Measuring the Cross-Country Distribution of Gains from Trade

Transcription

1 Measuring the Cross-Country Distribution of Gains from Trade B. Ravikumar Federal Reserve Bank of St. Louis and Arizona State University Michael E. Waugh New York University and NBER September 9, 2015 ABSTRACT We show how to measure a country s welfare gain from the world moving to a frictionless trade regime as a simple function of data: a country s relative position in the income distribution and the trade elasticity. We quantify the model and find that the world in welfare terms is effectively in autarky and that a substantial portion of possible the gains from trade arise from the unilateral elimination of trade barriers. - Please check the hyper link in the title for the most recent version. [email protected].

2 1. Introduction How open is a country to trade? How large are the welfare gains from international trade? In this paper, we show how to measure the potential gains to moving from the observed equilibrium to a frictionless benchmark using readily available data from the Penn World Tables. A typical answer to these questions involves computing the change in real income due to a change from the observed equilibrium to autarky. In other words, the welfare cost of autarky. A recent example is Arkolakis, Costinot, and Rodriguez-Clare (2012). They compute a country s welfare cost of autarky using a country s home trade share (i.e., one minus the country s import penetration ratio) and trade elasticity. How would one estimate the potential gains? In the class of models in Arkolakis, Costinot, and Rodriguez-Clare (2012), we show how to measure the gains from frictionless trade using observed trade shares, endowment, and GDP data. Our method is useful because it illustrates how different countries have different potentials depending upon their technology, endowments, etc. Or, the welfare cost of autarky being small is not informative about the potential gains available to a country if it were to go to frictionless trade. Furthermore, our approach complements the typical answer by providing a sense of magnitudes. To understand if a country is relatively closed or open, one should know where it stands between autarky on the one extreme and frictionless trade on the other. We illustrate our measurement by embedding the multi-country trade model developed by Eaton and Kortum (2002) (EK, henceforth) into a neoclassical growth model. Each country is endowed with a stock of capital and a labor force. Both factors are immobile across countries. There is a continuum of tradable goods. The distribution of productivity over the continuum is different across countries. International trade is subject to barriers in the form of iceberg costs. All markets are competitive. The amount of trade between any two countries, in equilibrium, depends on wages, rental rates, and trade costs. In our model, the average productivity in each country can be measured easily using a simple development accounting approach based on the neoclassical growth model. This measurement requires standard estimates of capital share and trade elasticity and country-specific data on home trade shares, GDP per worker, and the capital-labor ratio. That is, each country s average productivity is pinned down by current observations. Armed with each country s average productivity, we can measure the potential gains from frictionless trade using our formula which involves all of the average productivities and factor endowments. Our measure implies that a country whose GDP is low relative to the world average (either because of factor endowments or because of productivity) gains more relative to the average country. It follows that in the space of welfare gains the distance to frictionless trade equilib- 2

3 rium from the observed equilibrium is not the same across countries. We take our measure to the data and find two important results. First, the world is effectively in autarky. That is the distance between the observed equilibrium and autarky is small relative to the large potential gains. Second, trade has large potential cross-country distributional consequences. Because all countries are relatively close to autarky, but low technology/poor countries have the most potential to gain, this implies that the potential gains have strong ability to eliminate cross-country income inequality. Frictionless trade is obviously an extreme case, so we complement our theoretical results with a quantitative assessment of the gains associated with plausible changes in trade costs. We keep our quantitative work simple with a relatively parsimonious description of the barriers to trade one trade cost per country. This structure of trade costs allows us to calibrate our model without any more data than that available in the Penn World Table. And, it provides one parameter per country to succinctly summarize the trade frictions. With our calibrated trade frictions, we ask how much of the potential can be achieved if the world had the same trade cost as that of the U.S. We show that this can deliver about onefourth of the overall gains, on average. More interestingly, this counterfactual delivers nearly all the reduction in cross-country income inequality that the frictionless trade economy would. 2. Model We outline the environment of the multi-country Ricardian model of trade introduced by EK. We consider a world with N countries, where each country has a tradable final-goods sector. There is a continuum of tradable goods indexed byj [0,1]. Within each countryi, there is a representative consumer of sizel i. This consumer supplies labor inelastically in the domestic labor market and also owns physical capitalk i that is supplied to the domestic capital market. This consumer also enjoys the consumption of a CES bundle of final tradable goods with elasticity of substitution ρ > 1: [ 1 U i = 0 ] ρ x i (j) ρ 1 ρ 1 ρ dj. (1) To produce quantity x i (j) in country i, a firm employs a Cobb-Douglas production function combining capital and labor with factor shares α and 1 α and productivity z i (j). Country i s productivity for good j is, in turn, the realization of a random variable (drawn independently for each j) from its country-specific Fréchet probability distribution: F i (z i ) = exp( T i z θ i ). (2) 3

