Inefficient Entry: A Comparative Average-Cost

Analysis

Carlos A. Cinquetti (São Paulo State University)

Department of Economics. Rod. Araraquara-Jaú, Km 01. Araraquara, SP 14800-901. Brazil.

Phone:55(16) 3334-6214. Email: cinquett@fclar.unesp.br

Abstract

With a composite fixed-cost variable, consisting of both a technology coefficient and firm

scale, we perform a comparative cost analysis to examine the scale effect of trade protec-

tion. Evidence from the manufacturing industry is based on Brazil’s import-substitution

industrialization (ISI), relatively to that of the USA. The panel-data analysis clearly shows

a positive correlation between the number of firms and the average costs, which is highly

dictated by the mean firm size.

Key Words: Scale Effect; Average Cost; Trade Protection; Inefficient Entry; Monopolistic Com-

petition; Brazil

1 IntroductionInternational competition turns more stringent the scale barrier to entry, thus reducing a firm’sdeviation from the maximum efficient scale. Assuming monopolistic competition with en-dogenous market power, we develop a comparative average-cost framework to re-examine thisindustry-level issue, namely, the “scale effect” (Feentra, 2004).

The empirical analysis is built on a composite fixed-cost variable, consisting of operative-

labor technical coefficient and the mean size of firms, whose performance in 20 industries of a

highly protected economy – Brazil during four referential years of its ISI period – is compared

to a rather open baseline economy.

An exploratory panel-data analysis shows that comparative entry is strongly correlated with

industries’ average cost, thus corroborating the hypothesis of inefficient entry.

We begin the analysis, in Section 2, by revisiting the scale (elimination) effect and the se-

lection effect, outlining their empirical content and emphasizing that they should hinge on inter-

industries and inter-firms frameworks, respectively. After briefly discussing data and variables,

we implement the empirical analysis in Section 4. Concluding remarks follow in Section 5.

2 Price Competition and Cost AdjustmentIn a monopolistically competitive industry i ∈ I, the equilibrium number of (homogeneous)firms, ni, follows from the return function

πi(ni) = πoi (ni, ϕi, θi) − fi = 0, (1)

where ϕi stands for marginal cost and θi for demand for varieties, which equals ni because offi. Operating profit πo(.) is non-increasing in ni because it pushes θi (price-elasticity) up in bothspatial (Lancaster, 1979, 1984; Schmitt, 1990) and Chamberlinian (Melitz and Ottaviano, 2008)monopolistic competition.1

We may separate the several forms of fixed-costs into plant and corporate fixed cost, Gi

and Fxi, respectively, and assume that Gi + Fxi = Fi > fi. Gi covers production as well as basic

marketing and logistic, whereas Fxi covers research and development, as well as more advanced

logistics.2 Simultaneously shifting to an international economy, this higher fixed-cost barriers

1Which excludes Dixit and Stigitz (1977), where the exogenous market power(1 − 1

ϕi

)−1enforces a constant

firm size, regardless of ni. Vogel (2008) advances an alternative spatial model featuring heterogeneous firms.2This two-ladder fixed cost fits several sorts of pricing and R&D competition in the IO literature (see Boccard,

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lowers ni in (1), whereas marginal trade cost, τ, only reduces the relative value of foreign sales

before the relative value of domestic sales.

In an international Industrial-Organization (IO) model, the number of competing varieties

is Ni = ni + n∗i , so that competition in a domestic market not only intensifies, but also becomes

independent of the number of domestic firms therein. For instance, a reduction in trade-policy

barriers for country k∗into k, τk∗k, causes n∗′

i > n∗i ≡ N′i > Ni, squeezing the markup from

the increased θ′i > θi, which eventually drives domestic firms out, n′i < ni. This increase in

Ni, stemming from τ abides both the varieties effect (Melitz and Trefler, 2012) and the pro-

competitive effect (Markusen, 1981) from international trade. The latter occurs in a paradoxical

manner, because it causes the exit of domestic firms.

Given that the industry becomes less rationed, active domestic firms increase their size,

which indicates the scale effect (Horstmann and Markusen, 1986; Feentra, 2004), and summa-

rizes the impact of international trade on entry. This effect must ultimately be considered as a

worldwide fact because asymmetric changes in τk∗k means that firms from some countries may

undergo greater loss in domestic market than gains in foreign ones, or vice versa. Lastly, the

requirement of internationally integrated markets (Markusen and Venables, 1988) is reinforced

by monopolistic competition (Lancaster, 1984; Head and Ries, 1999).

