Cost relationships and challenges in the Spanish apparel industry

Abstract

In the twenty-first century, the Spanish textile and apparel industries have faced substantial challenges, resulting in declining sales and employment. This study concentrates on the apparel industry, since its economic challenges and opportunities differ from those of the textile industry. The analysis employs a transcendental logarithmic cost function to investigate the presence of scale economies and the interrelationships among inputs of domestic capital, labour and intermediate goods as well as outsourced intermediate products for the Spanish apparel industry and discusses the implications for its future competitiveness and the demand for domestic inputs. The results are consistent with diseconomies of scale or, in the case of one model, possibly constant returns to scale, indicating that some contraction of the industry due to international competition will not raise unit costs. All of the inputs except for capital and intermediate goods were found to be substitutes. An important finding is that the cross elasticity values of both labour and domestic intermediate goods with respect to the price of outsourced goods have risen over time, indicating an increased sensitivity of the quantity demanded of these home-country inputs to the price of imported intermediate goods. It follows that domestic input markets will be more substantially affected by international prices for outsourced inputs as the industry tries to maintain its competitiveness in the global environment.

Keywords:

• Spain
• apparel industry
• globalization
• Agreement on Textiles and Clothing

JEL Classification:

• D24
• F14
• L67

Acknowledgement

We appreciate the helpful comments of an anonymous referee

Notes

¹ Between 2001 and 2007, total revenue for the industry fluctuated between a low value of nearly 7.0 million euros in 2005 and a high value for that period of about 7.7 million euros in 2006. Just published data show total revenue for the industry continued to drop after 2009 to about 5.2 million euros in 2010. See Instituto Nacional de Estadística, online database, www.ine.es, and Euromonitor International (2011).

² While the liberalization occurred in stages, the bulk of it was delayed until 2005, so the 1 January date was especially significant (Liu and Sun, 2004, pp. 53–4).

³ For example, the agreement that admitted China to the WTO included a provision that allowed the other members to place restrictions on all imports subject to the ATC until 2008, as well as a China-specific measure effective until 2013 (Liu and Sun, 2004, p. 54; and Ghori, 2011). The United States determined that import surges in early 2005 were disrupting domestic markets and reimposed the limits on imports of some Chinese textiles in April of that year (Federal Reserve Bank of Atlanta, 2005, p. 13). Spain (and the European Union) also had an agreement with China to limit exports that was in effect from June 2005 until December 2007. Another provision covered all goods until 2012, but that provision apparently has not been widely used. Moreover, the restrictions on Chinese imports apparently had the effect of increasing other developing country exports (Curran, 2009; Madrid Emprende: Agencia de Desarrollo Económico, 2008, p. 16).

⁴ See Jorgenson (2000, Chapter 4), Greene (2000, pp. 640–4), Berndt and Christensen (1973); Christensen et al. (1973) and Guilkey et al. (1983, p. 615) for more detailed discussions on translog functions. Also see Binswanger (1974, p. 380) and Kohli (1991, pp. 103–6) for a discussion of the technological change variable.

⁵ 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 labour market in Spain is particularly noted for its rigidities and, apparently, there are also some capital access issues (Bozdemir et al., 2009; Marimon and Zilibotti, 1998).

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:

   where

2. monotonically increasing in input prices and output:

3. concave 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, must equal

⁶ The principal advantages of using a translog cost function rather than a translog 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 derivative of the cost function in logarithmic form with respect to factor prices yields 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, p. 377; and Jorgenson, 2000, Chapter 1).

⁷ 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. Although this normalization procedure is followed and 1975 is used as the base year, the estimated translog cost function is not assumed to be exact. Thus, the logarithm of α₀ may not be equal to 0. Separate stochastic error terms, to reflect errors in optimizing behaviour, are implicitly added to the estimated cost and share equations. The iterative Zellner efficient method (IZEF, Zellner, 1963) is used to obtain the parameter estimates.

Barten (1969, pp. 24–5) shows 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, pp. 279–86) show that iteration of the Zellner procedure until convergence yields maximum likelihood estimates.

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, p. 94) compares the I3SLS results of Berndt and Christensen (1974) with those of his model using the maximum likelihood method and finds they are 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.

⁸ As a result of the linearly homogeneous in prices assumption,

⁹ The assumption of homotheticity requires that the ρ_Yi terms equal zero, and the more restrictive assumption of homogeneity requires that δ_YY also equal zero (Christensen and Greene, 1976, p. 661). A cost function corresponds to a homothetic production function if and only if the former function is separable with respect to output and the input prices, and the elasticity of cost with respect to output must be constant for a homogeneous production function.

¹⁰ Theil (1971, p. 397) shows that −2 ln λ = −2 ln (restricted/unrestricted) likelihood estimates is distributed asymptotically as χ² with degrees of freedom equal to the number of independent restrictions imposed.

Although the regularity conditions are violated at one point for the model corresponding to a homogeneous production function, the result does not necessarily mean that the translog estimates are unacceptable. See Wales (1977) and Caves and Christensen (1980). Nevertheless, the results for both the model with only the initial restrictions imposed and no regularity condition violations as well as those for the more restricted (homogeneous production function) model are presented here.

The conventional single-equation Durbin–Watson statistic for the total cost with the initial restrictions only is 2.417, while that for the cost function with restrictions required for a homogeneous production function is 2.324. In both cases, these values are in the inconclusive range at the 5% level of significance. See Durbin (1957), Malinvaud (1970, p. 509) and Berndt and Christensen (1973, p. 95) for a discussion of the Durbin–Watson statistic as a criterion for autocorrelation 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, pp. 112–17 and Greene, 2000, pp. 540–1). The null hypothesis of ρ = 0 could not be rejected at the 5% level of significance for any of the lag specifications for either model.

¹¹ Most, but not all of the estimated coefficients for the model with only the initial restrictions were also significant at the 5% significance level. All but α₀, γ_LL, γ_DD, ρ_YL and ρ_YF were significant at the 10% level.

¹² 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

Estimates of the cross price elasticities of demand can be calculated as:

¹³ The cost shares of labour and domestic intermediate goods also decreased slightly over time.

¹⁴ ‘Labor Reform Makes It Cheaper to Fire Workers,’ El País, English Edition with The International Herald Tribune, 11 February 2012, pp. 1, 6.

¹⁵ Spain is apparently considering relocating some of their partial manufacturing operations from China to Vietnam in an effort to lower production costs. See (NewsBank, 2011).

¹⁶ Also see the discussion in Taplin (2006) and Stengg (2001).