4 The country-specific parameter T i > 0 governs the location of the distribution; higher values of it imply that a high productivity draw for any good j is more likely. The parameter θ > 1 is common across countries and, if higher, generates less variability in productivity across goods. Having drawn a particular productivity level, a perfectly competitive firm from country i incurs a marginal cost to produce good j of ri α w 1 α i /z i (j), where w i is the wage rate and r i is the rental rate of capital in country i. Shipping the good to a destination n further requires a per-unit iceberg trade cost of τ ni > 1 for n i, with τ ii = 1. We assume that cross-border arbitrage forces effective geographic barriers to obey the triangle inequality: For any three countries i,k,n, τ ni τ nk τ ki. Below, we describe equilibrium prices, trade flows, and aggregate output. Prices. Perfect competition implies that the price of good j from country i to destination n to be equal to the marginal cost of production and delivery: p ni (j) = τ niri αw1 α i. (3) z i (j) So, consumers in destination n would payp ni (j), should they decide to buy good j from i. Consumers purchase good j from the least-cost supplier; thus, the actual price consumers in n pay for good j is the minimum price across all sources k: { } p n (j) = min p nk (j). (4) k=1,...,n The pricing rule and the productivity distribution allow us to obtain the following CES exact price index for each destination n: P n = γφ 1 θ n where Φ n = [ N ] T k (τ nk w k ) θ. (5) In the above equation,γ = [ Γ ( )] 1 θ+1 ρ 1 ρ is the Gamma function, and parameters are restricted θ such that θ > ρ 1. Trade Flows. To calculate trade flows between countries, let X n be country n s expenditure on final goods, of which X ni is spent on goods from country i. Since there is a continuum of goods, the fraction of income spent on imports fromi,x ni /X n, can be shown to be equivalent to the probability that country i is the least-cost supplier to country n given the joint distribution of productivity levels, prices, and trade costs for any good j. The expression for the share of k=1 4

5 expenditures that n spends on goods from i or, as we will call it, the trade share, λ ni, is: λ ni := X ni X n = T i (τ ni ri αw1 α i ) θ N k=1 T k(τ nk rk αw1 α k ) θ. (6) Expressions (5) and (6) allow us to relate trade shares to trade costs and the price indices of each trading partner via the following equation: λ ni λ ii = ( ) θ Pi τ ni, (7) where λ ii is country i s expenditure share on goods from country i, or its home trade share. P n While well known, this point is worth reiterating: expression (7) is not particular to EK s model. Several popular models of international trade relate trade shares, prices and trade costs in the same exact manner. These models include Anderson (1979), Krugman (1980), Bernard, Eaton, Jensen, and Kortum (2003), and Melitz (2003), when parametrized as in Chaney (2008). Aggregate GDP per Worker. A feature of the EK model (and other trade models) is that it has a convenient representation of real gross domestic product (GDP) per worker that is similar to a standard one-sector growth model with a total factor productivity term and capital-labor ratio raised to a power term. The key feature is that in our setup measured TFP is endogenous and depends on the country s home trade share. This simple connection between trade and the tools of growth accounting is something that we will exploit continually in this paper. To arrive at this representation, a couple of steps are needed. First, with competitive factor markets, the rental rate on capital is pinned down by the following relationship between the wage rate and the capital to labor ratio: r i = α 1 α w ik 1 i, where k is the aggregate capital to labor ratio. Second, combining this relationship with (6) yields an expression for each country s home trade share. λ ii = [ ] k α θti i w i N k=1 T (8) k(τ nk k α i w i ) θ. Third, a rearrangement of (8) provides an expression for the real wage w i = T 1 θ P i i λ 1 θ ii k α i, (9) in which wages, deflated by the aggregate price index, are a function of each country s technology parameter, its home trade share and its capital-labor ratio to the power α (the capital share). Abstracting from the role that capital is playing, this is the same expression discussed extensively in Arkolakis, Costinot, and Rodriguez-Clare (2012). 5

