housebuilding project (Cho, 2000). Overhead expense includes overhead expenditure in both the main office and building site, expenditure for leasing construction machinery or facilities, and expenditures such as interest and financial costs. The use of sales (revenue) as a measure of output could be problematic if market prices of input factors are systematically related to measures of output of building firms. However, this is not a problem since input prices are constructed by dividing by total sales or employment (Goldberg et al., 1991; Mitchell and Onvural, 1996; Murray and White, 1983; Sealey and Lindley, 1977). Table 3 gives summary statistics for the total cost, outputs, and input prices. All monetary values are discounted with the GNP deflator index (base 1993). 4.3. Estimation methods The translog cost function is estimated simultaneously with the cost share equations as a multiple regression system. In this case, current endogenous variables in Eq. (3) are used as regressors in other cost share equations (4). The seemingly unrelated regressions (SURs) method is used to estimate the system of equations since this method is useful when error terms are contemporaneously correlated across equations. The SUR estimation method uses the estimates of the covariance of residuals across equations in an attempt to improve the efficiency of estimates (Goldberg et al., 1991). Furthermore, we gain additional degrees of freedom by estimating the cost function and the derived cost share equations together as a multiple regression system, because the cost share equations do not introduce any additional unknown parameters into the estimation (SAS Institute, 1985). The system estimation method is more efficient than the single equation estimates generated by the cost function alone. The ÔSyslinÕ procedure in the SAS statistical programme was used.
5. Estimation results Estimation is carried out for the entire sample and by firm size category. The results are reported in Table 4. The model is fairly precisely estimated. About
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Table 3 Summary of major variables (unit: million won) Variables
Large
Medium
Small
Total
Dependent variable
Total cost
Mean Std. Deviation Maximum Minimum
839465.66 673616.14 3903057 283846
189194.39 49090.29 305280 110283
55723.37 37298.41 140378 926
243817.63 405696.91 3348763 61
Output variable
Other construction sales
Mean Std. Deviation Maximum Minimum Mean Std. Deviation Maximum Minimum Mean Std. Deviation Maximum Minimum
510959.63 550240.90 3527995 36163 225546.03 171938.94 829068 6723 94262.39 161295.20 885003 401
110271.71 53445.29 244930 1757 67112.39 47699.84 180179 320 12850.81 24726.76 121601 19
30934.50 31162.12 122532 201 21722.37 22619.10 100479 186 2369.46 6276.69 41286 37
171405.10 341416.06 3527995 201 84274.90 123510.63 829068 186 28091.03 90268.18 885003 19
Mean Std. Deviation Maximum Minimum Labour Mean expenses Std. Deviation Maximum Minimum Subcontracting Mean expenses Std. Deviation Maximum Minimum Overhead Mean expenses Std. Deviation Maximum Minimum
237500.52 217973.43 937642 45677 66333.34 62073.65 304112 16992 285820.92 243091.59 1558640 78940 86549.61 79151.84 341271 18711
51153.47 27884.89 146056 19690 16674.97 7726.43 41448 4176 71603.58 19513.04 116487 29508 20526.20 9716.57 57793 4348
17965.33 23494.13 193094 53 6481.78 5329.44 26087 25 23503.28 20317.23 133188 0 6793.11 7144.11 42930 51
