Intra- and inter-industry misallocation and comparative advantage

Transcription

1 Intra- and inter-industry misallocation and comparative advantage José Pulido Vancouver School of Economics University of British Columbia Job Market Seminar January 2018

2 Introduction Comparative advantage (CA) is one of the main explanations of bilateral trade flows. This paper shows that firm-level factor misallocation (FM) can alter the relative unit costs of producing a good across industries, distorting the natural CA of a country. I I FM: The extent in which the marginal returns of the factors varies across firms. Literature on FM has focused on closed economies: e ect on aggregate TFP.

3 Two types of FM In an open economy, FM can shape CA at two levels of aggregation: I I Di erences in FM within industries: Larger extent of intra-industry FM ) larger TFP losses. FM between industries: If firms in an industry exhibit on average larger marginal returns to factors ) industry size is too small and average productivity is too high. Examples: East Asian industry policies during post-war period, import substitution schemes in Latin America during s.

4 Main questions 1 Are observed patterns of CA related to both types of FM? 2 What are the implications of removing FM for CA taking into account general equilibrium e ects?

5 Outline (I) 1 Are both types of FM related to observed patterns of CA? Using Colombian firm-level data, I present evidence on how metrics of FM are related to measures of revealed comparative advantage (RCA). I Colombian prices at the firm-level makes it possible to obtain direct measures of physical productivity. I As a RCA measure, I use the estimates of the exporter-industry fixed e ect derived from a gravity equation. I find that both types of FM have a quantitative importance similar to the Ricardian and Heckscher-Ohlin determinants.

6 Outline (II) 2 What are the implications of removing FM for CA taking into account general equilibrium e ects? I use a general equilibrium model of international trade with endogenous selection of heterogeneous firms and both types of FM, to compute a counterfactual in which FM is removed in Colombia. Removing FM allows Colombia to specialize in industries with natural CA. I Industrial composition substantially changes. I decompose the change in the RCA in the contributions of the extensive (number of varieties produced) and intensive margin (average price). I Extensive margin drives the results.

7 Related literature 1. On FM: - Endogenous selection: Bartelsman et al. (2013), Yang (2017), Adamopoulos et al. (2017). - Intra/inter-industry types: Oberfield (2013), Brandt et al. (2013). - Wedge analysis: Restuccia and Rogerson (2008) and Hsieh and Klenow (2009) (inspired by the business cycle literature). 2. On trade: - Trade reforms and intra- and inter-industry factor reallocation: Bernard et al. (2007), Balistreri (2011). - CA measures: Costinot et al. (2012), Levchenko and Zhang (2015), Hanson et al. (2016), French (2017). - Sources of CA: Beck (2002), Levchenko (2007), Bombardini et al. (2012), Nunn and Trefler (2015). 3. Intersection of 1 and 2: - Trade liberalization in an economy with factor distortions: Ho (2012), Tombe (2015), åwiícki (2017).

8 Contents 1 Introduction 2 Definitions and motivation Revealed comparative advantage (RCA) measure Intra and inter-industry misallocation measures RCA and misallocation 3 Theoretical framework Model Gravity equation 4 Empirical implementation Counterfactual exercise Baseline results

9 1 Introduction 2 Definitions and motivation Revealed comparative advantage (RCA) measure Intra and inter-industry misallocation measures RCA and misallocation 3 Theoretical framework Model Gravity equation 4 Empirical implementation Counterfactual exercise Baseline results

10 RCA measure New trade models deliver theoretically grounded gravity equations. Gravity structure allows to decompose bilateral log of exports x ijs (i exporter, j importer, s sector) in three terms: lnx ijs = d is + d js + d ij + # ijs 1 d is : Exporting country s export capability in s 2 d js : Importing country s demand for foreign goods in s 3 d ij + # ijs : Bilateral accessibility of destination to exporter (trade costs + other bilateral frictions)

11 RCA measure New trade models deliver theoretically grounded gravity equations. Gravity structure allows to decompose bilateral log of exports x ijs (i exporter, j importer, s sector) in three terms: lnx ijs = d is + d js + d ij + # ijs I Let ˆd is an estimate of d is. A revealed comparative advantage (RCA) measure is: RCA is = exp[( ˆd is ˆd is 0) ( ˆd i 0 s ˆd i 0 s 0)] Same as Costinot et al. (2012) or Hanson et al. (2016). I Set of 48 Countries, 26 Sectors for 1995, global means for i 0 and s 0,as in Hanson et al. (2016). Estimated by Poisson-PML

12 RCA for Colombia Leather Petroleum Printing Apparel Footwear Pottery Oth. non-metal. minerals Food Chemicals Glass Textiles Plastic Oth chemicals Paper Non-ferrous metal Rubber Metal products not M&E Beverage Furniture Iron and steel Wood Elec. / profess. M&E Transport Tobacco RCA measure for Colombian manufacturing industries* (PPML estimation) RCA measure Numbers indicate export shares (%) *Relative to the mean industry and the mean country in the world, for Manufacturing exports are 65% of the total exports in Colombia PPML vs Tobit Export composition

13 1 Introduction 2 Definitions and motivation Revealed comparative advantage (RCA) measure Intra and inter-industry misallocation measures RCA and misallocation 3 Theoretical framework Model Gravity equation 4 Empirical implementation Counterfactual exercise Baseline results

14 An e cient allocation of resources Assume firms are heterogenous in TFP, but all firms in an industry use the factors with the same intensity. Under the standard monopolistic competition setting (Dixit-Stiglitz preferences and constant returns to scale production functions), in an e cient allocation: 1 Marginal revenue products (MRP) of factors are equalized across all firms. 2 Industry s TFP is a power mean of firm-level physical productivities (TFPQ).

