Lerner index: estimation and the impact of its market structure determinants.
| Autor | Casta |
Abstract: Using the reasoning that assumes that a pro-cyclical Solow residual is an indication of the presence of market power, the paper estimates the Lerner index. At the same time in which we estimate the Lerner index, we measure the impact of industry structure variables (concentration and imports) on this index. Because we have panel data, we also allow for a change in the impact of these variables across time. For the whole manufacturing sector, we find that concentration and imports have a differing impact on the Lerner index across the business cycle. We find evidence that shows that the Lerner index behaves anticyclically. And we also make the analysis by type of good (durables and non-durables) and find differing impacts of concentration and imports by type of good.
Keywords: Lerner index estimation, concentration, import-penetration, pro-cyclical Solow residual.
Resumen: Asumiendo que un residual de Solow procíclico es evidencia de poder de mercado, el trabajo calcula el índice de Lerner. Al mismo tiempo en que se estima el índice de Lerner, se mide el impacto de variables industriales (concentración e importaciones) sobre el índice. Debido a que tenemos datos en panel, también se estima cómo cambia, a través del tiempo, el impacto de estas variables. Se encuentra que la concentración y las importaciones tienen un impacto diferente sobre el índice de Lerner a lo largo del ciclo económico. Asimismo, se encuentra evidencia de que el índice de Lerner se comporta anticíclicamente. También se hace el análisis por tipo de bien (durables y no durables) y se encuentran impactos diferentes de la concentración y las importaciones por tipo de bien.
Palabras clave: Estimación del índice de Lerner, concentración, penetración de importaciones, residual de Solow procíclico.
JEL Classification: L00, L11, L60.
Introduction
There is a long tradition in industrial organization that has studied the determinants of price-cost margins (1) A typical model would establish the price cost margin as the dependent variable with concentration indexes, the capital-output ratio and other variables as explanatory variables. In this framework, the price-cost margin is calculated with industry data, assuming that variable cost is an appropriate surrogate for marginal cost. Also, this kind of studies has mainly used cross-section observations.
More new approaches use the Solow equation (1959) to detect the presence of market power. In this tradition, Hall (1988) states that the finding of a pro-cyclical Solow residual is an implication of market power. Under the assumption that the true Solow residual is not intrinsically pro-cyclical, Hall has suggested an econometric method that gives us an estimate of the markup.
This paper uses data obtained from the Encuesta Industrial Anual, published by INEGI, to pool cross-section and time series observations to estimate the Lerner Index, with the help of Hall's methodology. In contrast with traditional industrial organization approaches, the measurement of the Lerner index does not assume a particular form for marginal costs (similar to variable costs). Rather, the econometric approach based on Hall's methodology has sound basic principles. The data used is at the four-digit level that allows us to study the price setting behavior of industries that produce similar products. Previous studies (Castañeda, 1996a, 1996b), have used two-digit data. These data set may have included, in the same industry, rather dissimilar products.
Similarly to the traditional industrial organization literature, the paper introduces variables that affect this latter index, such as concentration indexes and an import penetration index. The rationale for using some of these variables emerges from one stage game theoretic models. From these settings, we can obtain the following results: first, a higher level of concentration has a positive impact on the (average) Lerner index of the industry. Second, a reduction in protection through quotas or tariffs diminishes the Lerner index. Finally, a change in the elasticity of market demand changes the ability of firms to raise prices above marginal cost. (2) Thus, this approach gives us the way some industry variables affect the Lerner Index. (3)
The paper also allows for interaction between business cycle and market structure variables. Green and Porter (1984), Rotemberg and Saloner (1986), Haltiwanger and Harrington (1991), and Athey, Bagwell and Sanchirico (2002) argue that oligopolistic industries have varying incentives to collude across the business cycle. A reason consistent with these theories would predict that the impact of industry concentration would not be stable across time. Also, the disciplining impact of imports may vary across the business cycle because peso depreciations have accompanied several downturns in the recent Mexican experience. We investigate for these possibilities. The behavior of the Lerner index across the cycle is also important for macroeconomics. Bils (1987) shows that the Lerner index behaves anti-cyclically in the United States. Several papers of imperfect competition in macroeconomics try to model this situation.