6 Finally, market clearing conditions allow us to connect the real wage in (9) with real GDP per worker. Balanced trade and equating production of the aggregate commodity with total factor payments gives y i = w i P i + r ik i P i. (10) And then using (9) and the observation above that the wage-rental ratio is proportional to the capital-labor ratio gives y i = A i k α i, where A i = T 1 θ i λ 1 θ ii (11) Real GDP per worker in the model can be expressed in the exact same way as in the standard one-sector growth model with a TFP term and capital-labor ratio raised to a power term. The one difference is that measured TFP contains an endogenous trade factor, λ θ ii, and an exogenous domestic factor, Ti θ. A couple of comments are in order regarding (11). First, the balance trade assumption may seem strong, but it s not. A similar expression, but with an additive term representing the difference between the balanced and imbalanced trade equation, is easily derivable. For now we simply abstract from this distinction. Second, given that the expressions for trade shares are not specific to the EK model, this implies there is nothing unique about (11) and its association with the EK model. In some ways, this observation is the essence of the isomorphism result in Arkolakis, Costinot, and Rodriguez-Clare (2012). Many trade models share the same gravity equation (i.e. equation 6), so inverting the home trade share (as we did when going from (8) to (9)) delivers the same expression for real wage irrespective of the micro-details of trade. The point that we find most interesting is the close connection between (11) and the uses of the (closed-economy) growth model in accounting exercises such as Hall and Jones (1999) and Caselli (2005). This closeness provides a method to identify a country s technology parameter adjusted for its degree of openness. Identifying a country s technology parameter is important, because as we show below, the set of technology parameters is sufficient to completely characterize the distribution of income per worker in the frictionless economy. 3. Cross-Country Income Distribution and the Frictionless Gains From Trade This section characterizes the world distribution of income in the frictionless economy and then provides a mapping from this distribution to easily observable data. A country s income level in frictionless trade is computed by making the observation that a 6

7 country s share in world GDP will equal its home trade share. This simple observation then allows us to solve a country s home trade share as a function of its capital and labor endowments, technology parameter, and some elasticity parameters. Proposition 1 summarizes this result. Proposition 1 (GDP Per Worker and Trade in a Frictionless Economy.) GDP per worker in the frictionless trade economy is y FT i ( Ti and a country ss home (and bilateral) trade share is L i ) 1 1+θ k αθ 1+θ i. (12) λ ii = L i yi FT N k=1 L. (13) kyk FT There are many interesting points regarding Proposition 1. First, these expressions are not specific to the EK model, but rather general. Following the logic described, these results, again, are just working off of the expressions for trade shares and market clearing conditions neither of which are specific to the EK model. A second point is that equation (12) clearly shows that this model (and other trade models) has a type of weak scale effect in that level of output per worker depends on the labor force. Holding all else fixed, equation (12) implies that smaller countries will have higher levels of output per worker relative to larger countries. Alvarez and Lucas (2007) suggest one way to kill these scale effects by assuming thatl i T i. However, this implies a counterfactual relationship between measures of TFP from (11) and labor endowments. Proposition 1 and equation (7) say a lot about how much a country can gain from trade. Inspection of (12) and (13) reveals that countries with low levels of technology or little capital per worker trade more intensely relative to countries with high levels of technology or plentiful capital. Because countries with low levels of technology or little capital per worker have smaller home trade shares, equation (7) tells us that they will gain relatively more. Finally, these potential gains are easily measurable from data (e.g. the Penn World Table). Development accounting procedures and (7) allow for estimates of the technology parameter. And then one can construct a country s income level in frictionless trade. Proposition 2 summarizes this result. Proposition 2 (Measuring the Frictionless Trade Income Distribution.) GDP per worker in the 7

