The Dynamics of Trade and Competition
Natalie Chen, Jean Imbs, Andrew Scott (2007)
Inspired from Melitz and Ottaviano (2005).
Links prices, productivity and markups to the number of competing firms.
Trade openness, as it affects the market structure, influences firm level performances in a way that depends on the time horizon considered (pro-competitive effects in the SR vs. ambiguous effects in the LR).
L consumers, supplying one unit of labour.
Preferences are defined over a continuum of sectors indexed by i. Utility of consumption in each sector is derived from preferences over a continuum of varieties indexed by u Є (0,1).
The representative agent maximises:
Solving this program yields the following inverse demand for each variety u:
Also implies the following aggregate demand for variety u in sector i:
Observe that the individual consumption in each sector can be written as:
where N is the measure of consumed varieties, with average price:
Substituting (4) in (3) yields the aggregate demand for variety u in sector i:
This price goes down with tougher competition in the sector, which implies higher N (with ) or smaller average price.
Following Ottaviano, Tabuchi and Thisse (2002), the price elasticity of demand changes with the number of competing firms (one variety per firm). Then markup depends on N as well.
=> Contrary to models with CES preferences, elasticity and markup are not exogenously fixed (but are affected by trade openness as N denotes both domestic and foreign firms). Variable markups are more consistent with empirical evidence.
Single input, which is internationally immobile: labour, with unit cost c, different across countries.
Prior to entry, firms face uncertainty on their unit cost of production.
Entry cost (≈irreversible investment), which is country-specific and varies with the degree of openness (fE ≠ fE*). Assume fE* = λ (τ*,τ) fE(τ) and fE’>0.
=> contrasts with Melitz and Ottaviano (2005), who consider a fixed entry cost, which does not allow for ambiguous trade effects in the LR.
Firm productivity is revealed: this is a draw from a common cost distribution G(c) with support on [0,cM] or [0,cM*]. Cross-country productivity differences. Productivity differences across firms as well.
Then, production and export decisions are made. Firms can sell to domestic and foreign markets. τ* > 1 denotes cost of domestic export to foreign market (symmetrically, τ > 1 denotes cost for foreign goods entering the domestic economy). Firms, which cannot cover their marginal cost, exit.
In the SR, firms cannot change their location.
Domestic market Foreign market
Producer Domestic firm Foreign firm Domestic firm Foreign firm
Unit cost of the marginal firm cD cX* = cD/τ cX = cD*/τ* cD*
Price ensuring zero sales p(cD) = cD p(cX*) = cD/τ p(cX) = cD*/τ* p(cD*) = cD*
Production choice qD(c) qX*(c) qx(c) qD*(c)
Surviving firms maximise their profits facing the demand function (3). Monopolistic competition implies that the average price level and number of firms are taken as given.
A domestic firm with productivity c will solve the following programmes:
Following Melitz and Ottaviano (2005), the costs for firms that produce for the domestic market or that export follow a Pareto distribution.
In the domestic economy, optimal pricing and distributional assumptions yield the following average sectoral price index and average cost:
Average sector markup is given by:
The same relation holds for the foreign economy, where prices, markups, costs and productivity all depend on the value of the cost for marginal firm still in activity (cD*).
Need to solve for the number of active firms in both markets, which can be derived from the threshold costs of the marginal firm in both markets.
Using (6), one get: (12)
Combining this with the average sectoral price index (derived earlier) yields the number of firms selling in each market:
(14) and (15) describe the demand side of the economy, which is invariant to trade costs.
They imply a negative relationship between the number of active firms supported by the market and the cost cut-off, as high costs (i.e. high values for cD) => high prices, limited demand and a limited number of firms (and varieties).
In the SR, the number of firms in each market is exogenous, but firms still decide whether to produce or not and which markets to supply.
3 types of firms: (i) high cost firms, which do not produce (but cannot relocate); (ii) lowest cost firms, which produce for domestic and foreign markets, and (iii) intermediate firms, which produce only for the domestic market.
The supply side of the economy is given by:
Production decisions are affected by changes in transport costs. Positive relationship between the number of active firms and the cost cut-off.
Short-run supply (cont.)
In equilibrium, N rises and cD falls in response to a fall in transport costs.
