Do Falling Iceberg Costs Explain Recent U.S. Export Growth? Revised August 2014 George Alessandriay Federal Reserve Bank of Philadelphia and University of Rochester [email protected] Horag Choi Monash University [email protected]

Abstract We study empirically and theoretically the growth of U.S. manufacturing exports from 1987 to 2007. We use plant-level data on exporters’export intensity to identify the changes in iceberg costs over this period. Given this change in iceberg costs, we …nd that a GE model with heterogeneous establishments and dynamic exporting decision from a sunk cost of starting to export is consistent with both aggregate U.S. export growth and the changes in the number and size of U.S. exporters. The model also captures the gradual response of U.S. exports to the cut in iceberg costs. A model with a static exporting decision generates substantially less trade growth and misses out on the timing of export growth. We also study the interplay between changes in the structure of manufacturing and trade. We …nd the growth in trade contributed little to the contraction in U.S. manufacturing while changes in the structure of manufacturing from changes in sectoral productivity, capital intensity, idiosyncratic shocks, and corporate taxation reduced US export growth by as much as 10 percent. JEL classi…cations: E31, F12. Keywords: Export Growth, Trade, Sunk Costs.

The authors thank Andrew Atkeson, Ariel Burstein, Satayjit Chatterjee, Joe Kaboski, Virgiliu Midrigan, Alex Monge, Richard Rogerson, Kim Ruhl, Yoto Yotov, and Kei-Mu Yi for helpful discussions and seminar participants at the SED Meetings in Prague and Istanbul, NYU, Toronto, Wisconsin, and the Federal Reserve Banks of Minneapolis, Philadelphia, and San Francisco for their useful comments. The views expressed here are those of the authors and do not necessarily re‡ect the views of the Federal Reserve Bank of Philadelphia or the Federal Reserve System. y Corresponding author: [email protected], Economics Dept. University of Rochester.

1. Introduction The world has become much more integrated. For instance, the share of US manufacturing shipments exported doubled from 1987 to 2007. This integration is generally attributed to a decline in trade barriers such as tari¤s, transport costs, and non-tari¤ barriers. This …nding though is mostly tautological since most empirical studies of trade integration use a gravity framework1 with a linear relationship between the trade share and trade costs. These studies then either estimate the trade elasticity using a measure of changes in some observed trade costs (Baier and Bergstrand, 2001) or estimate the decline in unobserved trade costs given a calibrated trade elasticity (Head and Ries, 2001, Jacks, Meissner, and Novy, 2010). These approaches do not directly distinguish between the di¤erent types of trade barriers2 , from per unit iceberg costs3 to …xed costs of entering or continuing in export markets, to taxes or subsidies, that are the crucial microeconomic determinants of export participation by heterogenous producers. They thus provide limited guidance to policymakers on the impact of various trade policies. In this paper, we propose an alternative approach to measuring the change in trade barriers and estimating the contribution of these changes to growing trade integration in a model with a non-linear relationship between trade costs and aggregate trade volumes. This approach builds on the new trade theories of producer heterogeneity and …xed export costs pioneered in a series of papers by Baldwin, Dixit and Krugman4 and generalized by Melitz (2003) along with the increased availability of rich micro data on the characteristics of exporters and non-exporters. We apply this approach to study US export growth from 1987 to 2007. This is a period of rapid but uneven export expansion and substantial changes in the structure of the manufacturing sector related to trade 1

For a comprehensive review of the literature on gravity equations see the recent handbook chapter by Head and Mayer (2013). 2 These studies try to identify the source of these trade barriers by regressing them on many features of bilateral trade partners such as distance, trade relations, language, colonial links, common currency, etc. In this way these barriers are converted into iceberg cost equivalents. 3 In what follows we do not distinguish between tari¤s and iceberg costs. 4 See, in particular, Baldwin (1988, 1989), Baldwin and Krugman (1989), and Dixit (1989a, b). These papers attribute the non-constant relationship between trade and relative prices to the dynamics of entry and exit from the export market.

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and longer term trends. Consistent with previous work, we …nd falling trade costs, speci…cally per unit iceberg costs, do indeed account for the dynamics of the US export share of manufacturing shipments. Unlike previous work though, this wasn’t guaranteed. These changes in iceberg costs could have induced di¤erent changes in export participation and the characteristics of exporters than predicted by the model. Indeed, we show it takes a model with a dynamic exporting decision from a sunk cost to match the data. Our …rst goal is to show how producer level data can be used to measure the decline in variable costs of trade. Speci…cally, we decompose the change in the share of manufacturing shipments exported into three margins. First, there is the familiar extensive margin that measures the change in the fraction of producers that export. Second, the exporter premium measures the change in the size of exporters relative to all establishments. Third, the export intensity margin measures the change in the fraction of shipments exported among exporters. In most theories, this last margin is primarily determined by iceberg costs and thus can be used to infer the change in iceberg costs. Previous work that decomposes export growth into just two margins5 by combining our last two margins only identi…es the change in variable trade costs under very speci…c parametric assumptions about the distributions of productivity and iceberg costs.6 It does not generalize to a dynamic environment. We also apply our decomposition to di¤erent time periods in our sample and …nd that there is a non-linear relationship between the change in iceberg costs and aggregate trade growth. Trade grows more relative to iceberg costs in the long-run (over 20 years) than the short-run (…rst 10 years). This evidence of an increasing response of trade to changes in iceberg costs is consistent with the evidence presented by Yi (2003) for US exports in periods that overlap with ours. The rising trade elasticity can be attributed to the slow changes in the stock of US exporters as suggested 5

See Eaton et al. (2004) and Chaney (2008). This approach only identi…es the change in iceberg costs when there is no sunk export cost and productivity is Pareto. 6

2

by Baldwin and Krugman (1989). Our second goal is to examine whether a standard heterogeneous producer model can capture the long run change in the export share of manufacturing shipments as well as non-linear growth in US export growth and changes in variable trade costs at di¤erent horizons. We …nd a model with a dynamic exporting decisions from a sunk cost in the spirit of Das, Roberts, and Tybout (2007) captures the timing and size of the increases in export participation and declines in the size premium of exporters. The benchmark model is a variation of our heterogenous producer general equilibrium model (Alessandria and Choi, 2011) extended to capture more aspects of plant heterogeneity and the changing aggregate structure of the US economy. Unlike our earlier paper, the focus here is on applying this model to a particular trade liberalization episode. This model has heterogenous producer’s moving in and out of export markets in response to idiosyncratic shocks to productivity and …xed export costs. There is a sunk cost of exporting as the cost of starting to export is larger than the per period cost of continuing. Numerous papers …nd this type of dynamic model more accurately captures the characteristics and micro dynamics of exporters. It has been suggested that this type of model can generate a di¤erent short-run and long-run trade response (Ruhl, 2008). We …nd this is indeed the case. The model provides a relatively close …t to the non-linear trade dynamics observed in the data. Some of the export growth from 1997 to 2007 re‡ects the time it takes for export participation to respond to the earlier declines in iceberg costs. We show that a simpler model with a static export decision is inconsistent with the observed overall change in trade and the change in export intensity. This is perhaps surprising since it is well-known that under certain assumptions this model has a gravity structure (Chaney, 2008). That is, there is linear relationship between the trade share and variable trade costs that is governed by the heterogeneity in producer ability. While this insight is true, it requires treating the producer distribution as a free parameter. In our quantitative assessment, by calibrating to US producer and

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exporter heterogeneity as well as exporter intensity, the model is disciplined in a way that restricts the trade elasticity. To make the static exporting model consistent with the data thus requires introducing a second set of aggregate shocks to the …xed cost of exporting. To capture the observed non-linear dynamics between iceberg costs and the export share requires these …xed cost shocks to be a relatively large driver of export growth in the second half of the time period studied. Thus, we …nd that abstracting from important elements of the producer export decision leads to very di¤erent conclusions about the changing nature of trade barriers. The third, and …nal, contribution of this paper is to estimate the two-way interaction between trade and structural change in manufacturing. It is well known that lowering iceberg costs will concentrate production in larger establishments: A prediction that is violated strongly in the data. Plants became considerably smaller in this period. It is also well-known that changes in producer heterogeneity will a¤ect trade growth. This is a potentially important consideration since the period studied included substantial changes in the manufacturing sector that may or may not be related to international trade. To evaluate the interplay between trade and manufacturing we consider four particular changes in the manufacturing sector. First, manufacturing’s share of overall employment has fallen drastically, while its share of value added has held roughly constant. This implies relatively strong productivity growth in manufacturing and a less than unitary elasticity of substitution between manufacturing and non-manufacturing. Second, within manufacturing, the size distribution shifted away from large scale operations. This shift to smaller manufacturing operations at a time of growing trade integration is a puzzle for heterogeneous producer models since they predict the opposite changes. We capture some of this shift to smaller plants by making a fraction of entry costs paid in …nal goods. With the biased productivity growth in manufacturing this lowers the average plant size; however, the shift to smaller establishments re‡ects more than a decline in the mean plant but also a change in the shape of the distribution. To capture this feature of the data we allow the idiosyncratic

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shock process facing …rms to be a bit less volatile. Third, capital intensity has changed both within manufacturing and between manufacturing and non-manufacturing. This requires allowing capital intensity to vary across sectors and by size. Fourth, there was a substantial increase in the tax rate on pro…ts from export sales. This policy does not change iceberg costs but does change the bene…ts from exporting. It is particularly relevant since it highlights the rich array of policies used by policymakers.7 In terms of the e¤ects of trade on manufacturing, we …nd that the observed decrease in iceberg costs account for only about 3 percent of the decline in manufacturing employment and counterfactually predicts production should be concentrated in larger establishments. In terms of the e¤ects of structural change in manufacturing on trade, we …nd that changes in idiosyncratic productivity and the taxation of exporter pro…ts lower overall export growth by about 10 percent (roughly equally split). We …nd the changes in capital intensity and sectoral productivity growth have almost no impact on aggregate export growth, but do a¤ect our measures of the margins of export growth, particularly among relatively large manufacturers and explain most of the shift to smaller scaled establishments. We undertake the …rst empirical and quantitative examination of the dynamics of U.S. aggregate and establishment-level trade ‡ows. Previous work relating aggregate trade ‡ows to establishmentlevel heterogeneity primarily focuses on the cross-section of export participation. For instance, Bernard, Eaton, Jensen, and Kortum (2003) study export participation among U.S. manufacturers in a version of the Eaton and Kortum (2002) model extended to allow for Bertrand competition,8 while Alessandria and Choi (2011) study export participation among U.S. manufacturers9 in a model with a sunk export costs. These papers examine the counterfactual impact of changes in trade policy 7

One could consider this a change in trade barriers rather than a structural change in manufacturing. Alvarez and Lucas (2007) also study the role of producer heterogeneity for trade but in a model in which there is no notion of an establishment. Hence, all heterogeneity can be thought of as being at the industry level. 9 In addition to having a di¤erent focus than our companion paper, on the model side here we must explicitly take into account the interplay between changes in international trade and the structure of manufacturing. 8

5

on aggregate and establishment trade ‡ows in their models. In terms of examining observed changes in trade ‡ows,10 Bernard, Jensen, and Schott (2006) use an empirical model to show that across industries in the U.S. from 1987 to 1997, declines in measured trade costs are associated with an increased likelihood of exporting and an increase in sales by exporters. Unlike their analysis, which focuses on the qualitative predictions of heterogeneous plant models for trade growth, we focus on quantitative predictions of the model for the magnitude and timing of aggregate and disaggregate changes in exports. Given the prominence of heterogeneous plant models in trade policy analysis,11 evaluating these models is an important next step in their use. Our paper is also related to a number of papers that study the growth in trade. Some important papers that attribute trade growth to changes in income, tari¤s, and trade costs include Baier and Bergstrand (2001), Yi (2003), and Bridgman (2008). Hummels (2007) identi…es the challenges in measuring the change in trade costs, showing that the decline in aggregate measures of trade costs are understated because they do not take into account how the decline in relatively expensive air freight has led to a massive expansion of air freight. A second line of research uses models with …xed costs of trade to understand trade dynamics and international business cycle ‡uctuations. Early partial equilibrium work by Baldwin (1988), Baldwin and Krugman (1989) and Dixit (1989a, b) develop models of export decisions with an exogenous exchange rate process. Roberts and Tybout (1997), Das, Roberts, and Tybout (2007, henceforth DRT) develop these models to identify an important role of sunk costs in the exporter decision. Alessandria and Choi (2011) embeds the DRT model into a neoclassical growth model and use it to estimate the welfare e¤ects of changes in tari¤s. The paper is organized as follows. The next section describes the change in the share of U.S. manufacturing output exported and the changes in export participation, the characteristics of exporters, and iceberg trade costs. In section 3 we develop a two-country dynamic general equilibrium 10

Bernard and Jensen (2004) use similar data to decompose U.S. export growth at the establishment level for the period 1987 to 1992. 11 Some additional papers studying trade policy in heterogeneous plant models include Roberts and Tybout (1997), Melitz (2003), Ruhl (2008), Das, Roberts and Tybout (2007), and Atkeson and Burstein (2010).

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model with a dynamic exporting decision. Section 4 discusses the calibration of the model. Section 5 examines the success of the model at explaining the changes in exports at the aggregate and disaggregate level from the observed change in iceberg costs. Section 6 considers the e¤ect of the changes in manufacturing on our results. Section 7 examines how well a heterogenous plant model with a static exporting decision approximates the …ndings of the richer dynamic model. Section 8 concludes.

2. U.S. Export Growth: Aggregate and Disaggregate We describe some of the changes in U.S. manufacturing exports from 1987 to 2007. This is a period in which exports grew quite fast relative to overall shipments and so the US become more globally integrated. We consider data on exports from both the Census of Manufactures and Customs.12 The Census data allows us to examine how the characteristics of exporters and nonexporters changed. Table 1 summarizes the key changes in the manufacturing exports over this period. To account for the role of changes in export participation in aggregate export growth, suppose that only n of the N manufacturing establishments export. Let establishment i have total sales salesi = di + exi with di and exi being the domestic and export sales then the ratio of exports to total sales can be decomposed as, Pn exi Exports = PNi=1 = Total sales i=1 salesi

Pn ex =n Pn i=1 i i=1 salesi =n

Pn

i=1 salesi =n

PN

i=1 salesi =N

!

n : N

Over time, taking logs, the change in the ratio of exports to total sales can be decomposed into three components, Export intensity Exporter premium Export share Export participation = + : z z }| { }| { + z }| { z }| { X X exy (n=N ) ex=sales sales =sales

All of these components can be measured using data from the Census of Manufactures. For plants 12 The data analysis is based on special tabulations by the Census using the 1987, 1992, 1997, 2002, and 2007 Census of Manufactures.

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with 100 or more employees, the export share increased 61.1 percent. This represented a 44.9 percent increase in exporter intensity, a 21.4 percent decline in the exporter premium, and a 37.7 percent increase in export participation. Thus, in an accounting sense,13 slightly more than one-quarter of U.S. export growth was an endogenous response of export participation and the size of exporters to changes in exporter intensity. The same decomposition can be applied to the full sample of plants (that is including those with less than 100 employees). For this decomposition the exporter premium and participation margins are combined since this survey is not well-suited to measuring export participation by the smallest plants (most small plants are generally not surveyed). The measure of exporter intensity is less likely to be a¤ect by the survey methodology since it does not change much with size. Moreover, small changes in export participation by small plants will have a large e¤ect on the exporter premium and export participation but not aggregate trade ‡ows since plants with less than 20 employees account for 69 percent of establishments but only 4.7 percent of sales (based on 2007 data).14 Focusing on all plants, aggregate exports grow slightly more (67.7 percent vs 61.1 percent) and exporter intensity increases slightly less (44.6 percent vs. 44.9 percent). Thus, aggregate exports grew 53.1 percent more than export intensity alone. Most decompositions of export growth will divide export growth into an intensive (combining export intensity with the exporter premium) and extensive margin (export participation). The decomposition into three margins has the advantage that it allows us to identify the change in iceberg costs and clari…es how changes in the characteristics of exporters and non-exporters can a¤ect trade. In terms of identifying the change in iceberg costs, in all symmetric models with a constant 13 We say in accounting sense since changes in the size distribution of plants from trade and changes in the size of manufacturing establishments a¤ect the exporter premium holding export participation constant. 14 Indeed, a 1 percentage point increase in export participation by plants with <20 employees has almost a fully o¤setting e¤ect on the growth in export participation (+3.0%) and the reduction of the export premium (-3.0%).

