Production and costs in the South African motor vehicle industry

Abstract

This study investigates the existence of economies of scale in the South African motor vehicle industry as well as the substitution possibilities between input pairs and the direct and cross-price elasticities of demand for the various inputs. Because of data limitations, a translog cost function was estimated for only a three input model corresponding to a homogeneous production function involving capital, labour and intermediate goods. The issue of the existence of economies of scale in the South African motor vehicle industry is a particularly important one because South Africa once again is a member of GATT and a full participant in the international trade arena. The null hypothesis of constant returns to scale was rejected at the 0.5% level of significance. Thus, the results of this model are certainly consistent with economies of scale in the South African motor vehicle industry. The estimated direct price elasticities were consistent with the hypothesis that, during the past two decades, capital was the productive factor with the most elastic demand, and the estimated cross-elasticities between input pairs generally supported the hypothesis that all inputs are substitutes.

Notes

¹ See Adler (1989, pp. 419–22), Central Statistical Service (1997, pp. 12.4, 12.16) and Green (1986, p. 67).

² See Central Statistical Service (1997, pp. 12.4, 12.16 and 21.9).

³ An appreciation of the importance that the South African government places on the motor vehicle industry can be attained by reviewing the Mid Term Review of the Motor Industry Development Programme. This programme was begun in September of 1995. Originally scheduled to end in 2002, it has recently been extended to 2007.

⁴ In addition to Ford and GM, the assemblers included South African Motor Assemblers and Distributors Limited (SAMAD), National Motor Assemblers Ltd., Motor Assemblers Limited, Chrysler South Africa (Pty) Ltd., Car Distributors Assembly Limited (CDA, now Mercedes Benz), and British Motor Company (Leyland). Although SAMAD was originally set up to produce Studebaker products at Uitenhage, near Port Elizabeth, Volkswagen obtained a majority interest in the company in 1956 and sole ownership in 1974. National Motor Assemblers, in Johannesburg, assembled vehicles such as Peugeots on a contract basis. Motor Assemblers was established in Durban and later became Toyota. See Bell (1990, pp. 63–4); Dix (1995, p. 23); and Oberhauser (1993, p. 113, note 4).

⁵ Peugeot dropped out of the market and Leyland stopped producing passenger cars (Adler, 1989, p. 420). Alfa Romeo and Renault also ceased production in South Africa in 1985.

⁶ As a result, Ford operations in Port Elizabeth were transferred to the Amcar plant at Silverton, near Pretoria. In 1987, Ford disinvested its share of Samcor, which then became wholly-owned by Amcar. However, Ford still maintained close connections with Samcor as a supplier of components, tools, technology and management expertise (Bell, 1990, pp. 69–70). See Green (1986) for a more thorough discussion of the Ford-Amcar merger.

⁷ For a discussion of the GM divestiture see Adler (1989).

⁸ There is additional domestic production of industrial vehicles. In 1978, Atlantis Diesel Engine was set up by the government to produce engines for heavy vehicles. Another company, Astas, produces truck transmissions. See Bell (1990, pp. 62–3).

⁹ On the other hand, domestic ownership appears to be relatively more common in East Asia. See Fujimoto (1983) and Jenkins (1984). In recent years, however, the trend towards greater domestic ownership of these facilities in South Africa has been reversed. In 1994, Ford bought 45% of Samcor, and the company increased its ownership share to 90% in January of 2000. General Motors has also purchased a 49% share of Delta, and Toyota and Nissan have purchased equity interests in the industry. Daimler Benz has increased its equity share in Mercedes Benz as well. See Barnes and Kaplinsky (2000, p. 799) and ‘Ten Years After: South Africans Who Fought for Sanctions Now Scrap for Investors,’ The Wall Street Journal, 11 February 2000, p. A4.

¹⁰ The last version of these regulations based local content requirements on value, rather than weight, as was the case previously, and enabled manufacturers to receive credit on imports by exporting components. For more detailed discussions of the provisions of Phases I though VI of the local content programme see Bell (1989), Bell (1990, pp. 60–3), Dix (1995), Oberhauser (1993), van Zyl and Kotze (1994).

