AI Gravity, Latent Trade, and Zero Flows

Transcription

1 AI Gravity, Latent Trade, and Zero Flows James E. Anderson Penglong Zhang December 2018 Abstract The Almost Ideal gravity model generates zero trade flows from variable trade cost interaction with demand structure (variable price and income elasticity) as well fixed trade cost. The Tobit estimator applied to trade of 75 countries and 25 sectors in 2006 predicts the latent value of trade between non-partners. Latent Trade Bias (LTB) is the difference between the latent trade share and the as-if frictionless trade share. The variance of estimated LTBs decomposes into 54% variable trade cost, 24% fixed trade cost and 22% income effect. Fixed cost reductions are much less potent on the extensive margin of trade than are variable cost reductions. Keywords: Zero Flows, Variable Costs, Fixed Costs, Latent Trade Anderson: Department of Economics, Boston College, Chestnut Hill, MA ( Zhang: School of Public Policy and Management, Tsinghua University, Beijing, (

2 1 Introduction Zeros dominate bilateral disaggregated trade flows, with changes on the extensive margin (entry or exit) of trade accounting for a significant portion of changes in trade volume. 1 Observed bilateral zeroes are uninformative to policy makers or potential exporting firms about how close or far from entry the market may be. Understanding the causes of zeros is needed to guide trade policy and trade negotiations. Theory suggests that two sorts of costs fixed and variable may be responsible, and they interact with demand side structure. Elasticities differ across sectors and source countries, and prices and incomes differ across destination countries. The Almost Ideal (AI) gravity model of this paper encompasses all these sources of explanations for zeros. The variation in the causes of zeros implies differences in the efficacy of export promotion policy on the extensive margin. Some types of export promotion are permissible under WTO rules, basically affecting fixed costs, e.g., providing information, facilitating links, helping with licensing and regulation requirements, and negotiating bilateral fair treatment in the application of regulations. Exporter countries could target export promotion more effectively if they knew which cost were more important. Exporting firms could target entry markets more effectively with a sense of which of the zeroes were viable for given cost advantages. This paper gives guidance based on the estimation of AI gravity on bilateral manufacturing trade data of 75 countries and 25 sectors in The Tobit estimator of AI gravity predicts the latent value of bilateral trade for nonpartners at the inferred bilateral trade costs and fixed entry costs. Latent Trade Bias (LTB) is the difference between the latent trade share and the as-if frictionless trade share. LTB is a natural extension of the trade bias concept of positive trade flows in standard gravity models. The estimated sectoral trade AI gravity model implies that on average, variable trade cost explains 54% of the variation of LTBs, while fixed cost explains 24%. The remaining 22% is explained by income effect due to variation of per capita income interacting with variable income elasticities. Variable cost dominates fixed cost and income effect for all sectors. 2 The difference of those latent values across destinations also provides exporters the guidance to optimally allocate promotion resources. The modeling environment of the paper is the Almost Ideal Demand System com- 1 A report about the incidence of zeros in US trade in 2005 by Baldwin and Harrigan (2011) shows that US imports nearly 17,000 different HS10 categories from 228 countries, but over 90 percent of these potential trade flows are zeros. Besedes and Prusa (2006) have looked at time-series variation in product-level zeros. They find that there is a remarkable amount of entry and exit in the U.S. import market, and the period of time a country is in the market is often fleeting. About 30% of trade relationships experience flipping on and off. 2 We refer to variable (fixed) trade cost as variable (fixed) cost to save notation in the whole paper. 1

3 bined with heterogeneous firms facing variable and fixed costs of exporting to multiple destinations. This yields a tractable AI gravity model that allows variable cost, fixed cost, and income effect separate roles in generating zero flows. In contrast to constant elasticity of substitution (CES) gravity, even if fixed costs are zero, AI gravity admits zeros due to variable bilateral trade costs that exceed a cutoff (choke) value. 3 In contrast to homothetic demand systems, choke prices can be due to the combined effect of high income elasticity with low per capita income. Another key feature of our model is price (variable cost) elasticity heterogeneity across exporters. This is important because countries considering facilitate policies would be differentially affected according to their demand characteristics, given that all incur the same distance costs and fixed costs of entering a particular export destination. The general bilateral price elasticity matrix of AIDS has N (N 1)/2 parameters in Deaton and Muellbauer (1980). AI gravity as applied here reduces the parameters to N 1, a generalization from 1-parameter symmetric translog model in Feenstra (2003) to a N-parameter asymmetric AIDS model. This generalization allows variable cost to affect trade (including latent trade) flows differently across exporters. We estimate AI gravity equation with both aggregate and sectoral trade data. In order to reduce the parameter dimension, we project the price elasticity as a linear function of exporters export sophistication. Intuitively, more sophisticated goods are more likely to be inelastic and less likely to be substituted for. The estimation results show that the bilateral distance reduces trade by less for more sophisticated exporters. This suggests that there is a significant distance (price) elasticity heterogeneity across exporters. In addition, the size of the heterogeneity is quite different across sectors. Since theory implies that latent trade is bilateral trade left-censored at zero, a Tobit specification is indicated. The predicted latent values are found to be mostly negative and thus the majority of the zero relationships in data are successfully predicted by our model. AI gravity is applied below to measure the distance from trade for non-partner relationships based on the latent value of the bilateral trade that is censored at zero. It is 3 Fixed costs of bilateral exporting combined with heterogeneously productive firms and CES demand are the explanation for zeros in an influential literature based on Melitz (2003). Helpman, Melitz, and Rubinstein (2008) develop a theory that predicts zero trade flows between countries when no firm from one country may be productive enough to profitably export to another country. Firms draw productivities from a bounded distribution. The value of the boundary is essential to the model, because there would be no zeros with a sufficiently high bound. In this sense fixed cost alone explains zeros sufficiently high variable cost cannot generate zeros in the CES structure with elasticity of substitution greater than one. Baldwin and Harrigan (2011) add quality-selection to the Melitz (2003) model and, together with productivity-selection, show that only firms with lowest quality-adjusted price export. Choke prices could be generated also in quadratic preferences, e.g. in Melitz and Ottaviano (2008). But Pollak and Wales (1992) offer evidence that the translog somewhat outperforms the quadratic expenditure system in household budget studies. 2

4 convenient to measure this in the same way that distance from positive trade to as-if frictionless trade is measured. The difference between the predicted trade share and the as-if frictionless trade share is the trade bias due to frictions, an absolute value of a negative number. Apply the logic to latent trade to yield Latent Trade Bias (LTB). Breakeven exports occur where a demand curve is tangent to the falling (if fixed cost is positive) unit cost curve. LTB is the absolute value of the difference between the latent trade share and the as-if frictionless trade share. Across trade partners and sectors, variation in LTB is decomposed into the contributions of variable cost, fixed cost and income effect. 4 First we construct LTBs using the latent value of the Tobit regression. Then we project each component of variable cost, fixed cost, and income effect separately in AI gravity using the structural parameter estimates. Specifically, we compute the variable cost term by combing bilateral variable cost and the multilateral resistances using the structural parameter estimates. Similarly, we compute fixed cost term which is the combination of bilateral fixed cost and corresponding multilateral resistance. Income effect term is computed as the income elasticity times per capita income relative to the world. AI gravity shows the sum of the three terms is exactly LTB. Lastly, we regress each term on the constructed LTB, together with a constraint that all three coefficients are sum to one. Results show that variable cost explains zero trade flows more than fixed cost does for all sectors. We also analyze how decreases in trade costs raise the chance of trade relationships. Marginal changes in trade probability due to a one-standard-deviation decrease in variable cost is larger than for the same one-standard-deviation decrease in fixed cost for all sectors. Price (variable cost) elasticity variance helps shape the frequency difference in zeroes. We find that the average estimated price elasticity is positively correlated with zero flow frequency across sectors. The most price-elastic and most frequently-trading product is tobacco while the least price-elastic and least frequently-trading product is machinery. In contrast, fixed cost elasticity is uncorrelated with zero frequency across sectors. Lastly, we conduct the counterfactual experiments that apply variable cost and fixed cost reductions that shift the trade cost sufficiently to be below the break-even price associated with the breakeven quantity, so that positive trade occurs. On average, bilateral trade cost elimination decreases the number of current sectoral zero flows by 85%, while bilateral fixed cost elimination decreases the zeros by 27%. They are the upper bounds for what the hypothetical export promotion could do. More importantly, it is found that reducing variable cost (e.g. subsidy) improves the probability of building a new trading 4 A minor issue in interpretation arises when the projected latent quantity demanded given the trade frictions is negative. LTB is always an absolute value of a negative number, so the measurement procedure is unaffected. More important, the interpretation of the latent trade bias remains the same. 3