Among the main findings are the following: For the 1986-1998 period, concentration has a positive impact on the Lerner index. Most of the results show that the impact of concentration appears to behave anti-cyclically for this period. This evidence is consistent with the theories advanced by Rotemberg and Saloner (1986) and Haltiwanger and Harrington (1991). When controlling for pro-cyclical impacts, the import-penetration ratio has a negative impact on the Lerner index. The disciplining impact of imports behaves anti-cyclically. There are also differing impacts of industry variables depending upon the type of good (durables and non-durables).
Methodology
Let the technology be given by constant returns to scale production function with no intermediate inputs:
Y(t) = F(L(t), K(t)A(t)) (1)
A(t) represents technical progress, L(t) represents labor input, K(t) is the stock of capital and Y(t) is value added. Differentiating with respect to time the last equation and rearranging:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
The dots over the variables denote derivatives with respect to time and the sub-indexes express partial derivatives. Using Euler's theorem for homogenous functions and assuming homogeneity of degree 1 in technical progress, the last expression can be written in the following form:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
Define c, p and w as marginal cost, price and wages, respectively. The first order conditions of a profit-maximizing firm that has some degree of market power can be expressed in the following way:
[F.sub.L] = [beta](w/p)
[beta] represents the markup (i.e. the ratio of price to marginal cost). By using the last expression, condition (3) can be written in the following way:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
Divide both sides of equation (4) by [beta]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
Define the Lerner index as [gamma] = p u c/p with p representing price and c marginal cost. Then [beta] = 1/1- [gamma]. Using the last expression, equation (5) can be rewritten in the following fashion:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Rearranging the last expression we obtain:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
Solow assumed that [gamma] = 0 in the last expression and calculated the so-called Solow residual. In contrast, Hall assumed that A followed a random walk with drift and used a similar equation to (4) to estimate b (which implies a value for [gamma]). He advocated the use of instrumental variables to solve for the potential endogeneity present in equation (6). Domowitz, Hubbard and Petersen (1988) estimated the last equation for the U.S. manufacturing.
Define [??]/Y u [??]/K = yk, similarly [??]/L u [??]/K = lk, [??]/Y u [??]/L = yl, WL/pY = [alpha] And a = [??]/A. Then expression (6) can be written in the following way:
yk u [alpha]lk = [gamma]yk + a(1 - [gamma]) (6')
We could estimate the last equation to obtain a measure of the price-cost margin. The advantage of that approach would be that we would be estimating the Lerner index from first principles, without the need to assume that variable cost is an appropriate surrogate for marginal cost. The standard procedure would be either to use instrumental variables as in Hall (1988), or an OLS approach as suggested by Caballero and Lyons (1989). Instrumental variables are used when concerns about potential endogeneity of yk in (6') are present. However, we are interested in estimating the impact of industry variables on the Lerner index, thus we substitute the price cost margin ([gamma]) by the variables that affect it. So, the next step in our procedure is to make the price cost margin ([gamma]) a function of industry specific factors. Among them the following:
[gamma] = c + [[delta].sub.1]C4 + [[delta].sub.2]M/TS (7)
With C4 denoting the four firm concentration ratio obtained from INEGI and M/TS is the ratio of imports to total sales. Thus, substituting (7) in expression (6') and proceeding with the estimation, we obtain the estimates of these factors on the price-cost margin. After substituting (7) in (6') we get the following equation:
yk u [alpha]lk = cyk + [[delta].sub.1]C4yk + [[delta].sub.2]M/TS yk + a(1 - [gamma]) (6")
Once we recover the values of [[delta].sub.1] and [[delta].sub.2] from (6"), we can have an estimate of the price cost margin from equation (7). To control for cyclical behavior, a modified version of equation (7) (equation (7')) is also substituted in expression (6'):
[gamma] = c + [[delta].sub.1]C4 + [[delta].sub.2]M/TS + [[delta].sub.3]DC4 + [[delta].sub.4]DM/TS (7')
D is a pro-cyclical dummy. (4) The resulting equation is:
yk - [alpha]lk = cyk + [[delta].sub.1]C4yk + [[delta].sub.2]M/TSyk +...
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