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elasticity of demand and an iceberg trade cost15 the change in export intensity is driven only by changes in the iceberg cost alone16 exi

di = (1

)

:

While the change in export intensity provides an estimate of the change in variable trade costs,17 because of the other two margins there is not a direct link between the change in iceberg trade costs and aggregate export growth. This is particularly likely if it takes time, as is conventionally thought, for export participation to respond to a change in iceberg costs (which include tari¤s). The typical gravity approach of backing out trade costs from aggregate trade ‡ows would attribute the slow exporter entry to additional declines in iceberg cost. Indeed, when we split the sample we see that the ratio of the change in export growth to the change in exporter intensity is smaller from 1987 to 1997 than over the whole period. This decomposition also clari…es how the characteristics of exporters a¤ect trade. One can clearly see that any changes in the manufacturing sector that a¤ect big producers di¤erently from small producers will a¤ect the exporter premium and trade holding export participation constant. Given that the period considered coincides with large changes in the size and structure of manufacturing this is a source of changes in export growth that must be controlled for in the quantitative work. The change in exports can also be measured with customs data. These are shipment-level data and thus are likely to provide a more accurate measure of overall U.S. export growth than the survey based census. The concern with this data is that an increase in the costs of getting goods from the manufacturer to the port will increase exports in the customs-level data but will not a¤ect 15

This relationship holds even in a model with vertical specialization. Changes in relative demand across countries also will determine export intensity. However, from an establishment’s standpoint, it doesn’t matter whether the change in export intensity is from a drop in iceberg trade costs or an increase in the relative size of the foreign market. For this reason, in the next sections all of the changes in export intensity are attributed to changes in iceberg costs in a two-country symmetric world. 17 Direct measures of the change in iceberg costs exist but vary substantially. For instance, according to Hummels (2007) since 1990 air freight and ocean liner rates have fallen by about one-third. This decrease in transportation costs has also been associated with a shift toward more air freight, suggesting smaller declines in measured shipping costs. Moreover, Anderson and van Wincoop (2004) …nd that direct measures of trade costs are small compared with indirect measures implied by trade ‡ows and theory. 16

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the measure of exports from the census. Additionally, goods exported by intermediaries will also be included in the customs data. The seventh column in Table 1 shows that using customs data, the ratio of U.S. exports to manufacturing shipments grew 74.3 log points compared to 67.7 log points for the census data.18 Removing the change in internal distribution margins reduces the increase in exports to 71.3 percent.19 The remaining gap of about 4 percentage points between the census and the customs data may arise from measurement problems in the Census data (for all plant sizes) or a rising importance of intermediated trade by wholesalers. Thus, in what follows we view models that overpredict trade relative to the census data more favorably than those that underpredict all else equal. In what follows we ask: Given the characteristics of the U.S. manufacturers in 1987 and the observed changes in trade costs from 1987 to 2007, can the benchmark model of export participation and dynamics explain the change in overall exports and the characteristics of exporters in the U.S.?

3. The Model A variation of the dynamic model of exporting and trade developed in Alessandria and Choi (2011) is presented. This model contains the two key features of the Melitz (2003) model20 of exporting: producer heterogeneity and …xed costs of exporting. Unlike in Melitz, producers face uncertainty over both productivity and …xed export costs and sunk export costs as originally envisioned by Baldwin, Dixit, and Krugman. Each period a mass of existing establishments is distributed over productivity, …xed costs, countries, and export status. Idiosyncratic shocks to productivity and …xed export costs generate movements of establishments into and out of exporting. Unproductive 18

Our measure of exports excludes re-exports - essentially foreign products that are exported with no value added. Re-exports have become relatively more important over time and including the growth of re-exports would boost export growth to 82 log points. 19 According to the census’ Direct Exports report, in 2009 the wholesale margin added about 10.5 percent to the cost of goods. We assume that these margins increased by about 30 percent from 1987 to 2007, which is the same amount by which the ratio of wholesale to manufacturing shipments increased. 20 The Melitz model is a general equilibrium model of plant heterogeneity and exporting. It embeds the decision to export, studied in the partial equilibrium models of Baldwin and Krugman (1989), Dixit (1989a, b) and Roberts and Tybout (1997), into the general equilibrium model of plant heterogeneity, exit, and entry of Hopenhayn and Rogerson (1993). Despite its antecedents in models of plant dynamics, it is usually formulated with no meaningful plant dynamics.

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establishments also shut down,21 and new establishments are created by incurring a sunk cost. We focus on this dynamic variation of the Melitz model, since work by Das, Roberts, and Tybout (2007) and Alessandria and Choi (2011) …nd that it more accurately captures plant-level exporter dynamics. The model is extended to be made consistent with the data. There are two symmetric countries, home and foreign. Each country is populated by a continuum of identical, in…nitely lived consumers with unit mass. Consumers inelastically supply L units of labor each period. In each country there are two intermediate good sectors, tradable and non-tradable, denoted T or N . In each sector, there is a large number of monopolistically competitive establishments, each producing a di¤erentiated good. The mass of varieties in the tradable and non-tradable goods sectors are NT;t and NN;t , respectively. Foreign variables are denoted with an asterisk. A non-tradable good producer uses capital and labor inputs to produce its variety, whereas a tradable good producer uses capital, labor, and material inputs to produce its variety.22 In each sector, establishments di¤er in terms of total factor productivity and the markets they serve. The non-tradable sector is necessary to capture the large changes in the sectoral composition of output. All establishments sell their product in their own country, but only some establishments in the tradable good sector export. When an establishment in the tradable good sector exports, the establishment incurs some international trading cost, an ad valorem transportation cost23 with the rate of .24 Additionally, an establishment has to pay a …xed cost to export its goods abroad. We follow Dixit (1989a, b), Baldwin and Krugman (1989), and Roberts and Tybout (1997) and 21

Unlike the Melitz model, our model does not have …xed costs of continuing to produce each period. Instead, we capture the higher exit rates of small establishments in the shock process. 22 Materials are included in the tradable sector for two reasons even though the use of materials does not a¤ect the trade share in the tradable sector directly. First, the model with material inputs in the tradable sector is consistent with the observation that trade as a share of gross output is considerably smaller than trade as a share of value-added. Second, with non-unitary substitution between non-tradables and tradables materials a¤ect the allocations across sectors. 23 All iceberg costs are attributed to physical transportation costs rather than a combination of transport costs and tari¤s. This distinction matters primarily for welfare but has almost no impact on the division of activity across countries. 24 ’Iceberg’transportation costs require 1 + units to be shipped for 1 unit to arrive at the destination.

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allow the …xed cost of starting to export to di¤er from the cost to stay in the export market. In particular, the size of the …xed cost depends on the producer’s export status in the previous period and an idiosyncratic shock

. To start exporting, an establishment must incur a relatively high

up-front sunk cost e f0 > 0 and then can sell any amount in the export market in the next period. For an establishment that is currently exporting, to continue exporting into the following period it must incur its idiosyncratic period-by-period …xed continuation cost e f1 , where f1 < f0 . If an establishment does not pay this continuation cost, then it ceases to export. In future periods, the establishment can begin exporting only by incurring the entry cost e f0 where

is a new draw.

These costs are valued in a combination of domestic …nal goods, gf ; and domestic labor, lf ; with a Cobb-Douglas function, gf lf1

))1

, and have a unit cost PE = (P= ) (P W= (1

; where P

and W are the price of the …nal goods and real wage rates, respectively. The cost of exporting implies that the set of goods available to consumers and establishments di¤ers across countries and is changing over time. The …xed costs is incurred in the period prior to exporting so that the set of foreign varieties is …xed at the start of each period. Domestic consumers own establishments. A potential establishment makes a once and for all decision to enter a sector by incurring fE units of the entry good. Entrants start producing and selling in the next period. Establishments di¤er by their technology, export status, sector, …xed costs, and nationality. The measure of home country tradable establishments with technology z, export status, m = 1 for exporters and m = 0 for non-exporters, and …xed cost shock, , equals

T;t (z;

; m).

In each country, competitive …nal goods producers purchase intermediate inputs from those establishments actively selling in that country.25 The cost of exporting implies that the set of goods available to competitive …nal goods producers di¤ers across countries. The entry and exit of exporting establishments implies that the set of intermediate goods available in a country is changing over time. The …nal goods are also used for domestic consumption and investment. 25

The …nal good production technology does not require capital or labor inputs. It is used to regulate a country’s preferences over local and imported varieties.

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There exists a one-period single nominal bond denominated in the home currency.26 Let Bt denote the home consumer’s holding of the bonds purchased in period t. The bond pays 1 unit of home …nal good in period t + 1. Let Qt denote the nominal price of the bond Bt . We focus on symmetric policies and so the price level in each country can be normalized to P = 1 and B = 0: With capital and trade barriers, the measure of establishments by productivity, export status, …xed cost, sector and source country is the aggregate state of the economy. For notational ease, we omit these state variables but maintain the time subscript to clarify that we are not dealing with a steady state. A. Consumers Home consumers choose consumption and investment to maximize their utility: VC;0 = max

1 X

t

U (Ct ) ;

t=0

subject to the sequence of budget constraints, Ct + Kt + Qt Bt where

Wt Lt + Rt Kt

1

+ (1

) Kt

1

+ Bt

1

+

t;

2 (0; 1) is the time discount factor; Ct is the consumption of …nal goods; Kt

1

is the capital

available in period t; Qt and Bt are the price of bonds and the bond holdings; Wt and Rt denote the real wage rate and the rental rate of capital;

is the depreciation rate of capital; and

t

is the

sum of real dividends from the home country’s producers. The …rst-order conditions for home consumers’utility maximization problems are Qt = and 1 =

UC;t+1 UC;t

(Rt+1 + 1

UC;t+1 UC;t ;

) where UC;t denotes the derivative of the utility function with respect

to its argument. The price of the bond is standard. The foreign consumer’s problem is analogous. Foreign country prices and allocations are represented with an asterisk. 26

Our focus will be on a symmetric model and so there is no reason for intertemporal trade. Nonetheless, we introduce the possibility of intertemporal trade for completeness of exposition and to introduce the stochastic discount factor Q:

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B. Final Good Producers In the home country, …nal goods are produced combining home and foreign intermediate goods. A …nal good producer can purchase from any of the home intermediate good producers but can purchase only from those foreign tradable good producers active in the home market. The …nal good can be produced by combining a composite good produced of tradables, DT , and a composite good produced of non-tradables, DN ; using a CES function. 1

(1)

1

Dt = a DT;t + (1

1

a) DN;t

The production technologies of the composite tradable and non tradable goods are,

(2)

DT;t =

1 Z X

d yH;t (z; ; m)

m=0 z

+ (3)

DN;t =

Z

z

Z

d yF;t (z; ; 1)

z

d yN;t (z)

1

1

T;t (z;

; m) dzd 1

T;t (z;

; 1) dzd

;

1

1

N

(z) dz

;

d (z; ; m) and y d (z; ; 1) are inputs of intermediate goods purchased from a home tradable where yH;t F;t

good producer with technology z, …xed cost shock

; and export status m and foreign tradable

d (z) is the input of intermediate good purchased exporter with state (z; ; 1); respectively, and yN;t

from a home non-tradable good producer with technology z. The elasticity of substitution between intermediate goods within a sector is

> 1.

The …nal goods market is competitive. Given the …nal good price at home Pt , the prices charged by each type of tradable good, the …nal good producer solves the following problem

(4)

max

F;t

= Dt Z

z

1 Z X

m=0 z

d PH;t (z; ; m) yH;t (z; ; m)

d PF;t (z; ; 1) yF;t (z; ; 1)

14

T;t (z;

T;t (z; ; 1) dzd

; m) dzd Z

z

d PN;t (z) yN;t (z)

N;t (z) dz;

subject to the production technology (1), (2), and (3).27 Here PH;t (z; ; m) and PF;t (z; ; 1) are the prices of tradable intermediate goods produced by a home producer with (z; ; m) and a foreign producer with (z; ; 1) ; respectively, and PN;t (z) is the price of non-tradable intermediate goods produced by a home producer with z: Solving the problem in (4) gives the input demand functions,

(5)

d yH;t (z; ; m) = a

(6)

d yF;t (z; ; 1) = a

PH;t (z; ; m) PF;t (z; ; 1)

PT;t

PT;t

d yN;t (z) = (1

(7)

(PT;t )

PT;t

PN;t (z)

a)

Dt ; Dt ;

PN;t

PN;t

Dt ;

where the price indices are de…ned as

PT;t =

(8)

1 Z X

m=0 z

+ (9)

PN;t =

(10)

Z

Z

T;t (z;

; m) dzd 1

1

z

z

PH;t (z; ; m)1

PF;t (z; ; 1)

1

T;t (z;

; 1) dzd

;

1

1

PN;t (z)

1

;

N;t (z) dz

h 1 + (1 Pt = 1 = aPT;t

1 a) PN;t

i

1 1

:

Final goods are used for consumption, investment, …xed export costs, and new establishments. C. Intermediate Good Producers Intermediate good producers di¤er by their sector, productivity, export costs,28 and export status. An incumbent’s idiosyncratic productivity, z, and …xed cost shock, , follow a …rst-order Markov process with a transition probability

(z 0 ; 0 jz; ), the probability that the productivity

of the establishment will be (z 0 ; 0 ) in the next period, conditional on its current productivity (z; ), provided that the establishment survived. An entrant draws productivity next period based 27 Notice that the production function is de…ned only over the available products. It is equivalent to de…ne the production function over all possible varieties but constrain purchases of some varieties to be zero. 28 This implicitly assumes non-tradable intermediates export costs are in…nite and hence dropped from the notation.

15

on

E

(z 0 ; 0 ). An establishment’s exogenous survival probability, ns (z) 2 [0; 1] ; depends on its

productivity, z. Non-Tradable Good Producers The problem of a non-tradable good producer from the home country in period t with technology z is to choose its current price PN;t (z), inputs of labor lN;t (z) and capital kN;t (z) ; given a CobbDouglas production technology, yN;t (z) = ez kN;t (z) lN;t (z)1

(11)

VN;t (z) = max

N;t (z) + ns (z) Qt

Z

VN;t+1 z 0

z 0 jz dz 0 ;

z0

(12)

N;t (z)

= PN;t (z) yN;t (z)

Wt lN;t (z)

to solve

Rt kN;t (z)

subject to the production technology, and the constraint that the supply of the non-tradable goods, d (z) in (7). yN;t (z) equals the demand by …nal good producers yN;t

Tradable Good Producers A producer in the tradable good sector is described by its technology, …xed cost shock, and export status, (z; ; m). Each period, it chooses current prices, PH;t (z; ; m) and PH;t (z; ; m), inputs of labor lT;t (z; ; m) ; capital kT;t (z; ; m) ; and materials xt (z; ; m) ; and the next period’s export status, mt+1 (z; ; m). Total materials, xt (z; v; m); are composed of tradable intermediate goods with the CES function as in (2). The producer has a Cobb-Douglas production technology, h (13) yT;t (z; ; m) = ez kT;t (z; ; m) lT;t (z; ; m)1 The value of a producer is 1 0 (14) VT;t (z; ; m) = max VT;t (z; ; m) ; VT;t (z; ; m)

16

i1

x

xt (z; ; m)

x

:

where the value of exporting in period t + 1 is 1 VT;t (z;

; m) = max

T;t (z;

; m) PE;t fm e +ns (z) Qt

Z

z0

VT;t+1 z 0 ; 0 ; 1 0

z 0 ; 0 jz;

dz 0 d 0 ;

and the value of not exporting in period t + 1 is 0 VT;t (z;

; m) = max

T;t (z;

; m) + ns (z) Qt

Z

z0

VT;t+1 z 0 ; 0 ; 0 0

z 0 ; 0 jz;

dz 0 d 0 :

Period pro…ts are de…ned as

(15)

T;t (z;

; m) = PH;t (z; ; m) yH;t (z; ; m) + PH;t (z; ; m) yH;t (z; ; m) Wt lT;t (z; ; m)

Rt kT;t (z; ; m)

PT;t xt (z; ; m) :

The producer makes decisions subject to the production technology (13) and the constraints that the supply to home and foreign tradable goods markets, yH;t (z; ; m) and yH;t (z; ; m) with yT;t (z; ; m) = yH;t (z; ; m) + (1 + ) yH;t (z; m), is equal to the demand by …nal good producers from (5) and the foreign analogue of (6), and demand by intermediate good producers for material inputs. Clearly, the value of a producer depends on its export status and is monotonically increasing and continuous in z given m and , and the states of the world. Moreover, VT1 intersects VT0 from below as long as there are some establishments that do not export. Hence, it is possible to solve for the cuto¤ productivity at which an establishment is indi¤erent between exporting or not exporting; that is, the increase in establishment value from exporting equals the cost of exporting. This level of establishment productivity di¤ers by the establishment’s current export status. For an export cost , the critical level of technology for exporters and non-exporters, z1;t ( ) and z0;t ( ), satisfy

(16)

1 0 VT;t (z1;t ( ) ; ; 1) = VT;t (z1;t ( ) ; ; 1) ;

(17)

1 0 VT;t (z0;t ( ) ; ; 0) = VT;t (z0;t ( ) ; ; 0) :

17

D. Entry Each period, a new establishment can be created by incurring fE entry costs. Establishments incur these entry costs in the period prior to production and must choose one sector to enter. Once the entry cost is incurred, establishments receive an idiosyncratic productivity shock from the initial distribution

E

(z 0 ; 0 ). Entrants are free from death shocks. New entrants can not export in their

…rst productive period. Thus, the entry conditions are

(18) (19)

E VT;t

=

E VN;t =

PE;t fE + Qt

Z

VT;t+1 z 0 ; 0 ; 0

z0

PE;t fE + Qt

Z

0

VN;t+1 z 0

z0

E

z 0 dz 0

E

z0;

0

dz 0 d

0

0;

0:

In the non-tradable good sector, let NN E;t denote the mass of entrants in period t and let the mass of incumbents be NN;t =

R

z

N;t (z) dz:

In the tradable sector, let NT E;t denote the mass

of entrants in period t, while the mass of incumbents is NT;t . The masses of exporters and nonexporters are then N1;t =

R

z

T;t (z;

; 1) dzd ; and N0;t =

R

z

T;t (z;

; 0) dzd ; and the mass

of establishments in the tradable good sector equals NT;t = N1;t + N0;t : The …xed costs of exporting imply that only a fraction nX;t = N1;t =NT;t of home tradable goods are available in the foreign country in period t. The starter ratio, n0;t+1 ; denotes the the fraction of establishments that start exporting among non-exporters and the stopper ratio, n1;t+1 , denotes the fraction of exporters who stop exporting among surviving establishments.29 E. Aggregate Variables Aggregate investment, It ; is given by the law of motion for capital It = Kt

(1

) Kt

1:

Nominal exports and imports, EXtN and IMtN ; are equal to the sum of nominal exports by home and foreign exporters respectively. Nominal GDP of the home country is de…ned as the sum of value added from non-tradable, tradable, and …nal goods producers, YtN = Ct + It + EXtN 29

The evolution of the distribution is described in the technical appendix.

