metadata: authors: 0: author: Easterly, William
1: author: Reshef, Ariell
2: author: Schwenkenberg, Julia
count: World
docna: 0: docna: The power of exports
docty: Policy Research Working Paper
theme: Other trade and integration
majtheme: Trade and integration
subtopic: Private Sector Economics,Construction Industry,Common Carriers Industry,Food & Beverage Industry,General Manufacturing,Pulp & Paper Industry,Plastics & Rubber Industry,Private Sector Development Law,International Trade and Trade Rules,Marketing,Business Cycles and Stabilization Policies,Global Environment
teratopic: Law and Development,Transport,Macroeconomics and Economic Growth,International Economics and Trade
abstracts: cdata!: The authors systematically document
            remarkably high degrees of concentration in manufacturing
            exports for a sample of 151 countries over a range of 3,000
            products. For every country manufacturing exports are
            dominated by a few "big hits" which account for
            most of the export value and where the "hit"
            includes both finding the right product and finding the
            right market. Higher export volumes are associated with
            higher degrees of concentration, after controlling for the
            number of destinations a country penetrates. This further
            highlights the importance of big hits. The distribution of
            exports closely follows a power law, especially in the upper
            tail. These findings do not support a "picking
            winners" policy for export development; the power law
            characterization implies that the chance of picking a winner
            diminishes exponentially with the degree of success.
            Moreover, given the size of the economy, developing
            countries are more exposed to demand shocks than rich ones,
            which further lowers the benefits from trying to pick winners.
repnme: repnme: The power of exports
display_title: The power of exports
listing_relative_url: /research/2009/10/11227756/power-exports
topicv3: Private Sector Development m1326060 1921,Manufacturing Sectors m1326521 1281,Trade m1326924 698,Environment, Natural Resources and Blue
            Economy m1327391 566,Industry Policy m1327403 1075
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Law and Development,Transport,Macroeconomics and Economic Growth,International Economics and Trade
no_of_pages: 52
model_extractions: WPS5081 Policy Research Working Paper 5081 The Power of Exports _William Easterly Ariell Reshef Julia Schwenkenberg_ The World Bank Development Research Group Trade and Integration Team & Latin America and the Caribbean Region Office of the Chief Economist October 2009
Policy Research Working Paper 5081

# **Abstract**

The authors systematically document remarkably high degrees of concentration in manufacturing exports for a sample of 151 countries over a range of 3,000 products. For every country manufacturing exports are dominated by a few "big hits" which account for most of the export value and where the "hit" includes both finding the right product and finding the right market. Higher export volumes are associated with higher degrees of concentration, after controlling for the number of destinations a country penetrates. This further highlights the importance of big hits. The distribution of exports closely follows a power law, especially in the upper tail. These findings do not support a "picking winners" policy for export development; the power law characterization implies that the chance of picking a winner diminishes exponentially with the degree of success. Moreover, given the size of the economy, developing countries are more exposed to demand shocks than rich ones, which further lowers the benefits from trying to pick winners.

This paper—a product of the Trade and Integration Team, Development Research Group and the Office of the Chief Economist, Latin America and the Caribbean Region—is part of a larger effort in both departments to study how the structure of trade affects development. Policy Research Working Papers are also posted on the Web at http://econ.worldbank. org. The author may be contacted at ar7kf@eservices.virginia.edu.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **The Power of Exports**<sup>**1**</sup>

William Easterly Ariell Reshef New York University New York University and NBER Julia Schwenkenberg New York University

> 1 We thank Peter Debare, Jorg Stoye, Yijia Wang, Michael Waugh, participants at the World Bank invited session at LACEA 2008 and an anonymous referee for useful comments.
# 1 Introduction

How do countries succeed at economic development? Many descriptions of success stories have stressed the important role of manufacturing exports as a vehicle for success. Indeed, manufacturing exports per capita have a striking correlation with GDP per capita across countries, see Figure 1. Causality could go either way in this association, or both variables may re‡ect other factors. The ...gure does support a descriptive statement that success at manufacturing exports and success at development are close to being the same thing. This naturally warrants a close examination of the characteristics of success in export.

In this paper we show that manufacturing export success shows a remarkable degree of specialization for virtually all countries. Manufacturing exports in each country are dominated by a few “big hits”, which account for most of export value and where the “hit” includes both ...nding the right product and ...nding the right market. Moreover, we show that higher export volumes are associated with higher degrees of concentration, after controlling for the number of destinations a country penetrates (i.e. absolute advantage and size). This highlights the importance of big hits. In addition, we estimate that most of the variation, and hence concentration, in export is driven by technological dispersion of the exporting country, rather than demand shocks from the importing destinations. However, given the size of the economy, developing countries are more exposed to demand shocks than rich ones.

Hausmann and Rodrik (2006), in a seminal paper which helped inspire this one, had previously pointed out the phenomenon of hyper-specialization, although only for a few countries and products, and not including the destination component, in contrast to the comprehensive scope of our work. We also make a very signi...cant addition to the Hausmann and Rodrik ...ndings, in that we characterize the probability of "big hits" as a function of the size of the hit –by a power law.

