Micro to Macro: Optimal Trade Policy with Firm Heterogeneity

Transcription

1 Micro to Macro: Optimal Trade Policy with Firm Heterogeneity Arnaud Costinot, Andrés Rodríguez-Clare, Ivan Werning MIT, UC Berkeley, MIT March 29th, 2017 Optimal Policy in New Trade Models March 29th, / 51

2 Motivation Large firms tend to export, whereas small firms do not What are the policy implications of that empirical observation? Optimal Policy in New Trade Models March 29th, / 51

3 This Paper Optimal trade policy in generalized version of Melitz (2003) Two polar assumptions about set of available policy instruments: 1 Unconstrained taxes across firms 2 Uniform taxes across firms Optimal Policy in New Trade Models March 29th, / 51

4 Optimal Unconstrained Taxes At the micro-level: No discrimination across domestic exporters Discrimination against most profitable foreign exporters At the macro-level: Standard ToT considerations pin down the optimal level of trade policy. Given ToT elasticities, level of protection not affected by heterogeneity Though heterogeneity affects optimal pattern of protection at the micro-level Optimal Policy in New Trade Models March 29th, / 51

5 Optimal Uniform Taxes A generalized optimal tariff formula Gros (1987), Demidova and Rodriguez-Clare (2009), Felbermayr et al. (2013) Three sufficient statistics for optimal tariffs: Foreign s share of expenditure on domestically produced goods Foreign s EoS between domestically produced and imported goods Foreign s EoT between domestically produced and exported goods Selection of heterogeneous firms tends to: Create aggregate non-convexities (negative EoT) Lower optimal tariff (given other two statistics) Lerner paradox: Optimal tariff may become an import subsidy Optimal Policy in New Trade Models March 29th, / 51

6 Related Literature Firm Heterogeneity in International Trade: Extensive literature has revisited positive results of Helpman and Krugman 85; see Melitz and Redding s handbook chapter Few papers have revisited normative results of Helpman and Krugman 89; see Demidova and Rodriguez-Clare (2009), Felbermayr, Jung and Larch (2013), Haaland and Venables (2014), Bagwell and Lee (2015), and Demidova (2015) Methodology: Primal approach and general Lagrange multiplier methods, as in Costinot, Lorenzoni, Werning (2014) and Costinot, Donaldson, Vogel, Werning (2015) New micro-to-macro strategy that breaks down the design of optimal taxes into a series of micro problems and a macro problem Optimal Policy in New Trade Models March 29th, / 51

7 Outline of Presentation 1 Introduction 2 Basic Environment 3 Relaxed Planning Problems 4 Optimal Unconstrained Taxes 5 Optimal Uniform Taxes 6 Intra- and Inter-Industry Trade 7 Conclusion Optimal Policy in New Trade Models March 29th, / 51

8 Technology Two countries i = H, F : L i = labor endowment w i = wage Firms pay fixed entry cost f e i > 0 in order to draw ϕ Φ: N i = measure of entrants G i = distribution of ϕ Technology of a firm with draw ϕ: l ij (q, ϕ) = a ij (ϕ)q + f ij (ϕ), if q > 0, l ij (q, ϕ) = 0, if q = 0. Melitz (2003) = special case s.t. a ij (ϕ) = τ ij /ϕ and f ij (ϕ) = f ij Optimal Policy in New Trade Models March 29th, / 51

9 Preferences Representative agent with two-level homothetic utility function: U j = U j (Q Hj, Q Fj ), Q ij = [ N i (q ij (ϕ)) 1/µ i dg i (ϕ)] µ i. Φ with µ i σ i /(σ i 1) and σ i > 1 = EoS between varieties from country i. Melitz (2003) = special case s.t. µ H = µ F = µ and U j (Q Hj, Q Fj ) = [Q 1/µ Hj + Q 1/µ Fj ] µ Optimal Policy in New Trade Models March 29th, / 51

