ECONOMICS WORKING PAPER SERIES

WORKERS: A STRUCTURAL APPROACH

Scott Baier

Serge Shikher

Yoto V. Yotov

Working Paper 2017–03–A

500 E Street SW
Washington, DC 20436

March 2017

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Trade Liberalization with Heterogeneous Workers: A Structural Approach
Scott Baier, Serge Shikher, Yoto V. Yotov
Office of Economics Working Paper 2017–03–A

Abstract

We build a multi-sector general equilibrium model of trade and production with heterogeneous workers. The model features intersectoral linkages on the demand side, via consumption substitution links, and intersectoral linkages on the supply side, via the use of intermediates. Importantly, we also allow for three different types of workers, based on education, who can be affected differentially by trade. Thus, the model can be used to study the implications of trade liberalization for both across- and within-country income inequality. To demonstrate the usefulness and effectiveness of our methods, we employ a data set of 45 countries and 22 sectors in 2010 to simulate the effects of the hypothetical formation of a regional trade agreement (RTA) between the United Stated and Great Britain.

Scott Baier
The John E. Walker Department of Economics
Clemson University
sbaier@clemson.edu

Serge Shikher
Research Division
Office of Economics
serge.shikher@usitc.gov

Yoto V. Yotov
School of Economics
Drexel University
yotov@drexel.edu

### 1 Introduction and Motivation

Globalization has brought many benefits, but it has not benefited everyone. Some workers do not feel enriched by globalization. Instead, they feel hurt by the intensive integration and trade liberalization efforts that took place in the past quarter century. These workers have become a significant political force. “Some 58% of people in professional and higher management jobs [in Great Britain] wanted to remain [in the European Union] compared with only 27% of people in unskilled jobs. Not surprisingly, high-status individuals with marketable skills favour UK membership of the EU, whereas people who lack these skills and are vulnerable in the labour market are opposed.” (Independent, UK, June 26, 2016).

At the same time, stimulated by the elegant and intuitive theories of Eaton and Kortum (2002) and Anderson and van Wincoop (2003) and by the remarkable empirical success of the structural gravity model, the academic field of international trade witnessed the rise of a new generation of computable general equilibrium (CGE) trade models with solid theoretical foundations and and tight connection to the data, cf. Costinot and Rodríguez-Clare (2014).1

We augment a structural gravity model with worker heterogeneity, which allows us to link trade and labor market outcomes and quantify the impact of trade liberalization (or, alternatively a move toward autarky) simultaneously on across- and within-country income inequality. Our tractable general equilibrium trade framework incorporates multiple countries, multiple industries, inter-industry linkages on the supply and on the demand side, and, most importantly, different types of labor.

Our model complements and extends a series of recent sectoral gravity models (e.g. Egger, Larch and Staub2012Costinot, Donaldson and Komunjer2012Shikher2011Larch and Wanner2014Caliendo and Parro2015Anderson and Yotov2016). While intermediates still play a key role both in our theory and in the empirical analysis, the main difference between our framework and this previous literature is that our model also includes heterogeneous types of labor.

The links between trade and labor market outcomes have been previously studied using a variety of methodologies and data from past trade liberalization episodes. For example, Haskel and Slaughter (2003) find that in 1970s and 1980s cuts in tariffs and transportation costs in the United States mostly occurred in the low skill intensive industries. However, they find that falling tariffs and transport costs did not result in significant rise in inequality. Autor, Dorn and Hanson (2013) find that increased Chinese imports had negative effects on local labor markets in the United States. Caliendo, Dvorkin and Parro (2015) study the effects of increased Chinese imports on US labor markets at the state level using a dynamic labor search model.

McLaren and Hakobyan (2016) use US Census data to estimate effects of NAFTA on US wages disaggregated by industry, location, and also education. They find that wages of blue-collar workers in some industries and localities were significantly negatively affected. Caliendo and Parro (2015) use a computable model to show that NAFTA resulted in an overall increase in US real wages. Lee (2017) extends the Eaton-Kortum model to include worker heterogeneity, which allows her to study the link between trade and inequality. Haskel et al. (2012) provide a review of the literature on the effects of globalization on US wages.

In comparison to some of these papers, we contribute by using a structural approach. In comparison to the newer papers that also use a structural approach, e.g. Caliendo, Dvorkin and Parro (2015), we introduce heterogeneous workers.2 In comparison to Lee (2017), our model is easier to solve quantitatively and can provide a much more detailed industry breakdown and analysis.3 We also account for differences in education quality across countries.

Our model generates clear predictions about two channels though which trade liberalization may affect the demand for each type of labor in each country and in each sector. The first channel is via the outward multilateral resistance index of Anderson and van Wincoop (2003), which measures the incidence of trade costs on the producers in each sector and in each country. The relationship is inverse. Intuitively, a higher multilateral resistance for the producers in a given sector translates into lower factory gate prices, which, in turn, lead to lower demand for all factors of production, including each type of labor in this industry. Importantly, since the outward multilateral resistance is a general equilibrium index, the demand for labor of each type can be affected by changes in trade costs in any country in the world. Finally, we note that the impact of trade liberalization via this channel will be stronger when the share of this labor’s type is in production is larger.

The second channel through which trade liberalization affects labor market outcomes is via the inward multilateral resistance, which measures the incidence of trade costs on the consumers (of both final and intermediate goods) in each country. Once again, the relationship is inverse. The intuition behind this result is that the inward multilateral resistance appears in the theoretical demand equations for each type of labor as the price of intermediate goods. Thus, when intermediates become more expensive consumers will substitute away from them and in favor of other production factors including labor of each type. Importantly, the impact of trade liberalization via this channel captures several general equilibrium relationships both at the country and at the sectoral level. At the extreme, this channel implies that a change in trade costs in any sector and in any country may affect the demand for a specific type of labor in any other sector and other country in the world. The strength of such impact will depend on how strong are the input-output links in the world trade and production system as well as on the share of the labor’s type in production.

In order to demonstrate the effectiveness of our theory and to show how the model can be used in trade policy analysis, we quantify the impact of a hypothetical regional trade agreement between the US and Great Britain with a novel dataset that covers 22 sectors and 45 countries in 2010 and includes data on international trade flows, production, three types of labor, and wages, all at the sectoral level. The three types of labor are distinguished by education: primary, secondary, and tertiary. We assemble a unique collection of data regarding the use of these three types of labor in various industries and countries, and their wages. Differential use of the three types of labor across industries combine with different costs of these types of labor in various countries to create a Heckscher-Ohlin motive for trade.

We use an empirical gravity model to construct trade costs. This enables us to confirm that gravity works well at the sectoral level. Then, we combine our trade cost estimates with actual data and values for the other structural parameters, which we construct directly from the data, calibrate from the structural model, or simply borrow from the literature.

Our model generates the effects of a new US-UK RTA on macroeconomic, industry-specific, and labor market variables. Importantly, it generates separate effects on the three types of labor distinguished by education. For brevity and for expositional simplicity, we focus on two sets of results, which are obtained from a version of our model that allows for reallocation of labor of each type. The first set of estimates includes a series of cross-section indexes at the country level that are obtained as aggregates across all sectors for each country in our sample. Overall, the results are intuitive and with reasonable magnitudes. We find that Great Britain gains the most in terms of total exports (an increase of about 12 percent), in terms of lower prices (a fall of 0.7 percent), and in terms of real GDP (an increase of 3.6 percent). The United States gains too, but the gains are much smaller. Specifically, our estimates suggest that US total exports will increase by about 3 percent, consumer prices will fall by 0.12 percent, and real GDP will increase by about 1 percent. Country size is a natural explanation for the differential effects of the bilateral agreement on the two economies.

An UK-US RTA will also affect all other countries in the world. Our estimates reveal that the effects on outside countries will be relatively small. However, we do find these effects vary intuitively with larger losses for countries that are more closely related (economically and geographically) to the two liberalizing nations. Thus, for example, the largest negative impact of -0.42 percent is for the real GDP of the Dominican Republic, followed by Ireland and Mexico. The average real GDP change across all outside countries is -0.11 percent. Based on these results, we conclude that the US-UK RTA may have significant implications for the member countries, however, the implications for income-inequality in the rest of the world will be quite small.

The second set of estimates that we obtain and discuss in the main text are the GE effects of the UK-US RTA on individual sectors and labor types in the United States. Our results reveal significant variation in the effects of the agreement on sectoral US exports. Specifically, we find that the sectors that will gain the most include Manufacture of wood, Manufacture of machinery and equipment, and Manufacture of radio, television and communication equipment and apparatus. The smallest increase will be observed in Manufacture of tobacco products and Manufacture of wearing apparel; dressing and dyeing of fur. Interestingly, despite an initial positive impact of the UK-US RTA, we also document a decrease in US exports in Other Manufacturing. The explanation for this result is a combination of strong GE forces and a very strong positive impact for UK exports in this industry.

We also take advantage of the ability of our model to capture the effects of trade liberalization on heterogeneous labor. Two main findings stand out from the sectoral estimates for the United States. First, we find that the number of workers employed in some sectors will increase, while the number of workers employed in other sectors will fall. The sectors that will accept the largest number of new workers are Manufacture of radio, television and communication equipment and apparatus, Manufacture of textiles, Manufacture of wood and of products of wood and cork, except furniture, and Manufacture of paper and paper products. This is expected since these are exactly the sectors for which our model predicts that producer prices and production will increase the most. Our estimates suggest that the number of workers will actually decrease in more than half of the US sectors. The biggest negative impact on labor will be felt in the sectors where exports decrease (or increase the least). These sectors include Tanning and dressing of leather; manufacture of luggage, footwear, etc., Manufacture of furniture; manufacturing n.e.c., Manufacture of office, accounting and computing machinery, and Manufacture of wearing apparel; dressing and dyeing of fur.

Second, despite the fact that we are considering a hypothetical trade liberalization scenario between two very similar economies, we do obtain differential effects on labor across the different types of workers in each country. Specifically, a comparison between the effects on labor with primary and with higher education reveals that the number of workers with the highest level of education in US will increase more in the industries that hire more workers and will decrease less in the industries that let workers go. All else equal, this points to potential increase in income inequality in the US even from trade liberalization within a very similar developed partner such as the UK.

The corresponding estimates for the United Kingdom reveal that the impact on labor in the UK will be stronger and that the differential impact of the UK-US agreement on the different types of workers is more pronounced in the UK. Relative size between the liberalizing partners is a natural explanation for this result. In addition, we find that the UK-US RTA will lead to a stronger negative impact and to a weaker positive effect on the workers with the highest education as compared to the less educated workers, thus pointing to a potential decrease in income inequality in the UK.

The remainder of the paper is organized as follows. Section 2 develops our theoretical model. Section 3 discusses our simulation approach. Section 4 describes the data and the data sources. Section 5 presents and discusses sectoral gravity estimates. Section 6 describes the analysis of the general equilibrium impact of a hypothetical RTA between the United States and Great Britain. Section 7 concludes and discusses possible extensions. Finally, the Appendix offers some additional empirical results and robustness analysis.

### 2 Sectoral Gravity with Skills and Intermediates

This section develops a sectoral general equilibrium trade model with intermediate inputs and three types of labor and discusses our contributions in light of the previous literature.

Consumption. On the demand side, we employ a two-tier utility specification, which has become standard in the trade literature. At the upper level, consumers choose across goods from different industries $k$ subject to Cobb-Douglas (CD) preferences, which translate into constant expenditure shares such that total expenditures on goods from industry $k$ in country $j$ are:

 ${\left({E}_{j}^{k}\right)}^{c}={\psi }^{k}{I}_{j},$ (1)

where, superscript $c$ is used to denote consumption of final goods,4 ${\psi }^{k}\ge 0$, ${\sum }_{k}{\psi }^{k}=1$, is a globally common CD share parameter, and ${I}_{j}={\sum }_{k}{I}_{j}^{k}$ is the total income of consumers in country $j$. The Cobb-Douglas preferences across goods nest Constant Elasticity of Substitution (CES) preferences across varieties $i$ within each industry:

 ${\left(\sum _{i}{{\beta }_{i}^{k}}^{\frac{1-{\sigma }^{k}}{{\sigma }^{k}}}{{c}_{ij}^{k}}^{\frac{{\sigma }^{k}-1}{{\sigma }^{k}}}\right)}^{\frac{{\sigma }^{k}}{{\sigma }^{k}-1}}.$ (2)

Here, ${c}_{ij}$ is consumption in destination $j$ of goods in industry $k$ imported from origin $i$; ${\sigma }_{k}$ is the elasticity of substitution for goods in industry $k$; and ${\beta }_{i}^{k}$ is a CES share parameter. Given the level of total expenditure in each industry, ${\left({E}_{j}^{k}\right)}^{c}$, consumers maximize (2) subject to a series of standard budget constraints:

 $\sum _{i}{p}_{ij}^{k}{c}_{ij}^{k}={\left({E}_{j}^{k}\right)}^{c},\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\forall k,j.$ (3)

Equation (3) simply states that expenditure on consumption for each type of good $k$ in each country $j$ is the sum of bilateral expenditures from all possible partners including country $j$ itself, at delivered prices ${p}_{ij}^{k}$. Here, ${p}_{ij}^{k}={p}_{i}^{k}{t}_{ij}^{k}$ is the price of origin $i$ goods in industry $k$ for region $j$ and ${t}_{ij}^{k}\ge 1$ denotes the standard iceberg variable trade cost factor on shipment of goods in industry $k$ from $i$ to $j$.