We specify a “hit”as a product-by-destination export ‡ow. We chose this categorization because some export products are shipped to several destinations, while the typical export product is shipped to few destinations (with a mode of one). A few examples of big hits and their relationship to concentration are in order. Out of 2985 possible manufacturing products in our dataset and 217 possible destinations, Egypt gets 23 percent of its total 1
manufacturing exports from exporting one product –“Ceramic bathroom kitchen sanitary items not porcelain”–to one destination, Italy, capturing 94 percent of the Italian import market for that product. Fiji gets 14 percent of its manufacturing exports from exporting “Women’s, girl’s suits, of cotton, not knit” to the U.S., where it captures 42 percent of U.S. imports of that product. The Philippines gets 10 percent of its manufacturing exports from sending “Electronic integrated circuits/microassemblies, nes”to the U.S. (80 percent of U.S. imports of that product). Nigeria earns 10 percent of its manufacturing exports from shipping “Floating docks, special function vessels nes”to Norway, making up 84 percent of Norwegian imports of that product.

Examining big hits that are exported almost exclusively to one destination for what one would think would be fairly similar countries reveals a surprising diversity of products and destinations. Why does Colombia export paint pigment to the U.S., but Costa Rica exports data processing equipment, and Peru exports T-shirts? Why does Guatemala export candles to the U.S., but El Salvador exports toilet and kitchen linens? Why does Honduras export soap to El Salvador, while Nicaragua exports bathroom porcelain to Costa Rica? Why does Cote d’Ivoire export perfume to Ghana, while Ghana exports plastic tables and kitchen ware to Togo? Why does Uganda export electro-diagnostic apparatus to India, while Malawi exports small motorcycle engines to Japan?

The remarkable specialization across products and destinations shows up in high concentration ratios. The top 1 percent of product-destination pairs account for an average of 52 percent of manufacturing export value for 151 countries on which we have data.<sup>1</sup> The di¤erence between successful and unsuccessful exporters is found not just in the degree of specialization, but also in the scale of the “big hits.”For example, a signi...cant part of South Korea’s greater success than Tanzania as a manufacturing exporter is exempli...ed by South Korea earning $13 billion from its top 3 manufacturing exports, while Tanzania earned only $4 million from its top 3.

The probability of ...nding a big hit ex ante decreases exponentially with the magnitude of the hit. We show that the upper part of the distribution of export value across products

> 1 At this point we do not analyze specialization (concentration) along the time dimension. One attempt to do so is Imbs and Wacziarg (2003). However, they address specialization in total production, not exports, and, hence, do not analyze the destination dimension, which we believe captures additional product di¤erentiation.

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(de...ned both by destination and by six-digit industry classi...cations) is close to following a power law.<sup>2</sup> On average across our sample, the value of the 10th ranked product-destination export category is only one-tenth of the top ranked product-destination export category.<sup>3</sup> The value of the top ranked product-destination export category is on average 770 times (median 34 times) larger than the 100th ranked product-destination export category. In this paper we will estimate just how much the entire distribution of export values within each country is explained by a power law, and will place it in the context of a trade model with demand and productivity shocks.<sup>4</sup> Realizing that export success is driven by a few big hits changes our understanding of “success” and poses challenges for economic policy. Power laws may arise because many conditions have to be satis...ed for a “big hit,”and hence the probability of success is given by multiplying the probability of each condition being satis...ed times each other (if probabilities are independent). Source country s’s success at exporting product p to destination country d depends on industry-speci...c and country-speci...c productivity factors in country s, the transport and relational connections between s and d in sector p, and the strength of destination country d’s demand for product p from country s. All of these components are subject to shocks in country-industry technology, ...rms, country policy, input sectors, shipping costs and technologies, trading relationships, brand reputation, tastes, competitors, importing countries, etc.

The policy discussion about making such success more likely tends to be sharply polarized. Hausmann and Rodrik argue that a ...rm in country s that ...rst succeeds at exporting product p (they do not examine the destination dimension) is making a discovery that such a product export is pro...table, which then has an externality to other ...rms who can imitate success. They argue therefore that such a discovery process should receive a public subsidy,

> 2 Pareto distributions follow a so-called "power law", in which the probability of observing a particular value decreases exponentially with the size of that value. The distributions of word frequencies (Zipf’s law), sizes of cities, citations of scienti...c papers, web hits, copies of books sold, earthquakes, forest ...res, solar ‡ares, moon craters and personal wealth all appear to follow power laws; see Newman (2005). See also Table 1 in Andriani and McKelvey (2005) for more examples. Describing concentrated distributions in economics has a long tradition, starting with Pareto (1896). Sutton (1997) provides a survey of the literature on the size distribution of ...rms starting with the observation of proportional growth by Gibrat (1931) (Gibrat’s law).

> 3 The corresponding median is lower –one fourth –because of the skewness of this number in our sample.

