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A joint initiative of Ludwig-Maximilians University’s Center for Economic Studies and the Ifo Institute CESifo Conference Centre, Munich Area Conferences 2012 CESifo Area Conference on Global Economy 25 – 26 May Gravity with Unemployment Benedikt Heid and Mario Larch CESifo GmbH · Poschingerstr. 5 · 81679 Munich, Germany Tel.: +49 (0) 89 92 24 - 14 10 · Fax: +49 (0) 89 92 24 - 14 09 E-mail: [email protected] · www.CESifo.org Gravity with Unemployment∗ Benedikt Heid † and Mario Larch ‡ May 23, 2012 Abstract The gravity equation is the workhorse of international trade ow studies and has been the basis for numerous evaluations of the trade and welfare impact of trade liberalization. However, its theoretical foundations have neglected labor market frictions. We extend a standard structural gravity model by modeling these frictions within a search and matching framework. Our framework allows counterfactual analysis of changes in trade costs and labor market reforms on trade ows, prices, employment, and welfare. We demonstrate that standard gravity models which neglect adjustments on the labor market typically underestimate welfare eects of trade liberalization by deriving a sucient statistic for welfare. We apply our methodology to evaluate the trade eect of endogenous preferential trade agreements (PTA) for a sample of OECD countries and reconsider the border puzzle. Our estimates imply that welfare eects of PTAs are magnied when taking into account employment eects. However, some countries experience higher unemployment and lower welfare after trade liberalization. Keywords : International trade; gravity equation; trade costs; unemployment; structural estimation JEL-Codes : J60; F12; F13; F16 Funding from the DFG under project 592405 is gratefully acknowledged. We thank participants at the GEP Postgraduate Conference 2012 for helpful comments. As always we have a property right on any remaining mistakes and errors. † Aliations: University of Bayreuth and ifo Institute, Address: Universitätsstraÿe 30, 95447 Bayreuth, Germany, Email: [email protected] ‡ Aliations: University of Bayreuth, CESifo, ifo Institute, and GEP at University of Nottingham. Address: Universitätsstraÿe 30, 95447 Bayreuth, Germany, Email: [email protected] ∗ 1 Introduction The quantication of the welfare eects of trade liberalization is one of the core issues in empirical international trade. The workhorse models for evaluating trade policies all feature a gravity equation for international trade ows which captures key stylized facts: Trade increases with market size and decreases with distance. Despite the multitude of theoretical underpinnings of the gravity equation all models so far assume perfect labor markets. This implies that changes in real welfare neglect changes in the total number of employed workers due to trade liberalization. We propose the rst structural gravity model in international trade accounting for imperfect labor markets. We derive a simple, structural framework that allows for and employment price adjustments and show how counterfactual trade ow, GDP, employment, and welfare changes can be calculated. We therefore contribute to the vast literature on structural gravity estimation by augmenting it by search and matching labor market frictions. We derive a simple sucient statistic for welfare, relating welfare changes to employment changes, changes in the share of spending on domestic goods and the (partial) import trade elasticity similar to Arkolakis et al. (2012). Our applications show that welfare eects are substantially magnied when allowing for imperfect labor markets. The additional richness of incorporating labor market frictions comes at minimal cost: function. it only requires an estimate of the elasticity of the matching Hence, our suggested framework can easily be applied in all elds where the gravity equation has been used successfully. We apply our Armington (1969) type model with a one-shot simplication of Pissarides (2000) search and matching labor market frictions as discussed in Rogerson et al. (2005) to two dierent data-sets. First, we use a sample of 28 OECD countries from 1950 to 2006 in order to evaluate the eects of preferential trade agreements (PTAs) and a hypothetical labor market reform in the US. We nd that introducing PTAs as observed in 2006 implies that on average, estimated GDP increases are roughly one third larger when accounting for employment eects arising from imperfect labor markets. Countries with only slight increases in GDP even see negative employment eects. These negative employment eects translate into a magnication of the negative welfare eects predicted for those countries. Our second counterfactual analysis assumes an improvement of labor market institutions in the US. As expected, GDP and welfare increases in the US but also in all trading partners due to positive spillover eects of the labor market reform. We next use our methodology to reconsider the McCallum (1995) border puzzle accounting for employment eects. McCallum (1995) showed that trade between US states and Canadian provinces is reduced by a factor of 22 in comparison to trade within a country. When comparing the GDP changes between the perfect and imperfect labor markets, we see that on average, GDP changes are more than twice as large. On average, US states gain far less than Canadian provinces. Finally, turning to the welfare implications, we calculate a doubling in the equivalent variation when comparing the perfect with the imperfect labor market scenario, similar to the eect found for GDP. Gravity models have been used successfully to explain observed trade ows. has spurred the development of their theoretical underpinnings. This Anderson (1979) and Bergstrand (1985) addressed the role of multilateral price eects on trade ows, while more recent contributions by Eaton and Kortum (2002) and Anderson and van Wincoop (2003) rened the theoretical foundations for the gravity equation to emphasize the importance of accounting properly for the endogeneity of prices. Fieler (2011) and Waugh (2010) build on the former and stress the importance of non-homothetic preferences and asym- 1 metric trade costs, respectively. Anderson and Yotov (2010) elaborate on the incidence of bilateral trade costs in the latter framework. All these frameworks emphasize that in order to calculate the eects of a counterfactual situation taking into account general equilibrium eects, one needs to take care of changes of GDP. To do so, one needs to calculate prices in the counterfactual equilibrium. produced are assumed xed In all these frameworks this is easy as ...quantities (p. 190), Anderson and van Wincoop (2003). However, this assumption is also very restrictive, as it implies that GDP and welfare changes do not account for changes in the total number of employed workers. Theoretical contributions have stressed the eects of trade liberalization with imperfect labor markets. Labor market frictions may arise due to fair wages or eciency wages (Amiti and Davis (2012), Egger and Kreickemeier (2009)), minimum wages (Brecher (1974), Davis (1998), Egger et al. (2011a)) or due to search and matching frictions (Davidson et al. (1988), Davidson et al. (1999), Felbermayr et al. (2011a), Helpman and Itskhoki (2010), Helpman et al. (2010)). One of the main ndings in this literature is that trade liberalization is likely to reduce unemployment rates. Recently, Dutt et al. (2009) as well as Felbermayr et al. (2011b) provide reduced-form evidence that more open economies have lower unemployment rates on average. 