Solving the consumer’s problem obtains the demand for consumption goods $c$ of industry $k$ shipped from origin $i$ to destination $j$ as:

 ${\left({x}_{ij}^{k}\right)}^{c}={\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}∕{P}_{j}^{k}\right)}^{\left(1-{\sigma }^{k}\right)}{\left({E}_{j}^{k}\right)}^{c},$ (4)

where, for now, ${P}_{j}^{k}={\left[{\sum }_{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}\right]}^{1∕\left(1-{\sigma }^{k}\right)}$ is the standard CES price aggregator. Following Anderson and van Wincoop (2003), below ${P}_{j}^{k}$ will be redefined as ‘inward multilateral resistance’. However, retaining the meaning of ${P}_{j}^{k}$ in their role as CES aggregators, the inward multilateral resistances may, in principle, be interpreted as ideal price indexes, and their variation across countries might be expected to reflect variation in consumer price indexes (CPIs).5

Production. Production in each sector ${k}^{\prime }\in K$ in country $j$ uses domestic factors of production including sector-specific domestic technology ${A}_{j}^{{k}^{\prime }}$;6 and sector-specific domestic labor, ${L}_{j}^{{k}^{\prime },s}$, with different skills $s\in S$. In addition, production in each sector also employs intermediates ${M}_{j}^{k,{k}^{\prime }}$ from every other sector $k$, including own intermediates.7 Thus, the output in a given sector is split between two uses: final consumption and intermediate use for production, which both are internationally traded. All factors of production in sector ${k}^{\prime }$ in country $j$ are combined subject to a Cobb-Douglas production function, which results in the following specification for the value of production:

 ${Y}_{j}^{{k}^{\prime }}={p}_{j}^{{k}^{\prime }}{A}_{j}^{{k}^{\prime }}\prod _{s=1}^{S}{\left({L}_{j}^{{k}^{\prime },s}\right)}^{{\alpha }_{j}^{{k}^{\prime },s}}\prod _{k=1}^{K}{\left({M}_{j}^{k,{k}^{\prime }}\right)}^{{\alpha }_{j}^{k,{k}^{\prime }}}.$ (5)

Here, ${Y}_{j}^{{k}^{\prime }}$ is sectoral income/value of production in country $j$. ${p}_{j}^{{k}^{\prime }}$ is the corresponding factory-gate price. ${L}_{j}^{{k}^{\prime },s}$ is the number of workers of skill type $s$ who are employed in sector ${k}^{\prime }$ in country $j$, and ${\alpha }_{j}^{{k}^{\prime },s}$ is the corresponding labor share in production, ${\sum }_{s}{\alpha }_{j}^{{k}^{\prime },s}+{\sum }_{k}{\alpha }_{j}^{k,{k}^{\prime }}=1$. Finally, the amount of intermediates from sector $k$ used in sector ${k}^{\prime }$ in country $j$ is defined as a CES composite of domestic components, ${m}_{jj}^{k,{k}^{\prime }}$, and imported components„ ${m}_{ij}^{k,{k}^{\prime }}$, from all other countries $i\ne j$:

 ${M}_{j}^{k,{k}^{\prime }}={\left(\sum _{i}{{\beta }_{i}^{k}}^{\frac{1-{\sigma }^{k}}{{\sigma }^{k}}}{{m}_{ij}^{k,{k}^{\prime }}}^{\frac{{\sigma }^{k}-1}{{\sigma }^{k}}}\right)}^{\frac{{\sigma }^{k}}{{\sigma }^{k}-1}}.$ (6)

As is standard in most models with intermediates, we assume that the elasticity of substitution within industry $k$ is the for the consumption and intermediate inputs.

With perfectly competitive markets, factors are paid the values of their marginal products. This enables us to express the the wages for the different labor types as:8

 ${w}_{j}^{{k}^{\prime },s}={\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}∕{L}_{j}^{{k}^{\prime },s}.$ (7)

(7) implies that the income of workers of type $s$ in industry ${k}^{\prime }$ in country $j$ is a constant share of ${Y}_{j}^{{k}^{\prime }}$ or:

 ${w}_{j}^{{k}^{\prime },s}{L}_{j}^{{k}^{\prime },s}={\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}.$ (8)

Thus, the total income of all workers in industry ${k}^{\prime }$ in country $j$ can be obtained after summing across all types of labor:

 $\sum _{s}{w}_{j}^{{k}^{\prime },s}{L}_{j}^{{k}^{\prime },s}=\sum _{s}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}.$ (9)

Finally, the total income of all workers in country $j$ is obtained after summing labor income across all sectors ${k}^{\prime }$:

 ${I}_{j}=\sum _{{k}^{\prime }}\sum _{s}{w}_{j}^{{k}^{\prime },s}{L}_{j}^{{k}^{\prime },s}=\sum _{{k}^{\prime }}\sum _{s}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}.$ (10)

In combination with equation (1), equation (10) implies that the total expenditure ($E$) on consumption goods ($c$) from industry $k$ in country $j$ can be expressed as:

 ${\left({E}_{j}^{k}\right)}^{c}={\psi }^{k}{I}_{j}={\psi }^{k}\sum _{{k}^{\prime }}\sum _{s}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}.$ (11)

Turning to the demand for intermediates, we can solve for the demand for composite intermediates $k$ used in sector ${k}^{\prime }$ as:

 ${M}_{j}^{k,{k}^{\prime }}={\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}∕{P}_{j}^{k}.$ (12)

Equation (12) implies that total expenditure ($E$) on intermediates ($m$) from industry $k$ in country $j$ can be expressed as the sum of the expenditure on those intermediates in each sector ${k}^{\prime }$:

 ${\left({E}_{j}^{k}\right)}^{m}=\sum _{{k}^{\prime }}{P}_{j}^{k}{M}_{j}^{k,{k}^{\prime }}=\sum _{{k}^{\prime }}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}.$ (13)

Note also that we can express the total expenditure on intermediates that are used for production in sector ${k}^{\prime }$ as the sum across the expenditure on intermediates across all sectors $k$:

 $\sum _{k}{P}_{j}^{k}{M}_{j}^{k,{k}^{\prime }}=\sum _{k}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}.$ (14)

This will enable us to obtain an alternative expression for the total income of labor in sector ${k}^{\prime }$ as the difference between the total value generated in this sector, ${Y}_{j}^{{k}^{\prime }}$, less the payments for all the intermediates that are used for production in ${k}^{\prime }$:

 ${I}_{j}^{{k}^{\prime }}={Y}_{j}^{{k}^{\prime }}-\sum _{k}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}$ (15)

Finally, combining equation (12) with the definition of intermediates as CES composites of domestic and foreign varieties (6), we can also solve for the nominal demand of intermediate varieties $m$ in sector $k$ that are exported from source $i$ for production in sector ${k}^{\prime }$ at destination $j$ as:

 ${\left({x}_{ij}^{k,{k}^{\prime }}\right)}^{m}={\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}∕{P}_{j}^{k}\right)}^{\left(1-{\sigma }^{k}\right)}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }},$ (16)

where, ${p}_{ij}^{k}={p}_{i}^{k}{t}_{ij}^{k}$ is the price of origin $i$ goods in industry $k$ for region $j$ and ${t}_{ij}^{k}\ge 1$ denotes the standard iceberg variable trade cost factor on shipment of goods in industry $k$ from $i$ to $j$. ${P}_{j}^{k}={\left[{\sum }_{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}\right]}^{1∕\left(1-{\sigma }^{k}\right)}$ is the standard CES price aggregator. Thus, we can express the total demand in country $j$ for intermediates in sector $k$ from country $i$ as the sum of the bilateral demands across all sectors ${k}^{\prime }\in K$:

 ${\left({x}_{ij}^{k}\right)}^{m}=\sum _{{k}^{\prime }}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}∕{P}_{j}^{k}\right)}^{\left(1-{\sigma }^{k}\right)}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}={\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}∕{P}_{j}^{k}\right)}^{\left(1-{\sigma }^{k}\right)}{\left({E}_{j}^{k}\right)}^{m},$ (17)

where, to obtain the rightmost equation, we have employed the definition of the expenditure on intermediates from equation (13). In addition to the standard relationships between the demand for intermediate goods and their prices, equation (17) captures the intuitive link that more intermediates will be demanded, the larger their share in production in each sector, ${\alpha }_{j}^{k,{k}^{\prime }}$, and the larger the size of the sectors that they are used in, ${Y}_{j}^{{k}^{\prime }}$.

Closing the Model. The total bilateral demand for goods in industry $k$ from country $i$ in country $j$ is equal to the sum of the bilateral demand for consumption goods ${\left({x}_{ij}^{k}\right)}^{c}$, and the bilateral demand for the goods in industry $k$ as intermediates ${\left({x}_{ij}^{k}\right)}^{m}$:

 ${X}_{ij}^{k}={\left({x}_{ij}^{k}\right)}^{c}+{\left({x}_{ij}^{k}\right)}^{m}.$ (18)

Substitute in (18) the demand expressions for final consumption and for the intermediate use from equations (4) and (17), respectively, and simplify to obtain:

 ${X}_{ij}^{k}={\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}∕{P}_{j}^{k}\right)}^{\left(1-{\sigma }^{k}\right)}\left({\left({E}_{j}^{k}\right)}^{c}+{\left({E}_{j}^{k}\right)}^{m}\right).$ (19)

Use the solution for expenditure on consumption goods in industry $k$, ${\left({E}_{j}^{k}\right)}^{c}$, from equation (11), and the solution for expenditure on intermediate goods in industry $k$, ${\left({E}_{j}^{k}\right)}^{m}$, from equation (13), and define:

 ${E}_{j}^{k}\equiv {\left({E}_{j}^{k}\right)}^{c}+{\left({E}_{j}^{k}\right)}^{m}={\psi }^{k}\sum _{{k}^{\prime }}\sum _{s}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}+\sum _{{k}^{\prime }}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}.$ (20)

Impose market clearance for goods in each industry from each origin, so that (at delivered prices) the total value of production of goods $k$ in country $i$, ${Y}_{i}^{k}$, is equal to the sum of total final consumption of these goods across all countries, ${\sum }_{j}{\left({x}_{ij}^{k}\right)}^{c}$, and the total consumption of these goods as intermediates in production across all sectors and all countries, ${\sum }_{j}{\left({x}_{ij}^{k}\right)}^{m}$:

 ${Y}_{i}^{k}=\sum _{j}{X}_{ij}^{k}=\sum _{j}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}∕{P}_{j}^{k}\right)}^{\left(1-{\sigma }^{k}\right)}{E}_{j}^{k}.$ (21)

Define ${Y}^{k}\equiv {\sum }_{i}{Y}_{i}^{k}$ and divide the preceding equation by ${Y}^{k}$ to obtain:

 ${Y}_{i}^{k}∕{Y}^{k}={\left({\beta }_{i}^{k}{p}_{i}^{k}{\Pi }_{i}^{k}\right)}^{1-{\sigma }^{k}},$ (22)

where ${\Pi }_{i}^{k}\equiv {\sum }_{j}{\left({t}_{ij}^{k}∕{P}_{j}^{k}\right)}^{1-{\sigma }^{k}}\frac{{E}_{j}^{k}}{{Y}_{}^{k}}$. Finally, use (22) to substitute for ${\beta }_{i}^{k}{p}_{i}^{k}$ in the CES price index ${P}_{j}^{k}$: $\begin{array}{rlll}{\left({P}_{j}^{k}\right)}^{1-{\sigma }^{k}}& =& \sum _{i}{\left(\frac{{t}_{ij}^{k}}{{\Pi }_{i}^{k}}\right)}^{1-{\sigma }^{k}}\frac{{Y}_{i}^{k}}{{Y}^{k}},& \text{(23)}\text{}\text{}\end{array}$

and use the solution for ${\beta }_{i}^{k}{p}_{i}^{k}$ from (22) and the definition of ${E}_{j}^{k}$ to substitute in the demand equation (19): $\begin{array}{rlll}{X}_{ij}^{k}& =& \frac{{Y}_{i}^{k}{E}_{j}^{k}}{{Y}^{k}}{\left(\frac{{t}_{ij}^{k}}{{\Pi }_{i}^{k}{P}_{j}^{k}}\right)}^{1-{\sigma }^{k}},& \text{(24)}\text{}\text{}\end{array}$