> 4 Luttmer (2007) constructs a general equilibrium model with ...rm entry and exit that yields a power law in ...rm size. He combines a preference and a technology shock multiplicatively to obtain a variable he refers to as the ...rm’s total factor productivity.

3
which may imply a conscious government industrial policy.

Our analysis raises a new issue. In addition to the possible knowledge externality to a successful export, there is also a knowledge problem about the discovery itself. Who is more likely to discover the successful product-destination category –the public or private sector? We show that success (in both the product and destination dimensions) closely follows a power law. Hence, ex ante picking a winning export category (or discoverer) would be very hard indeed. A traditional argument for private entrepreneurship against the government "picking winners" is that private entrepreneurship is a decentralized search process characterized by many independent trials by agents who have many di¤erent kinds of speci...c knowledge about sectors, markets, and technologies. This a priori seems more likely to ...nd a "big hit" than a process relying on centralized knowledge of the state. However plausible these arguments may be, in the end it is an empirical question which approaches work. We hope to stimulate this debate in this paper, but do not believe that we can resolve it de...nitively.

A complementary point to ours is made by Besedes and Prusa (2008). They ...nd that most new trade relationships fail within 2 years and that the hazard rate of such failure is higher for developing countries.<sup>5</sup> Nevertheless, developing countries have the highest increase in trade relationships: there seems to be a lot of attempts in discovery as it is. However, entry (the extensive margin) does not account for much growth in trade. Together with our stress on the importance and di¢ culty of discovering big hits (at a higher level of disaggregation), this implies that Hausmann and Rodrik’s point might be misplaced.

Although addressing the Hausmann-Rodrik argument is our main goal, our work is related to a few other recent papers. The observation that trade is concentrated has not been lost on economists. Bernard, Jensen, Redding, and Schott (2007) document concentration across U.S. exporting ...rms, while Eaton, Eslava, Kugler, and Tybout (2007) ...nd that Colombian exports are dominated by a small number of very large (and stable) exporters. Arkolakis and Muendler (2009) make a similar point for Brazilian and Chilean exporting ...rms and ...nd that the distribution is approximately Pareto.

In contrast to these and other contributions, we document concentration and Pareto-like distributions for many more countries (151); we do so at the product-destination level; and

> 5 Their sample is 1975-2003 and relates to bilateral 4-digit SITC relationships.

4
we try to assess how much of this concentration is driven by technological dispersion versus demand. Eaton, Kortum, and Kramarz (2008) also relate trade patterns to productivity and demand shocks. But while they dissect trading patterns only for French ...rms, regardless of which products each ...rm exports (there could be more than one product per ...rm), we analyze trade at the product level for many countries.<sup>6</sup> In the next section we document concentration and distributions of exports for 151 countries in the product-destination dimension and perform preliminary analysis. In section 3 we estimate the contribution of technology versus demand to the distribution and concentration of exports. Section 4 concludes.

# 2 Empirical Facts

Our main data source is the UN Comtrade database. The U.N. classi...es exported commodities and manufactured products by source and destination at the six-digit level (roughly 5000 categories). We use the 1992 Harmonized System classi...cation (HS1992) for the year 2000, to maximize the available bilateral trade pairs. Using a less disaggregated classi...cation might have lead to better coverage of countries (say, 4-digit SITC), but would miss the extreme concentration within ...nely de...ned products.<sup>7</sup> We restrict our sample to manufactured categories, i.e. we drop from the sample all agriculture and commodities exports. Our focus on manufactured products stems from our interest on exports that are not dependent on country-speci...c natural endowments, and could potentially be produced everywhere in the world. We basically exclude products that rely directly on natural resources. Natural resources create strong comparative advantage for extracables and agricultural products. Therefore, a priori, focusing on manufacturing also reduces the degree of concentration, especially for developing countries.

Some importers in the original dataset did not correspond to well-de...ned destinations, so we dropped those destinations from the analysis.<sup>8</sup> Eventually, our sample contains 151 exporters, 2984 export categories, which may be shipped to at most 217 destinations (importers).

> 6 The distribution of exports across products is similar to what they ...nd for French ...rms.

> 7 An analysis of the distribution of product-destination export ‡ows at the 4-digit SITC level reveals similar patterns, but lower levels of concentration, as one might expect.

> 8 For example, “Antarctica”, “Areas, nes”, “Special Categories”, etc.

5
# 2.1 Concentration of exports

Our ...rst observation is that exports are highly concentrated. That is, for each country a few successful products and destination markets account for a disproportionately large share of export value. We initially examine manufactured products, while ignoring the destination market dimension (we will incorporate the destinations shortly). Table 1 shows that the median export share of the top 1%, 10% and 20% within nonzero export products for a country is 49%, 86% and 94%, respectively.<sup>9</sup> In fact, for the median country, the top 3 products account for 28% of exports, and the top 10 products account for a staggering 52%. The median share for the bottom 50% of exported products is a mere 0.57%. This implies a high degree of concentration indeed.<sup>10</sup> One issue that complicates the interpretation of the concentration ratios is that countries also di¤er a lot in how many export products they export at all (i.e. product exports with nonzero entries for each country) –from a minimum of 10 to a maximum of 2950, with a median of 1035. We will examine the role of number of products in the next section.