1 The remainder of the paper is structured as follows: Section 2 presents the structural gravity model accounting for employment eects. It also includes a discussion of how to calculate counterfactual employment, GDP, trade ow, and welfare changes. Section 3 discusses the parameter estimation. Section 4 evaluates the eects of preferential trade agreements and labor market reforms for a sample of 28 OECD countries. Section 5 revisits the McCallum (1995) border puzzle. Section 6 presents robustness checks, and Section 7 concludes. 2 A gravity model with imperfect labor markets In order to derive the gravity model with imperfect labor markets, we rst describe the goods and labor market, and then derive the gravity equation given the assumptions about the goods and factor market. Afterwards we discuss the comparative static analysis. 2.1 Goods market j The representative consumer in country is characterized by the utility function Uj . We assume goods that are dierentiated by country of origin following Armington (1969). The quantity of purchased goods from country i is given by qij , leading to the following utility function Uj = " n X (1−σ) σ βi # qij σ−1 σ σ σ−1 , (1) i=1 where βi n is the number of countries, σ is the elasticity of substitution in consumption and is a positive distribution parameter. 1 Another strand of the literature uses the quasi-natural experiment of the opening up of Japan in the 19th century to infer welfare gains from trade arising from sectoral reallocations (Bernhofen and Brown (2005)). Artuc et al. (2010) infer welfare eects of trade shocks at the worker arising from sectoral reallocation of workers in a structural dynamic framework. Both abstract from welfare eects due to changes in the number of employed workers. 2 i to j International trade of goods from and tij = 1 for i = j i pij = pi tij . such that all goods from Prot maximization then implies that > 1 for all i 6= j , price pi domestically. imposes iceberg trade costs tij sell at the same Therefore, the representative consumer maximizes (1) subject to the budget constraint ỹj = n X pi tij qij , (2) i=1 where ỹj = yj (1 + dj ), with yj denoting nominal income in country j of trade decit or surplus of country j and dj the share in terms of GDP. The according demand for each variety is given by βi1−σ (pi tij )−σ ỹj , Pj1−σ qij = (3) where the CES price index is dened by " Pj = n X #1/(1−σ) (βi pi tij )1−σ . (4) i=1 The value of aggregate exports from i to j can then be expressed as xij = pi tij cij = βi pi tij Pj 1−σ ỹj . (5) In general equilibrium the total amount of exports corresponds to nominal income, i.e. yi = n X xij . (6) j=1 Assuming labor to be the only factor of production, GDP in a world with imperfect labor markets is given by: yi = wi (1 − ui )Li . (7) wi We next describe the labor market, which determines wages rate and the unemployment ui . 2.2 Labor market We model the labor market using a one-shot version of the search and matching frame- 2 work (SMF, see Mortensen and Pissarides (1994) and Pissarides (2000)). Search-theoretic frameworks t stylized facts of labor markets in developed economies as e.g. the simulta- 3 neous existence of unlled vacancies and unemployed workers. The labor market is characterized by frictions. All potential workers in country have to search for a job, and rms post vacancies 2 Vj at a unit cost of cj Pj j , Lj , (measured in See Rogerson et al. (2005) for a survey of search and matching models including an exposition of the simplied one-shot version. For recent trade models using a similar static approach see Keuschnigg and Ribi (2009) and Helpman and Itskhoki (2010). 3 They are less successful in explaining the cyclical behavior of unemployment and vacancies, see Shimer (2005). This deciency is not crucial in our case as we purposely focus on the steady state. 3 terms of the nal output good) in order to nd workers. The number of successful matches Mj , between an employer and a worker, is given by the elasticity of the matching function and 4 mj Mj = mj Lµj Vj1−µ , where µ ∈ (0, 1) is measures the overall eciency of the labor Mj /Vj = mj (Vj /Lj )−µ = mj ϑ−µ j , 1−µ 1−µ and only a fraction of all workers will nd a job, Mj /Lj = mj (Vj /Lj ) = mj ϑj , where ϑj ≡ Vj /Lj denotes the degree of labor market tightness in country j . This implies that market. Only a fraction of open vacancies will be lled, 5 the unemployment rate is given by uj = 1 − mj ϑ1−µ . j (8) After a match has been established, the rm and the worker bargain over the match surplus. The worker's surplus from the match is the dierence between the wage the worker earns while being employed and the unemployment benets she receives when she is unemployed. The unemployment benets are expressed as a fraction Denote by Jjo γj of the ongoing wage rate. Jjv the value of − Jjv ), i.e. by the the value of expected prot from an occupied job and v expected prot from a vacant job. Jj is given by −Pj cj + Mj /Vj (Jjo sum of negative of the cost of posting a vacancy and the probability of lling the vacancy multiplied with the surplus of lling it. Jjo is given by Jjo = pj − wj , of marginal revenues and marginal costs of an employed worker. until all prot opportunities are exploited, hence pj − wj = Pj cj Vj /Mj . Jjv = 0 i.e. by the dierence Firms post vacancies in equilibrium. This implies that Hence, the worker's wage has to be strictly smaller than the value of output of the rm. Rewriting, one nds the job creation curve wj = p j − Pj cj . mj ϑ−µ j (9) It is increasing in the value of output and decreasing in the expected costs of lling a vacancy Pj cj /(mj ϑ−µ j ). Following Stole and Zwiebel (1996), we use a generalized Nash bargaining solution to determine the surplus splitting rule: max (wj − γj wj )ξj (Jjo − Jjv )1−ξj (10) ⇒ max (wj − γj wj )ξj (pj − wj )1−ξj , (11) wj wj where the bargaining power of the worker is given by ξj ∈ (0, 1) . Note that both the worker and the rm neglect the fact that in general equilibrium, higher wages lead to higher unemployment benets, i.e. they both treat the replacement rate as exogenous. The rst order conditions of the bargaining problem yield for wj results in the wage curve wj = wj − γj wj = ξj /(1 − ξj ) (pj − wj ). ξj pj . 1 + γ j ξj − γ j Due to the one-shot matching, the wage curve does not depend on wage increases in the value of output replacement rate pj , Solving (12) ϑj . The bargained in the worker's bargaining power ξj and in the γj . 4 Note that we assume a constant returns to scale matching function in line with empirical studies, see Petrongolo and Pissarides (2001). 5 Note that the matching eciency has to be suciently low to insure job nding rates and job lling rates to be strictly between 0 and 1. 