10 Market Structure All goods markets are monopolistically competitive with free entry. All labor markets are perfectly competitive. Optimal Policy in New Trade Models March 29th, / 51

11 Policy Instruments Full set of ad-valorem consumption and production taxes t ij (ϕ) = tax charged by country j on the consumption of a variety with blueprint ϕ produced in country i. For i j, t ij (ϕ) > 0 a tariff, t ij (ϕ) < 0 an import subsidy. s ij (ϕ) = subsidy paid by country i on the production by a domestic firm of a variety with blueprint ϕ sold in country j. For i j, s ij (ϕ) > 0 an export subsidy, s ij (ϕ) < 0 an export tax. Tax revenues rebated through a lump-sum transfer, T i. Optimal Policy in New Trade Models March 29th, / 51

12 Decentralized Equilibrium with Taxes In a decentralized equilibrium with taxes: 1 consumers choose consumption in order to maximize their utility subject to their budget constraint; 2 firms choose their output in order to maximize their profits taking their residual demand curves as given; 3 firms enter up to the point at which expected profits are zero; 4 markets clear; 5 the government s budget is balanced in each country. Notation: p ij (ϕ) µ i w i a ij (ϕ)/(1 + s ij (ϕ)) q ij (ϕ) [(1 + t ij (ϕ)) p ij (ϕ)/p ij ] σ i Q ij Optimal Policy in New Trade Models March 29th, / 51

13 Equilibrium Conditions q ij (ϕ) = p ij (ϕ) = { q ij (ϕ), if (µ i 1)a ij (ϕ) q ij (ϕ) f ij (ϕ), 0, otherwise, { p ij (ϕ), if (µ i 1)a ij (ϕ)q ij (ϕ) f ij (ϕ),, otherwise, (1) (2) Q Hj, Q Fj arg max {U j ( Q Hj, Q Fj ) P ij Q ij = w j L j + T j }, (3) Q Hj, Q Fj i=h,f P 1 σ j ij = N j [(1 + t ij (ϕ))p ij (ϕ)] 1 σ i dg i (ϕ), (4) Φ fi e = [µ i a ij (ϕ)q ij (ϕ) l ij (q ij (ϕ))]dg i (ϕ), (5) j=h,f Φ L i = N i [ l ij (q ij (ϕ), ϕ)dg i (ϕ) + fi e ], (6) j=h,f Φ T i = [ N j t ji (ϕ)p ji (ϕ)q ji (ϕ)dg j (ϕ) N i s ij (ϕ)p ij (ϕ)q ij (ϕ)dg i (ϕ)]. j=h,f Φ Φ (7) Optimal Policy in New Trade Models March 29th, / 51

14 Home Government s Problem Definition The home government s problem is max U H (Q HH, Q FH ) T H,{t jh,s Hj} j=h,f,{q ij,q ij,p ij,p ij,w i,n i } i,j=h,f subject to equilibrium conditions (1)-(7). We assume that only the home government is strategic, whereas the foreign government is passive, with all foreign taxes equal to zero. We solve the home government s problem using the primal approach: 1 Consider a relaxed planning problem in which domestic consumption, output, and the measure of entrants can be chosen directly 2 Show that the solution can be implemented through linear taxes and characterize the structure of these taxes. Optimal Policy in New Trade Models March 29th, / 51

15 Outline of Presentation 1 Introduction 2 Basic Environment 3 Relaxed Planning Problems 4 Optimal Unconstrained Taxes 5 Optimal Uniform Taxes 6 Intra- and Inter-Industry Trade 7 Conclusion Optimal Policy in New Trade Models March 29th, / 51