Then, collect equations to obtain a familiar system: $\begin{array}{rlll}{X}_{ij}^{k}& =& \frac{{Y}_{i}^{k}{E}_{j}^{k}}{{Y}^{k}}{\left(\frac{{t}_{ij}^{k}}{{\Pi }_{i}^{k}{P}_{j}^{k}}\right)}^{1-{\sigma }^{k}},& \text{(25)}\text{}\text{}\\ {\left({\Pi }_{i}^{k}\right)}^{1-{\sigma }^{k}}& =& \sum _{j}{\left(\frac{{t}_{ij}^{k}}{{P}_{j}^{k}}\right)}^{1-{\sigma }^{k}}\frac{{E}_{j}^{k}}{{Y}^{k}},& \text{(26)}\text{}\text{}\\ {\left({P}_{j}^{k}\right)}^{1-{\sigma }^{k}}& =& \sum _{i}{\left(\frac{{t}_{ij}^{k}}{{\Pi }_{i}^{k}}\right)}^{1-{\sigma }^{k}}\frac{{Y}_{i}^{k}}{{Y}^{k}},& \text{(27)}\text{}\text{}\\ {p}_{i}^{k}& =& {\left(\frac{{Y}_{i}^{k}}{{Y}^{k}}\right)}^{\frac{1}{1-{\sigma }^{k}}}\frac{1}{{\beta }_{i}^{k}{\Pi }_{i}^{k}},& \text{(28)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {Y}^{k}& =& \sum _{i}{Y}_{i}^{k}=\sum _{i}{p}_{j}^{k}{A}_{j}^{k}\prod _{s=1}^{S}{\left({L}_{j}^{k,s}\right)}^{{\alpha }_{j}^{k,s}}\prod _{{k}^{\prime }=1}^{K}{\left({M}_{j}^{{k}^{\prime },k}\right)}^{{\alpha }_{j}^{{k}^{\prime },k}},& \text{(29)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {E}_{j}^{k}& =& {\psi }^{k}\sum _{{k}^{\prime }}\sum _{s}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}+\sum _{{k}^{\prime }}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }},& \text{(30)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {M}_{j}^{k,{k}^{\prime }}& =& {\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}∕{P}_{j}^{k},& \text{(31)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {L}_{j}^{{k}^{\prime },s}\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}& =& \phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}{\left[\frac{{\alpha }_{j}^{{k}^{\prime },s}}{{w}_{j}^{{k}^{\prime },s}}{\left(\frac{{Y}_{j}^{{k}^{\prime }}}{{Y}^{{k}^{\prime }}}\right)}^{\frac{1}{1-{\sigma }^{{k}^{\prime }}}}\frac{{A}_{j}^{{k}^{\prime }}}{{\beta }_{j}^{{k}^{\prime }}{\Pi }_{j}^{{k}^{\prime }}}\prod _{{s}^{\prime }\ne s}{\left({L}_{j}^{{k}^{\prime },{s}^{\prime }}\right)}^{{\alpha }_{j}^{{k}^{\prime },{s}^{\prime }}}\prod _{k=1}^{K}{\left(\frac{{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}}{{P}_{j}^{k}}\right)}^{{\alpha }_{j}^{k,{k}^{\prime }}}\right]}^{\frac{1}{1-{\alpha }_{j}^{{k}^{\prime },s}}},& \text{(32)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {L}_{j}^{s}& =& \sum _{k}{L}_{j}^{k,s}.& \text{(33)}\text{}\text{}\end{array}$

The equations in system (25)-(33) are intuitive and most of them are familiar since, as we demonstrate next, the system nests a series of influential theoretical models from the structural gravity literature. Equation (25) is the traditional structural gravity equation, which has served as a theoretical foundation to hundreds of empirical papers that study the determinants of bilateral trade flows. Intuitively, equation (25) captures the fact that trade between two countries is proportional to their sizes and inversely proportional to the trade frictions between them.

In combination, equations (26)-(27) are the equations for the multilateral resistances of Anderson and van Wincoop (2003). The multilateral resistances are general equilibrium indexes that consistently aggregate all possible bilateral trade cost links ${t}_{ij}$ to the country level, and decompose the incidence of trade costs on the consumers (Inward Multilateral Resistance, IMR) and the producers (Outward Multilateral Resistance, OMR) in each country and sector, as is they ship to a unified world market. Larch and Yotov (2016) offer a detailed description of the main properties and importance of the MR terms.

Equation (28) is a version of the goods market-clearing condition, which states that, at delivered prices, the value of production in each sector should be equal to the total expenditure on the goods from this sector in the world, including domestic sales. Restated in the form of (28), the market-clearing condition clearly demonstrates the inverse relationship between the outward multilateral resistance and factory-gate prices. Combining the market-clearing conditions (28) with equations (25)-(27) corresponds directly to the sectoral gravity system of Anderson and Yotov (2016), which demonstrates the sectoral separability of the structural gravity model and allows for inter-sectoral linkages that arise on the demand side, i.e. due to the substitutability of goods across goods industries. The sectoral gravity system (25)-(28) nests the original aggregate systems of Anderson (1979) and Anderson and van Wincoop (2003), on the demand side, and Eaton and Kortum (2002), on the supply side.9

As defined earlier, equation (29) is the production value function and equation (30) is the expenditure in sector $k$, which is a combination of expenditure on final goods and expenditure on intermediates. The demand for intermediates is captured by Equation (31). Intuitively, the demand for intermediates is proportional to a sector’s size and inversely proportional to the price of intermediates. In combination, equations (25)-(31) correspond directly to the sectoral gravity system with intermediates from the influential paper by Caliendo and Parro (2015). The role of intermediates can clearly be seen from equations (29) and (30). Equation (29) accounts for the use of intermediates in production, while equation (30) captures the fact that the expenditure on goods from industry $k$ in each country is split between expenditure on final goods and on intermediate goods from this industry. The structural links with intermediates on the production side imply that changes in trade policy between any pair of countries and each sector in the world will have ripple effects through all other sectors and countries.

Finally, and most important for the current purposes, the last two equations from system (25)-(33) are the labor market equations in our model. Equations (32) and (33) reflect the introduction of a labor market with different types of workers, which is our main contribution relative to existing literature. Equation (33) is the market-clearing equation for labor of each type $s$. Equation (45) is the equation for labor demand by sector and by type of skill, which is central for our analysis. Equation (45) captures several well-established and intuitive relationships as well as the novel links through which trade affects the sectoral demand for labor of each type. Specifically, for each type of labor in each sector, equation (45) captures the inverse (and standrad) relationship between the quantity of labor demanded and its price, ${w}_{j}^{{k}^{\prime },s}$, as well as the positive relationship between the demand for labor and the other factors of production and the share of this labor’s type.

Most important for our purposes, equation (45) reveals two channels through which trade liberalization may affect the demand for labor. Both of these effects are channeled via the general equilibrium multilateral resistance indexes. The first impact of trade liberalization on the demand for labor is via the outward multilateral resistance, ${\Pi }_{j}^{{k}^{\prime }}$. The relationship is inverse. Intuitively, a higher multilateral resistance for the producers in a given sector will translate (see equation 28) into lower factory gate prices, which, in turn, will lead to lower demand for labor in this industry. Importantly, since the the the outward multilateral resistance is a general equilibrium index, the labor demand ${L}_{j}^{{k}^{\prime },s}$ can be affected by changes in trade costs of any country in the world.10

The second channel through which trade liberalization affects labor market outcomes is via the inward multilateral resistance, ${P}_{j}^{k}$. Once again, the relationship is inverse. To gain intuition we first recognize that ${P}_{j}^{k}$ is the price of intermediate inputs. Thus, the explanation for the inverse relationship is that when intermediates become more expensive they will be substituted away from in favor of other factors including labor. Importantly, the impact of trade liberalization via this channel captures several general equilibrium relationships both at the country and at the sectoral level. At the extreme, this channel implies that a change in intrude costs in any sector and any country in the world may have potential impact of the demand for a specific type of labor in any other sector and other country in the world. The strength of such impact will, of course, depend on how strong are the specific input-output links in the world trade and production system.

### 3 From Theory to Empirics

This section demonstrates how system (25)-(33) can be used to quantify the impact of trade liberalization on the labor market. To that end, we follow the seminal work of Eaton and Kortum (2002) to characterize two extreme scenarios. One, where labor of each type and in each sector is taken as given. In this case all effects of trade liberalization will be channeled through wages. And one, where labor is mobile across sectors within a given labor type. In that case, the wage across sectors for each type will be equalized and changes in the wages we result in a reallocation of workers across sectors.

Immobile Labor. Consider the immobile labor scenario first. Our general approach to quantify the impact of trade liberalization on labor market outcomes will be developed in two steps. First, we will estimate and/or calibrate some of the model parameters, e.g. trade costs and the elasticity of substitution, and calibrate the remaining (exogenous) parameters, e.g. the CES preference parameters, so that our model fits the data at initial factory-gate prices. This will be our baseline scenario. Then, we will ‘shock’ the system by changing the trade cost vector for a counterfactual scenario of our choice, and we will solve for the corresponding changes in factory-gate prices and other variables of choice.

We start by simplifying the structural system in order to decrease its dimensionality. Use the definition of ${Y}^{k}={\sum }_{i}{Y}_{i}^{k}$, the expression for the outward multilateral resistance from equation (26), and the expression for the CES price aggregator to replace these three elements in the market clearing conditions system (28). Then simplify. System (25)-(33) transforms into: $\begin{array}{rlll}\frac{{Y}_{i}^{k}}{\sum _{i}{Y}_{i}^{k}}& =& \sum _{j}\frac{{\left({p}_{i}^{k}{\beta }_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}}{\sum _{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}}\frac{{E}_{j}^{k}}{\sum _{i}{Y}_{i}^{k}},& \text{(34)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {Y}_{i}^{k}& =& {p}_{j}^{k}{A}_{j}^{k}\prod _{s=1}^{S}{\left({L}_{j}^{k,s}\right)}^{{\alpha }_{j}^{k,s}}\prod _{{k}^{\prime }=1}^{K}{\left({M}_{j}^{{k}^{\prime },k}\right)}^{{\alpha }_{j}^{{k}^{\prime },k}},& \text{(35)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {E}_{j}^{k}& =& {\psi }^{k}\sum _{{k}^{\prime }}\sum _{s}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}+\sum _{{k}^{\prime }}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }},& \text{(36)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {M}_{j}^{k,{k}^{\prime }}& =& {\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}∕{\left[\sum _{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}\right]}^{1∕\left(1-{\sigma }^{k}\right)}.& \text{(37)}\text{}\text{}\end{array}$

Note that we have omitted the labor market equations. The reason is that the scenario with immobile labor is essentially an endowment scenario, where the change in wages will correspond one-to-one to the change in the value of production.

Replace the definition of intermediates from equation (37) in the production value function: $\begin{array}{rlll}\frac{{Y}_{i}^{k}}{\sum _{i}{Y}_{i}^{k}}& =& \sum _{j}\frac{{\left({p}_{i}^{k}{\beta }_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}}{\sum _{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}}\frac{{E}_{j}^{k}}{\sum _{i}{Y}_{i}^{k}},& \text{(38)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {Y}_{i}^{k}& =& {p}_{j}^{k}{A}_{j}^{k}\prod _{s=1}^{S}{\left({L}_{j}^{k,s}\right)}^{{\alpha }_{j}^{k,s}}\prod _{{k}^{\prime }=1}^{K}{\left({\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}∕{\left[\sum _{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}\right]}^{1∕\left(1-{\sigma }^{k}\right)}\right)}^{{\alpha }_{j}^{{k}^{\prime },k}},& \text{(39)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {E}_{j}^{k}& =& {\psi }^{k}\sum _{{k}^{\prime }}\sum _{s}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}+\sum _{{k}^{\prime }}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}.& \text{(40)}\text{}\text{}\end{array}$

Replace the definition of expenditure from (40) in the market clearing conditions (38) to obtain: $\begin{array}{rlll}\frac{{Y}_{i}^{k}}{\sum _{i}{Y}_{i}^{k}}& =& \sum _{j}\frac{{\left({p}_{i}^{k}{\beta }_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}}{\sum _{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}}\frac{{\psi }^{k}\sum _{{k}^{\prime }}\sum _{s}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}+\sum _{{k}^{\prime }}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}}{\sum _{i}{Y}_{i}^{k}},& \text{(41)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {Y}_{i}^{k}& =& {p}_{j}^{k}{A}_{j}^{k}\prod _{s=1}^{S}{\left({L}_{j}^{k,s}\right)}^{{\alpha }_{j}^{k,s}}\prod _{{k}^{\prime }=1}^{K}{\left({\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}∕{\left[\sum _{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}\right]}^{1∕\left(1-{\sigma }^{k}\right)}\right)}^{{\alpha }_{j}^{{k}^{\prime },k}}.& \text{(42)}\text{}\text{}\end{array}$

System (41)-(42) consists of $N×K×2$ equations. As noted above, we will solve the system in two steps. First, we will solve it in the baseline scenario, where all factory-gate prices are equal to one. This is equivalent to treating our baseline values of output ${Y}_{i}^{k}$ as endowments. Under this treatment, system (41)-(42) can be solved for the $N×K$ CES share parameters ${\beta }_{i}^{k}$ and for the $N×K$ technology parameters ${A}_{j}^{k}$. This should complete the data and parameter requirements.11 Then, in the second step, we solve the system again in response to a change in bilateral trade costs. This time, we solve for the $N×K$ factory-gate prices and for the $N×K$ values of output.