5 partner more (1) in sectors with higher average price elasticities, (2) if the source country exports less sophisticated products, (3) if the export promotion is bilateral (than unilateral). Reducing fixed cost (e.g. regulation cost) improves the probability symmetrically across exporters and sectors. This is consistent with our intuition that less-sophisticated products are more price-elastic and thus are more likely to induce trade to occur when trade costs decrease. The marginal effect of reducing fixed cost on turning zero trade to positive is smaller than reducing variable cost. This paper contributes to the gravity literature in various aspects. Related gravity literature uses the CES form (Anderson and van Wincoop, 2003; Eaton and Kortum, 2002), with firm heterogeneity added in (Chaney, 2008; Helpman et al., 2008). Non-homothetic gravity is treated in Fajgelbaum and Khandelwal (2016), translog gravity in Novy (2013) following Feenstra (2010). Treatment of zeros in the gravity literature include treatments in the trade model by Eaton, Kortum, and Sotelo (2012), in a statistical model by Armenter and Koren (2014), a macro model by Uy (2015) and the estimation bias issue in log gravity models raised by Silva and Tenreyro (2006). The next section presents the key empirical facts. Section 3 presents the model we construct to accounts for these facts. The model estimation is discussed in Section 4, and the main results on zero flows are shown in Section 5. Section 6 conducts counterfactuals on export promotion policies. The last section concludes. 2 Zeros in the Data We use trade and production data for 75 countries in the year of 2006 sourced from CEPII. The data records bilateral trade flows and production data across 25 industrial sectors in the ISIC Revision 2 (International Standard Industrial Classification). Figure 2 shows that 3.6% of the country pairs do not trade manufacturing products at all. There are much higher zero frequencies in sectoral trade than aggregate trade. For example, 65% of the trade flows in tobacco sector among the country pairs are zero. On average, the zero frequency across sectoral trade is 28%. Zero trade flows are more likely to occur in furniture, petroleum, and tobacco sectors, while less likely to occur in machinery, electrics, and textiles sectors. One might think that these zeros are simply a result of a group of countries not trading with one another. Figure 3 plots the trade matrix among all importers in rows and exporters in columns in ascending order ranked by GDP. Blue dots are zero flows and yellow dots are positive flows. Diagnose relationships are internal trade of each country and are all positive. Zero relationships are concentrated in the upper-left corner, implying 4

6 smaller countries are less likely to trade with each other. Since there are much fewer zeros in aggregate trade, we further investigate the results by sectors. Figure 4 plots the trade flow matrix for the leather sector. 5 First, similarly to the trade in aggregate manufacturing products, there are large amount of zero relationships in the upper-left corner, which implies that smaller countries trade with each other less often. Second, we also find zeros in the lower-left (upper-right) corner, which suggests that even very large importers (exporters) do not import (export) leather products everywhere. Third, more zero relationships are distributed in the upper triangular matrix than in the lower triangular matrix. This implies that small importers generate more zero flows than small exporters in leather sector. Figure 5 and Figure 6 plot zero flow distributions in all the other sectors. Although the zero frequency is different across sectors, the distribution pattern is very similar to that in leather sector. In sum, the figures show that the prevalence of zeros in sectoral trade does not just come about because of a certain group of countries, but every country is involved to some extent. For example, Turkey does not import beverage from Japan, Japan does not import footwear from Chile, France does not export tobacco to Nigeria, and Korea does not export furniture to Ireland. 3 Model This section outlines a general equilibrium model with AIDS preference and heterogeneous firms, and derives a gravity equation which can reconcile both positive and zero international trade flows. 3.1 Preferences We consider a world economy with N countries, a continuum of goods ω Ω, and labor as the only factor of production. Denote the exporter as i and the importer as j. Consumers have the Almost Ideal Demand System (AIDS) preference introduced by Deaton and Muellbauer (1980), which can be rationalized as a non-homothetic second-order approximation to an arbitrary expenditure system. Specifically, in any country j, there is a representative consumer with a expenditure function given in logarithmic form as ln e j = ln Q j + u j ω Ω j p j (ω) φ(ω), (1) 5 Zero frequency of international trade in leather sector is 30%, which is very close to the average zero frequency, 28%. So we take leather sector as an average sector to discuss the zero flow distributions. 5

7 where e j is the minimum expenditure at which the consumer can obtain utility u j given prices p j (ω). The Ω j denotes the set of goods available in country j. The price index ln Q j is given in logarithmic form as 1 ln Q j = α(ω) ln p j (ω)dω + γ(ω, ω ) ln p 2 j (ω ) ln p j (ω)dω dω. (2) ω Ω j ω,ω Ω j To satisfy homogeneity of degree one, the parameters are constrained by α(ω) (0, 1), α(ω)dω = 1 and γ(ω, ω )dω = 0 for any ω. Symmetry is imposed to satisfy Young s Theorem, γ(ω, ω ) = γ(ω, ω). Concavity is imposed by the requirement that {γ(ω, ω)} is negative semi-definite. We let γ(ω, ω γβ(ω)β(ω ), if ω = ω ) = γβ(ω), otherwise, where β(ω) (0, 1) and β(ω)dω = 1. Specialization (3) satisfies the general restrictions of the translog but imposes a tight restriction on the cross-effects. In particular, complementarity is ruled out, all off-diagonal terms of the substitution effects matrix are non-negative. Imposing substitutability is reasonable in the typical gravity context of modeling demand for groups of regional varieties of goods classified by sectors defined on the basis of similarity. 6 Applying Shephard s lemma and differentiating the expenditure function with respect to log price p j (ω) generates the expenditure share in good ω for consumer at country j equal to ( ) pj (ω) s j (ω) = α(ω) γβ(ω) ln + φ(ω) ln r p j, (4) j (3) where ln p j = ω Ω j β(ω) ln p j (ω)dω. (5) These expenditure shares have some nice features. First, α(ω) is a taste parameter for the good ω which shifts the expenditure share independently from the prices and income. Second, γβ(ω) is the price elasticity for good ω. The variation of β(ω) allows for asymmetric demand responses to price changes. This gives AIDS preference CES-like components because the price terms γβ(ω) ln(p j (ω)/ p j ) captures cross-effects in sub- 6 β(ω) = β(ω ), α(ω) = α(ω ) for all ω and ω, is the special case proposed by Feenstra (2003) followed by Arkolakis, Costinot, and Rodriguez-Clare (2010), Novy (2013), and Fajgelbaum and Khandelwal (2016). 6

