International Prices and Exchange Rates Econ 2530b, Gita Gopinath Model variable mark-ups CES demand: Constant mark-ups: ( ) εin µ in = log ε in 1 Given that markups are constant, Γ in = 0. ( ) θ = log. θ 1 () April 2, 2013 1 / 11
Non CES demand Kimball (1995): homothetic aggregator over individual varieties implicitly defined by: ( ) 1 Ωn Q in A in Υ di = 1, Ω n Ω n A in Q n Υ (1) = 1, Υ (.) > 0 and Υ (.) < 0. Under CES, Υ ( Ωn Q in A in Q n ) = ( ) θ 1 Qin θ A in Q n Cost minimization (or utility maximization) λ n : Lagrange multiplier, P in = Υ ( Ωn Q in A in Q n. ) λn Q n, P n Q n = Q in P in di = λ n D n, Ω n where P n is the price index and D n Ω n Υ ( Ω n Q in A in Q n ) Qin Q n di. () April 2, 2013 2 / 11
Non CES demand inverse demand function for variety i in country n is ( ) Υ Ωn Q in P = in D n, A in Q n P n ( ) P Q in = in A in ψ D n Q n, P n ψ (.) = Υ 1 (.) / Ω > 0 and ψ (.) < 0 Υ (.) < 0. In logs, q in = a in + log (ψ (exp (x in ))) + q n, x in = log (D n ) + p in p n, a in = log (A in ). Demand elasticity: ε in = ψ (.) D n P in, ψ (.) P n () April 2, 2013 3 / 11
Non CES demand Klenow-Willis (2006) choose a specification Υ that results in a demand function: demand elasticity is log (ψ (x)) = θ log [1 ηx]. η log ψ (x) θ ε in = = x 1 ηx in which is constant when η = 0 and increasing in x when η > 0. log markup is ( ) θ µ in = log θ 1 + ηx in and the elasticity of the markup with respect to the relative price is η Γ in =. θ 1 + ηx in when η > 0 markups are decreasing in the relative price. () April 2, 2013 4 / 11
Strategic complementarities in pricing with CES demand Atkeson-Burstein (AER) () April 2, 2013 5 / 11
Model Two symmetric countries i =1, 2. Two types of final goods: tradeable and non tradeable Firms in each country produce differentiated goods Heterogeneous productivities across firms Trade costs for tradeable goods Nested CES Goods grouped into sectors, few goods per sector, many sectors high elasticity within sectors low elasticity across sectors Imperfect competition 13
Production of final goods Tradeable and nontradable consumption c i = c T i γ c N i 1 γ Symmetric Dixit Stiglitz aggregate using continuum of sectors c T i = Z 1 y T 1 1/η ij dj η/(η 1) 0 14
Traded sector (drop T super-script for now) Competitive firm uses output of continuum of sectors j Demand for sector j [ 1 c i = 0 [ 1 P i = 0 P ij P i = ] η y 1 1/η η 1 ij dj ] 1 P 1 η 1 η ij dj ( yij c i ) 1 η
In country i and sector j there are K domestic firms selling distinct goods and an additional K foreign firms that may, in equilibrium, sell goods in that sector. Output in each sector y ij = P ij = [ 2K k=1 [ 2K P ijk P ij = (q ijk ) ρ 1 ρ P 1 ρ ijk dj k=1 ( qijk y ij ) 1 ρ Production costs: Production function ] ρ ρ 1 ] 1 1 ρ A i zl W i A i z z is idiosyncratic. Fixed labor cost F for firm if it exports. Also, iceberg marginal cost D 1
Costs: Production function A i zl z is idiosyncratic. W i A i z Fixed labor cost F for firm if it exports. Iceberg marginal cost D 1
Firms play a static game of quantity competition. Choose q ijk taking as given quantities chosen by other firms in the economy and W. Each firm recognizes that sectoral prices P ij vary when the firm changes q ijk Firms problem is to and quantities y ij subject to max P ijk q ijk q ijk MC ijk P ijk P i = Take c i and P i as given. y ij = ( qijk y ij [ 2K k=1 ) 1 ρ ( y ij c i ) 1 η ] ρ (q ijk ) ρ 1 ρ 1 ρ