Mobile Labor. Now consider how the system will change if we allow for mobile labor. First, we need to add the labor market equations. $\begin{array}{rlll}\frac{{Y}_{i}^{k}}{\sum _{i}{Y}_{i}^{k}}& =& \sum _{j}\frac{{\left({p}_{i}^{k}{\beta }_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}}{\sum _{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}}\frac{{\psi }^{k}\sum _{{k}^{\prime }}\sum _{s}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}+\sum _{{k}^{\prime }}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}}{\sum _{i}{Y}_{i}^{k}},& \text{(43)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {Y}_{i}^{k}& =& {p}_{j}^{k}{A}_{j}^{k}\prod _{s=1}^{S}{\left({L}_{j}^{k,s}\right)}^{{\alpha }_{j}^{k,s}}\prod _{{k}^{\prime }=1}^{K}{\left({\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}∕{\left[\sum _{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}\right]}^{1∕\left(1-{\sigma }^{k}\right)}\right)}^{{\alpha }_{j}^{{k}^{\prime },k}},& \text{(44)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {L}_{j}^{{k}^{\prime },s}& =& {\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}∕{w}_{j}^{s},& \text{(45)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {L}_{j}^{s}& =& \sum _{k}{L}_{j}^{k,s}.& \text{(46)}\text{}\text{}\end{array}$

Note that we have expressed the wage equation as a labor demand equation, which also captures the fact that with mobile labor wages in each countries and for each type of labor are equalized. Replace ${L}_{j}^{{k}^{\prime },s}$ from equation (45) into the production value function (44) and in the labor market clearing conditions (46): $\begin{array}{rlll}\frac{{Y}_{i}^{k}}{\sum _{i}{Y}_{i}^{k}}& =& \sum _{j}\frac{{\left({p}_{i}^{k}{\beta }_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}}{\sum _{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}}\frac{{\psi }^{k}\sum _{{k}^{\prime }}\sum _{s}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}+\sum _{{k}^{\prime }}{\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}}{\sum _{i}{Y}_{i}^{k}},& \text{(47)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {Y}_{i}^{k}& =& {p}_{j}^{k}{A}_{j}^{k}\prod _{s=1}^{S}{\left({\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}∕{w}_{j}^{s}\right)}^{{\alpha }_{j}^{k,s}}\prod _{{k}^{\prime }=1}^{K}{\left({\alpha }_{j}^{k,{k}^{\prime }}{Y}_{j}^{{k}^{\prime }}∕{\left[\sum _{i}{\left({\beta }_{i}^{k}{p}_{i}^{k}{t}_{ij}^{k}\right)}^{1-{\sigma }^{k}}\right]}^{1∕\left(1-{\sigma }^{k}\right)}\right)}^{{\alpha }_{j}^{{k}^{\prime },k}},& \text{(48)}\text{}\text{}\\ \phantom{\rule{1em}{0ex}}& & & \text{}\\ {L}_{j}^{s}& =& \sum _{k}{\alpha }_{j}^{{k}^{\prime },s}{Y}_{j}^{{k}^{\prime }}∕{w}_{j}^{s}.& \text{(49)}\text{}\text{}\end{array}$

As compared to the system with immobile labor, system (47)-(49) has $N×S$ more equations and $N×S$ more unknowns. Thus, it is exactly identified. The additional equations will pin down the wages for each type $S$ in each of the $N$ countries. This will ensure clearance at the labor market.

Quantification. We proceed in three steps in order to quantify the impact of trade liberalization on the labor market. First, we will obtain (estimate, calibrate, take from data, and/or borrow from the literature) all model parameters, which are needed to fit the model to the data in the baseline scenario. Then, we will ‘shock’ the system according to a counterfactual scenario of interest, e.g. the formation of a regional trade agreement between U.S. and U.K., and we will solve the model again. Finally, we will construct and analyze a series of indexes of interest that capture the impact of the hypothetical trade policy change.

Arguably, the first of the three steps is most challenging, both in terms of data requirements as well as in terms of computational challenges. We discuss those in turn. In order to fit the model to the data in the baseline scenario, we need values for the following parameters:

• Bilateral trade costs, ${t}_{ij}^{k}$. As is standard in the literature, bilateral trade costs are recovered from the structural gravity equation (25). Theory suggests trade separability, which means that we can recover the bilateral trade costs for each sector independently. There are two general approaches to obtain estimates of trade costs: estimation vs. calibration. Each approach has advantages and disadvantages and both approaches have been used widely in the literature.12 Without loss of generality, and subject to the caveats of the estimation approach, will use standard gravity econometric techniques to recover the bilateral trade costs ${t}_{ij}^{k}$.
• Shares of intermediates used in production, ${\alpha }_{j}^{k,{k}^{\prime }}$. The main analysis is performed with intermediate shares that do not vary across countries, i.e. ${\alpha }^{k,{k}^{\prime }}$. One limitation of our analysis, again due to data availability, is that we only cover manufacturing industries. Thus, by construction, the shares of intermediates do not add up to one. As a result, the total expenditure on goods from each sector in our data does not add to the total value of production, at delivered prices. Our solution is to construct a vector of residual intermediate share indexes ${a}_{m}$ (of dimension $K×1$), which, when combined with the actual intermediate shares, ensures consistency in the model by equating the value of production and expenditure in each sector.
• Shares of different labor types used in production, ${\alpha }_{j}^{k,s}$. Similar to our assumption for common sectoral shares of intermediates across countries, we use labor-type shares that are also common across countries, i.e. ${\alpha }^{k,s}$. Construction of the labor-type using wage and employment data for multiple industries and countries is one of the unique features of our data and analysis.
• Cobb-Douglas share parameters, ${\psi }^{k}$. The Cobb-Douglas preference shares will be constructed directly from baseline data on sectoral output as:
${\psi }^{k}=\frac{{Y}^{k,0}}{\sum _{k}{Y}^{k,0}},$

where ${Y}^{k,0}={\sum }_{j}{Y}_{j}^{k,0}$. Note that, in principle, ${\psi }^{k}$ can be allowed to vary in the baseline vs. counterfactual analysis. In our main experiments we keep ${\psi }^{k}$ constant at the baseline level. However, allowing for changes in ${\psi }^{k}$ due to changes in the value of production does not have qualitative and significant quantitative implications for our results.

• Elasticity of substitution, ${\sigma }^{k}$. Estimates of the elasticity of substitution can be recovered directly from gravity estimations when data on some direct price-shifter are available, e.g. data on tariffs. Such data were not available to us. Therefore, we follow the standard approach in the literature and we assign a common value of the elasticity of substitution ${\sigma }^{k}=6$. We recognize and recommend that a rigorous policy analysis work should employ sector-specific estimates of the elasticity of substitution. However, given the demonstrative purposes of our analysis and, more importantly, in order to more clearly trace and decompose the key structural links in our model, we will use a common value for the trade elasticity of substitution across all sectors.
• CES share parameters, ${\beta }_{i}^{k}$. CES share parameters will be recovered from the market-clearing conditions in system (25)-(30).13 In order to solve for the CES share parameters, we use data and parameters covering: Bilateral trade costs (${t}_{ij}^{k}$); Shares of intermediates used in production (${\alpha }^{k,{k}^{\prime }}$); Cobb-Douglas share parameters (${\psi }^{k}$); and baseline data on the sectoral value of production (${Y}_{i}^{k}$). The CES share parameters in the baseline will be obtained and initial/baseline prices, i.e. ${p}_{j}^{k},\phantom{\rule{3.26212pt}{0ex}}\forall j,k$. Finally, we discuss a couple of technical notes. First, we note that system (25)-(30) can only be solved up to a normalization for the the multilateral resistances, cf. Anderson and Yotov (2010a). Second, we note that, at initial prices, (25)-(30) can actually deliver the power transform of the CES share parameters ${\left({\beta }_{i}^{k}\right)}^{1-\sigma }$ without the need to use a value for the trade elasticity of substitution. To see this, rewrite the market-clearing condition (28) by taking the $\left(1-\sigma \right)$ power transformation on both sides. The power transforms of the CES parameters is what we will recover and use throughout the analysis.
• Capital-augmented technology values, ${A}_{j}^{k}$. The capital-augmented technology values will be recovered from system (25)-(31) at initial prices. In addition to all data needed to recover the CES share parameters, the capital-augmented technology parameters will require data on (the power transforms of) the CES share parameters (${\beta }_{i}^{k}$), as well as data on baseline labor allocations (${L}_{j}^{k,s}$), and data on labor shares (${\alpha }^{k,s}$).

The set of parameters $\left\{{t}_{ij}^{k},{\alpha }^{k,{k}^{\prime }},{\alpha }^{k,s},{\psi }^{k},\sigma ,{\beta }_{i}^{k},{A}_{j}^{k}\right\}$ along with sectoral data on trade flows ${X}_{ij}^{k}$, output ${Y}_{j}^{k}$, and labor shares ${L}_{j}^{k,s}$ will deliver the baseline solutions of system (25)-(33) both for the case of immobile labor as well as for the case of mobile labor. For given values of the parameters, a shock to the system (e.g. in the form of a trade policy change that will affect the vector of bilateral trade costs ${t}_{ij}^{k}$) will result into changes in consumer prices, producer prices, trade flows, output, expenditure, and labor allocations. The (percentage) difference between the new, counterfactual values of any variable of interest and its initial/baseline value will measure the effect of the trade policy change. We demonstrate in Section 6. Before that, we describe our data and we discuss the sectoral partial equilibrium gravity estimations that are used to construct the baseline vector of bilateral trade costs.

### 4 Data: Description and Sources

Our sample includes data on bilateral trade flows, gravity variables, production, and wages for 45 countries and 22 sectors in 2010. Industries are classified using ISIC rev. 3 industrial classification at the two-digit level. A list of all sectors in our sample, their IDs and corresponding ISIC codes appear in Table 1. A list of all countries in our sample and their corresponding ISO codes is included in Table 2. Next, in turn, we describe the data used to construct the key variables that we employ in our analysis, their sources, their advantages, and their limitations.

Labor Types. Critically for the analysis in our model, labor is disaggregated into three types, based on its level of education. The basis for the level of education is the International Standard Classification of Education (ISCED-97). The three levels of education distinguished by this paper are primary (first six years of schooling), secondary (years 7-12 of schooling), and tertiary (more than 12 years of schooling). Tertiary education includes Vocational Associate’s programs and equivalents.

Wages. Wages for each country and type of labor come mostly from the Occupational Wages around the World (OWW) database, which uses data obtained by the ILO’s October Inquiry. OWW includes wages for 161 occupations in 171 countries. Each occupation in OWW is mapped to a ISCO-88 occupation code, which is in turn linked to a particular level of education as described in the ISCO-88 manual. For example occupation Chemical Engineer is linked to the tertiary level of education. The wages by education in each country are calculated by taking the average across all occupations with a given level of education. Wages are then converted to earnings using the conversion factors supplied in the OWW documentation. For countries in our dataset that do not report wages in the OWW database, we calculate wages by education using Mincerian regression estimated reported in the literature. We account for quality of education differences across countries. More details on this procedure can be found in Shikher (2015).

Labor shares. Labor shares in output for 18 industries were obtained from the OECD database of input-output tables for 43 countries. We use the average labor shares across countries for each industry. The 18 industries provided by the OECD database are based on the ISIC rev. 3 classification, but with some of the 22 two-digit industries aggregated together. In order to disaggregate the aggregated industries and obtain labor shares for all 22 industries, we use input-output tables for Germany and United Kingdom provided by Eurostat. These input-output tables include data for 22 two-digit ISIC rev. 3 industries. Labor shares in output described above are then combined with the shares of the three types of labor in total labor income. The shares of the three types of labor in total labor income are obtained using data from the World Bank Enterprise Surveys (WBES). More detail on labor data construction can be found in Shikher (2015).

Intermediate goods shares. Shares of each industry in total spending on intermediate goods by each industry were obtained from Eurostat’s database of individual countries’ input-output tables. Specifically, we use the average of the shares obtained from the intput-output tables of Germany and United Kingdon. These input-output tables include 22 manufacturing industries based on the ISIC rev. 3 classification.