4 Combining the job creation and wage curves determines the equilibrium labor market tightness as ϑj = where Ωj := 1−γj +γj ξj 1−γj +γj ξj −ξj ≥1 pj Pj 1/µ cj Ωj mj −1/µ , (13) ξj is increasing in the worker's bargaining power and in the replacement rate market tightness decreases and the unemployment rate increases when Ωj pj /Pj increases. An increase of Ωj summarizes the eective bargaining power of workers. mj or cj γj . Labor decrease or increases the marginal revenue of an additional worker relative to the cost of posting the vacancy. Hence, rms will create more vacancies, thereby increasing labor market tightness and lowering unemployment. pj /Pj The relative price is determined via goods demand and supply. It therefor pro- vides the link between the labor and goods market. Specically, changes in trade costs will aect the relative price, therefore inuence labor market outcomes. This can best be seen by using equation (12) to replace wages wj and equations (8) and (13) to replace uj in equation (7) ξj yj = pj mj 1 + γj ξj − γj Given trade costs tij , labor endowments (5), (6) and (14) to solve for the trade ows xij , GDPs yj pj 's Lj pj Pj 1−µ µ cj Ωj mj µ−1 µ Lj . (14) and the parameters, we can use equations (4), and subsequently for relative prices and the unemployment rate pj /Pj , wages wj , uj . 2.3 Derivation of the gravity equation In order to derive the gravity equation in our setting we rst use equation (6) that summarizes the general equilibrium nature of our model and implies market clearing, i.e. yi = n X xij = j=1 n X βi tij pi 1−σ Pj j=1 1−σ ỹj = (βi pi ) θj ≡ βi pi and dening y W = θ̃j ≡ ỹj /ỹ W , we can write yi ỹj xij = W y P j tij Πi Pj Πi ≡ n X tij 1−σ j=1 Pj yj , ỹ W = P j ỹj ỹj . (15) and income shares 1−σ where Pj j=1 Solving for scaled prices yj /y W and n X tij 1−σ , (16) 1/(1−σ) θ̃j . (17) Substituting equilibrium scaled prices into equation (4), we obtain Pj ≡ n X tij 1−σ i=1 Πi !1/(1−σ) θi . (18) Note that this system of equations exactly corresponds to the system given in equations (9)-(11) in Anderson and van Wincoop (2003) or equations (5.32) and (5.35) in Feenstra (2004) assuming balanced trade, di = 0 for all 5 i, even when labor markets are imperfect. If trade costs are symmetric, i.e. tij = tji , and trade is balanced Πi = Pi (see AvW). This is what Anderson and van Wincoop (2003) assumed throughout. Bergstrand et al. (2012) relaxed this assumption and we follow their approach here. The intuition for this results is that in equation (16) GDPs appear. Observed GDPs already take care of the actual number of employed peoples. total spending is total production. achieved by Hence, it still holds that The only dierence is that now total production is employed workers, not all workers, as is assumed with perfect labor markets. We summarize this result in the following implication: Implication 1 The estimation of trade costs is unchanged when allowing for imperfect labor markets. An immediate consequence of Proposition 1 is that parameter estimates of the gravity equation are not aected by allowing for imperfect labor markets. But then the question arises whether imperfections on the labor market matter at all for the evaluation of trade policies? The answer is yes, they do matter in the counterfactual analysis, to which we turn next. 2.4 Comparative statics As pointed out in Proposition 1, the gravity equation derived from our model does not dier from the standard gravity equation (see for an overview Feenstra (2004)). The secret of the power of our approach lies in the counterfactual analysis. As Anderson and van Wincoop (2003) emphasize in Appendix B, in order to calculate the counterfactual situation without borders, one needs to take into account that income and spending shares θi and θ̃i change. In doing so, one needs to calculate prices in the borderless equilibrium. In the framework of Anderson and van Wincoop (2003) assuming perfect labor markets, this is easy as ...quantities produced are assumed xed (p. 190). However, this assumption is also very restrictive, as it implies that GDP and welfare changes are solely due to changes in (real) prices. Hence, whereas a change in a country's GDP only translates into price changes in the perfect labor market framework, our model leads to price and quantity adjustments. When GDP falls, unemployment will rise, which in turn will impact wages. In essence, our model allows labor market variables to aect income. Hence, in the proper counterfactual analysis assuming perfect or imperfect labor markets matters. We derive and discuss in turn counterfactual (un)employment, GDP, and trade ows. Afterwards we discuss how to calculate welfare and derive a sucient statistics for welfare along the lines of Arkolakis et al. (2012). 2.4.1 Counterfactual (un)employment Noting that the p's are not observed, we follow Anderson and van Wincoop (2003) and use equation (15) to solve for scaled prices as follows: yj (βj pj )1−σ = P 1−σ tji n i=1 where j ≡ θj Πσ−1 . j replacing ϑ Pi = ỹi yW yW σ−1 θ Π = j , j j ỹ W ỹ W We then use the denition of ui given in equation equation (8), by the expression given in equation (13) and 6 (19) Ξj = mj cj m j Ωj µ−1 µ and κ̂j = Ξcj /Ξj , we may write: 1 − uci = κ̂j 1 − ui pci pi 1−µ 1−µ Pi Pic µ µ . (20) Pj1−σ = Noting from the derivation of equation (19) and the fact that P 1−σ i tij i (see Appendix A) that we can express the ratios of the prices and price indices as functions of i , we end up with 1 − uci = κ̂j êj ≡ 1 − ui 1−µ c µ(1−σ) j j 1−σ i tij i P 1−σ i tij,c i,c P ! 1−µ µ(1−σ) . (21) Note that employment changes are homogeneous of degree zero in prices, implying that the normalization does not matter for the employment eects. In contrast to the setting assuming perfect labor markets, our framework allows for employment eects. We summarize in the following implication: Implication 2 Whereas in the setting with perfect labor markets employment eects are zero by assumption, the employment eects in our gravity system with imperfections on the labor market are given by: ecj 1−µ c µ(1−σ) j = κ̂j j 1−σ i tij i P 1−σ i tij,c i,c P ! 1−µ µ(1−σ) (1 − ui ) . When data on replacement rates and unemployment rates for all countries are available, we can also calculate counterfactual changes in the unemployment rate. 2.4.2 Counterfactual GDP We next derive counterfactual GDPs. Dening Ξj = mj cj mj Ωj µ−1 µ , we can write equation (14) as: ξj yj = pj 1 + γ j ξj − γ j Now take the ratio of counterfactual GDP, parameters and constants, like yjc yj where = κ̂j ξj , γj , Ξj pcj pj and Lj , pj Pj 1−µ µ Ξj Lj . (22) yj , while noting that all stay constant: µ j Pjc 1−µ and observed GDP pc 1−µ = κ̂j µ pcj pj µ1 Pj Pjc ! 1−µ µ , (23) κ̂j = Ξcj /Ξj . Using again (19) and the fact that ŷj ≡ with yjc pj Pj D̂W ≡ yjc yj y W,c ỹ W ỹ W,c y W = D̂W 1 1−σ 1 1−σ Pj1−σ = 1−σ i tij i (see Appendix A), we can write P 1−µ µ(1−σ) P 1−σ 1 c µ(1−σ) j i tij i κ̂j . P 1−σ j c c i i tij (24) indicating the endogenous change in the world trade decit to keep trade decit GDP shares dj 's constant. 