Another striking fact is just how few destination markets each product penetrates. Figure 2 shows the average across all 151 exporters of the share of export value accounted for by products that have the number of destinations shown on the X-axis. The largest shares go to products that are exported to only one destination, the next largest share goes to products that are exported to only two destinations, and then it falls o¤ to a long tail. This observation led to our decision to treat the product-destination pair as the unit of analysis for the bulk of our analysis.

We now incorporate the destination dimension. In all the analysis that follows, we stick to one unit of account: the product-destination export ‡ow. The same observation about concentration at the product level holds for product-destination trade ‡ows, i.e. when each observation is an export of a particular product to a particular destination. Table 2 shows that for the median exporter the top 1% of product-destination pairs account for 52.5% of total export value! The top 10% account for 89% and the bottom 50% for only 0.8%.<sup>11</sup> Once again, the number of nonzero entries in the product-destination matrix varies enor-

> 9 Our basis for comparisons are always nonzero export ‡ows for each country separately. In calculating percentages we never compare to potential export products that are exported by all countries (2984 in total).

> 10 Table A1 in the appendix reports these shares for all 151 countries in our sample.

> 11 Table A2 in the appendix shows these numbers for all countries.

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mously across countries, and is always far below the potential number implied by exporting all products to all destinations. The median number of nonzero product-destination entries per exporter is 3,055, going from a minimum of 10 to a maximum of 195,417. The median number of nonzero entries is less than half of one percent of the potential number. Baldwin and Harrigan (2007) have previously made the observation that many potential productdestination ‡ows are absent and relate the incidence of zeros to distance and importer size. Here we show that this is another important dimension of variation in the degree of success of exports. In the next section we systematically relate this to concentration and the prevalence of big hits.

# 2.2 Correlates of concentration

Our main focus is on the distribution of value across product-destination export ‡ows. However, we want to ...rst place the statistics above in context. To do so, we provide a brief descriptive analysis of export patterns and concentration ratios. We start by illustrating the very strong (log-linear) association between the number of nonzero product-destination export ‡ows and the value of total manufacturing exports, as can be seen in Figure 3. One way to succeed at exporting is to export more products to more places. This is a result of absolute advantage, which allows penetrating more markets with more products.

Larger economies export more products to more destinations by virtue of sheer size and diversity, and richer countries might have a better chance to penetrate more markets due to better technology. This relationship between the number of product-destination export ‡ows, size and income is well captured by the following regression, which we ...t to data on 135 countries log (number of nonzero export ‡ows) = �12:73<sup>percapita);</sup> (0:084)<sup>+ 0</sup> (0:<sup>:</sup> 043)<sup>64�log (GDP)+ 0</sup> (0:<sup>:</sup> 084)<sup>65�log (GDP</sup> where robust standard errors are reported in parentheses and R<sup>2</sup> = 0:8.<sup>12</sup> Poorer and smaller economies indeed penetrate less markets with less products.

However, in terms of explaining export success, this is not the entire story, as Figure 4 shows. Even after controlling for size (GDP) and income (GDP per capita) the association between export success and the number of nonzero product-destination export ‡ows remains

> 12 We could obtain GDP data for only 135 countries in our sample.

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strong. In addition, Table 3 shows that the number of nonzero export ‡ows is the most important factor: the beta coe¢ cient is three times larger and six times larger than those of GDP and GDP per capita, respectively. We take this feature into account in our model. We show how favorable productivity or demand shocks are necessary to overcome a threshold to realize a non-zero entry (for either product or destination). Therefore, countries that exhibit higher productivity levels also get to draw from a more favorable productivity distribution and penetrate more destinations with more products.

We now return to describe concentration of exports across products and destinations. Table 4 shows the bivariate correlations between all the concentration statistics given above. We see that the “top x”and “top x percent”concentration ratios are not measuring the same thing; they are sometimes actually negatively related to each other. The problem is that neither statistic is invariant to the number of nonzero product-destination ‡ows, which varies a lot across countries, as we have seen. For mechanical reasons, a larger number of nonzero product-destinations drives down the share of the “Top 3”or “Top 10”, but drives up the share of the “Top 1 percent” or “Top 10 percent” (exactly the same e¤ect on the concentration ratios is true for total manufacturing export value).

It is not clear whether we can construct an ideal concentration ratio when the number of nonzero product-destinations varies so much. Our main results below don’t rely on concentration ratios; instead, we characterize the entire shape of the distribution of nonzero entries. The statistics on ratios of the top product-destination to the 10th ranked or 100th ranked are closely related to the shares of the top 3 or top 10, and are related to the other variables in the same way.