8 stitution with the log of a ratio of own price to an average price ln p j. Third, φ(ω) is the income elasticity which captures the non-homothetic component of the preference. Positive φ(ω) implies luxury goods (with high quality) while negative φ(ω) implies necessary goods (with low quality). 7 We refer to r j = e j /Q j as adjusted real income (expenditure) by individual price index. When φ(ω) = 0 for all ω, AIDS becomes the homothetic translog preference. When β(ω) = 0 and φ(ω) = 0 for all ω, AIDS becomes the Cobb-Douglas preference. The shares must be non-negative. It allows for choke prices beyond which demand is zero, which is ln p max j = [α(ω) + γβ(ω) ln p j + φ(ω) ln r j ]/γβ(ω). (6) 3.2 Firms In any country i, there is a large pool of monopolistically competitive firms. With the demand function (4), firm ω maximizes its profit p j (ω)q j (ω) w it ij z(ω) q j(ω) where q j (ω) is the quantity, t ij > 1 reflects bilateral iceberg trade cost between country i and country j, and w i is the wage rate. Then optimal markup is 1 + (γβ(ω)) 1 s j (ω). Assume firms cannot observe their productivities until they set their markups. Firm ω sets its markup based on the average firm share in the world market which is denoted as s. That means all firms from a same country are, ex ante, identical in term of the markup. 8 We denote it as µ i. Assume, among the goods produced at the same country i, we have α(ω) = α i, β(ω) = β i, and φ(ω) = φ i. Thus µ i = 1 + (γβ i ) 1 s. (7) And the coefficients satisfy i N i α i = 1, i N i β i = 1, and i N i φ i = 0, where N i is the measure of firms in country i. Then a firm receives a productivity in log-level ln z randomly from a distribution F(.). The equilibrium price in log is ln p ij (z) = ln µ i w i t ij ln z. (8) 7 Note that γβ(ω) and φ(ω) are semi-elasticities since they relate expenditure shares to logs of prices and income, but we refer to them as elasticities to save notation. Actually the price elasticities are 1 + γβ(ω)(1 β(ω))/s j (ω) + s j (ω), and the income elasticities are 1 + φ(ω)/s j (ω). 8 Compared to models of monopolistic competition with CES preferences, we allow mark-ups now vary with country of origin. 7

9 From equation (4), firm z s market share in country j is s ij (z) = α i γβ i ln(µ i w i t ij / p j ) + φ i ln r j + γβ i ln z, (9) and its profit π ij (z) = (1 µ 1 i )s ij (z)e j F ij, (10) where E j is the total expenditure of country j, F ij denotes the fixed cost for firms from country i export to country j. Then from zero profit condition π ij (zij ) = 0, we can get the cutoff productivity in log is µ i ln zij = (γβ i) 1 [ µ i 1 f ij α i + γβ i ln(µ i w i t ij / p j ) φ i ln r j ], (11) where f ij = F ij /E j (12) denotes the adjusted fixed cost by the total market expenditure. For simplicity, let s denote a = ln z and assume a follows a special bounded Pareto distribution with accumulative density function as G(a) = ln a, 1 < a < H, (13) ln H where 1 and H are the lower and upper bounds of the distribution, respectively. Parameter H also reflects the dispersion of the productivity. The larger H is, the more heterogeneous firms are. 9 Then we have 3.3 Aggregates H a adg(a) = H a, 1 < a < H. (14) ln H Let S ij denote the total market share of country j imports from all firms of country i. By definition, the bilateral import share can be expressed as 9 More details are in Appendix A.1. S ij = N i H ln z ij s ij (a)dg(a). (15) 8

10 Then equation (9) and (11) give the aggregate shares. That is, 10 S ij /N i = α i γβ i ln(µ iw i t ij / p j ) λ i f ij + φ i ln r j, (16) where α i = (1 + 1/ ln H)α i + (H/ ln H)γβ i (17) β i = (1 + 1/ ln H)β i (18) λ i = (1/ ln H)µ i /(µ i 1) (19) φ i = (1 + 1/ ln H)φ i. (20) Note that α i, γβ i, and φ i are productivity-adjusted tastes, productivity-adjusted price elasticities, and productivity-adjusted income elasticities. Relative to α i, γβ i, and φ i, they include dependence on the supply side productivity distribution parameter, H. Finally the λ i s are the marginal effects of fixed cost on trade shares. The coefficients satisfy i N i α i = (1 + 1/ ln H) + (H/ ln H)γ, i N i β i = (1 + 1/ ln H), and i N i φ i = 0, where N i is the measure of firms in country i. And thus β i = β i / i N i β i. Aggregate share per firm in (16) is decomposed into four parts. The first term α i includes all origin-specific factors and the last term φ i ln r j includes all destination-specific factors multiplied by a origin-specific coefficient. The two terms in the middle are the effects of bilateral variable costs and fixed costs. 3.4 Gravity Market clearance for each origin i is given by Y i = S ij E j, (21) j where Y i is the total income of country i. Using market clearance in the AIDS share equation yields AI gravity equation. 11 Thus: 10 Proof in Appendix A Proof in Appendix A.3. S ij /N i Y i Y /N i = γβ i ln( t ij Π i P j ) λ i ( f ij Ψ i ) + φ i ln(r j/r), (22) 9

11 where Y is world total income, and ln Π i (E j /Y) ln t ij, (23) j ln P j i N i β i ln(t ij /Π i ), (24) Ψ i (E j /Y) f ij, (25) j ln R (E j /Y) ln r j. (26) j On the left hand side, S ij /N i Y i Y /N i is the deviation of bilateral trade per firm from its frictionless level Y i Y /N i. There are three terms on the right hand side, which capture the( variable cost effect, fixed cost effect, and income effect, respectively. The first term, tij γβ i ln Π i P ), is the effect of relative bilateral trade resistance from origin i to destination j where ln Π i and ln P j are the outward and inward multilateral resistances in j log, respectively. This term is very similar to the CES structural gravity in Anderson and van Wincoop (2003). The last term, φ i ln(r j /R), is the non-homothetic component of the gravity equation and captures the effect of relative income per capita of market j where ln R is the average world income per capita in log. The second term, λ i ( f ij Ψ i ) exploits the AI structure to capture the effect of relative trade fixed cost that reduce bilateral trade via extensive margin from origin i to destination j. The intuition is that fixed cost raises the market entry barrier and less firms export. We refer to Ψ i as the outward multilateral fixed resistance that summarize the average trade fixed cost between a country and its trading partners. 4 Estimation In this section, we estimate AI gravity derived in Section 3. Section 4.1 describes the data and specification. We present the estimation results using aggregate level trade data in Section 4.2 and using sectoral trade data in Section Data and Specification To estimate AI gravity equation we use trade and production data for 75 countries in the year of We follow Novy (2013) to measure number of goods that originate from 12 As discussed in Section 2. 10

12 each country, N i, with the extensive margin data constructed by Hummels and Klenow (2005). 13 Bilateral variable cost can be projected by ln t ij = ρ ln dist ij + ε t ij, (27) where d ij is bilateral distance. The geographical data are from CEPII. We follow Helpman, Melitz, and Rubinstein (2008) to use the regulation costs of firm entry, collected and analyzed by Djankov, La Porta, Lopez-de Silanes, and Shleifer (2002). These entry costs are measured via their effects on the number of days, the number of legal procedures, and the relative cost (as a percentage of GDP per capita) for an entrepreneur to legally start operating a business. We use the monetary cost in our baseline estimation and non-monetary costs in the robustness check. 14 Specifically, we construct the bilateral fixed cost as the average cost for an entrepreneur to start a business in the exporter and the importer country. Thus it is country-pair specific. Then we divide this cost by the importer s total expenditure, according to equation (12), to compute the adjusted bilateral entry cost f ij. Recall that real expenditure per capita is defined as ln r j = ln(e j / Q j ) where e j, nominal expenditures per capita, are observable. Aggregate price index ln Q j can be proxied by a Stone index following literature, 15 that is ln Q j = N i=1 S ij ln(p ii dist ρ 0 ij ), (28) where p ii are the quality-adjusted prices estimated by Feenstra and Romalis (2014). We pick ρ 0 = following Fajgelbaum and Khandelwal (2016). Recall that AI gravity is S ij /N i Y i Y /N i = γβ i ln( t ij Π i P j ) λ i ( f ij Ψ i ) + φ i ln(r j/r), where there are a large number of parameters to be estimated, a set of productivityadjusted variable cost (price) elasticities {γβ i }, a set of fixed cost elasticity parameters {λ i }, and a set of productivity-adjusted income elasticities {φ i }. In order to reduce the number of estimated parameters, we impose some restrictions. First, we impose the constraint φ i = c 0 + c ln r i where c > 0 meaning rich countries are more likely to export 13 We also use other measures for the number of goods as robustness checks in Section See Section Deaton and Muellbauer (1980) first time use a Stone index to proxy the AIDS price index. The trade literature, like Atkin (2013) and Fajgelbaum and Khandelwal (2016), follows this approximation. 11