16 Home s Relaxed Planning Problem Start from home government s problem and drop all constraints with Home s tax instruments, T H, {t jh, s Hj } j=h,f, and Home s prices, w H, {p Hj } j=h,f Idea: planner directly chooses quantities, q HH {q HH (ϕ)}, q HF {q HF (ϕ)}, q FH {q FH (ϕ)}, and measure of domestic entrants, N H, subject to [ ] N H l Hj (q Hj (ϕ), ϕ)dg H (ϕ) + fh e = L H, j=h,f as well as foreign equilibrium conditions Φ Check later that we can implement solution to this problem using linear taxes Optimal Policy in New Trade Models March 29th, / 51

17 Home s Relaxed Planning Problem max U H (Q HH, Q FH ) {q ij,q ij } i,j=h,f,p FF,p FH,P FF,P HF,{N i } i=h,f subject to resource constraint in H and F, and { q FF (ϕ), if (µ F 1)a FF (ϕ) q FF (ϕ) f FF (ϕ), q FF (ϕ) = 0, otherwise, { p Fj (ϕ), if (µ F 1)a Fj (ϕ)q Fj (ϕ) f Fj (ϕ), p Fj (ϕ) = for j = H, F, otherwise, Q HF, Q FF arg max {U F ( Q HF, Q FF ) P HF Q HF + P FF Q FF = w F L F }, Q HF, Q FF P 1 σ j FF = N F [p FF (ϕ)] 1 σ F dg F (ϕ), Φ ff e = [µ F a Fj (ϕ)q Fj (ϕ) l Fj (q Fj (ϕ))]dg F (ϕ), j=h,f Φ Q ij =[ N i (q ij (ϕ)) 1/µ i dg i (ϕ)] µ i for i = H or j = H. Φ Optimal Policy in New Trade Models March 29th, / 51

18 Micro to Macro: an Overview Micro problem (I): Home s Production Possibility Frontier (q HH, q HF, N H ) Micro problem (II): Foreign s Offer Curve (q FH, N F, Q FF ) Macro problem: Manipulating terms-of-trade (Q HH, Q FH, Q HF ) max U H (Q HH, Q FH ) Q HH,Q FH,Q HF Q FH Q FH (Q HF ) L H (Q HH, Q HF ) L H with L H (Q HH, Q HF ) determined by the solution to micro problem (I) and Q FH (Q HF ) determined the solution to micro problem (II) Optimal Policy in New Trade Models March 29th, / 51

19 Micro Problem (I): Home s Production Possibility Frontier L H (Q HH, Q HF ) N H min q HH,q HF,N H N H Φ j=h,f Φ l Hj (q Hj (ϕ), ϕ)dg H (ϕ) + fh e (q Hj (ϕ)) 1/µ H dg H (ϕ) Q 1/µ H Hj, for j = H, F. For q HH and q HF, solve good-by-good using a Lagrangian approach, min l Hj (q, ϕ) λ Hj q 1/µ H q Discontinuity of l ij (q, ϕ) at q = 0 due to fixed cost cut-off rule, { qhj(ϕ) (µh a = Hj (ϕ)/λ Hj ) σ H, if ϕ Φ Hj, 0, otherwise, with the set of varieties with non-zero output such that Φ Hj {ϕ : µ H a Hj (ϕ)(µ H a Hj (ϕ)/λ Hj ) σ H l Hj ((µ H a Hj (ϕ)/λ Hj ) σ H, ϕ)}. Optimal Policy in New Trade Models March 29th, / 51

20 Micro Problem (I): Home s PPF L H (Q HH, Q HF ) N H min q HH,q HF,N H N H Φ j=h,f For NH, linearity of the Lagrangian implies j=h,f Φ l Hj (q Hj (ϕ), ϕ)dg H (ϕ) + fh e (q Hj (ϕ)) 1/µ H dg H (ϕ) Q 1/µ H Hj, for j = H, F. Φ Hj [µ H a Hj (ϕ)q Hj(ϕ) l Hj (q Hj(ϕ), ϕ)]dg H (ϕ) = f e H. Conditional on (Q HH, Q HF ), output and number of entrants in decentralized equilibrium w/o taxes and at the solution to the planner s problem coincide. Government will not want to use micro-level taxes for domestic varieties. Optimal Policy in New Trade Models March 29th, / 51