Finally, Table 5 examines the partial correlations between the concentration ratios and the number of nonzero product-destinations export ‡ows and total manufacturing export value (both in logs). The interesting result is that controlling for the number of nonzero product-destination export ‡ows, total value is always positively associated with concentration (with both the top x and top x percent measures). It seems that the most successful exporters by total value also have the highest concentration ratios for top x products or top x percent of product-destination exports, conditional on the number of nonzero productdestination export ‡ows they have. Given the level of total export value, a larger number of product-destinations is associated with lower concentration. This makes sense, because 8
the same amount of export value must be distributed across more product-destinations. We take this into account in our estimation below, in which we allow destination-speci...c demand shocks.

The di¤erent e¤ects on concentration of the number of nonzero product-destination export ‡ows versus total export value can be related to absolute and comparative advantage. Countries that export a large number of products to many destinations exhibit absolute advantage, or higher productivity, on average. For a given exporter facing all possible destinations with entry ...xed costs, a higher average productivity will allow it to penetrate more destinations and export more products. But given the number of destinations an exporting country penetrates, higher values come from productivity draws that are high relative to the rest, which increases concentration. In our estimation procedure below we will take this into account.

# 2.3 The distribution of exports: mixed lognormal-power law

A country’s most successful products account for the bulk of its total export value and therefore the distribution of export values appears to be highly right-skewed. A candidate distribution to describe this distribution would be the Pareto distribution which, as detailed above, is used to explain a variety of highly skewed phenomena.

The Pareto distribution would imply a straight line on a log-log scale of export rank and export value. We plot these rank graphs for all countries but observe that we have a straight line only in the tails of the distributions as illustrated in Figure 5 for a selection of countries.<sup>13</sup> Eaton, Kortum, and Kramarz (2008) document similar rank graphs for French ...rms. Here we show that the shape holds for practically every country in our dataset. These graphs indicate that the whole distribution does not ...t the Pareto. But this is not unusual in economic applications of the Pareto distribution; the same holds for income, ...rm size and city size.<sup>14</sup> In all cases, a log normal distribution explains well the bottom of the distribution, whereas the Pareto distribution ...ts well the upper tail.

> 13 U.S. (an established industrialized OECD economy), Ghana (a poor African country), Argentina (a middle-income South American country), South Korea (a newly industrialized country, new to the OECD), China (the fast-growing giant) and Estonia (a small open transition economy). The data is by product category by destination and is demeaned by destination to control for the e¤ects of gravity and trade barriers.

> 14 For example, see Eeckhout (2004).

9
We simulated a mixed Pareto-log normal random variable and a log-normal random variable, and plotted their respective rank graphs in Figure 6. The simulated mixed Paretolog-normal random variable remarkably resembles our empirical distributions in Figure 5. A visual comparison of the two simulated random variables in Figure 6 indicates that the empirical graphs are “too straight”to ...t the log normal. In other words, the distribution of “success” across exports is so skewed that not even the highly skewed log normal can be used to characterize it; it seems to require some combination of the log normal –which is necessary at the least for the lower ranked product-destinations – and the power law (Pareto) –which is required for the top ranked product-destinations. The simulated mixed Pareto-log normal distribution seems to provide a better ...t.

To formally reject lognormality of the data we performed two di¤erent normality tests on log export values: the Kolmogorov-Smirno¤ test and a Normality test based on D’Agostino, Belanger, and D’Agostino (1990). Normality is rejected in 85% with the former and in 93% of the cases using the latter test. We conclude that the data cannot be described by a log-normal alone.

In what follows we construct a simple demand-supply framework that yields a distribution of export values which is determined by log normal demand shocks and Pareto productivity dispersion. Our innovation is to derive the lognormal-Pareto mixture distribution for export values and determine the relative role the power law part plays.<sup>15</sup>

# 3 Technology versus Demand

In this section we raise the following question: How much of the variation in export values is driven by technological dispersion in the source country versus demand shocks from destination countries? Our interpretation of demand is broad, and includes true taste shocks, ...nding a good match and successful marketing. Answering this question can advise policy on the types of tools that might –and those that might not –be relevant for promoting trade.

Suppose that demand shocks are more important. This would imply that the stress on ...nding one’s comparative advantage is misplaced, because other forces determine trade

> 15 Arkolakis (2008) develops a model with market penetration that takes into account marketing costs and matches the distribution of exports better than a simple Pareto or log normal can.

10
‡ows. An implication is that penetrating markets is more about marketing and ...nding a good match than high productivity. On the other hand, if technological dispersion is more important, and if it follows a power law, then it would be very hard to predict big hits, because the probability of predicting diminishes exponentially with the size of the hit (this is the de...nition of a power law).

To this end we lay out a demand-supply framework which is similar to the backbone of many modern trade models. This framework will allow us to estimate a parameter that governs the distribution of technological dispersion and a parameter that governs demand shocks. We examine empirically which accounts for a larger share of the variation in the data, country by country. Our results indicate that productivity explains a larger percent of variation in exports than demand shocks, and that this share is larger for less developed countries.

In order not to burden the reader with familiar structure we present only the necessary minimum of our framework and relegate the rest to the appendix.