13 high-quality goods, similar to Fajgelbaum and Khandelwal (2016). The theoretical restriction N i=1 N iφ i = 0 implies c 0 = c N i=1 N i ln r i, transforming this linear relationship to φ i = c(ln r i ln r) where ln r = N k=1 N k ln r k, and reducing the number of productivityadjusted income elasticities to be estimated from N to one, i.e. c. Second, we assume productivity-adjusted price elasticities satisfy γβ i = b 0 b 1 ln soph i, (29) where soph i is the export sophistication of exporter i and b 1 > More sophisticated goods are more likely to be inelastic, which implies larger soph i results in smaller price elasticity. We use Sophistication of Exports (EXPY) collected by CEPII from Trade Outcomes Indicators of World Integrated Trade Solution (WITS). 17 Then we reduce the number of productivity-adjusted price elasticities to be estimated from N to 2, i.e. b 0 and b Third, we impose a symmetric fixed cost effect, i.e. λ i = λ, (30) and λ > 0. This is reasonable because we focus on aggregate and sectoral trade instead of firm level trade, and thus the markup differences implicitly in λ i are not the interests of the paper. 19 Then the specification of AI gravity is S ij /N i = b 0 ρ ln dist ij + b 1 ρ ln soph i ln dist ij λentrycost ij + c ln r i ln r j + δinternal ij + ln P j ln soph i + f e i + f e j + ε ij, (31) where f e i = Y i Y /N i + γβ i ln Π i + λψ i φ i ln R, and f e j = b 0 ρ ln P j c ln r j ln r are exporterand importer-specific fixed effects. The multilateral resistance terms ln P j are not observable since they have inside parameters {β i } i=1 N. But they can be estimated as exporterspecific coefficients on ln soph i. We also add a dummy variable Internal ij, which is 0 for import and 1 for internal trade, to capture all the other unobservable trade cost across border, similar to Ramondo, Rodríguez-Clare, and Saborío-Rodríguez (2016) and Anderson and Yotov (2017). Unfortunately ρ cannot be identified from b 0 and b 1. So we pick 16 Novy (2013) and Fajgelbaum and Khandelwal (2016) assume symmetric price elasticities. 17 Sophistication of Exports (EXPY) estimates the level of technological sophistication embodied in a country s export portfolio and gives an indication of that country s economic development. Sophistication captures more than technical characteristics: it includes product differentiation, production fragmentation, resource availability, and other factors. 18 We also use exporter-specific fixed effects to estimate γβ i as robustness checks in Section See equation (20). We also estimate the asymmetric case as robustness checks in Section

14 ρ = directly following the literature, and then b 0 and b 1 are identified. Therefore, the parameters of interest are {b 0, b 1, λ, c}. We expect the coefficients of ln dist ij and entrycost ij are both negative, while those of the interaction terms ln soph i ln dist ij and ln r i ln r j are both positive. In other word, all parameter estimates {b 0, b 1, λ, c} should be positive. The productivity-adjusted elasticity parameters are identified by γβ i = b 0 b 1 ln soph i λ i = λ φ i = c ln(r i / r). And the demand structural parameters are identified by β i = (b 0 b 1 ln soph i )/ k N k (b 0 b 1 ln soph k ), (32) while the other parameters α i, γ, β i, and φ i cannot be identified from the productivity distribution parameter H. We only observe non-negative trade flows in the data. When trade frictions are large enough or income is low enough, systematic zero flows are observed, while random observation error may account for other observed zeros. Let Sij be the latent value of the systematic trade share S ij. Then S ij /N i = { S ij /N i, if S ij 0 0, if S ij < 0. (33) Note that (33) can be estimated by the Tobit model given the data censoring at zero. 20 To investigate more variation of zero trade flows, we also estimate sectoral AI gravity equations using more disaggregate level data. Specifically, we estimate S k ij /N i = b k 0 ρ ln dist ij + b k 1 ρ ln soph i ln dist ij λ k entrycost ij + c k ln r k i ln rk j + δ k Internal ij + ln P k j ln soph i + f e k i + f ek j + εk ij, (34) where all variables with a superscript k is defined in the same way to those without any superscript but in sector k. Since the sectoral data on export sophistication, entry cost, and extensive margin are not available, we still use the aggregate level measures. We run the 20 Helpman, Melitz, and Rubinstein (2008) also pointed out the potential use of Tobit model. If such zero trade values were just the outcome of censoring, then a Tobit specification would provide the best fit to the data. 13

15 regression separately with corresponding data and obtain the estimates across all sectors. 4.2 Aggregate Results We begin by estimating AI gravity model in equation (31) with aggregate manufacturing trade data. Results are reported in column (1) in Table 1. The estimated exporter- and importer-specific fixed effects are dropped since they are not the parameters of interest. As always in gravity estimation, the coefficient of distance is significantly negative distance reduces the bilateral trade share. More novel, the coefficient of the interaction term of Distance and Sophistication is significantly positive, implying that the distance reduces trade by less for more sophisticated exporters. This suggests that there is a significant distance (price) elasticity heterogeneity across exporters, and the magnitude of the coefficient reflects the size of the distance elasticity dispersion. Since we assume ρ = 0.177, the estimates imply ˆb 0 = /0.177 = 38.3 and ˆb 1 = /0.177 = Thus the productivity-adjusted variable cost (price) elasticity γβ i = ˆb 0 + ˆb 1 ln soph i. And { ˆβ i } N i=1 can be calculated by equation (32). As discussed earlier, γ and H cannot be identified from each other. The coefficient of entry cost is significantly negative, which implies that the entry cost also reduces the bilateral trade share. The fixed cost elasticity parameter ˆλ = The coefficient of the income interaction term is not significantly different from zero. This suggests that there is little income elasticity heterogeneity across exporters nonhomotheticity is not statistically significant in aggregate trade. The income elasticity parameter ĉ = This positive coefficient implies that richer importers (higher ln r j ) are more likely to spend larger shares on products from richer exporters (higher ln r i ), conditional on trade costs. The productivity-adjusted income elasticity ˆφ i = ĉ ln(r i / r). 21 The productivity-adjusted income elasticity is 1 + φ i where ˆφ i = ĉ ln(r i / r). The coefficient of the internal trade dummy is also significant, implying internal trade share is larger given all else equal. This home-bias term picks up all the relevant forces that discriminate between internal and international trade. Column (2) and (3) report the estimates of the same equation but with different methods. First one is by OLS with the full sample, and the second one is by OLS too but with only positive trade relationships. Since there are very few zeros in aggregate trade flows, the three methods give very similar results. This will not be true of sectoral estimation when there are higher zero frequencies. 21 Note that ˆφ i are semi income elasticities, which measure the deviations from the unitary elasticity. We call them income elasticities to save notation as discussed earlier in the model. Actually, the income elasticities are 1 + ˆφ i /(S ij/n i ). 14

16 Table 2 reports the estimates of AI gravity with different specifications. Column (1) is our baseline result for equation (31). When we drop the elasticity heterogeneity term measured by interaction of distance and sophistication in column (2), the distance elasticity is The coefficients on distance and its interaction with sophistication are robust for the translog model in which the non-homothetic term is dropped in column (3). When we further shut down the distance elasticity heterogeneity in column (4), all coefficients are still significant with intuitive signs. The estimation one our data of the Fajgelbaum and Khandelwal (2016) and Novy (2013) specifications are reported in the last two columns as special cases. Comparing column (1) and column (5), we find that income elasticities are less dispersed when heterogeneous price elasticities are added to the model. 4.3 Sectoral Results Next we report AI gravity estimates by sectors in row (2)-(26) of Table 3. The estimation results using aggregate data are reported again in row (1), which is exactly the same as column (1) in Table 1. Overall, the disaggregated AI gravity model works well. The coefficients of the variables are, in most cases, significant and the estimates vary across sectors in a sensible way. First, distance is a large impediment to sectoral trade: all estimated distance coefficients are negative and statistically significant. Distance elasticities vary greatly by sectors, consistently with variation in value to weight and the physical requirements of transportation. All the coefficients of the interaction term of Distance and Sophistication are significantly positive, implying that the distance elasticity heterogeneity is common across all sectors. Products produced by more sophisticated exporters are less distance elastic. The coefficients of this interaction term are different in magnitude, which suggests different sizes of the distance elasticity dispersion. Furniture, Tobacco and Beverages are the three sectors with the biggest distance elasticity heterogeneity, while Machines, Rubber, and Chemicals are among the sectors with the smallest distance elasticity dispersion. This is intuitive because products in the former sectors are more differentiated than those in the latter sectors. Second, all estimated entry cost coefficients are negative and only six of them are insignificant entry costs impede bilateral trade significantly for nineteen of twenty-five sectors in our sample. Insignificant entry cost effects are found in sectors including Non- 22 The estimates of the distance elasticity is in Novy (2013) and in Fajgelbaum and Khandelwal (2016). Our result is in between. 15