21 Micro Problem (II): Foreign s Offer Curve Q 1/µ F FH (Q HF ) max q FH,Q FF,N F Φ N F q 1/µ F FH (ϕ)dg F (ϕ)) L F = P FF (Q FF, N F )(Q FF + MRS F (Q HF, Q FF )Q HF ) N F ff e = Π FF (Q FF, N F ) + N F [µ F a FH (ϕ)q FH (ϕ) l FH (q FH (ϕ), ϕ)]dg F (ϕ), L F = N F ff e + L FF (Q FF, N F ) + N F l FH (q FH (ϕ), ϕ)dg F (ϕ), µ F a FH (ϕ)q FH (ϕ) l FH (q FH (ϕ), ϕ), For q FH, maximize the Lagrangian good-by-good max q q1/µ F λ E µ F a FH (ϕ)q + (λ E λ L )l FH (q, ϕ) µ F a FH (ϕ)q l FH (q, ϕ), Φ Optimal Policy in New Trade Models March 29th, / 51

22 Micro Problem (II): Foreign s Offer Curve Let qfh u (ϕ) = solution ignoring constraint, and let qc FH (ϕ) = q that satisfies the constraint with equality If q u FH(ϕ) > q c FH(ϕ) then q FH(ϕ) = q u FH(ϕ). But otherwise two possibilities: constraint with equality or zero imports. Profitability index of foreign varieties in the home market, θ FH (ϕ) (λ FH /χ FH µ F )[(µ F 1)Q FH (a FH (ϕ)) 1 σ F /f FH (ϕ)] 1/σ F Optimal imports are (µ F χ FH a FH (ϕ)) σ F, if ϕ Φ u qfh(ϕ) FH, = f FH (ϕ)/((µ F 1)a FH (ϕ)), if ϕ Φ c FH, 0, otherwise, For ϕ Φ c FH {ϕ : θ FH(ϕ) [λ L /(λ L + (µ F 1)λ E ), 1)}, Home finds it optimal to alter its importing decision so that foreign firms are willing to produce and export strictly positive amounts. Government will want to impose import taxes that vary across firms. Optimal Policy in New Trade Models March 29th, / 51

23 Macro Problem: Manipulating TOT Goal of Home s planner is max U H (Q HH, Q FH ) s.t. resource constraint and Foreign s offer curve. Resource constraint can be expressed as L H (Q HH, Q HF ) = L H Foreign s offer curve can be expressed as Q FH Q FH (Q HF ). Hence, optimal aggregate quantities must solve max U H (Q HH, Q FH ) Q HH,Q FH,Q HF Q FH Q FH (Q HF ), L H (Q HH, Q HF ) = L H, Optimal Policy in New Trade Models March 29th, / 51

24 First-Order Conditions Let us define Home s terms-of-trade as with P(Q FH, Q HF ) P HF (Q HF )/ P FH (Q HF, Q FH ), P HF (Q HF ) = P FF (Q FF (Q HF ), N F (Q HF ))MRS F (Q HF, Q FF (Q HF )), P FH (Q HF, Q FH ) = N F (Q HF ) µ F a FH (ϕ)q FH (ϕ Q HF )dg F (ϕ)/q FH. FOCs imply Φ MRT HP /MRS H = 1/η, with MRS H U HH/U FH, MRT H L HH/L HF, and η d ln Q FH /d ln Q HF is the elasticity of Foreign s offer curve Optimal Policy in New Trade Models March 29th, / 51

25 Outline of Presentation 1 Introduction 2 Basic Environment 3 Relaxed Planning Problems 4 Optimal Unconstrained Taxes 5 Optimal Uniform Taxes 6 Intra- and Inter-Industry Trade 7 Conclusion Optimal Policy in New Trade Models March 29th, / 51