90489.88 151965.74 937642 53 26564.45 42394.39 304112 25 112450.23 172924.65 1558640 0 33595.35 54973.50 341271 51
0.2747 0.1058 0.6647 0.0958 52.23 120.87 981.01 6.56 0.3588 0.0880 0.5356 0.1111 0.1035 0.0420 0.2992 0.0288
0.2659 0.1228 0.7608 0.1285 33.81 17.59 136.00 5.51 0.3869 0.0887 0.5515 0.2007 0.1059 0.0355 0.2310 0.0305
0.3157 0.3041 2.9166 0.0290 41.34 38.16 286.15 1.09 0.3835 0.1752 1.3202 0.0000 0.1090 0.0760 0.5463 0.0148
0.2904 0.2196 2.9166 0.0290 42.45 70.41 981.01 1.09 0.3773 0.1338 1.3202 0.0000 0.1066 0.0581 0.5463 0.0148
Housebuilding sales
Other business sales
Input factor variable
Material expenses
Unit price of Material unit input factor price
Mean Std. Deviation Maximum Minimum Labour unit Mean price Std. Deviation Maximum Minimum Subcontracting Mean unit price Std. Deviation Maximum Minimum Overhead unit Mean price Std. Deviation Maximum Minimum
a1 (other construction) a2 (housebuilding) a3 (other business)
h11 h12 h13 h22 h23 h33
Output
Cross product of output
Cross product of input factor prices
c11 c12 c13 c14 c22 c23 c24
(materials) (labour) (subcontracting) (overhead)
a0
Constant
Input factor prices b1 b2 b3 b4
Parameters
Variables
Table 4 Estimation translog cost functions
1.050 11.207 9.738 )3.684 35.534 )34.993 0.657 23.029 2.410 4.363 17.481 7.347 12.448 11.642 63.337 )4.204 )25.793 )40.716 2.036 0.988 )0.663
0.499 0.566 0.684 )0.112 0.168 )0.176 0.001 0.155 0.006 0.007 0.292 0.218 0.260 0.231 0.170 )0.011 )0.067 )0.093 0.009 0.003 )0.002
0.179 )0.003 )0.071 )0.104 0.009 0.006 )0.011
0.218 0.266 0.309 0.207
51.347 )0.947 )22.224 )35.121 1.761 1.653 )3.268
5.010 4.522 7.524 5.245
17.672 )10.439 )0.950 10.864 0.045 0.506
)1.557 2.396 0.884
)0.371 0.586 0.078 0.218 )0.145 )0.005 0.135 0.000 0.002
2.303
6.120
Parameter T value estimates
Parameter estimates
T value
Large firms
Total firms
0.171 0.003 )0.060 )0.113 )0.009 0.008 )0.001
0.461 )0.013 0.393 0.159
0.096 )0.195 )0.003 0.073 )0.011 0.007
43.109 0.609 )14.295 )30.750 )0.979 1.401 )0.261
11.051 )0.159 8.253 2.906
7.222 )9.456 )0.699 5.152 )2.446 3.431
4.312 5.377 1.379
)2.781
)10.702 1.477 1.855 0.129
T value
Parameter estimates
Medium firms
0.162 )0.014 )0.068 )0.081 )0.009 0.009 0.013
0.331 0.531 0.091 0.048
0.127 )0.199 )0.006 0.161 0.002 0.003
1.257 0.930 0.035
)4.969
Parameter estimates
Small firms
31.590 )2.799 )14.871 )18.801 )0.865 1.398 1.980
6.154 5.239 1.402 0.659
6.310 )11.964 )0.754 6.788 0.168 0.514
4.506 2.856 0.276
)1.781
T value
348 Y. Cho / Journal of Housing Economics 12 (2003) 337–355
0.002 0.014
)5.123 0.295 2.601 )1.972 )0.038 9.127 )7.688
)0.013 0.001 0.004 )0.001 0.000 0.008 )0.007
Adjusted R2
d31 (other business/ materials) d32 (other business/labour) d33 (other business/ subcontracting) d34 (other business/ overhead) 0.98
)0.006
5.395
0.008
d21 (housebuilding/ materials) d22 (housebuilding/labour) d23 (housebuilding/ subcontracting) d24 (housebuilding/ overhead)
)0.010
0.007
)0.012 )0.001
0.97
)9.481
1.352 12.661
)4.900
3.208
)3.506 )0.340
2.135
4.678
0.011
4.766 0.005
2.632 )1.633 )5.010
0.007 )0.006 )0.012
)2.868 0.131 )2.364
d11 (construction/materials) )0.004 0.000 d12 (construction/labour) d13 (construction/ )0.004 subcontracting) d14 (construction/overhead) 0.007
27.821 )19.426 37.552
Statistically significant from zero at the 5% level of significance on a two-tailed test. Statistically significant from zero at the 1% level of significance on a two-tailed test.