17 Metal, Leather, Wood, Footwear, Apparel, and Paper. At the other extreme Tobacco and Furniture are the sectors most sensitive to entry cost in international trade. Third, all estimated coefficients of the income interaction term are positive, but only fourteen of them are significant. This suggests that the non-homothetic effect is weak in the other eleven sectors. Significant non-homothetic income effects are found in sectors including Furniture, NonMetal, Glass, Leather, Apparel, Chemicals, OthChem, Rubber, Textiles, Transport, and Paper, marginally in Food, IronSteel and Machines. In these sectors, rich countries are more likely to export high-quality goods and also more likely to import high-quality goods. Last, international borders reduce trade, all else equal. All the estimates of the coefficients on internal (the dummy variable capturing internal trade) are positive, large, and significant at any level. Furniture, Food, and Beverages are the sectors with the highest internal estimate, while Machines and Tobacco are the ones with the lowest estimate. This is intuitive because the other unobservable trade barriers, like consumer tastes, play an important role in the former sectors while are weak in the latter. 5 Quantitative Analysis In this section, we use AI gravity in Section 3 and the estimation results in Section 4 to quantitatively study the roles of variable and fixed costs in forming international zero trade flows. Section 5.1 constructs a hypothetical negative trade variable that measures how far from trade a not-trade relationship observed as zero is. in In Section 5.2, we decompose this distance into variable cost effect, fixed cost effect, and income effect to check to what extent the zero flows is explained by each component. Lastly, we analyze how decreases in trade costs raise the chance of trade relationships. 5.1 Latent Trade How to understand the latent value of bilateral trade censored at zero in our model? We start with a diagram to illustrate the economic meaning of this negative value. Recall demand D(p) for good z is given by equation (9), i.e., p ij (z)q ij (z)/e j = α i γβ i ln(µ i w i t ij / p j ) + φ i ln r j + γβ i ln z, (35) and breakeven-condition S(p) for good z is determined by price equaling to average cost p ij (z) = w i t ij /z + F ij /q ij (z). (36) 16

18 p ij p ij p c ij virtual subsidy S(p ij ) D(p ij ) p v ij virtual quantity p g ij D(p ij ) q* ij q ij 0 latent resistance q ij q ij LTB ij E j /p ij Figure 1: Latent Trade As Figure 1 shows, D(p) is the actual demand and S(p) is the breakeven-condition of product z which is produced at i and sold in market j. And pij c is the choke price. Since the demand curve is below the breakeven condition, no trade occur. The demand D(p) which is tangent to the breakeven-condition curve is the minimal level to make the firm to enter the market. And q ij is the breakeven quantity. To assure the consumer to consume the breakeven quantity to make the trade occur, the price should decrease to pij v which we define as virtual price. 23 One way to make the trade occur is to subsidize the consumer by p ij pij v which we define as virtual subsidy. Another way is to supplement consumer the quantity in the amount of q ij qij (also equals to q ij + qij ) which we define as latent resistance. We use this distance from the negative value to the breakeven demand to measure how far from breakeven is the implied demand, i.e., how far from occur is the trade. In the negative region the consumer would 23 virtual price developed by Neary and Roberts (1980) is the price that would induce an initially unconstrained consumer to demand the level of a good when under quantity control (rationing). 17

19 hypothetically sell the product if they have inventory. If the consumer owned the full amount q ij qij to enable consumption q ij, the amount qij is sold in the world market and the remainder is consumed in the amount q ij. The virtual resistance q ij qij is welfare equivalent to the virtual subsidy p ij pij v. 24 One plausible way to make the virtual variables actual is as follow. The government buys the amount q ij qij from the world market at the breakeven price. It resells the amount qij on the world market at that price, while sells the amount OE on the domestic market at the virtual price pij v. The net loss is ( p ij pij v ) q ij, just as in the virtual subsidy case where the virtual subsidy is implemented. Note that p g ij is the factory gate price and ˆq ij is the frictionless level quantity when all trade costs are zero. We define the distance from the quantity for breakeven-price to the quantity for frictionless-price as the latent quantity bias. Since trade share is our variable of interest, we further define latent trade bias in terms of the expenditure share of the latent quantity bias of the product. Specifically, LTB ij (z) = p ij (z)( ˆq ij (z) q ij (z))/e j, (37) where qij (z), the latent value of quantity demand, is negative. We use this full distance to measure how far from frictionless is the implied demand, i.e., how far from the maximum is the trade of product z. It includes the effects of trade costs, as well as the effects of price elasticity γβ i and income elasticity φ i. 5.2 Latent Trade Bias Decomposition In last section, we theoretically show that the latent trade is crucial in understanding the zero flows. In this section, we quantitatively project the latent trade bias and identify the extent to which zero trade flow is explained by variable cost, fixed cost, and income effect respectively. Generally in gravity literature, we define the trade bias as Bias ij Y i Y /N i S ij /N i, which measures the total effect acting to deviate each country pair s trade share from the frictionless benchmark. However, this measure is not observable when the trade flow, S ij, is censored at zero. Importantly, equation (37) implies that the latent trade bias of a 24 Virtual quantity in literature, e.g., Neary (1985) and Squires (2016), is the quantity of a good that the initially quantity-constrained consumer would demand once unconstrained, given that quantity control s market or accounting price. It is q ij on the diagram. Latent resistance in our paper is distinct. 18

20 product could be expressed as the difference between frictionless and latent expenditure shares. Thus, we can define the aggregate latent trade bias (LTB) as LTB ij Y i Y /N i S ij /N i, (38) where Sij is the latent trade share when the actual trade share is zero, and it could be predicted by the Tobit regression. On one hand, the latent trade bias can be predicted by AI gravity equation (22) with all the gravity parameters estimated by the Tobit regression in equation (31), i.e. LTB ij = Y i Y /N i Ŝ ij /N i. (39) On the other hand, AI gravity equation (22) shows that the LTB could be decomposed into three effects LTB ij = γβ i ln( t ij ) + ˆλ( f ij ˆΨ i ) ˆφ i ˆΠ i ˆP j }{{} ln(r j/ ˆR), (40) }{{}}{{} Xij t X f Xij r ij where components Xij t, X f ij, and Xr ij are the effects of variable cost, fixed cost, and income. All of them can be computed with the parameter estimated. Then we can decompose the LTB variation cross country pairs into three margins following the literature. 25 Specifically, we regress each component in equation (40) on the LTB and estimate the simultaneous equations X t ij = η t LTB ij + ɛ t ij, (41) X f ij = η f LTB ij + ɛ f ij, (42) X r ij = η r LTB ij + ɛ r ij, (43) with the constraint η t + η f + η r = 1. (44) By the properties of OLS, the coefficients η t, η f, and η r provide us with a measure of how much of the variation in the LTB for zero flows can be attributed to the effect of variable cost, fixed cost, and income, respectively. This helps us to discuss which of the components is the more important one to cause non-partner relationships. Replacing the 25 See Eaton, Kortum, and Kramarz (2004), Hottman, Redding, and Weinstein (2016), and Bernard, Dhyne, Magerman, Manova, and Moxnes (2017). 19