15 MRP distributions To visualize MRP, assume Cobb-Douglas technology, no fixed costs. MRP of factors: some industries Capital Skilled labor Unskilled labor Density Density Density log(mrp) log(mrp) log(mrp) Food Wood products Chemicals Motor vehicles *MRP: Marginal revenue product. CD-GO specification, controlling for year FE. Source: Colombian AMS. Other explanations

16 Measures of misallocation Two possible measures of intra-industry FM: 1 Ratio sectoral TFP to e cient TFP: A is /A e is = AEM is 2 Dispersion in firm-level revenue productivity (TFPR): s 2 TFPR is I Since TFPR (revenues/composite factor) is a geometric average of the factors MRP. Formulas To measure inter-industry FM, I compute an appropriate average of factors MRP in the industries. I Sectoral TFPR can be expressed as the geometric average of the inter-industry measures. Importance

17 1 Introduction 2 Definitions and motivation Revealed comparative advantage (RCA) measure Intra and inter-industry misallocation measures RCA and misallocation 3 Theoretical framework Model Gravity equation 4 Empirical implementation Counterfactual exercise Baseline results

18 RCA and misallocation: A simple test (I) RCA is determined by P is P is 0 / P i 0 s P i 0 s 0,whereP is is the sectoral PPI. PPI is simply: P is = TFPR is I I A is Proof Sectoral TFP, A is, is the product of: 1 E cient TFP: A e is (Ricardian CA). 2 Measure 1 of intra-industry FM, AEM is. Sectoral TFPR is is the product of the geometric average of: 1 Factor prices in the e cient allocation: They depend on factor endowments and factor intensities (Heckscher-Ohlin CA) 2 Inter-industry FM measures. Formula To use the direct measures of TFPQ available in Colombia, I use a two-stage strategy that exploits the variation over time of the Colombian RCA in panel data.

19 RCA and misallocation: A simple test (II) 1 1st stage: Estimate the panel-version of the FE regression: lnx ijst = d ist + d ijt + d jst + # ijst where ˆd ist identifies drca ist, the change of RCA is from t 0 to t. I ˆd ist should be related to ( P ist P / P ist 0 is 0 t P )/( P i 0 st is 0 t 0 P / P i 0 st 0 i 0 s 0 t P ) i 0 s 0 t 0 2 2nd stage: Regress ˆd ist for Colombian industries on the 4 determinants of CA, using for each independent variable v ist the transformation: I ṽ ist =( v ist / v ist 0 )/( P i 0 st / P i 0 st 0 ) v is 0 t v is 0 t 0 P i 0 s 0 t P i 0 s 0 t 0 where i 0 US, t 0 first year and s 0 sector with the median number of zeros.

20 Results Both types of FM have a quantitative importance similar to Ricardian and Heckscher-Ohlin determinants. Second-stage results. First stage: FE by PPML (1) (2) Measure 1 of intra-industry FM 0.358*** (AEM is ) (0.082) Measure 2 of intra-industry FM ** (stfpr 2 is ) (0.060) Measure of inter-industry FM *** *** (0.081) (0.088) E cient TFP 0.244** 0.234** (0.090) (0.098) Factor prices *** ** (0.066) (0.076) Observations R-square *p<0.10,**p<0.05and***p<0.01.dependentvariableisdrca ist, thechangeintherca measure with respect to the first period. All independent variables are transformed to be changes with respect to the first period relative to the reference industry, normalized by the corresponding changes in the US PPI. Standardized coe cients and heteroskedastic robust errors.

21 1 Introduction 2 Definitions and motivation Revealed comparative advantage (RCA) measure Intra and inter-industry misallocation measures RCA and misallocation 3 Theoretical framework Model Gravity equation 4 Empirical implementation Counterfactual exercise Baseline results

22 Model outline Model: Multi-country, multi-sector and multi-factor Melitz (2003) model (as in Bernard et al., 2007), with dispersion in factor s MRP. Main di erence with allocative e cient Melitz: FMdistorts selection in the domestic and exporting markets: I There are zombie and shadow firms (Yang, 2017).

23 Model description (I) Notation: I I I m =variety, i =exporting country, j =importing country, s =industry, l =homogenous production factor. N countries, S industries, L primary factors. I omit sector subscripts for firm variables. Demand system: Upper-level Cobb-Douglas with expenditure shares b is ; lower-level CES, elasticity of substitution s, letr = s 1 s. Trade costs: Iceberg trade cost t ijs fixed cost f xijs. 1, with t iis = 1andaccess Fixed cost of production: f is.definef ijs = f xijs if j 6= i; f iis = f xiis + f is otherwise.

24 Model description (II) Firms: Characterized by a TFPQ a im and a vector of L factor-distortions: ~ qim = {q i1m, q i2m,...q ilm } drawn from a joint ex-ante distribution G is (a,~ q). I Technology to produce q im units of m is Cobb-Douglas, using factors z ilm with intensities a ls. I For the firms with ~ qim = 0, factor price of l is w il. I Cost to sell in country j : c ijm (q ijm )=w is Q im ( t ijsq ijm a im + f ijs ) with: Q im = L l MRP of factor l: (1 + q ilm ) w il r (1 + q ilm ) a ls and w is = L w a ls il l and TFPR: Q im w is r.

25 Model description (III) Entry/exit: Exogenous probability of exit d is, entry cost f e is. Inter-industry misallocation: Define (1 + q ls )=( M s 1 c  im (1+q m lm ) Cis ) 1, with c im =  N c ijm and C is =  S c im. j m I (1 + q ls ) is an inter-industry wedge : It a ects factors that are use for production. Competitive equilibrium: Defined by free entry, aggregate stability, zero profit, factor market clearing and trade balanced conditions. Equilibrium

26 E ects of FM on selection In the standard Melitz model, there is a productivity cuto for each i, j, s given by the zero profit (ZP) condition: p ijs (ea ijs )=0 Productivity cuto (ea M )ofcountryi in sector s for destination j! (TFPQ) Active firms in destination j!" # Non-active firms in destination j

27 E ects of FM on selection With FM, ZP condition is: p ijs (a ijs (Q), Q) =0. Define a ijs a ijs (1), then: a ijs (Q) = a ijs Q 1 r Cuto frontier aijs (Q) of country i in sector s for destination j * (TFPQ) * -./ *4 5!"#$%&' Active firms in destination j O * -./ (Θ) Non-active firms in destination j (h*+",' Θ6 5 = * 89 -./ (*4 5 ) 1 Θ (TFPR)