¹¹Central Statistical Service (1997, pp. 16.9, 16.10, 16.11, and 16.12).

¹² In a recent article, Nordås (1996, pp. 725–8) compared the competitiveness of some South African industries with those in the United States by calculating an index based on the ratio of wage per worker to value added per worker for the United States relative to South Africa ((W _US/W _SA)/(VA _US/VA _SA)]. The calculated index value for motor vehicles was 0.51, while that for other transport equipment was 0.46. These values are consistent with the hypothesis that the transport equipment industry in South Africa is far less competitive than its counterpart in the United States. (A ratio of 1.0 would be consistent with the hypothesis that the industry is equally competitive in the two countries. Non-ferrous metals, with an index of 1.67, was the only industry with a calculated index above 0.8.) Moreover, since this index does not take into account the cost of capital or intermediate inputs, it is only a rough measure. The relatively high cost of capital goods and intermediate inputs in South Africa could make the situation even worse.

¹³ Translog cost functions can provide a local, second-order approximation to an arbitrary cost function. See Bjørndal et al . (1988) and (Truett and Truett (1996a, b) for a more thorough discussion of the translog cost function. With appropriate restrictions on their parameters, the translog production or cost functions can provide a local, second-order approximation to CES or Cobb–Douglas frontiers. However, a CET-CES production functional form implies that the partial elasticities of substitution between all input pairs are constant and equal, and the partial elasticity of substitution between all input pairs is equal to unity for a Cobb–Douglas production function. Translog functions allow for more possibilities regarding the substitutability of inputs. See Berndt and Christensen (1973, p. 82), Burgess (1975, pp. 105–6) and Christensen et al . (1973, pp. 30–8). Another advantage of the translog cost function is that it contains fewer parameters than some other flexible functional forms. See Guilkey et al . (1983, p. 615).

¹⁴ See Binswanger (1974a, p. 380; 1974b, pp. 967–9), Caves et al . (1984, footnote 5, p. 473), and Kohli (1991, pp. 103–6) for a discussion of the technological change variable.

¹⁵ Technically, the estimation of this cost function requires that input markets be perfectly competitive so that firms view input prices as independent of the quantity demanded of them. Although many of the input markets relevant to this study are not perfectly competitive, administered or negotiated prices (such as union wage rates) that do not change frequently in response to volume changes can perform a similar role for estimation purposes. Administered or negotiated prices perform a similar function to a competitive market in the sense that the input supply price appears to be fixed, at least during some period of time, from an individual firm's perspective. For a discussion of market intervention in South Africa see Davis (1994, pp. 113–23, esp. p. 119) and Williams (1989, pp. 66–95). The principal advantages of using a translog cost function such as Equation 3 over a translog production function are found in the following features of the cost function: (a) the partial derivatives of a cost function with respect to input prices yield the corresponding input demand functions (Shephard's Lemma); (b) it follows from (a) and the definition of elasticity that the partial derivative of the cost function in logarithmic form with respect to factor prices yields the cost shares; and (c) the partial derivative of the cost function in logarithmic form with respect to output yields the cost elasticity with respect to output level. See Binswanger (1974a, p. 377) for a discussion of additional advantages of estimating a cost function rather than a production function.

¹⁶ With only one output specified, this cost function implicitly assumes that the various products of the motor vehicle industry are homogeneous. While such an assumption could result in biased estimates, disaggregating output to reflect production of individual products was not feasible with the available data. See Dudzinski et al . (1998) and Berry et al. (1996) for a more thorough discussion of this potential problem.

¹⁷ Barten (1969, pp. 24–5) has shown that maximum-likelihood estimates of a set of share equations less one are invariant to which equation is omitted. Kmenta and Gilbert (1968) have demonstrated that iteration of the Zellner (1962, 1963) procedure (IZEF) until convergence yields maximum-likelihood estimates. Ruble (1968, pp. 279–86) has also shown that the IZEF and maximum likelihood methods are computationally equivalent.