Price, costs and markups (which all depend on cD in the model) fall as well.
In the LR, location decisions and the number of firms active in each market are endogenous:
Under Pareto assumption, using free entry conditions (i.e. zero profits) gives the cut-offs in both markets:
Long-run supply (cont.)
In contrast to the SR, the cost of the marginal firm (i.e. cD) is not affected by the number of active firms (due to endogenous entry and exit).
In the LR, the cost cut-off depends on the distribution of costs, the level of fixed costs, market size and trade costs.
Long-run supply (cont.)
Consider (20) and (21) :
If fixed costs are equal and constant (i.e. λ(.)=1 and fE(τ)=fE), a fall in domestic trading costs leads to an increase in marginal costs: N falls and cD rises (higher prices and markups and lower productivity) => exact opposite of the SR impact of falling trade costs => anti-competitive effects.
In the LR, firms relocate to more protected foreign markets (the fall in trade costs and the lower degree of competition overseas makes it more attractive to serve the domestic market through exports).
Long-run supply (cont.)
Consider (20) and (21) :
If fixed costs are variable such that fE=fE(τ) and fE’>0, a decrease in τ implies a decrease in ø(τ), which induces a downward shift in the horizontal line (increase in N and pro-competitive effects).
The overall net effect of the impact of trade liberalisation in the LR is ambiguous and depends on the relative weight of both opposite effects.
As economy opens up, more foreign firms export to domestic market => increase in the number of competing firms at home.
Simultaneously lowers mark-ups because of higher perceived elasticity of demand (lower market shares).
Also raises productivity, as with lower prices, fewer firms can break-even.
Both channels reduce prices at home.
In the long run, domestic firms can chose where to locate. A closed economy is attractive, as the number of competing firms is limited. It is also cheaper to export to home market from there. Domestic firms relocate abroad => trade effects may revert in the long run.
Key indicators of trade openness in the model (τ and τ*) are unknown => replaced by model-implied observable variables: import shares (Ѳ and Ѳ*), which depend only on transport costs and relative productivity.
Pareto distributional assumption implies:
And by symmetry:
In the SR, equations (12) and (13) give: (22)
N is unknown, but data on D, the number of domestic firms producing for the home market (with D = NSR (cD/cM)k and D = ψ(τ,τ*)N, with ψτ
In the LR, equations (20) and (21) give:
The effect of openness is no longer conditional on N and depends on whether λ is allowed to depend on openness.
Larger markets have lower prices.
Combining SR and LR in a specification that allows the LR impact of openness to vary from its SR impact : ECM model
Variables must be integrated of order one (I(1)) and cointegrated.
Difference in difference approach: all variables are expressed in first differences/identification of differential effects across the same sector i in different countries.
Intercepts to control for cross-country and cross-sector variations in technology (cM≠cM*).
Relative markups depend directly on relative cut-off costs (just as relative prices):
The model was specified in terms of unit costs (c).
Average sectoral labour productivity is approximate by w/c, where w denotes nominal wage at the sector level => strong assumption, as it implies no difference in capital costs across countries (omitted variable bias?):
Perfect labour mobility in a same sector implies
Using equation (22) yields an expression for relative productivity in the SR:
Using equation (23) yields an expression for relative productivity in the LR:
Combining both effects in a single specification gives the following ECM model:
Lagged Dependent variables
Estimating an ECM model requires variables, which are I(1), thus their first difference will be stationary.
Unit-root testing strategies.
Failure to reject the null of a unit-root => ECM yields more efficient estimates.
Risk: unit-root tests lack in power (tend to tell there is a unit root when there is no unit-root).
Equations will be estimated with and without the ECM specification.
Lagged Dependent Variables
Controls for sluggish price adjustment : coefficient on lagged price = gradual effect of price adjustment.
Risk of correlation between the lagged dependent variable and individual specific effects => OLS estimated could be biased and inconsistent.
Solution: Generalised Method of Moments (GMM).
Model of real relative prices at the sector level
Need to purge the effects of nominal aggregate influences, which may correlate with openness (Romer, 1993)/omitted variable bias
Inclusion of aggregate price indices (P) for each country:
Assumption: monetary shocks affect all sectors homogeneously (or at least if some heterogeneity exists, it is uncorrelated with openness)
Estimation in differences in differences: cross-section of bilateral international differences in all the variables of interest.
