JKU A Search and Learning Model of Export Dynamics Essay

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A Search and Learning Model of Export Dynamics1 Jonathan Eatona,e , Marcela Eslavab , David Jinkinsc , C. J. Krizand , and James Tyboutc,e This draft: February 2014 1 We gratefully acknowledge support from the National Science Foundation (Grant SES-0922358), the United States Census Bureau, and Banco de la República de Colombia. We also thank Monica Hernández, Gustavo Caballero and Camilo Acosta for excellent research assistance, as well as Enrique Montes for expert data advice. This paper was written in part by Census Bureau staff. It has undergone a more limited review than official Census Bureau publications. All results were reviewed to ensure confidentiality. Any views, findings and opinions in the paper reflect the views of the authors and do not reflect the views of the U.S. Census Bureau. Abstract Customs record data reveal a number of patterns in relationships Colombian firms have with their U.S. buyers. We interpret these patterns in terms of a continuous-time model in which heterogeneous sellers search for buyers in a market. Success in selling to a buyer reveals information to the seller about the appeal of her product in the market, affecting her incentive to search for more buyers. Fit using the method of simulated moments, the model replicates key patterns in the customs records and allows us quantify several types of trade costs, including the search costs of identifying potential clients and the costs of maintaining business relationships with existing clients. It also allows us to estimate the effect of previous exporting activity on the costs of meeting new clients, and to characterize the cumulative effects of learning on firms’ search intensities. Finally, we use our fitted model to explore the effects of these trade costs and learning effects on aggregate export dynamics. 1 Introduction Research on exporting has been digging deeper into microeconomics data to understand the barriers that producers face in entering foreign markets and their implications for export dynamics. Firm-level datasets have provided insights first into the costs of exporting at all, and then, as data became available, to penetrating individual markets. We take this analysis one step forward by examining exporters’ relationships with individual buyers in a market, both descriptively and through the lens of a dynamic model. 1.1 Scope We begin by summarizing patterns in a decade’s worth of data on individual merchandise shipments from Colombia to the United States. First, following work by some of the authors (Eaton et al., 2008), we review patterns of entry into the U.S. market of individual Colombian exporters across different cohorts. We note that most new exporters drop out of the U.S. market within a year, but those who survive this shakedown period have much lower exit rates in the future. Indeed, surviving members of new cohorts tend to expand their sales very rapidly, causing their market shares to grow as they mature. After a decade, nearly a quarter of total Colombian exports to the U.S. originate from firms that were not supplying the U.S. market at the beginning of the period. We then look at relationships between buyers and sellers. Colombian firms which export to the U.S. ship at least once per year to an average of 1.3 U.S. clients. In contrast, U.S. firms place at least one order per year with an average of 2.2 Colombian suppliers if they deal with Colombian firms at all. Overall, the distribution of U.S. clients across Colombian exporters is very nearly Pareto, with a handful of large sellers accounting for a substantial fraction of total shipments. Most buyer-seller matches are short-lived, lasting less than two years, on average. Matches are even less durable if they begin with a small initial shipment. But enough exporters gain buyers each period that the ergodic distribution implied by the transitions and by entry replicates closely the distribution in the cross section. Finally, we develop a model that is consistent with these facts. It is based on the conjecture that firms’ exporting behavior reflects search and learning processes in a foreign market. That is, producers who are interested in a particular market devote resources to identifying potential buyers there. When they find one, they learn something (receive a noisy signal) about the appeal of their products in this market. Taking stock of the available information, these firms update their beliefs concerning the scope for export profits, and they adjust the intensity of their search efforts accordingly, seeking to maximize their expected profit streams. At the same time, firms manage their portfolio of existing clients, investing in their profitable business relationships and letting the others expire. These features of the model are not only motivated by the exporting patterns observed in the data, but also by the exporting strategies documented by a series of interviews with Colombian exporters (Domı́nguez et al, 2013). Interviewed exporters described engaging in costly strategies both to search for new clients and to maintain existing relationships alive. They also frequently mentioned learning from previous relationships about the appeal of their products in a particular market, and using that information to adjust their searching behavior. Fit to our data on shipments and business relationships, the model quantifies the role of several frictions in shaping firm-level export dynamics. We estimate that for non-exporters, 2 the costs of maintaining low-level searches for clients in the U.S. are small, amounting to $1,405 per year for an expected yield of one potential client every two years. However, search costs are very convex in buyer arrival hazards, rising to $51,471 for an expected yield of one potential client per year. Both of these figures describe the search costs for a firm that has not yet established a successful business relationship abroad. But network effect are very important. We estimate that after the first relationship is formed, search costs for one client every two years drop to $106, and $3,898 for one client per year. Finally, once a successful match is formed, we estimate that it costs exporters $2,855 dollars per shipment to maintain the relationship. As a benchmark, the Doing Business project of the World Bank estimates that procedures required to export a one-container shipment cost $1,745 in Colombia in 2005. Even when a seller pays the fixed cost, her relationship dissolves with probability 0.27 per year for exogenous reasons. In addition to trade costs, the model quantifies the effects of learning on exporter behavior. We estimate that on average, only 1 in 5 potential buyers that an exporter meets will be interested in forming a business relationship. However, this success rate varies substantially across sellers, so they adjust their search intensities dramatically as they form opinions concerning the scope of the market for their particular product. A typical firm which has met four potential buyers will choose a match hazard of 1.35 (new clients per year) if all of its encounters have led to successful business relationships, while it will choose a hazard of 0.22 if each encounter has been a failure. This learning process, in combination with the various trade costs mentioned above, induces frictions and irreversibilities in export responses to marketwide shocks. We conclude our 3 analysis with some experiments that quantify their implications for export dynamics. A 20 percent reduction in the cost of searching for new clients leads to an increase in total exports of around 5 percent, which takes some time to kick in. Increased exports are mostly explained by the entry of new sellers into exporting, and to a lesser extent by an increase in the mean number of clients per seller. In turn, a decrease of 20 percent in the per-shipment fixed cost leads to a much more marked increase in both the number of exporters and the mean number of clients, and also to an increase in mean sales per client. The latter occurs despite the entry into exporting of less productive sellers, and is explained by increased search by the more productive firms. 1.2 Relation to literature While we look at the evolution of firms’ sales in a particular market, our analysis is related to the literature on the dynamics of firm size in general. The model explains the size distribution of firm sales through two interacting mechanisms. One, as in Melitz (2003), Bernard et al. (2003), Luttmer (2007), and Irarrazabal and Opromolla (2006), is firm efficiency: More efficient firms sell more to a given set of buyers by having a lower price or a higher quality product. A second is that some firms have larger networks of buyers than others, as in Jackson and Rogers (2007) or Chaney (2011). Investments in building a client base constitute a type of sunk cost, so our model also relates to the export hysteresis literature (Dixit, 1989; Baldwin and Krugman, 1989; Das, et al., 2007; Alessandria and Choi, 2007; Alessandria et al., 2010), where firms pay a one-shot start-up cost to break into new markets. But unlike these formulations, our sunk costs are 4 incurred on the client margin rather than the country margin, and they pay off in terms of market knowledge and reputation as well as revenue streams. These features of our model allow us to explain why new exporters who don’t exit tend to rapidly expand, and why established exporters’ sales are relatively stable. They also explain why many firms export for short periods on a very small scale. Our formulation is also related to the two-period learning models developed by Rauch and Watson (2003) and Albornoz et al (2012). In the former, importers experiment with foreign suppliers by placing trial orders with them, and they gain access to a supplier network if they establish a successful business relationship. In the latter, firms choose to experiment in markets with low entry costs in order to learn about their product’s appeal elsewhere. Like our model, these formulations provide interpretations for the fact that when new exporters survive, their exports tend to grow rapidly.1 Finally, in allowing firms to attract more buyers by incurring greater costs, our analysis relates to Drozd and Nozal (2012) and Arkolakis (2009, 2010). By positing that firms face marketing costs that are convex in the number of foreign clients they service, Arkolakis also accounts for small-scale exporters and the age-dependence of export growth rates. However, since all exporting relationships last a single period in his models and learning is absent, Arkolakis’s models do not explain the irreversibilities observed in firms’ exporting behavior, nor do they speak to the duration of matches. 