18

IMtN :

The total labor used for production, LP;t ; is given by (20) LP;t =

1 Z X

lT;t (z; ; m)

T;t (z;

m=0 z

; m) dzd +

Z

lN;t (z)

z

N;t (z) dz:

Labor hired by exporters, LX;t ; and new establishments, LE;t ; to cover …xed costs are given by # "Z Z Z Z 1 1 PE;t (21) LX;t = (1 ) f1 e T;t (z; ; 1) dzd : f0 e T;t (z; ; 0) dzd + Wt z1;t ( ) z0;t ( ) (22) LE;t = (1

) fE

PE;t Wt

(NT E;t + NN E;t ) :

From (21), we see that the trade cost depends on the exporter status from the previous period. Final goods used for …xed costs by exporters , GX;t ; and new establishments, GE;t ; are given by # "Z Z Z Z 1 1 f0 e T;t (z; ; 0) dzd + f1 e T;t (z; ; 1) dzd : (23) GX;t = PE;t z0;t ( )

z1;t ( )

(24) GE;t = fE PE;t (NT E;t + NN E;t ) : Aggregate pro…ts are equal to the di¤erence between pro…ts and …xed costs,

t

=

F;t +

1 Z X

T;t (z;

; m)

m=0 z

T;t (z;

; m) dzd +

Z

N;t (z)

z

N;t (z) dz

GE;t + GX;t

:

F. Equilibrium De…nition In equilibrium variables satisfy several resource constraints. The …nal goods market clearing conditions are given by Dt = Ct + It + GX;t + GE;t and Dt = Ct + It + GX;t + GE;t . Each individual goods market clears; the labor market clearing conditions are L = LP;t + LX;t + LE;t and the foreign analogue; and the capital market clearing conditions are Kt

1

=

1 Z X

m=0 z

kT;t (z; ; m)

T;t (z;

; m) dzd +

Z

kN;t (z)

N;t (z) dz

z

and the foreign analogue. Pro…ts are distributed to shareholders,

t,

and the foreign analogue. The

international bond market clearing condition is given by Bt + Bt = 0. An equilibrium of the economy is a collection of allocations for home consumers Ct , Bt , Kt ;

19

allocations for foreign consumers Ct , Bt , Kt ; allocations for home …nal good producers; allocations for foreign …nal good producers; allocations, prices, and export policies for home tradable good producers; allocations, prices and export decisions for foreign tradable good producers; labor used for exporting costs in both home and foreign; labor used for entry costs; real wages Wt ; Wt ; real rental rates of capital Rt , Rt ; and bond prices Qt that satisfy the following conditions: (i) the consumer allocations solve the consumer’s problem; (ii) the …nal good producers’allocations solve their pro…t maximization problems; (iii) the tradable good producers’allocations, prices, and export decisions solve their pro…t maximization problems; (iv) the non tradable good producers’allocations and prices solve their pro…t maximization problems; (v) the entry conditions for each sector holds; and (vi) the market clearing conditions hold.

4. Calibration We now describe the functional forms, parameter values, and targets of our benchmark economy. Our approach departs slightly from that in Alessandria and Choi (2011) in that we also consider the changes in some aggregates related to trade and the structure of manufacturing and allow for more general functional forms in the substitution across sectors, the labor content of …xed costs, and the shocks to …xed export costs. The parameter values used in the simulation exercises are reported in Table 2. The instantaneous utility function is U (C) = C 1

= (1

) ; where 1= is the

intertemporal elasticity of substitution. The discount factor, ; depreciation rate, ; and risk-aversion, ; are standard in the literature, = 0:96;

= 0:10; and

= 2. Labor supply is normalized to L = 1.

The characteristics of establishments are targeted to match those of U.S. manufacturing establishments in 1987 and a set of moments about establishment dynamics and exporter transitions. The establishment size distribution is largely determined by the structure of shocks, the elasticity of substitution, ; and …xed costs. We also target how export intensity changes from 1987 to 2007. The appendix shows the shocks and costs can be rewritten so the size distribution is invariant to 20

:30 Atkeson and Burstein (2010) make a similar adjustment. The productivity process is the same in the tradable and non-tradable sectors. An incumbent’s productivity evolves as z 0 =

" z +";

with "

iid

N (0;

2 ): "

The assumption that productivity follows an

AR(1) with shocks drawn from an iid normal distribution implies that this conditional distribution follows a normal distribution

z

unconditional distribution z 0 =

(z 0 jz) = N

E

" z;

+ "E ; with "E

iid

2 "

. Entrants draw productivity based on the 2= "

N 0;

1

2 "

where and

E

< 0 is chosen

to match the observation that entrants start out small relative to incumbents. Fixed cost shocks are log normally distributed,

N (0;

2

(z)): Similar to Das, Roberts, and

Tybout (2007), the standard deviation of shocks depends on a plant’s productivity. Speci…cally, it is a convex combination of the variance of small plants, (z) = ! (z)

S

+ (1

! (z))

2

S;

and large plants,

2

L;

L

where the function ! (z) 2 [0; 1] decreases in z. We set ! (z) = 1 for z < zl and ! (z) = 0 for z > zh ; where zl and zh are the critical productivity values that mark the bottom and top 1 percent of establishments, respectively. For z 2 [zl ; zh ], we use linear interpolation, ! (z) = (zh We set

S

and

L

z) = (zh

zl ) :

to match the distribution of export participation in 1987.

Establishments are assumed to receive an exogenous death shock that depends on its last period productivity, z, so that the probability of death is nd (z) = 1

n n ns (z) = max 0; min e

ez

oo + nd0 ; 1 :

This formulation of the exit rate allows small plants to have a higher exit rate than big plants and allows some big plants to fail.31 30

Increasing the elasticity of substitution will generate more sales dispersion for a given productivity distribution. Since the size distribution is pinned down by the data, the choice of only a¤ects the relationship between productivity and sales dispersion. 31 The assumption of exogenous exit is a departure from Melitz and Hopenhayn models and so one might suspect that our results may depend on the way we model exit. However, previous quantitative analyses of heterogeneous plant models that focus on labor market frictions (see Veracierto 2001, for example) …nd similar results with endogenous or exogenous exits. For this reason, we are not concerned about the e¤ect of this modelling assumption.

21

The parameter

determines both the producer’s markup as well as the elasticity of substitution

across varieties. It is set to 5 to yield a markup of 25 percent. The tradable share parameter of the …nal good producer, a, is set to match the ratio of manufacturers’nominal value-added relative to private industry GDP, excluding agriculture and mining for the U.S. from 1987 to 1992 of 21 percent. The elasticity of substitution between tradables and non-tradables, ; is set to 0:5: It is chosen to be consistent with the changes in output and productivity in the sector over this period and is within the range of empirical estimates.32 A low

also

implies reductions in trade costs will shift labor out of manufacturing. The labor share parameter in the production,

, is set to match the labor income to GDP ratio of 66 percent. In the model,

the ratio of value-added to gross output in manufacturing equals 1 ratio averages 2.75 from 1987 to 1992 and implies that

x

x(

1) = : In the U.S., this

= 0:795. The goods share in …xed costs

is set to match the growth rate of the average establishment size in the tradable good sector over 1987-2007,

= 0:889.

The entry cost parameter, fE ; is set to normalize the total mass of establishments, NT;t + NN;t , to 2. The mean establishment size of the tradable sector is set initially to match the U.S. in 1987. The following is a list of the empirical targets: 1. An exporter intensity of 9:9 percent in 1987 (1987 Census of Manufactures). 2. An exporter intensity of 15:5 percent in 2007 (2007 Census of Manufactures). 3. A stopper rate of 17 percent as in Bernard and Jensen (1999), based on the Longitudinal Research Database (LRD) of the Bureau of the Census 1984-1992.33 4. Five-year exit rate of entrants of 37 percent based on establishments that …rst began producing (Dunne et al. 1989). 5. Shutdown establishments’labor share of 2:3 percent (Davis et al. 1996). 6. Entrants’ labor share of 1.5 percent reported in Davis et al. (1996), based on the Annual Survey of Manufactures (Annual Survey of Manufactures). 7. Establishment employment size distributions (fractions of establishments given the employment sizes) as in the 1987 Census of Manufactures. 32

Our estimate is a bit below Mendoza’s (1995) estimate of 0.74 for a group of industrialized countries and slightly above the estimate in Stockman and Tesar (1995) of 0.44 for a broader cross-section of countries. 33 Bernard and Jensen …nd an average stopper rate of about 17 percent in this period. We adjust this by matching the 17 percent stopper rate among establishments with 100+ employees since the sample in Bernard and Jensen is severely biased toward large plants.

22

8. Distribution of export participation of establishments (1987 Census of Manufactures).

The …rst two targets, along with , pin down the level of iceberg costs in 1987 and 2007. Given = 5, trade costs increase export prices by 73.8 percent in 1987 and 52.9 percent in 2007. Because, we are targeting the change in export intensity, changing only a¤ects the inferred decline in variable trade costs. While this is of independent interest, it does not matter for the change in overall exports since exporter pro…ts are proportional to exporter intensity. The appendix shows that the decomposition of trade growth is invariant to the elasticity of substitution. While it is well-known that trade elasticity in some heterogenous plant models is governed by dispersion in productivity not the elasticity of substitution, the discipline implied by the size distribution and changes in export intensity imply that the trade elasticity is independent of the productivity dispersion. That is, for a particular ; we can not change the productivity distribution to generate a larger trade elasticity since that would be inconsistent with the observed size distribution. Fixed export costs (f0 ; f1 ;

S;

L)

are primarily determined by the stopper rate and the dis-

tribution of export participation. As is well known, not all establishments export. Those that do are much bigger than the average establishment. There is also substantial churning in the export market, with the typical exporter exiting after six years of exporting (measured as the inverse of the exporter exit rate). The next three targets help to pin down the establishment creation, destruction, and growth process ( ;

";

";

; nd0 ). New establishments and dying establishments tend to be small, respec-

tively accounting for only 1.5 percent and 2.3 percent of employment. Moreover, new establishments have high failure rates, with a 37 percent chance of exiting in the …rst …ve years. The model is calibrated to match the …rst 6 observations, and to minimize distance between the distribution of establishments and exporters by employment size in the model and the data (measured by the sum of squared residuals).34 The parameter values are reported in Table 2 and the …t of the benchmark 34

Speci…cally, we use the following 6 bins for employment sizes: 1-99, 100-249, 250-499, 500-999, 1000-2499, and

23

model is summarized in Table 3. Figure 1 plots the distributions of plants over productivity levels and export status, and entrants. We also plot the start and stopper hazard rates together with the probability of the death shock. The costs of starting to export are twice larger than the costs of continuing to export, but only 6 percent of the cost of creating a plant. Export costs are more volatile for small than large plants (

S=

L

7).

Establishment Distribution The model does a very good job of matching the cross-sectional and dynamics of plants and exporters. The three panels of Figure 2 plot the key characteristics of establishment and exporter heterogeneity in the data and our calibrated model. The top and bottom panels were targeted. The top panel displays the share of establishments (on a log scale) by establishment size. The model captures the feature that most establishments are relatively small and that there are relatively few large establishments. The middle panel displays the share of employment accounted for by establishments in each size class. Finally, the third panel shows that the share of establishments exporting by establishment size increases with establishment size in the model and the data. Overall, the …t is close, with the mean absolute di¤erence of 0.2 percent.35 The …t suggests the model captures the distribution of marginal exporters and non-exporters.

5. Results We now return to our main question: Do falling iceberg costs explain US export growth from 1987 to 2007? To answer this question we consider the impact of a cut in the iceberg costs necessary to raise export intensity as in the data: from 9.9 percent in 1987 to 15.5 percent in 2007. We compare steady states of the model economy that only di¤er in terms of the iceberg cost. The transition is 2500 and more employees. For the export participation rate distribution, we use 3 bins 1-99, 100-499, and 500 and more employees as the data for export participation rate distribution are limited to these bins. The model is solved by discretizing the idiosyncratic shock process and then using value function iteration to solve for the marginal starters and stoppers. More details are available upon request. 35 Both the assumption about the lag in starting to export and the stochastic …xed costs are crucial to match the rise in export participation with establishment size. Without these assumptions there would be too low (high) export participation among small (large) establishments.

24

considered in the section 7. The changes in the model economy and the data are reported in Table 4. The model generates overall export growth quite close to the data (71.7 percent compared to 67.7 percent in the census and 71.3 percent from customs). The endogenous movement in and out of exporting by heterogenous producers in response to the change in iceberg costs increase exports by an additional 55 percent (24.8 percentage points).36 The model also captures the main changes in the characteristics of exporters. It slightly overpredicts export growth by plants with 100+ employees (68.4 percent compared to 61.1 percent) as export participation rises by slightly less than the data (33.4 percent compared to 37.7 percent) and the exporter premium does not shrink by enough (it drops 9.8 percent compared to 21.4 percent in the data). While the model captures the overall change in exports we are cautious about its success related to exporter characteristics since the model misses out on some important changes relating to the structure of manufacturers and manufacturing. First, the change in the size distribution di¤ers a lot from the data. The theory predicts plant size should rise by 0.9 percent while in the data it fell by 20.3 percent. Moreover, the share of employment in large plants with 1000+ employees falls 7.9 percent while in the model it rises 0.3 percent. Second, the theory predicts manufacturing is too large as a share of the private economy. In the data, the share of employment in manufacturing fell 51.4 percent, while in the model it only falls 1.4 percent. We now examine how the changes in manufacturing a¤ect our …ndings on changes in exporter characteristics.

6. Getting the Size Distribution Right We now evaluate how changes in the structure of manufacturing a¤ected the growth in trade. The change in producer heterogeneity is potentially an important determinant of the change in trade. Indeed, in certain formulations of the Melitz model it is producer heterogeneity (the slope 36

This calculation takes into account that the change in exporter intensity increases the exporter premium holding export participation constant. Thus, the cut in iceberg costs increase exports by 46.9 percent.

25

of the Pareto parameter on productivity) that determines the trade elasticity and so accounting for changes in the structure of manufacturing in this period is potentially important. Two types of changes are considered: changes in the importance of manufacturing in the overall economy and changes that a¤ect the distribution of activity across manufacturers. Speci…cally, we consider the contribution of changes in manufacturing productivity and capital intensity on trade. Most of the shift of employment out of manufacturing and the shift towards smaller establishments within manufacturing can be accounted for by manufacturers becoming more productive relative to the whole economy. These changes in the structure of manufacturing have a negligible impact on export growth but do a¤ect the distribution of export participation since they a¤ect the average plant size. We also consider how a change in the dispersion of idiosyncratic shocks and the change in US corporate taxes alter our …ndings on export growth. Small reductions in the dispersion of shocks can explain the shift to smaller plants and this reduces export growth since the biggest plants are no longer so big. The changes in the U.S. corporate tax code also reduce export growth by reducing export participation.37 A. Manufacturing and Non-manufacturing Figure 3 summarizes some key aspects of the changes in U.S. manufacturing relative to the private economy. The top panel shows that the share of the private economy in manufacturing has fallen over time. The share of employment (measured by workers or compensation) has fallen less than the share of physical capital. This shift away from manufacturing starts prior to the period studied. The middle panel shows that the capital-labor ratio in manufacturing relative to the capital labor ratio in the whole economy has risen over this period. The bottom panel shows that the share of output in manufacturing in the private economy fell about 15 percent from 1987 to 2007 and manufacturing labor productivity grew about 30 percent relative to the non-farm business 37 Many of these changes are taken as exogenous to explore their quantitative impact. Some of these changes such as capital intensity or the dispersion in idiosyncratic shocks could be the endogenous response to changes in trade or some more structural shock.