21 aggregate LTB and its three components with the corresponding sectoral variables, we can determine the variance decomposition for each sector. The results are reported in Table 4. Row (1) shows the LTB decomposition for the aggregate trade. Variable cost (Distance) explains 77%, fixed cost (Entry cost) explains 13%, and income effect explains 10% of the zero flows. Since there are much fewer zeros in aggregate trade, we further investigate the results by sectors in row (2)-(26). All coefficients in all sectors are significantly positive and between zero and one. On average, variable cost explains 54%, Fixed cost explains 24%, and income effect explains 22% of the zero flows. The entry cost effect is usually less important aggregate trade (13%) than in sectoral trade (24%), which is consistent with our intuition. To visualize the results, Figure 7 plots the decomposition. We find that variable cost effect is larger than both fixed cost effect and income effect for all sectors. Variable cost effect is strongest in shaping zeros in Apparel, OthChemicals, and Textiles, while is weakest in Rubber, Wood, and Machines sectors. Fixed cost impedes the trade to occur most likely in Rubber, Wood, and ProfSci sectors, while least likely in Apparel, Transport, OthChemicals, and Food sectors. The income effect is the most strongest in shaping zeros in Rubber, Wood, and Machines, while is weakest in Apparel, OthChemicals, and Textiles sectors. Variable cost explains zero flows more than fixed cost does not only within sector, but also across sectors. Figure 8 plots the cross-sector zero trade frequency and average price elasticity. We find significant positive correlation between them, which implies price elasticity variation accounts for zero frequency variation across sectors well. This is quite different to the effect of fixed cost elasticity that is not correlated to zero frequency across sectors at all, which is plotted in Figure 9. Thus across-sector zeros are more attributed to variable cost than fixed cost. 5.3 Trade Probability In this part, we analyze the marginal effect of a change in trade costs on the trade probability. In order to compare the marginal effect of variable cost (VC) and fixed cost (FC) properly, we standardize both trade costs, and then investigate the change in trade probability due to one standard deviation decrease in VC and FC, respectively. First we construct VC = ρ ln dist and FC = f where ρ = Then we standardize them by subtracting their means and divided by their standard deviations, resulting in variables of zero sample mean and unit sample variance. In order to get an average marginal effect of variable cost across exporters with heterogeneous price elasticities, we shut down the export sophistication terms (the interaction terms ln soph i ln dist ij and ln P j ln soph ij ) 20

22 in equation (31). Then we have the specification of the symmetric AI gravity equation as S ij /N i = b v VC ij b f FC ij + c ln r i ln r j + δinternal ij + f e i + f e j + ε ij, (45) and S ij /N i = { S ij /N i, if S ij 0, 0, if S ij < 0, where Sij is the latent value of the systematic trade share S ij. f e i and f e j are exporterand importer-specific fixed effects. The dummy variable Internal ij is 0 for import and 1 for the internal trade, capturing all the other unobservable trade cost across borders. We assume the error term ε Normal (0, σ 2 ). Then the probability that a given country pair trade with each other is Prob(S > 0) = Prob(ε > Xb) = Φ(Xb/σ) (46) where matrix X is the vector of all independent variables and b is the vector of all their coefficients in equation (45). Φ(.) is the standard normal cumulative distribution function. Thus the marginal change in trade probability due to trade costs are computed by Prob(S > 0) VC = ˆb v φ( X ˆb/ˆσ)/ˆσ (47) and Prob(S > 0) FC = ˆb f φ( X ˆb/ˆσ)/ˆσ (48) where φ(.) is the standard normal probability density function, and X denotes the vector of mean values. The results are reported in Table 5. Row (1) shows the marginal changes in trade probability for the aggregate trade. One standard deviation decrease in VC improves the trade probability by 5 percentage point, while one standard deviation decrease in FC improves the trade probability by 3 percentage point. Since there are much fewer zeros in aggregate trade, we further investigate the results by sectors in row (2)-(26). All numbers are positive which implies lowering trade cost increases the trade probability. On average, one standard deviation decrease in VC improves the trade probability by 10 percentage point, while one standard deviation decrease in FC improves the trade probability by 2 percentage point. To visualize the results, Figure 11 plots the results of marginal effects of VC and FC on trade probability respectively, as well as their 95% confidence intervals. VC raises the trade probability most in Petroleum, Wood, and Tobacco sector, while least in 21

23 ProfSci, Electrics, and Printing sectors. FC raises the trade probability most in Transport, Textiles, and Machines sector, while least in Electrics, Paper, and ProfSci sectors. More importantly, marginal changes in trade probability due to VC are larger than to FC for all sectors, implying that variable cost is more important than fixed cost in trade policy adjustment to make trade to occur. 6 Counterfactuals In this section, we conduct the counterfactuals to analyze whether zero flows turn positive (i.e., zero-to-one transition) or not if trade costs are reduced by export promotion policies? There are two sets of promotion policies. One is proportional to export volume and acts as negative variable cost, e.g, subsidy, tax and financial benefits, duty drawback, export insurances, and exchange rate management. 26 The other set is not dependent on how much the export is and works as negative fixed cost, e.g., providing information, facilitating links, helping with licensing and regulation requirements, and negotiating bilateral fair treatment in the application of regulations. Now we consider the effects of the two types of promotion policies on zero trade flows. First of all, we calculate the latent values of the trade shares with zero flows by AI gravity equation (22), i.e., Ŝ ij /N i = Y i Y /N i γβ i ln( t ij ˆΠ i ˆP j ) ˆλ( f ij ˆΨ i ) + ˆφ i ln(r j/ ˆR), (49) and then check the signs of those values. If a latent value is negative, the corresponding country pair is predicted as a zero relationship. Figure 12 displays the distribution of both zero and nonzero relationships for leather trade. The majority of the zero relationships are successfully predicted by our model. In addition, the latent trade measured by the predicted latent value of trade share implies how far the current relationship is from trade. We take some exporters in some sectors as examples to illustrate the implications of the latent trade. Figure 10 plots the potential markets of six exporters respectively in some particular sectors. U.K. does not export Tobacco to Lithuania but the absolute value of the latent trade is much smaller than other markets, which suggests the relationship between U.K. and Lithuania is much closer to trade. Georgia and Peru are the next two potential markets of U.K. Tobacco export. Ecuador is the country least likely to import Tobacco from U.K.. Similarly, we find 26 Most of this set of policies are not permissible under WTO rules with some exceptions, e.g., improving transportation infrastructure to reduce freight costs. 22

24 that Moldova, Albania, and Azerbaijan are the three potential markets on the margin of Canadian Footwear export, while Yemen, Tunisia, and Morocco are the three potential markets on the margin of Australian Leather export. We also provide examples for exporters that are developing countries. Mexican IronSteel products are more likely to enter Madagascar, Macedonia, and Moldova. Textile products from Colombia are more likely to enter Tajikistan, Mongolia, and Nigeria. Mongolian Food products are more likely to enter Moldova, Latvia, and Armenia. Now we ask our first question that what is the proportion of zeros that turn positive if we reduce the bilateral cost by 10%, 50%, and 100%, respectively? The answer to this question is important because it tells us the effectiveness of the promotion policy, i.e., the probability of building a new relationship given a country pair not trading with each other yet. Specifically, for any zero flow, we calculate the bilateral cost direct effect as well as its indirect effect(s) through the multilateral resistance(s). 27 And then we predict the new latent value of the trade share of that country pair using AI gravity equation (22). If the predicted latent share becomes positive, the country pair switch to trade (zero-to-one transition). If the predicted latent share is still negative, the flow remains zero. We first take leather sector as an example. Figure 13 plots the zero-to-one transition if we reduce bilateral variable cost by 100% for each country pair, it is found that most of the relationships turn positive now, which means those zeros are gone. In contrast, we find most of the zeros remain the same when we reduce bilateral fixed cost by 100% for each country pair in Figure 14. Then we investigate all sectoral zero flows, and the results are reported in Table 6. All numbers are positive which implies eliminating trade cost decreases the number of zeros in sectoral trade. On average, zeros in sectoral trade decrease by 85% due to VC elimination, while by 27% only due to FC elimination. Similar results are found for 10% and 50% trade cost cut. The higher trade cost cut is, the more zero-to-one transitions we get. Furthermore, the return in terms of building new trading partners is increasing faster for VC cut than FC cut. Comparison of the results for 10%, 50%, and 100% shows that the marginal return of VC cut is decreasing. Lastly, eliminating VC reduces the trade zeros most in Tobacco, Footwear, and Wood sectors, while least in Furniture, ProfSci, and Plastic sectors. Eliminating FC reduces the trade zeros most in Wood, ProfSci, and Rubber sectors, while least in Food, NonMetal, Textiles and Printing sectors. But effects of FC cut are less dispersed than those of VC cut. More importantly, the decreases in zero trade frequency due to VC elimination are larger than due to FC elimination for all sectors, 27 The indirect effects are usually limited because the weight of bilateral cost, importer s GDP share, are usually very small. See equation (23) and (25). 23