7 It equals one in the case of balanced yj , tij and tcij , we can solve counterfactual GDPs, yjc , as soon as c we have j , j , σ and µ. Even with imperfect labor markets we just need one additional parameter alongside σ , namely, µ, the elasticity of the matching function, in order to trade. Hence, given calculate counterfactual GDPs. P1 = P1c data-set. = 1, 6 In order to ensure a common numéraire, we normalize i.e. GDP changes are in terms of the price level of the rst importer in the If we assume balanced trade and if µ = 1, we end up in the case of perfect labor markets employed by AvW, i.e. yjc = yj 1 c 1−σ j . j (25) We summarize our ndings in the following implication: Implication 3 Counterfactual GDPs are given by: 1 1−σ imperfect labor markets: yjc perfect labor markets: 1 1−σ yjc = D̂W = D̂W c j κ̂j j c 1 j 1 µ(1−σ) 1−σ j 1−σ i tij i P c 1−σ c i i tij P 1−µ µ(1−σ) yj . ( ) yj . We can now go a step further and disentangle the change in GDP in changes due to real price changes and changes due to employment changes as follows: ŷj = = = D̂W 1 1−σ D̂W 1 1−σ D̂W 1 1−σ κ̂j p̂j êj 1 c µ(1−σ) j κ̂j j 1−σ i tij i P 1−σ c i tij,c i P µ 1−µ c µ(1−σ) c µ(1−σ) j j κ̂j j j | {z } | price change with p̂j ! 1−µ µ(1−σ) 1−σ i tij i P ! 1−σ i tij,c i,c P {z employment change 1−µ µ(1−σ) , (26) } denoting the price change. Taking logs, we can attribute the share of log change in GDP divided by D̂W 1 1−σ , ŷj? , due to changes in institutions, prices and employment as follows: 1= ln κ̂j ln p̂j ln êj + + . ln ŷj? ln ŷj? ln ŷj? Let us focus on country 1 for a moment. As we use its price index (27) P1 as our numéraire, the last expression in brackets of equation (26) is equal to one for country 1. Then, the equation simplies to the change in κj (which is solely driven by changes in exogenous parameters) and to two terms which are equal except their exponents: The price change term is risen to the power of µ and the employment change term to the power of Hence, the relative importance of price and employment changes only depends on 1 − µ. µ. If µ approaches zero, the labor market rigidities vanish, and the total GDP change is due to the price change, as in models assuming perfect labor markets. With any value of 6 µ between As mentioned in footnote 12 in AvW, the solution of the multilateral resistance terms adopts a particular normalization. In general this applied normalization may vary between the baseline MRTs and the counterfactual MRTs. In order to ensure the same normalization for the baseline and counterfactual scenario, we normalize P1 = P1,c = 1. 8 zero and one, the share of the GDP change attributable to the price change is share due to the employment change 1 − µ. Hence, with µ = 0.5, µ and the half of the change in GDP is due to the price change and the other half due to the employment change. 2.4.3 Counterfactual trade ows With estimates of tij , data on yi and a value for ows as: where Πi xij y W = yi ỹj and Pj σ , we can calculate (scaled) baseline trade tij Πi P j 1−σ , (28) are given by equations (17) and (18), respectively. With counterfactual GDPs given by (24), we can calculate counterfactual trade ows as !1−σ tcij Πci Pjc xcij y W,c = yic ỹjc , (29) where Πci n X = j=1 Pjc θ̃jc n c 1−σ X tij = i=1 1/(1−σ) !1−σ tcij Pjc Πci , (30) !1/(1−σ) θic , (31) c c c c i ỹi . i yi and θ̃j = ỹj / c c Note that Pj and Pj are homogeneous of degree one in prices while Πi and Πi are homoW c W,c /(y c ỹ c ) geneous of degree minus one. Hence, scaled trade ows xij y /(yi ỹj ) and xij y i j and θjc = yjc / P P are homogeneous of degree zero in prices. In other words, they do not depend on the normalization chosen. Due to direct eects of trade costs changes via tij and non-trivial changes in Πi and Pj it is theoretically ambiguous whether trade will change more or less assuming imperfect labor markets in comparison with the baseline case with perfect labor markets. This will also become obvious when we present our results for trade ow changes of the empirical examples in Section 5.2. 2.4.4 Calculating welfare eects The equivalent variation in percent can in our framework be expressed as follows: EVi = ỹi?,c PPic − ỹi? i ỹi? = ỹi?,c Pi Pi − 1 = ỹˆi? c − 1. ỹi? Pic Pi (32) We next derive a similar sucient statistics for the welfare eects of trade liberalization as Arkolakis et al. (2012). to serve the own market, We therefore consider a foreign shock that leaves the ability τjj , unchanged as in Arkolakis et al. (2012). Additionally, we follow their normalization and set labor in country j , wj equal to one and assume balanced trade. We then come up with the following sucient statistics (see Appendix B for the derivation): 9 Implication 4 Welfare eects of trade liberalization in our model with imperfect labor markets can be expressed as 1 1−σ Ŵj = êj λ̂jj . Hence, welfare depends on the employment change, expenditures λ̂jj and the partial elasticity of imports with respect to variable trade costs, given in our case by 1/(1−σ) Ŵj = λ̂jj êj , the change in the share of domestic 1/(1 − σ). Note that in the case of perfect labor markets êj = 1 and , which is exactly equation (6) in Arkolakis et al. (2012). Assuming that λ̂jj is observed, assuming imperfect or perfect labor markets would lead to dierent welfare predictions. The dierence in the welfare change is given by êj . Hence, assuming perfect labor markets neglects the eects on employment and the welfare eects thereof. Recent empirical ndings suggest that trade liberalization lowers unemployment (see Dutt et al. (2009) and Felbermayr et al. (2011b)). Hence, falling trade costs will increase welfare due to to a decreasing share of domestic expenditures and increasing employment. The sucient statistics of Arkolakis et al. (2012) neglects the employment eect and therefore likely underestimates the welfare eects of trade liberalization. 3 Parameter estimation Having laid out our structural model and described how to obtain counterfactual GDPs, trade ows, employment levels and welfare, we next describe our estimation strategy for the gravity variables and the key parameters needed for the counterfactual analysis, the elasticity of substitution, σ, and the elasticity of the matching function, µ. 3.1 Estimating the gravity variables We start by writing (16) in stochastic form as follows zij ≡ where εij xij = exp k − (1 − σ) ln tij − ln Πi1−σ − ln Pj1−σ + εij , yi yj (33) is a random disturbance term or measurement error of exports, assumed to be identically distributed and mean-independent of the remaining terms of the right-hand side of equation (33). We employ country-specic importer and exporter xed-eects to control for the outward and inward MRT terms Πi and Pj , respectively, as was already suggested by Anderson 7 and van Wincoop (2003) and Feenstra (2004). We then solve for the multilateral resistance terms based on the xed eects trade friction parameter estimates. Additionally to estimating equation (16) log-linear, we also use the approach suggested by Santos Silva and Tenreyro (2006) and estimate the multiplicative version of the model using PPML. 7 Egger and Larch (2012) show that even in the US-Canada example of Anderson and van Wincoop (2003), a disadvantage of the structural approach as compared to xed eects estimation is that correlation between trade friction variables in the model and unobserved country/region-specic determinants leads to inconsistent parameter estimates and, hence, to inconsistent estimates of the impact of trade frictions such as international borders on bilateral trade. They show that the AvW model produces biased parameter estimates according to a