¹⁸ If the data are normalized so that total cost, the output quantities, and the input prices are equal to one in the base period and if the translog cost function is exact, the logarithm of α₀ is equal to zero. In this case, the addition of the translog cost function to the set of equations to be estimated increases the number of observations and adds only three parameters to be estimated. See Burgess (1975, p. 110). Although this normalization procedure was followed in the present study, the estimated translog cost function was not assumed to be exact. Thus, α₀ is not necessarily equal to zero.

¹⁹ The following data were used in estimating the total cost function. Total cost was equal to the sum of total salaries and wages, cost of materials, rent paid, depreciation, and net profit in millions of rand. Total output was calculated as the gross output of the industry in current rand (millions) divided by a price index for transport equipment output (1990 = 100). As indicated above, transport equipment industry data were used for the first model and before 1972 in the second model. However, beginning in 1972, it was possible to obtain output and cost data for the motor vehicle industry, and those data were utilized for those years in the second model. Because of data availability, the price of capital was given by the interest rate on first mortgage bonds before 1963, the yields on new issues of company stock debentures and notes from 1963–1980, and after 1980 by yields on company loan securities traded on the stock exchange. Again because of data availability, the price of labour was given by an index of South African motor industry minimum wage rates for journeymen before 1970, an index of average wages and salaries per employee in the motor trade industry between 1970 and 1973, and after 1973 an index of South African metal engineering industry wage rates. The price of intermediate goods was given by the price index for materials in mechanical engineering (1990 = 100). The variables in the total cost function were normalized with 1956 as the base year. The share of capital was calculated from the sum of rent paid, depreciation, and net profit. The data sources, International Monetary Fund, International Financial Statistics, Bureau of Statistics, Statistical Year Book, and Bureau of Statistics, Central Statistical Service, and Department of Statistics, South African Statistics, are listed in the references.

²⁰ A second set of total cost functions with a second dummy variable with a value of one in 1985 was also estimated. That year was a relatively disastrous one for the motor vehicle industry as the South African economy slumped and the industry went through a major restructuring. See Adler (1989, pp. 419–20); Bell (1990, p. 64); Green (1986, p. 67); and Oberhauser (1993, p. 109). However, the estimated coefficient of this dummy variable was not significantly different from zero at even the 10% level of significance. Since it appeared not to add anything of value to the estimated total cost functions, this variable was omitted in the final set of equations.

²¹Central Statistical Service (1997, p. 12.16).

²² The cross price elasticities of demand (E_ij  = ∂ln X_i /∂ln P_j ) can be expressed in terms of the cost shares and the estimated parameters of the model as E _ij  = S _j  + (γ _ij /S_i ). The general formula for the direct price elasticity of demand for input i in terms of the parameters of this model is .

²³ The monotonicity in input prices and output and the concavity conditions were satisfied at all of the data points for both models. The conventional single-equation Durbin–Watson statistic for the total cost function using only transport equipment data was 2.41, while its value for the total cost function using the motor vehicle industry data for the later years was 2.63. Unfortunately, the small number of degrees of freedom prevented the calculation of the exact probabilities associated with these values. See Durbin (1957), Malinvaud (1970, p. 509), and Berndt and Christensen (1973, p. 95) for a discussion of the Durbin–Watson Statistic to check for serial correlation in the case of simultaneous equations. A Lagrange multiplier test for serial correlation was also conducted on the total cost equation for each data set using lagged values of the error term ranging from one to five periods (see Godfrey, 1988, pp. 112–17). In the case of a one period lag using the transport equipment data, the value of the LM statistic was 2.576, so that the hypothesis that ρ = 0 could not be rejected at even the 10% level of significance. The LM values for higher order lags were also such that the null hypothesis of ρ = 0 could not be rejected at the 10% level of significance. For the estimated total cost function using the motor vehicle data for later years, the value of the LM statistic was 4.140, and the hypothesis that ρ = 0 could not be rejected at the 2.5% level of significance. For higher order lags, the value of the LM statistics were such that the null hypothesis could not be rejected at the 5% level of significance, except for the case of a three period lag, where the null hypothesis could not be rejected at the 2.5% level of significance.

²⁴ If the total cost function is linearly homogeneous in inputs, 1/E _C is equal to the percentage increase in output relative to the percentage increase in all inputs, or a measure of returns to scale.