25 implying that variable cost is more important than fixed cost in trade policy adjustment to make trade to occur. We are also interested in the effect difference across exporters with different trade (price) elasticities. Intuitively, more sophisticated exporters export inelastic products and thus is less affected by VC cut., while less sophisticated exporters increase the (latent) trade share a lot. 28 Specifically we divide all countries into three groups in terms of their export sophistication and check the difference across groups. 29 Table 7 reports the zero-to-one transitions by reducing bilateral costs by 10%. First three columns outlines the average number of non-partners for exporters in different groups. On average, a less-sophisticated exporter has 41 non-partners out of A more-sophisticated exporter has only 8 zero trade relationships. This is consistent with our intuition that moresophisticated products are less price-elastic and thus are more likely to induce trade to occur even with high trade costs. The last three columns reports the effect of VC cut and it is much larger for less sophisticated exporters than more sophisticated exporters. The reason is that the demand is more sensitive to the price change of less sophisticated products and thus the effect of VC cut for less sophisticated exporters is stronger. Now we ask our second question that what is the proportion of zeros that turn positive if exporters unilaterally reduce trade cost by 10%, 50%, and 100%, respectively? The answer to this question is important because it tells us the effectiveness of the promotion policy, i.e., the probability of building new relationships given an exporter. Specifically, for any zero flow, we calculate the bilateral cost direct effect as well as its indirect effect(s) through the multilateral resistance(s). 31 And then we predict the new latent value of any trade share of that exporter using AI gravity equation (22). If the predicted latent share becomes positive, the destination country becomes a trading partner (zero-to-one transition). If the predicted latent share is still negative, the flow remains zero. The results are reported in Table 8. On average, zeros in sectoral trade decrease by 28 More discussion on the relationship between export sophistication and price elasticity in 15 in Section More sophisticated exporters are Ireland, Finland, Japan, Switzerland, Sweden, Germany, United States, Singapore, Denmark, Korea, Hungary, United Kingdom, France, Malaysia, Austria, Czech, Canada, Netherlands, Slovenia, Italy, Iceland, Hong Kong, and Spain. Median sophisticated exporters are Mexico, Philippines, New Zealand, China, Slovakia, Poland, Thailand, Portugal, Norway, Estonia, Nigeria, Lithuania, Indonesia, Greece, Turkey, Australia, Latvia, Russia, Yemen, Brazil, Uruguay, Romania, Azerbaijan, India, South Africa, Bulgaria, Ukraine, and Colombia. Less sophisticated exporters are Kazakhstan, Tunisia, Georgia, Ecuador, Jordan, Viet Nam, Tajikistan, Macedonia, Moldova, Morocco, Kyrgyzstan, Albania, Armenia, Chile, Kenya, Pakistan, Sri Lanka, Peru, Niger, Madagascar, Tanzania, Ghana, Mongolia, and Ethiopia. 30 There are 75 countries in our sample and thus each exporter has 74 trading partners at most. 31 The indirect effects are also important because multilateral resistances change at the same speed as trade costs do. See equation (23) and (25). 24

26 44% due to VC elimination, while by 27% due to FC elimination. No differences between VC and FC are found for 10% and 50% cut. Furthermore, the return in terms of building new trading partners is increasing slow for both VC cut and FC cut. Lastly, eliminating VC reduces the trade zeros most in Apparel, Footwear, and Wood sectors, while least in Printing, MetalProd, and Plastic sectors. Eliminating FC reduces the trade zeros most in Wood, ProfSci, and Chemicals sectors, while least in Food, NonMetal and Textiles sectors. Dispersion of the effects of FC cut and VC cut are similar. Importantly, the decreases in zero trade frequency due to VC elimination are similar to FC elimination for most sectors. 7 Robustness We demonstrate the robustness of our baseline estimates in Section 4 and LTB decomposition in Section 5.2 to alternative measures of number of goods (firms) in Section 7.1, to an alternative specification without projection on export sophistication in Section 7.2, to alternative measures of fixed costs in Section 7.3, to an alternative specification with heterogeneous fixed cost effect in Section Alternative measure of number of goods In this part, we go through a number of robustness checks to ensure that our baseline estimation patterns do not solely depend on the particular measure of the number of goods. We replace the extensive margin by Hummels and Klenow (2005) by two alternative variables. The first one is total number of firms for each country sourced from CEPII, and the second one is log GDP for each country. For each variable, we normalize it by dividing the sum across all countries to obtain a share measure. The results, together with our baseline estimates, are reported in Table 9. In column (2), we use the number of firms to replace the extensive margin. The coefficient of distance is significantly negative. The coefficient of the interaction term of distance and sophistication is significantly positive, implying that the distance reduces trade by less for more sophisticated exporters. This suggests that there is a significant price elasticity heterogeneity across exporters. Both coefficients are smaller than the baseline results in column (1) due to less variation in number of firms compared to the extensive margin measure. But the price elasticity heterogeneity pattern is consistent. Similar results obtained when we use log GDP in column (3). The coefficients of entry cost are all significantly negative; in column (2) and in column (3), which are very close to in column (1). The coefficient of the income interaction term is insignifi- 25

27 cant from zero in last two regressions. This suggests that there is little income elasticity heterogeneity across exporters for aggregate manufacturing trade. The coefficient of internal trade dummy is also significant, implying internal trade share is larger given all else equal. 7.2 Heterogeneous distance elasticity without constraint In this part, we remove the constraint equation (29) on price elasticities. Exporter-specific coefficients are estimated instead. Then the specification for AI gravity is S ij /N i = γβ i ρ ln dist ij λentrycost ij + c ln r i ln r j + γβ i ρ ln P j + f e i + f e j + ε ij, (50) where f e i = Y i Y /N i + γβ i ln Π i + λψ i φ i ln R, and f e j = c ln r j ln r are exporter- and importer-specific fixed effects, respectively. We expect the coefficients of ln dist ij are exporterspecific and all negative. Unfortunately, both γβ i ρ and ln P j are unobservable. If we take both unobservables as parameters to be estimated, the interactive terms will cause nonlinearity in regression. Bai (2009) extends the argument in Mundlak (1978) and Chamberlain (1984) to models with interactive effects, and shows that more consistent estimates are obtained with a projection of the interactive term onto an average of regressors when interest is centered on coefficients of non-interactive terms. We follow his idea to project the unobservables such that ln P j = η ln P j + ɛ j where ln P j = (1/N) N i=1 Then the econometric specification of AI gravity equation becomes ln dist ij. (51) S ij /N i = b i ρ ln dist ij λentrycost ij + c ln r i ln r j + b i ρη ln P j + f e i + f e j + v ij, (52) where v ij = ε ij + γβ i ρɛ j. There are N + 2 parameters of interest in total, {b 1,..., b N, λ, c}. And {b i ρ} can be estimated as exporter-specific coefficients on ln dist ij. We still pick ρ = and then {b i } are identified. We expect the coefficients of ln dist ij and entrycost ij are all negative, while the coefficient of the interaction term ln r i ln r j is positive. In other word, all parameters {b 1,..., b N, λ, c} should be positive. The productivity-adjusted elas- 26