Hausman test. 10 3.2 Estimating σ There are many possible ways to estimate to obtain estimates for σ σ. However, Bergstrand et al. (2012) show how within their proposed framework with a production structure without relying on additional data. We show here that their approach which only relies on trade ows and observed baseline variables is still applicable, even when assuming imperfect labor markets. We therefore follow this approach in order to obtain an estimate for σ. First, note that we can rewrite trade ows as given in equation (5) by using equation (12) as follows: xij = βi (1 − γi + ξi )wi tij ξi P j 1−σ yj . (34) Estimation of equation (16) using observable determinants of bilateral trade costs generates estimates 1−σ 8 td ij . We next substitute analogue to generate x̂mj . wi = yi /[(1 − ui )Li ], we end up with 1−σ td ij in equation (16) to generate 1−σ x̂ij , td mj in its Using observations on unemployment rates and observing that xij = βi (1 − γi + ξi )yi tij ξi (1 − ui )Li Pj Taking ratios of predicted trade ows x̂ij and x̂mj , 1−σ yj . (35) we end up with: 1−σ td x̂ij βi (1 − γi + ξi )yi ξm (1 − um )Lm 1−σ ij = . 1−σ x̂mj βm (1 − γm + ξm )ym ξi (1 − ui )Li td mj (36) Now we are left with an equation with only observables and parameters. Hence, we can solve for σ: 1−σ x̂ij td βi (1 − γi + ξi )ξm yi (1 − um )Lm mj / ln σ = 1 − ln . 1−σ βm (1 − γm + ξm )ξi ym (1 − ui )Li x̂ td (37) mj ij yi , ym , Li , Lm , ui and um are observables.9 We can then calculate n2 (n − 1) such values of σ by using all combinations i, j , and m (m 6= i). As a measure of central tendency, we use the average value of all positive estimates of σ as our (summary) estimate. Standard 10 errors for σ are obtained via bootstrapping. Assuming that labor market parameters and β 's are equal, this simplies to: where t1ij−σ x̂ij = [ −σ x̂mj t1mj [ yi (1 − um )Lm ym (1 − ui )Li 8 1−σ . (38) 1−σ For instance, in the AvW context, td would be determined by the exponentiated value of ij \ \ [(1 − σ)ρ] ln dij + [(1 − σ) ln bU S,CA ]Borderij . 9 Alternatively, we can use the predicted Y s from the model. We show in our empirical results that the correlation coecient between observed and predicted Y s is 0.992. 10 Standard errors for all other parameters are the analytical standard errors of the corresponding models. However, the bootstrapped standard errors of those parameters are very similar to the analytical ones. 11 3.3 Estimating µ The other crucial parameter for our counterfactual analysis is the elasticity of the matching function, µ. A rst attempt to estimate and Ωj µ is to assume that labor market variables, such as mj , cj are identical across countries. Then 1 − uj = Ξj Noting that we observe uj pj Pj 1−µ µ =Ξ pj Pj 1−µ µ . (39) in the baseline, we may take ratios for two countries and the log of this ratio to obtain: ln 1 − uj 1 − um = ⇒µ = Using (βj pj )1−σ = θj Πσ−1 = j j and pj Pm p m Pj 1 . 1−uj p 1 + ln 1−um / ln pmj PPmj 1−µ ln µ Pj1−σ = 1 + (1 − σ) ln (40) Pn 1−σ i=1 tij i , we can reformulate as follows: µ = 1−uj 1−um 1 / ln (41) Pn d 1−σ j i=1 tim i m Pn d 1−σ i=1 tij i n2 (n=1) such values of µ by using all combinations j, m, and m(m 6= j). 2 From those values we can then calculate n (n=1) µ's. As a (summary) estimate of µ, we use the average of all estimated values of µ within the unit interval. Standard errors for µ We then calculate are obtained via bootstrapping. 4 Preferential trade agreements and labor market frictions We now turn to evaluate the trade eects of preferential trade agreements and labor market 11 reforms in a sample of 28 OECD countries for the years 1950 to 2006. are taken from Head et al. (2010), available from the CEPII 12 website. The trade data In order to obtain an estimable gravity equation as given in (33), we have to parametrize trade costs. We follow the literature and proxy tij by a vector of trade barrier variables in the following way t1−σ ijτ = exp(β1 P T Aijτ + β2 ln DISTij + β3 CON T IGij + β4 COM LAN Gij ), DISTij is bilateral distance, CON T IGij is a dummy variable indicating whether countries i and j are contiguous, and COM LAN Gij indicates whether two countries share a common ocial 13 The data for the P T A's are constructed from the notications to the World language. where P T Aijτ (42) is an indicator variable of preferential trade agreement membership, 11 The 28 countries are Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Korea, Netherlands, New Zealand, Norway, Poland, Portugal, Slovak Republic, Spain, Sweden, Switzerland, Turkey, United Kingdom, and United States. 12 13 http://www.cepii.fr/anglaisgraph/bdd/gravity.htm. We do not use common colonizer indicators or similar variables regularly used in the literature as these have hardly any variation in the employed OECD sample. 12 Trade Organization (WTO) and were augmented and corrected by using information from PTA secretariat webpages. The remaining geography variables are taken from the CEPII geography data-set. Table 1 gives summary statistics of the data. [Table 1 about here.] As is well known in the literature, countries do not randomly sign PTAs. Recently, Baier and Bergstrand (2004), Baier and Bergstrand (2007), Baier and Bergstrand (2009), Magee (2003), Egger et al. (2008), Egger et al. (2011b), Anderson and Yotov (2011) allowed for PTAs to be endogenous to trade in an econometric sense and showed that the exogeneity assumption is harmful for quantifying the eects of regional trade agreements. In order to avoid the potential endogeneity we follow Baier and Bergstrand (2007) and Anderson and Yotov (2011) and use a two-step estimation approach to obtain consistent estimates of trade cost coecients. In a rst step, we estimate equation (33) including (directional) bilateral xed eects, i.e. we estimate zijτ = exp (k + β1 P T Aijτ + ϕiτ + φjτ + νij + εij ) , where ϕiτ and φjτ (43) are exporter- and importer-time varying xed eects and 14 constant (directional) bilateral xed eects. tilateral resistance terms Πi and Pj , Note that ϕiτ and φjτ νij is a time- control for the mul- and the bilateral xed eects also capture the time- invariant geography variables. In a second step we re-estimate equation (33) in order to obtain estimates for the coecients of the time-invariant geography variables, β2 to β4 . We therefore only use exporter- and importer-time varying xed eects and constrain the coecient of P T A, β1 , to the estimate of the rst step, β̂1 . We follow Wei (1996) and Anderson and van Wincoop (2003) and set the internal distance in a country i, DISTii , to one quarter of the distance to the closest neighboring country. 