For example, of the twelve listed in Chung (1994), only five have a homogeneous linear production technology. More importantly, the implication that the Elasticity of Substitution is unity completely misses one of the goals of this work. In addition to allowing for a potentially more accurate representation of the underlying technology, elasticities can vary across the sample.
The cost allocation equations (9) will be estimated along with the cost function (equation 6) using Zellner's seemingly unrelated regressions (SUR) model, which exploits the correlations between the errors in each of the stock equations to improve efficiency. The constraints exist because the cost parts are derivatives of the cost function, so some coefficients are the same. By construction, the sums of the coefficients ai in all factor part equations are equal to unity for each observation.
However, this approach fails to exploit one of the advantages of translog estimates over other functional forms, namely the change in elasticity estimates across the sample. The difficulty lies in the fact that elasticity estimates are highly non-linear combinations of coefficients and data (Greene, 2003). 3 "Significant" can refer to rejecting a null hypothesis of an elasticity of zero, in which case we can be sure that the factors are complements or substitutes, or we can refer to a Cobb-Douglas elasticity of unity.
Anderson and Thursby (1986) find that Allen Elasticities of Substitution asymptotically follow the normal or ratio-of-normal distribution only if the means of the actual factor shares are used, but this study does not have the option to use the result as no actual shares are available.
Data Description and Construction
Moll (1996) also shows how extensions of bargaining agreements lead to convergence of technologies and wages in the industry. There is therefore support for the convergence of wages across industries and justification for calculating wages at a firm level for use in firm-level studies. It classifies workers as skilled or unskilled and generates firm-level wages using the human capital characteristics observed among the sampled workers for each firm.
The sales/administrative own price elasticity is persistently positive in system estimates, which demonstrate a poorly specified sales/administrative equation. Part of the reason for the poor specification is that this is a quite diverse group in terms of skill level, so wages in this occupation are likely to be more inaccurate. Furthermore, in system estimation, errors in one equation can propagate themselves to other parts of the system.
Therefore, the harm to other outcomes from including the sales/administrative profession is most likely greater than the harm from excluding it. Factors considered include differences in log wages, the number of observations, and comparisons of the confidence intervals of the individual and combined groups. The first row contains wages for all skilled workers in the food and beverage industry, regardless of location or union membership.
After adjusting for firm size, as discussed in Section 5, wages are also used to determine cost shares and total costs. Total factor cost (Cf) is the sum of factor costs and is the dependent variable in the cost function. Although the NE survey does not contain total costs and does not contain raw material costs, it does contain information on raw materials as a percentage of total costs.
It is possible to construct an adequate proxy for added value by multiplying raw materials as a percentage of total cost (p) by turnover (y). It operates on the perfectly competitive assumption that turnover equals total cost including opportunity cost. The similarities are significant despite the completely different calculations, so there are grounds for confidence in the constructed data.
Accounting for Firm Size Effects on Wages
The measures of central tendency are close, but there is moderate spread at the 25th and 75th percentiles. The following sections analyze the impact of ignoring this effect on translog estimates and show that the estimates are more likely to (falsely) reject homothetic technology and linear price homogeneity and overestimate returns to scale. From the characteristics of individuals, wages for occupation i can be seen as a simple function of firm size measured by sales (y) and a vector of the variables available from the household survey (x).
The coefficients that contain value added can be very different from what they are supposed to be. Furthermore, assuming linear price homogeneity and constant returns to scale in 1; ij ij 0; iy yy 0; y 1. Linearly homogeneous prices, however, imply that if all the values of γi for each industry are close enough to the average across industries, the result will tend to be an upward bias on the value added coefficient.
If the firm-size effect is not the same for each occupation, there is the possibility of Similar analysis concludes that the coefficient on Ω′ may be found significant and therefore falsely reject homotheticity, or that linear price homogeneity is rejected by distorted coefficient values. To understand the likely effects on returns to scale, assume for clarity a common firm size effect across all industries.
