The motor vehicle industry in an emerging nation: the case of Brazil

ABSTRACT

As in other emerging nations, in Brazil, the motor vehicle industry is considered to be strategically important for economic development because of its backward and forward linkages and possibilities for export-led growth. This study analyses prospects for the industry by estimating an industry-level cost function that includes output of both vehicles and component parts with capital, labour and intermediate goods as inputs. The cost elasticity of output (an indicator of scale properties) and the elasticity relationships among inputs are explored. One unexpected outcome of the work that appears to be robust is that during early years of the study period, the industry had constant returns or even diseconomies of scale. However, during later years, when output was greater, there were economies of scale. This finding is likely the result of some combination of the entry of new firms, the development of new models or technological change. The study concludes that if firm output can be increased, economies of scale can be expected to strengthen the position of the Brazilian industry in the international marketplace.

KEYWORDS:

• Motor vehicle industry
• Brazil
• globalization

JEL CLASSIFICATIONS:

• D24
• F14
• L62

Acknowledgements

The authors are grateful for the helpful comments of two anonymous referees.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The Brazil IBGE online database www.ibge.gov.br indicates that the number of vehicles produced in Brazil in 2008 was not quite 3.1 million, increasing to slightly over 3.1 million in 2009. According to Sturgeon (2011, 187), the number of vehicles produced in Brazil in 2009 was nearly 3.2 million. The source of the discrepancy among these figures is unknown; however, Brazil’s motor vehicle industry world ranking remains the same with any of them.

² ‘Fiat comemora a marca de 10 milhões de carros produzidos no Brasil’, 6 February 2009. http://carplace.virgula.uol.com.br/fiat-comemora-a-marca-de-10-milhoes-de-carros-produzidos-no-Brasil.

³ These figures differ somewhat from those of Stevens (1987, 10) in Table 1.

⁴ For further discussion of the establishment of new assembly plants during this period, see Lopes (2006) and Perobelli et al. (2006).

⁵ Arza (2011, 131) uses the term ‘commonalization’ to refer to the global use of common platforms and other parts, a practice that reduces the number of locations required for design activities. Modularization denotes the shift of production from parts assembly to a greater emphasis on the assembly of subsystems or modules. Lean production refers to high-level flexibility in the production process, including flexible machines and the relationship between an assembler and its suppliers (see, e.g. Kotabe, Parente and Murray 2007, 85; Ó H Uallacháin and Wasserman 1999; and Wallace 2004, 804–805). First-tier suppliers are firms that supply parts and materials directly to manufacturers.

⁶ Arza (2011) bases this conclusion on the seeming implication by Humphrey and Oeter (2000, 61–63) that 50 000 units represents the minimum efficient scale for light vehicle assembly. In that paper, Humphrey and Oeter (2000, 63) argue that by 1998, the Brazilian industry had reached an efficient scale of operations.

⁷ A translogarithmic (translog) cost function is a flexible functional form that allows one to estimate an unknown cost function to a second-order approximation (Greene 2000, 217). The principal advantages of using a translog cost function rather than a production function are found in the following features of the cost function: (1) the partial derivatives of a cost function with respect to input prices yield the corresponding input demand functions (Shephard’s lemma), (2) it follows from (1) that the partial derivatives of the cost function in logarithmic form with respect to factor prices yield the cost shares and (3) the partial derivative of the cost function in logarithmic form with respect to output yields the cost elasticity with respect to level of output (Binswanger 1974, 377; and Jorgenson 2000, Chapter 1).

⁸ See Jorgenson (2000, Chapter 4), Greene (2000, 640–644), Berndt and Christensen (1973), Christensen, Jorgenson and Lau (1973) and Guilkey, Lovell and Sickles (1983, 615) for more detailed discussions of translog functions. Also see Binswanger (1974, 380) and Kohli (1991, 103–106) for a discussion of the technological change variable.

⁹ Technically, the estimation of this cost function requires that input markets be perfectly competitive or at least that firms view input prices as ‘given’. Although many of the input markets relevant to this study are not perfectly competitive, administered prices that do not change frequently in response to volume changes can perform a similar role for estimation purposes. The motor vehicle market in Brazil was subject to a number of restrictions that reduced price flexibility. See, for example, Fischer et al. (1988, especially 81, 106–108, and161) and Kotabe et al. (2007, 93).

The minimum requirements for the cost function to describe a ‘well-behaved’ technology are that it be (1) linearly homogeneous in input prices, (2) positive and monotonically increasing in input prices and output and (3) concave in input prices. These regularity conditions for the cost function require the following restrictions on its parameters:

1. linearly homogeneous in input prices:∑β_i = 1, ∑ρ_iY = 0, ∑γ_iT = 0 and ∑γ_ij = 0 for all j, where i, j = K, L and M;

2. monotonically increasing in input prices and output:

   $\frac{\mathrm{\partial }\mathrm{l}\mathrm{n}TC}{\mathrm{\partial }\mathrm{l}\mathrm{n}{P}_i}\mathrm{a}\mathrm{n}\mathrm{d}\frac{\mathrm{\partial }\mathrm{l}\mathrm{n}TC}{\mathrm{\partial }\mathrm{l}\mathrm{n}Y}>0$

3. concavity in input prices:A sufficient condition for concavity of the cost function is that the Hessian matrix of second partial derivatives with respect to factor prices is negative semidefinite. Also, γ_ij must equal γ_ji.

¹⁰ Barten (1969, 24–25) has shown that maximum-likelihood estimates of a set of share equations with one deleted are invariant to which equation is omitted. Kmenta and Gilbert (1968) and Ruble (1968, 279–286) have shown that iteration of the Zellner procedure until convergence yields maximum-likelihood estimates.