28 Evidence on the e ects of FM on selection: exporters Factor misallocation a ects the selection of exporters. LPM of being a exporter explained by TFPQ and TFPR for Colombia (1) (2) (3) (4) TFPR 0.043*** *** *** *** (0.004) (0.005) (0.007) (0.007) TFPQ 0.177*** 0.148*** 0.150*** (0.004) (0.005) (0.005) Demand shock 0.093*** 0.080*** 0.080*** (0.001) (0.002) (0.002) Year FE Yes Yes Yes Yes Sector FE Yes Yes Yes Yes Firm controls Yes Yes Location FE Yes N R * p<0.10, ** p<0.05 and *** p<0.01. Dependent variable: probability of being a exporter. All independent variables are in deviations over industry means. Firm controls: Size, age and lagged capital. Heteroskedastic robust errors. Source: EAM Colombia, Probit Domestic

29 1 Introduction 2 Definitions and motivation Revealed comparative advantage (RCA) measure Intra and inter-industry misallocation measures RCA and misallocation 3 Theoretical framework Model Gravity equation 4 Empirical implementation Counterfactual exercise Baseline results

30 Assumptions For tractability, consider: A1.Pareto distribution 8a i > ā, Gis a (a) =1 ( āis a )k ; k > s 1; A2.Ex-ante independence G is = G is (a,~ q)=g a is (a)g q is ( ~ q)

31 Results under A1 and A2 1 The total inter-industry wedge is: v ils = 1 (1 + q ils ) (1 r k )+r k and we can express: w il Z ils = a ls v ils R is 2 We can write: log( X ijsx i 0 js 0 X ijs 0X i 0 js with G is = R q i1... R q il Q i 1 )=log[ $ is $ i 0 s 0 G is G i 0 s 0 R is R i 0 s 0 ( w is w i 0 s 0 $ is 0 $ i 0 s G is 0 G i 0 s R is 0R i 0 s w is 0 w i 0 s {z } Exp Ind FE=RCA k r dg q is ( ~ q) and $is = āk is d is f e is ) k r ]+B ijs 1 Further, RCA can be decomposed in its 3 determinants: i) Average TFP; ii) factor prices; iii) number of varieties. Decomposition Simulation

32 1 Introduction 2 Definitions and motivation Revealed comparative advantage (RCA) measure Intra and inter-industry misallocation measures RCA and misallocation 3 Theoretical framework Model Gravity equation 4 Empirical implementation Counterfactual exercise Baseline results

33 Counterfactual exercise I perform the counterfactual exercise of removing both types of factor misallocation in Colombia. I For solving the model l use the exact hat algebra approach of Deckle et al. (2008). I Set of 48 Countries, 25 Sectors for 1995 I GO production function with 3 primary factors (capital, skilled and unskilled labor) and materials. I Parameters: k = 4.6 ands = 3.5. Wedges are measured assuming log-normal joint distribution to link ex-post to ex-ante parameters, and taking into account measurement error in both revenues and inputs (following Bils et al., 2017). Wedges

34 Solving the model with exact hat algebra Denote Z ils the share of factor l ( Z ils Z ils Z il )andp ijs trade shares. For any x in the initial equilibrium denote x 0 its counterfactual value and ˆx x 0 x.undera1anda2wehave: ŵ il = S Â s Z ils ˆR is ˆv ils R is ˆR is = Â N p 0 ijs b js ( Â S R js ˆR js D j ˆD j ) j s p 0 ijs = N Â k p ijs ( L ŵ il l p kjs ( L ŵ kl l ka ls r ka ls r )Ĝ is ˆR is )Ĝ ks ˆR ks Objective: derive the impact of removing misallocation (through Ĝ is zzzzzz and zzzzzz).

35 Solving the model with exact hat algebra Denote Z ils the share of factor l ( Z ils Z ils Z il )andp ijs trade shares. For any x in the initial equilibrium denote x 0 its counterfactual value and ˆx x 0 x.undera1anda2wehave: ŵ il = S Â s Z ils ˆR is ˆv ils R is ˆR is = Â N p 0 ijs b js ( Â S R js ˆR js D j ˆD j ) j s p 0 ijs = N Â k p ijs ( L ŵ il l p kjs ( L ŵ kl l ka ls r ka ls r )Ĝ is ˆR is )Ĝ ks ˆR ks Objective: derive the impact of removing misallocation (through ˆv ils and Ĝ is ) on ˆR is and ŵ il.

36 Solving the model with exact hat algebra Denote Z ils the share of factor l ( Z ils Z ils Z il )andp ijs trade shares. For any x in the initial equilibrium denote x 0 its counterfactual value and ˆx x 0 x.undera1anda2wehave: ŵ il = S Â s Z ils ˆR is ˆv ils R is ˆR is = Â N p 0 ijs b js ( Â S R js ˆR js D j ˆD j ) j s p 0 ijs = N Â k p ijs ( L ŵ il l p kjs ( L ŵ kl l ka ls r ka ls r )Ĝ is ˆR is )Ĝ ks ˆR ks Required info: observable p ijs, Z ils R is,d i,coe cientsa ls,b is ; assumptions on ˆD j and parameters k and s.

37 Welfare Once ˆR is and ŵ il are obtained, it is straightforward to compute changes in aggregate expenditure and trade shares: Ê i and ˆp ijs. The cost of each type of misallocation in terms of welfare, measured as total real expenditure, can be computed from: Ê i ˆ P d i = " S Ê s i 1 k 1 r 1 ˆpiis k ˆR is Ĝ is L l # bs a ls ŵ r il

38 1 Introduction 2 Definitions and motivation Revealed comparative advantage (RCA) measure Intra and inter-industry misallocation measures RCA and misallocation 3 Theoretical framework Model Gravity equation 4 Empirical implementation Counterfactual exercise Baseline results

39 Aggregate results Change in each variable after removing factor misallocation in Colombia Value Exports Variable Revenue Exports RCA s.d.* Welfare added /GDP* Counterfactual ˆR Col GDP ˆ Col ˆX Col D( GDP X ) ÊCol Col Ds RCACol ˆPCol Baseline results Both types Only intra-industry Only inter-industry Note: Each cell shows the proportional change in each variable between the counterfactual equilibrium and the actual data. For variables marked by *, the simple difference in the measure is displayed.