26 Micro-Level Taxes on Domestic Varieties Lemma To implement solution to relaxed problem, need to set domestic taxes s.t. (1 + s HH(ϕ))/(1 + t HH(ϕ)) = (1 + s HH)/(1 + t HH) if ϕ Φ HH. Lemma To implement solution to relaxed problem, need to set export taxes s.t. s HF (ϕ) = s HF if ϕ Φ HF. Optimal Policy in New Trade Models March 29th, / 51

27 Micro-Level Taxes on Imported Varieties Lemma To implement solution to relaxed problem, need to set import taxes s.t. t FH(ϕ) = (1 + t FH) min{1, θ FH (ϕ)} 1 if ϕ Φ FH Φ u FH + Φ c FH. Higher taxes on more profitable exporters Like anti-dumping duties, but here to import from less profitable exporters Optimal Policy in New Trade Models March 29th, / 51

28 Overall Level of Taxes Lemma To implement solution to relaxed problem, need to set (1 + tfh )/(1 + t HH ) (1 + shf )/(1 + s HH ) = Φ FH ((min{1, θ FH (ϕ)}) µ F a FH (ϕ)) 1 σ F dg F (ϕ) η Φ FH ((min{1, θ FH (ϕ)})a FH (ϕ)) 1 σ F dg F (ϕ). If Φ c FH is measure zero then min{1, θ FH(ϕ)} = 1 for all ϕ Φ FH so optimal import taxes are uniform and (1 + t FH )/(1 + t HH ) (1 + s HF )/(1 + s HH ) = 1/η. This is what would happen w/o fixed exporting costs, as in Krugman (1980). Optimal Policy in New Trade Models March 29th, / 51

29 Overall Level of Taxes Lemma To implement solution to relaxed problem, need to set (1 + tfh )/(1 + t HH ) (1 + shf )/(1 + s HH ) = Φ FH ((min{1, θ FH (ϕ)}) µ F a FH (ϕ)) 1 σ F dg F (ϕ) η Φ FH ((min{1, θ FH (ϕ)})a FH (ϕ)) 1 σ F dg F (ϕ). If Φ c FH is not measure zero, then µ F > 1 implies (1 + t FH )/(1 + t HH ) (1 + s HF )/(1 + s HH ) > 1/η. To implement same wedge, need higher import taxes on varieties ϕ Φ u FH Optimal Policy in New Trade Models March 29th, / 51

30 Implementation Lemma Augmented with high enough taxes on the goods that are not consumed, previous taxes are sufficient to implement solution to relaxed problem. There exists a decentralized equilibrium with taxes that implements the solution to relaxed problem. Since Home s planning problem is a relaxed version of Home s government problem, its solution must also satisfy previous necessary properties. Proposition At the micro-level, unilaterally optimal taxes should be s.t.: (i) domestic taxes are uniform across all domestic producers; (ii) export taxes are uniform across all exporters; (iii) import taxes are uniform across Foreign s most profitable exporters and strictly increasing with profitability across a set of marginally unprofitable ones. At the macro-level, unilaterally optimal taxes should reflect standard terms-of-trade considerations. Optimal Policy in New Trade Models March 29th, / 51

31 Firm heterogeneity and Trade Policy Macro-elasticity, η, determines the wedge between Home and Foreign s marginal rates of substitution at the first-best allocation. Like in ACR, this relationship is not affected by firm heterogeneity. At the macro-level, Home s planning problem can still be reduced to a standard ToT manipulation problem. But even conditioning on macro-elasticity, firm heterogeneity affects policy: Optimal trade taxes are heterogeneous across foreign exporters. To lower the price of its imports, P FH, Home s government imposes tariffs that are increasing with the profitability of foreign exporters. Very different micro-level policies under perfect and monopolistic competition: Ricardian model: uniform import taxes, discriminatory export taxes (CDVW). Melitz model: discriminatory import taxes, uniform export taxes. Optimal Policy in New Trade Models March 29th, / 51