Because average-cost pricing adjusts the entry (exit) of plants in (1), we could thereby exam

it by focusing on Gi. Duality (cost) also provides an ampler picture of technology and produc-

tivity. Brainard (1997) empirically proxies Gi with the technological coefficient of operative

labor,3 which we amplify with N:

PLANTit(nit) =(lit/yit)nit

Gt=

lit/xit

Gt, (2)

where lit and yit stand for employment of operative workers and output in each industry at timet, respectively, whereas xit is the mean scale (size) of firms. Normalization in terms of the meanvalue of the numerator, Gt, removes both business-cycle variations and international (neutral)technology differences. Industry wage has no effect on inter-industry variation and was thus

2010), as well as standard monopolistic competition, which does not rule out entry with no previous R&D.3While corporate fixed cost was proxied by the ratio of skilled to unskilled labor. Apart from the specific input,

cross-industry variations in sales can reveal how large unobserved fixed costs are relative to market size (Berry andReiss, 2007)

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omitted in (2).By considering firms to be heterogeneous in (operational) productivity, (1) becomes:

πi j(ϕi) = πo[ϕi j, θi,Ni] − Fi = 0, (3)

where ϕi j is the productivity of firm j. Melitz and Ottaviano (2008) propose a continuous

distribution, φ(ϕi j), from which two entry (equilibrium) conditions follow: entry into domestic

markets, at the cumulative value Φ(ϕi), whose correspoinding revenue covers up to Gi; and

entry into export markets, at Φ(ϕxi ), for firms that also cover a positive Fxi – for simplicity, we

are skiping the two separate equilibrium at 4. The pro-competitive effect acts on entry through

φ(ϕi j): selecting out the least productive non-exporters and amplifying the most productive

ones that export, and thus changing the weighted average productivity, ϕ = ϕ(ϕ). That is how

ϕi j introduces a new productive effect, for a given Fi.

In this context, what best characterizes an international equilibrium is the distribution of a

firm’s productivity:

PRODT j = g(li j/yi j

Zi

), ∀i ∈ I, j ∈ J. (4)

where Zi is the mean productivity of industry i, such that PRODT j is the industry-centeredproductivity of a firm j. Placing all firms together renders the distribution of their productivitydenser and thus more well-defined. In Melitz and Trefler (2012), the impact of trade opennessin Canada appears in the first and the third moment of distribution (4), reducing firms withproductivity below the average value; Φ(ϕ′i) > Φ(ϕi), which pushes PRODT j up.

In sum, change in conduct (θi) pushes prices down, which is met by two cost adjustments: in

the marginal cost by selecting out the least productive firms, and in the average cost by enforcing

larger-scale firms.4 Each of these adjustments is analyzed assuming the other one away. In

(3), one has a continuum of firms – leaving no room for largeness – to highlight the marginal

cost adjustment, whereas (4) dissolves industries to characterize productivity adjustment among

firms. In contrast, (1) focuses on xi, whereas (2) considers inter-industry variations in yit/Nit that

4Because investment in product quality can be cost saving (Boccard, 2010), this analysis is not greatly affectedby our ignoring that productivity competition might entail product-quality competition, a point that the trade lit-erature has addressed using both firm-level (Kluger and Verhoogen, 2011) and industry-level (Hallak and Schott,2011) models.

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affect the mean firm’s average-cost.

Hence, by pushing prices close to the marginal cost – reducing firms’ market power – trade

policy engenders two productive gains: gains from the selection effect and gains from the scale

effect (reducing the endogenous inefficiency in scale).

A theoretical analysis may handle both forms of barriers to entry (firm’s scale and firm’s

heterogeneity) from international trade,5 but an empirical analysis can hardly do so, except in

distinct analytical stages and with differently aggregated data. The scale (elimination) effect

is an industry-level issue that begs for an inter-industry empirical framework. The selection

effect, in turn, is a firm-level issue whose corresponding inter-firm framework either dissolves

the industry’s identity, or otherwise cannot properly address an industry-level phenomenon.

3 Data and VariablesMajor trade-policy changes are often accompanied by general policy change, making it diffi-cult to single out the former in an inter-period statistical experiment, as remarked by Trefler(2001). Accordingly, rather than an inter-period analysis (before and after policy change) of thescale effect, we perform a within-period international comparison between 21 manufacturingindustries in a protected country (Brazil) against a baseline country. Ideally, the latter shouldbe closer to free trade, and have a large domestic market.6 Together with data availability, thisfactor led us to choose the USA.

The comparison is repeated over four referential years of Brazil’s ISI: 1967, 1973, 1980,

and 1987/88 – the last referential year is considered for smoothing extremely unstable years. In

addition to providing a better picture of this policy experiment, this panel-data analysis compen-

sates for the small number of observations compared to that usually considered in a firm-level

analysis.

Data on output and employment come from both UNIDO database and some yearly Indus-

trial Statistics, whereas the number of establishments comes from PIA (Annual Survey of the

Industry) for Brazil and from the County Business Patterns for the USA.

5Bernard et al (2007) perform an inter-industry cum inter-firm analysis, but its exogenous θi, following Melitz(2003), leaves out entry from largeness.

6In a small home market, changes in trade policy can shift a market structure from an oligopoly to amonopoly(Pomfret , 1992).

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4 International Deviation from Scale Efficiency

There is a great amount of evidence linking intra-industry trade to monopolistic competition,from which Heckscher-Ohlin comparative advantages can be derived (see Romalis, 2004), re-lying on both homothetic technology and exogenous θi. Comparative average-cost linkagescan also be derived by making θi endogenous to N, in conjunction with (1)-(2), in-so-far asthe ordering of industries’ input coefficient is internationally stable. This latter requirementfavors plant-fixed cost because corporate-fixed cost is bound to cover distinct activities (e.g.,technology generation and technology transfers) across a developed and a developing economy.