26

sector. To capture these changes in productivity and output the change in average productivity in the tradable sector relative to the non-tradable sector is inputted into the model. To capture the change in capital intensity the capital share parameter, , in the tradable sector is changed. The column labeled A reports the impact of only increasing tradable productivity. Making the tradable sector more productive primarily lowers the average size of plants (plant size falls 25.1 percent compared to a 0.9 percent increase in the benchmark) and reduces the share of employment in manufacturing (-49.7 percent vs -51.4 percent in the data). Export growth at the aggregate is essentially unchanged, while export growth at large plants rises slightly as the increase in participation exceeds the fall in the premium more. With a smaller average plant size, the model capture some of the shift out of large plants as the share of employment in plants with 1000+ employees falls 4.1 percent compared to a drop of 7.9 percent in the data. The shift from manufacturing arises because the productivity gains in manufacturing reduce the price of manufacturing goods relative to non-manufacturing goods. With a less than unitary elasticity of substitution across sectors, this then reduces the size of manufacturing. The shift to smaller plants arises because entry costs are partly denominated in goods, which have become cheaper. Thus, the share of plants in manufacturing falls about 37.2 percent (compared to 33.7 percent in the data). B. Changes in Plant Size: Capital Intensity and Dispersion Figure 4 depicts changes in the distribution of activity across plants within manufacturing from 1987 to 2007. The solid and dashed lines show that the change in the share of employment and payroll by each employment-size bin is decreasing with size. The share of employment in plants with less than 100 employees rose by 4.7 percent (5.1 percent when measured in payroll), while the share of employment at plants with greater than 2500+ employees fell 6.1 percent (9.1 percent in payroll). Compared to the changes in payroll, there is a much more muted shift in value added by plant size. Indeed, the value added share of employment of the smallest plants rose only 1.0 percent,

27

while the value added of the largest plants fell only 6.9 percent. To capture the di¤erent changes in value added and employment in the most parsimonious fashion, the capital intensity of plants in the manufacturing sector is made to depend on productivity. Speci…cally, the capital share parameter, (z) ; is a function of the productivity h yT;t (z; ; m) = ez kT;t (z; ; m) For the 1987 economy

0 (z)

=

i (z)

lT;t (z; ; m)1

but choose

1 (z)

i (z)

i1

x

xt (z; ; m)

x

:

is set to match the change in value added by

plant size in 2007. Speci…cally, for the bottom 97.1 percent, which corresponds to <250 plants, is set so that there is a rise in the value added to wage bill ratio by 5.5 percent, and for the top 0.3 percent of plants, which corresponds to plants with 1000+ employees,

H

is set so that the ratio of

value added to wage bill drops by 3.6 percent. In between the capital share is linearly interpolated. To capture the rise in the capital intensity of manufacturing relative to to non-manufacturing of 28.2 percent, the capital share in non-manufacturing is lowered. The column titled KnoNT shows the impact of changing the dispersion of capital intensity only within manufacturing. The increase in capital intensity leads to an increase in average plant size of 3.2 percent compared to our benchmark model’s increase of 0.9 percent. However, the share of employment in plants with 1000+ plants falls by 2.98 percent. The impact on international trade is primarily distributional as now trade grows 68.3 percent when looking at 100+ employee plants and 71.4 percent for all plants. The column labeled K shows the impact of also changing the capital intensity between manufacturing and non-manufacturing. In short, the across-sector changes in capital intensity imply that average plant size is now only 1.7 percent larger. With the smaller plants, the share of employment in plants with 1000+ employees falls by 2.96 percent. Again, the impact on trade is minor. The changes in capital intensity do not fully capture the changes in the distribution of plant size. Thus, to capture the shift out of very large scale manufacturing, we next consider a change in 28

the dispersion of idiosyncratic productivity shocks. In particular, we reduce the standard deviation of productivity shocks hitting plants by 3.8 percent. This shift compresses the unconditional size distribution of plants. This case is considered in the column labeled KA . Average plant size goes up slightly while the share of employment in plants with 1000+ employees falls an additional 4.4 percentage points and is now quite close to the data (-8.5 in the model vs. -7.9 in the data). The reduction in dispersion lowers export growth from 71.7 percent to 68.4 percent. The reduction is entirely attributed to a reduction in the exporter premium as the largest exporters are no longer as large and small non-exporters are no longer as small. C. Corporate Taxes We now evaluate how the increase in U.S. corporate taxes on export pro…ts may have a¤ected export growth in this period. This tax increase undid a tax advantage for exporters and was the result of a WTO case brought by the EU. The actual tax increase occurred in 2004, but had been expected from 1997.38 The tax bene…t was much less valuable for plants that were part of multinationals given other aspects of the tax code. We abstract from these aspects of the tax code and thus our analysis provides upper bound on the e¤ect of this change in policy To allow for corporate taxes, after-tax pro…ts are de…ned as where D

D

D

= 1

D

+ (1

x) t

x,

is the pro…ts on domestic sales net of …xed export costs and the cost of capital. Let

= 0:35 and

X 87

= 0:2975 and then raise the tax rate on exports to

x

=

D.

The results for

the new steady state are reported in the row labeled KA T of Table 4. Lowering the corporate tax bene…t weakens export growth by about 2.7 percentage points. This arises through a 3.8 percentage point reduction in export participation growth and a 1.1 percentage increase in the change of the size 38

From 1971 to 2004, the U.S. corporate tax code allowed U.S. exporters to pay a lower tax rate on export income. From 1984 to 2004, this tax bene…t implied that export income was taxed at 29.75 percent, while domestic income was taxed at 35 percent. This favorable treatment of export income was disputed by the EU with the WTO beginning in 1997. From early on in the dispute process, the WTO …ndings pointed to the eventual removal of this bene…t. Indeed, Desai and Hines (2008) …nd that on the day the EU announced its dispute, November 18, 1997, that there was a sizeable drop in the stock market capitalization of U.S. exporters; thus, the dispute was expected to lead to the elimination of the tax bene…t.

29

premium as most of the reduction in export participation is among relatively small producers. Thus, if the tax changed applied to everyone, and this is a big if, it would have reduced the endogenous component of trade expansion by almost 12.5 percent.

7. The Importance of Exporter Dynamics for Aggregate Export Growth We studied U.S. export growth in a GE variation of the benchmark model of exporter dynamics. Previous work …nds this model is quite successful at explaining both the substantial dispersion of exporter characteristics and the high persistence of export participation.39 This work …nd the costs of starting to export are higher than the costs of continuing in the market. These types of trade frictions are thought to contribute to the slow aggregate export growth (Baldwin and Krugman, 1989) in response to aggregate shocks. Despite its successes and acknowledged relevance, the challenges of embedding a dynamic exporting model in GE has led most studies of trade frictions with heterogeneous producers to use a simpli…ed version with a static export decision. We now ask: Can a model with a static export decision explain the changes in US aggregate exports from the observed changes in iceberg trade costs? The short answer is, No. The static exporting model generates much less endogenous trade growth from the extensive margin than the dynamic exporting model. It also misses out on the non-linear dynamics between trade and exports in this period. To get this simpler model to match the data requires a second set of shocks to …xed export costs. A. Static Export Decision: No Sunk Cost The exporting decision is static when the cost of starting to export equals the continuation cost (f0 = f1 ) and there is no lag. The static model is calibrated to hit the same targets except the persistence of exporting. Parameters are reported in Table 2, and the …t is reported in Table 3 in the column Fixed cost. The …t is similar to the benchmark in terms of the initial distribution of 39

See Roberts and Tybout (1997) and Das, Roberts, and Tybout (2007).

30

exporters and establishments. However, the …xed cost model requires more volatile shocks to …xed export costs and generates 4 times the churning in the data.40 The last three columns in Table 4 report the changes in exports in the …xed cost model from a change in iceberg costs and various changes in the structure of manufacturing. As before, the exporter intensity is calibrated to match the data in 1987 and 2007. Because exporter intensity only depends on the iceberg cost and elasticity of substitution, the inferred change in iceberg costs is the same as in the sunk cost model. Focusing on the the case that captures the observed changes in the structure of manufacturing (column Fixed KA ),

41

overall export growth in the static model is much lower than both the data

and the dynamic exporting model (53.7 percent with …xed vs 65.0 percent with a sunk cost and between 67.7 and 71.3 percent in the data). The model does slightly better when considering plants with 100+ employees (57.3 percent compared to 61.1 percent in the data); however, the …xed cost model generates a smaller increase in export participation of 24.1 percent (37.7 percent in the data). A key feature of the …xed cost model is that aggregate growth is lower than growth for 100+ plants while in the data it is much higher. In the …xed cost model the threshold for exporting is quite high so that it is mid-sized plants that start exporting while most small plants do not. Thus, while the …xed cost model might seem like a reasonable …t for the 100+ plants that is only because it is a very poor …t for overall export growth. To get the …xed cost model to match the data on aggregate exports would then require a substantial reduction in the …xed costs of exporting, particularly for small plants. The static exporting model generates export growth above the intensive margin by only 6.8 percentage points compared to the sunk cost models increase of 18.1 percentage points. Two main factors lead to weaker export growth in the static exporting model. First, there is less growth in export participation than in the sunk cost model since the value of being an exporter increases 40 41

The exit rate is 46 percent vs. 17 percent in the data. The results from a change in corporate taxes and no changes in manufacturing are also included for completeness.

31

more steeply with idiosyncratic productivity than in the sunk cost model. The steeper slope arises because with …xed costs export pro…ts are solely determined by current productivity, while with a sunk cost future productivity also matters. This means that with sunk costs more plants are at the margin in the long run. Second, to match the initial export participation rate distribution, the …xed cost model requires large shocks to the …xed costs even for big plants. The standard deviation of the shock for the top 1 percent plants is over 4 times larger than in for the benchmark model. With volatile …xed export costs, exporting is more from random selection than selection by productivity. B. Transition and Non-linear Dynamics We next consider the timing of U.S. export growth. Panel (a) of Figure 5 shows the ratio of exporter intensity growth to aggregate trade growth from 1987 to 1997 and over the whole period.42 This measure is relevant since it compares the change in aggregate exports to exporter intensity which is a measure of the change in iceberg costs. In the …rst ten years, the intensive margin accounted for 73.5 percent of the change in exports shipments, while by 2007 the intensive margin accounted for only 60 percent of the growth in export shipments. Thus, there is a non-linear relationship between trade and iceberg costs. The e¤ect of the changes in iceberg costs depends on the actual and expected path of iceberg costs. It is assumed that in 1987 agents expect a new path of iceberg cost that will fall linearly until 2007. The linear trend in iceberg costs is chosen to be consistent with the average growth of imports and exports. Additionally, it is assumed that there are iid temporary shocks each year that a¤ect the iceberg cost but not the trend. These shocks are chosen to match the export intensity in census years and minimize the distance between exports in the model and data over the sample.43 Panel (b) of Figure 5 shows the path of exporter intensity (which is linearly related to iceberg costs) 42

In this analysis we use the customs data as a measure of total exports, since we require annual data on exports. There is not an exact match between our model and the data because we are choosing 16 iceberg costs but have 20 observations on trade. Our approach shows that there is a sequence of iceberg costs consistent with the non-linear dynamics of exports and export intensity. 43

32

as well as the trend.44 To match the movements in trade requires iceberg costs (export intensity) to fall (rise) more than trend initially and then return strongly to trend 1998 to 2007. Panel (a) of Figure 5 shows the relationship between the changes in iceberg costs and export growth in the static and dynamic exporting models.45 The static exporting model predicts a nearly constant relationship between the intensive margin and aggregate export growth of about 78 percent. It thus does not generate any of the non-linearities in the data. This should not be surprising since many formulations of this model with a Pareto productivity distribution yield a constant trade elasticity. To get the static exporting model to explain the dynamics in the data would thus require …xed export costs to decline substantially from 1997 to 2007. The benchmark model can capture the non-linear dynamics in the data because it takes time to build up the stock of exporters.

8. Conclusions We undertake the …rst empirical and quantitative analysis of the change in plant-level and aggregate U.S. exports in a GE dynamic heterogeneous plant model. Given the common use of variants of this model in policy analysis, this provides an important …rst evaluation. Measuring the change in trade costs is an important element to analyzing trade growth. The characteristics of exporters, particularly exporter intensity, can be used to identify the change in iceberg trade costs. The growing availability of data on exporter characteristic makes this a potentially important input into future empirical work. Given the observed decline in U.S. iceberg trade costs, the model closely matches the growth in the share of manufacturing output exported as it generates reasonable changes in export participation and exporter characteristics. We …nd that the way the export decision is modeled matters. When exporting is a dynamic decision, the model matches both the volume and timing of export growth. Export growth starts out low relative to the change in exporter intensity and then increases over time. When exporting 44

We can not plot export intensity over time here since we only have measures every …ve years. The model simulations abstract from changes in the structure of manufacturing since we have found these have a relatively small e¤ect on export growth. 45

33

is a static decision, the model generates none of the dynamics of exporting and less than a third of the observed changes in the extensive margin. To get the static exporting model to match aggregate export growth requires a substantial reduction in the costs of exporting. The dynamic exporting model thus can more accurately capture both the micro and macro dynamics of trade. That the dynamic exporting model can explain the dynamics of trade may not be surprising since heterogeneous plant models were originally developed to explain slow trade adjustment. What is surprising is that it does so well and that the static exporting model generates much smaller long-run changes in trade. Finally, the paper accounts for the interplay between changes in trade and changes in the structure of manufacturing. Changes in iceberg cost have a small role on the structure of manufacturing. On the other hand, changes in manufacturing from di¤erential productivity gains relative to nonmanufacturing, changes in idiosyncratic shocks, and capital intensity reduced export growth by 3 to 4 percentage points and point to a role of the size distribution in understanding the determinants of trade growth. Changes in corporate taxation of export pro…ts also reduced export growth up to a few percentage points.

References Alessandria, G., and H. Choi (2011): “Establishment Heterogeneity, Exporter Dynamics, and the E¤ects of Trade Liberalization,” Working Paper no. 11-19, Federal Reserve Bank of Philadelphia. Alvarez, F., and R. Lucas Jr. (2007): “General equilibrium analysis of the Eaton-Kortum model of international trade,” Journal of Monetary Economics, 54(6), 1726-1768. Anderson, J. E., and E. van Wincoop (2004): “Trade Costs,”Journal of Economic Literature, 42(2), 691-751. Atkeson, A., and A. Burstein (2010): “Innovation, Firm Dynamics, and International Trade,”Journal Political Economy, 118(3), pp. 433-484. Baier, S.L., and J.H. Bergstrand (2001): “The Growth of World Trade: Tari¤s, Transport Costs, and Income Similarity,” Journal of International Economics, 53(1), 1-27. Baldwin, R. (1988): “Hysteresis in Import Prices: The Beachhead E¤ect,” American Economic Review, 78(4), 773-85. (1989): “Sunk-Cost Hysteresis,” NBER Workng Paper 2911, National Bureau of Economic Research. 34

Baldwin, R., and P.R. Krugman (1989): “Persistent Trade E¤ects of Large Exchange Rate Shocks,” Quarterly Journal of Economics, 104(4), 635-654. Bernard, A. B., and J. B. Jensen (1999): “Exceptional Exporter Performance: Cause, E¤ect, or Both?” Journal of International of Economics, 47(1), 1-25. Bernard, A. B., and J. B. Jensen (2004): “Entry, Expansion and Intensity in the U.S. Export Boom, 1987-1992,” Review of International Economics, 12(4), 662-675. Bernard, A. B., J. Eaton, J.B. Jensen, and S. Kortum (2003): “Plants and Productivity in International Trade,” American Economic Review, 93(4), 1268-1290. Bernard, A. B., J. B. Jensen, and P. Schott (2006): “Trade Costs, Firms and Productivity,”Journal of Monetary Economics, 53 (5), pp. 917-937. Bridgman, B. (2008): “Energy Prices and the Expansion of World Trade,” Review of Economic Dynamics, 11(4), pp. 904-916. Chaney, T. (2008): “Distorted Gravity: The Intensive and Extensive Margins of International Trade,” American Economic Review, 98 (4), 1707-1721 Das, S., M. Roberts, and J. Tybout (2007): “Market Entry Costs, Producer Heterogeneity, and Export Dynamics,” Econometrica, 75(3), 837-873. Davis, S., J. Haltiwanger, and S. Schuh (1996): Job Creation and Destruction, Cambridge, MA: MIT Press. Desai, M., and R. Hines (2008): “Market Reactions to Export Subsidies,” Journal of International Economics, 74(2), 459-474 Dixit, A. (1989a): “Entry and Exit Decisions Under Uncertainty,” Journal of Political Economy, 97(3), 620-38. (1989b): “Hysteresis, Import Penetration, and Exchange Rate Pass-Through,” Quarterly Journal of Economics, 104(2), 205-228. Dunne, T., M. Roberts, and L. Samuelson (1989): “The Growth and Failure of U.S. Manufacturing Plants,” Quarterly Journal of Economics, 104(4), 671-698. Eaton, J., and S. Kortum (2002): “Technology, Geography, and Trade,”Econometrica, 70(5), 17411779. Eaton, J., S. Kortum, and F. Kramarz (2004): “Dissecting Trade: Firms, Industries, and Export Destinations,” American Economic Review, 94 (2), 150-154. Head, K., and T. Mayer (2013): “Gravity Equations: Workhorse, Toolkit, Cookbook,”Handbook of International Economics, Vol. 4,eds. Gopinath, Helpman, and Rogo¤, Elsevier. Head, K., and John Ries, (2001): “Increasing Returns versus National Product Di¤erentiation as an Explanation for the Pattern of U.S.-Canada Trade,” American Economic Review, 91(4), 858-876. Hopenhayn, H., and R. Rogerson (1993): “Job Turnover and Policy Evaluations: A General Equilibrium Analysis.” Journal of Political Economy, 101(5), 915-38.