40 Counterfactual RCA - Removing both types (I) The e cient allocation involves much more specialization, and a substantial change in industrial composition (4 industries disappear). RCA for Colombia, removing all misallocation (Initial vs Counterfactual - estimation by PPML) Counterfactual RCA Footwear, 17 Pottery, 18 Glass Chemicals Oth chemicals Tobacco Food18 17 Paper Printing 7 Leather Iron and steel Rubber Textiles Apparel Beverage Oth. non-metal. minerals Metal products not M&E Plastic Furniture Wood Non-ferrous metal Petroleum Transport M&E Elec. / profess Initial RCA Note: Marker' sizes represent export shares in the actual data Revenue shares

41 Counterfactual RCA - Removing both types (I) The e cient allocation involves much more specialization, and a substantial change in industrial composition (4 industries disappear). RCA for Colombia, removing all misallocation (Initial vs Counterfactual - estimation by PPML) Counterfactual RCA Footwear, 17 Pottery, 18 Glass Chemicals Oth chemicals Tobacco Food18 17 Paper Printing 7 Leather Iron and steel Rubber Textiles Apparel Beverage Oth. non-metal. minerals Metal products not M&E Plastic Furniture Wood Non-ferrous metal Petroleum Transport M&E Elec. / profess Initial RCA Note: Marker' sizes represent export shares in the counterfactual data Revenue shares

42 Counterfactual RCA - Removing both types (II) The change in industrial composition is due to the increase in the dispersion of RCA. RCA world distribution, actual data RCA world distribution, removing both types of misallocation in Colombia Density Density log(rca) Note: Each line represents the position of a Colombian industry in the RCA world distribution log(rca) Note: Each line represents the position of a Colombian industry in the RCA world distribution

43 Changes in RCA by type of misallocation The magnitude of the change in RCA due to removing each type of misallocation is explained by the extent of each misallocation: Change in RCA Transport Change in RCA for removing only intra-industry misallocation and intra-industry variance of TFPR* Leather Food Furniture Footwear Paper Pottery Rubber Glass BeverageOth chemicals Wood Metal products not M&E Plastic Electric. / Profess. Petroleum M&E Non-ferrous metal Chemicals Tobacco 4 Textiles, 5 Apparel, 11 Printing, 19 Other non-metallic minerals, 20 Iron and steel Intra-industry variance of log TFPR* *Note: Caused by dispersion only in the MRP of capital, skilled and unskilled labor.

44 Changes in RCA by type of misallocation The magnitude of the change in RCA due to removing each type of misallocation is explained by the extent of each misallocation: Change in RCA Furniture Wood Oth. non-metal. minerals Apparel Non-ferrous metal Change in RCA for removing only inter-industry misallocation and sectoral TFPR* Beverage Footwear Plastic Printing Rubber TextilesLeather Metal products not M&E Petroleum Electric. / Profess. M&E Iron and steel Chemicals Paper Pottery Transport Food Oth chemicals Tobacco Glass Sectoral TFPR* *Note: Computed using only capital, skilled and unskilled labor as inputs.

45 Disentangling the impacts: extensive and intensive margin The contribution of the extensive margin (number of varieties produced) in the adjustment of the RCA is the most important. Food Beverage Tobacco Textiles Apparel Leather Footwear Wood Furniture Paper Printing Chemicals Other chemicals Petroleum Rubber Plastic Pottery Glass Other non-metallic Iron and steel Non-ferrous metal Metal products Mach. & equipment Electric. / Profess. Transport Change in RCA of Colombian industries (Removing both types of misallocation) Log points Number of varieties Factor prices Average TFP Intra Inter

46 Robustness checks and additional exercises Gradual reforms Changes in k and s Gradual Parameters One sector vs. multiples industries Closed vs. open economy Autarky OneSector

47 Conclusions Resource misallocation at the firm level can distort natural CA. Models of FM in closed economies omit a series of general equilibrium adjustments that take place when removing FM in open economies. I This paper o ers a framework to compute RCA under a country s frictionless factor markets, considering the whole set of general equilibrium e ects in an open economy.. Removing FM both at the intra and the inter-industry level not only boosts aggregate productivity, but also allows the country to specialize in industries with true comparative advantage.

48 Thank you!

49 Appendix Definitions and motivation Theoretical framework Empirical implementation RCA for Colombia: PPML vs. EK s (2001) Tobit RCA for Colombia Exp-Ind FE by Poisson PML Ind. chemicals Petroleum Oth. n-metal. mineral Footwear Beverage Pottery Plastic Textiles Tobacco Printing Furniture Paper Glass Wood Metal products Other chemicals Rubber Transport Iron and steel Non-ferrous metal Electric & profess. Machinery, equipment Leather Apparel Food Exp-Ind FE by EK-Tobit *Markers' sizes represent export shares, and the line the best linear fitting Return

50 Appendix Definitions and motivation Theoretical framework Empirical implementation Composition of Colombian exports in 1995 ($10.2B) Coffee Cut flowers 4.47% Bananas and plantains 4.00% 19.34% Raw sugarcane Crustaceans 0.89% 2.63% 0.27% Books, brochures etc. Extracts of coffee, tea or mate 1.02% Prepare Petroleum oils, crude Women's suits and pants 1.17% Men's suits and 1.29% Medicament 0.76% 16.46% Women's 0.62% Socks, 0.60% pants 0.73% 0.56% 0.31% 0.94% Insecticid Polymers Polyme of vinyl chloride 0.76% 0.31% 0.53% 0.33% 0.29% Coal 6.29% Petroleum oils, refined Precious stones 3.50% Ferroalloys 1.38% 4.24% Gold 2.32% Return

51 Appendix Definitions and motivation Theoretical framework Empirical implementation Alternative explanations of variation in MRP Source Variable Contribution* Countries Paper Adjustment costs 1% China, Colombia, David and Uncertainty about TFP smrpk 2 7% Mexico Venkateswaran Variable markups 5% China (2017) Heterogeneity in technology 17% Heterogeneity in workers ability smrpl 2 9% Denmark Bagger et al. (2014) Additive measurement error in revenues and inputs stfpr 2 45% India Bils et al. (2017) *Average contribution if the number of countries is greater than 1. Return