1 Ruhl and Willis (2008) also note this pattern in plant-level export data and show that market entry costs are insufficient to explain it. 5 2 Firm-Level Trade: Transaction Level Evidence 2.1 Data The empirical motivation for our model comes from a comprehensive data set that describes all imports by buyers in the United States from Colombian exporters (as well as other origins ) during the period 1992-2009. The source is the U.S. Census Bureau’s Longitudinal Foreign Trade Transactions Database (LFTTD). Each record includes a date, the US dollar value of the product shipped, a 6-digit harmonized system product code, a quantity index, and, critically, ID codes for both sellers and buyers. These IDs allow us to identify the formation and dissolution of business relationships between individual buyers in the U.S. and sellers in Colombia, hereafter referred to as “matches.”2 To identify foreign exporters, the U.S. import transactions records include a manufacturer’s identification code.3 This field is an amalgamation of the manufacturer’s country, company name, street address, and city. Anecdotal information from customs brokers indicates that commonly used software constructs it automatically as the name and address information is entered in other fields. So this variable is sensitive to differences in the way exporters’ names and addresses are recorded as they pass through customs, and shipments from the same exporter can appear to originate from distinct Colombian firms. To gauge the importance of this problem, we have conducted various checks on the matches that are based on this 2 There are two ways to track U.S. importers in the LFTTD: Employment Identification Numbers (EINs) and the firm identifiers in the Longitudinal Business Database (”alphas”). Though an EIN does not necessarily identify a complete firm, it is unique to a firm, and there is one associated with every import transaction. Alphas map to entire firms, but the match rate between trade transactions and alphas is only about 80 percent (Bernard, Redding, and Schott, 2009). To maximize the coverage of our sample, we use Employment Identification Numbers (EIN) to identify U.S. buyers. 3 This variable is based on Block 13 of CBP form 7501, the import declaration form and customs brokers are required to input the data. 6 variable; these are explained in the Appendix. We limit our analysis to transactions between non-affiliated trade partners, and we consider only imports of manufactured goods. The latter restriction notably excludes oil and coffee exports, which constitute the bulk of trade between the two countries and are dominated by a few Colombian sellers.4 Our final data set of manufacturing transactions spans the years 1992-2009. It contains 26,625 unique Colombian exporters, 12,921 unique U.S. importers, and 42,767 unique trading pairs. Value data have been deflated to 1992 prices using the U.S. CPI. Since we exclude a number of large HS codes from our data, as well as affiliated trade, and because we also lose information due to disclosure restrictions, the total value covered by our data is not comparable to total Colombian exports to the U.S. Table 13 in Appendix A compares patterns in our sample to patterns in official aggregates from both the U.S. and Colombia. In addition to U.S. customs records, we use establishment level survey data from Colombia’s national statistics agency (Departmento Administrativo Nacional de Estadistica, or DANE). These data provide annual information on the sales volumes, exports, and other characteristics of all Colombian manufacturing plants with at least 10 workers. Because they have been widely analyzed, we do not discuss summary statistics for this data set herein. Later, however, when estimating our search and learning model, we use such statistics to characterize the size distribution of Colombian firms, the fraction of Colombian plants that export and, among these firms, the relationship between exports and domestic sales. 4 Colombian commercialization of coffee is centralized to an important degree by the National Federation of Coffee Growers. A few players also dominate oil exports. 7 2.2 Exports and exporters Following Brooks (2006) and Eaton et al. (2008), Tables 1-3 provide various annual measures of Colombian exports of manufactured goods to the United States for the years 1992-2009.5 Each column follows an exporting cohort—i.e., a group of firms that began exporting in a particular year—from the year of its appearance through time. The tables report number of exporters, total exports, and exports per firm, respectively. Note that, since we don’t know the history of firms before 1992, the 1992 “cohort” consists of all firms present that year, regardless of when they began exporting; given re-entry. This implies that the first few cohorts are in general overestimated in terms of their initial size. Nonetheless, the patterns highlighted below apply also to the most recent cohorts. Consider Table 1 first. Naturally, each cohort’s membership falls as it matures. But note that there is especially high attrition the first year, with more than 60 percent of firms dropping out. Conditional on making it to the second year, the survival probability is much higher, however, with an attrition rate around 40 percent the second year, and further declines occur thereafter. Thus, in terms of numbers, the most recent cohort is always larger than any previous one. Firms that were exporting to the United States in 1992 account for less than five percent of the firms exporting to the United States towards the end of the sample. Table 2 shows that the rapid initial decline in its membership is not followed by a similar collapse of the total sales of a cohort. The decline in number of firms per cohort along with their relatively stable total sales means, of course, that sales per firm are growing substantially From the first to the second year of any cohort average sales more than double (Table 3). 5 Similar tables for Colombian exports of all goods and to all destinations appear in Eaton, et al, 2008. 8 9 1992 2,232 823 583 440 372 321 268 232 203 187 173 165 150 140 122 113 93 80 year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 1,235 330 213 163 128 104 85 85 70 64 51 52 52 46 37 29 25 1993 1,160 339 178 133 124 87 79 65 62 58 41 47 44 39 30 28 1994 899 248 153 117 103 85 68 62 63 54 44 42 38 28 1996 877 256 187 136 109 88 77 76 77 71 55 50 40 1997 893 262 170 145 112 86 80 69 65 48 45 39 1998 1,026 344 229 171 140 132 115 110 91 74 60 1999 1,372 389 242 185 164 145 131 101 90 72 2000 1,251 399 301 223 196 157 132 117 88 2001 1,373 440 327 235 168 156 130 97 2002 1,719 616 398 308 240 184 145 2003 1,768 661 410 305 198 175 2004 1,902 564 365 230 157 2005 Table 1: Number of Exporting Firms, by Entry Cohort 953 255 170 132 114 91 79 72 62 53 39 39 31 24 24 1995 1,896 548 331 230 2006 1,681 447 248 2007 1,455 386 2008 1,378 2009 2,232 2,058 2,073 1,945 1,867 1,877 1,930 2,110 2,583 2,609 2,824 3,346 3,745 4,130 4,175 3,984 3,565 3,300 total 10 1992 469 352 336 313 256 247 225 207 180 150 124 147 156 150 117 103 95 68 year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 83 83 75 67 84 49 51 53 22 23 42 43 22 31 7 6 22 1993 92 102 62 43 42 49 55 51 47 51 53 75 52 18 9 7 1994 60 48 45 39 51 28 27 42 57 52 64 67 33 13 1996 119 131 197 102 57 28 24 21 18 43 58 37 24 1997 63 74 53 36 23 22 23 23 17 19 17 10 1998 81 158 80 45 37 42 43 38 30 33 23 1999 109 101 65 71 78 78 61 28 26 16 2000 111 83 107 106 80 79 64 34 16 2001 40 50 60 58 32 22 20 14 2002 78 107 81 51 35 31 22 2003 90 75 52 33 37 41 2004 84 112 66 54 25 2005 78 67 42 39 2006 Table 2: Value of Exports, by Entry Cohort (millions of $US) 58 40 41 36 41 37 41 34 31 19 17 14 11 8 6 1995 62 53 37 2007 57 36 2008 64 2009 469 435 510 549 484 581 590 739 799 677 538 702 855 855 838 689 591 485 total 11 1992 210 428 576 712 687 771 839 893 885 801 716 891 1,039 1,071 958 915 1,023 855 year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 67 251 353 411 652 468 601 623 316 353 827 828 413 675 175 208 864 1993 79 300 346 321 339 561 697 783 757 870 1,281 1,593 1,177 466 283 262 1994 67 192 297 336 496 329 399 677 900 967 1,448 1,606 860 478 1996 136 510 1,054 750 521 318 315 281 231 605 1,048 747 607 1997 71 281 313 251 207 257 291 326 256 391 379 255 1998 79 460 350 260 260 318 375 341 327 443 389 1999 80 259 268 385 478 535 464 278 289 221 2000 89 207 355 476 408 505 481 287 176 2001 29 114 183 248 188 140 153 143 2002 46 174 204 165 145 166 152 2003 51 113 126 108 186 235 2004 44 198 181 236 162 2005 41 123 125 169 2006 Table 3: Exports per Firm, by Entry Cohort (thousands of $US) 61 158 241 269 361 407 519 473 493 358 444 356 357 341 266 1995 37 120 151 2007 39 93 2008 47 2009 210 211 246 282 259 310 306 350 309 260 191 210 228 207 201 173 166 147 pooled 2.3 Evidence on buyer-seller matches We next use the data to characterize the buyer-seller matches that took place during 19922009. 2.3.1 Monogamous and polygamous matches The number of Colombian exporters appearing in our sample grew from 2,232 in 1992 to 3,300 in 2009, a growth of 2 percent per annum, while the number of U.S. importing firms grew by 3 percent per annum (Table 4). The number of Colombian exporter-U.S. importer pairs (representing at least one transaction between them in a year) also grew at an annual rate of 2 percent. Roughly 80 percent of matches are monogamous in the sense that the buyer deals with only one Colombian exporter and the exporter ships to only one buyer in the United States. However, since the remainder of the matches are polygamous, the average Colombian exporter was involved in relationships with around 1.3 U.S. firms while the average U.S. buyer was involved with around 2.3 Colombian firms. Both figures declined slightly over the period. Table 4: Size of Data Set Year Colombian Sellers U.S. Importers Pairs 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2,232 2,058 2,073 1,945 1,867 1,877 1,930 2,110 2,583 2,609 2,824 3,346 3,745 4,130 4,175 3,984 3,565 3,300 1,190 1,183 1,212 1,173 1,191 1,208 1,191 1,386 1,661 1,698 1,826 2,110 2,296 2,457 2,471 2,343 2,221 2,079 3,087 2,824 2,810 2,588 2,490 2,480 2,495 2,793 3,411 3,483 3,733 4,483 5,071 5,552 5,607 5,307 4,751 4,467 12 2.3.2 Transition Probabilities Like exporting stints (Table 1), most matches are short-lived. Of the 3,087 buyer-seller matches that existed at the beginning of the period, 70 percent didn’t make it to 1993. But, of those that made it into the next year, almost 50 percent made it into the next year. Similarly, of the relationships that existed in 2005, 57 percent started that year but of those that started before, 37 percent had been around at least three years before. Of the 3,210 matches identified in 1992, less than 25 endure (are present every year) throughout the period. Table 5 reports the probability with which a Colombian firm participating in certain number of relationships with buyers transits into a different number of relationships the following year. (Confidentiality restrictions prevent us from reporting numbers for cells that are too sparsely populated.) This table reports the annual average for 1992-2009 across all industries. A firm that stops exporting but re-appears as an exporter sometime later in our sample period is considered to have gone ”dormant”, while those exporters that drop to zero foreign sales for the extent of our sample are considered to have gone ”out” of exporting. Those that have never been observed to export constitute the pool of potential entrants. Among first-time exporters, 93.2 percent sell to only one firm. Of these, 62 percent don’t export the next year, and only about six percent go on to establish a larger number of relationships. For firms with three relationships in a year, about twelve percent enter into a larger number of relationships the next year. Hence there is an enormous amount of churning at the lower end. Even for firms with a large number of relationships the most likely outcome is to have fewer the next year. We can ask what this pattern of entry and growth implies about the ergodic distribution 13 of relationships. If we assume that entrants in a year replace exiting firms, the ergodic distribution implied by this transition matrix is given by Table 6. For purposes of comparison, the year-specific average share of Colombian firms in each group is reported as well. Note that the ergodic distribution implied by the transition matrix is very close to the cross-sectional distribution in the data, suggesting that over the period we observe the process has been quite stationary. Interestingly, both distributions are very nearly Pareto, reflecting the coexistence of many small scale exporters with a few ”super-exporters.” 