35

Hummels, D. (2007): “Transportation Costs and International Trade in the Second Era of Globalization,” Journal of Economic Perspectives, 21(3), 131-154. Jacks, D. S., C. M. Meissner, and D. Novy (2010): “Trade Costs in the First Wave of Globalization,” Explorations in Economic History, 47(2), 127-141. Melitz, M. (2003): “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,” Econometrica, 71(6), 1695-1725. Mendoza, E. (1995): “The Terms of Trade, the Real Exchange Rate, and Economic Fluctuations,” International Economic Review, 36(1), 101-137. Roberts, M., and J. Tybout (1997): “The Decision to Export in Colombia: An Empirical Model of Entry with Sunk Costs,” American Economic Review, 87(4), 545-564. Ruhl, K. (2008): “The International Elasticity Puzzle,” mimeo, University of Texas. Stockman, A., and L. Tesar (1995): “Tastes and Technology in a Two-Country Model of the Business Cycle: Explaining International Comovements,” American Economic Review, 85(1), 168-185. Veracierto, M. (2001): “Employment Flows, Capital Mobility, and Policy Analysis,” International Economic Review, 42(3), 571-595. Yi, K. (2003): “Can Vertical Specialization Explain the Growth of World Trade?”Journal of Political Economy, 111(1), 52-102.

Data Appendix Table 1, Figure 2c, and Figure 5 1. Based on Census’ 1987 Analytical Report (1987AR) on Establishments that Export and a special tabulation from 2007 Census of Manufactures (CM). (a) Measuring aggregate exports and export participation in the census requires imputing participation by non-surveyed and non-respondent establishments. In the 1987AR, the census imputed export participation based on the size, industry, and location of nonrespondents. We follow a similar approach to measure exporting in 2007 but base it on only size, since we lack industry and location data. To make things concrete, suppose there are three types of establishments exporters, non-exporters, and non-respondents, fX; N; N Rg ; by each size bin: We impute the probability of exporting of plants in bin i as pi = NiX = N X + NiN : We assume that all exporters in a bin have the same export X intensity so that exsi = ExportsX i =Salesi . Sales of exporters are imputed assuming that non-respondent exporters are bigger than non-respondent non-exporters by the same amount that respondent exporters are bigger than respondent exporters. Speci…cally, we calculate exporter sales in size bin i NR Exporter Salesi = SalesX i + pi Salesi

SalesX i N SalesX i +Salesi

pi

SalesX i = SalesX i + N SalesX + Sales i i Exportsi = exsi Exporter Salesi

NR SalesN i + Salesi

and …nally exports equal (b) Export intensity in Figure 5 for 1997 and 2007 is based on special tabulation of CM. 36

2. Customs data (Table 1 and Figure 5): Shipments: All Manufacturing Industries SIC product code, Census, ends in 2000; Mfrs’ Shipments: All Manufacturing Industries NAICS product code, Census; Exports: Manufactured Commodities (f.a.s.), Census Bureau, Trade in Goods (census basis) by selected SIC-Based Product Code (1986 to 1999); Exports: Manufacturing, Total (f.a.s.), Census, (1999 to 2011); Reexports: Manufactured Goods (f.a.s.), Census, Trade in Goods: Principal Commodity Grouping, NSA, We estimate re-exports in 87m1 to m6 using the growth from Q3 to Q4; Exports: Manufactured Goods (f.a.s.) by Principal SITC Commodity Groupings: Census Basis [starts Jul-1987] Since data is based on a partial year in 1987, we base the change in exports from 87 to 88 on the manufactured commodities series. Table 4 1. Employment share of manufacturing in private economy from BEA: Compensation of Employees: Private Industries (Mil.$) and Compensation of Employees: Manufacturing (Mil.$) 2. Establishment share: Plants from CM (1987 to 2007) divided by private establishments in County Business Patterns (1987 to 2007). Adjusting the census data for the NAICS changeover (there are 4 percent fewer plants and workers measured in NAICS vs SIC in 1997) reduces the decline in plants to -30.0 percent. 3. Employment distribution based on CMs. Figures 2-4 1. Figures 2a, 2b, and 4 based on 1987CM and 2007CM. 2. Figure 3 manufacturing-non-mfr facts based on: Capital stock (BEA): Net Stock: Private Equipment & Software (Bil.$); Net Stock: Private Nonres Equip & Software: Manufacturing (Bil.$); Employment (BLS): All Employees: Total Private Industries (SA, Thous) and All Employees: Manufacturing (SA, Thous); Labor compensation (BEA): Compensation of Employees: Private Industries (Mil.$) and Compensation of Employees: Manufacturing (Mil.$). The BEA has 4 series for each variable that are based on di¤erent industry classi…cations/time periods. These series line up in the year of the change in classi…cations (1947 and 1987) but not in 1998 with the change to NAICS. However, from 98 to 2000 both series are measured using SIC87 and NAICS and so we splice these series. That is, we increase the NAICS series by the average di¤erence from 98 to 00; K/L ratio is measured as the ratio of the capital stock of equipment & software in manufacturing to the private economy at historical cost; Productivity and Business Sector Output (BEA): Nonfarm Business Sector: Real Output per Hour of All Persons (2005=100); Nonfarm Business Sector: Real Output (2005=100); Manufacturing Sector: Real Output Per Hour of All Persons (2005=100); Manufacturing Sector: Real Output (2005=100).

37

38

5.9 12.2 73.5

All Plants 1987 2007 Log Change 5.5 10.9 67.7

6.3 11.6 61.1

Exports/Sales

148.0 119.5 -21.4

Premium

Participation + Premium 55.8 70.3 23.1

43.2 63.0 37.7

Participation

9.9 15.5 44.6

9.9 15.5 44.9

Intensity

8.1 17.1 74.3

7.5 15.3 71.3

Customs Adjusted for wholesales Customs margins

** 1987 Data based on Analytical Report on Establishments that export. 2007 data applies the methodology from the 1987 report to a special tabulation of the 2007 Census to adjust for non-response. ** Data is based on the ratio of Exports of Manufactured Commodities (f.a.s. Value, Mil.$) excluding re-exports and Mfrs’Shipments: All Manufacturing Industries (SA, Mil.$). Note the 1987 data is based on SIC and 2007 is based on NAICS. Adjusted for wholesale margins assumes wholesale costs from plant to port increased from 8 percent to 10.5 percent. *** For all plants we do not break out the Participation and Premium margins as division into these margins is very sensitive to assumptions about participation by the smallest plants in the survey while the division into the sum and exporter intensity is quite stable.

6.7 13.2 66.9

100+ 1987 2007 Log Change

Exports/Domestic Sales

Census of Manufactures

Table 1: US Exports and Exporters over Time

Table 2: Parameter Values Common Parameters

= 0:96;

= 2;

= 5;

= 0:10; a = 0:091;

= 0:5;

87

= 0:738;

07

= 0:529;

x

= 0:795

Sunk Cost

= 0:113; = 7:562; nd0 = 0:022; = 0:889; = 0:690; fE = 0:971 f0 =fE = 0:060; f1 =f0 = 0:483 S = 4:400;

E L

= 0:354; = 0:600.

"

= 0:331:

"

= 0:330;

Fixed Cost

= 0:118; = 7:564; nd0 = 0:022; = 0:862; = 0:690; E = fE = 0:926; f0 = f1 = 0:109fE S = 5:200; L = 2:600.

0:354;

Exporting Cost Shock Weight

! (z) =

8 < 1; :

zH z zH zL ;

0;

z < zL where Pr (zL ) = 0:01; z 2 (zL ; zH ) ; z zH where Pr (zH ) = 0:99:

Productivity Growth: ln (AT;07 =AN;07 ) = 0:291 Capital Deepening T;new

N;new

(z) =

8 <

= 1 e0:055 (1 z zL L + ( zH zL ) ( H e 0:036 (1 H =1 i 1

old ) ;

L

: h = 1 + e0:282

1

T;new

T;new

L) ; old ) ;

z < zL where Pr (zL ) = 0:971; z 2 (zL ; zH ) ; z zH where Pr (zH ) = 0:997:

:

Low Dispersion ( ): Sunk Cost: ";new = 0:961 " ; Fixed Cost:

";new

= 0:958

":

Table 3: Target Moments 5-year exit rate Startups’labor share Shutdowns’labor share Stopper rate (100+) Exporter intensity (100+) Squared sum of residuals (%) Establishments Export participation

Target Value 0.370 0.015 0.023 0.170 0.100

Sunk Cost 0.370 0.015 0.023 0.170 0.100

Fixed Cost 0.370 0.015 0.023 0.461 0.100

0.304 0.211

0.331 0.194

* denotes moment not targeted. **Employment size bins are: <99, 100-249, 250-499, 500-999, 1000-2499, and 2500+. Export bins are: <99, 100-499, and 500+.

39

Table 4: Changes in Export Characteristics and Trade (Steady State) Data NT NT +NN LT LT +LN LT NT

Bench.

A

-33.6 -51.4 -20.3 7.7 -7.9 4.7 -8.0

-2.1 -1.4 0.9 -0.9 0.3 -1.6 2.1

-37.2 -49.7 -25.1 4.9 -4.1 3.5 -3.3

Trade** Intensity

67.7-71.3 44.6

71.7 44.9

71.7 44.9

Trade Intensity Part. Premium

61.1 44.9 37.7 -21.4

68.4 44.9 33.4 -9.8

70.9 44.9 38.6 -12.6

L250 L1000+ L100 L500+

KnoN T

K

-2.3 -1.4 0.3 -2.4 3.2 1.7 -0.1 -0.1 -3.0 -3.0 -0.4 -0.4 -0.2 -0.2 All plants 71.4 71.4 44.9 44.9 100+ plants 68.3 68.3 44.9 44.9 33.4 33.4 -10.0 -10.0

KA

KA T

Fixed KA -30.7 -46.5 -20.3 7.4 -8.3 6.9 -9.0

KA T -31.1 -43.8 -21.7 8.8 -8.4 7.4 -9.4

-32.8 -46.0 -20.3 7.2 -8.5 5.5 -8.8

-32.5 -46.2 -20.3 7.4 -8.6 5.7 -9.0

Bench. -1.4 -1.4 -0.1 -1.9 0.4 0.8 0.7

68.4 44.9

65.0 44.9

58.9 44.9

55.4 44.9

53.7 44.9

68.4 44.9 36.1 -12.6

65.7 44.9 32.3 -11.5

60.0 44.9 26.4 -11.3

58.6 44.9 26.1 -12.3

57.3 44.9 24.1 -11.7

* denotes percentage point changes, others are percentage. ** Aggregate exports equal census and customs data. A denotes the benchmark model with tradable productivity rising 29.1 percent. KnoNT denotes changing the capital intensity across tradable plants. K denotes changing the capital intensity across tradable plants and between tradables and non-tradables. KA includes the changes with K and A as well as lowering the dispersion of idiosyncratic shocks by 3.8 percent. KA T includes the change in the tax rate on export income.

Figure 1: Establishment Characteristics by Employment Size 1

Stopper hazard rate

All establishments

0.8

Probability

Non-exporters Starter hazard rate

0.6 Shutdown probability

0.4 Exporters Entrants

0.2

0 -1.6

-1.2

-0.8

-0.4 0 0.4 Productivity (z)

40

0.8

1.2

1.6

Figure 2: Establishment Characteristics by Employment Size (a) Establishment Share 100

Percent (log scale)

Data Model 10

1

0.1

0.01 1-99

100-249

250-499

500-999

1,000-2,499

2,500+

Employment of an establishment

(b) Employment Share 35 Data Model

30

Percent

25 20 15 10 5 0 1-99

100-249

250-499

500-999

1,000-2,499

Employment of an establishment

(c) Export Participation 70 60

Data Model

Percent

50 40 30 20 10 0 1-99

100-499

Employment of an establishment

41

500+

2,500+

U S M aa nn uuf faacct tuur riningg

U S M aofnU.S. u fManufacturing a c t u r in gover Time Figure 3: Relative Importance

Share Share Share .25 .25 .25

.5.5 .5

A .Share S h a rin e iPrivate n P r i v aIndustry e In d u s t r y A. A . S h a re in P r iv a tt e In d u s t r y

C o m p e n s a t io n C o m p e n s a t io n

000

W o rk e rs W o rk e rs C C aa pp iitt aa ll

1945 1945

1955 1955

1965 1965

1975 1975

1985 1985

1995 1995

.5.5 .5

B ..Change C hh aa nn ggin iLabor t aa ll llaa bbRatio M aa nn uu ffaa cc ttuu to B. B C ee Capital ii nn cc aa pp it oo rr rr aa tt(Manufacturing iioo (( M rriinnAll) gg ttoo

2005 2005

A llll)) A

C o m p e n s a t io n C o m p e n s a t io n

log change change log logchange 000 .25 .25 .25

W o rk e rs W o rk e rs

1982 1982

1987 1987

1992 1992

1997 1997

2002 2002

2007 2007

2012 2012

.3.3 .3

C.C Businss C Output Ou u tt pp uuand & Productivity i v iitt yy(Relative l a tt iv i v eetottooNonfarm m .. O tt & pp rr oo dd uu cc tt iv (( rr ee la nn oo nn ffaa rrm bb uu ss iinnOutput) ee ss ss oo uu ttpp uu tt)) P rroo dd uu cc tt iivviitt yy P

-.15 -.15

log change log logchange 000 .15 .15 .15

O uu tt pp uu tt O

11 99 88 22

11 99 88 77

1 99 9 92 2 1

1 99 19 97 7

42

22 0 0 00 22

22 00 00 77

22 00 11 22

Figure 4: Change in Establishment Characteristics by Employment Size 6%

4%

2%

0% 1-99 employees

100-249 employees

250-499 employees

500-999 employees

1000-2499 employees

2,500 or more employees

-2%

-4%

-6%

-8%

Workers Compensation Value added

-10%

Figure 5: Export and Export Intensity Dynamics b. Change in Export Intensity (Trend and Imputed)

80

50 Data Benchmark Fixed

75

Change in Export Intensity (%)

Intensive Margin Share of Growth (%)

a. Contribution of Intensive Margin to US Export Growth

70

65

60

55

40

30

20 Intensity Trend

10

0 1997

2007

1987

Year

1992

1997

2002 Year

43

2007

2012

Appendix not for Publication Here we describe some details related to solving our model (Technical Appendix) and some aspects of the data on plant heterogeneity (Data Appendix).

Technical Appendix Here we show 1. 2. 3. 4.

Results are independent of the elasticity of substitution. Results generalize to asymmetric countries. Multi-stage production in the spirit of Yi (2003) The solution of the model.