8 frictionless trade economy is y FT i ( λii L i ) 1 1+θ ( ) 1 yi PWT k α(θ2 1) θ(1+θ) i, (14) where y PWT i is output per worker as observed in the Penn World Table. Equation (14) now represents potential income of a country in the frictionless trade economy as a function of the country s statistics today. It is this equation that we exploit in the next section to understand the magnitude of the gains and distance of each country from its frictionless trade equilibrium Quantifying the Frictionless Trade Income Distribution. The remarkable feature of (14) is all country specific data required to compute output per worker in the frictionless trade economy is downloadable from the Penn World Table. Below we discuss the specific measures from the PWT that we use. Output per worker, capital per worker, the number of workers are standard measures used in development and growth accounting exercises. In our computations, we use the expenditure side of output measure because this measure of real GDP treats trade balances more in line with how we treat them in the model (i.e., where exports and imports are deflated together and not separately as in production side measures of GDP). See, for example, the discussions in Feenstra, Heston, Timmer, and Deng (2004) and Waugh (2010) for more in depth explanation of these issues. We measure a country s home trade shareλ ii, as one minus a country s ratio of imports to GDP at current prices. A complicating issue with our approach is that imports are largely intermediates and measured in gross terms, while GDP is a value added measure. One approach to correct this mismatch is to gross up GDP by a multiplier that represents intermediates share in value added. Another alternative would be to model intermediates directly as in Eaton and Kortum (2002) or Waugh (2010) and construct measures of trade penetration using gross production rather than value added. Both these alternatives only affect the level and not the relative difference in the gains from trade. If intermediates share varies systematically with level of development the inference about the distributional effects of trade would be affected. We focus on the year 2005 which is the the benchmark year for the PWT 8.1. We drop any countries that have missing data. We also drop the few countries (e.g. Belgium, Panama, etc.) that have imports to GDP larger than one. This leaves us with 160 countries. Given the model s structure resulting in equation (11), we want α to be consistent with the 8

9 Share of Countries Observed Distribution of Output Per Worker 1/64 1/32 1/16 1/8 1/4 1/ Data Log GDP Per Woker (USA = 1) (a) Data: Distribution of Output Per Worker Share of Countries Frictionless Distribution of Output Per Worker 1/64 1/32 1/16 1/8 1/4 1/ Log GDP Per Woker (USA Data = 1) (b) Frictionless Distribution of Output Per Worker Figure 1: Distribution of Output Per Worker: Data vs. Frictionless Economy 9

10 exercises in the income accounting literature. To do so, we set α equal to 1/3. Gollin (2002) provides an argument for setting α equal to 1/3 by calculating labor s share for a wide crosssection of countries and finding it to be around 2/3. As a baseline we setθ equal to four. This is consistent with the estimates from Simonovska and Waugh (2014). Figure 1(a) plots the data the observed distribution of the logarithm of output per worker. The x-axis reports output per worker relative to the US value. There is a large amount of cross-country dispersion in output per worker. The difference between a country in the top 10th percentile and the bottom 10th percentile is a factor of 38. The standard deviation is Not surprisingly, this is consistent with previous development facts regarding cross-country inequality discussed in Caselli (2005) or Hall and Jones (1999). On the same panel, Figure 4(b) plots the distribution of output per worker in the frictionless economy. Note everything is normalized relative to the US value in the data. First, notice that the distribution shifted to the right by a large amount. On average, countries experience a large gains from trade. Second, the dispersion in the distribution shrank by a large amount as well. In particular, the standard deviation of log output per worker shrinks from 1.20 to nearly one. This relates to the discussion surrounding equation 14. The poorest countries have relatively more to gain from trade. A corollary of this is that the poorest countries relative to the frictionless trade benchmark are relatively closed. As a final point of comparison, Figure 2 plots the autarky distribution of output per worker. The key thing to notice is that the autarky distribution is nearly identical to the observed distribution of output per worker. In other words, the world looks as if it is in autarky. 4. Away From Frictionless Trade The previous results focused on a comparison between autarky, current levels of trade, and frictionless trade. Frictionless trade is an extreme case, so we explore the gains associated with plausible changes in trade costs. Below, we describe how we infer trade costs using the same data described above. We then present the results from several counterfactuals Calibration Calibrating trade models of this type present the challenge in that there are a large number of trade costs to discipline. Our objective is to (i) add no more data than we have already been working with and (ii) have a relatively parsimonious description of the barriers to trade. To achieve these objectives we reduce the parameter space such that each country faces only 10