Ignoring trade linkages, the analysis boils down to examining comparative average cost,

PLANT it/PLANT ∗it, against comparative entry, nit/n∗it. This simple non-parametric analysis,

which is somewhat reminiscent of Melitz and Trefler (2012), follows Schmalensee (1989):

inter-industry studies of imperfect competition should rely first and foremost on basic statis-

tic tools and good data.

Plotted in Figure (1), both nit/n∗it and PLANT it/PLANT ∗it are transformed into log values

to avoid large concentration of points in the [0,1] interval. As shown, nit/n∗it (the vertical axis)

is positive and highly correlated with comparative average cost in manufacturing industries.

Hence, from this behavior of comparative average-cost in the highly-protected economy, we

cannot reject that protectionism leads to inefficient entry, reducing the scale effect.

Figure 1: Number of Firms versus Plant-Fixed Cost

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This nexus of trade policy incentives and comparative entry is reinforced by the fact that Brazil

had no legal barrier to entry except for some sub-sectors in two industries (metals and other sec-

tors). In addition, Brazil’s messy protectionism and consequent unplanned negative protection

in some industries (Tyler, 1985) may explain sub-entry – those points in the negative quadrant.

The above findings also indirectly confirm the stable international ordering of the lit/yitl∗it/y

∗it,

which is somewhat surprising when dealing with countries that are vastly different in their levels

of development, factor prices and international integration. Were the opposite true, then com-

parative advantages would drive comparative entry, as in the Ricardo-Hecksher-Ohlin (RHO)

prediction by Morrow (2010), an extension of Romalis (2004), and the above correlation would

fail: nitn∗it

would cancel out opposite movements in the terms within parents in (2). However, their

cost function which varies internationally in factors prices alone, warrants compatibility with

the above ordering – except for Ricardian technology differences – whereas their homothetic

technology makes international cost invariable to xit, despite their assumed constant θi making

xit invariable to Nit.

The contribution of firm scale to the above cost relationship can be more accurately observed

by isolating xit from PLANT , whose result is displayed in Figure (2). As shown, nit/n∗it is strong

and negatively correlated with xit/x∗it, confirming that a firm’s relative size greatly contributed to

observed comparative average (fixed) cost. At the same time, the weaker correlation in Figure

(2) before the correlation in (1) confirms that the comprehensive PLANT incorporates valuable

fixed-cost information.

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Figure 2: Number of Firms versus Mean Scale

Finally, one may argue that comparative entry would affect the distribution of firms’ pro-

ductivity and thus comparative cost, yit/lity∗it/l

∗it, but Melitz and Ottaviano (2008), likewise the RHO,

is not incompatible with a stable ordering of industries’ input coefficient. Most importantly, we

cannot reject a theoretical inter-firm relationship with inter-industry evidence.

This final point made above prompts some comments on the previous analyses (Head and

Ries, 1999; Tybout et al., 1991; Trefler, 2001) that tested the selection effect against the scale

effect, in which the latter was rejected in all of the analyses. The difference in the analyzed ex-

periences can justify our distinct evidence. At the same time, we can object that the elimination

(scale) effect must be examined with an inter-industry empirical framework, which does not

sufficiently characterize the industry dummies, or the number of firms in firm-level regression

models. Aggregating the latter database to the industry level, if the data allow, would equally

be necessary.

Conversely, a variable for economies of scale is justified for controlling the selection effect

in firm-level analyses — as long as one does not claim that it is testing either (1) or (2). One

can thus equally avoid duality and follows a production-function approach, as in the above-

mentioned analyses.

5 ConclusionsUpon comparing manufacturing industries in a heavily protected economy against a benchmark

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free-trade economy, we observed that comparative number of firms was positively correlatedwith average cost. An additional analysis reinforced the central role of firm size.

The findings confirm the inter-industry relationship between conduct and productivity: as

price becomes less distorted (demand becomes more elastic), deviation from maximum efficient

scale is minimized (the average cost falls). From the opposite perspective, as domestic markets

become more closed, smaller firms can enter, or they do not exit.

If the data allow, the analysis of productive efficiency can be improved with a heterogeneous-

firm model; however this shift means moving away from the present inter-industry framework.

The latter, in turn, can be expanded into a multivariate trade model, in which the singular link-

ages from PLANT are controlled for marginal costs, fixed costs, and some non-intrinsic variable

of market structure.

Acknowledgments

I wish to thank, with the usual disclaimers, valuable comments and suggestions by Russell Hill-

berry, Keith Maskus, Thibault Fally, Carlos Martins Fo. , Luciana T. de Almeida, participants

at various conferences and seminars, as well as assistance in gathering data provided by the

staff of the Colorado University Library. Financial support from CAPES, Fapesp, and UNESP

is gratefully acknowledged.

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