A. Invariance to Elasticity of Substitution The invariance of the decomposition of trade growth to elasticity of substitution comes from the calibration that requires the use of the elasticity adjusted iceberg cost and the elasticity adjusted productivity process in matching the export intensity and the size distribution in the data. In the model, the export intensity of an exporter is given by intensity =

(1 + )1 1 + (1 + )1

:

To match the export intensity in the data, the model is calibrated to get the elasticity adjusted iceberg cost = (1 + )1 which is given by =

intensity : 1 intensity

Thus, the elasticity adjusted iceberg cost that matches the data is invariant to the elasticity of substitution. The size distribution of producers is determined by the elasticity adjusted productivity = ( e 1)z and the elasticity adjusted iceberg cost : The model is calibrated to match the size distribution with and : These transformations result in invariance of the trade growth (and compositions) with respect to the elasticity of substitution. The following section provides detailed derivations of the equations for the invariance in a more general, asymmetric country, environment. B. Asymmetric Countries Here, we assume that two countries can be asymmetric and show that results are invariant to the relaxation of the symmetric two-country assumption. Speci…cally, we assume that home and foreign have population L and L ; respectively; have country-wide productivity zc and zc , respectively; and may have di¤erent producer speci…c productivity and the cost shock processes. Here, we will focus on the conditions that determine the trades in the steady state. We will normalize the price indices in two countries with Pt = Pt = 1: With the country-wide productivity, the producers in the tradable good sector have the Cobb1 x x x : The elasticity adjusted productivity is Douglas production function y = ezc +z k l1 given by A = e( 1)zc ; and = e( 1)z :

1

Consumers: The consumers’ problem is identical to the one in the main text. The …rst order condition gives (1)

1=

UC;t+1 (Rt+1 + 1 UC;t

):

Final Good Producers: Solving the …nal good producers’ problem gives the input demand functions, (2)

d yH;t ( ; ; m) = a

(3)

d yF;t ( ; ; 1) = a

(4)

PH;t ( ; ; m) PT;t

PT;t Dt ;

PF;t ( ; ; 1) PT;t

PT;t Dt ;

PN ( ) PN

PN;t Dt ;

d yN;t ( ) = (1

a)

where the price indices are de…ned as (5)

1 Z X

PT;t =

PH;t ( ; ; m)1

T;t (

; ; m) d d

m=0

+ (6) (7)

PN;t =

Z

Z

1

1

PF;t ( ; ; 1)

1

T;t (

; ; 1) d d

;

1 1

1

PN;t ( )

N;t (

h 1 + (1 Pt = 1 = aPT;t

)d

1 a) PN;t

; i

1 1

:

Tradable Good Producers: A tradable good producer is described by its technology, …xed cost shock, and export status ( ; ; m) : Each period, it chooses its current prices at home and foreign, PH;t ( ; ; m) and PH;t ( ; ; m) ; inputs of labor lT;t ( ; ; m) ; capital kT;t ( ; ; m) ; and materials xt ( ; ; m) ; and the exporting status m: Total materials, xt ( ; ; m) ; are composed of tradable goods with a CES function 2 1 Z X 1 4 xdH;t ( ; $; ; ; ; m) (8) xt ( ; ; m) = T;t ( ; $; ) d d$ =0 $

+

Z

$

xdF;t ( ; $; 1; ; ; m)

1

1

T;t (

; $; 1) d d$

;

where xdH;t ( ; $; ; ; ; m) and xdF;t ( ; $; 1; ; ; m) are inputs of intermediate goods purchased by a home producer with ( ; ; m) from a home producer with ( ; $; ) and a foreign exporter with ( ; $; 1) ; respectively. From the cost minimization problem, the input demand for each good by a home producer with ( ; ; m) is given by (9)

xdH;t ( ; $; ; ; ; m) = PH;t ( ; $; )

PX;t xt ( ; ; m) ;

(10)

xdF;t ( ; $; 1; ; ; m) = PF;t ( ; $; 1)

PX;t xt ( ; ; m) ;

2

where PX;t is the price index of material inputs. Since the total materials and the tradable aggregate have the same CES function with the same varieties, PX;t = PT;t : Analogously, we have the input demand for each good by a foreign producer with ( ; ; m) as (11)

d xF;t ( ; $; ; ; ; m) = PF;t ( ; $; )

PX;t xt ( ; ; m) ;

(12)

d xH;t ( ; $; 1; ; ; m) = PH;t ( ; $; 1)

PX;t xt ( ; ; m) :

The total demands for goods produced by a home producer with ( ; ; m) from a home and a foreign d ( ; ; 1) ; are given by producers for the use of material inputs, xdH;t ( ; ; m) and xH;t xdH;t (

(13)

d xH;t (

(14)

1 Z X

; ; m) =

=0 $

1 Z X

; ; 1) =

=0 $

xdH;t ( ; ; m; ; $; ) d xH;t ( ; ; 1; ; $; )

T;t (

T;t (

; $; ) d d$;

; $; ) d d$:

The producer with ( ; ; m) has a Cobb-Douglas production technology, 1

(15) yT;t ( ; ; m) = At

1

1 1

h kT;t ( ; ; m) lT;t ( ; ; m)1

i1

x

xt ( ; ; m)

x

:

Given the export status m; the pro…ts, excluding the …xed costs in production and exporting, of a producer with ( ; ; m) is given by (16)

T;t (

; ; m) = PH;t ( ; ; m) yH;t ( ; ; m) + mqt PH;t ( ; ; m) yH;t ( ; ; m) Wt lT;t ( ; ; m)

Rt kT;t ( ; ; m)

Px;t xt ( ; ; m) ;

where qt is the real exchange rate de…ned with home …nal goods as numeraire46 , and yH;t ( ; ; m) and yH;t ( ; ; m) are the total demands for its good at home and foreign, (17)

d yH;t ( ; ; m) = yH;t ( ; ; m) + xdH;t ( ; ; m) ;

(18)

d yH;t ( ; ; 1) = yH;t ( ; ; 1) + xdH;t ( ; ; 1) ;

d ( ; ; 1) is given by where yH;t

(19)

d yH;t (

; ; 1) = a

"

PH;t ( ; ; 1) PT;t

#

PT;t Dt ;

The producer with ( ; ; m) maximizes its pro…t subject to the production technology (15), and the constraint that the supply to home and foreign markets is equal to the demand by …nal and tradable good producers at home and foreign (17) and (18), (20) yT;t ( ; ; m) = yH;t ( ; ; m) + m (1 + ) yH;t ( ; ; m) ; where

is the iceberg trade cost that home tradable good producers face.

46

With the normalization of Pt = Pt = 1; the real exchange rate qt = et Pt =Pt = et ; where et is the nominal exchange rate de…ned with home currency as numeraire.

3

Form the pro…t maximization problem, we have the prices set by the producer with ( ; ; m) as (21) (22)

1 M Ct (At ) 1 ; 1 PH;t ( ; ; 1) PH;t ( ; ; 1) = (1 + ) ; qt

PH;t ( ; ; m) =

where M Ct is the marginal cost of production for a tradable good producer with (23) M Ct =

PT;t

x

x

"

1

Wt

Rt

1

1

1

x

#1

=A

1;

x

:

The demands for inputs in production are given by (24)

xt ( ; ; m) =

(25)

lT;t ( ; ; m) =

(26)

kT;t ( ; ; m) =

x

PT;t (1

M Ct (At ) 1 x ) (1

1

yT;t ( ; ; m) ;

x)

M Ct (At ) 1

Wt x (1

Rt

x)

M Ct (At ) 1

1

1

yT;t ( ; ; m) ;

yT;t ( ; ; m) ;

With the demands for goods produced by a home producer with ( ; ; m) from each producer at home and foreign (9) and (12), and the demand for material inputs (24) together with the prices set by the producer with ( ; ; m) in (21) and (22), the total demand for goods produced by a home producer with ( ; ; m) for the use of material inputs at home and foreign (13) and (14) can be rewritten as (27)

xdH;t ( ; ; m) =

x PH;t ( 1 Z X

PT;t 1 M Ct

; ; m) (At ) 1

1

yT;t ( ; $; )

=0 $

(28)

d xH;t ( ; ; 1) =

x PH;t ( 1 Z X

=0 $

T;t (

; $; ) d d$;

T;t (

; $; ) d d$:

PT;t 1 M Ct

; ; 1) (At ) 1

1

yT;t ( ; $; )

Thus, the total output of a producer, yT;t ( ; ; m) ; is given by (29)

h i d d d yT;t ( ; ; m) = yH;t ( ; ; m) + xdHt ( ; ; m) + m (1 + ) yH;t ( ; ; m) + xHt ( ; ; m) = PH;t ( ; ; m)

where Jt = aPT;t Dt + (22) we have (30)

x M Ct PT;t

1 P1

yT;t (a; ; m) = PH;t (a; ; m) =

M Ct 1

Jt + m (1 + ) PH;t (z; ; 1) R

(At ) 1

=0 $

1

yT;t ( ; $; )

Jt 1 + m (1 + )1

(At )

1

Jt (1 + m t ) ;

4

qt

Jt Jt

Jt :

t(

; $; ) d d$. Then, with

where t = (1 + )1 we have (31)

Jt Jt

qt

1 Z X

Ht =

. Multiplying both sides with (At ) 1

(At ) 1

1

yT;t ( ; ; m)

T;t (

1

and integrating over ( ; ; m) ;

; ; m) d d

m=0

M Ct 1

= where

T;t ;

X;t ;

(32)

T;t

=

(33)

X;t

=

(34)

NT;t =

Jt At NT;t

T;t

+

t

X;t

;

and NT;t are de…ned as 1 Z 1 X NT;t m=0 Z 1 NT;t 1 Z X

T;t (

T;t (

T;t (

; ; m) d d ;

; ; 1) d d ;

; ; m) d d :

m=0

With (31), we can rewrite Jt as (35) Jt = aPT

"

1

D 1

M Ct 1

x

1 1

PT;t At NT;t

T;t

+

X;t

t

#

1

:

Marginal Producers and the Value of Producers: With the …rst order conditions for the pro…t maximization problem, excluding …xed costs in production and exporting, we can rewrite the pro…t (16) as (36)

T;t (

; ; m) =

1

M Ct 1

1

At Jt (1 + m t ) :

The value of a producer is given by (37)

(38)

0

m VT;t (z; ; m) =

; ; m) Z +ns ( ) Qt

m0 PE;t fm e

T;t (

0

VT;t+1 0

; 0 ; m0

0

0

; 0j ;

d 0d 0;

0 1 VT;t (z; ; m) = max VT;t (z; ; m) ; VT;t (z; ; m) ;

and the critical level of technology for exporters and non-exporters, Z (39) PE;t fm e = ns m;t ( ) Qt VT;t+1 0 ; 0 ; 1 VT;t+1 0

0

; 0j

m;t (

);

0

d 0d 0:

The entry condition with equality is given by Z (40) PE;t fE = Qt VT;t+1 0 ; 0 ; 0 E 0 ; 0

0

0

5

d 0d 0:

m;t ( 0

) ; satis…es

; 0; 0

Now, we can normalize the variables with (39) and (40) with t , we have (41)

m0 VeT;t ( ; ; m) = (1 + m t )

PE;t

m0

Z

t+1

+ns ( ) Qt

t

(42)

PE;t

fm e

= ns

t

0

(43)

PE;t

; 0j

Z

t+1

fE = Qt

t

(44)

m;t (

t

0 VeTm ( ; ; m) = (1 + m )

+ns ( )

(46)

0

0

fm e

0

Z

VeT;t+1 0

0

d 0d 0; VeT;t+1

0

0

; 0 ; m0

h VeT;t+1

; 0; 0

0

0

E

;

0

; 0j ; VeT;t+1

; 0; 1

0

d 0d 0; 0

; 0; 0

i

d 0d 0;

o n 0 1 ( ; ; m) ; VeT;t ( ; ; m) ; VeT;t ( ; ; m) = max VeT;t

where VeT;t (z; ; m) = VT;t (z; ; m) = as (45)

0

t

);

At Jt : Dividing both sides of (37), (38),

t

t+1

m;t ( ) Qt

1

M Ct 1

1

=

t

fm fE

ns ( e

=

m(

Z ))

t:

Using (43), we can rewrite (41) and (42) in the steady state fm fE

m0

0

R

0 0

VeT h 0

Z

e 0

0

; 0 ; m0

0

VeT 0

0

; 0; 0

E

0

;

0

d 0d 0; i VeT ( 0 ; 0 ; 0) ( 0 ; 0 j

d 0d

0

; 0j ;

VeT ( 0 ; 0 ; 1) R 0 0 ; 0) e 0 0 VT ( ;

E

( 0; 0) d 0d

m(

0

) ; ) d 0d

0

;

0 e where m0 = 1 if m ( ) and m = 0 otherwise. Thus the normalized value of producers VT is determined by fm =fE and given productivity and trade cost shock processes.

Total Sales, and Exports: Total sales of a tradable good producer are given by (47)

st ( ; ; m) = PH;t ( ; ; m) yH;t ( ; ; m) + mqt PH;t ( ; ; m) yH;t ( ; ; m) M Ct 1

=

1

At Jt Nt (1 + m t ) :

Total sales of all tradable good producers are given by (48)

1 Z X

St =

st ( ; ; m)

T;t (

; ; m) d d

m=0

M Ct 1

=

1

At Jt Nt

T;t

+

t

X;t

:

The total exports are given by Z h i d d (49) EXt = qt PH;t ( ; ; 1) yH;t ( ; ; 1) + xHt ( ; ; 1) d d =

M Ct 1

At Jt Nt

t

X;t :

6

The export share of total sales is given by (50)

T Rt =

EXt St t

=

T;t +

X;t

: X;t

t

Size Distribution: From (25) and (30), we have (51)

lT;t ( ; ; m) =

(1

x ) (1

x)

Wt (1

1

=

M Ct (At ) 1

x ) (1

x)

Wt

1

yT;t ( ; ; m) M Ct 1

At

1

Jt (1 + m t ) ;

The total labor in production is given by (52)

Lp;t =

1 Z X

lT;t ( ; ; m) d d

m=0

=

1

(1

x ) (1

Wt

x)

At

M Ct 1

1

Jt Nt

T;t

+

t

X;t

:

The labor input of a producer relative to the average labor in production is given by (53)

lt ( ; ; m) = Lp;t =Nt

(1 + m t ) : T;t + t X;t

Proposition 1. Once the model is calibrated to match the size and export participation distributions, the export intensity and the exporter characteristics at home, then the trade share of sales at home and the trade growth with respect to a change in the export intensity are independent of: (i) the elasticity of substitution across varieties, ; (ii) the variables that determine the size of home country, such as the country-wide productivity and population; and (iii) all variables in the foreign country. Proof of Proposition 1 In the calibration, we set to match the export intensity, intensity = = (1 + ) : To match the producer level characteristics, we calibrate parameters for the productivity and …xed cost shock processes E ( ; ) ; ( 0 ; 0 j ; ) ; and ns ( ) ; and the relative …xed costs f0 =fE and f1 =fE with (45), (46), and (53). The total sales of a producer is then proportional to (1 + m ) from (47). Since all these equations do have have the elasticity of substitution parameter, ; the trade share and its component, intensity, export participation rate, and the exporter premium are independent of : Furthermore, All home and foreign countries’variables that a¤ect the trade share are summarized by . So the growth rates of the trade share and its components are dependent only on a change in : C. Multi-stage Production In this subsection, we separate the material input production from the tradable good producers. We assume that two countries, home and foreign are symmetric, and we normalize …nal good prices in two countries with Pt = Pt = 1: 7

The stages of production in the economy are de…ned as follows. In the …rst stage heterogeneous producers produce di¤erentiated goods with a Cobb-Douglas production function 1

(54) y1;t ( ; ; m) =

1

k1;t ( ; ; m) l1;t ( ; ; m)1

:

where y1;t ( ; ; m) is the output, k1;t ( ; ; m) and l1;t ( ; ; m) are the capital and labor inputs, and is the capital share in production. Stage-1 producers face the sunk/…xed cost in exporting f1m : Each period, new producers can enter the stage-1 sector by incurring the sunk cost of entry, f1E : In the second stage, producers produce di¤erentiated goods with a Cobb-Douglas production function h i1 x 1 1 1 k (55) y2;t ( ; ; m) = ( ; ; m) l ( ; ; m) xt ( ; ; m) x ; 2;t 2;t where xt ( ; ; m) is the aggregate material input in production which is given by 2 1 Z X 1 4 xdH;t ( ; $; ; ; ; m) (56) xt ( ; ; m) = 1;t ( ; $; ) d d$ =0 $

+

Z

xdF;t ( ; $; 1; ; ; m)

$

1

1

1;t (

; $; 1) d d$

;

where xdH;t ( ; $; ; ; ; m) and xdF;t ( ; $; ; ; ; m) are inputs of stage-1 goods purchased by a stage–2 home producer with ( ; ; m) from a stage-1 home producer with ( ; $; ) and a stage-1 foreign exporter with ( ; $; 1) ; respectively; 1;t ( ; $; ) and 1;t ( ; $; ) are the measures of home and foreign stage-1 producers with ( ; $; ) ; respectively. Stage-2 producers face the sunk/…xed cost in exporting f2m : Each period, new stage-2 producers can be created upon the payment of the sunk cost, f2E : The …nal good producers have the production function 1

(57)

Dt =

(58)

DT;t =

1

a DT;t + (1 1 Z X

1

a) DN;t

d y2H;t ( ; ; m)

1

2T;t (

; ; m) d d

m=0

+ (59)

DN;t =

Z

Z

d yN;t ( )

d y2F;t ( ; ; 1)

1

1

2T;t (

; ; 1) d d

;

1

1

N

( )d

;

d d ( ; ; m) are demand for and operate under the perfect competition. Here, y2H;t ( ; ; m) and y2F;t goods produced by home and foreign stage-2 producers with ( ; ; m) ; respectively; and 2T;t ( ; ; m) and 2T;t ( ; ; m) are the measures of home and foreign stage-2 producers with ( ; ; m) ; respectively.

Model Solution We start from the …nal good producer’s problem and move to earlier stage producers’problems.