Trade, Production, and Gravity Variables. Bilateral trade flows are sourced from COMTRADE. Sectoral production comes from the IndStat database of UNIDO. Missing values were estimated using nearby years and employment data. Data on various standard gravity variables, i.e., distance, common borders, common language, and colonial ties come from the CEPII’s GeoDist database,14 which includes data on these variables for 225 countries, and to the accompanying paper by Mayer and Zignago (2011) for detailed information on these commonly used gravity covariates. Data on regional trade agreements come from the Database on Economic Integration Agreements (EIAs) on Jeffey Bergstrand’s website (www.nd.edu/ jbergstr). Baier and Bergstrand’s EIA database categorizes bilateral EIA relationships from 1950-2005 for pairings of 195 countries using a multichotomous index. In our study, $RT{A}_{ij,t}=1$ denotes a regional trade agreement between trading partners $i$ and $j$ in year $t$of any type (i.e. a free trade agreement, a customs union, common market, or economic union), or 0 otherwise. The main source of original data used to construct the Baier and Bergstrand’s EIA database is the World Trade Organization (WTO).15

### 5 Gravity Estimation Results

This section delivers estimates of the vector of bilateral trade costs, which are needed for the counterfactual analysis. In addition, the estimation analysis will enable us to validate the underlying trade data sample and will generate some useful and interesting policy insights about the direct impact of trade costs and their variation across sectors. In order to estimate trade costs, we set up the following econometric model, which corresponds to the structural gravity equation (25) from our theoretical system:16 $\begin{array}{rlll}{X}_{ij}^{k}& =& exp\left[{\beta }_{0}^{k}+{\beta }_{1}^{k}lnDIS{T}_{ij}+{\beta }_{2}^{k}CNT{G}_{ij}+{\beta }_{3}^{k}LAN{G}_{ij}+{\beta }_{4}^{k}CLN{Y}_{ij}\right]×& \text{}\\ & \phantom{\rule{0.3em}{0ex}}& exp\left[{\beta }_{5}^{k}BRD{R}_{ij}+{\beta }_{6}^{k}RT{A}_{ij}+{\eta }_{i,t}^{k}+{\theta }_{j,t}^{k}\right]×{ϵ}_{ij,t}^{k},\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\forall k.& \text{(50)}\text{}\text{}\end{array}$

Here, as defined previously, ${X}_{ij}^{k}$ denotes the nominal bilateral trade flows from exporter $i$ to importer $j$ in sector $k$, and we have used the following observable or constructed variables to proxy for the unobservable sectoral bilateral trade costs ${t}_{ij}^{k}$. $lnDIS{T}_{ij}$ is the logarithm of bilateral distance between trading partners $i$ and $j$. $CNT{G}_{ij}$, $LAN{G}_{ij}$ and $CLN{Y}_{ij}$ capture the presence of contiguous borders, common language and colonial ties, respectively. $BRD{R}_{ij}$ as a border dummy variable equal to $1$ when $i\ne j$ and zero elsewhere, which captures the effect of crossing the international border by shifting up internal trade, all else equal. Finally, $RT{A}_{ij}$ is an indicator variable that takes a value of one for the presence of regional trade agreements in our sample. It is equal to one when trading partners $i$ and $j$ are partners of the same RTA, and it is equal to zero otherwise.

Following the recommendations of Santos Silva and Tenreyro (2006), we estimate specification (50) with the Poisson Pseudo Maximum Likelihood (PPML) estimator, which accounts for heteroskedasticity in trade data and takes advantage of the information that is contained in the zero trade flows because it is estimated in multiplicative form. Finally, we use exporter fixed effects, ${\eta }_{i,t}^{k}$, and importer fixed effects, ${\theta }_{j,t}^{k}$ to control for the unobservable multilateral resistances as well as for any other observable or unobservable country feature (e.g. size) on the importer and on the exporter side.

We use specification (50) to obtain gravity estimates for each of the 22 sectors in our sample. Our findings are reported in Tables 35. We start in column (1) of Table 3 with estimates for aggregate manufacturing, then each of the following columns in this table as well as all columns in Tables 45 report gravity estimates for each individual sector. Overall, our estimates are consistent with existing counterparts from the literature, which usually are obtained at the aggregate level. For a benchmark reference and comparisons, we refer to the meta analysis gravity estimates from Table 4 of Head and Mayer (2014).

Several findings stand out based on the estimates from Tables 35. First, as expected, we find that distance is a significant impediment to trade. Without any exception, all estimates of the effects of distance are negative, highly statistically significant and with magnitudes that are comparable to estimates from the literature. The estimate of the effect of distance for total manufacturing (see column (1) of Table 3) is not statistically different from, and in fact almost identical to, the corresponding meta analysis estimate of the distance effects in Head and Mayer (2014). We also find significant (but intuitive and within reasonable bounds) variation in the distance effects. The smallest estimate is -0.465 (std.err. 0.117) for Light Transport Equipment and the largest estimate is -1.336 (std.err. 0.176) for sector Petroleum and Coal products. We find the variation of the estimates of the effects of distance mostly intuitive and mainly reflecting transportation costs.

All else equal, sharing a common border promotes trade. This is confirmed by our estimates of the effects of contiguity ($CNT{G}_{ij}$). Twenty one of the twenty two estimates on $CNTG$ are positive, and sixteen of them are statistically significant. The average manufacturing estimate from column (1) of Table 3) is not statistically different from the corresponding meta analysis estimate of the distance effects in Head and Mayer (2014), and the latter falls comfortably within the distribution of $CNTG$ estimates that we obtain across the different sectors in our sample. As is well documented in the literature, sharing a common language promotes bilateral trade, all else equal. We confirm this regularity with twenty positive estimates on $LANG$, and most of them being statistically significant. Once again, our average manufacturing estimate for the effect of $LANG$ from column (1) of Table 3) does not seem to be statistically different from the corresponding meta analysis estimate in Head and Mayer (2014), and the latter is within the distribution of $CNTG$ estimates that we obtain across the different sectors in our sample.

We also obtain mostly positive and significant estimates of the effects of colonial ties. However, the results are weaker as compared to the findings for contiguity and for language. Thus, for example, our average manufacturing estimate of the effects of $CLNY$ is not statistically significant and is significantly smaller as compared to the corresponding estimate in Head and Mayer (2014). This result is consistent with the estimates from Anderson and Yotov (2010b), who explain it with a decrease of the political importance of colonial relationships in favor of comparative advantage forces. It should also be noted that about a quarter of our $CLNY$ estimates are positive, statistically significant and comparable to the meta analysis estimate from Head and Mayer (2014).

The most robust finding from Tables 35 is that international borders have large and strong effects. With only one exception, we obtain large, negative, and statistically significant estimates of the effects of $BRD{R}_{ij}$. The only insignificant border estimate that we obtain is for Other Manufacturing and, due to the nature of this industry, we cannot offer an intuitive explanation for this result. The average $BRDR$ estimate implies that, all else equal, international trade is about 10 times smaller than intra-national trade. This estimate is significantly smaller as compared to the famous border estimate of McCallum (1995) but it is still very large, suggesting that there are still very large potential gains to be realized from trade liberalization. The variation of the $BRDR$ estimates across sectors makes sense for the most part. Thus, for example, the largest border estimate is for Tobacco (-6.426, std.err. 0.575) and the smallest, but still sizable, is for Medical Equipment (0.619, std.err. (0.286). We find both of these estimates, as well as the overall variation of the $BRDR$ estimates to be quite intuitive with respect to the nature of the products within a given sector.

Finally, and as expected, we find that forming a regional trade agreement promotes international trade. Eighteen of the RTA estimates that we obtain are positive and fourteen of them are statistically significant.17 In terms of magnitude, the average RTA estimate from column (1) of Table 3) is smaller than the meta analysis number in Head and Mayer (2014).18 However, the variation of the RTA estimates across the sectors in our sample is wide and many of them are readily comparable to existing estimates from the literature, e.g. those from Baier and Bergstrand (2007), Anderson and Yotov (2016), and Baier, Yotov and Zylkin (2016). The largest effect that we obtain is for Tobacco (1.971, std.err. 0.373) and the smallest positive and significant estimate that we obtain is for Fabricated Metal Products (0.283, std.err. 0.127). An additional advantage of the sectoral RTA estimates is that they are less susceptible to endogeneity issues since it is less likely that considerations for specific sectors may influence the decision to sign an agreement at the country level.

Overall, we find the gravity estimates that we obtain in this section to be intuitive and in accordance with estimates that have been validated by the existing literature. Therefore, we are comfortable using our estimates to construct bilateral trade costs and to use them to perform the counterfactual analysis in the next section.

### 6 On the Effects of U.S–U.K. Trade Liberalization

This section demonstrates how our framework can be employed to evaluate the effects of trade liberalization on labor market outcomes with heterogeneous workers. For demonstrative purposes we simulate a hypothetical (but also likely to take place) trade liberalization scenario between the United States and Great Britain. Consistent with our gravity estimation analysis and with the intuition that RTAs stimulate international trade beyond simply removing tariffs, we use an RTA estimate to reduce trade costs between the two countries.

Given the demonstrative purpose of the analysis in this section, we choose to employ a common RTA estimate, i.e. an RTA effect that exerts the same initial partial effect in all sectors. This way, we will ensure that none of the heterogeneous effects that we obtain are driven by the initial RTA effects and we will be able to better judge the validity and performance of our framework. In addition, instead of employing the average manufacturing RTA estimate from column (1) of Tables 3, which, as discussed earlier, may be subject to endogeneity critiques, we rely on the RTA estimate of 0.76 from the original work of Baier and Bergstrand (2007). We view the RTA estimate from Baier and Bergstrand (2007) as appropriate because it falls comfortably in the middle of the distribution of our own sector-specific RTA estimates from Tables 35. Under these assumptions, our baseline trade costs are constructed as: $\begin{array}{rlll}{\left({{t}_{ij}^{k}}^{1-\sigma }\right)}^{bsln}& =& exp\left[{\beta }_{1}^{k}LN\text{_}DIS{T}_{ij}+{\beta }_{2}^{k}CNT{G}_{ij}+{\beta }_{3}^{k}LAN{G}_{ij}\right]×& \text{}\\ & \phantom{\rule{0.3em}{0ex}}& exp\left[{\beta }_{4}^{k}CLN{Y}_{ij}+{\beta }_{5}^{k}BRD{R}_{ij}+{\beta }_{6}^{k}RT{A}_{ij}\right],& \text{(51)}\text{}\text{}\end{array}$

where, “$bsln$” stands for baseline scenario and all other variables are defined before. And the counterfactual trade costs are constructed as:

 ${\left({{t}_{ij}^{k}}^{1-\sigma }\right)}^{ctrf}={\left({{t}_{ij}^{k}}^{1-\sigma }\right)}^{bsln}×exp\left[0.76×RTA\text{_}UK\text{_}U{S}_{ij}\right],$ (52)

where, “$ctrf$” stands for counterfactual scenario, and $RTA\text{_}UK\text{_}U{S}_{ij}$ is an indicator variable that is equal to one for trade between UK and US, and it is equal to zero otherwise.

With these trade costs and with all other data and parameters, we proceed to solve our model in the baseline and in the counterfactual scenario. Due to the rich dimensionality of our counterfactual indexes data set, we had to make presentation choices. We decided to present two sets of results, which are central to the analysis.19 These include: (i) a series of cross-section indexes at the country level that are obtained as aggregates across all sectors, and which are reported in Table 6; and (ii) a series of indexes for the US, which are reported in Table 7. The cross-country indexes would enable us to establish the validity of our methods by comparing them with results from previous studies, while the US-specific sectoral results will enable us to discuss sectoral dimension of our findings. The latter is important since one of our main contributions is to allow for different labor types and we expect to see action across the sectoral dimension. In the main text we report the results that are based on the scenario with mobile labor. Corresponding estimates from the scenario with immobile labor are included in the Appendix. Finally, all counterfactual indexes that we present and discuss in this report are constructed as percentage changes:

 $%\Delta IND=100×\frac{IN{D}^{ctrf}-IN{D}^{bsln}}{IN{D}^{bsln}},$ (53)

where: $IND$ can be any index of interest.

We start with an analysis of the cross-country estimates from Table 6. Column (1) of this table reports percentage changes in total exports for each country in our sample. To construct the percentage changes between the baseline and the counterfactual exports for each country, we simply calculate total exports in each scenario as the sum of bilateral exports (excluding domestic sales):

 ${X}_{i}=\sum _{j\ne i}{X}_{ij},$ (54)

where, as defined earlier, ${X}_{ij}$ denotes nominal bilateral trade flows at delivered prices.

The results are intuitive and with reasonable magnitudes. Britain gains the most, about 12 percent increase in total exports. US follows with a much smaller increase in total exports of about 3 percent. The rest of the world is affected negatively. Trade diversion is a natural explanation for the smaller exports in the rest of the world. We note that, in principle, it is possible that the exports of some countries increase due to the UK-US agreement. The intuition is that in the GE scenario UK and US will become richer/larger and they will buy more from all trading partners. However, we do not see such strong size effects here. The biggest “losers”, in terms of decreased exports, are the Dominican Republic, Ireland, and Mexico. Close trade ties with the liberalizing nations explains the trade diversion patterns.

Next, we turn to the results in column (2) of Table 6, which reports the percentage changes in the IMR indexes per country. Consistent with theory, these indexes can be interpreted as percentage changes in consumer prices. In order to aggregate the sectoral IMRs to the country level, we follow Anderson and Yotov (2016) to define:

 ${P}_{i}=exp\left(\sum _{k}{\alpha }_{k}ln{P}_{i}^{k}\right).$ (55)

The effects on the consumers in the world from column (2) of Table 6 are constructed as the percentage difference between the aggregate IMRs from (55) in the counterfactual scenario and the corresponding indexes in the baseline scenario.

The percentage changes in consumer prices from column (1) make intuitive sense. Overall the effects on consumer prices are small. Britain experiences the largest decrease in consumer prices of 0.7 percent. US follows with a much smaller decrease of 0.12 percent. The natural explanation for the differences in the price changes between the two liberalizing partners is country size. The effects on consumer prices in outside countries are really small. We observe some positive and some negative price effects in the rest of the world. It is tempting to interpret the negative indexes as price decreases in the rest of the world due to the UK-US agreement (e.g. due to increased production efficiency in the liberalizing countries, which is passed on consumers everywhere in the world). However, we caution the reader that the IMRs for all countries are constructed relative to the German IMR and, therefore, should be interpreted accordingly.