11 Share of Countries /64 Autarky Distribution of Output Per Worker 1/32 1/16 1/8 1/4 1/ Log GDP Per Woker (USA Data = 1) Figure 2: Autarky Distribution of Output Per Worker one trade cost, τ i, to import from all other countries. And this one number will succinctly summarize the frictions that each country face to trade. Given the T s inferred from our development accounting equation in (7), we then chose a τ s to such that the model in equilibrium exactly fits each country s observed home trade share. What this procedure implies is that the equilibrium of the model will exactly match the observed distribution of output per worker across countries and the volume of trade for each country. This also implies that the fricitonless trade equilibrium of our calibrated economy will be the same as the results presented above Calibrated Trade Costs Table 1 presents some summary statistics regarding the trade costs. One prominent feature of these results is that calibrated trade costs are large. The mean and the median trade cost are about seven and six and a half. This result is an analog of our findings in Section 3.1. Relative to the frictionless benchmark the observed levels of trade are small. Thus, to reconcile the small levels of trade, the model needs large frictions. The trade elasticity plays an important role. With a larger θ, the inferred trade costs would be smaller. However, this is because a larger θ shrinks the potential gains from trade and the 11

12 Table 1: Calibrated Trade Costs Mean τ Medianτ All Countries Rich Poor Note: Rich is the set of countries above the median GDP per worker. Poor is the set below Log Trade Cost /128 1/64 1/32 1/16 1/8 1/4 1/2 1 2 Log GDP Per Worker (Data, USA = 1) Figure 3: Trade Costs level of trade associated with it. Whenθ is large, our inference about the world s distance from frictionless benchmark shrinks. With a larger θ, the current levels of trade do not look as small relative to the frictionless benchmark, and thus the model needs smaller frictions to reconcile the data. Table 1 also shows that the trade costs are substantially larger for poorer countries. Here poor countries have trade costs that are almost twice as large as those in rich countries. Figure 3 further illustrates this point by plotting the trade costs for each country versus GDP per worker data. 12

13 The intuition for this result is closely related (again) to our findings in Section 3.1. Poor countries with low levels of technology and capital have the most to gain relative to frictionless trade. Thus, one infers that poor countries require even larger trade costs to reconcile their levels of trade Counterfactual: Toward the US Trade Cost We now perform several exercises to understand plausible, intermediate levels of trade costs. The first exercise endows all countries with the same trade costs that the US faces (which is approximately 2.25) and then computes the new equilibrium. To be clear, this is a simultaneous change and general equilibrium effects are taken into account as a new equilibrium is computed. The idea behind this exercise is to use the US trade costs a plausible benchmark without altering the technological considerations for moving goods across space. Table 2 reports the summary statistics. The move to the US trade costs gives rise to large gains. The average percent increase is almost 100 percent. Moreover, there is substantial heterogeneity, with the gains largely accruing to the poorest countries. Figure 4(a) illustrates this point by plotting the percent gain versus gdp per worker data. Poorer countries experience the largest gains. The second column of Table 2 summarizes this finding by showing that the standard deviation in income per worker declined by 13 percent. Table 2: Gains in Output Per Worker Mean% y σ(logy) Data 1.20 All USτ Frictionless trade The third row of Table 2 provides a point of comparison by reporting the same statistics in the frictionless trade economy. The most important (and surprising) result is that that crosscountry inequality is nearly the same as in the US trade cost economy. In other words, the US trade friction delivers all the reduction in inequality that the frictionless trade equilibrium delivers. The key difference between row two and row three of Table 2 is the level of the gains. The difference between going from a trade friction of 2.2 to frictionless trade amounts to an additional 300 percentage point increase in the gains from trade. 13

14 The difference between levels versus inequality reduction can be seen in Figure 4(b). Figure 4(b) plots the results from both the US trade friction economy and the frictionless trade economy with the same axis. The key thing to note is that the slope between output per worker and the gains are nearly the same. The only difference is the intercept or level. 14

15 Percent Increase in GDP Per Worker /128 1/64 1/32 1/16 1/8 1/4 1/2 1 2 Log GDP Per Worker (Data, USA = 1) (a) Counterfactual: US τ 1200 US trade friction Frictionless trade 1000 Percent Increase in GDP Per Worker /128 1/64 1/32 1/16 1/8 1/4 1/2 1 2 Log GDP Per Worker (Data, USA = 1) (b) Counterfactual: US τ vs. Frictionless Trade Figure 4: Change in Output Per Worker 15