The data were normalized at their means so that total cost, the output quantities and the input prices are equal to one at their mean values, except for the price of capital which was normalized at 1972. The price of capital was normalized at its 1972 value to satisfy the regularity conditions. Separate stochastic error terms, to reflect errors in optimizing behaviour, were implicitly added to the estimated cost and share equations.

One could argue that industry output is an endogenous variable and that an instrumental variable procedure should be used, since the regressor and the error terms may be correlated. Similar problems may arise with measurement errors; as a result, coefficient estimates may be inconsistent (Westbrook and Tybout 1993). However, using aggregate data for the United States, Applebaum (1978, 94) compared the I3SLS results of Berndt and Christensen (1974) with those of his model using the maximum-likelihood method and found they were similar. In addition, a potential problem with the instrumental variables methodology is that the results may be affected by the set of instrumental variables utilized. In the case of Brazil, the available data would have made that approach extremely difficult, if not impossible.

¹¹ Before 1986, these data were for material de transporte, which may have included some vehicles such as ships, trains and airplanes. These were the only data available prior to 1986. From 1986 onwards, the gross value of production, intermediate products, value added, and wages data were for automobiles, trucks and buses, including parts. (Data not including parts were not available.) The wage rate index and the index of output were for the entire transport manufacturing industry, because they were the only data available. However, the category of other transport equipment was small relative to that of automobiles, trucks and buses. For example, in 2009, the value of the production of the other transport equipment category was only about 15.5% of the value of the production of automobiles, trucks and buses. While the data are not ideal, the small relative size of the other transport equipment sector would make any issues raised less substantive. See Instituto Brasileiro de Geografía e Estatística (IBGE), online database: ww.ibge.gov.br.

¹² An anonymous referee expressed concern regarding whether the degrees of freedom were sufficient to estimate the total cost function. With the share equations included, the degrees of freedom were fully adequate to estimate the parameters of the total cost function with both the entire data set as well as the smaller sample period, discussed below. While not ideal, the degrees of freedom were also sufficient to estimate the coefficients of the total cost function by itself, even with the smaller sample. As explained above, although the motor vehicle industry did undergo a number of changes during the study period, the inclusion of any time trend variable resulted in violations of the regularity conditions, so they were omitted in the final model. While this referee was also concerned that the inclusion of a dummy variable during the recession period might distort the results, omitting it resulted in a violation of the regularity conditions. While not statistically significant, its estimated coefficient did have the hypothesized sign.

¹³ See Theil (1971, 397) for a discussion of this application of the log-likelihood test.

¹⁴ The conventional single-equation Durbin–Watson statistic for the total cost equation was 2.10, a value that was in the inconclusive range at the 5% level of significance. See Durbin (1957), Malinvaud (1970, 509) and Berndt and Christensen (1973, 95) for a discussion of utilizing the Durbin–Watson statistic to check for serial correlation in the case of simultaneous equations. A Lagrange multiplier test for serial correlation was also done on the total cost equation using lagged values of the error term ranging from one to nine periods (see Godfrey 1988, 112–117; and Greene 2000, 540–541). The null hypothesis of ρ = 0 could not be rejected at the 5% level of significance.

¹⁵ For a cost function with only the initial regularity restrictions, the cost elasticity is given by E_C = α_Y + δ_YY ln Y + Σρ_Yi ln W_i.

¹⁶ It is a bit surprising that the estimated value of E_C was significantly greater than one at the 10% significance level, as shown in Table 4. Perhaps this finding occurred because of all of the changes as well as periods of downturns in demand in the industry during the study period.

¹⁷ First-tier suppliers are firms that supply intermediate products and materials directly to manufacturers of a product.

¹⁸ Sufficient data to include 1991 in this effort are not available. The price, output and total cost data were normalized at the new sample means, except for P_K. P_K was normalized using 2009 as the base year.

¹⁹ Limited degrees of freedom made it impossible to check autocorrelation diagnostics with the cost function estimated as a single equation with a more elaborate version of the time trend variable.

²⁰ The Durbin–Watson statistic also did not lead us to reject the hypothesis of no serial correlation in the model with DUM3 only included. The degrees of freedom were not sufficiently large for Shazam to compute a probability value for the model with the time trend variable.

²¹ The violation of the concavity conditions at a small number of datapoints does not preclude the translog system estimates from being acceptable. See Caves and Christensen (1980) and Wales (1977) for a discussion of this issue.

²² Estimates of the direct-price elasticity of demand for input i can be calculated using the estimated input shares and parameters of the cost function as

${\mathrm{E}}_i=\frac{{\gamma }_{ii}+{\mathrm{S}}_i^2-{\mathrm{S}}_i}{{\mathrm{S}}_i}$

²³ See Eakin, McMillen and Buono (1990) and Kerkvliet and McMullen (1997) for a discussion of the bootstrap methodology. Sufficient degrees of freedom were not available to enable the bootstrap methodology for the estimated parameters of the cost function for the shorter time period, so only the elasticity estimates for the complete period are presented here.

²⁴ Estimates of the cross-price elasticities of demand (E_ij = ∂ln X_i/∂ln W_j) can be calculated as:

${\mathrm{E}}_{ij}={\mathrm{S}}_j+\frac{{\gamma }_{ij}}{{\mathrm{S}}_i}$

²⁵

$E_{KL}=(\mathrm{\partial }{X}_K/\mathrm{\partial }{P}_L)(P_L/X_K).$