Finally, columns (3) and (4) of Table 6 report percentage changes in nominal GDP and real GDP, respectively. Nominal GDP is constructed by adding up all sectoral values of production for each country:

 $GD{P}_{i}=\sum _{k}{Y}_{i}^{k}=\sum _{k}{p}_{i}^{k}{q}_{i}^{k},$ (56)

and real GDP is defined as the ratio between nominal GDP and the aggregate consumer price index:

 $RGD{P}_{i}=\frac{GD{P}_{i}}{{P}_{i}}=\frac{\sum _{k}{p}_{i}^{k}{q}_{i}^{k},}{exp\left(\sum _{k}{\alpha }_{k}ln{P}_{i}^{k}\right)}.$ (57)

The effects on nominal and real GDP are qualitatively identical to each other. Therefore, we only focus on the real GDP effects. As expected, the main gains are concentrated in the liberalizing countries. Our estimates imply a 3.6 percent gain in real GDP for the UK and a smaller but still positive and sizable gain of 1 percent for the US. All outside countries register real GDP losses, which vary intuitively with the larger losses for countries that are more closely related to the liberalizing nations. It should also be noted that the effects on the outside world is relatively small. The largest negative impact of -0.42 percent is for the Dominican Republic, and the average effect across all other countries is -0.11 percent. In sum, we view the aggregate GE estimates of the effects of the UK-US agreement as plausible, both for the member and for the non-member countries. This is encouraging evidence and represents a validation of sorts of our methods. Therefore, we are more confident to proceed with the sectoral analysis of the hypothetical impact of the UK-US on the United States.

The sectoral estimates are reported in Table 7.20 Column (1) of Table 7 reports percentage changes in US trade by sector. According to our estimates, the largest increase in US exports will be observed in Manufacture of wood and of products of wood and cork, except furniture, followed by Manufacture of machinery and equipment and Manufacture of radio, television and communication equipment and apparatus. The smallest increase will be observed in Manufacture of tobacco products and Manufacture of wearing apparel; dressing and dyeing of fur. Interestingly, we document a decrease in US exports in the industry Other Manufacturing. This is due to the GE forces in our model, in combination with very strong positive effects for UK exports in this industry (see Table 8 of the Appendix).

Column (2) of Table 7 reports effects on consumer prices at the sectoral level. Overall, the effects on consumer prices are small.21 The largest impact (a decrease of 1.4 percent relative to consumer prices in Germany) is on the prices in the industry Other Manufacturing. This result can be explained with the surge in imports from UK in this industry. The next two categories with comparably large decreases in relatively prices are Tanning and dressing of leather; manufacture of luggage, footwear, etc. (0.52 percent) and Manufacture of office, accounting and computing machinery (0.28 percent). Both of these sectors experience a significant increase in British exports to US, which explains the results for consumer prices. We also observe some positive (relative) price changes, e.g. in Manufacture of coke, refined petroleum products and nuclear fuel, Manufacture of wood and of products of wood and cork, except furniture, and Manufacture of paper and paper products. The explanation for these results is that US exports increase the most in those sectors and, therefore, when faced with more lucrative opportunities abroad, the US producers bid up domestic prices.

Columns (3) and (4) of Table 7 report percentage changes in nominal GDP and real GDP at the sectoral level, respectively. The results in the two columns are qualitatively identical and, therefore, we focus our analysis on the nominal GDP effects from column (3). The value of production will increase in most US sectors. The five sectors that will gain the most in terms of increase in the value of their production include Manufacture of radio, television and communication equipment and apparatus, Manufacture of textiles, Manufacture of wood and of products of wood and cork, except furniture, and Manufacture of paper and paper products, and Manufacture of rubber and plastics products. The value of production will fall in four US sectors, including Tanning and dressing of leather; manufacture of luggage, footwear, etc., Manufacture of furniture; manufacturing n.e.c., Manufacture of office, accounting and computing machinery, and Manufacture of wearing apparel; dressing and dyeing of fur. These results are consistent with our findings for the changes in US sectoral trade, as well as with the numbers for the impact on the UK economy, which are reported in Table 8 of the Appendix.

We finish our analysis with a discussion on the effects on labor in the US. The relevant indexes are reported in columns (5)-(7) of Table 7 and capture the effects on labor with primary education, labor with secondary education, and labor with higher education, respectively. Two main findings stand out from our estimates. First, we find that the number of workers employed in some sectors will increase, while the number of workers employed in other sectors will fall.22 The sectors that will accept the largest number of workers are Manufacture of radio, television and communication equipment and apparatus, Manufacture of textiles, Manufacture of wood and of products of wood and cork, except furniture, and Manufacture of paper and paper products, and Manufacture of rubber and plastics products. This is expected since these are exactly the sectors where producer prices and production will increase the most. Our estimates suggest that the number of workers will actually decrease in more than half of the US sectors. As expected, the biggest negative impact on labor will be felt in the sectors where exports decrease (or increase the least). These sectors include Tanning and dressing of leather; manufacture of luggage, footwear, etc., Manufacture of furniture; manufacturing n.e.c., Manufacture of office, accounting and computing machinery, and Manufacture of wearing apparel; dressing and dyeing of fur.

Second, despite the fact that we are considering a hypothetical trade liberalization scenario between two very similar economies, we do find some small differential effects on labor across the different types. Specifically, a comparison between the effects on labor with primary and with higher education reveals that the number of workers with the highest level of education in our sample will increase more in the industries that hire more workers and will decrease less in the industries that let workers go. All else equal, this points to potential increase in income inequality in the US even from trade liberalization within a very similar developed partner such as the UK.

The corresponding estimates for the United Kingdom, which are reported in Table 8 of the Appendix, reveal the following. First, the impact on labor in the UK will be stronger. Relative size between the liberalizing partners is a natural explanation for this result. Second, the differential impact of the UK-US agreement on the different types of workers is more pronounced in the UK. Third, the UK-US agreement would lead to a stronger negative impact and to a weaker positive effect on the workers with the highest education as compared to the less educated workers, thus pointing to a potential decrease in income inequality in the UK in response to the UK-US RTA. The heterogeneity in the effects on labor that we obtained and the intuitive variation across sectors and labor types demonstrates that the theoretical framework developed here is effective in capturing the impact of trade liberalization on heterogeneous labor, and we expect that the heterogeneous effects across labor types will be even more pronounced and more heterogeneous for an agreement between a developed and a developing country.

### 7 Conclusion

We augment a general equilibrium gravity model with multiple types of workers distinguished by education. We consider workers with primary, secondary, and tertiary levels of education. This model allows us to study the effects of trade policies on wage inequality.

We present the model and explain how trade policy shocks are transmitted to labor markets. We then use data for 45 countries and 22 industries to estimate model parameters. We show how the model can be used in trade policy analysis by considering a regional trade agreement (RTA) between the United States and United Kingdom. The results show that such an agreement would have heterogeneous effects on different worker types in different countries. Our results point to a potential increase in income inequality in the U.S. and decrease in income inequality in the U.K as the result of this RTA.

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Table 1: Sectoral Coverage
 (1) (2) (3) Sector ID ISIC Codes Sector Lable Sector Description 1 15 Food Manufacture of food products and beverages 2 16 Tobacco Manufacture of tobacco products 3 17 Textiles Manufacture of textiles 4 18 Apparel Manufacture of wearing apparel; dressing and dyeing of fur 5 19 Leather Tanning and dressing of leather; manufacture of luggage, footwear, etc. 6 20 Wood Manufacture of wood and of products of wood and cork, except furniture 7 21 Paper Manufacture of paper and paper products 8 22 Printing Publishing, printing and reproduction of recorded media 9 23 Petroleum Manufacture of coke, refined petroleum products and nuclear fuel 10 24 Chemicals Manufacture of chemicals and chemical products 11 25 Rubber Manufacture of rubber and plastics products 12 26 Minerals Manufacture of other non-metallic mineral products 13 27 Metals_A Manufacture of basic metals 14 28 Metals|_B Manufacture of fabricated metal products, except machinery and equipment 15 29 Machinery_A Manufacture of machinery and equipment n.e.c. 16 30 Machinery_B Manufacture of office, accounting and computing machinery 17 31 Electrical_A Manufacture of electrical machinery and apparatus n.e.c. 18 32 Electrical_B Manufacture of radio, television and communication equipment and apparatus 19 33 Medical Manufacture of medical, precision and optical instruments, watches and clocks 20 34 Transport_A Manufacture of motor vehicles, trailers and semi-trailers 21 35 Transport_B Manufacture of other transport equipment 22 36 Other Manufacture of furniture; manufacturing n.e.c. Notes: This table lists the Sector IDs, in column (1), the sector ISIC codes„ in column (2), the corresponding sector labels that are used in the paper, in column (3), and description of the sectors, in column (4), for the industries in our sample.

Table 2: Country Coverage
 ISO Country Code Country Name DZA Algeria ARG Argentina AUS Australia AUT Austria BEL Belgium BRA Brazil BGR Bulgaria CAN Canada CHN China CZE Czech Republic DNK Denmark DOM Dominican Republic EGY Egypt, Arab Rep. FIN Finland FRA France DEU Germany GRC Greece HUN Hungary IND India IDN Indonesia IRL Ireland ITA Italy JPN Japan KOR Korea LTU Lithuania MYS Malaysia MEX Mexico NLD Netherlands NOR Norway PHL Philippines POL Poland PRT Portugal ROM Romania RUS Russia SVK Slovakia ESP Spain SWE Sweden CHE Switzerland OAS Taiwan THA Thailand TUR Turkey UKR Ukraine GBR United Kingdom USA United States VNM Vietnam Notes: This table lists the ISO Country Codes, in column (1), and the Country Names, in column (2), for the countries in our sample.

Table 3: Sectoral Gravity Estimates I, PPML, 2010
 (1) (2) (3) (4) (5) (6) (7) (8) Manuf Food Tobacco Textiles Apparel Leather Wood Paper LN_DIST -0.869 -0.807 -0.926 -1.011 -1.097 -0.879 -0.891 -1.017 (0.056)${**}^{}$ (0.074)${**}^{}$ (0.180)${**}^{}$ (0.115)${**}^{}$ (0.090)${**}^{}$ (0.102)${**}^{}$ (0.107)${**}^{}$ (0.084)${**}^{}$ CNTG 0.354 0.582 0.516 0.026 0.467 0.320 1.071 0.538 (0.154)${*}^{}$ (0.192)${**}^{}$ (0.293)${+}^{}$ (0.257) (0.168)${**}^{}$ (0.160)${*}^{}$ (0.157)${**}^{}$ (0.166)${**}^{}$ LANG 0.306 0.441 0.031 0.191 0.375 -0.123 0.193 0.190 (0.117)${**}^{}$ (0.155)${**}^{}$ (0.377) (0.226) (0.167)${*}^{}$ (0.175) (0.164) (0.127) CLNY 0.069 0.166 0.475 0.090 0.005 -0.003 -0.183 0.018 (0.134) (0.140) (0.462) (0.232) (0.216) (0.194) (0.168) (0.180) BRDR -2.391 -3.845 -6.426 -2.472 -2.363 -2.069 -3.524 -3.031 (0.166)${**}^{}$ (0.195)${**}^{}$ (0.575)${**}^{}$ (0.314)${**}^{}$ (0.251)${**}^{}$ (0.296)${**}^{}$ (0.345)${**}^{}$ (0.232)${**}^{}$ RTA 0.184 0.621 1.971 0.555 0.318 -0.181 0.133 0.482 (0.104)${+}^{}$ (0.098)${**}^{}$ (0.373)${**}^{}$ (0.154)${**}^{}$ (0.145)${*}^{}$ (0.168) (0.169) (0.118)${**}^{}$ $N$ 2116 2116 2116 2116 2116 2116 2116 2116 Notes: This table reports sectoral gravity estimates that are obtained with the PPML estimator and exporter and importer fixed effects, which are omitted for brevity. The first column reports estimates for aggregate manufacturing and each of the following columns report estimates for individual sectors. Standard errors are clustered by country-pair and are reported in parentheses. ${+}^{}$ $p<0.10$, ${*}^{}$ $p<.05$, ${**}^{}$ $p<.01$