# 3.1 Revenue and selection equations

Each destination country n is represented by one consumer, whose preferences over products are represented by a CES aggregator. Products are indexed both by the product’s "name" j and by source i.<sup>16</sup> Optimal price taking behavior gives rise to the familiar CES demand schedule where �n (i; j) is a preference shock, pn (i; j) is the price to serve product j from source i in destination n, pn and Yn are the price level and income in country n, respectively.<sup>17</sup> As usual, �> 1 is assumed, which is the same in all countries. It is also assumed that �n (i; j) is independent of xn (i; j).

In source country i, producer j may export to any destination country n, including domestic sales (n = i). Technology is linear in labor inputs. For a particular destination n,

> 16 This follows the organization of the data in Comtrade and it implies product di¤erentiation at the goodsource level. So widgets from Kenya are di¤erentiated from widgets from Costa Rica, even if they are both called "widgets" in the data. This is essentially an Armington assumption.

> 17 See the appendix for a more complete description.

11
it chooses pn (i; j) to maximize pro...ts subject to the demand schedule. cn (i; j) is the producer’s (constant) marginal cost, which is given by where w(i) are wages in country i and zn (i; j) is labor productivity. Kn (i) > 0 is a ...xed setup cost for business in i to penetrate the n market<sup>18</sup> . The implicit assumption here is that there is just one such producer of product j in source country i that exports to destination n, and there are no multiple-destination exporters. Thus, it is possible to produce slightly di¤erent products per market.<sup>19</sup> There are no other trade frictions.

Optimal pricing is a ...xed markup over marginal cost. Thus, revenue for producer j in source country i selling in destination n is given by Taking logs we get the following expression where �<sup>r</sup> 0<sup>= (1 ��) ln</sup> ��� 1<sup>,�w</sup> i<sup>= (��1) ln w(i),�py</sup> n<sup>= (��1) ln pn+ ln Yn.</sup> Equation (1) describes observed revenue, but does not take into account the fact that overall pro...ts need to be non-negative, if we observe revenue at all. The selection equation is Using the previous results, optimal pricing yields This expression means that the demand shock and productivity must overcome a threshold.

> 18 These capture making connections with potential buyers, adjusting the good to comply with local regulations, shipping costs, bribes at the border, etc’.

> 19 The data is aggregated over all producers anyway, so one can think that this represents a di¤erent mix of producers.

12
The threshold is increasing in the size of the ...xed cost for entry relative to the size of the destination market (Kn (i) =Yn) and increasing in the real wage in the source country in terms of the destination country (w(i)=pn). Taking logs and rearranging yields where �<sup>s</sup> 0<sup>= ln</sup> �<sup>�</sup> (� � 1)<sup>1���</sup> , �<sup>k</sup> in<sup>= ln Kn(i)and�w</sup> i<sup>and�py</sup> n<sup>werede...nedabove.</sup> �

# 3.2 Empirical speci...cation

We would like to estimate the relative contribution of zn (i; j) versus �n (i; j) to the variation of export revenues. To this end we will make some distributional assumptions that will enable us to write down a likelihood function for export revenue. We will then maximize it in order to retrieve the distribution parameters of the underlying productivity and demand shocks. Using this information, we will be able to decompose the variance.

We assume that �n (i; j) is distributed log-normal such that ln �n (i; j) is distributed normal with zero mean and variance v<sup>2</sup> .<sup>20</sup> We do not index v<sup>2</sup> by destination n, which re‡ects our assumption that in percent terms demand shocks should not be di¤erent across countries. We assume that zn (i; j) in source country i is distributed Pareto, where z > mi > 0 and ai > 0. Note that mi varies by source country.<sup>21</sup> It is assumed that � and z are independent.

Equations (1) and (2) can then be written as and where �inj = ln �n (i; j) is distributed normal for each destination with zero mean and

> 20 Eaton, Kortum, and Kramarz (2008) also include lognormal demand shocks in their analysis of French ...rms exporting behavior.

> 21 Helpman, Melitz, and Yeaple (2004) also assume a Pareto distribution for productivity, but do not let it change by source country.

13
variance v<sup>2</sup> ; and "inj = (� � 1) ln zn (i; j) is distributed conditional exponential where we condition on " � (� � 1) ln(mi).<sup>22</sup> De...ne as the exponential parameter for ". So "inj is distributed exponential with conditional mean (� � 1) ln(mi) + 1=�i.

Note that naively estimating (3) by least squares is not feasible. This is so because the mean of "inj is not zero in general, so the intercept �<sup>w</sup> i<sup>is not separately identi...ed.However,</sup> using maximum likelihood will allow us to overcome this issue.

By applying the Convolution Theorem (see appendix), we can characterize the distribution of �inj = �inj + "inj. Dropping the subscripts to ease notation, it turns out that the p.d.f. of � is given by where � is the normal CDF. In (5) we assumed that mi = 1 for all i. This assumption is innocuous because it does not a¤ect the estimates of v and �— we get the right ones regardless. In the appendix we present the distribution of � for a general m, discuss identi...cation issues in detail and prove this last claim.<sup>23</sup> Loosely speaking, this follows from the characteristics of the underlying distributions: m is just a location parameter, while v and � determine the shape of the distribution. We know that for the Pareto distribution, the shape parameter a remains the same for any truncation from below. Similarly, for the exponential distribution the shape parameter � is the same for any truncation from below. As long as in all source countries some ...rms draw productivities lower than the selection cuto¤ and do not enter, assuming mi = 1 does not matter. This amounts to saying that mi = 1 is low enough to ensure this.