52 Appendix Definitions and motivation Theoretical framework Empirical implementation Definitions to evaluate the extent of misallocation Assume: I Monop. competition, CES demand (markup 1 r ), no fixed costs. I Variety m in industry s is produced with CD technology and L factors: q m = a m L l z a ls lm Physical productivity (TFPQ) Revenue productivity (TFPR) TFPQ m q m L = a m TFPR m p L mq m l z a ls lm L z a ls lm l = 1 r l ( w l a ls ) a ls stfpr,s 2 = ~a0 sv s ~a s where ~a s is a L-vector of factor intensities a ls and V s is the var-cov matrix of factor s marginal revenue products (MRP lm )withins. Without fixed costs, MRP lm p m q m z lm. Return

53 Appendix Definitions and motivation Theoretical framework Empirical implementation Intra and inter-industry misallocation To measure inter-industry misallocation, the appropriate average is the harmonic weighted average (HWA), with weights given by firms revenue shares. I Sector-level TFPR can be expressed as a geometric average of the HWA of the MRP. In a closed-economy with fixed mass of firms (HK), both types of misallocation play a role: I I In Colombia inter-industry type contributes up to 35% of the total gains in TFP (30% in China), computed at the 4-dig industry level. Graph Inter-industry misallocation also explains TFP gaps across countries. Graph Return

54 Appendix Definitions and motivation Theoretical framework Empirical implementation TFP gains, closed economy (HK) For Colombia and China, the inter-industry type contributes up to 35% and 30% of the total gains, respectively. Formulas CES case 140 TFP gains from removing misallocation, Colombia 170 TFP gains from removing misallocation, China Gains (%) Gains (%) Total gains, 4-dig Year Total gains, 3-dig Only intra-industry gains, 4-dig Only intra-industry gains, 3-dig Year Total gains, 4-dig Total gains, 3-dig Only intra-industry gains, 4-dig Only intra-industry gains, 3-dig Source: AMS, Colombia Return correspond to the values in HK (2009). Source: ASIP, China.

55 Appendix Definitions and motivation Theoretical framework Empirical implementation Inter-industry misallocation and income per capita. Inter-industry misallocation is also related with the TFP gaps across countries. Gains from removing distortions across sectors (%) IND IDN CHN BRA RUS BGR ROU TUR HUN MEX LTU LVA POL EST SVK CZE ITA IRL KOR GRC PRT FRA CYP NLD CAN ESP FIN DNK BEL AUT DEU AUS JPN GBRUSA SVN SWE Log GDP per capita (constant 2005 US$) Note: Averages Data source: WIOD (Timmer et al., 2015), World Bank Development indicators. Robustness checks Return

56 Appendix Definitions and motivation Theoretical framework Empirical implementation Decomposition of the PPI (P is ) Wedge analysis is used to characterize the variation in MRP lm. I Each firm is characterized by a vector of wedges, ~ qm = {q lm,...q Lm } where MRP lm = 1 r w l (1 + q lm ) I I 1 L TFPR at the firm level is: r (1 + q ilm ) a ls ( w il a l ls ) a ls HWA of factor-l wedges for firms in s, (1 + q ls ),arethe industry-analogue of firm-level wedges. Let Y is sector output and R is sectoral revenue. Then: P is = P isy is Y is = R is A is L l Z a ls ils = TFPR is A e is AEM is = L l (1 + q ils ) a ls ( w il ra e is AEM is a ls ) a ls where A e is is the allocative e cient TFP and AEM is A is /A e is a measure of intra-industry misallocation. Return

57 Appendix Definitions and motivation Theoretical framework Empirical implementation Factor prices in the e cient allocation Using FOC of the CD demand across sectors, it is possible to derive the solution for relative factor prices in the e cient closed economy: w l w k = Z kâ s a ls b s Z lâ s a ks b s where Z l is the total endowment of factor l and b s the CD expenditure shares b is. This relation is satisfied using as price for factor l: w l = rr Z l Âa ls b s s which is the price that ensures the HWA of HWA of firm-level wedges for factor l is equal to 1. Return

58 Appendix Definitions and motivation Theoretical framework Empirical implementation TFP gains - formulas Denote TFPR y ms and MRP x lms. Let ȳ s, x ls the corresponding HWA. 1 TFP in sector s: A s 1 s 2 E cient TFP in sector s: ea s 1 s = 1 M s Ms  m (a ms ȳ s /y ms ) s 1 = 1 M s Ms  m a s 1 ms 3 Gains from removing intra-industry misallocation in sector s: Gains intra s = 100( e A s A s 1)=100( M s (Â( a ms y s ) m ea s 1 ) 1 s y ms 1 s 1) 4 Total gains from removing intra-industry misallocation: Gains intra = 100( S s ( e As As )b s 1) 5 Total gains from removing inter-industry misallocation: Gains inter = 100( S L ez a ls ls bs s l Z a ls ls 1) =100( S l bs [ s l S Â(a ls b s / x ls ) s ] als bs (  S a ls b s )/ x ls s 6 Total gains from removing intra and inter-industry misallocation: Y Gains = 100( e Y 1)=100[( Gainsinter )( Gainsintra ) 1] Return 1)

59 Appendix Definitions and motivation Theoretical framework Empirical implementation TFP gains - CES across sectors Assume a two-tier CES demand, with upper-level Y j = S Â s b s Y s j, where j = f 1 f 80 TFP gains from removing misallocation, CES aggregator, Colombia Gains (%) Total gains, =1 Year Only intra-industry gains, =1 Total gains, =2 Only intra-industry gains, =2 Total gains, =0.5 Only intra-industry gains, =0.5 Return