**
*
Cross products of output and input factor prices
0.147 )0.081 0.196
37.829 )34.364 54.728
0.159 )0.096 0.191
c33 c34 c44
)0.004
0.001 0.005
)0.002
0.007
)0.008 )0.001
0.002
0.007
)0.015 0.021 )0.013
0.154 )0.102 0.217
0.96
)3.542
0.803 5.447
)2.990
2.661
)2.025 )0.305
0.862
1.927
)4.996 3.515 )4.132
19.692 )22.005 39.663
)0.003
)0.006 0.008
0.001
0.013
)0.028 0.006
0.009
0.010
)0.010 )0.006 0.007
0.168 )0.110 0.177
0.96
)1.207
)1.930 3.667
0.776
2.486
)3.748 1.178
2.272
2.516
)3.422 )1.166 1.945
24.753 )23.220 26.955
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Y. Cho / Journal of Housing Economics 12 (2003) 337–355
Table 5 AllenÕs own substitution elasticities of each input factor
Material factor Labour factor Subcontracting factor Overhead factor
Total firms
Large firms
Medium firms
Small firms
)0.0989 )0.8037 )0.1160 )0.1105
)0.0747 )0.8126 )0.1692 )0.1018
)0.0868 )0.9662 )0.1264 )0.0501
)0.1322 )0.9580 )0.0935 )0.1438
two-thirds of the 36 coefficient estimates are statistically significant at the 0.01 level, and adjusted R2 values are high. In order to examine whether the estimated cost function shows an adequate cost structure or not, we investigated AllenÕs own substitution elasticities (Diewert and Wales, 1987; Guilkey et al., 1983). The elasticities can be calculated as below: rii ¼ cii =SHi 1; where cii is the estimated coefficient of ith input price and SHi is the average share ratio of ith factor in the cost function. The elasticities must be estimated as negative to satisfy the condition. The substitution elasticities by group shown in Table 5 are negative for all groups. Therefore, we may consider that the cost functions are estimated adequately and can use the coefficients of this cost function to derive the efficiency measures. 5.1. Economies of scale Based on the coefficients estimated from Eq. (3), economies of scale can be obtained as expressed in Eq. (5). Table 6 summarises the results. In all cases, the estimated standard errors are very small, indicating precise coefficient estimates. For the total sample, the measure of economies of scale is 0.98. As this value is close to one, we can interpret it as constant returns to scale. However, firms in the total sample vary greatly in size, creating interest in separate estimation for the three size groups. In fact, this estimation yields results that vary by firm size class. As shown in Table 6, medium-size firms, with an economies of scale measure of 0.86, appear to enjoy increasing returns to scale. Large- and small-size firms have values of 0.97 and 0.94, respectively, leaving them closer to constant returns to scale. This suggests that Table 6 Economies of scale and economies of scope
Number of firms Average total sales (million won) Economies of scale (Se ) Economies of scope (SCe )
Total firms
Large firms
Medium firms
Small Firms
201 267,452
71 788,505
75 179,075
55 51,426
0.98 (0.002) 1.49 (0.005)
0.97 (0.006) 1.71 (0.005)
0.86 (0.014) 1.30 (0.007)
0.94 (0.013) 1.33 (0.009)
( ), standard error; Se < 1, increasing returns to scale; Se ¼ 1, constant returns to scale; Se > 1, decreasing returns to scale; SCe < 0, diseconomies of scope; SCe > 0, economies of scope.
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under the current cost structure, extending business size is most cost efficient for medium-size firms whose total sales fall in the 126,000–300,000 million won range. The advantage of expansion for large firms appears to be negligible. 5.2. Economies of scope Table 6 also shows that the results for economies of scope. For every group of firms, economies of scope are estimated as being greater than zero. Economies of scope for total firms is estimated to be 1.49. Economies of scope are somewhat lower for small- (1.33) and medium-size firms (1.30). However, large firms show higher scope economies (1.71). Diversifying into other businesses-related or unrelated- is cost efficient for all size categories of building firms in the current cost structure, and especially so for large firms. If Korean building firms operate more than one business besides housebuilding, the total cost is lower than that when individual firms operate businesses, i.e., housebuilding, other construction, and other business, separately. A single firm can operate the three groups of different businesses at a lower cost than the aggregated cost of other firms which specialised and attempted to operate the businesses individually. 5.3. Optimum size of business The estimated economies of scale differ by firm size category. Medium-size firms exhibit the greatest increasing returns to scale, whereas large firms are very close to constant returns to scale. This suggests that there may be an optimum range of firm size where economies of scale are enjoyed but diminish as firm size increases. Figs. 1–3 provide further detail on patterns in economies of scale and economies of scope by size of firm. For small firms, increasing returns to scale do not become apparent until total sales reach about 50,000 million won (Fig. 1). This is a reasonable result: firms typically need to reach a certain critical size before significant increasing returns occur. A firm with sales less than 50,000 million won is quite small. For medium-size firms, increasing returns generally continue, with the most pronounced increasing returns occurring for firms with sales of more than 175,000 million won (Fig. 2). Large firms (300,000+ million won), constant returns to scale have come to dominate (Fig. 3). Thus, the firm-size benefits in terms of economies of scale are largely exhausted by the time firms reach total sales of 300,000 million won—the low end of our large firm category. With respect to economies of scope, Figs. 1–3 reflect the firm-size category results presented above. Economies of scope are fairly constant for the small- and mediumsize firms, and considerably higher for the large firms. It has been shown that there is no specific relationship between economies of scale and economies of scope, and that scale and scope economies can exist independently or simultaneously (Panzar and Willig, 1981). In Figs. 1–3, we observe the existence of economies of scope at all firm sizes, with larger economies of scope accruing to the larger firms. Increasing returns to scale, however, are found mainly in the sales range
352
Y. Cho / Journal of Housing Economics 12 (2003) 337–355
Fig. 1. Scale and scope economies in small firms.