Thus one can rewrite the revenue equation (3) and the selection equation (4) in terms

> 22 Notice that (� � 1) ln(mi) can be positive or negative, but since mi > 0 and �> 1, (� � 1) ln(mi) is bounded away from �1. This is not a standard exponential random variable, in the sense that " can be less than zero, but all the properties of the exponential distribution are preserved.

> 23 We thank Yijia Wang for useful discussions of this matter.

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of �.

# 3.3 Maximum likelihood estimation

We can rewrite the revenue equation to get an expression for �inj and then use it in the selection equation to get where t<sup>r</sup> in<sup>is the cuto¤ for observed revenue.Rearranging the expression for tr</sup> in<sup>and plugging</sup> it into the selection equation yields Of course, this follows directly from (6), if we replace rinj with its minimum value. Eventually, we have a modi...ed pair of equations for revenue (6) and selection (7) in terms of � . inj We estimate the model separately for each source country. Therefore, to ease notation we drop the index i of the source country. For a given source country equations (6) and (7) can be collapsed into the following representation and where �n = �<sup>r</sup> 0<sup>��w + �py</sup> n<sup>.Inprinciple,wecouldplugall�</sup> n<sup>coe¢cientsstraightintothe</sup> likelihood function, but estimating all �n dummy variables is not feasible, because they are not identi...ed. This follows from the fact that �nj has a non-zero mean. Luckily, we are not interested in these estimates. Therefore, we take the following route.

For each destination let 15
which is just the average export value per destination, and is the OLS estimator from a regression of export values on a set of destination-speci...c constants and a zero-mean error 0 term. The estimator bn<sup>isabiasedestimatorof�</sup> n<sup>,butweknowthatthebiasisequalto</sup> 1=�, i.e. E(b0n<sup>) = �</sup> n<sup>+ 1=�.Wetakeadvantageofthisinatwo-stepestimationprocedure</sup> in the following way.

- Step 2: De...ne

as our corrected � and truncation values, and maximize the following likelihood with respect to �<sup>b</sup> and bv. Note that<sup>e</sup> t<sup>r</sup> n<sup>= tr</sup> n<sup>�b</sup> 0n<sup>+1=�b, so that ftr</sup> n<sup>g are also parameters</sup> to be estimated. In principle, we could also maximize the likelihood with respect to ft<sup>r</sup> n<sup>g.However,aconsistentestimatoroftr</sup> n<sup>is</sup> We use<sup>b</sup> t<sup>r</sup> n<sup>toreplacetr</sup> n<sup>intheestimationprocedure,whichsimpli...estheestimation</sup> and is very robust.

In order to make sure that our procedure works, we performed Monte Carlo simulations and backed out the original parameters successfully. The initial values for the maximum likelihood numerical optimizer were chosen as empirical moments from the data. For each source country the initial value for � was chosen as the average trade ‡ow, demeaned by destination. The initial value for v was chosen as the standard deviation from that same data. Changing the initial values for the search within a reasonable range did not a¤ect the results.

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# 3.4 Estimation results and variance decomposition

Figure 7 plots the estimated � parameters by country against log GDP per capita. Almost all estimates of � fall within 0.5 and 1.<sup>24</sup> Recall our interpretation for � = a= (� � 1). This means that the technology distribution has remarkably similar Pareto coe¢ cients across income levels, assuming elasticities of demand are also similar. Typical estimates of � in similar settings are well above 2, in the range of 5-12 . This would place the estimate of the Pareto coe¢ cient, a, above 2, which is reassuring, because it restricts the primitive distribution of productivity in the model to have ...nite ...rst and second moments.

However, this would not imply that the level of the distributions of technology are the same in all countries. As discussed in the end of section 3.2, we do not estimate the mi parameters, which govern the actual level of productivity. Higher mi makes it more likely to penetrate any given destination market. Countries that penetrate more destinations must have higher mi. Nevertheless, the shape of the productivity distribution across countries is similar.

We want to decompose the variance of � into variance due to the normal demand shocks �, and the exponential technology component, ". We need to perform the variance decomposition under the condition that the selection equation holds. For a given cuto¤ of a speci...c destination n, we have where t (n) varies over destinations and captures the fact that the cuto¤ changes by destination. The covariance term is zero due to the assumed independence of � and ". Closed form solutions for the last two variance expressions are very complicated to derive, so we simulate these expressions instead.<sup>25</sup> The simulation procedure is described in the appendix. A complication arises from the fact that the cuto¤, t, varies by destination n. In order to address this issue, we decompose each conditional variance according to the variance version of The Law of Iterated Expectations as follows

> 24 Table A3 in the appendix presents all the estimates for �. The countries with extremely high estimates of � are Burundi (2.9) and Benin (2), both of which have few observations.