²⁵ The years covered by the study were 1961–1984 for Canada and the United States, 1968–1984 for Japan and 1961–1981 for Germany.

²⁶ Other studies using earlier US data have mixed findings. For example, Knox Lovell (1973, p. 510) used cross section data from the US transportation equipment industry for 1958. With a homothetic specification of the production function, his results were consistent with the hypothesis that returns to scale fell monotonically from a high of 1.278 at the smallest level of output. With a homogeneous production function, his results yielded an estimated returns-to-scale parameter equal to 1.099, and this value was significantly greater than one. Also using cross-section data for 1958, a Cobb–Douglas production function, and dividing the data into two groups based on the relative share of labour, Ferguson (1967, p. 215) obtained estimates of the returns to scale coefficient for the transportation equipment industry ranging from a high of 1.824 to a low of 0.878. However, these estimated values were not significantly different from one. Using 1957 US data and adjusting for technology changes, Hildebrand and Liu (1965, pp. 109 and 130) estimated a returns to scale parameter for the transportation equipment industry of 1.014; this value was also not significantly different from one. Again using 1957 US data, Besen (1967, pp. 281–2), estimated a returns to scale coefficient for the transportation equipment industry equal to 1.454. This value was significantly different from zero at the 5% level of significance. In a third study using US data for 1957, Moroney (1967, p. 46) estimated a returns to scale coefficient for the transportation equipment industry of 1.023.

²⁷ See Truett and Truett (1996a, b).

²⁸ However, the results of the more recent study involving Mexican data did not support the hypothesis of economies of scale for the auto parts industry as a whole. See Truett and Truett (1989, p. 76) and (1996b, p. 440).

²⁹ It is certainly possible that utilizing industry level data to estimate economies of scale can yield results that do not accurately reflect the situation at the level of the individual firm. However, the results here are quite robust and are consistent with what observers of the South African industry and policy makers clearly believe to be the case. Nevertheless, the reader should also see the discussion of this issue in Mountain (1986, pp. 707–8).

³⁰ See Adler (1989, p. 419), Bureau of Trade and Industry (1977), Dix (1995, pp. 26, and 33–35), Green (1986, p. 67), and Oberhauser (1993, pp. 109 and 112).

³¹ For example, the volume of motor vehicle exports increased from less than 20 000 units in 1997 to about 68 000 units in 2000. (Data supplied by the National Association of Automobile Manufacturers of South Africa at www. naamsa.co.za/.). While motor vehicle industry tariffs have fallen in recent years, they are still substantial. In 2001, the tariff on complete vehicles was still 43.5% and that on components 32.5%, with a proposed phasing down of these levels to 30% and 25%, respectively, in 2007.

³² See the Board on Tariffs and Trade, ‘Mid Term Review Proposals for the Motor Industry Development Programme’. The sources were www.cartoday.com and the National Association of Manufacturers of South Africa [www.naamsa.co.za/].

³³ However, in 1987 the three original equipment manufacturers best poised to take advantage of economies of scale from larger output volumes also had the lowest ratio of employees to vehicles produced. Specifically, this ratio was 0.0723 for Nissan, Samcor and Toyota, while it was a nearly double 0.1366 for BMW, Delta, Mercedes-Benz and Volkswagen. See Bell (1990, p. 92).

³⁴ See Williams (1989) for a discussion of these policies.

³⁵ One source has estimated that the optimum local content level is approximately 75% to 80%. See Bell (1990, p. 95).

³⁶ An apparently ‘permanent’ ad valorem duty was imposed in 1995 by the South African Revenue Services (see the Mid Term Report on the Motor Industry Development Programme).

³⁷ Barnes and Kaplinsky (2000, p. 800) argue that export and other incentives for the assembly firms has resulted in a situation where the effective import protection for the domestic components manufacturers is nearly negligible.

³⁸ For more discussion of this issue see Adler (1989, pp. 419–20); Bell (1990, pp. 76–8); Oberhauser (1993, p. 102); and van Zyl and Kotze (1994, pp. 36–7).