Table 4: Sectoral Gravity Estimates II, PPML, 2010
 (1) (2) (3) (4) (5) (6) (7) Printing Petroleum Chemicals Rubber Minerals Metals_A Metals_B Machinery_A LN_DIST -0.919 -1.336 -0.892 -0.972 -1.040 -0.938 -0.837 -0.716 (0.086)${**}^{}$ (0.176)${**}^{}$ (0.071)${**}^{}$ (0.089)${**}^{}$ (0.074)${**}^{}$ (0.100)${**}^{}$ (0.084)${**}^{}$ (0.067)${**}^{}$ CNTG 0.566 0.745 0.072 0.502 0.410 0.237 0.621 0.454 (0.183)${**}^{}$ (0.297)${*}^{}$ (0.166) (0.191)${**}^{}$ (0.177)${*}^{}$ (0.267) (0.163)${**}^{}$ (0.167)${**}^{}$ LANG 0.810 0.590 0.346 0.265 0.329 0.380 0.124 0.348 (0.168)${**}^{}$ (0.241)${*}^{}$ (0.156)${*}^{}$ (0.140)${+}^{}$ (0.147)${*}^{}$ (0.180)${*}^{}$ (0.166) (0.153)${*}^{}$ CLNY 0.353 -0.046 0.464 0.013 0.462 0.659 0.138 0.196 (0.186)${+}^{}$ (0.326) (0.164)${**}^{}$ (0.163) (0.230)${*}^{}$ (0.175)${**}^{}$ (0.151) (0.135) BRDR -3.257 -4.996 -1.776 -3.091 -3.336 -2.835 -3.411 -2.218 (0.270)${**}^{}$ (0.494)${**}^{}$ (0.203)${**}^{}$ (0.226)${**}^{}$ (0.199)${**}^{}$ (0.243)${**}^{}$ (0.238)${**}^{}$ (0.182)${**}^{}$ RTA 0.327 1.048 0.460 0.514 0.151 0.749 0.283 0.087 (0.153)${*}^{}$ (0.254)${**}^{}$ (0.120)${**}^{}$ (0.115)${**}^{}$ (0.124) (0.134)${**}^{}$ (0.127)${*}^{}$ (0.120) $N$ 2116 2116 2116 2116 2116 2116 2116 Notes: This table reports sectoral gravity estimates that are obtained with the PPML estimator and exporter and importer fixed effects, which are omitted for brevity. Standard errors are clustered by country-pair and are reported in parentheses. ${+}^{}$ $p<0.10$, ${*}^{}$ $p<.05$, ${**}^{}$ $p<.01$

Table 5: Sectoral Gravity Estimates III, PPML, 2010
 (1) (2) (3) (4) (5) (6) (7) Machinery_B Electrical_A Electrical_B Medical Transport_A Transport_B Other LN_DIST -1.009 -0.965 -0.780 -0.888 -0.798 -0.465 -1.105 (0.161)${**}^{}$ (0.080)${**}^{}$ (0.078)${**}^{}$ (0.089)${**}^{}$ (0.138)${**}^{}$ (0.117)${**}^{}$ (0.137)${**}^{}$ CNTG 0.198 0.304 0.038 -0.130 0.517 1.160 0.500 (0.349) (0.246) (0.219) (0.145) (0.258)${*}^{}$ (0.460)${*}^{}$ (0.197)${*}^{}$ LANG 0.294 0.183 0.478 0.457 0.410 -0.145 0.208 (0.413) (0.209) (0.165)${**}^{}$ (0.157)${**}^{}$ (0.294) (0.332) (0.219) CLNY -1.061 0.067 -0.175 -0.157 -0.376 0.589 0.373 (0.465)${*}^{}$ (0.164) (0.279) (0.204) (0.246) (0.348)${+}^{}$ (0.251) BRDR -2.597 -1.598 -1.552 -0.619 -2.636 -2.700 -0.086 (0.457)${**}^{}$ (0.212)${**}^{}$ (0.210)${**}^{}$ (0.286)${*}^{}$ (0.365)${**}^{}$ (0.357)${**}^{}$ (0.439) RTA 0.123 0.170 0.331 -0.215 1.038 -0.090 -0.740 (0.232) (0.142) (0.146)${*}^{}$ (0.177) (0.204)${**}^{}$ (0.184) (0.235)${**}^{}$ $N$ 2116 2116 2116 2116 2116 2116 2116 Notes: This table reports sectoral gravity estimates that are obtained with the PPML estimator and exporter and importer fixed effects, which are omitted for brevity. Standard errors are clustered by country-pair and are reported in parentheses. ${+}^{}$ $p<0.10$, ${*}^{}$ $p<.05$, ${**}^{}$ $p<.01$

Table 6: Cross-country GE Effects of the UK-US RTA, Mobile Labor
 ISO NAME $%\Delta$ Trade $%\Delta$ CPI $%\Delta$ GDP $%\Delta$ Real GDP ARG Argentina -0.282 0.0001 -0.089 -0.089 AUS Australia -0.174 0.0003 -0.031 -0.032 AUT Austria -0.350 -0.0007 -0.115 -0.114 BEL Belgium -0.344 -0.0002 -0.108 -0.108 BGR Bulgaria -0.258 0.0001 -0.072 -0.072 BRA Brazil -0.370 -0.0011 -0.121 -0.119 CAN Canada -0.392 0.0022 -0.083 -0.085 CHE Switzerland -0.421 -0.0006 -0.132 -0.131 CHN China -0.212 -0.0006 -0.068 -0.068 CZE Czech Republic -0.321 -0.0002 -0.100 -0.0100 DEU Germany -0.358 0.000 -0.102 -0.102 DNK Denmark -0.331 0.0001 -0.099 -0.100 DOM Dominican Republic -1.106 0.0003 -0.421 -0.422 DZA Algeria -0.321 0.0002 -0.106 -0.106 EGY Egypt, Arab Rep. -0.230 -0.0003 -0.051 -0.051 ESP Spain -0.320 0.0001 -0.103 -0.103 FIN Finland -0.429 -0.0002 -0.143 -0.143 FRA France -0.361 0.0002 -0.117 -0.117 GBR United Kingdom 11.980 -0.692 2.889 3.606 GRC Greece -0.258 -0.0001 -0.076 -0.076 HUN Hungary -0.345 -0.0005 -0.104 -0.103 IDN Indonesia -0.290 -0.001 -0.094 -0.093 IND India -0.192 -0.0003 -0.0489 -0.0485 IRL Ireland -0.851 0.0026 -0.309 -0.311 ITA Italy -0.350 -0.0004 -0.106 -0.106 JPN Japan -0.299 -0.0012 -0.096 -0.095 KOR Korea -0.300 -0.0011 -0.104 -0.103 LTU Lithuania -0.367 -0.0002 -0.124 -0.124 MEX Mexico -0.590 0.0001 -0.177 -0.177 MYS Malaysia -0.291 -0.0011 -0.096 -0.092 NLD Netherlands -0.431 -0.0003 -0.141 -0.141 NOR Norway -0.407 0.0002 -0.142 -0.143 OAS Taiwan -0.287 -0.0009 -0.092 -0.091 PHL Philippines -0.285 -0.0005 -0.087 -0.088 POL Poland -0.344 -0.0006 -0.114 -0.113 PRT Portugal -0.341 0.0001 -0.108 -0.108 ROM Romania -0.299 0.0001 -0.091 -0.091 RUS Russia -0.260 -0.0003 -0.077 -0.073 SVK Slovakia -0.348 -0.0002 -0.112 -0.112 SWE Sweden -0.394 -0.0001 -0.124 -0.124 THA Thailand -0.311 -0.001 -0.102 -0.101 TUR Turkey -0.257 -0.0002 -0.067 -0.067 UKR Ukraine -0.233 -0.0001 -0.064 -0.064 USA United States 3.004 -0.118 0.789 0.908 VNM Vietnam -0.313 -0.0005 -0.111 -0.110 Notes: This table reports the GE effects of a hypothetical RTA between UK and US on all countries in our sample. The simulated scenario allows for labor to be mobile across sectors. Column (1) reports effects on total exports. Column (2) reports effects on consumer prices. Columns (3) and (4) report estimates for nominal and real GDP. See text for further details.

Table 7: GE Effects of the UK-US RTA on the US Economy, Mobile Labor
 SECTOR LABEL SECTOR ID ISIC $%\Delta$ Trade $%\Delta$ CPI $%\Delta$ Income $%\Delta$ Real Income $%\Delta$ L_Prim $%\Delta$ L_Sec $%\Delta$ L_Ter Food 1 15 3.650 -0.010 1.010 1.130 0.210 0.240 0.240 Tobacco 2 16 0.200 -0.010 0.300 0.420 -0.480 -0.460 -0.460 Textiles 3 17 5.740 0.010 1.710 1.830 0.910 0.930 0.930 Apparel 4 18 1.160 -0.230 -0.290 -0.170 -1.070 -1.050 -1.050 Leather 5 19 1.360 -0.520 -1.800 -1.690 -2.570 -2.550 -2.550 Wood 6 20 7.620 0.020 1.640 1.760 0.840 0.850 0.860 Paper 7 21 4.810 0.020 1.620 1.740 0.820 0.840 0.840 Printing 8 22 1.960 -0.050 0.740 0.860 -0.0500 -0.0300 -0.0300 Petroleum 9 23 1.610 0.030 0.770 0.890 -0.0300 -0.0100 0.000 Chemicals 10 24 2.370 -0.140 0.540 0.650 -0.260 -0.240 -0.230 Rubber 11 25 4.530 0.000 1.160 1.280 0.370 0.390 0.390 Minerals 12 26 3.680 -0.030 0.670 0.780 -0.120 -0.100 -0.100 Metals_A 13 27 6.100 -0.010 0.970 1.090 0.170 0.200 0.200 Metals|_B 14 28 1.240 -0.060 0.440 0.560 -0.350 -0.330 -0.330 Machinery_A 15 29 4.480 -0.190 0.550 0.670 -0.240 -0.220 -0.220 Machinery_B 16 30 2.820 -0.280 -0.560 -0.440 -1.340 -1.320 -1.320 Electrical_A 17 31 3.020 -0.170 0.450 0.570 -0.330 -0.310 -0.310 Electrical_B 18 32 6.820 -0.050 2.020 2.140 1.220 1.240 1.240 Medical 19 33 3.100 -0.190 1.060 1.180 0.260 0.280 0.280 Transport_A 20 34 2.950 -0.090 0.710 0.830 -0.0800 -0.0600 -0.0600 Transport_B 21 35 3.880 -0.140 0.670 0.780 -0.120 -0.100 -0.100 Other 22 36 -0.910 -1.370 -1.690 -1.580 -2.460 -2.450 -2.440 Notes: This table reports the GE effects of a hypothetical RTA between UK and US on all US sectors in our sample. The simulated scenario allows for labor to be mobile across sectors. Column (3) reports effects on total exports. Column (4) reports effects on consumer prices. Columns (5) and (6) report estimates for nominal and real GDP. Finally, columns (7)-(9) report impact on each type of labor. See text for further details.

This Appendix includes additional GE results as referred to in the main text. The following tables are included:

• Table 8: GE Effects of the UK-US RTA on the British Economy, Mobile Labor.
• Table 9: GE Effects of the UK-US RTA on the US Economy, Immobile Labor.
• Table 10: GE Effects of the UK-US RTA on the British Economy, Immobile Labor.
• Table 11: Cross-country GE Effects of the UK-US RTA, Immobile Labor.

Table 8: GE Effects of the UK-US RTA on the British Economy, Mobile Labor
 SECTOR LABEL SECTOR ID ISIC $%\Delta$ Trade $%\Delta$ CPI $%\Delta$ GDP $%\Delta$ Real GDP $%\Delta$ L_Prim $%\Delta$ L_Sec $%\Delta$ L_Ter Food 1 15 3.170 -0.350 -0.270 0.420 -3.130 -3.480 -3.540 Tobacco 2 16 3.390 0.0900 1.910 2.620 -1.000 -1.350 -1.420 Textiles 3 17 0.620 -1.180 -0.530 0.160 -3.380 -3.730 -3.800 Apparel 4 18 19.94 0.0500 7.280 8.030 4.210 3.840 3.760 Leather 5 19 15.63 0.0300 6.720 7.460 3.660 3.290 3.220 Wood 6 20 1.390 -1.010 -0.350 0.350 -3.200 -3.550 -3.620 Paper 7 21 -4.680 -1.680 -5.500 -4.840 -8.210 -8.530 -8.600 Printing 8 22 2.770 -0.700 -0.0600 0.640 -2.930 -3.270 -3.340 Petroleum 9 23 -0.900 -0.640 -0.630 0.0600 -3.480 -3.820 -3.890 Chemicals 10 24 12.72 -0.820 4.390 5.120 1.410 1.040 0.980 Rubber 11 25 1.610 -0.790 -0.0900 0.610 -2.950 -3.290 -3.360 Minerals 12 26 12.93 -0.0700 3.340 4.060 0.380 0.0200 -0.0500 Metals_A 13 27 8.370 -0.360 2.850 3.570 -0.100 -0.450 -0.520 Metals|_B 14 28 7.300 -0.160 3.280 4.000 0.320 -0.0300 -0.100 Machinery_A 15 29 19.32 -0.750 5.600 6.330 2.560 2.200 2.130 Machinery_B 16 30 24.59 0.0200 8.610 9.370 5.510 5.130 5.060 Electrical_A 17 31 22.26 -0.350 7.940 8.690 4.850 4.470 4.400 Electrical_B 18 32 13.12 -2.040 3.940 4.660 0.960 0.600 0.530 Medical 19 33 15.68 -3.820 5.020 5.750 2.000 1.640 1.570 Transport_A 20 34 8.660 -0.580 2.850 3.570 -0.100 -0.450 -0.520 Transport_B 21 35 11.07 -0.830 1.940 2.650 -0.980 -1.330 -1.400 Other 22 36 17.14 -0.420 7.460 8.210 4.390 4.010 3.940 Notes: This table reports the GE effects of a hypothetical RTA between UK and US on all UK sectors in our sample. The simulated scenario allows for labor to be mobile across sectors. Column (3) reports effects on total exports. Column (4) reports effects on consumer prices. Columns (5) and (6) report estimates for nominal and real GDP. Finally, columns (7)-(9) report impact on each type of labor. See text for further details.