4.1 Estimation results Concerning the estimation, we present results estimating log-linearized trade ows by OLS as well as the Poisson pseudo-maximum-likelihood (PPML) estimator for the trade ows in levels following the recommendation by Santos Silva and Tenreyro (2006). Results are shown in Table 2. [Table 2 about here.] Columns (1)-(4) present results using bilateral xed eects, i.e. assuming symmetric trade costs tij = tji . Columns (5)-(8) allow for asymmetric trade costs, i.e. by employing directional bilateral xed eects. specications. zijτ . tij 6= tji , Each of these two blocks presents four Columns (1) and (5) report OLS estimates for logged scaled trade ows Column (2) and (6) present PPML estimates for the scaled trade ows in levels to control for heteroskedasticity and zero trade ows. columns (1) and (5) for unscaled trade ows xijτ . Columns (3) and (7) reproduce Finally, columns (4) and (8) present PPML estimates for unscaled trade ows. The slightly larger number of observations for unscaled trade ows stems from the fact that GDP data are not available for all countries in all years where we have trade data and control variables. Our estimates reproduce well-known results from the empirical trade literature. Distance is a large obstacle to trade, whereas contiguity, a common language and PTAs spur 14 We report results for regressions including bilateral xed eects, i.e. νij = νji , and directional bilateral xed eects, i.e. νij 6= νji . 13 trade. Comparing the results from columns (1)-(4) with those of columns (5)-(8) reveals that allowing for asymmetric trade costs does not change our parameter estimates substantially. Comparing with PPML estimates shows a clear pattern. While distance coecients are smaller in absolute values with PPML, all other coecients are larger. The dierences are larger for estimates using scaled trade rather than unscaled trade ows. Note that in the case of specications using unscaled trade ows, GDP eects are captured by the time-varying importer- and exporter-xed eects. Hence, those specications implicitly allow for non-unitary GDP coecients. PTAs increase trade by 30.60% (column (3)) to 40.64% (column (8)) when neglecting general equilibrium eects. The general equilibrium eects will be taken into account in the comparative static results, to which we turn next. 4.2 Comparative static results We perform two counterfactual experiments in our OECD sample. First, we evaluate the eects of PTAs. Therefore we take PTAs as observed in 2006 and contrast it with a counterfactual situation without any PTAs. Second, we evaluate a hypothetical improvement of labor market institutions in the US. In all scenarios we assume that trade is balanced multilaterally. 4.2.1 Introducing PTAs as observed in 2006 Our rst counterfactual experiment evaluates the eects of introducing PTAs as observed in 2006 from a counterfactual situation with no PTAs in place. We base our counterfactual analysis on parameter estimates from column (6) of Table 2. [Table 3 about here.] The results can be found in Tables 3, 4, and 5. Table 3 is organized as follows: The rst column (1) labeled AvW %GDP gives the percentage change in nominal GDP in terms of the price index of Australia for the baseline case of perfect labor markets. Column (2) labeled SMF %GDP gives the same change for our gravity model using a search and matching framework. Columns (3) and (4) use equation (26) and decompose the change in nominal GDP of column (2) due to the price and employment changes. Column (5) reports the percentage change in the employement share for the case of imperfect labor markets. Finally, columns (6) and (7) report the equivalent variation (EV) for the case of perfect and imperfect labor markets, respectively. Table 3 reveals that all countries gain in terms of GDP when introducing PTAs as observed in 2006. This translates into an average gain in terms of GDP of 0.89% when assuming perfect labor markets. The average GDP gain increases by 29% to 1.15% when accounting for employment eects. Hidden behind these average eects is substantial heterogeneity. While some countries gain substantially more than the average, e.g. Canada with a gain of 2.80%, countries like the US experience a very modest increase of 0.60%. The decomposition of (log) GDP in (log) price and (log) employment changes highlights that for many countries in the sample, roughly one third of the increase in GDP is driven by the increase in employment. Countries with only slight increases in GDP see negative employment eects, as can be seen in in column (5) of Table 3. We graphically illustrate the employment eects in Figure 1. These negative employment eects translate into a magnication of the negative welfare eects predicted for those countries in comparison with the assumption of perfect labor markets, see columns (6) and (7). In general, welfare 14 eects are magnied when taking into account employment eects. For example, the standard welfare estimate for Canada is about two thirds of the welfare eect when taking into account labor markets imperfections. [Figure 1 about here.] Tables 4 and 5 report goods trade changes for perfect and imperfect labor markets, respectively. Trade changes are heterogeneous across importers and exporters. To summarize this heterogeneity, we present moments of calculated trade ow changes across all destination countries for all exporters. Both tables report the minimum and maximum changes, alongside with the 2.5%, 25%, 50%, 75% and 97.5% quantiles. Comparing numbers across columns for each row reveals the heterogeneity amongst importers, while comparing numbers across rows for each column highlights the heterogeneity across exporters. In general, we see that for every country there are both positive and negative bilateral trade ow changes. By and large, median trade ow changes tend to be larger for small (e.g., Austria and Switzerland) and remote (e.g., Korea and Japan) countries. For example, the introduction of PTAs as observed in 2005 implies that the change in trade ows for the UK is larger than 12.77% for 25% of all countries importing goods from the UK. Turning to the trade ow results of our model with imperfect labor markets given in Table 5, we nd a similar pattern for trade ow changes. Again, changes are heterogeneous both across importers and exporters and again small and remote countries experience larger changes. The implied trade ow changes dier from the case with perfect labor markets, even though they are very similar in magnitude. [Table 4 about here.] [Table 5 about here.] 4.2.2 Evaluating the eects of a labor market reform in the US Our second counterfactual experiment evaluates the eects of a labor market reform in the US which improves their labor market institutions. We implement this reform by a 3% increase in κ for the US, i.e. changing κ from 1 to 1.03 for the US. Note that with our framework we do not have to be explicit about the specic changes in labor market institutions. [Table 6 about here.] The results can be found in Tables 6 and 7. Table 6 is organized as Table 3. Table 6 reveals that all countries gain in terms of GDP when improving US labor market institutions. This highlights the positive spill-over eects, recently suggested theoretically by Egger et al. (2011a) and Felbermayr et al. (2009), and documented empirically in a reduced-form setting in Felbermayr et al. (2009). Trivially an evaluation of any change of labor market institutions cannot be analyzed when assuming perfect labor markets. Therefore, columns (1) and (6) are uninformative in this setting. The decomposition of (log) GDP in (log) price and (log) employment changes highlights that in the US prices fall and all GDP increases are brought about by employment increases. In the trading partner countries of the US the positive GDP eects are composed of roughly 60-80% of price changes and 20-40% changes in employment. This is also