International Economics: Selection and Sorting of Heterogeneous Firms through the Procompetitive Effect

Abstract:
We study how an increase in market size causes selection and sorting of firms with different productivity by intensifying competitive pressures. To this end, we introduce the procompetitive effect into the Melitz (2003) model of monopolistic competition with heterogeneous firms, using the H.S.A. (Homotheticity with a Single Aggregator) class of demand systems, which has many advantages relative to other non-CES demand systems used in the literature.
First, it is homothetic. Market size can be thus defined unambiguously because the composition of market demand does not matter. It also helps to isolate the effects of variable markups from those of
nonhomotheticity. Furthermore, the homotheticity makes it straightforward to use H.S.A. as a building block in multi-sector general equilibrium models.
Second, it is nonparametric. This makes it flexible enough to allow not only for Marshall’s Second Law, which implies incomplete pass-through. It also allows for what we call the (weak and strong) Third Law--the pass-through rates for less efficient firms are no lower (under the weak Third
Law) or strictly higher (under the strong Third Law). Furthermore, since this class contains CES (as well as translog) as a special case, H.S.A. helps us understand which predictions of the Melitz model are
critically dependent on CES and which ones are not.
Third, because the single aggregator serves as a sufficient statistic for competitive pressures, it is simple to establish the existence and uniqueness of free-entry equilibrium with firm heterogeneity. H.S.A. also retains much of the tractability of CES; most of comparative statics can be conducted by means of simple diagrams, and the key qualitative results are free of any further parametric restrictions on the demand systems and productivity distribution. In a one-sector setting, we show, among others, that an increase in competitive pressures, -- whether it is caused by an increase in market size, a lower entry cost, or a first-order stochastically dominant improvement in productivity distribution--, leads to a tougher selection of firms, larger dispersion of profit across surviving firms under the Second Law (and of revenue across firms under the weak Third Law), and smaller dispersion of markup rates under the strong Third Law. An increase in market size also leads to higher (lower) profits for the more (less) efficient among the surviving firms under the Second Law. If the weak Third Law holds additionally, an increase in market size leads to higher revenue for all surviving firms with large enough overheads, but only for the more efficient with small enough overheads. We also show that employment could be hump-shaped in the firm productivity under the Second and weak Third Laws, in which case employment could be inversely related to productivity among surviving firms with overheads large enough relative to market size.
Then, in a multi-sector/region setting, we show that, under the Second Law, competitive pressures are stronger in larger markets, which causes more efficient firms to sort themselves into larger markets. Due to this composition effect, the average markup rates are not necessarily lower in larger markets. This result offers a caution against testing the procompetitive effect of market size by comparing the average markup rates in a cross-section of cities with different sizes.