Table 9: GE Effects of the UK-US RTA on the US Economy, Immobile Labor
 SECTOR LABEL SECTOR ID ISIC CODE $%\Delta$ Trade $%\Delta$ CPI $%\Delta$ GDP $%\Delta$ Real GDP Food 1 15 3.650 -0.0100 0.990 1.110 Tobacco 2 16 0.200 -0.0100 0.290 0.410 Textiles 3 17 5.740 0.0200 1.680 1.800 Apparel 4 18 1.160 -0.230 -0.270 -0.150 Leather 5 19 1.360 -0.520 -1.730 -1.610 Wood 6 20 7.620 0.0200 1.620 1.740 Paper 7 21 4.810 0.0200 1.590 1.710 Printing 8 22 1.960 -0.0500 0.720 0.840 Petroleum 9 23 1.610 0.0300 0.750 0.860 Chemicals 10 24 2.370 -0.140 0.520 0.640 Rubber 11 25 4.530 0.000 1.150 1.270 Minerals 12 26 3.680 -0.0300 0.650 0.770 Metals_A 13 27 6.100 -0.0100 0.960 1.080 Metals|_B 14 28 1.240 -0.0600 0.430 0.550 Machinery_A 15 29 4.480 -0.190 0.540 0.660 Machinery_B 16 30 2.820 -0.280 -0.540 -0.430 Electrical_A 17 31 3.020 -0.170 0.450 0.570 Electrical_B 18 32 6.820 -0.0500 1.970 2.090 Medical 19 33 3.100 -0.190 1.020 1.140 Transport_A 20 34 2.950 -0.0900 0.700 0.820 Transport_B 21 35 3.880 -0.140 0.650 0.770 Other 22 36 -0.910 -1.380 -1.640 -1.520 Notes: This table reports the GE effects of a hypothetical RTA between UK and US on all US sectors in our sample. The simulated scenario does not allow for labor to be mobile across sectors. Column (3) reports effects on total exports. Column (4) reports effects on consumer prices. Columns (5) and (6) report estimates for nominal and real GDP. See text for further details.

Table 10: GE Effects of the UK-US RTA on the British Economy, Immobile Labor
 SECTOR LABEL SECTOR ID ISIC CODE $%\Delta$ Trade $%\Delta$ CPI $%\Delta$ GDP $%\Delta$ Real GDP Food 1 15 3.170 -0.370 -0.240 0.460 Tobacco 2 16 3.390 0.0800 1.900 2.610 Textiles 3 17 0.620 -1.190 -0.460 0.240 Apparel 4 18 19.94 0.0600 7.110 7.860 Leather 5 19 15.63 0.0500 6.560 7.300 Wood 6 20 1.390 -1.020 -0.380 0.320 Paper 7 21 -4.680 -1.710 -5.350 -4.690 Printing 8 22 2.770 -0.730 -0.0100 0.690 Petroleum 9 23 -0.900 -0.650 -0.660 0.0400 Chemicals 10 24 12.72 -0.820 4.350 5.080 Rubber 11 25 1.610 -0.810 -0.0700 0.630 Minerals 12 26 12.93 -0.0700 3.300 4.030 Metals_A 13 27 8.370 -0.360 2.810 3.530 Metals|_B 14 28 7.300 -0.160 3.230 3.950 Machinery_A 15 29 19.32 -0.740 5.470 6.210 Machinery_B 16 30 24.59 0.0400 8.440 9.200 Electrical_A 17 31 22.26 -0.340 7.740 8.500 Electrical_B 18 32 13.12 -2.040 3.880 4.610 Medical 19 33 15.68 -3.820 4.910 5.650 Transport_A 20 34 8.660 -0.580 2.830 3.550 Transport_B 21 35 11.07 -0.830 1.980 2.690 Other 22 36 17.14 -0.410 7.280 8.030 Notes: This table reports the GE effects of a hypothetical RTA between UK and US on all UK sectors in our sample. The simulated scenario does not allow for labor to be mobile across sectors. Column (3) reports effects on total exports. Column (4) reports effects on consumer prices. Columns (5) and (6) report estimates for nominal and real GDP. See text for further details.

Table 11: Cross-country GE Effects of the UK-US RTA, Immobile Labor
 ISO NAME $%\Delta$ Trade $%\Delta$ CPI $%\Delta$ GDP $%\Delta$ Real GDP ARG Argentina -0.300 -0.0001 -0.104 -0.104 AUS Australia -0.191 0.0001 -0.0488 -0.0488 AUT Austria -0.373 -0.0008 -0.136 -0.135 BEL Belgium -0.366 -0.0004 -0.128 -0.127 BGR Bulgaria -0.280 -0.0002 -0.0925 -0.0923 BRA Brazil -0.389 -0.00140 -0.138 -0.137 CAN Canada -0.407 0.0021 -0.101 -0.103 CHE Switzerland -0.443 -0.0009 -0.152 -0.151 CHN China -0.231 -0.0011 -0.0863 -0.0852 CZE Czech Republic -0.342 -0.0003 -0.119 -0.119 DEU Germany -0.380 0.000 -0.121 -0.121 DNK Denmark -0.354 0.0001 -0.120 -0.120 DOM Dominican Republic -1.125 0.0003 -0.439 -0.439 DZA Algeria -0.351 -0.0001 -0.131 -0.131 EGY Egypt, Arab Rep. -0.250 -0.000500 -0.0700 -0.0695 ESP Spain -0.344 0.0001 -0.124 -0.124 FIN Finland -0.453 -0.0004 -0.163 -0.163 FRA France -0.386 0.0002 -0.138 -0.138 GBR United Kingdom 11.89 -0.694 2.845 3.563 GRC Greece -0.282 -0.0004 -0.0968 -0.0963 HUN Hungary -0.365 -0.0007 -0.123 -0.122 IDN Indonesia -0.308 -0.0014 -0.111 -0.109 IND India -0.214 -0.0006 -0.0692 -0.0685 IRL Ireland -0.874 0.0026 -0.331 -0.333 ITA Italy -0.373 -0.0005 -0.126 -0.126 JPN Japan -0.318 -0.0014 -0.114 -0.113 KOR Korea -0.319 -0.0013 -0.123 -0.122 LTU Lithuania -0.393 -0.0003 -0.146 -0.146 MEX Mexico -0.607 -0.0002 -0.195 -0.195 MYS Malaysia -0.309 -0.0014 -0.111 -0.110 NLD Netherlands -0.453 -0.0005 -0.161 -0.161 NOR Norway -0.434 0.0002 -0.165 -0.165 OAS Taiwan -0.303 -0.00130 -0.109 -0.108 PHL Philippines -0.305 -0.0008 -0.108 -0.107 POL Poland -0.367 -0.0006 -0.134 -0.133 PRT Portugal -0.366 -0.0001 -0.130 -0.130 ROM Romania -0.321 -0.0002 -0.112 -0.111 RUS Russia -0.280 -0.0005 -0.0917 -0.0912 SVK Slovakia -0.369 -0.0005 -0.132 -0.132 SWE Sweden -0.419 -0.0001 -0.146 -0.146 THA Thailand -0.330 -0.0013 -0.119 -0.118 TUR Turkey -0.281 -0.0003 -0.0885 -0.0882 UKR Ukraine -0.255 -0.0003 -0.0843 -0.0840 USA United States 2.983 -0.118 0.773 0.891 VNM Vietnam -0.332 -0.0007 -0.129 -0.128 Notes: This table reports the GE effects of a hypothetical RTA between UK and US on all countries in our sample. The simulated scenario does not allow for labor to be mobile across sectors. Column (3) reports effects on total exports. Column (4) reports effects on consumer prices. Columns (5) and (6) report estimates for nominal and real GDP. See text for further details.

1Some examples include Anderson and Yotov (2010a), Egger et al. (2011), Egger and Larch (2011), Ossa (2011), Fieler (2011), Shikher (2011), Costinot, Donaldson and Komunjer (2012), Eaton, Kortum and Sotelo (2013), Arkolakis et al. (2013), Behrens et al. (2014), Allen, Arkolakis and Takahashi (2014), Felbermayr et al. (2015), Heid (2015), Caliendo and Parro (2015), Caliendo, Dvorkin and Parro (2015), Heid and Larch (2016), Anderson, Larch and Yotov (2015b), and Eaton et al. (2016). Anderson (2011), Head and Mayer (2014), Costinot and Rodríguez-Clare (2014), and Larch and Yotov (2016) offer reviews of this literature and its development over time.

2There is also a literature that studies transitional dynamics and costs of adjustment to new trade policy. These short-term effects are not part of our model. Instead, we focus on medium- and long-term effects of trade on labor markets.

3The computational complexity arises from several layers of productivity heterogeneity that exist in her model.

4Below, we will introduce expenditure on intermediates, ${\left({E}_{j}^{k}\right)}^{m}$, where the superscript $m$ will be used to denote intermediates.

5The IMRs may have more variation than the corresponding CPIs and the former may only loosely track variations in consumer price indexes. See Anderson and Yotov (2010a) for a discussion on the differences between the IMRs and the CPIs.

6Since capital is not explicitly introduced in our analysis, ${A}_{j}^{{k}^{\prime }}$ should be thought of as capital-augmented technology.

7To model intermediates we essentially follow Eaton and Kortum (2002). The original Eaton-Kortum model was recently extended to accommodate intermediates at the sectoral level by Shikher (2012) and Caliendo and Parro (2015). On that front, our analysis is parallel to those of Caliendo and Parro (2015). The expositional difference is that we are building a sectoral model with intermediates on the basis on the demand-side gravity models of Anderson (1979) and Anderson and van Wincoop (2003), while Caliendo and Parro (2015) depart from the supply-side gravity foundation of Eaton and Kortum (2002). Larch and Yotov (2016) use the demand-side notation to re-derive various versions of the Eaton and Kortum (2002) model to demonstrate that the basic aggregate and sectoral supply-side and demand-side gravity models are indeed identical subject to parameter interpretation.

8Alternatively, the demand equation (7) can be used to solve for the amount of labor ${L}_{j}^{{k}^{\prime },s}$.

9As demonstrated by Arkolakis, Costinot and Rodriguez-Clare (2012), the structural gravity systems of Anderson (1979), Anderson and van Wincoop (2003), and Eaton and Kortum (2002) can be obtained from a wide range of theoretical micro foundations. SeeHead and Mayer (2014), Costinot and Rodríguez-Clare (2014), and Larch and Yotov (2016) for informative surveys of the literature.

10While the net impact of changes in trade costs cannot be characterized analytically, empirical evidence and numerical simulations suggest that, in most cases, the impact on producer prices is positive for a country that liberalizes its trade policy and negative, via trade diversion effects, for a country that is left out of integration efforts that take place in the rest of the world. For further discussion on these general equilibrium links see Yotov et al. (2016).

11Note that in addition to the CES share parameters and the technology parameters, we will need data on (i) baseline output; (ii) data on trade costs, which require trade, policy, and gravity data; (iii) labor data, including quantities and shares; (iv) data on the CD preference parameters; and, (v) finally, we need data on the shares of intermediates.

13As noted earlier, the analysis can be performed without the need to recover the CES share parameters (as well as the capital-augmented technology values, ${A}_{j}^{k}$, which we discuss next). See for example Dekle, Eaton and Kortum (2007, 2008) and Caliendo and Parro (2015). If all other model parameters are the same, our approach and the methods from the above-mentioned papers deliver identical results.

14http://www.cepii.fr/cepii/en/bdd_modele/presentation.asp?id=6

15The WTO preferential trade agreements data are available at http://www.ewf.uni-bayreuth.de/en/research/RTA-data/index.html.

16Separability of structural gravity allows us to estimate the empirical gravity model for every sector.

17The only negative and statistically significant RTA estimate is for sector Other Manufacturing. The same sector for which our estimate of the effect of international borders was not significant.

18A possible explanation for the small RTA estimate that we obtain here for aggregate manufacturing is the fact that we do not control for possible endogeneity of regional trade agreements. Availability of panel data would have allowed us to implement the average treatment effect methods of Baier and Bergstrand (2007) in order to account for potential endogeneity of RTAs.

19The complete set of all counterfactual indexes are available by request.

20Sectoral estimates for all countries are available by request. We report estimates for the UK in Table 8 of the Appendix.

21We remind the reader that the IMR indexxes are relative to the corresponding effects on consumers in Germany, which is our reference country.

22We remind the reader that in this scenario wages for each type across the different industries in the United States are equalized since workers will relocate to the industries with higher wages. Our estimates reveal that wages for each type or labor will increase by about 0.7 percent.