2.3.3 Match maturation The survival probability of new matches increases with initial sales volume. Table 7 sorts observations on matches according to their size in their first year of existence and reports year-to-year separation rates. In addition to the very low survival rates, two patterns stand out. First, those matches that begin with sales in the top quartile among all new matches are more likely to survive than matches that begin with smaller sales volumes. Second, survival probabilities improve after the initial year. Further features of the match maturation process are evident in Figure 1, which shows the log of annual sales per match, broken down by initial size quartile. For each size quartile, Table 5: Transition Probabilities, Number of Clients t \t+1 Out Dormant 1 2 3 4 5 6-10 11+ Out Dormant 1 2 3 . . 0.539 0.194 0.090 0.059 . . . . . 0.080 0.077 0.042 . . . 0.000 0.932 0.876 0.321 0.375 0.220 0.129 0.095 0.039 0.000 0.055 0.100 0.048 0.241 0.271 0.216 0.184 0.073 0.000 0.009 0.015 0.010 . 0.210 0.215 0.181 0.089 . 14 4 5 6-10 11+ 0.002 0.001 0.001 0.008 . . 0.002 . 0.001 0.024 0.009 0.004 0.092 . 0.027 0.184 0.083 0.095 0.181 0.126 0.178 0.123 0.157 0.419 . . 0.432 0.000 0.000 . . . . . 0.073 0.526 Figure 1: Log annual sales per match, by initial size quartile matches are further distinguished according to their life span: less than one, 1 to 2 years, and so forth. And for each cluster of bars, the left-most bar corresponds to sales in the initial year of the match’s existence, the next bar corresponds to sales during the second year of the match’s existence, and so forth. The first message of these graphs is that initial sales are a good predictor of sales in subsequent years, conditioning on survival. Those matches with first-year sales in the smallest Table 6: Ergodic Client Distribution Implied by Transitions Erg Distribution Data 1 2 3 4 5 0.792 0.778 0.112 0.116 0.031 0.043 0.016 0.021 0.009 0.011 15 6-10 11+ 0.022 0.016 . . Table 7: Separation Rates, by Age of Match and Initial Sales Quartile Quartile Quartile Quartile 1 2 3 4 1 year 2 years 3 years 4 years 5+ years 82.9 75.6 67.7 52.1 63.2 58.4 52.1 44.5 57.3 49.4 44.6 40.3 55.0 46.8 40.8 39.2 49.7 43.7 37.6 36.7 quartile systematically generated the lowest annual sales in subsequent years, and more generally, first-year sales are monotonically related to annual sales in subsequent years. Second, sales tend to jump from the first to the second year, in large part simply because observations on a match’s first year correspond to less than a full calendar year. (There is an analogous effect at work in the final year of a match’s life.) Looking at complete-year observations reveals a tendency for annual sales to grow among matches that start small and survive, but no such tendency among matches that start in the largest quartile. Finally, looking across matches with different life spans, those that survive more years tend to have higher sales in all (full) years than matches that fail relatively quickly. This pattern is robust across matches in the different quartiles for initial sales. 2.3.4 Number of clients and sales per client Finally, firms that are successful at building a large client base also manage to sell relatively large amounts to each client. To summarize this relationship we fit the following regression: ln Rjt = φr0 + φr1 ln(ncjt ) + φr2 ln(ncjt )2 + rjt Here Rjt is exporter j 0 s average revenue per client in year t, and ncjt is the number of clients who received shipments from j during the same year. The regression implies R is an increasing br = 2.67; φ br = −0.14. concave function of nc : φ 1 2 16 3 A Model of Exporting at the Transactions Level We now develop a model of exporter behavior consistent with the patterns reviewed above. Buyer-seller relationships form and disband at irregular intervals. Similarly, export shipments are discrete events distributed unevenly through time. To capture these features of the data, and to allow agents to update their behavior each time their circumstances change, we formulate our model in continuous time, treating all of the exogenous processes in our model as Markov jump processes. Explaining the evolution of a firm’s exports and domestic sales requires modeling both its sales to existing buyers and the evolution of its portfolio of clients. We can treat these two components sequentially. We first consider the relationship between a seller and an individual buyer. Having characterized the seller’s profits from a relationship with an individual buyer, we then turn to her learning about the popularity of her product, i.e., the chance that a potential buyers likes her product. Finally, we characterize her search for buyers. 3.1 A Seller-Buyer Relationship This section characterizes the profit streams that sellers generate from successful business relationships. The expressions we develop here describe relationships between domestic firms and foreign buyers, but with appropriate relabelling of market-wide variables they apply equally to relationships between domestic firms and domestic buyers. 3.1.1 Profits from a single shipment Several features of our model are standard. First, at any time t seller j can hire workers at a wage wt in real local currency units, each of whom can produce ϕj ∈ {ϕ1 , .., ϕNϕ } units of 17 output.6 Hence seller j’s unit cost in local currency is wt /ϕj . If she sells at price pjt in foreign currency her unit profit in local currency is pjt /et − wt /ϕj , (1) where et is the exchange rate. Second, goods markets are monopolistically competitive and each producer supplies a unique differentiated product. Once buyer i has agreed to form a business relationship with seller j, he periodically places sales orders with j. For j, an order from i that arrives at time t generates revenue:  Xijt = pjt Pt 1−η yijt X t , (2) where η > 1 is buyers’ elasticity of demand, pjt is the price of seller j’s product, X t is the average spending level among all potential foreign buyers, Pt is the relevant price index for all competing products in the foreign market, and yijt ∈ {y 1 , .., y N y } is a time-varying demand shifter idiosyncratic to the ij relationship.7 For simplicity, and to keep the analysis as close as possible to other heterogenous firm models, we assume that the seller posts a non-negotiable price, charging the optimal markup over unit cost:8 pjt = η e t wt η − 1 ϕj (3) By (1), (2), and (3), an order from buyer i at time t therefore generates the following profits for seller j: 6 We treat ϕ as time-invariant to facilitate model identification. Other sources of idiosyncratic temporal variation in sales will be discussed shortly. 7 Not all buyers necessarily face the same range of goods and hence the same aggregate price index P . We treat idiosyncratic components of the price index as P as reflected in yijt . 8 An alternative specification would introduce bilateral bargaining between buyer and seller. 18 π ijt 1 Xt = η et  et wt η/(η − 1) ϕ j Pt 1−η yijt . We can combine all the macroeconomic variables affecting the profit of any seller from this source selling in this destination, along with constants, as: 1 Xt xt = η e  et wt η/(η − 1) Pt 1−η , where x ∈ {x1 , .., xNx } is general to all potential buyers in the foreign market. Suppressing subscripts on state variables, this allows us to write the profits from a sale as: π ϕ (x, y) = xϕη−1 y, (4) In what follows, (4) is all we take from our specification of preferences and pricing behavior into the dynamic analysis. Any set of assumptions that deliver this simple multiplicative expression for a firm’s profit from a sale would serve us equally well. 3.1.2 Relationship dynamics At any point in time, each seller maintains business relationships with an endogenous number of buyers. These relationships form as a consequence of a search process that will be characterized in the following section, and they dissolve for several reasons. First, there is a constant exogenous hazard δ that any particular relationship will terminate, which could be due to the demise of the buyer or the buyer no longer finding the seller’s product useful. Second, after each sale to a particular buyer, the seller evaluates whether it is worth sustaining her relationship with him. Doing so keeps the possibility of future sales to him alive, but it 19 also means paying the fixed costs F of maintaining the account, providing technical support, and maintaining client-specific product adjustments.9 When deciding whether to maintain a particular business relationship, the seller knows her own type, ϕ, the macro state, x and profits from the current sale, π ϕ (x, y) to the buyer in question. She can therefore infer this buyer’s current y value and calculate the value of her relationship with him to be: π eϕ (x, y) = π ϕ (x, y) + max {b π ϕ (x, y) − F, 0} . Here π bϕ (x, y) is the expected value of continuing a relationship that is currently in state (x, y). Clearly the seller terminates this relationship if π bϕ (x, y) < F. If a seller pays F to keep a relationship active, and if the relationship does not end anyway for exogenous reasons, one of several events will next affect it: with hazard λb the buyer will X 0 place another order, with hazard qxx 0 x will jump to some new marketwide state x 6= x, or Y 0 10 with hazard qyy Let τ b be the random 0 y will jump to some new buyer-specific shock y 6= y. time that elapses until one of these events occurs. Given that x and y are Markov jump Y processes, τ b is distributed exponentially with parameter λb + λX x + λy , where λX x = X X qxx 0 (5) Y qyy 0, (6) x0 6=x and λYy = X y 0 6=y 9 For instance, Colombian producers of construction materials interviewed for a related project (Domı́nguez et al, 2013) referred that it is frequent for foreign buyers to request adjustments in the specifications of products or packages. In turn, these require adjustments in the production process that are costly to maintain. 10 Since sales in the data are discrete events rather than flows, we model the buyer’s purchases accordingly. We think of the buyer not as making use of the products continually but in discrete spurts. For example, the buyer might be a producer of a product that it makes in batches. At the completion of each batch it buys inputs for the next batch. 20 are the hazards of transiting from x to any x0 6= x, and from y to any y 0 6= y, respectively. Then assuming the seller has a discount factor ρ, the continuation value π bϕ (x, y) solves the Bellman equation: " π bϕ (x, y) = Eτ b 1 e−(ρ+δ)τ b b Y λ + λX x + λy 1 = Y b ρ + δ + λ + λX x + λy !