28 ticity parameters are identified by γβ i ρ = b i. (53) And the demand structural parameters are identified by β i = b i / k N k b k. (54) The results are reported in Table 10. The entry cost reduces bilateral trade share significantly. The estimate of the income elasticity parameter is marginally significant from zero. The table also reports the estimates of the 75 distance elasticities b i, one corresponding to each exporter, in the subsequent rows. The estimates are all significantly negative. The three exporters with the biggest distance elasticity are Ethiopia, Yemen, and Moldova. The three exporters with the smallest distance elasticity are Hong Kong, Switzerland and Netherlands. This means products from the former exporters are very distance elastic whereas products from the latter are inelastic. Figure 15 shows that the correlation assumption on the price elasticities and the export sophistication in equation (29) in our baseline estimation is very consistent with data. More sophisticated products are less price elastic. The R-square is Figure 16 displays both the price and income elasticities for each exporter s products. We find the variation of price elasticities is larger than income elasticities. 7.3 Alternative measure of fixed cost In this part, we examine other measures for fixed cost to ensure that the coefficient patterns and variation decomposition in our baseline regression do not hinge on a particular measure. In Table 11, we replace entry cost with entry days & proc which is the sum of the number of days and the number of legal procedures for an entrepreneur to legally start operating a business. 32 It is a measure for non-monetary fixed cost in additional to the entry cost that is monetary. We take an average of the exporter and importer sides as the bilateral measure. By construction, entry days & proc. reflects regulation costs that should not depend on a firm s volume of exports to a particular country. The purpose of using the additional fixed cost variable is to check whether the distance coefficient patterns in Table 3 are driven by the measurement of fixed costs. We find that the coefficients on distance and its interaction with sophistication are very similar to the baseline Table. This implies that distance elasticity heterogeneity is robust. And the order of the sectoral 32 Helpman, Melitz, and Rubinstein (2008) also use the sum of the two to have enough variations. 27

29 results are close to the baseline results also, suggesting that the relative size of the elasticity dispersion among sectors are also robust. The coefficients of entry days & proc. are significantly negative for aggregate trade and seventeen sectors. Once AI gravity with an alternative fixed cost measure is estimated, we can redo the variation decomposition again. The reason to do this is to check whether variable cost is attributed too much to zero trade flows in our baseline results in Table 5. The results are reported in Table 12. Row (1) reports the virtual bias decomposition for the aggregate trade. Variable cost (Distance) explains 62%, entry days & proc. explains 31%, and income effect explains 7% of the zero flows. Although fixed cost contributes by 31%, variable cost still dominates in explaining the zero flows. We further investigate the results by sectors in row (2)-(26). Coefficients of all variables, including entry days & proc., in all sectors are significantly positive and between zero and one. On average, variable cost explains 48%, entry days & proc. explains 35%, and income effect explains 17% of the zero flows. The contribution of the non-monetary fixed cost is strongest in shaping the zeros in Textiles, Transport, and Apparel sectors, while is weakest in OthChemicals, Plastic, and Food sectors. 7.4 Heterogeneous fixed cost effect In this part, we remove the symmetry constraint equation (30) on fixed cost elasticities. The purpose is to check whether the price elasticity heterogeneity is robust when we allow fixed cost effect asymmetry, and ensure that the variation decomposition in our baseline regression do not hinge on this particular symmetry assumption. The structural model suggests that the coefficient on fixed cost is a function of the markup in equation (20), and thus a function of the price elasticity parameters implied in equation (7). Then we have λ i = (1/ ln H)(1 + γβ i/ s). (55) Since the fixed cost coefficient is linear in the price elasticity, we can estimate λ i in a way similar to distance elasticities. Specifically, similar to (29), we assume λ i = b f 0 b f 1 ln soph i, (56) where soph i is the export sophistication of exporter i and b f 1 > 0. More sophisticated goods are more likely to have smaller price elasticity, higher markup, and thus smaller 28

30 fixed cost effect on trade. Then the specification for AI gravity becomes S ij /N i = b 0 ρ ln dist ij + b 1 ρ ln soph i ln dist ij b f 0 entrycost ij + b f 1 ln soph i entrycost ij + c ln r i ln r j + δinternal ij + ln P j ln soph i + f e i + f e j + ε ij, (57) where f e i and f e j are exporter- and importer-specific fixed effects, respectively. We expect the coefficients of ln dist ij and entrycost ij are both negative, while the coefficient of the three interaction terms are all positive. In other words, parameters {b 0, b 1, b f 0, b f 1, c} are the parameters of interest and should be all positive. The results are reported in Table 13. Row (1) shows the estimates for the aggregate trade. The coefficients of distance and its interaction term with sophistication are and 0.708, which are very close to the results ( and ) in our baseline regression. The coefficient of entry cost is significantly negative, which implies that the entry cost reduces the bilateral trade share. The coefficient of the interaction term of entry cost and sophistication is significantly positive, implying that the entry cost reduces trade by less for sophisticated exporters. Row (2)-(26) report the sectoral results. We find that the coefficients of the entry cost interaction term are, in most cases, significant and the estimates vary across sectors in a sensible way. Importantly, we find that the coefficients on distance and its interaction with sophistication are very similar to those in Table 3. This implies the robustness of the distance elasticity heterogeneity. And the order of the sectoral results are also close to the baseline regressions, suggesting that the relative size of the elasticity dispersion are also robust although we allow asymmetric fixed cost effect. Once AI gravity with asymmetric fixed cost effects is estimated, we can redo the variation decomposition again in Table 14. The reason to do this is to check whether variable cost carries too much contribution to zero flows in our baseline results in Table 5. Row (1) reports the LTB decomposition for the aggregate trade. Variable cost (Distance) explains 64%, Entry cost explains 29%, and income effect explains 7% of the zero flows. The fraction explained by distance decreases by 14 percentage point (compared to Table 4), which is attributed to fixed cost effect heterogeneity. But variable cost still dominates in explaining the LTB variation. We further investigate the results by sectors in row (2)-(26). Coefficients of all variables in all sectors are significantly positive and between zero and one. On average, variable cost explains 47%, entry cost explains 36%, and income effect explains 17% of the zero flows. 29

31 8 Conclusion This paper imposes Almost Ideal Demand System (AIDS) preference to firm heterogeneity framework and derives AI gravity equation which reconciles zero trade flows theoretically and analytically. AI gravity allows variable cost, fixed cost, and income effect to work independently to generate zero flows. We develop the latent trade to theoretically measure the distance from trade for any non-partner relationship. AI gravity also include price (variable cost) elasticity heterogeneity across exporters. This is important because countries considering facilitate policies would be differentially affected according to their demand characteristics. This theory promises to shed more light on trade promotion policies for non-partners, especially developing countries with higher zero trade frequencies. The latent trade measured by the predicted latent value has very important policy implications. Promotion policy could be targeted on the potential markets on the margin that are much close to zero. We quantitatively assess the roles of variable and fixed costs in forming international zero trade flows. Results show that variable cost explains the zero trade flows by more than fixed cost does for all sectors. The marginal effect of reducing fixed cost on turning zero trade to positive is smaller than reducing variable cost. The empirical results presented in this paper are based on country level trade flows. A natural extension would be an application to firm level data, which has important implications for firm decisions on new market entrants. Although our goal in this article is to demonstrate the importance of trade cost reduction for the potential trading partners, we believe that a promising avenue lies in income policy on the importer side. We leave this for future work. 30

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35 Tables and Figures Aggregate manufacturing Machinery except electrical Machinery electric Textiles Food products Fabricated metal products Other chemicals Wearing apparel Prof. and sci. equipment Transport equipment Plastic products Printing and publishing Industrial chemicals Paper and products Rubber products Leather products Glass and products Iron and steel Other non metal min. prod. Non ferrous metals Beverages Wood products except furniture Footwear Furniture except metal Petroleum refineries Tobacco Percent of country pairs No trade Trade Figure 2: Zero Trade Frequency across Sectors 34

36 Aggregate Exporter ranked by GDP Importer ranked by GDP Figure 3: Zero Trade Flows by Country Pairs: Aggregate Manufacturing Leather Exporter ranked by GDP Importer ranked by GDP Figure 4: Zero Trade Flows by Country Pairs: Leather Sector 35

37 Machines Electrics Textiles Food MetalProd OthChem Apparel ProfSci Transport Plastic Printing IndChem Figure 5: Zero Trade Flows by Country Pairs: All Other Sectors I 36

38 Paper Rubber Glass IronSteel NonMetal NfMetals Beverages Wood Footwear Furniture Petroleum Tobacco Figure 6: Zero Trade Flows by Country Pairs: All Other Sectors II 37