16 5. Conclusion 16

17 References ALVAREZ, F., AND R. J. LUCAS (2007): General Equilibrium Analysis of the Eaton-Kortum Model of International Trade, Journal of Monetary Economics, 54(6), ANDERSON, J. E. (1979): A Theoretical Foundation for the Gravity Equation, American Economic Review, 69(1), ARKOLAKIS, C., A. COSTINOT, AND A. RODRIGUEZ-CLARE (2012): New Trade Models, Same Old Gains?, American Economic Review, 102(1), BERNARD, A., J. EATON, J. B. JENSEN, AND S. KORTUM (2003): Plants and Productivity in International Trade, American Economic Review, 93(4), CASELLI, F. (2005): Accounting for Cross-Country Income Differences, in Handbook of Economic Growth, ed. by P. Aghion, and S. Durlauf, vol. 1. Amsterdam: Elsevier. CHANEY, T. (2008): Distorted Gravity: The Intensive and Extensive Margins of International Trade, American Economic Review, 98(4), EATON, J., AND S. KORTUM (2002): Technology, Geography, and Trade, Econometrica, 70(5), FEENSTRA, R. C., A. HESTON, M. P. TIMMER, AND H. DENG (2004): Estimating Real Production and Expenditures Across Nations: A Proposal for Improving the Penn World Tables, NBER Working Paper 10866,. GOLLIN, D. (2002): Getting Income Shares Right, Journal of Political Economy, 110(2), HALL, R., AND C. JONES (1999): Why Do Some Countries Produce So Much More Output Per Worker Than Others?, Quarterly Journal of Economics, 114(1), KRUGMAN, P. (1980): Scale Economies, Product Differentiation, and the Pattern of Trade, American Economic Review, 70(5), MELITZ, M. J. (2003): The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity, Econometrica, 71(6), SIMONOVSKA, I., AND M. E. WAUGH (2014): The elasticity of trade: Estimates and evidence, Journal of International Economics, 92(1), WAUGH, M. E. (2010): International Trade and Income Differences, American Economic Review, 100(5),

18 Appendix Below, we walk through the derivation of some of the relationships that we exploit. What we want to do is find an expression for a country s real GDP per worker in frictionless trade. First, we want walk through a balanced trade condition. In general the balanced trade condition is L i (w i +r i k i ) = N L k (w k +r k k k )λ ki (15) k=1 which says that total income payments in country i must equal the total purchases of i s goods made by all countries. These country-specific purchases equal the income in country k times the expenditure share that country k spends on goods from country i, i.e. λ ki. Note the right hand side of (15) includes purchases of country i from itself. In frictionless trade, all countries purchase the same amount from country i. That is, λ ki = λ ii. This then simplifies the equation to be N L i (w i +r i k i ) = λ i L k (w k +r k k k ) (16) which states that the share of goods all countries purchase from country i must equal country is share in world GDP: λ ii = k=1 L i (w i +r i k i ) N k=1 L k(w i +r i k i ), (17) Now the goal is to solve for real GDP per worker in frictionless trade. To do so we will use the other home trade share expression λ ii = [ ] k α θti i w i N k=1 T (18) k(k α i w i ) θ. for which we can now match coefficients and solve for the wage and real GDP per worker. Doing so gives real GDP per worker in frictionless trade y FT i ( Ti which is identified up to a constant of proportionality. L i ) 1 1+θ k αθ 1+θ i. (19) 18

19 Equation 19 then allows us to compute the home trade share. λ ii = ) 1 (T 1+θ L i i L i k αθ 1+θ i ) 1 N k=1 k( L T 1+θ i L i, (20) k αθ 1+θ i Algorithm for Calibrating the Model The strategy is we want to pick T s and one τ per country to exactly replicate the distribution of income per worker and home trade shares λ ii. Below we describe the procedure to calibrate the model in this way. Step 1. We first use our development accounting results to recover the T s. So T i = This is very straightforward. ( yi k α i ) θ λ ii. (21) Step 2. With the assumption of one importing trade barrier per country, the home trade share can be expressed as λ ii = 1 τ θ Ω i (w,τ,t,k) i Φ i (w,τ,t,k) (22) whereω i isφ i minus the term for countryiin the sum. This equation provides a mapping from observed trade, two endogenous objects Ω and Φ, into the unobserved trade friction. What this allows us to do is to set up a system of equations to find theτ i that satisfies the relationship above subject to the equilibrium constraints, i.e. that wages are consistent with market clearing. 19