FOC P ijk + q ijk P ijk q ijk MC ijk = 0 ( qijk ) 1 ( ) 1 ρ y ij η P ijk = Pi y ij c i ln P ijk = ln P i 1 ( 1 ρ ln q ijk + ρ 1 η = 1 ( 1 1 + q ijk ρ q ijk ρ 1 ) ln yij η 1 P ijk P ijk q ijk ) ln y ij + 1 η (ln c i)
y ij = ln y ij q ijk = = [ 2K k=1 ρ ρ 1 ] ρ (q ijk ) ρ 1 ρ 1 ρ 1 [ 2K k=1 (q ijk) ρ 1 ρ 1 [ 2K k=1 (q ijk) ρ 1 ρ ]q 1 ρ ijk ] ρ 1 ρ ρ 1 q ρ 1 ijk
P ijk 1 1 ρ + ( 1 ρ 1 η ) 1 [ 2K k=1 (q ijk) ρ 1 ρ 1 ρ ]q +1 ijk = MC ijk s = P ijk P ij q ijk y ij = ( qijk y ij ) 1 ρ +1 [ 1 P ijk [1 ρ (1 s) + 1 ]] η s = MC ijk
Define ε(s) = [ 1 ρ (1 s ijk) + 1 ] 1 η s ijk P ijk = K non-linear equations. (implicit) ε(s ijk) ε(s ijk ) 1 MC ijk When ρ > η, mark-ups rise with market share s ijk ρ from ρ 1 when s ijk = 0 from η η 1 when s ijk = 1
Step 1: Only K domestic varirties Step 2: The most productive foreign firm enters, re-solve, if profitable then next one enters re-solve and so on. s ijk = P ijkq ijk P j y ij = (P ijk) 1 ρ (Pijl ) 1 ρ
Markups and elasticities, η=1.01, ρ=10 10 Percieved elasticity of demand 9 8 7 6 5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Sectoral market share 5.5 Markup 5 4.5 4 3.5 3 2.5 2 1.5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Sectoral market share
Pricing to market: simple example Sector j: Country 1 producers face no foreign competitors when selling in country 1. Country 1 exporter (firm k) face foreign competitors when selling abroad. Ŵ1 > 0, Ŵ 2 =0 ˆP 1jk = Ŵ1 ˆP 2jk < Ŵ1 Pricing to market: ˆP 1jk > ˆP 2jk 20
Constant markup version ρ = η Two illustrative alternatives Frictionless trade version D =1,F =0. 20
Quantitative example K =20,η=1,ρ=10,D=1.59, F =0.0002, θ =0.38,σ=0.20. Share of imports in gross tradeable output =16.5% 25% tradeable firms exports Plausible distribution of markups and Herfindahl indices Other micro trade patterns: G L indices for intra sectoral trade Plants export small fraction of output. Exporters are larger than non exporters. Large dispersion of value added per worker across firms. Value added per worker higher for exporters relative to non exporters. 21
Parameters and Symmetric Equilibrium Implications Benchmark Model Parameters K 20 0.38 0.20 1.01 10.0 D 1.59 0.0002 F/c T Symmetric Equilibrium Implications US Data Source Exports / Manufacturing Gross Output 16.6% 16.5% US Input-Output Fraction of exporting firms in tradeable sector 25.0% 25% Bernard - Jensen Median exporter's intensity 13.2% < 10% BEJK Average Grubel-Lloyd index 25.8 25 Schott Average exporter's - non-exporter's 11.3% [15% - 33%] BEJK log value added per worker Average domestic exporter's sales 9.9 4.8-28 BEJK, EKK / average non exporter's sales Median Herfindahl Index 1511 Average markup 27.8%
Figure 3: Herfindahl Indices and Markups in Symmetric Equilibrium 0.25 Herfindahl Indices 0.2 0.15 0.1 0.05 0 500 1000 1500 2000 2500 3000 3500 0.8 Markups 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6
Two illustrative alternatives Frictionless trade version D =1,F =0. All firms export. Export intensity = 50% Import share = 50% Constant markup version ρ = η. No dispersion in markups and value added per worker. 24