8

Final Good Producers: Given the prices of stage-2 goods, and the price of the …nal good in the market, the …nal good producers at home and foreign have demands for stage-2 goods as (60) (61) (62) (63)

d y2H;t ( ; ; m) = a [P2H;t ( ; ; m)] d y2H;t ( ; ; 1) = (1

PT;t Dt ;

a) P2H;t ( ; ; 1)

d y2F;t ( ; ; m) = a P2F;t ( ; ; m) d y2F;t ( ; ; 1) = (1

PT;t Dt ;

PT;t Dt ;

a) [P2F;t ( ; ; 1)]

PT;t Dt :

Where the price indices of the aggregate goods are given as (64)

1 Z X

PT;t =

P2H;t ( ; ; m)1

2T;t (

; ; m) d d

m=0

+ (65) (66)

PN;t =

Z

Z

1 1

1

P2F;t ( ; ; 1)

2T;t (

; ; 1) d d

;

1 1

1

PN;t ( )

N;t (

h 1 + (1 Pt = 1 = aPT;t

;

)d

1 a) PN;t

i

1 1

:

Stage-2 Producers: From the cost minimization problem of stage-2 producers, we have the 1 marginal cost of production for a stage-2 producer with ( ; ; m) as 1 M C2;t . Here M C2;t is the marginal cost of production for the stage-2 producer with = 1; (67) M C2;t =

PX;t

x

x

"

Wt

Rt

1

(1

1

1

x)

#1

x

;

where PX;t is the price index of the aggregate material input in stage-2 production. A stage-2 producer with ( ; ; m) sets its prices at home and foreign if it is an exporter with a constant mark-up as (68) (69)

1 M C2;t 1 ; 1 P2H;t ( ; ; 1) = (1 + 2 ) P2H;t ( ; ; 1) ;

P2H;t ( ; ; m) =

where 2 is the iceberg cost for stage-2 goods. Using the prices, and symmetry, the price of tradable good PT;t can be written as (70) PT;t =

M C2;t 1

1 1 N2;t

h

2T;t + (1 +

1 2)

2X;t

9

i

1 1

;

where (71)

2T;t

=

(72)

2X;t

=

(73)

N2;t =

1 Z 1 X N2;t m=0 Z 1 N2;t 1 Z X

2;t (

2;t (

2;t (

; ; m) d d ;

; ; 1) d

;

; ; m) d d :

m=0

The demand for inputs are given by (74) (75) (76)

xt ( ; ; m) =

l2;t ( ; ; m) = (1 k2;t ( ; ; m) =

1

1 x PX;t M C2;t

1

) (1

(1

y2;t ( ; ; m) ;

x ) Wt 1

x ) Rt

1

M C2;t

M C2;t

1 1

1 1

y2;t ( ; ; m) ;

y2;t ( ; ; m) :

From the cost minimization problem, the demand for each material input by the stage-2 producer with ( ; ; m) for the goods produced by a stage-1 producer with ( ; $; ) is given by (77)

xdH;t ( ; $; ; ; ; m) = [P1H;t ( ; $; )]

PX;t xt ( ; ; m) ;

(78)

xdF;t ( ; $; ; ; ; m) = [P1F;t ( ; $; )]

PX;t xt ( ; ; m) ;

(79)

d xF;t ( ; $; ; ; ; m) =

P1F;t ( ; $; )

PX;t xt ( ; ; m) ;

(80)

d xH;t ( ; $; ; ; ; m) =

P1H;t ( ; $; )

PX;t xt ( ; ; m) :

The price index of the aggregate material input in stage-2 production, PX;t ; is given by ( 1 Z X (81) PX;t = [P1H;t ( ; ; m)]1 1;t ( ; ; m) d d m=0

+

Z

1

1

[P1F;t ( ; ; 1)]

1

1;t (

; ; 1) d d

:

The total output of a stage-2 producer with ( ; ; m) is given by (82)

d ( ; ; m) + (1 + y2;t ( ; ; m) = y2H;t

= a [P2H;t ( ; ; m)]

d 2 ) y2H;t (

PT;t

; ; m) h Dt 1 + m (1 +

The pro…t of a stage-2 producer with ( ; ; m) is given by (83)

2;t (

1 2)

i

:

d d ; ; m) = P2H;t ( ; ; m) y2H;t ( ; ; m) + P2H;t ( ; ; m) y2H;t ( ; ; m)

PX;t xt ( ; ; m) =

a

M C2;t 1

Wt l2;t ( ; ; m)

Rt k2;t ( ; ; m)

1

PT t Dt (1 + m 2 ) ;

10

where (84)

2

1 2)

= (1 +

: The total sales of all stage-2 producers are given by

1 Z X

S2;t =

h i d d P2H;t ( ; ; m) y2H;t ( ; ; m) + P2H;t ( ; ; m) y2H;t ( ; ; m)

m=0

2;t ( 1 aPT;t

=

; ; m) d d Dt ;

and the total exports of stage-2 producers are given by Z d (85) EX2;t = P2H;t ( ; ; 1) y2H;t ( ; ; 1) 2;t ( ; ; 1) d d 2X;t

2

= 2T;t

+

S2;t : 2X;t

2

The trade share of total sales in stage-2 production is given by (86)

T R2;t =

EX2;t S2;t 2X;t

2

=

+

2T;t

2

: 2X;t

The value of a stage-2 producer with ( ; ; m) is given by (87)

(88)

0

m V2T;t ( ; ; m) =

; ; m) Z +n2s ( ) Qt

m0 PE;t f2m e

2T;t (

0

0

V2T;t+1

0

; 0 ; m0

2

0

; 0j ;

d 0d 0;

0 1 V2T;t ( ; ; m) = max V2T;t ( ; ; m) ; V2T;t ( ; ; m) ;

and the critical level of technology for exporters and non-exporters, 2m;t ( ) ; in stage-2 production satis…es Z (89) PE;t f2m e = n2s 2m;t ( ) Qt V2T;t+1 0 ; 0 ; 1 V2T;t+1 0 ; 0 ; 0 0

0

2

0

; j

2m;t (

);

0

d 0d 0:

Here, 2 ( 0 ; 0 j ; ) is the transition probability of productivity and the cost shock, and n2s ( ) is the survival probability of stage-2 producers. The entry condition in stage-2 with equality is given by Z (90) PE;t f2E = Qt V2T;t+1 0 ; 0 ; 0 2E 0 ; 0 d 0 d 0 ; 0

where

2E

0

( 0 ; 0 ) is the initial distribution of entrants in stage-2 production. Now, we can normalize

the variables with

2;t

=

a

M C2;t 1

1

PT t Dt : Dividing both sides of (87), (88), (89) and (90)

11

with (91)

2;t ,

we have

m0 Ve2T;t ( ; ; m) = (1 + m t )

PE;t

m0

Z

2;t+1

+n2s ( ) Qt

2;t

(92)

PE;t

f2m e

= n2s

2m;t (

2;t

0

2

(93)

PE;t

0

; j

2m;t (

Z

0

);

Ve2T;t+1

Z

0

0

0

d d ; Ve2T;t+1

h

0

; 0 ; m0

Ve2;T;t+1

; 0 ; 0 2E o n 0 1 ( ; ; m) ; Ve2T;t ( ; ; m) ; Ve2T;t ( ; ; m) = max Ve2T;t 2;t

m0 Ve2T ( ; ; m) = (1 + m )

m Z

f2m f2E

n2s ( e =

2m (

))

R

0

0

0

0

0

;

0

2

; 0j ;

Ve2T;t+1

; 0; 1

0

d 0d 0; 0

; 0; 0

i

d 0d 0;

Using (93), we can rewrite (91) and (92) in the steady

f2m f2E 0

0

0

2;t :

0

+n2s ( )

(96)

0

2;t

where Ve2T;t ( ; ; m) = V2T;t ( ; ; m) = state as (95)

0

2;t+1

) Qt

2;t+1

f2E = Qt

2;t

(94)

fm e

2;t

Z

e

0

0

Ve2T

0

; 0; 0

2E

0

;

0

Ve2T 0 ; 0 ; m0 2 0 ; 0 j ; d 0 d 0 ; h i 0 0 ; 1) e Ve2T ( 0 ; 0 ; 0) 2 ( 0 ; 0 j 0 V2T ( ; R 0 0 ; 0) 0 0 0 0 e 0 0 V2T ( ; 2E ( ; ) d d

d 0d

2m (

0

) ; ) d 0d

0

;

0 e where m0 = 1 if 2m ( ) and m = 0 otherwise. Thus the normalized value of producers V2T is determined by f2m =f2E and 2 given productivity and trade cost shock processes.

Stage-1 Producers: From the cost minimization problem of stage-1 producers, we have the 1 marginal cost of production for a stage-1 producer with ( ; ; m) as 1 M C1;t . Here M C1;t is the marginal cost of production for the stage-1 producer with (1; ; m) ; (97) M C1;t =

Rt

1

Wt

:

1

A stage-1 producer with ( ; ; m) sets its prices at home and foreign if it is an exporter with a constant mark-up as (98) (99)

1 M C1;t 1 ; 1 P1H;t ( ; ; 1) = (1 + 1 ) P1H;t ( ; ; 1) ;

P1H;t ( ; ; m) =

where 1 is the iceberg cost for stage-1 goods. With the prices and symmetry, the price index of the material input can be rewritten as (100) PX;t =

M C1;t 1

1 1 N1;t

h

1T;t

+ (1 +

1)

1

12

1X;t

i

1 1

:

where (101)

1T;t

=

(102)

1X;t

=

(103)

N1;t =

1 Z 1 X N1;t m=0 Z 1 N1;t 1 Z X

1;t (

1;t (

1;t (

; ; m) d d ;

; ; m) d d ;

; ; m) d d :

m=0

The demand for inputs are given by ) Wt 1 M C1;t

(104) l1;t ( ; ; m) = (1

Rt 1 M C1;t

(105) k1;t ( ; ; m) =

1 1

1 1

y1;t ( ; ; m) ;

y1;t ( ; ; m) :

The total demand for goods produced by stage-1 home producer with ( ; ; m) by stage-2 producers at home, xdH;t ( ; ; m) is given by (106)

xdH;t (

1 Z X

; ; m) =

=0 $

= a

xdH;t ( ; ; m; ; $; ) 1

x

2;t (

; $; ) d d$

1 Dt : PX;t1 PT;t

[P1H;t ( ; ; m)]

Similarly, the total demand for goods produced by the stage-1 home producer with ( ; ; m) by d ( ; ; m) ; is given by stage-2 producers at foreign, xH;t (107)

d xH;t (

1 Z X

; ; m) =

=0 $

= a

d xH;t ( ; ; m; ; $; )

1

x

2;t (

; $; ) d d$

PX;t 1 PT;t1 Dt :

P1H;t ( ; ; m)

The total demand for goods produced by the stage-1 producer at home with ( ; ; m) ; which equals to total output of the producer, is given as (108) y1;t ( ; ; m) = a

1 x

1 PX;t1 PT;t Dt (1 + m 1 ) ;

[P1H;t ( ; ; m)]

where 1 = (1 + 1 )1 : Here, we directly applied the symmetry. The pro…t of a stage-1 producer with ( ; ; m) is given by (109)

1;t (

d ; ; m) = P1H;t ( ; ; m) xdH;t ( ; ; m) + mP1H;t ( ; ; m) xH;t ( ; ; m)

=

Wt l1;t ( ; ; m)

Rt k1;t ( ; ; m)

a

M C1;t 1

x

1

13

1 1 PX;t1 PT;t Dt (1 + m 1 ) :

The total sales of all stage-1 producers are given by 1 Z X

(110) S1;t =

h i d P1H;t ( ; ; m) xdH;t ( ; ; m) + mP1H;t ( ; ; m) xH;t ( ; ; m)

m=0

1;t (

; ; m) d d 1

= a

1 PT;t Dt

x

1

=

S2;t ;

x

and the total exports of stage-1 producers are given by Z d (111) EX1;t = P1H;t ( ; ; 1) y1H;t ( ; ; 1) 1;t ( ; ; 1) d d 1X;t

1

= 1T;t

+

S1;t : 1X;t

1

The trade share of total sales in stage-1 production is given by (112) T R1;t =

EX1;t S1;t 1X;t

1

= 1T;t

+

: 1X;t

1

The value of a stage-1 producer with ( ; ; m) is given by 0

m (113) V1T;t ( ; ; m) =

; ; m) Z +n1s ( ) Qt

m0 PE;t f2m e

1T;t (

0

0

V1T;t+1

0

; 0 ; m0

1

0

; 0j ;

d 0d 0;

0 1 (114) V1T;t ( ; ; m) = max V1T;t ( ; ; m) ; V1T;t ( ; ; m) ;

and the critical level of technology for exporters and non-exporters, 1m;t ( ) ; in stage-1 production satis…es Z (115) PE;t f1m e = n1s 1m;t ( ) Qt V1T;t+1 0 ; 0 ; 1 V1T;t+1 0 ; 0 ; 0 0

0

1

0

; j

1m;t (

);

0

d 0d 0:

Here, 1 ( 0 ; 0 j ; ) is the transition probability of productivity and the cost shock, and n1s ( ) is the survival probability of stage-1 producers. The entry condition in stage-1 with equality is given by Z (116) PE;t f1E = Qt V1T;t+1 0 ; 0 ; 0 1E 0 ; 0 d 0 d 0 ; 0

where

1E

0

( 0 ; 0 ) is the initial distribution of entrants in stage-1 production. Now, we can normalize

the variables with

1;t

=

a

x

1

M C1;t 1

1

1 PX;t1 PT;t Dt : Dividing both sides of (113), (114),

14

(115) and (116) with

1;t ,

we have

ym0 (117) Ve1T;t ( ; ; m) = (1 + m 1 )

PE;t

m0

1;t+1

+n1s ( ) Qt

1;t

(118)

PE;t

f1m e

= n1s

1m;t (

1;t

0

1

PE;t

fm e

1;t

0

; j

Z

0

0

1;t+1

) Qt

1;t 1m;t (

Z

1;t+1

0

);

y Ve1T;t+1

Z

0

0

0

d d ; y Ve1T;t+1

h

0

; 0 ; m0

y Ve1;T;t+1

; 0 ; 0 1E o n y0 y1 y (120) Ve1T;t ( ; ; m) ; Ve1T;t ( ; ; m) ; ( ; ; m) = max Ve1T;t

(119)

f1E = Qt

1;t

1;t

y where Ve1T;t ( ; ; m) = V1T;t ( ; ; m) = state as ym0 ( ; ; m) = (1 + m 1 ) (121) Ve1T

+n1s ( )

(122)

n1s (

f1m f1E

e =

1m (

1;t :

))

R

0

0 0

0

0

0

0

;

0

; 0j ;

Ve1T;t+1

; 0; 1

0

d 0d 0; 0

; 0; 0

i

d 0d 0;

Using (119), we can rewrite (117) and (118) in the steady

f1m f1E

0

m Z

0

1

e

Z

0

0

y Ve1T

0

; 0; 0

1E

0

;

0

y 0 0 Ve1T ; ; m0 1 0 ; 0 j ; d 0 d 0 ; i h y y 0 ; 0 ; 0) 0 0 0 ; 0 ; 1) e e ( ( V V 0 1( ; j 1T 1T R 0 0 ; 0) 0 0 0 0 e 0 0 V1T ( ; 1E ( ; ) d d

d 0d

0

1m (

) ; ) d 0d

0

0 ey where m0 = 1 if 1m ( ) and m = 0 otherwise. Thus the normalized value of producers V1T is determined by f1m =f1E and 1 given productivity and trade cost shock processes.

Total Sales and Exports: The total sales in the tradable good sector are given by (123) ST;t = S1;t + S2;t 1

=

x

1 Dt : + 1 aPT;t

The total exports in the tradable good sector are given by (124) EXT;t = EX1;t + EX2;t 1 1 = T R1 + T R2 aPT;t Dt : x The trade share of the total sales in the tradable good sector is given as (125) T RT;t =

1

x x

T R1 + T R2 1

+1

:

Proposition 2. The trade share of total sales in the tradable good sector is an weighted average of stage-1 and stage-2 trade shares, and the growth rate of the trade share in the tradable good sector

15

;

is an weighted average of the trade share growths in two stages: T RT d T RT

= ! 1 T R1 + (1 d = !2T R1 + (1

b = Xnew =Xinitial where X

1:

! 1 ) T R2 ; d !2) T R2 ;

Proof of Proposition 2 As shown in (125), the trade share in the tradable good sector is an weighted average of stage-1 and stage-2 export shares of sales with 1

x

!1 = x

1

+1

;

the sales share of stage 1 production, ! 1 = S1 =ST : The growth rate of T RT is given as d d T RT = ! 2 T R1 + (1

d !2) T R2 ;

where the weight ! 2 is given by !2 =

! 1 T R1 ; ! 1 T R1 + (1 ! 1 ) T R2

the contribution of stage-1 trade share to the overall trade share.

Proposition 3. If stage-1 and stage-2 have (i) the same productivity and …xed cost shock processes, = ff2m ; and (iii) the same iceberg costs, 1 = 2 ; then the (ii) the same relative sunk/…xed costs, ff1m 1E 2E steady state trade shares and their growth rates in two stages are identical. Proof of Proposition 3 From (95), (96), (121), and (122), if the conditions hold with 1E ( ; ) = 2E ( ; ) ; 1 ( 0 ; 0 j ; ) = 0 0 2 ( ; j ; ) ; and n1s ( ) = n2s ( ) ; the normalized value functions and the distributions of producy ( 0 ; 0 ; m0 ) = Ve2T ( 0 ; 0 ; m0 ) and 1 ( ; ; m) =N1 = 2 ( ; ; m) =N2 : ers are identical in two stages, Ve1T d Thus, the trade shares and their growth rates are identical in two stages, T R1 = T R2 and T R1 = d T R2 : D. Solution The simulation of the model is straightforward, once we keep track of the distributions of establishments and the value functions of producers. Here, we …rst describe the approximation method for the evolution of the productivity distribution of establishments and the value functions in the tradable good sector.47 Then, we brie‡y describe the simulation steps for the steady state and transition dynamics computations. Approximating Distribution of Establishments: Here, we describe the approximation method for the evolution of productivity densities in the tradable good sector (the non-tradable sector is similar). 47

The evolution of productivity density and the value function for non-tradable good producers can be obtained using the same methods.