Fig. 2. Scale and scope economies in medium firms.
of 50,000 to 300,000 million won. At roughly 300,000 million won, the advantages of scale economies disappear, while economies of scope become distinctly greater. In comparing economies of scale with economies of scope, it is the medium-size group of firms that deserves the most attention because they do well by both measures. Even though scope economies of the large firms are higher than those of the medium firms, the results suggest that the medium group of firms is operating the multi-product business rather efficiently.
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Fig. 3. Scale and scope economies in large firms.
6. Findings and discussion Research on diversification has been actively carried out since the 1970s, as diversified business groups increasingly dominated private-sector industrial and service activity in many of the worldÕs economies. Much research has focused on the nature and efficiency of diversification at business group level. In Korea, several studies have examined the efficiency of diversified business groups since the mid-1980s. However, there has been little investigation of the efficiency of the multi-product structure at the firm level. The present study is the first to investigate whether or not building firmsÕ multi-product structure that evolved during the rapid growth period is cost efficient. The empirical results presented here are consistent with cost efficiency, and we conclude that Korean housebuilding firms can achieve cost efficiency from the multi-product structure. Korean firms exhibit increasing returns to scale over an important range of firm sizes. However, economies of scale do not provide a sufficient raison d0^etre for diversified building firms. We suggest that one factor driving the diversification of Korean building firms into other business is economies of scope. If positive scope economies did not exist, the multi-product building firms would do better if broken up into several specialised firms without any increase in cost. The economies of scope provide the incentive for firms to expand the range of their businesses. The sharing of industry technological knowledge across building work would appear to be a strong motive for diversification between housebuilding and other construction activities. The estimated scope economies may be used as information for firmsÕ decisions to further diversify.
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Y. Cho / Journal of Housing Economics 12 (2003) 337–355
The estimates have important implications. First, the Korean governmentÕs policy to encourage large construction firms to participate in the housebuilding industry is well founded. Cost efficiency may have contributed to the high and rapid growth of the housebuilding industry in the 1980s and 1990s. Second, taking into consideration the fact that most of the Korean building firms are diversified into various related and unrelated businesses, these results suggest that the diversification of Korean housebuilding firms is a cost efficient strategy. Third, the results presented here suggest that a very large scale is not necessarily optimal. The medium-size firms achieve significant scale economies as well as scope economies, while the large firms do not enjoy increasing returns to scale even though they are achieving greater economies of scope. These results also suggest that the medium-size firms have some efficiency advantages over the large firms. The large firms exhibit quite a substantial difference in business scale from that of the medium and small firms. The average size of the large firms (790,000 million won) is about four times greater than that of medium-size firms (180,000 million won). The results suggest that the current scale of Korean housebuilding firms may be larger than is optimal. More clearly, they also suggest that the large firms should consider other approaches rather than simply further expansion of business scale. The Korean housebuilding industry has recently experienced another re-structuring process, as part of the Korean economyÕs experience of tremendous structural change along with the Asian Financial Crisis at the end 1990s (Ministry of Construction and Transportation, 1995). Several large building firms went bankrupt, some of which survived and have since grown further. Further research is needed on these successful building firms in terms of their nature, business scale, and strategy.
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