60 Appendix Definitions and motivation Theoretical framework Empirical implementation Inter-industry misallocation and income: robustness All WIOD sectors, GO spec., own country's cost shares, homogenous inputs All WIOD sectors, VA spec., US cost shares, homogenous inputs Gains (%) IND IDN CHN TUR BRA MEX RUS HUN BGR ROU LTU POL LVA SVK EST CZE IRL CYP GRC ITA KOR PRT ESP FIN GBRUSA FRA CAN AUT DEU JPN NLD SVN DNK AUSBEL SWE Gains (%) IND IDN CHN TUR IRL RUS BRA ITA ROU MEX KOR BGR LVA LTU POL GRC PRT FINCAN NLD HUN CYP DEU AUT DNK ESP FRA USA EST SVK CZE SVN BEL GBR AUS JPN SWE Log GDP per capita Log GDP per capita All WIOD sectors, GO spec., US cost shares, heterogenous inputs All WIOD sectors, GO spec., own country's cost shares, heterogenous inputs Gains (%) IND IDN CHN BGR ROU RUS BRA TUR LVA LTU POL MEX EST HUN SVK CZE ITA IRL GRC CYP FRA KOR NLD PRT BEL DNK FIN ESPDEU CAN AUT GBR SVN AUS SWE USA JPN Gains (%) IND IDN CHN TUR MEX BRA POL ROU BGR RUS LTU SVK LVA HUN EST CZE IRL ITA GRC CYP GBR KOR FIN AUT ESP FRA NLD USA PRT DEU CAN DNK SVN BELJPN AUS SWE Log GDP per capita Log GDP per capita Only manufacturing, GO spec., US cost shares, homogenous inputs Only manufacturing, GO spec., own country's cost shares, homogenous inputs Gains (%) IND IDN CHN HUN BRA LTU RUS BGR TUR ROU EST MEX SVK LVA POL CZE IRL KOR GRC CYP FIN PRT BEL FRA AUS CAN NLD SVN ESP SWE DEUITA JPN USA AUT DNK GBR Gains (%) IND IDN CHN HUN LTU RUS BRA TUR FIN IRL BGR ROU GRCCYP EST KOR MEX SVK PRT BEL CAN POL SVN LVA CZE ESP AUS DEUITA JPN NLD FRA SWE USA AUT DNK GBR Log GDP per capita Log GDP per capita Return

61 Appendix Definitions and motivation Theoretical framework Empirical implementation Evidence on the e ects of FM on selection: domestic firms Factor misallocation also a ects the selection of domestic firms LPM of exit explained by TFPQ and TFPR for Colombia (1) (2) (3) (4) TFPR *** 0.047*** 0.057*** 0.057*** (0.003) (0.003) (0.004) (0.004) TFPQ *** *** *** (0.002) (0.003) (0.003) Demand shock *** *** *** (0.001) (0.001) (0.001) Year FE Yes Yes Yes Yes Sector FE Yes Yes Yes Yes Firm controls Yes Yes Location FE Yes N R * p<0.10, ** p<0.05 and *** p<0.01. Dependent variable: probability of exit. All independent variables are in deviations over industry means. Firm controls: Size, age and lagged capital. Heteroskedastic robust errors. Source: EAM Colombia, Return

62 Appendix Definitions and motivation Theoretical framework Empirical implementation Evidence on the e ects of FM on selection: exporters (probit) Probit: exit explained by TFPQ and TFPR for Colombia (1) (2) (3) (4) TFPR 0.219*** *** *** *** (0.018) (0.034) (0.039) (0.040) TFPQ 0.983*** 0.973*** 0.991*** (0.025) (0.029) (0.029) Demand shock 0.520*** 0.517*** 0.524*** (0.007) (0.009) (0.009) Year FE Yes Yes Yes Yes Sector FE Yes Yes Yes Yes Firm controls Yes Yes Location FE Yes N * p<0.10, ** p<0.05 and *** p<0.01. Dependent variable: probability of exit. All independent variables are in deviations over industry means. Firm controls: Size, age and lagged capital. Heteroskedastic robust errors. Source: EAM Colombia, Return

63 Appendix Definitions and motivation Theoretical framework Empirical implementation Aggregation definitions To define the competitive equilibrium, we need first the following definitions of aggregates: Industry-destination aggregates - Mass of firms selling to j: M ijs -Bilateralexports: X ijs = M ijs  m p ijm q ijm - Expenditure in access cost: F ijs = M ijs  m w is Q im f ijs - Total cost of exporting to j: C ijs = rx ijs + F ijs. - HWA of exporter wedges: (1 + q ijls ) Industry aggregates - Mass of entrants: H is - Gross output: R is =  N j X ijs - Expen. in fixed costs: F is =  N F ijs j - Total cost: C is =  N C ijs j -Factorl allocated to entry: Zils e -Factorl to produce and delivery: Z o ils M ijs  m z ilm - HWA of firm wedges: (1 + q ils ) Return

64 Appendix Definitions and motivation Theoretical framework Empirical implementation Equilibrium conditions Free entry: 8 i, s: N M ijs  j Aggregate stability: 8 i, j, s:  m p ijm = w is f e is H is d is M ijs =[1 G is (aijs(q), Q)]H is Factor market clearing: Let Z il factor l endowment.8 i, l: Z il = S  s Z ils = S ÂZ o s ils + Z e Balance trade condition: 8 i: S ils =  s R i = E i + D i a ls C is w il (1 + q ils ) + a lsw is f e w il is H is where R i =  S R is, E i =  S E is and D i is the country s trade balance. s s Global trade balance requires:  N D i = 0. Return i

65 Appendix Definitions and motivation Theoretical framework Empirical implementation Simulation Assume a simple 2x2x2 world: I Sector 1 is factor 1-intensive, and country 1 is relatively abundant in factor 1. I Trade/fixed costs and ā is,k,d is do not vary across sectors. Misallocation: I Country 1 in sector 1 faces misallocation. I q 1lm logn(µ 1l1, s1l1 2 ) and zero covariances. With A1 and A2, we obtain: ln(1 + q 1l1 )=µ 1l1 +[(1 k r )a l1 1 2 ]s2 1l1 Parameters

66 Appendix Definitions and motivation Theoretical framework Empirical implementation GE e ects of intra-industry misallocation E ects of intra-industry misallocation on RCA of sector 1 of country 1 0 RCA: (1) + (2) + (3) 0 (1) TFP (2) Inverse of factor prices (3) Mass of firms 1.5 Ex-post average wedge 1 Values of parameters Wedges on fac. 1 Wedges on fac

67 Appendix Definitions and motivation Theoretical framework Empirical implementation GE e ects of inter-industry misallocation E ects of inter-industry misallocation on RCA of sector 1 of country 1 RCA: (1) + (2) + (3) (1) TFP (2) Inverse of factor prices (3) Mass of firms Ex-post average wedge 0.5 Values of parameters Wedges on fac. 1 Wedges on fac