32 Outline of Presentation 1 Introduction 2 Basic Environment 3 Relaxed Planning Problems 4 Optimal Unconstrained Taxes 5 Optimal Uniform Taxes 6 Intra- and Inter-Industry Trade 7 Conclusion Optimal Policy in New Trade Models March 29th, / 51

33 Optimal Uniform Taxes Now suppose that government can only impose taxes that are uniform across firms: t HF (ϕ) = t HF ; t HH (ϕ) = t HH ; s HF (ϕ) = s HF ; and s HH (ϕ) = s HH With this restricted set of instruments, one can check that (1 + t FH )/(1 + t HH ) (1 + s HF )/(1 + s HH ) = 1/η Next: What determines elasticity of Foreign s offer curve, η? Optimal Policy in New Trade Models March 29th, / 51

34 Foreign Equilibrium Conditions with Uniform Taxes With uniform taxes, Foreign will be on its PPF, with L F (Q FH, Q FF ) N F In line with our previous notation, let L F (Q FH, Q FF ) = L F [ ] min N F l Fj (q Fj (ϕ), ϕ)dg F (ϕ) + ff e q FH,q FF,N F j=h,f Φ Φ (q Fj (ϕ)) 1/µ F dg F (ϕ) Q 1/µ F Fj, for j = H, F. MRT F (Q FH, Q FF ) L FH /L FF Optimal Policy in New Trade Models March 29th, / 51

35 Foreign Equilibrium Conditions with Uniform Taxes Lemma Conditional on Q HF and Q FH, the decentralized equilibrium abroad satisfies MRS F (Q HF, Q FF (Q FH )) = P HF /P FF, MRT F (Q FH, Q FF (Q FH )) = P FH /P FF, P HF Q HF = P FH Q FH, with local production, Q FF (Q FH ), given by the implicit solution of L F (Q FH, Q FF ) = L F. In terms of aggregate quantities and prices, this is isomorphic to a neoclassical equilibrium with three goods: FF, FH, HF Only difference is that under monopolistic competition, Foreign s production set may not be convex. Optimal Policy in New Trade Models March 29th, / 51

36 Aggregate Nonconvexities with Firm Heterogeneity Q FF Q FH Optimal Policy in New Trade Models March 29th, / 51

37 Terms-of-Trade Elasticities Let ɛ d ln(q HF /Q FF ) d ln(p HF /P FF ) denote the EoS between imports and domestic goods and let κ d ln(q FH/Q FF ) d ln(p FH /P FF ) denote the EoT between exports and domestic goods Previous lemma plus homotheticity of MRS F and MRT F implies that ( ) 1 d ln MRSF (Q HF /Q FF, 1) ɛ =, d ln(q HF /Q FF ) ( ) 1 d ln MRTF (Q FH /Q FF, 1) κ =. d ln(q FH /Q FF ) Optimal Policy in New Trade Models March 29th, / 51

38 Elasticities with Uniform Taxes Previous lemma also implies that P(Q FH, Q HF ) = MRS F (Q HF, Q FF (Q FH ))/MRT F (Q FH, Q FF (Q FH )). Foreign offer curve can then be represented as P(Q FH, Q HF )Q HF = Q FH, Differentiating w.r.t. Q HF and Q FH, we get η = (1 + ρ HF )/(1 ρ FH ), with ρ ij ln P(Q FH, Q HF )/ ln Q ij s.t. ρ HF = 1/ɛ, ρ FH = (1/x FF 1)/ɛ 1/(x FF κ), where x FF P FF Q FF /L F is the share of expenditure on domestically produced goods in Foreign. Optimal Policy in New Trade Models March 29th, / 51