# X X qxx bϕ (x0 , y) + 0π x0 6=x X Y qyy bϕ (x, y 0 ) + λb π eϕ (x, y) 0π y 0 6=y ! X X qxx bϕ (x0 , y) + 0π x0 6=x X Y qyy bϕ (x, y 0 ) + λb π eϕ (x, y) 0π y 0 6=y Before a seller has met her next buyer, she does not know what state y this buyer will happen to be in. So when choosing her search intensity for new business relationships, she must base her decisions on the ex ante expected pay-off to forming a new business relationship. Given the market state x, a type-ϕ seller calculates this expected value as: π eϕ (x) = X Pr(y s )e π ϕ (x, y). s where Pr(y s ) is the probability that a randomly selected buyer is currently in state y s ∈ {y 1 , .., y N y }.11 For the purposes of the search model that follows, all that matters about an individual relationship is π eϕ (x), and this object can be estimated directly from data on the revenue streams generated by matches. Nonetheless, the history of a seller’s interactions with a given buyer affects its overall sales trajectory and hence matters for our characterization of aggregate export dynamics. Hereafter, we will denote the expected value of a relationship with a foreign buyer by π efϕ (x) and the expected value of a relationship with a home market buyer by π ehϕ (x). These two objects are calculated in the same way, but since expenditure levels (X t ) and price indices (Pt ) differ 11 Here we take the probabilities Pr(y m ) to be the ergodic distribution of y implied by the transition hazards We could assume that the distribution at the time of the first purchase is different from the ergodic one. Y qyy 0. 21 across markets, and no exchange rate factor e is necessary for domestic profit calculations, each has its own process for the market-wide state variable, x. These market-wide demand shifters are denoted xf and xh below. 3.2 Learning about Product Appeal Sellers conduct market-specific searches for buyers. When searching in market m ∈ {h, f }, each recognizes that some fraction θm ∈ [0, 1] of the potential buyers she meets there will be willing to do business with her. An encounter with one of these willing buyers generates an expected profit stream worth π em ϕ,x , while an encounter with any of the remaining potential buyers does not generate a sale then or subsequently. Each seller’s θh and θf values are drawn before she has met any clients. These draws remain fixed through time, inducing permanent cross-market differences in her product’s popularity. All θm draws are independently beta-distributed across sellers and markets: b(θm |α, β) = where Γ(φ) = R∞ 0 Γ(α + β) m α−1 (θ ) (1 − θm )β−1 , m ∈ {h, f }, Γ(α)Γ(β) z φ−1 e−z dz is the gamma function (needed to ensure that the distribution has the proper limits). However, the independence of θh and θf does not mean sellers’ domestic and foreign sales are likewise independent. Rather, cross-market correlation in sales will be induced by the firm type ϕ, which can be viewed as capturing aspects of product appeal that are common to both markets.12 12 The firm effect is similarly interpreted to reflect both productive efficiency and product appeal in Melitz (2003) and many other papers based on CES demand systems. However in the present context, the global aspects of product appeal captured by ϕ are qualitatively distinct from the market-specific product appeal effects captured by θ. The former determines the amount of a product each buyer purchases, given that he is interested, while the latter determines what fraction of potential buyers are willing to place orders with the seller, should they happen to meet her. 22 Sellers are presumed to have already met many potential customers in the domestic market, and thus to have learned their θh draws. But sellers typically have far less experience abroad, so we allow them to still be learning about their θf draws. Specifically, each seller recognizes that for any given θf , the probability a random sample of n potential foreign buyers will yield a customers is binomially distributed:   q a|n, θf =   n−a n  f a  θ 1 − θf . a So after she has met n potential buyers abroad, a of whom were willing to buy her product, a seller’s posterior beliefs about her θf draw are distributed:   p(θf |a, n) ∝ q a|n, θf · b(θf |α, β) where the factor of proportionality is the inverse of the integral of the right-hand side over the support of θf . Since the beta distribution is the conjugate prior for the binomial, a firm’s expected success rate after a successes in n trials has a convenient closed-form representation: f θa,n   = E θf |a, n = 1 Z θp(θ|a, n)dθ = 0 This posterior mean converges to p lim 3.3 a n  a+α . n+α+β (7) = θf as n gets large. Searching for Buyers To complete our model we now consider sellers’ search intensities in each market. Each seller continuously chooses the market-specific hazard sm , m ∈ {h, f }, with which she encounters a potential buyer, recognizing that this involves the instantaneous flow cost c(sm , a), where c(sm , a) is increasing and convex in sm .13 Whether c(sm , a) increases or decreases in the number 13 Interviews conducted with Colombian exporters revealed a variety of activities firms pursue to meet potential buyers abroad (Domı́nguez, et al, 2013). Ranked roughly in terms of decreasing cost, these included 23 of successful matches, a, depends upon the relative strength of several forces and will be left for the data to determine. Costs might fall with a because encounters with interested buyers increase the seller’s visibility and enhance her opportunities to meet additional potential buyers. Alternatively, costs might rise if the pool of easy-to-reach buyers becomes ”fished out,” as in Arkolakis (2007). We can now describe optimal search behavior, beginning with the foreign market. Recall that when the foreign market state is xf , a type-ϕ seller expects the value of a new business relationship will be π efϕ (xf ). Further, she believes the next match will yield such a relationship f with probability θa,n . Combined with search cost function c(sf , a) and the jump process for xf , these objects imply sellers’ optimal search policy abroad. To characterize this policy, let τ fs be the random time until the next foreign search event, which could be either a change in the marketwide state xf or an encounter with a potential buyer. Then, suppressing market superscripts, the optimal search intensity s for a type-ϕ firm with foreign market search history (a, n) solves the following the Bellman equation: " Z Vϕ (a, n, x) = max Eτ s −c(s, a) s τs e−ρt dt + 0  e−ρτ s · s + λX x X X 0 qxx 0 Vϕ, (a, n, x ) x0 6=x π ϕ (x) + Vϕ (a + 1, n + 1, x) + (1 − θa,n )Vϕ (a, n + 1, x) + s θa,n (e   maintaining a foreign sales office; paying the exports promotion office to organize visits with prospective clients abroad, and sending their sales representatives to those visits; sending sales representatives abroad to visit potential clients on their own; attending trade fairs; paying a researcher to search the web for foreign firms that purchase products similar to their own; paying browsers to ensure that their site appear near the top of a search for their product type; maintaining a web site in English. Interviewees also reported that relatively low-cost activities, such as traveling to trade fairs, or translating their websites to English, led to relationships with one or two clients every few years. Establishing a larger network of clients required much more costly activities. 24 (Recall that λX x is given by (5).) Taking expectations over τ s yields: " Vϕ (a, n, x) = max s X 1 X 0 −c(s, a) + qxx 0 Vϕ, (a, n, x ) X ρ + s + λx x0 6=x (8)   + s θa,n [e π ϕ (x) + Vϕ (a + 1, n + 1, x)] + (1 − θa,n )Vϕ (a, n + 1, x) Applying the multiplication rule for differentiation and using expression (8) for Vϕ (a, n, x), the optimal search intensity s∗ satisfies: ∂c(s∗ , a) = θa,n [e π ϕ (x) + Vϕ (a + 1, n + 1, x)] + (1 − θa,n )Vϕ (a, n + 1, x) − Vϕ (a, n, x) ∂s (9) That is, the marginal cost of search must equal the expected marginal benefit of a match, eϕ (x), and the expected which includes the expected value of the associated profit stream, θa,n π value of the information generated. Now consider the home market. Since we assume sellers have already learned their true success rates at home, θh , new encounters do not influence expectations, and we need not condition the value function or the expected success rate on search histories. Again suppressing market superscripts, the Bellman equation collapses to: # " Vϕ (x) = max s 1 X 0 qxx eϕ (x) −c(s, a) + 0 Vϕ (x ) + sθ j π X ρ + λx x0 6=x X and the first-order condition is simply: ∂c(s∗ , a) = θj π eϕ (x). ∂s The marginal cost of search equals the expected profit from a successful relationship times the probability of success. 25 4 4.1 An empirical version of the model The search cost function To implement our model empirically, we impose additional structure in several respects. First, we specify a functional form for our search cost function. Generalizing Arkolakis (2007) to allow for network effects, we write these costs as: [(1 + s)](1+1/κ1 ) − 1 c(s, a) = κ0 . (1 + a)γ(1+1/κ1 ) (1 + 1/κ1 ) (10) Several properties of this function merit note. First, marginal costs fall at a rate determined by γ with the number of successful matches a seller has already made, so γ > 0 implies “network” effects and γ < 0 implies ”congestion” effects.14 Second, a seller who is not searching in a particular market incurs no search cost: c(0, a) = 0. Third, given the cumulative number of successful matches, a, the marginal cost of search increases with λs at a rate inversely related to κ1 : cs (s, a) = κ0 [(1 + s)/(1 + a)γ ]1/κ1 . Finally, network effects endure, even if a firm is not actively searching. 4.2 Processes for exogenous state variables Next we impose more structure on the exogenous state variables, ϕ, xh , xf , y h and y f . All are assumed to have zero means in logs, and the net effect of these normalizations is undone by introducing scalars Πh and Πf into the home and foreign profit functions, respectively: π fϕ (xf , y f ) = Πf xf ϕη−1 y f , π hϕ (xh , y h ) = Πh xf ϕη−1 y f 14 To contain the dimensionality of the computational problem we solve, we assume that firms with more than a∗ buyers have (i) exhausted their learning effects, and (ii) reap no additional network effects at the margin from further matches. We choose a∗ to exeed the observed maximum a for 99 percent of sellers in the foreign (United States) market. Also, we set a = a∗ for all sellers in their home (Colombian) market. 26 More substantively, we impose that the cross-firm distribution of ϕ is log normal with standard deviation σ ϕ , and we treat all of the Markov jump processes (xh , y h , xf , y f ) as independent Ehrenfest diffusion processes. The idiosyncratic match shocks, y f and y h , are assumed to share the same distribution, but we allow the xf and xh processes to differ. Among other things, the latter accommodates the fact that the exchange rate affects aggregate demand and price indices in the two markets differently. Any variable z generated by an Ehrenfest process can be discretized into 2g + 1 possible values, g ∈ I + : z ∈ {−g∆, −(g − 1)∆, .., 0, .., (g − 1)∆, g∆}. Further, it jumps to a new value with hazard λz , and given that a jump occurs, it goes to z 0 according to:      z+∆  0 z − ∆ with probability z =    other  1 2  1−  1 1+ 2 0  Thus, given a grid size g, the intensity matrices QX = qijX z g4  z g4  i,j=1,N X .  and QY = qijY i,j=1,N Y that were introduced in section 3.1 are each block-diagonal and characterized by a single parameter, ∆. 