68 Appendix Definitions and motivation Theoretical framework Empirical implementation Decomposition of Exp-Ind FE From gravity: ln X ijsx i 0 js 0 X ijs 0X i 0 js = ln( M ijsm i 0 js 0 M ijs 0M i 0 js ) + ln( ȳijs ȳi 0 js 0 ȳ ijs 0 ȳ i 0 js ) 1 s + ln( A ijsa i 0 js 0 A ijs 0A i 0 js Under A1 and A2, from the stability condition: M ijs = H is U is U is = R q i1... R q il Q i k r dg q is ( ~ q). After some algebra, the RHS is: ) s 1 + ln( t ijs t i 0 js 0 ) 1 s t ijs 0 t i 0 js d is ( āis aijs ) k with =log[ $ is $ i 0 s 0 R is R i 0 s 0 $ is 0 $ i 0 s R is 0R i 0 s + log[( Q is Q i 0 s 0 Q is 0 Q i 0 s 0 ) s U is U i 0 s 0 ( w is U is 0 U i 0 s w is 0 1 ( w is w is 0 w i 0 s 0 ) k r 1 w ] + log[ is w i 0 s Q 0 is Q i 0 s 0 w i 0 s w is 0 w i 0 s Q ] is 0 Q 1 i 0 s 0 w i 0 s 0 ) s G is G i 0 s 0 U is 0 U i 0 s ] + B ijs w i 0 s G is 0 G i 0 s U is U i 0 s 0 i.e., the decomposition of the RCA in number of varieties (extensive margin) andfactor returns + average TFP (intensive margin) Return s

69 Appendix Definitions and motivation Theoretical framework Empirical implementation Measuring wedges Assume a log-normal joint distribution for wedges. Thus: ln(1 + q ils )=µ ils [(~a s) 0 V is ~a s ( ~a ls ) 0 V is ~a ls ] where ~a s and ~a ls are functions of factor intensities, k and s. I need estimates of V is (var-cov of MRP within industries) and observed measures of (1 + q ils ) to recover µ ils. I use Bils et al. (2017, BKR) method to measure dispersion in MRP under measurement error in both revenues and inputs. I Additive error analogous to (heterogenous) overhead costs. I Main idea: Estimate a compression factor l to correct observed dispersion on TFPR (stfpr 2 ) as a measure of dispersion in MRP (l = s2 Q )usingpaneldata. stfpr 2 BKR method I For Colombia, : ˆl = 0.88 (0.05). BKR results

70 Appendix Definitions and motivation Theoretical framework Empirical implementation Parameters for the simulation Parameter Description apple Value a ls Factor intensities b is Expenditure shares i, s s Varieties elasticity of substitution 3.8 k Pareto s shape parameter apple Z il Factor endowments ā is Pareto s location parameter 1 8 i, s d is Exogenous probability of exit i, s fis e Fixed entry cost 2 8 i, s f ijs Fixed trade cost 2 8 i, j, s t ijs Iceberg trade cost Free trade: 1 8 i, j, s Costly trade: 2 8 s ^ i 6= j; 18 s ^ i = j s l1 Log-normal shape par. in sector 1 For figure 1: [0, 0.5] 8 l For figure 2: 0 8 l µ l1 Log-normal location par. sector 1 For figure 1: ( 1 k 2 (1 r )a l1)sl1 2 8 l For figure 2: [ 0.5, 0.5] 8 l Return

71 Appendix Definitions and motivation Theoretical framework Empirical implementation Sectors in the empirical exercise No. Sector Sector Description ISIC Rev. 2 1 Food Food manufacturing Beverage Beverage industries Tobacco Tobacco manufactures Textiles Manufacture of textiles Apparel Wearing apparel, except footwear Leather Leather and products of leather and footwear Footwear Footwear, except vulcanized or moulded rubber or plastic footwear Wood Wood and products of wood and cork, except furniture Furniture Furniture and fixtures, except primarily of metal Paper Paper and paper products Printing Printing, publishing and allied industries Chemicals Industrial chemicals Other chemicals Other chemicals (paints, medicines, soaps, cosmetics) Petroleum Petroleum refineries, products of petroleum and coal Rubber Rubber products Plastic Plastic products Pottery Pottery, china and earthenware Glass Glass and glass products Other non-metallic Other non-metallic mineral products (clay, cement) Iron and steel Iron and steel basic industries Non-ferrous metal Non-ferrous metal basic industries Metal products Fabricated metal products, except machinery and equipment Machinery, equipment Machinery and equipment except electrical Electrical Electrical machinery apparatus, appliances and supplies Transport Transport equipment Profess., scientific Professional and scientific, and measuring and controlling equipment 385 Return 1 Return 2

72 Appendix Definitions and motivation Theoretical framework Empirical implementation Sample of countries OECD Country (I) Code OECD Country (II) Code Australia AUS Korea KOR Austria AUT Mexico MEX Belgium BEL Netherlands NLD Canada CAN New Zealand NZL Chile CHL Norway NOR Denmark DNK Poland POL Finland FIN Portugal PRT France FRA Czech Republic CZE Germany DEU Spain ESP Greece GRC Sweden SWE Hungary HUN Switzerland CHE Ireland IRL Turkey TUR Israel ISR United Kingdom GBR Italy ITA United States USA Japan JPN Return 1 Return 2 Non-OECD Country Argentina Brazil China Colombia Ecuador Hong Kong India Indonesia Malaysia Philippines Rest of the World Romania Russia Saudi Arabia Singapore South Africa Thailand Taiwan Venezuela Code ARG BRA CHN COL ECU HKG IND IDN MYS PHL ROW ROU RUS SAU SGP ZAF THA TWN VEN

73 Appendix Definitions and motivation Theoretical framework Empirical implementation Values used in the counterfactual Number Factor intensities HWA of firm-level Intra-industry variances Intra-industry covariances of firms (GO specification) wedges of log-wedges of log-wedges Sector (in 1995) ak as au (1 + qk ) (1 + qs ) (1 + qu) Q sk 2 ss 2 su 2 sks sku ssu Food Beverage Tobacco Textiles Apparel Leather Footwear Wood Furniture Paper Printing Chemicals Other chemicals Petroleum Rubber Plastic Pottery Glass Other non-metallic Iron and steel Non-ferrous metal Metal products Mach. & equipment Electric. / Profess Transport One-sector Return