39 A Generalized Optimal Tariff Formula W.l.o.g set t HH = s HH = s HF = 0 to focus on optimal tariff, t FH Previous results for η combined with imply Proposition Optimal uniform tariffs are such that (1 + t FH )/(1 + t HH ) (1 + s HF )/(1 + s HH ) = 1/η t FH = 1 + (ɛ /κ ) (ɛ 1)x, FF where ɛ, κ, and x FF are the values of ɛ, κ, and x FF evaluated at those taxes. Optimal Policy in New Trade Models March 29th, / 51

40 A Generalized Optimal Tariff Formula Our new formula: t FH = 1 + (ɛ /κ ) (ɛ 1)x FF This is a strict generalization of Gros (1987) formula obtained in an economy without firm heterogeneity, as in Krugman (1980) Utility is CES, ɛ = σ H = σ F σ. All firms export to all markets and MRT F is constant, MRT F = ( Φ (a FH(ϕ)) 1 σ F dg F (ϕ)) 1/(1 σ F ) ( Φ (a FF (ϕ)) 1 σ F dgf (ϕ)) 1/(1 σ F ). Hence, the elasticity of transformation κ goes to infinity so t FH 1 = (σ 1)xFF > 0. New formula clarifies the importance of TOT considerations, which depend on ɛ, relative to markup distortions, which depend on σ (HK 89) Optimal Policy in New Trade Models March 29th, / 51

41 A Generalized Optimal Tariff Formula Our new formula: t FH = 1 + (ɛ /κ ) (ɛ 1)x FF This is a strict generalization of the formulas in Demidova and Rodriguez-Clare (2009) and Felbermayr, Jung and Larch (2013) where Utility is CES, ɛ = σ H = σ F σ Firms only differ in productivity, productivity distribution is Pareto, so that κ σθ (σ 1) = θ (σ 1) < 0 where θ > σ 1 is the shape parameter of the Pareto distribution. Hence the optimal tariff is t FH 1 = (θµ 1)xFF > 0. Optimal Policy in New Trade Models March 29th, / 51

42 Nonconvexities and Optimal Trade Policy Our new formula, t FH = 1 + (ɛ /κ ) (ɛ 1)x, FF and the fact that ɛ 1 > 0 (needed for FOC), then κ (firms are homogeneous) leads to Corollary Conditional on (ɛ, xff ), optimal uniform tariffs are strictly lower with than without firm heterogeneity iff heterogeneity aggregate nonconvexities, κ < 0. Home s trade restrictions derive from the negative effects of exports and imports on its terms of trade. By reducing elasticity of Home s ToT w.r.t. its imports, aggregate nonconvexities dampen this effect and reduce optimal level of protection. Optimal Policy in New Trade Models March 29th, / 51

43 Firm Heterogeneity and Nonconvexities Lemma When do we have κ < 0? If N F (Q FH, Q FF )/ Q Fj 0 for j = H, F, then firm heterogeneity creates aggregate nonconvexities, κ 0, with κ < 0 if selection is active in at least one market. Combining this result with our optimal tariff formula leads to: Proposition If the measure of foreign entrants increases with aggregate output to any market, then conditional on (ɛ, xff ), optimal uniform tariffs are lower with than without firm heterogeneity, with strict inequality whenever selection is active in at least one market. Optimal Policy in New Trade Models March 29th, / 51

44 Firm Heterogeneity and Lerner Paradox Firm heterogeneity may actually lower the overall level of trade protection so much that the optimal uniform tariff may become an import subsidy. As ɛ goes to infinity, the optimal uniform tariff converges towards t FH = 1/(κ x FF ), which is strictly negative if aggregate nonconvexities abroad, κ < 0. Government may lower the price of its imports by raising their volume and inducing more foreign firms to become exporters Derives from nonconvexities unique to MC models with selection Optimal Policy in New Trade Models March 29th, / 51