5 5.1 Estimation Stage 1: estimating observable jump processes Shimer (2005) shows that if z follows a continuous time Ehrenfest diffusion process, it asymptotes to an Ornstein-Uhlenbeck process with mean zero as the fineness of the grid increases:15 dz = −µzdt + σdW. √ Specifically, replacing the parameter vector (λ, g, ∆) with (λ/, g/, ∆ ),  > 0, leaves the autocorrelation parameter µ and the instantaneous variance parameter σ unchanged. But as  → 0, the innovation dW approaches normal. 15 27 Table 8: Market-wide Demand Shifters Parameter home macro state jump hazard λxxh foreign macro state jump hazard λ f home macro state jump size ∆ xh foreign macro state jump size ∆xf Here µ = λz /g, σ = value 1.200 1.215 0.003 0.053 √ λz ∆, and W follows a Weiner process. Accordingly, since it is possible to observe proxies for xf and xh , these can be viewed as discrete time observations on underlying Ornstein-Uhlenbeck processes, and the parameters of these processes can be econometrically estimated. Then, given µ and σ, estimates of ∆ and λ for these processes can be inferred. Measuring xf as real expenditures on manufacturing goods in the U.S., and measuring xh as real expenditures on manufacturing goods in Colombia, we obtain the results reported in Table 8.16 They imply that xf and xh both jump 1.2 times per year, on average. However, jumps in the U.S. market tend to be much larger, essentially because they reflect movements in the real exchange rate as well as movement in dollar-denominated expenditures. 5.2 Stage 2: Indirect inference Our data are relatively uninformative about the rate of time discount ρ and the demand elasticity η, so we do not attempt to estimate either one. For the former we follow convention and assume ρ = 0.05. For the latter, following many previous trade papers, we fix the demand elasticity at η = 5. All of the remaining parameters we estimate using the method of indirect inference (Gouriéroux and Monfort, 1996). These parameters include the exogenous match separation hazard (δ), the market size scalars (Πh , Πf. ), the fixed costs of maintaining 16 Our foreign market size mesaure is the OECD time series on American GDP in ’Industry, including energy’ adding imports and subtracting net exports of manufactures. Our home market size measure is real Colombian expenditures on manufacturing goods, taken from DANE. We converted all of the data used for the estimation into real 1992 US dollars, deflating nominal US dollars with the consumer price index available on the US Bureau of Labor Statistic website. We used an official Colombian Peso - US Dollar exchange rate time series downloaded from the Central Bank of Colombia to convert Pesos to nominal US Dollars 28 a match (F ), the parameters of the product appeal distributions (α,β), the dispersion of the productivity distribution (σ ϕ ), the jump hazards for the idiosyncratic buyer shocks (λy ), the hazard rate for shipments (λb ), the network/congestion parameter (γ), the cost function convexity parameter (κ1 ), and the cost function scaling parameter (κ0 ). For notational convenience we hereafter collect these parameters in the vector Λ : Λ = Πh , Πf. , δ,F, α, β, σ ϕ , λy , λb , γ, κ0 , κ1  We seek the value of Λ that allows our model to replicate the features of the transactionslevel data summarized in Section 2 above. In addition to the joint distribution of home and foreign sales across firms, these include the distribution of clients across exporters, the probabilities than a particular exporter will move up or down in this distribution, given its current position, the hazard that a given match will end, given its current age and size, the survival rates of exporting cohorts as they mature, and the distribution of shipment frequencies across matches. The sample statistics that we use as a basis for inference are listed in Table 9. These same statistics are also repeatedly constructed using data simulated with the model at alternative candidate values for Λ. The method of indirect inference amounts to choosing the Λ value that minimizes a metric of the distance between sample and simulated statistics.17 17 More precisely, our estimator for Λ is: h i0 h i b = arg min M c − MS (Λ) W c −1 M c − MS (Λ) Λ c is the vector of data-based statistics listed in the right-most column of Table 9, MS (Λ) is their where M c is a compatible matrix with counterpart based on S simulations of our model at candidate vector Λ, and W c se( b M ) on its diagonal and zeros elsewhere. These standard errors are constructed using the sample data. In addition to giving the greatest weight to those statistics that are most precisely estimated, W −1 serves to eliminate h units of measurement ih ias0 a factor in determining the fit. The efficient GMM estimator of φ would c c c c use E M − E(M ) M − E(M ) (adjusted for simulation error in M (Λ)) as its weighting matrix. But since our data on establishments and matches come from several sources, it computationally infeasible for us to 29 Table 9: Statistics used for Indirect Inference Data feature Summary method Distribution of home and foreign sales c) Statistics (M OLS cross-plant regression: hf hf hf f hf h b ,φ b , sb φ e(hf ) ln Xjt = φhf 0 + φ1 ln Xjt + jt 0 1 f f b b Cross-plant moments E(1 X f >0 ), E(ln Xjt |Xjt > 0), jt Distribution of clients across exporters, Φ(nc ) Sales per client given number of clients Standard deviation of foreign sales f se(ln Xjt ) OLS regression for nc ∈ I + : ln [1 − Φ(nc )] = φc ln(nc ) + n c bc , sb φ e(n ) f OLS cross-match regression: ln Xijt = r r r c 2 c φ0 + φ1 ln(njt ) + φ2 ln(njt ) + m br , φ br , φ br , sb φ e(r ) 0 1 2 h + h φh0 + φh1 ln Xjt−1 bh , sb e(h ) φ 1 Cross-plant year-to-year average transition rates Pb[ncjt+1 = m|ncjt = k], m, k = 0, 1, 2, 3+ Autoregression, log domestic sales Transition probabilities, number of clients (ncjt ) Cross-match average given match age (Am ) year-to-year death rates, given age Am ijt−1 = 0, 1, 2, 3, 4+ Cross exporter average exit rate, b f |Acjt ], E[1 X =0 given years exporting Acjt = 0, 1, 2, 3, 4+ Cross-exporter mean log exports b X f |Acjt ), E(ln jt Acjt = 1, 2, 3, 4+ Exporter exit hazard b f E[1 X f |Xijt−1 > 0, Am ijt−1 ], Match death hazards, ijt =0 jt by cohort age (Ac ) Cohort-specific exports per plant Match-specific shipments per year (nsijt ) Cross-match mean shipments per year b (ns ) (trimmed) E f f bf + β bf ln X f ln Xijt =β 0 1 ijt−1 + ijt bf , sb β e(f ) 1 Autoregression, matchf specific sales (Xijt ) Match death prob. and match sales 1X f ijt =0 bd + β bd =β 0 1st year 1Am ijt−1 =0 d f d b +β lsales ln Xijt−1 + ijt bd , β bd bd β e(d ) 0 1st year , β lsales , sb Variable definitions: ncjt : number of foreign clients served by firm j in year t Φ(nc ) : cumulative frequency distribution of number of foreign clients in population of exporters Am ijt : age of match (in years) between seller j and foreign buyer i in year t c Ajt : number of consecutive years exporter j has made at least one shipment abroad. 30 While there is no exact mapping between the statistics in the last column of Table 9 and the parameters we wish to estimate, it is possible to comment in general terms on sources of identification. First, several parameters are closely associated with sample means. Specifically, the profit function scaling parameters Πh and Πf are identified by average levels of sales in f h each market, E(ln Xjt ) and E(ln Xjt ), given market participation, as well as the fraction of firms that export, E(1X f >0 ). And the shipment hazard λb is closely related to the average jt b (ns ) . number of shipments per year, E Second, the match-specific shock hazard, λy , the exogenous match separation hazard, δ, and the fixed costs of maintaining a match, F, are key determinants of the persistence and dispersion in client-specific sales trajectories. Accordingly, key statistics that help to identify bf , sb e(f ), match these parameters include estimates of autoregressions for match-specific sales β 1 b f death hazards by age of match, E[1 X ijt =0 f > 0, Am |Xijt−1 ijt−1 ], and parameters of the regression bd , β bd bd relating match death hazards to match size: β e(d ). Since the fixed costs 0 1st year , β lsales , sb of sustaining a match are incurred after each shipment, the difference in separation hazards between the first and all subsequent years helps to distinguish F from δ. Also, in the absence of shocks to market-wide conditions (x) or idiosyncratic buyer demands (y), all matches would survive A periods with probably (1 − δ)A . Accordingly, the rate at which hazard rates decline with match age is informative about δ. Further identification comes from the fact that δ affects all firms equally, while the effect of F declines as π bϕ,x increases. This makes the association between shipment size and match longevity informative regarding the importance of F. Third, the θ distribution parameters, α and β, determine the cross-firm joint distribution construct this set of weights. Our weighting matrix yields a consistent estimator, provided that our model is properly specified. 31 of success rates in home and foreign markets and, similarly, the dispersion in firm types σ ϕ helps determine the cross-distribution of domestic and foreign sales. The combined effects of these parameters is reflected in the means, variances, and covariances of foreign and domestic f bhf , sb sales, which are implied in turn by φ e(hf ), and se(ln Xjt ). Similarly, the cross-firm distri1 c bc and sb bution of numbers of foreign clients, summarized by φ e(n ), responds to (α,β). This distribution also responds to σ ϕ , since the firm effects ϕ strongly influence search intensities. But the role of the firm effects ϕ is distinct from that of the popularity indices θf and θh because ϕ induces correlation in sales across markets. This correlation, which is implied by f bhf , sb b X f |Acjt ), φ E(ln e(hf ), and se(ln Xjt ), helps to isolate the variance in firm effects, σ ϕ . 1 jt Finally, the marginal cost of search and its sensitivity to previous matches are determined by γ, κ0 , and κ1 . Match rates, transition probabilities for numbers of clients, Pb[njt+1 = m|njt = k], and the client distribution are informative about the convexity of the matching bc and sb cost function. Accordingly, β e(n ) are useful in their identification. Differences in match arrival rates among firms that have made many versus few matches help to distinguish the convexity parameter β from the network effect parameter, γ. And importantly, the shape of the client-per-seller distribution is informative about network effects, since these effects critically impact the ability of firms to sustain large client bases, and thus affect the ”fatness” of the right-hand tail. 5.3 Parameter estimates Table 11 reports estimates based on the data moments described in the previous subsection. c, are reported and juxtaposed with their simulated Data-based estimates of these moments, M 32 Table 10: Parameters Estimated using indirect inference (Λ) Parameter rate of exogenous separation domestic market size foreign market size fixed cost First θ distribution parameter Second θ distribution parameter demand shock jump hazard demand shock jump size shipment order arrival hazard std. deviation, log firm type network effect parameter search cost function curvature parameter search cost function scale parameter δ Πh Πf F α β λy ∆y λb σϕ γ κ1 κ0 value std. error 0.267 11.344 10.675 7.957 0.716 3.161 0.532 0.087 8.836 0.650 0.298 0.087 111.499 0.001 0.017 0.017 0.018 0.007 0.029 0.001 0.001 0.006 0.002 0.001 0.001 0.512 counterparts, MS (Λ), in Table 11.18 The Euclidean distance between these two vectors divided by the length of the latter vector is 0.118. 