> 25 We thanks Jorg Stoye for suggesting this.

17
where X represents either � or ". We report the percent contribution to the variance of � of � and ": In doing so, we report two sets of results; once where we do not use weights in (9), and then using the number of observations per destination as weights.

Table 6 presents our main result: on average 66% of the variance is due to the Pareto part of the distribution.<sup>26</sup> In Table 7 we report some correlates of p� in order to investigate potential determinants of the percent of variance due to technology.

Figure 8 and column (1) of Table 7 indicate a negative relationship between the percent of variance due to technology and the log of GDP. As we know from above, large countries export to more destination and that should expose them to more demand shocks. Indeed, there is also a negative relationship between the number of product-destination export ‡ows and the percent of the variance due to technology, as can be seen in Figure 9 and in columns (2) and (3) of Table 7.

In column (4) of Table 7 we control for both the number of export ‡ows and for income (GDP per capita). We ...nd that the contribution of technology to the dispersion of export is in fact higher in richer countries, controlling for the number of destinations they export to.<sup>27</sup> This is a point of interest. We know that richer countries do export more products to more markets due to absolute advantage, which should expose them to more demand shocks. However, it seems that developing countries are more exposed to demand shocks, over and above their ability to penetrate more markets with more products.

# 4 Conclusion

In this paper we document the high degree of specialization in exports in a sample of 151 economies. Specialization is remarkably high in exporting manufactures, as in many other areas in economics. The distribution is remarkably skewed. We ...nd that very few "big hits" account for a disproportionate share of export volumes and can also explain high

> 26 Table A4 in the appendix shows the percent of the variance due to the Pareto component for all countries.

> 27 Given the result in Figure 7, it is not surprising that we did not ...nd a univariate correlation between income and p�.

18
degrees of specialization. We also ...nd that higher concentration (i.e., big hits) is positively correlated with higher trade volumes, after controlling for the number of products that are exported and destinations that are reached. Larger countries export more products to more destinations and so do richer countries, where the latter is driven by absolute advantage. Controlling for the number of product-destination export ‡ows, overall export volumes are positively correlated with higher concentration, which are explained by big hits. This is driven by comparative advantage.

We analyze the determinants of these big hits. We ...nd that technology explains most of the variation in export trade ‡ows, relative to demand shocks. This means that export success is mainly driven by technological dispersion, which also explains high levels of specialization. Developing countries export less products to fewer destinations, which helps explaining this. Exporting to more destinations exposes a country to more demand shocks that are uncorrelated with technological dispersion. Therefore, as a country penetrates more markets with more products, demand shocks from those markets and for those products account for a larger percent of variation –and hence concentration –in exports. When we control for the number of markets and products we ...nd that the relative contribution of technology to the variation in exports is lower in developing countries. This implies that developing countries are more exposed to demand shocks within the set of product-destinations that they export.

Our analysis leads us to some important conclusions that are relevant for policies that aim to promote trade. We ...nd that a power law plays an important role in the distribution of export value across possible product-destination pairs. This makes the ...erce debate about the relative weights on the government and the market in “picking winners” even more relevant than previously realized in the literature. A power law means that successfully picking a winner becomes less likely exponentially with the degree of success that is predicted. Over and above this mechanism, the higher relative exposure of developing countries to demand shocks, given their successful export ‡ows, implies an even smaller role for picking winners.

The "picking winners" debate is about two things: probability of discovering a "winner" and externalities from identifying the winner to other ...rms. The traditional argument for relying on free markets to decide what to produce is that they make possible a decentralized 19
search by myriads of entrepreneurs, and provide means for scaling up successful hits through reinvestment of pro...ts and ...nancing by capital markets. The probability of any one agent –such as a government policymaker –...nding which product-destination combination will be the big hit is very small. In fact, the track record of governments in picking winners is not great, as Lee (1996) demonstrates for Korea.<sup>28</sup> Hence, an alternative implication – nearly the opposite of the Hausmann-Rodrik conclusion – of the hyper-specialization phenomenon is that entrepreneurs and ...nanciers should be as unhindered as possible from any government intervention.

However, if there are externalities from the discovery of a "big hit" to other ...rms who can also export the same good-destination pair, then there is a market failure leading to too little discovery e¤ort by any one entrepreneur. This leads to the traditional argument for government intervention to subsidize "discovery", as Hausmann and Rodrik emphasized. Perhaps one could try to get the best of both worlds by designing a blanket government subsidy to all "discovery" e¤orts, while leaving the process of identifying the winners to private entrepreneurs. How to design such a policy in practice, and whether the traditional arguments fully apply to the stylized facts we have uncovered is far from de...nitive. Our main contribution is to show that ...nding winning hyper-specializations is even harder — and yet the rewards to ...nding these hyper-specializations are also even larger –than previously thought.

> 28 We are not saying that industrial policy in Korea did not contribute to its subsequent success. We only point out that the "picking winners" part of that policy has not proven to be successful.

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