45 Outline of Presentation 1 Introduction 2 Basic Environment 3 Relaxed Planning Problems 4 Optimal Unconstrained Taxes 5 Optimal Uniform Taxes 6 Intra- and Inter-Industry Trade 7 Conclusion Optimal Policy in New Trade Models March 29th, / 51

46 Intra- and Inter-Industry Trade Multiple sectors, homothetic uper tier preferences: U i = U i (U 1 i,.., U K i ), Ui k = Ui k (QHi, k QFi), k Qji k = [ Nj k (qji k (ϕ)) 1/µk j dg k j (ϕ)] µk j Φ Same results at the micro level: domestic taxes should be uniform across firms within the same sector import taxes should be lower on the least profitable exporters from Foreign At the macro level, little that can be said in general, as in a perfectly competitive environment, so we turn to simple example Optimal Policy in New Trade Models March 29th, / 51

47 Intra- and Inter-Industry Trade One homogeneous outside sector and one differentiated sector Optimal uniform taxes are such that (1 + t D FH )/(1 + t D HH ) (1 + s D HF )/(1 + sd HH ) = (1 )/η D, (1 + t D FH)/(1 + t O H ) = /η O. with η D d ln QFH D (QD HF, X H O)/d ) ln QD HF, ηo d ln QFH D (QD HF, X H O)/d ln X H O, and ( P FH D QD FH PD HF QD HF / P FH D QD FH Offer curve elasticities can be computed as we did before ( ) 1 + ρ η D D = HF ( 1) ρ D HF + (1 ) ρd FH ζ, FH η O = + (1 ) ρd X ζ X 1 + ( 1) ρ D FH + ζ, FH with ρ D HF ln PD / ln Q D HF, ρd FH ln PD / ln Q D FH, ρ D X ln PD / ln X O H, ζ FH ln P D FH / ln QD FH, and ζ X ln P D FH / ln X O H. Optimal Policy in New Trade Models March 29th, / 51

48 Intra- and Inter-Industry Trade If Home is small (i.e., cannot affect NF D ζ FH = 1/κ D, and so nor QD FF ) then ζ X = ρ D X = 0 and (1 + t FH D )/(1 + t HH D ) (1 + s HF D )/(1 + sd HH ) = ɛd /κ D ɛ D 1, (1 + t D FH)/(1 + t O H ) = 1 + 1/κ D. Trade protection within differentiated sector same as in one-sector case If κ D < 0, less trade protection in the differentiated sector relative to the homogeneous sector: Import subsidy in the differentiated sector or export subsidy in the homogeneous sector Optimal Policy in New Trade Models March 29th, / 51

49 Outline of Presentation 1 Introduction 2 Basic Environment 3 Relaxed Planning Problems 4 Optimal Unconstrained Taxes 5 Optimal Uniform Taxes 6 Intra- and Inter-Industry Trade 7 Conclusion Optimal Policy in New Trade Models March 29th, / 51

50 Conclusion Few economic mechanisms have received as much empirical support as the selection of heterogeneous firms into exporting Policy makers have paid attention: Prior to 1990, there were only two regional trade agreements (RTA) with provisions related to small- and medium-sized enterprises (SME) prior to 1990 As of March 2016, 133 RTAs, representing 49% of all the notified RTAs, include at least one provision mentioning explicitly SMEs Ironically, little academic work about the policy implications of the endogenous selection of firms into exporting Optimal Policy in New Trade Models March 29th, / 51

51 Conclusion In this paper, we have shown that when taxes are unrestricted, optimal trade policy requires micro-level policies: Import taxes that discriminate against the most profitable foreign exporters. Export taxes that discriminate against or in favor of the most profitable domestic exporters can be dispensed with. When taxes are uniform, firm heterogeneity tends to create aggregate nonconvexities that lowers the overall level of trade protection. A lot more to do on the normative side of the literature: Variable markups, global value chains, industrial policy Optimal Policy in New Trade Models March 29th, / 51