16

In the model, the shocks to the …xed cost in exporting are drawn from a log normal distribution, ( jz) = N (0; 2 (z)) in which the standard deviation of the shock depends on the productivity level. Since the productivity follows a normal distribution, z (z 0 jz) = N " z; 2" ; it is straightforward to construct the joint distribution of the two shocks. Let the transition probabilities of the shock to the …xed cost in exporting and the productivity be (z 0 ; 0 jz; ) : From the processes of productivity and …xed cost shocks, we can construct the joint density of z 0 and 0 conditional on z and 0 as z 0 ; 0 jz;

(126)

0

=

jz 0 ; z; 0

=

z 0 jz;

jz 0

z 0 jz :

z

For the entrants’distribution, we have E (z 0 ; 0 ). The measure of producers in the tradable good sector depends on the evolution of the idiosyncratic shocks and the export decisions, which are a function of the idiosyncratic and aggregate state, and evolves as (127)

0

0

z ; ;1 =

T;t+1

1 Z Z X

m=0

(128)

0

z ; 0; 0

T;t+1

=

1

ns (z)

T;t (z;

zm;t ( )

1 Z Z X

m=0

+NT E;t

z 0 ; 0 jz;

; m)

zm;t ( )

ns (z) 1 E

z0;

0

T;t (z;

; m)

dzd ;

z 0 ; 0 jz;

dzd

;

where NT E;t is the mass of entrants in the tradable good sector in period t. We discretize the state space and interpolate to approximate the density functions as follows: First, we choose uniformly spaced nodes for the productivity z 2 z 1 ; z 2 ; ; z J with an interval 48 1 J ! z : We choose z and z so that their absolute values are su¢ ciently large to not a¤ect the results. 0 We approximate the transition probability and the entrants’ initial distribution, cz z j jz j and 1; 2; c z j 0 . Next, we choose uniformly spaced nodes for the …xed cost shocks 2 ; G E with an interval ! : We approximate the probability of the shocks with the smallest and the largest H standard deviations as cL ( g ) and c ( g ) : The probability of …xed cost shocks conditional on

productivity is given as (129) c

(130)

g

jz j

! z

j

= ! z j cL ( 8 > < 1; j zH z = zH zlL ; > : 0;

g

(132) 48

g0

jz j ;

c zj0 ; E

g g0

= c

= c

g

);

z j < zL where Pr (zL ) = 0:01; z j 2 (zL ; zH ) ; z j zH where Pr (zH ) = 0:99:

Finally the joint probability of z and 0 (131) b z j ;

c H (

! zj

)+ 1

is constructed as

g0

jz j

0

g0

jz j

0

c z j 0 jz j ; z b

E

zj

0

:

We set n = 200: Increasing the number of nodes above 200 has a negligible impact on the results.

17

The approximated densities of establishments evolve as 0 (133) b T;t+1 z j ;

g0

;1 =

1 X G X J X

ns z j b T;t z j ;

m=0 g=1 j=1

0 (134) b T;t+1 z j ;

g0

;0

=

1 X G X J X

m=0 g=1 j=1

0 ; m b zj ;

ns z j b T;t z j ; 0

g0

+NT E;t bE z j ;

where Im;t (j; g) is the weight function 8 > 0 < zm;t ( g ) z j +! z =2 (135) Im;t (j; g) = !z > : 1

g

g

;

g0

jz j ;

0 ; m b zj ;

g0

g

Im;t (j; g) ;

jz j ;

g

[1

Im;t (j; g)]

with

if z j + ! z =2 if z j if z j

zm;t ;

! z =2 < zm;t ( ! z =2 zm;t (

g)

< z j + !=2;

g) ;

and m 2 f0; 1g : This interpolation allows the approximated model to have continuity in the thresholds for the exporting decisions, zm;t (m) ; and smooth transition dynamics.

Value Function Approximation: We solve the model by value function iteration. The key issue in solving the model is to solve for the evolution of the marginal exporters fz0t ( g ) ; z1t ( g )g :Given the value functions for exporters and non-exporters in period t+2, VT;t+2 z j ; g ; 1 and VT;t+2 z j ; g ; 0 ; and the values of aggregate variables in period t + 1 and t + 2, we …rst obtain the value functions in period t + 1 as ( Ct+2 j g j g ; m + max (136) VT;t+1 z ; ; m = ns z j T;t+1 z ; Ct+1 G X J X

0

g0

VT;t+2 z j ;

g 0 =1 j 0 =1

Ct+2 Ct+1

ns z j

G X J X

g0

jz j ; 0

VT;t+2 z j ;

g

g0

g 0 =1 j 0 =1

Wt+1 fm e

(137)

0 ; 0 b zj ;

g

;

; 0 ; 1 b zj ;

g0

jz j ;

g

With these value functions in t + 1; we obtain the di¤erence of values for a producer with z j ; and current exporting status m between exporting and not exporting next period as (138) dVT;t z j ;

g

;m

=

Wt fm e

g

+

Ct+1 Ct

G X J h X 0 VT;t+1 z j ;

g 0 =1 j 0 =1

g;

ns z j g0

;1

0

VT;t+1 z j ;

g0

;0

i

b zj0 ;

g0

jz j ;

g

:

The di¤erence dVT;t z j ; g ; m is monotonically increasing in z and passes 0 value where the producer is indi¤erent between exporting and not exporting. The thresholds for exporting decisions,

18

and z1;t (

g)

(139) zm;t (

g

ztjm

where ztjm (

g)

z0;t (

g)

)=

are obtained from

(

g

!dVT;t ztjm ;

)

dVT;t ztjm +1 ;

= max z j jdVT;t z j ;

g; m

g; m

dVT;t ztjm ;

g; m

; g; m

<0 :

Parameterization and Initial Steady State Computation: Given the value for the elasticity of substitution, , the iceberg trade costs in 1987 and 2007, and 87 07 , are obtained based on the export intensities in 1987 and 2007. In the model, the export intensity is given as (140) intensity =

(1 + )1 1 + (1 + )1

:

Thus, we set the iceberg costs in 1987 and 2007 based on the export intensity in the data as (141)

=

1

intensity intensity

1 1

1

The other parameter values are obtained based on the key moments in the data with several steps of iterations within iterations. First, we set the parameter values for the productivity innovations and the …xed cost shock process. In this step we search for the critical levels of technology for exporters and non-exporters, z0 ( ) and z1 ( ) ; instead of the …xed costs in exporting, f0 and f1 : Then, we …nd f0 and f1 to match the values of z0 ( ) and z1 ( ) in the steady state computation. This replacement makes computations less complicated. 1. Guess the values of parameters for the innovation of establishment distribution, " ; " ; and E ; values of parameters for the shut down probability, ; and nd0 ; the smallest and the largest standard deviations of …xed cost shocks, (zL ) and (zH ) ; and critical levels of technology for exporters and non-exporters, z1 ( ) and z0 ( ) : 2. We approximate the density function of establishment level productivity described above and obtain the distributions of exporters, non-exporters, and non-tradable good producers with the normalization of entrants. 3. With the distributions, we obtain the 5-year exit rate of entrants. We search for the parameter value of ; given other parameter values and with the iteration in Step 2, which matches the 5-year exit rate of entrants in the data. 4. We obtain the distributions for establishments and export participation rate, entrants’labor share, shut-down establishments’labor share. Note that, in the model, the employment of an establishment is proportional to the productivity, h i lT (z; ; m) = 1 + m (1 + )1 e( 1)z ; where is constant. We set so that the model implied average employment level in the tradable good sector matches the data. 5. We search for the critical levels of technology for exporters and non-exporters, z1 ( ) and z0 ( ) ; with the iteration in Step 3 and 4, to match the overall export participation rate and the stopper ratio of exporters. 19

6. We search for the parameter values of the innovation of establishment distribution, " ; " ; and E ; and the shut down probability, nd0 , with the iteration in Step 5, to match entrants’labor share, and shut-down establishments’ labor share, and minimize the distances between data and model implied distributions for the establishment share and the export participation rate. 7. Then, with the iteration in Step 6, we set the parameter values for the process of ; (zL ) and (zH ) ; to minimize the distance between the model implied and data distributions. After setting the parameter values for the innovation of productivity, the …xed cost shocks, and the thresholds for exporting decisions, z0 ( ) and z1 ( ), we …nd the steady state values, the …xed costs in exporting, f0 and f1 ; and the sunk costs in entry, fE ; with the normalization of overall number of establishments. In the steady state computation, we use a two-step procedure. 1. First, given the initial guesses of the aggregate variables, the …xed costs in exporting, and the sunk costs in entry, we obtain the value functions of producers in the steady state with the thresholds for exporting decisions through the iteration of the value functions. 2. Then, we update the values of the aggregate variables, and the …xed/sunk cost parameters. 3. Repeat Steps 1 and 2 until all the steady state conditions are satis…ed. New Steady State: With the new iceberg costs, we obtain the new steady state using the following procedure: 1. Given distributions of producers, we obtain the value functions in the new steady state and the values for the aggregate variables. 2. Then, with the update of the values for the aggregate variables, we update the value functions, the thresholds for exporting decisions, z0 ( ) and z1 ( ), and the distributions of exporters and non-exporters. 3. Repeat Steps 1 and 2 until all the steady state conditions are satis…ed. Transition Dynamics: In the transition dynamics, we assume that the steady state with 1987 is achieved initially. Then, in 1987 the agents get a new path of iceberg costs. Each year there is a shock to iceberg costs that is assumed to be temporary. In the simulation exercises, we further assume that the new steady state is achieved in T periods. We set T su¢ ciently large so that the resulting transitions are extremely insensitive to an increase in T .49 We set the initial guesses of the sequences of variables, value functions, and densities of establishments based on initial and new steady state values.50 Then, we use two period overlapping blocks to update the guessed values, densities, and value functions. The two period overlapping block computation gives more ‡exibility in updating the values and reduces the initial value problems. We use the following procedure for the transition dynamics computation: (i) (i) 1. First, given the current period, t; densities of establishments, b T;t (z; ; m) and b N;t (z) ; and (i)

(i)

the future values of the value functions, VT;t+2 (z; ; m) and VN;t+2 (z) ; we obtain the current and next period, t and t + 1; variables’values with which the current and next period equilibrium conditions are satis…ed. Here, the superscript (i) denotes the ith iteration. In this step, we revise the densities of establishments in period t + 1 and t + 2, and the value functions in period t and t + 1 for each set of guessed variables’values.

49 In the simulations, we set T = 300: The results show that all the variables become very close to the new steady state in t = 100: 50 For example, we can set the initial guesses of sequences as the weighted averages of the two steady state values.

20

2. Once the equilibrium conditions for period t and t + 1 are satis…ed, we update the values of (i) (i) period t variables, next period densities, b (z; ; m) and b (z), and the next period T;t+1

(i+1)

N;t+1

(i+1)

value functions, VT;t+1 (z; ; m) and VN;t+1 (z). Note that the densities of establishments in pe-

(i) riod t+1 are determined in period t in the model. So, we use updated densities, b T;t+1 (z; ; m) (i) and b N;t+1 (z), for the computation in the next period t + 1 for the same ith iteration. Also note that the entrants and incumbents care about the expected value of producers next period not the current period for their entry and exporting decisions in the model. So, the updated (i+1) (i+1) value functions , VT;t+1 (z; ; m) and VN;t+1 (z) ; in ith iteration are used in (i + 1)th iteration on in tth iteration. 3. Do Steps 1 and 2 for t = 1 through t = T: 4. Repeat Steps 1 through 3 until all the sequences of variables, densities, and value functions converge. 5. Check if the convergence of variables to the new steady state are achieved many periods before T: Otherwise, increase the terminal period T and redo all steps again.

Data Appendix Here we summarize some additional aspects of the changing scale of U.S. manufacturing establishments over time. In particular, we consider two things. First, we examine how changes in industry composition have a¤ected the scale of establishments in manufacturing. Second, we consider how the change in industrial classi…cation in 1997 from SIC to NAICS a¤ects both the scale of establishments and the size of the manufacturing sector. With respect to industry composition, we …nd that changes in the industry composition actually have hidden some of the shift to smaller scale establishments within manufacturing. With respect to the change in classi…cation scheme, we …nd a very small e¤ect on the size distribution of establishments. We do …nd that some of the contraction in manufacturing (about 3.8 percentage points out of 17.2 percentage points) can be attributed to industries being moved out of the manufacturing classi…cation in NAICS. Industry composition: One possible explanation for the shift toward smaller scale establishments is that it re‡ects a change in the industry composition of manufacturing. Indeed, if the U.S. has a comparative advantage in industries with smaller establishments, then increased global integration would go hand-in-hand with smaller establishments. To see if this is the case, we control for changes in the scale of production from changes in the industry composition in production by calculating average employment per establishment as a weighted average of each industry’s share of employment in a base year (data from each CM). For simplicity, we choose our base year as 1972. Thus average employment per establishment in period t is calculated as lt

=

J X

j Lj;t =Nj;t ;

j=1

j

= Lj;1972 =

J X

Lj;1972 ;

j=1

where j is a 4 digit SIC industry.51 Figure A1 plots the change in average size (denoted unweighted), our weighted measure of size (denoted Laspeyres), and a measure that weights each industry the same (denoted even weights). Controlling for changes in industry composition, from 1972 to 1997 51

In 1987 a new SIC system was put in place to replace the 1972 SIC classi…cation and so industries were concorded.

21

we actually …nd even larger declines in scale than with our raw measure (39 percent vs. 22 percent). Thus, it appears changes in the industry composition actually hid an even larger change in the scale of production. SIC to NAICS in 1997: One problem in a time series study of U.S. manufacturing is the change in the classi…cation system in 1997 from the Standard Industrial Classi…cation (SIC) to the North American Industrial Classi…cation System (NAICS). At the level of manufacturing, some establishments were added to manufacturing while others were dropped.52 This switchover potentially a¤ects the size of manufacturing in the economy as well as the scale of production within manufacturing. Fortunately, in the switchover year, plants were classi…ed both ways and so it is possible to get a sense of the in‡uence of the switchover on both margins. We …nd that not accounting for the switchover tends to overstate the decline in manufacturing but has a much smaller e¤ect on the scale of establishments in manufacturing. For the size of the manufacturing sector, we …nd that the shift from SIC to NAICS lowers the number of manufacturing establishments by 3.8 percent and the number of employees by 3.7 percent. Given the similar drop in workers and establishments the average establishment size falls by less than 0.1 percent (from 46.47 to 46.43 employees). Thus, while the NAICS switchover contributes partly to the contraction of manufacturing, it appears to have very little impact on the average scale of production within manufacturing. While the switchover may have a small e¤ect on average scale, it may still have a¤ected the size distribution since it a¤ected many …rms. From a gross standpoint, as a share of the SIC-based Census, industries dropped from manufacturing accounted for 9.8 percent of establishments and 4.7 percent of employees, while those added accounted for 6.3 percent of establishments and 0.9 percent of employees (as a share of the NAICS-based census). Given that switchover a¤ected 5 to 10 percent of the establishments (and 0.9 percent to 4.7 percent of employment) the NAICS switchover may contribute to some of the shift toward small scale manufacturing. Indeed, the average plant leaving manufacturing had 22.3 employees while the average new plant had only 6.7 employees. Thus, some of the shift to smaller plants may be a measurement issue. To control for the role of this switchover during our sample period, we constructed the size distribution of plants in 1997 using both the SIC and NAICS classi…cation.53 We then calculated the total change in the size distribution as the change in the share of employment from 1987 to 1997 using the SIC code and the change from 1997 to 2002 using the NAICS classi…cation. Figure A2 plots our measure taking account the NAICS revision along with the raw measure in the text. Clearly, both measures tell the same story - there has been an important shift from large plants to small plants. 52

The prominent industries included in manufacturing from NAICS (but not in manufacturing in SIC) were bakeries, candy stores where candy is made on the premises, custom tailors, makers of custom draperies, and tire retreading, while the industries subtracted were primarily logging and publishing. Another change from NAICS is that auxiliaries with manufacturing are no longer included in the manufacturing date. These auxiliaries function primarily to manage, service, or support the activities of their company’s operating establishments, such as a central administrative o¢ ce or warehouse 53 To construct the SIC employment-size distribution, it was necessary to estimate the size distribution in a small number of industries that were a¤ected by the switchover. For each of the a¤ected industries we know the average size and number of plants plus some moments of the distribution (i.e. plants and employees within certain sizes) but lacked information on certain employment classes for disclosure reasons.

22

Change in Average Plant Size from 1972 -.4 -.3 -.2 -.1 0

Figure A1: Change in Average Employment Size in Manufacturing (1972 to 1997)

1972

1977

1982

1987

1992

1997

Year Laspeyres

Even weights Unweighted

Figure A2: Change in Employment size distribution adjusted for NAICS switchover 0.04

0.02

Percent

0.00

-0.02

Adjusted for NAICS Not Adjusted for NAICS

-0.04

-0.06 1-99

100-249

250-499

500-999

Employment of an Establishment

23

1000-2499

2500+

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