74 Appendix Definitions and motivation Theoretical framework Empirical implementation BKR (2017) method Define measured revenues and inputs as: ˆR m = R m + f m and Î m = I m + g m. Denote D log di erence and N abs di erence. Under reasonable assumptions, BKR (2017) find that the elasticity of D ˆR with respect to DÎ, b = s D ˆR,DÎ,satisfy: s 2 DÎ E {b ln(tfpr m )} =(1 W Q s W f 0)[1 (1 l)ln(tfpr)] where l = s2 lnq, our measure of interest, and W stfpr 2 Q = s DQ,DI sdi 2 Nf 0 = Nf m Îm. l can be estimated from:,w f 0 = s Nf 0,DÎ s 2 DÎ D ˆR m = fln(tfpr m )+ydî m y(1 l)ln(tfpr m )DÎ + D s + e m Return

75 Appendix Definitions and motivation Theoretical framework Empirical implementation BKR (2017) - results For Colombia, using GMM and following closely BKR (2017), I obtain: D ˆR m f 0.056*** (0.000) y 0.977*** (0.139) l 0.884*** (0.018) Observations *p<0.10,**p<0.05and***p<0.01. BKR estimates: India: ˆl = 0.55 (0.04), US: ˆl = 0.23 (0.03). Return

76 Appendix Definitions and motivation Theoretical framework Empirical implementation Results: Counterfactual RCA Comparative advantage in the e specialization cient allocation involves much more RCA for Colombia, removing all misallocation (Initial vs Counterfactual - estimation by PPML) Counterfactual RCA Footwear, 17 Pottery, 18 Glass Chemicals Oth chemicals Tobacco Food18 17 Paper Printing 7 Leather Iron and steel Rubber Textiles Apparel Beverage Oth. non-metal. minerals Metal products not M&E Plastic Furniture Wood Non-ferrous metal Petroleum Transport M&E Elec. / profess Initial RCA Note: Marker' sizes represent revenue shares in the actual data Return

77 Appendix Definitions and motivation Theoretical framework Empirical implementation Results: Counterfactual RCA Comparative advantage in the e specialization cient allocation involves much more RCA for Colombia, removing all misallocation (Initial vs Counterfactual - estimation by PPML) Counterfactual RCA Footwear, 17 Pottery, 18 Glass Chemicals Oth chemicals Tobacco Food18 17 Paper Printing 7 Leather Iron and steel Rubber Textiles Apparel Beverage Oth. non-metal. minerals Metal products not M&E Plastic Furniture Wood Non-ferrous metal Petroleum Transport M&E Elec. / profess Initial RCA Note: Marker' sizes represent revenue shares in the counterfactual data Return

78 Appendix Definitions and motivation Theoretical framework Empirical implementation Gradual reforms Even the smallest reform, which reduces 10% the extent of both types of FM, has a sizable impact on both welfare and exports (6.7% and 11% respectively) Panel A: Welfare gains Panel B: Export growth % of reduction in misallocation Both types Only intra-industry Only inter-industry % of reduction in misallocation Both types Only intra-industry Only inter-industry Return

79 Appendix Definitions and motivation Theoretical framework Empirical implementation Counterfactual RCA changing s and k RCA Tobacco Pottery Paper Iron and steel Rubber Beverage M&E Chemicals Glass Oth chemicals Food Leather Printing Footwear Textiles Apparel Plastic Oth. non-metal. minerals Metal products not M&E Furniture Wood Non-ferrous metal Petroleum Elec./profess. Transport Pottery Paper Iron and Tobacco steel Rubber Beverage M&E Chemicals Glass Oth chemicals Food Leather Printing Footwear Textiles Plastic Apparel Oth. non-metal. minerals Metal products not M&E Furniture Wood Non-ferrous metal Petroleum Transport Elec./profess. Tobacco Pottery Paper Iron and steel Rubber Beverage M&E Chemicals Glass Food Oth chemicals Leather Printing Footwear Textiles Apparel Plastic Oth. non-metal. minerals Metal products not M&E Furniture Wood Non-ferrous metal Petroleum Elec./profess. Transport RCA Tobacco Pottery Paper Iron and steel Rubber Beverage M&E Chemicals Glass Oth chemicals Food Leather Printing Footwear Textiles Apparel Plastic Oth. non-metal. minerals Metal products not M&E Furniture Wood Non-ferrous metal Petroleum Elec./profess. Transport Tobacco Pottery Paper Iron and steel Rubber Beverage M&E Chemicals Glass Oth chemicals Food Leather Printing Footwear Textiles Apparel Plastic Oth. non-metal. minerals Metal products not M&E Furniture Wood Non-ferrous metal Petroleum Elec./profess. Transport Pottery Tobacco Paper Iron and steel Rubber Beverage M&E Chemicals Glass Food Oth chemicals Leather Printing Footwear Textiles Plastic Apparel Oth. non-metal. minerals Metal products not M&E Furniture Wood Non-ferrous metal Petroleum Elec./profess. Transport Baseline (4.6) Kappa=4 Kappa=5 Assumption for kappa Baseline (3.5) Sigma=3 Sigma=4 Assumption for sigma Return

80 Appendix Definitions and motivation Theoretical framework Empirical implementation Baseline results and additional exercises Change in each variable after removing factor misallocation in Colombia Value Exports RCA Welfare - Variable Revenue Exports Welfare added /GDP* s.d.* autarky Counterfactual ˆR Col GDP ˆ Col ˆX Col D( X GDP ) h i closed ÊCol Col Ds ÊCol RCACol ˆPCol ˆPCol Baseline results Both types Only intra-industry Only inter-industry Robustness: Both types Decreasing s (to 3) Increasing s (to 4) Decreasing k (to 4) Increasing k (to 5) One-sector Only intra-industry Note: Each cell shows the proportional change in each variable between the counterfactual equilibrium and the actual data. For variables marked by *, the simple difference in the measure is displayed. Return

81 Appendix Definitions and motivation Theoretical framework Empirical implementation Welfare gains under autarky In the closed economy we have p iis = ˆp iis = 1and ˆR is = Ê is = Ê i,so the welfare change is: " Êi ˆ P d i # closed " = Ĝ 1 k s is l ( S Â s Z ils ˆv ils ) a ls r # bs The welfare cost of misallocation in a closed economy can be derived only with measures of misallocation and factor shares in autarky. Return