18 The share exporters, the coefficient of log foreign sales on log domestic sales, and the AR1 coefficient for log domestic sales in Table 11 are obtained from a combination of the Colombian Annual Manufacturing Survey (AMS) and the administrative records of exports transactions. The data used cover 1993-2007. Exports from administrative records are merged into the AMS using firm identifiers. This is done because the AMS has no export information for 1993-1999, and because the dynamics of aggregate exports reported in the EAM starting in 2004 differ substantially from aggregate reports from other sources. 33 c and MS (Λ)) Table 11: Data-based and simulated statistics (M Transition probs.19 No. clients (nc ) Pb[ncjt+1 = 0|ncjt = 1] Pb[ncjt+1 = 1|ncjt = 1] Pb[ncjt+1 = 2|ncjt = 1] Pb[ncjt+1 ≥ 3|ncjt = 1] Pb[nc = 0|nc = 2] jt+1 Data 0.618 Model 0.534 0.321 0.048 0.013 0.271 0.358 0.082 0.024 0.260 0.375 0.241 0.113 Data 0.694 0.321 0.281 0.135 Model 0.857 0.515 0.329 0.450 0.304 = 3] 0.424 0.281 = 4] 0.389 0.305 jt ijt−1 f b E[1 |Xijt−1 f Xijt =0 f b E[1 |Xijt−1 f Xijt =0 > > ijt−1 m 0, Aijt−1 0, Am ijt−1 Log sales per client on client no. regression bm β 1 m b β2 sb e(m ) Client number inverse CDF regression cc β 1 cc β 2 c sb e(n ) Match shipments per year b (ns ) E Match death prob regression bd β 0 d b β 1st year d b β lsales sb e(d ) Data 0.299 Model 0.351 Data Model 0.727 2.167 0.515 1.424 Data 0.709 Model 0.748 0.383 0.099 = 2] 0.300 0.121 = 3] 0.263 0.055 = 4] 0.293 0.100 Data 8.960 10.018 10.231 10.369 10.473 Data Model 9.306 10.806 10.755 10.679 10.669 Model 0.976 0.462 Data 0.896 0.683 Model 0.811 0.233 0.613 0.370 1.124 0.503 jt Pb[ncjt+1 = 1|ncjt = 2] Pb[ncjt+1 = 2|ncjt = 2] Pb[ncjt+1 ≥ 3|ncjt = 2] Match death hazards f b E[1 |Xijt−1 > 0, Am f ijt−1 = 0] Xijt =0 f b E[1 |Xijt−1 > 0, Am f ijt−1 = 1] Xijt =0 f b E[1 |X > 0, Am = 2] f Xijt =0 Share of firms exporting b E(1 ) X f >0 Data 2.677 -0.143 2.180 Model 0.842 0.042 1.622 Data -1.667 Model -1.587 -0.097 0.066 Data -0.280 0.128 Model 4.824 Data 3.770 Model 1.174 1.640 0.166 0.203 -0.070 0.453 -0.100 0.395 34 Log foreign sales on log domestic sales b hf β 1 sb e(hf ) Exporter exit hazards b E[1 |Ac = 0] f Xjt =0 jt−1 b E[1 |Ac = 1] f jt−1 c b E[1X f =0 |Ajt−1 jt b E[1 |Ac f Xjt =0 jt−1 b E[1 |Ac f Xjt =0 jt−1 Xjt =0 Log sales per exporter by cohort age f b E(ln Xjt |Acjt = 0) f b X |Ac = 1) E(ln jt jt f b E(ln Xjt |Acjt = 2) f b X |Ac = 3) E(ln jt jt b X f |Ac ≥ 4) E(ln jt jt Log dom. sales autoreg. bh β 1 sb e(h ) Log match sale autoreg. f b β 1 f β 1st year sb e(f ) 6 6.1 Analysis of results Fitting the moments Comparing the data-based moments to their simulated counterparts in Table 11, one finds the model does a reasonably good job of explaining the patterns we discussed in Section 2 above. In particular, the simulated transition probabilities for numbers of clients are close to the data, as are the match death hazards, the relationship between exit rates and cohort age, and the relationship between average exports and cohort age. The model also qualitatively (but less accurately) captures the concentration of exporters at the low end of the client count distribution and the tendency for average sales per client to co-vary positively with number of clients. Finally the model also captures the positive association between domestic and foreign sales. 6.2 Interpreting the coefficients Several immediate implications of the coefficient estimates merit note. First, although mature matches fail with probabilities exceeding 40 percent (Table 7), we estimate that the exogenous failure rate is only δ = 0.27. Thus idiosyncratic shocks to buyer-seller matches appear to play a significant role in match survival. Second, the fixed per-shipment costs of sustaining a match are roughly F = exp(7.957) = $US 2,855, about 70 percent higher than the per shipment costs of regulations by 2005, according to the Doing Business report. Third, the unconditional average success rate with potential U.S. buyers is α/(α + β) ≈ 0.184, so less than onefifth of the buyers that Colombian exporters meet are interested in establishing a business relationship. Fourth, however, success rates vary across exporters with standard deviation p αβ/ [(α + β)2 (α + β + 1)] ≈ 0.176, so some firms have much higher success rates than 35 others, and this creates considerable scope for learning. Fifth, network effects are extremely important. After a successful matches, search costs at any given s have fallen by the factor (1 + a)−γ(1+1/κ1 ) relative to the costs faced by a new exporter. Thus, for example, when a seller achieves her first successful match, her search costs for any given arrival hazard drop to 8 percent of their pre-match level, and after three success matches, they drop to 2 percent. Finally, there is considerable convexity in the search cost function (1 + 1/κ1 = 12.49), so holding the number of successful matches constant, intensifying the search process is very costly. This is how the model explains the fact that 80 percent of exporters have a single client. What are the combined implications of these estimates for sellers’ search policy? Figure 2a below shows search intensity (sf ) as a function of number of successes (a) and failures (n − a), taking expectations over marketwide shocks (x) and productivity shocks (ϕ). For any given number of previous failures, search intensity is increasing in the number of previous successes. This reflects the fact that successes build a network and thus reduce the cost of making future matches. It is also clear that the effect of a successful match has the most dramatic effect on search intensity when firms have little experience. Partly this is due to the fact that early successes contain the most information, and thus move priors relatively more. 6.3 Resticted versions of the model To explore identification of the learning effects and the reputation effects in our model, we consider two alternative specifications. The first, which we call the no-learning model, treats firms as knowing their exact θf draws, even before they acquire any experience in export markets. This specification involves the same set of parameters, none of which are constrained, 36 (a) baseline (b) no network Figure 2: Search policy functions by match history 37 Table 12: Parameter Estimates for Alternative Models Parameter rate of exogenous separation domestic market size foreign market size fixed cost First θ distribution parameter Second θ distribution parameter demand shock jump hazard demand shock jump size shipment order arrival hazard std. deviation, log firm type network effect parameter search cost function curvature parameter search cost function scale parameter δ Πh Πf F α β λy ∆y λb σϕ γ κ1 κ0 benchmark (Λ) 0.267 11.344 10.675 7.957 0.716 3.161 0.532 0.087 8.836 0.650 0.298 0.087 111.499 fit metric fit metric, no weighting D e D 9.97 e+04 0.117 no learning (ΛN L ) 0.516 12.670 12.245 10.238 0.512 0.351 0.713 0.060 10.028 1.268 0.112 0.0348 234.764 no network (ΛN N ) 0.119 10.884 10.321 8.539 1.807 0.963 1.581 0.087 10.347 1.355 0 0.057 175.953 2.155 e+05 0.182 1.17 e+05 0.143 so it isn’t a nested version of the benchmark model. Rather it replaces one characterization of beliefs with another. The second alternative, which we call the no-network model, is nested by the benchmark model. It shuts down reputation effects by imposing γ = 0, but it retains the benchmark assumption that firms must learn their θf draws through experience. Both alternative models are calibrated to the same statistics we use for our benchmark model. The resulting parameter estimates and the associated fit metrics are reported in Table 12. Below we discuss the ability of each to fit the data. 6.3.1 No learning Other things held fixed, the elimination of learning effects makes the rapid turnover of novice exporters less likely, both by discouraging inexperienced low-θf firms from exploring foreign markets and by eliminating learning-based exit. Shutting down learning effects also means 38 that high-θf firms do not intensify their search efforts as they receive positive feedback about their product appeal. With these mechanisms inoperative, the no-learning model must use other means to explain the rapid turnover of new exporters and the rapid expansion of sales per surviving exporter as young cohorts mature. To accomplish the former, lower productivity firms are induced to participate in export markets by a rightward shift in the θf distribution and higher values for Πf and λb , while match failure rates and market exit rates are sustained by higher values for F, δ, and λy (Table 12, column 3 versus column 2).20 To get sales per exporter growing with cohort age, the no-learning model relies more heavily on selection effects. Low productivity firms are enticed into the market by the bigger Πf value and the higher average popularity of their products. But these firms tend to end their matches as soon as the fixed costs (F ) come due, which–being relatively large–ensures that the surviving exporters have substantially higher sales. The relatively large value of λy also helps to generate growth in match sales conditioned on match survival, since buyers who draw negative shocks tend to fail, while matches with positive shocks tend to survive. Finally, the no-learning model facilitates new exporter growth by reducing the convexity of the search cost function, κ1 . While these parameter adjustments help the no-learning model qualitatively match patterns of exporter turnover and growth, the model’s overall fit metric is much worse than that of the benchmark model (Table 12, lower panel). The reason is that the no-learning model badly overstates the share of firms that export (Table 14 in Appendix B), severely understates the persistence in match-specific sales, given match continuation, overstates the relationship between sales per client and number of clients, and fails to match the Pareto shape of the 20   Recall that E(θf ) = α/(α + β) and var(θj ) = αβ/ (α + β + 1)(α + β)2 . 39 cross exporter client distribution 6.3.2 No network effect Network effects mean that sellers with a history of successful matches face relatively low search costs, given search intensity. This allows firms with popular products to build larger customer bases than the sharply convex search cost function would have otherwise allowed, and thereby helps the benchmark model match the Pareto distribution of clients across sellers. To determine the importance of this feature of the model, we set γ = 0 and re-estimated the remaining parameters, obtaining the no-network estimates reported in Table 12. Without network effects, the the model moves part way toward matching the Pareto shape by reducing the convexity of the search cost function, κ1 . But this is an imperfect fix because all exporters are equally affected by κ1 , not just the larger ones. Accordingly, various other adjustments occur, including a modest increase in F , a rightward shift in the θ distribution, an increase in the variance of ϕ, and an increase in the jump hazard for buyer shocks, λy . Interestingly, these adjustments are qualitatively similar to those that occurred when we shut down learning effects. Here, however, market sizes Πf and Πh shrink a bit rather than expand. Despite these adjustments, the no-network model does signficantly worse than the benchmark model (Table 12, bottom panel). In particular, the client distribution is far from Pareto, reflecting the model’s inability to explain the existance of very large exporters (Table 14 in Appendix B). The no-network model also overstates the fraction of firms that export and the average exports of surviving firms after the first year. Finally, it makes the correlation between domestic and foreign sales far too weak, and the log sales-per-client distribution far too non-linear in the log of the number of clients. 