reected in the relative magnitudes of the employment changes reported in column (5) of Table 6. We graphically 15 illustrate the employment eects in Figure 2. Concerning welfare, obviously US prots the most from its improvements in labor market institutions with an increase in welfare of 2.94%. However, importantly all other countries also gain, with the highest gains for Canada with 0.19%. [Figure 2 about here.] Table 7 summarizes the trade eects. A labor market reform in the US spurs trade changes across the whole sample. Eects of exports of the US range between -1.42% and 0.12%. Eects across other exporters range between -1.43% for Australia to 1.05% for Belgium and Switzerland. On average, 50% of trade ow changes are larger than 0.55%. The size pattern of the spill-over eects of labor market reforms in the US clearly depend on the distance and trade volumes between the corresponding countries and the US. [Table 7 about here.] 5 The US-Canadian border puzzle and labor market frictions We next use our methodology to reconsider the McCallum (1995) border puzzle accounting for employment eects. McCallum (1995) showed that trade between US states and Canadian provinces is reduced by a factor of 22 in comparison to trade within a country. This has spawned a vast literature on estimating border eects, which is too numerous to be 15 discussed here. Most notably, Anderson and van Wincoop (2003) made much progress in solving McCallum's border puzzle by showing that accounting for multilateral resistance terms reduces this eect to a factor of 1/5 to 1/2. While the subtleties of the price eects have now been widely acknowledged, the literature so far has abstracted from employment eects. We therefore turn to the classical data-set used by McCallum (1995) and Anderson and van Wincoop (2003) to reconsider the border eect and quantify the employment eects of counterfactually abolishing the US-Canadian border. For reasons of comparison we use data for the same 30 US states and 10 Canadian 16 provinces alongside an aggregate of OECD countries labeled ROW for the year 1993 as in Anderson and van Wincoop (2003). We also follow their specication of the trade costs function, which is given by t1−σ = exp(β1 ln DISTij + β2 BORDERij ), ij where DISTij is again bilateral distance and BORDERij (44) is a dummy variable indicates whether a trade ow crosses the US-Canadian border. 5.1 Estimation results We present results of our estimates for 6 dierent specications in Table 8. Column (1) reproduces the parameter estimates of Table 6, column (viii) using xed eects to control for the multilateral resistance terms. Column (2) estimates the gravity model as given in equation (16) multiplicatively using PPML on the same 1,511 observations as in column (1). This controls for the heteroskedasticity, a typical feature of trade ow data. reduces the estimated coecient for 15 16 BORDER from −1.551 in column (1) to For an in-depth review of this literature see Anderson and van Wincoop (2004). For a detailed description of the data-set see Anderson and van Wincoop (2003). 16 This −0.981. Assuming σ = 5, this implies a partial equilibrium tari equivalent of the US-Canadian border of 47.37% and 27.79%, respectively. 17 Hence, accounting for heteroskedasticity by estimating the gravity equation in multiplicative form more than halfs the estimate of the partial border eect. In column (3) we include the 49 zero trade ows, leading to a total of 1,560 observations. Compared to column (2), estimates hardly change. The coecient of the border dummy even slightly decreases. In column (4) we include internal trade ows for states and provinces. As internal trade ows are not readily available, we follow Anderson and Yotov (2012) and calculate them as yi − Pn j6=i xij . Using xed eects, we end up with somewhat larger distance and border eects as compared to column (1). Column (5) reproduces results with the PPML. Now, distance coecients get much larger and the border eect much smaller. Finally, column (6) includes both, zero trade ows and internal trade, leaving estimates virtually unchanged compared to column (5). Our preferred specication (6) implies a partial equilibrium tari equivalent of the border barrier of 22.26%. 5.2 Comparative static results [Table 8 about here.] [Table 9 about here.] Our counterfactual experiment abolishes the US-Canadian border. We base our counterfactual analysis on parameter estimates from column (1) of Table 8. Further, following Anderson and van Wincoop (2003), we add one aggregate region consisting of 20 OECD 18 countries labeled ROW and assume balanced trade. value for the elasticity of substitution use standard values for both and set µ = 0.75, Additionally, we have to chose a σ and the elasticity of the matching function µ. We σ = 5 as in Anderson and van Wincoop (2003) and as proposed in Hall (2005). We provide robustness results with respect to these parameter values in the Appendix. The results can be found in Tables 9, 10, and 11. Table 9 is organized as follows: The rst column (1) labeled AvW %GDP gives the percentage change in nominal GDP in terms of the price index of Alabama for the baseline case of perfect labor markets. Column (2) labeled SMF %GDP gives the same change for our gravity model using a search and matching framework. Columns (3) and (4) use equation (26) and decompose the change in nominal GDP of column (2) due to the price and employment changes. Column (5) reports the percentage change in the employement share for the case of imperfect labor markets. We graphically illustrate the employment eects in Figure 3. Finally, columns (6) and (7) report the equivalent variation (EV) for the case of perfect and imperfect labor markets, respectively. Table 9 reveals that all states and provinces gain both in terms of GDP and equivalent variation. This result holds irrespective of whether we consider perfect or imperfect labor markets. When comparing the GDP changes between the perfect and imperfect labor markets, we see that on average, GDP changes are more than twice as large. On average US states gain far less than Canadian provinces, in line with standard predictions of new trade theory models of larger gains for smaller regions/countries. This result is even magnied when considering search and matching labor market frictions. The decomposition of (log) GDP in (log) price and (log) employment changes highlights that in the US GDP changes 17 This is calculated as exp(BORDER/(1 − σ)). We dier from the optimization routine used in Anderson and van Wincoop (2003) by solving the system of multilateral resistance terms for all regions including ROW. 18 17 are predominantly brought about by price changes, whereas the increase in GDP of Canadian provinces depends relatively more on changes in employment. This reects the fact that the reduction in trade costs due to the abolition of the US-Canadian border leads to a bigger change in the domestic price index in the smaller country. This leads to a relatively larger reduction in real vacancy posting costs in Canada, explaining the larger importance of employment changes. In line with this fact, are the larger employment changes stated in column (5). Finally, turning to the welfare implications, we calculate a doubling