Measurement error (heteroscedasticity, i.e. the variance of the error terms is no longer constant) => solution: country fixed effects).
Country pair/sector specific intercepts in all estimations.
Need of instruments for import shares, as the degree of import penetration can be influenced by many factors (including prices, productivity).
Identification/what drives international differences between European countries and at the sector level?
Ratio of import weights to their value (excluding domestic prices from computations): import penetration in sector i and country j is instrumented with the average bulkiness of US imports in the same sector, where exports into the US from j are excluded from the computations of total weight and value.
where wjk denotes the inverse of distance between countries j and k
Number of anti-trust cases in ECJ interacted with a sector-specific index of NTBs. Variables vary across industries and over time.
Dummies for European policy changes: Single Market 1992 and the Euro 1999.
Taken together, these instruments explain more than 50% of variation in import shares.
Cover 1989-199, seven European countries (Belgium, Denmark, France, Germany, Italy, the Netherlands, Spain) and 10 manufacturing sectors.
Price data from Eurostat.
Labour productivity from OECD.
Markup data from BACH. Markups are computed as follows:
Summary statistics: some sectors opened up than others, within each sector, some countries opened up more than others.
Control for nominal exchange rates (varying across sectors).
Control for factor intensity (Heckscher-Ohlin argument => rising import shares and falling prices in sectors with shrinking domestic production).
Specification in deviation from benchmark country (Italy, for its lack of openness).*
Distinguish EU and non-EU imports.
Non-linearity in openness effects.*
Instrumentation of the number of firms.
*LR anti-competitive effects are muted
Model-implied observable variables and specifications.
Theoretical are supported by data.
In the short-run, import penetration has standard pro-competitive effects: negative and significant impact on manufacturing prices; positive and significant impact on manufacturing productivity; and negative and significant impact on profit margins.
Effects revert in the long run, as protected economies overseas become attractive locations from which to export to the liberalised domestic economy.
Effects of foreign openness and of relative numbers of active firms are also consistent with theory.
Focus on the microeconomic channels through which trade has pro-competitive effects on prices, markups and productivity.
Macroeconomic channels through which openness affects trade are overlooked.
Also, increasing openness contains wage growth and lowers inflation (labour market channel).
*Marginal firm = achieves zero sales (its price is pMAX)
=> e.g., the marginal exporting domestic firm has cost: cx
*Due to trade costs, markets in different countries are distinct and firms have to choose how much to produce for domestic market (1st and last columns) and how much to produce for export (2nd and 3rd columns).
*Trade cost make it harder for exporters to break even relative to domestic producers
F.O.C. : use (3) and L.qC=q
(7) => if c > α –ηQc =cD, we necessarily have qD(c) = 0.
Firms with profit maximising price exceeding the price bound will exit (condition is that cM > cD)
All firms with cost c larger number of firms choose to produce
About trade costs, (16): for a given cut-off, a fall in trade cost means that more foreign markets are selling to the domestic market (imports and N rise).
A rise in varieties => a rise in the elasticity of demand => less market power => fall in markups and prices
As a result, higher cost firms must exit. Domestic and foreign firms with lower costs maintain production (=> trade-induced rise in productivity)
Total effect: net increase in N
=> PRO-COMPETITIVE EFFECTS in the SR
*the supply side is represented by a horizontal line in the LR.
Upward shift in the horizontal line
Relative prices fall with domestic openness and increase with foreign openness
Conditional on the ratios N*SR/N* and NSR/N, trade openness (lower trade costs) induces a fall in relative prices.
Conditional on trade openness, relative prices fall with an increase in D and rise in D*.
*In the SR and the LR, openness is expected to have linear effects on prices.
*cointegration = existence of a long-term relationship
Sample: 10 years....
Heteroskedasticity does not cause OLS coefficient estimates to be biased. However, the variance (and, thus, standard errors) of the coefficients tends to be underestimated, inflating t-scores and sometimes making insignificant variables appear to be statistically significant.
e.g., consumers in high price economies buy more imports
Firms in low productivity sectors may lobby for protectionism
Significance of SR effects when using GMM
Reversal effects in the LR
SR effects stand significantly