40 The inability of the no-network model to generate a set of super-exporters can be traced back to the search policy function this model delivers. Figure 2b summarizes its properties. Note that learning effects appear to be relatively important for the first several clients, but unlike in figure 2b, the policy function quickly flattens out as successes accumulate. So, within the general structure of our search and learning framework, sustained growth in search intensity among relatively established exporters cannot be sustained without network effects. Note also the very different scales between Figures 2a and 2b, indicating much lower search intensities when the network effect is not present. 6.4 Counterfactual experiments It remains to use our model to explore the export dynamics in a search and learning world with network effects. These experiments will reveal the extent to which learning and network effects create deviations from the export path one would expect in a frictionless setting with the same marketwide shocks and idiosyncratic processes for buyer and seller shocks. We graph three experiments in Figures 3-5 below. Each figure has separate panels decomposing aggregate exports into number of exporters, mean per-client exports, and mean number of clients. In Figure 3, we reduce the scalar κ0 in the search cost function by 20% percent. In Figure 4, we decrease the fixed cost of maintaining a client relationship F by 20%, and in Figure 5, we reduce the size of foreign market jumps ∆xf by 20% percent. For all experiments, the shock takes place in 2002 and is unanticipated and permanent. The red line represents the time path that would have been observed in the absence of the shock, and the dashed blue line reflects the time path induced by the shock. We use the same draws for all stochastic processes, with and without the parameter change, so these changes are the 41 only reason that the blue line differs from the red line after 2002. In all exercises, we take the market-wide demand shifters xf and xh from the data. While the shock takes place in 2002, decreasing the cost of search has no noticeable net effect on exports until 2003. The slow reaction of firms to shocks is a theme in all of our counterfactuals. The decrease in search costs appears to mainly encourage inexperienced firms to search harder. Since exporters start small, and this is reflected in a decrease in mean sales per client, the initial effect on aggregate exports is small. Over time, however, a successful exporter will ramp up her search behavior, so that aggregate exports ultimately grow relative to the baseline. Exporters also react slowly to the fixed cost reduction in Figure 4, and different margins react with different speeds. While the number of active exporters does most of its jumping in 2002, the mean number of clients rises more gradually as it takes all exporters time to acquire the new equilibrium collection of clients. Somewhat surprisingly, decreasing fixed cost does not cause mean sales per client to drop. Mean sales are affected by two margins. For a particular firm, mean sales per client will decrease as poor clients that would have been let go are allowed to stick around. On the other hand, lowering fixed costs also encourages highly productive firms to search harder. Since the typical match relationship at one of the best firms is highly lucrative, a new match can cause economy-wide mean sales per client to rise. That mean sales per client rise after decreasing fixed costs suggests that productive firms gain more new clients than unproductive firms. Both a reduction in search costs and a reduction in fixed costs per shipment could be potentially interpreted as policy experiments. For instance, Proexport, the Colombian export 42 promotion agency, has several programs aimed at helping firms find foreign clients. These range from publishing lists of potential buyers in their website to firm-specific studies and trips organized by Proexport (some of which the firm itself pays for). The introduction of this type of programs, or subsidized prices for them could lead to reduced search costs. As for the fixed cost per shipment, regulations may also affect these costs. The World Bank, for instance, estimates that in 2005 the fees associated with procedures to export goods amounted to $1,745 per one-container shipment. Figure 4 shows the results of the experiment where the foreign market size suddenly increases by 20 percent. All matches become more lucrative. This mechanical rise in sales explains the sudden increase in exports and mean sales per client immediately after the shock. The gradual reaction of exports can be seen in the mean number of clients per exporter, which takes almost a decade to fully react to the shock. 43 6.35 Log Active Exporters Log Total Exports 18.7 18.6 18.5 18.4 18.3 1992 1997 2002 2007 6.2 6.15 1997 2002 2007 2012 1997 2002 2007 2012 0.6 Log Mean Number of Clients Log Mean Sales per Client 6.25 6.1 1992 2012 11.6 11.5 11.4 11.3 11.2 1992 6.3 1997 2002 2007 0.58 0.56 0.54 0.52 0.5 0.48 0.46 1992 2012 Figure 3: Time Series Effects of Search Cost Reduction 7 Summary Customs records reveal tremendous turnover among Colombian manufacturers who export to the U.S.. In a typical year, 48 percent of these exporters are new to the U.S. market, and 81 percent of these new exporters will be gone two years hence. New exporters ship small quantities, so despite their numbers they account for only 12 percent of total Colombian exports in value terms. But each new cohort of Colombian exporters contains a small number of firms that survive and rapidly expand, growing many times faster than aggregate Colombian exports. They do so by adding U.S. clients to their customer base at a rapid rate. 44 19 6.6 Log Active Exporters Log Total Exports 18.9 18.8 18.7 18.6 18.5 18.4 18.3 1992 1997 2002 2007 6.3 6.2 1997 2002 2007 2012 1997 2002 2007 2012 0.7 Log Mean Number of Clients Log Mean Sales per Client 6.4 6.1 1992 2012 11.7 11.6 11.5 11.4 11.3 11.2 1992 6.5 1997 2002 2007 0.65 0.6 0.55 0.5 0.45 1992 2012 Figure 4: Time Series Effects of Fixed Cost Reduction 45 6.6 19 6.5 Log Active Exporters Log Total Exports 19.2 18.8 18.6 18.4 18.2 1992 1997 2002 2007 6.2 1997 2002 2007 2012 1997 2002 2007 2012 0.7 Log Mean Number of Clients Log Mean Sales per Client 6.3 6.1 1992 2012 11.8 11.7 11.6 11.5 11.4 11.3 11.2 1992 6.4 1997 2002 2007 0.65 0.6 0.55 0.5 0.45 1992 2012 Figure 5: Time Series Effects of Positive Market-wide Shock 46 After documenting these patterns, we develop a continuous time model that explains them. Firms wishing to export must engage in costly search to identify potential buyers abroad. The buyers they encounter either reject their products or form finite-lived business relationships with them. Buyer who form business relationships with exporters send them favorable signals about the appeal of their products, and in doing so, encourage them to search more intensively for additional buyers. Successful business relationships also reduce search costs by improving sellers’ visibility (network effects). Finally, sellers’ search intensities depend upon their permanent idiosyncratic characteristics and marketwide conditions. Fit using the method of simulated moments, the model replicates the patterns in customs records described above and allows us quantify several types of trade costs, including the search costs of identifying potential clients and the costs of maintaining business relationships with existing clients. It also allows us to estimate the network effect of previous exporting successes on the costs of meeting new clients, and to characterize the cumulative effects of learning on firms’search intensities. Both the learning effect and the network effect prove to be quantitatively important. Finally, our model provides a lens through which to view the seemingly unpredictable responses of export flows to exchange rate fluctuations. 47 References Albornoz, Facundo, Hector Calvo Pardo, Gregory Corcos, and Emanuel Ornelas (2012) ”Sequential Exporting,” Journal of International Economics 88: 17-31. Alessandria, George and Horag Choi (2007) ”Do Sunk Costs of Exporting Matter for Net Export Dynamics?” Quarterly Journal of Economics, pp. 289-336. Alessandria, George, Joseph Kaboski and Virgiliu Midrigan (2010) ”Inventories, Lumpy Trade, and Large Devaluations,” American Economic Review, 100 (5) pp. 2304-39. Arkolakis, Konstantinos (2009) “A Unified Theory of Firm Selection and Growth,” Yale University, Department of Economics, Working Paper. Arkolakis, Konstantinos (2010) “Market Access Costs and the New Consumers Margin in International Trade,” Journal of Political Economy, 118(6), pp. 1151-1199. Baldwin, Richard. E. and Paul Krugman (1989): “Persistent Trade Effects of Large Exchange Rate Changes.” Quarterly Journal of Economics, 104, pp. 635-654. Bernard, Andrew and J. Bradford Jensen (1999) “Exceptional Exporter Performance: Cause, Effect, or Both?” Journal of International Economics , 47, pp. 1-25. Bernard, Andrew, J. Bradford Jensen, Samuel Kortum and Jonathan Eaton (2003) “Plants and Productivity in International Trade,” American Economic Review 93(4), pp. 12681290 Bernard, Andrew, J. Bradford Jensen, J. Stephen J. Reading, and Peter K. Schott (2007) “Firms in International Trade,” Journal of Economic Perspectives. 48 Besedes, Tibor (2007). “A Search Cost Perspective on Formation and Duration of Trade,” Working Paper, Department of Economics, Georgia Tech University. Blum, Bernardo S., Sebastian Claro, and Ignatius Horstmann (2009). “Intermediation and the Nature of Trade Costs: Theory and Evidence.” Working Paper, The University of Toronto. Brooks, Eileen (2006) “Why don’t firms export more? Product Quality and Colombian Plants” Journal of Development Economics, 80: 160-178. Chaney, Thomas (2011) “The Network Structure of International Trade,” University of Chicago. Clerides, Sofronis, Saul Lach and James Tybout (1998) “Is Learning-by-Exporting Important? Micro-dynamic Evidence from Colombia, Mexico and Morocco,” Quarterly Journal of Economics, pp. 903-947. Das, Mita, Mark Roberts and James Tybout (2007) “Market Entry Costs, Producer Heterogeneity and Export Dynamics,” Econometrica 75(3), pp. 837-874. Domı́nguez, Juan Camilo, Jonathan Eaton, Marcela Eslava, and James Tybout. (2010) ”Search and Learning in Export Markets: Case Studies for Colombia.” Pennsylvania State University, Working Paper. Drozd, Lukasz A. and Jaromir B. Nosal (2008) “Understanding International Prices: Customers as Capital,” Working Paper, The University of Wisconsin. 