Estimating market power using a composed error model
| Published date | 01 September 2019 |
| Date | 01 September 2019 |
| DOI | http://doi.org/10.1111/sjpe.12195 |
| Author | Mustafa U. Karakaplan,Levent Kutlu |
ESTIMATING MARKET POWER USING
A COMPOSED ERROR MODEL
Mustafa U. Karakaplan* and Levent Kutlu**
ABSTRACT
We present a maximum likelihood based composed error model to estimate mar-
ket powers of firms. In our model, the stochastic part of the supply relation
includes two random components: the conventional two-sided error term and a
random term, which is capturing firm-specific conducts. Moreover, we provide a
generalization of scaled Stevenson stochastic frontier model in the context of
doubly truncated normal distributions. We estimate the market powers of Chi-
cago based airlines as an empirical example that is showing the applicability of
our estimation procedure.
II
NTRODUCTION
Market power is the capability of a firm or a group of firms to increase the
price of a good or a service they supply above the competitive market levels.
A widely used proxy for market power is the Herfindahl–Hirschman Index
(HHI), which is the sum of squared market shares of firms. HHI is easy to
calculate but it is a measure of market concentration, that is, not a direct
measure of market power. Moreover, HHI is a market-specific measure and
thus it does not let us deduce airline-specific market powers. Another common
measure of market power is the Lerner (1934) index, which is difference
between the price (P) and marginal cost (MC) divided by the price, that is,
(PMC)/P. Traditionally, researchers estimate the marginal cost from the
cost function. Then, the Lerner index is calculated using (PMC)/P.A
problem with this approach is that estimated firm-specific Lerner index values
may be negative. Hence, most of the time, researchers announce the mean or
median Lerner index values. Recently, Kumbhakar et al. (2012) proposed a
way that handles this issue by using the stochastic frontier analysis.
1
Calculat-
ing the Lerner index, however, can still be problematic especially if the
required cost dataset is not completely available. Alternatively, market power
*Georgetown University
**University of Texas at Arlington
1
See also De Loecker (2011) for a production based method for estimating market power
and see Kumbhakar and Lovell (2003) for an extensive survey of the stochastic frontier liter-
ature.
Scottish Journal of Political Economy, DOI: 10.1111/sjpe.12195, Vol. 66, No. 4, September 2019
©2018 Scottish Economic Society.
489
can be measured by using a conduct parameter approach, which is also
known as conjectural variations approach.
2
One interpretation of this method
relies on the estimation of a generalized supply relation that incorporates mar-
ket settings such as perfect competition, Cournot competition, and monopoly
settings. The estimated values can be used to categorize the market using sta-
tistical tests. Another approach is considering the conduct as an index of mar-
ket power that can take a continuum of values. In this interpretation, the
conduct of a firm refers to what the firm does as a response to its expecta-
tions. We follow the latter interpretation of the conduct parameter. A major
advantage of the conduct parameter approach over the Lerner index is that a
detailed cost dataset is not necessary to measure the market power since the
method provides the estimates of marginal cost indirectly without requiring
the total cost data.
In principle, firms do not necessarily share the same conduct. Also, the con-
duct of a firm can change over time due to a variety of reasons, such as a
change in the business strategy in favor of cooperation. Unless these conduct
parameters are treated as random variables, a conduct parameter model
would suffer from overparameterization. Different conventional ways to solve
the overparameterization problem include estimating an average conduct for
the market as in Appelbaum (1982), allowing group-specific conducts as in
Gollop and Roberts (1979), allowing firm-specific but time-invariant conducts
as in Puller (2007), or modeling the conduct parameter as a function of some
variables that are suspected to affect the conduct as in Kim (2006) or Kutlu
and Wang (2018a). It is common in the literature to estimate the conduct
parameter without forcing it to be in its theoretical bounds because this
approach does not generally result in a major issue when estimating an aver-
age conduct for a market. On the other hand, if we estimate the firm- and
time-specific conducts, finding that some of the conduct estimates are out of
their theoretical bounds is highly likely, which is an estimation problem
requiring a solution.
3
In line with Orea and Steinbuks (2018), we suggest a new econometric
approach that deals with the overparameterization problem by summoning
econometric tools from the stochastic frontier literature.
4
This approach con-
siders the market power as a supply shock where identification relies on mak-
ing assumptions on the composed error term. More specifically, we assume
that the conduct parameter has a doubly truncated normal distribution. In
contrast to the standard conduct parameter models, identification of the con-
duct is achieved by utilizing the asymmetric (skewed) distribution of the com-
posed error term. The prominent advantage of this identification strategy is
2
See Perloff et al. (2007) for details about the conduct parameter approach.
3
Employing some parametric transformation to restrict the conduct to lie in its theoretical
bounds does not seem to solve the estimation problems in many occasions such as those
related to convergence problems.
4
Kumbhakar et al. (2012) also use a stochastic frontier analysis for estimating market
power. However, their model aims to estimate the Lerner index and, unlike us, they do not
estimate a demand–supply system. Hence, the data requirement and stochastic frontier
approach that they use is different.
490 MUSTAFA U. KARAKAPLAN AND LEVENT KUTLU
Scottish Journal of Political Economy
©2018 Scottish Economic Society
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