Using these assumptions, one can measure that omitting the firm size variable will underestimate the denominator by γ on average, so that returns to scale will be overestimated. This is intuitive: if wages rise for larger firms, the returns to scale are smaller than otherwise. Given the potentially serious problems of ignoring fixed-size effects, ways must be found to capture them.
Unfortunately, there is no information on the size of the firms that individuals in the household survey work for. One way to proceed is to attach previously estimated values of γi to the wage series. Bhorat and Lundall (2002) estimate the following manufacturing firm size wage effects for the Gauteng province.
Cost Function and Cost Share Estimations
Their estimates are imprecise, using only average firm wages and annual firm sales, but they are similar to the American study of Doms, Dunne, and Troske (1997). For example, larger firms have cheaper and easier access to capital and therefore employ more capital relative to labor. It may also be a true technological feature, driven by the relationship between firm size and type of manufacturing industry.
If the technology as implied by the cost function is heterothetic, this justifies the use of translog functions instead of more restricted functional forms. Values marked with an asterisk are drawn consistently over at least 95% of the sample; the other values are consistent across at least 75% of the sample. Note: *indicates consistent across 5th and 95th percentiles; all others are consistent across both quartiles.
For example, a 1% increase in unskilled wages relative to semi-skilled wages would lead to a 2.44% drop in the ratio of unskilled to semi-skilled employment. Adopting the terminology in Hamermesh (1993), if an increase in the price of one factor leads to a decrease in the quantity of another, as measured by the elasticity of factor demand, the pair p- are complements. If an increase in the price of one factor leads to an increase in the quantity of another, the pair is said to be p-substitutes11.
These led to nonsensical results, including estimates inconsistent with cost-minimizing behavior, leading to positive own-price elasticities and poorly fitting equations. 11 This is in contrast to q-complements and q-substitutes, which he uses in the context of the effects of exogenous changes in the quantity of one factor on the price of another factor. Skilled/craft occupations are p-supplemented with managers/experts and semi-skilled workers, but p-substituted with unskilled labor.
Unskilled workers are p-complements with managers/professionals and semi-skilled, but p-temps with skilled/craftsmen. In particular, we can say that based on firm-level production evidence, a 10% decrease in unskilled wages should lead to a 6.5% increase in unskilled employment, holding output constant. A 10% decrease in skilled/craft wages would lead to a 1.2% decrease in unskilled, while the same decrease in semi-skilled wages would lead to a 3.4% increase in unskilled employment.
Concluding Comments
The fact that all forms of labor appear roughly equally substitutable for capital suggests that capital can be separated from labor inputs (see Sato (1975)). First, research into the substitution of labor and capital would not entail large costs if different forms of heterogeneous labor were brought together. Second, if data limitations prevented the use of capital costs in intra-labor elasticity studies, omitting capital would not negatively affect the estimates.
This result is important and differs from two-factor studies, which by design will consider skilled and unskilled labor as proxies. Although the previous section suggested that simplifications of the model may not be harmful in some applications, using only two factors can be very misleading in other applications. Furthermore, the values imply that wage moderation in one occupation, by allowing relative wages to decline in relation to the cost of capital, would increase employment in that occupation and in the other occupations.
There are therefore gains from coordination in wage determination between professional groups (as opposed to coordination between branches). This may be one reason why unions within an industry tend to represent more than one occupation on the skills spectrum and tend to negotiate wages at all levels simultaneously. Given the complementarity between occupational types and the apparent possibilities for coordination, there is a clear basis for research into the interaction between different occupations through their trade unions.
Proof that Uzawa result holds under general technological conditions
Following Allen (1938), but without assuming constant returns to scale. distinguish the first-order terms with respect to wi , divide each equation by µ and define i and ij 2. 12 I am especially grateful to Dr Margaret Stevens for her role in establishing this result. where, as in equation 2,q is the determinant of the bounded Hessian of equilibrium conditions and qijis the cofactor of qij in q. by the first order conditions) and.
Proof that the link between AES and demand elasticities hold under general
Regression used as basis for final cost function elasticity results
The Centre for Social Science Research