Table 4 Implications of Model: 1% increase in (W1/A1) / (W2/A2) 1 2 3 Benchmark Constant Frictionless Model Markup Trade Terms of Trade and PPI-based-RER PPI 1 PPI 2 decomposition (% contribution): 1 EPI 1 IPI 1 53.4% 100.0% 100.0% 2 PPI 1 EPI 1 23.1% 0.0% 0.0% 3 IPI 1 PPI 2 23.6% 0.0% 0.0% 4 PPI 1 0.86% 1.00% 0.76% 5 EPI 1 0.69% 1.00% 0.76% 6 IPI 1 0.31% 0.00% 0.23% 7 PPI 2 0.14% 0.00% 0.23% CPI-based-RER 8 CPI 1 CPI 2 / PPI 1 PPI 2 (excl. distribution) 82.3% 66.9% 0.0%
Distribution Costs Corsetti and Dedola 2005 When country i firms sell to country n there is a retail (and wholesale) sector that bundles the imported good with distribution services to bring it to the final consumer. retail sector is competitive and combines the good and distribution services at fixed proportions retail price (in levels) P r in is given by: P r in = P in + η in P d n η in denotes the fixed distribution cost per good. () April 2, 2013 6 / 11
Distribution Costs Suppose P d n = P n. consider a CES demand at the retail level with elasticity of substitution θ: Q in = A in ( P r in P n ) θ Qn, where P n denotes the aggregate CES price inclusive of distribution costs. elasticity of demand country i firm faces when selling in country n is where sin d = retail price. η inp n P in +η in P n ε in = log Q ( ) in = θ 1 sin d log P in denotes the share of distribution services in the () April 2, 2013 7 / 11
Distribution Costs The optimal mark-up for a monopolistic price-setter is: [ ( ) ] θ 1 s d [ µ in = log in θ ( ) 1 sin d = log 1 θ θ 1 η in exp ( (p in p n )) The elasticity of the markup with respect to the relative price p in p n is 1 Γ in = θ 1 η in exp( (p in p n )) 1 = 1. (1) (θ 1) 1 sd in 1 sin d Clearly Γ in = 0 if s d in = 0 and Γ in > 0 if s d in > 0. ]. () April 2, 2013 8 / 11
Elasticity of markup to relative price Γ in non-ces demand: markup elasticity is higher for low relative price firms. CES demand with a finite number of firms: the markup elasticity is higher for higher market share firms. distribution costs: markup elasticity is higher for firms with higher distribution share. In all models, everything else the same, more productive firms have a lower relative price, a higher expenditure share, and a higher markup elasticity. () April 2, 2013 9 / 11
Empirical Evidence Berman et. al (QJE 2012): French firms higher productivity firms in France have lower ERPT than low productivity firms. Chatterjee et.al. (AEJ 2012) Brazilian data find similar results on ERPT across individual products exported by multi-product firms. Oleg-Amiti (2013) Belgian exporters with higher expenditures shares in the destination market have lower ERPT. This is both because of the the markup channel (i.e. Γ in ) and because larger exporters import a larger fraction of intermediate inputs that in turn lowers their sensitivity to bilateral exchange rate shocks, that is they have a lower α in. () April 2, 2013 10 / 11
Empirical Evidence Goldberg and Hellerstein (2006), Hellerstein (2008), Goldberg and Verboven (2001), Nakamura and Zerom (2010) structural models of international pricing featuring heterogeneous consumer choosing among horizontally differentiated varieties that better suit their preferences. These models, which give rise to richer and more flexible demand systems, are simulated and estimated using detailed micro data and econometric methods that are standard in the field of industrial organization. Goldberg and Hellerstein (2008) provide a recent survey of this work. () April 2, 2013 11 / 11