49 Dixit, Avinish (1989), “Hysteresis, Import Penetration, and Exchange Rate Pass-Through,” Quarterly Journal of Economics, Vol. 104, No. 2 (May), pp. 205-228. Eaton, Jonathan, Samuel Kortum, and Francis Kramarz (2004) “Dissecting Trade: Firms, Industries, and Export Destinations,” American Economic Review Papers and Proceedings, 94: 150-154. Eaton, Jonathan, Samuel Kortum, and Francis Kramarz (2011) “An Anatomy of International Trade: Evidence from French Firms,” Econometrica 79(5), pp. 1453-1498. Eaton, Jonathan, Marcela Eslava, Maurice Kugler and James Tybout (2008). “Export Dynamics in Colombia: Firm-Level Evidence,” in Elhanan Helpman, Dalia Marin and Thierry Verdier, eds., The Organization of Firms in a Global Economy, Cambridge, MA: Harvard U. Press. Eslava, Marcela, John Haltiwanger, Adriana Kugler, and Maurice Kugler (2004) “The Effects of Structural Reforms on Productivity and Profitability Enhancing Reallocation: Evidence from Colombia,” Journal of Development Economics, 75: 333-371. Gouriéroux and Monfort, 1996. Simulation-Based Econometric Methods. New York: Oxford U. Press. Irarrazabal, Alfonso A. and Luca David Opromolla (2006) “Hysteresis in Export Markets,” New York University, Working Paper. Jackson, Matthew and Brian Rogers (2007) “Meeting Strangers and Friends of Friends: How Random are Social Networks?” American Economic Review, 97: 890-915. 50 Jovanovic, Boyan (1982) “Selection and the Evolution of Industry,” Econometrica, 50: 649670. Kugler, Maurice (2006) “Spillovers from foreign direct investment: within or between industries?” Journal of Development Economics, 80(2): 444-477. Luttmer, Erzo (2007) “Selection, Growth, and the Size Distribution of Firms,” Quarterly Journal of Economics, 122: 1103-1144. Melitz, Marc (2003) “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,” Econometrica 71, 1695-1725. Rauch, James and Joel Watson (2003) “Starting Small in an Unfamiliar Environment,” International Journal of Industrial Organization 21: 1021-1042. Roberts, Mark and James Tybout (1997a) “The Decision to Export in Colombia: An Empirical Model of Entry with Sunk Costs,” American Economic Review 87(4), pp. 545-563. Roberts, Mark and James Tybout (1997b) What Makes Exports Boom? Directions in Development Monograph Series, The World Bank, Washington, DC. Ruhl, Kim and Jonathan Willis (2008) “New Exporter Dynamics,” New York University, Working Paper. Shimer, Robert (2005) ”The Cyclical Behavior of Equilibrium Unemployment and Vacancies,” The American Economic Review, 95(1), pp. 25-49. Tauchen, George (1986) “Finite State Markov-Chain Approximation to Univariate and Vector Autoregressions,” Economics Letters, 20.2. 177-181. 51 Table 13: Colombian versus U.S. Customs Records Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 A Colombia # exporters value 1775 1038 2026 995 2230 870 2800 1113 3035 1379 2861 1554 2689 1665 2420 1540 2161 1570 United States # exporters value 2721 1140 2744 1019 2986 855 3579 1119 4002 1415 4288 1438 4361 1552 4175 1496 3758 1474 % difference # exporters value 53% 10% 35% 2% 34% -2% 28% 1% 32% 3% 50% -7% 62% -7% 73% -3% 74% -6% Data Checks To investigate the quality of the exporter id (manuf id) in the U.S. import records, we ran a series of robustness checks. The Colombian and U.S. data overlap for the years 2000-2008 and both contain measures of the value of exports as well as the number of exporting firms. If the manuf id variable is error-prone and noisy, we would expect the U.S. data to over-report the number of Colombian firms exporting to the U.S. That is, each time a customs broker wrongly enters the data in the field, a new firm would be created. Table 13 below summarizes the total value of exports to the U.S. and the number of Colombian firms, by year, for each data set. The datasets align much more closely on value than they do on firm counts. The difference in value is never more than 10% while the firm count difference ranges from 18% to 74%. The differences are stable over time. To look more closely at the cause of the difference in firm counts, we compared the number of firms across sources by HS2 categories. The counts in the LFTTD were higher than the Colombian data in only 28 of the 82 codes and by far the biggest differences are in HS codes 52 61 and 62: textiles. In these two product classes the U.S. data identifies 4025 more firms than the Colombian data. If we remove these two sectors from the list, the difference in firm counts flips and the Colombian data contain 1001 more firms than the LFTTD. Interestingly, Title 19 of U.S. code specifically requires that the manuf id variable for textile products represent the manufacturer of the textile products, not an intermediary. That is, for this sector in particular the manufacturer, not an intermediary must be reported on the CBP 7501 form. By contrast, prior work by several authors of this paper has shown (Marcela’s 8/9/13 e-mail referenced this) that the Colombian data reports the exporter, which may or may not be the manufacturer. Given that revious research (Tybout, 2000 JEL) has shown that developing countries tend to have a disproportionately large share of small manufacturing firms, it is reasonable to assume that a large part of the reason why the U.S. data report so many more firms in the textile sector is that due to administrative reasons the U.S. data count many small manufacturers and the Colombian data are, in many cases, reporting aggregators and intermediaries. As a final check of the integrity of the manuf id variable - and the robustness of our main results - we experimented with a “fuzzy” version of the manuf id variable that did not contain any street numbers in the string (a likely source of input errors). The effect of this is to reduce the number of Colombian firms in the data, an approximation of fixing any extraneous noise from data entry errors. Next we re-ran Table 7 with the fuzzy data and compared the results to the original version. One of the key findings from Table 7 is the high match separation rates ranging from about 40% to 66%. Using the fuzzy version did not reduce the separation rates substantially and 53 left the patterns intact. The fuzzy separation rates ranged from 26% to 62%, a drop of 6% on average. It does not appear that our results are sensitive to a modest reduction in data entry errors. B Moments for Restricted Models Table 14: Restricted versus Full Model Fit data c M benchmark Ms (Λ) no learning Ms (ΛN L ) no network Ms (ΛN N ) 0.299 0.351 0.585 0.451 0.727 2.167 0.515 1.424 0.923 0.843 0.575 1.146 0.976 0.462 0.896 0.683 0.969 0.661 0.898 0.570 0.709 0.748 0.773 0.877 0.383 0.099 0.099 0.188 = 2] 0.300 0.121 0.032 0.012 = 3] 0.263 0.055 0.056 0.198 = 4] 0.293 0.100 0.098 0.185 log sales per exporter by cohort age b X f |Ac = 0) E(ln jt jt b X f |Ac = 1) E(ln jt jt b X f |Ac = 2) E(ln jt jt b X f |Ac = 3) E(ln jt jt b X f |Ac ≥ 4) E(ln jt jt Log match sale autoregression bf β 8.960 10.018 10.231 10.369 10.473 9.306 10.806 10.755 10.679 10.669 9.608 10.615 10.431 10.426 10.332 8.541 11.331 11.037 10.845 11.145 0.811 0.233 0.613 0.370 0.105 0.056 0.268 0.087 1.124 0.503 0.287 0.425 Share of firms exporting b E(1 ) X f >0 jt Log foreign sales on log domestic sales b hf β 1 sb e(hf ) log dom. sales autoreg. bh β 1 sb e(h ) exporter exit hazards b E[1 |Ac = 0] f Xjt =0 jt−1 b E[1 |Ac = 1] f jt−1 b E[1X f =0 |Acjt−1 jt b E[1 |Ac f Xjt =0 jt−1 b E[1 |Ac f Xjt =0 jt−1 Xjt =0 1 f β 1st year sb e(f ) 54 Match death hazards f b E[1 |Xijt−1 > 0, Am f ijt−1 = 0] Xijt =0 f b E[1 |Xijt−1 > 0, Am f ijt−1 = 1] Xijt =0 f b E[1 |X > 0, Am = 2] f 0.694 0.857 0.943 0.879 0.515 0.329 0.452 0.337 0.450 0.304 0.426 0.286 = 3] 0.424 0.281 0.434 0.332 = 4] 0.389 0.305 0.398 0.226 Match death prob regression bd β 1.174 1.640 1.843 2.087 0.166 0.203 0.031 0.055 -0.070 0.453 -0.100 0.395 -0.092 0.266 -0.140 0.343 4.824 3.770 2.064 4.525 0.618 0.321 0.048 0.013 0.271 0.375 0.241 0.113 0.534 0.358 0.082 0.024 0.260 0.321 0.281 0.135 0.677 0.255 0.056 0.010 0.456 0.291 0.166 0.086 0.643 0.307 0.045 0.004 0.165 0.306 0.427 0.100 Log sales per client on client no. regression bm β 1 bm β 2 sb e(m ) 2.677 -0.143 2.180 0.842 0.042 1.622 0.944 1.049 1.893 3.887 -1.451 2.067 Client number inverse CDF regression cc β 1 cc β 2 c sb e(n ) -1.667 -0.097 0.066 -1.587 -0.280 0.128 -1.395 -1.184 0.062 -1.655 -1.420 0.069 ijt−1 f b E[1 |Xijt−1 f Xijt =0 f b E[1 |Xijt−1 f Xijt =0 Xijt =0 > > ijt−1 0, Am ijt−1 0, Am ijt−1 0 d b β 1st year d b β lsales sb e(d ) Match shipments per year b (ns ) E Transition probabilities, No. clients (nc ) Pb[ncjt+1 = 0|ncjt = 1] Pb[ncjt+1 = 1|ncjt = 1] Pb[ncjt+1 = 2|ncjt = 1] Pb[ncjt+1 ≥ 3|ncjt = 1] Pb[ncjt+1 = 0|ncjt = 2] Pb[ncjt+1 = 1|ncjt = 2] Pb[ncjt+1 = 2|ncjt = 2] Pb[ncjt+1 ≥ 3|ncjt = 2] 55 Referee Report Please choose one recent working paper from the following topics and write a referee report. The report should be around 4-5 pages. Use the first half page to briefly describe the paper. Use 2-3 pages for the “Main Comments” that outline the major concerns or reservations you have with the paper. Try to be constructive in providing suggestions to the authors. Then use another 1-2 pages for the “Detailed Comments” which comment on the detailed implementation of the paper. 1. Gains from trade and variable markups https://www.sganapati.com/files/Ganapati_Wholesalers_2020.pdf 2. Export dynamics http://www.personal.psu.edu/jxt32/EEJKT_02_26_2014.pdf 3. Multinational firms https://www.dropbox.com/s/futd6kflbrqd8kj/GarettoOldenskiRamondo.pdf
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Title: A Search and Learning Model of Export Dynamic
Authors: Jonathan Eatona, e, Marcela Eslavab, David JinkinscC. J. Krizand, and James Tyboutc,
Source: Census Bureau staff
OVERVIEW
The article title a searching and learning model of export dynamics is authored by
Jonathan Eatona, e, Marcela Eslavab, David JinkinscC. J. Krizand, and James Tyboutc. The
central theme of this paper is to analyze the number of patterns of relationship between exporters
and individual buyers. This is because most researches focus on microeconomic data to try and
understand the hindrances in entering the foreign market and their impacts on export dynamics,
thus leaving a massive gap in the research on the relationship between exporters and individual
buyers (Eslava et al., 2014). The past study discovered that firm’s dataset provides insights on
the cost of exporting, and then the data is made available to be used in individual markets. The
literature reviews used in this study are relevant, extensive, and varied sources from different
times, thus making the study credible. The data on the export markets and individual exporters of
the two countries used in this study are taken from Enrique Montes and, therefore, are
trustworthy.

3

CONTRIBUTION
Although this study is not the first paper to address the patterns of relationship between
exporters and individual buyers, the article has gone an extra mile of examining the relationship
between the exporter and individual buyer in the market in both descriptive and via the lens of a
dynamic model thus making the paper to be relevant. As reviewed by different authors, the past
patterns on individual needs shipment from Colombia to the US revealed that most exporters
from Colombia drop out of the American market within the first year of their entry into the US
market (Eslava et al., 2014). However, a portion of exporters survive the shakedown and are said
to have low exit rates in the future. Besides, these survivors have the potential of rapidly
expanding their sales, and as a result, their market share grows as their maturity increases.
IDENTIFICATION STRATEGY
The study has developed a model that is consistent and with facts. The model is based on
the speculation that firms’ exporting behavior reflects the search and a learning process in a
foreign market, where interested producers devote their resources to a particular need or interest
to identify ...


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