in the equivalent variation when comparing the perfect with the imperfect labor market scenario, similar to the eect found for GDP. [Figure 3 about here.] [Table 10 about here.] [Table 11 about here.] Tables 10 and 11 reports goods trade changes for perfect and imperfect labor markets, respectively. Trade changes are heterogeneous across importers and exporters. To summarize this heterogeneity, we present moments of calculated trade ow changes across all destination countries for all exporters. Both tables report the minimum and maxi- mum changes, alongside with the 2.5%, 25%, 50%, 75% and 97.5% quantiles. Comparing numbers across columns for each row reveals the heterogeneity amongst importers, while comparing numbers across rows for each column highlights the heterogeneity across exporters. In general, we see that for every region there are both postive and negative bilateral trade ow changes. By and large, trade ow changes are larger for exporting Canadian provinces. Interestingly, this pattern is reversed for the largest quantiles. For example, the abolition of the border implies that the change in trade ows for the state of New York is larger than 80.50% for 25% of all regions importing goods from New York. Turning to our model with imperfect labor markets, we nd a similar pattern for trade ow changes. Again, changes are heterogeneous both across importers and exporters and again Canadian provinces experience larger changes. Even the implied trade ow changes dier from the case with perfect labor markets, albeit similar in magnitude. 6 Robustness checks In order to check the sensitivity of our results, we perform two sets of robustness checks. First, we allow for trade imbalances following Dekle et al. (2007). Second, as we have to set (or estimate) the unobserved parameters for the elasticity of substitution and of the matching function, σ and µ, we provide results for dierent values of those parameters. 6.1 Controlling for trade imbalances Our framework can easily accommodate trade imbalances following Dekle et al. (2007). With trade balance, ỹj = yj and θ̃j = θj . 19 GDP and total spending dier. However, as soon as we allow for trade imbalances, In Tables 12, 13 and 14 we reevaluate the eects of preferential trade agreements when allowing for trade imbalances. By and large our results are hardly eected by trade imbalances. The biggest dierence is in the decomposition of 19 We set the trade imbalance for the aggregate of OECD countries (ROW) equal to 0. 18 the GDP change. The price change share is smaller when accounting for trade imbalances. Aggregate average welfare eects are literally the same. In Tables 15 and 16 we recalculate the eects of the hypothetical US labor market reform. Average GDP, employment and welfare eects are literally unchanged. We also report results from counterfactually erasing the US-Canadian border taking into account trade imbalances in Tables 17, 18, and 19. Whereas GDP changes are somewhat larger for Canada and slightly smaller for the US when controlling for trade imbalances, welfare eects remain very similar. [Table 12 about here.] [Table 13 about here.] [Table 14 about here.] [Table 15 about here.] [Table 16 about here.] [Table 17 about here.] [Table 18 about here.] [Table 19 about here.] 6.2 Dierent parameter values for counterfactual analysis We check the sensitivity of our results to variations in the elasticity of substitution, well as the elasticity of the matching function average eects. µ. σ, as For expositional brevity, we only present In Tables 20 and 21 we present robustness checks for the US-Canadian border trade sample (without and with correcting for trade imbalances), whereas we present results for the OECD sample in Tables 22 and 23. Clearly, our GDP, employment and EV eects depend on the values of σ and µ. When the elasticity of substitution increases, GDP, employment and EV changes get smaller. This is due to the fact that varieties are higher substitutes, making trade less important. Hence, abolishing the US-Canadian border leads to smaller predicted gains in terms of GDP, employment and welfare. µ also show a clear pattern. Lower µ indicate higher GDP, employment and welfare changes. Lower µ corresponds to labor market imperfections. When µ approaches 1 we end up in the case of perfect Changes in the elasticity of the matching function values of larger labor markets. [Table 20 about here.] [Table 21 about here.] [Table 22 about here.] [Table 23 about here.] 19 7 Conclusion The gravity equation is the workhorse of international trade ow studies and has been the basis for numerous evaluations of the trade and welfare impact of trade liberalization. However, its theoretical foundations have neglected labor market frictions. We extend a standard structural gravity model by modeling these frictions within a search and matching framework. Our framework allows counterfactual analysis of changes in trade costs and labor market reforms on trade ows, prices, employment, and welfare. We apply our developed structural model to two dierent data-sets. First, we use a sample of 28 OECD countries from 1950 to 2006 in order to evaluate the eects of preferential trade agreements (PTAs) and a hypothetical labor market reform in the US. We nd that introducing PTAs as observed in 2006 leads to a signicant magnication of GDP increases when accounting for employment eects. Countries with only slight increases in GDP even see negative employment eects. These negative employment eects translate into a magnication of the negative welfare eects predicted for those countries. Our second counterfactual analysis assumes an improvement of labor market institutions in the US. Again, average welfare eects are doubled when taking into account employment eects. US GDP increases roughly ten times more than GDP of the other countries. While the US prots the most from its improvements in labor market institutions with an EV of 2.94%, all trading partners also experience an increase in welfare due to positive spill-over eects. We next use our methodology to reconsider the McCallum (1995) border puzzle accounting for employment eects. McCallum (1995) showed that trade between US states and Canadian provinces is reduced by a factor of 22 in comparison to trade within a country. When comparing the GDP changes between the perfect and imperfect labor markets, we see that on average, GDP changes are more than twice as large. On average US states gain far less than Canadian provinces. Finally, turning to the welfare implications, we calculate a doubling in the equivalent variation when comparing the perfect with the imperfect labor market scenario, similar to the eect found for GDP. 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(47) j=1 Similarly, equation (18) can be written as Pj1−σ n X = i=1 Dene i = θi Πσ−1 i leads to Pj1−σ = n X t1−σ ij i . (48) t1−σ ij Pj . (49) i=1 Now divide equation (46) by Π1−σ i 1 = Πσ−1 i n X j=1 Using again i = θi Πσ−1 i leads to 1= n i X 1−σ tij Pj . θi (50) j=1 And therefor to θi − i n X t1−σ ij Pj = 0. (51) j=1 1−σ Similarly, divide equation (48) by Pj 1= Pjσ−1 n X t1−σ ij i . (52) i=1 Using again Pj = θ̃j Pjσ−1 leads to: 1= n Pj X θ̃j And therefore to: θ̃j − Pj t1−σ ij i . (53) t1−σ ij i = 0. (54) i=1 n X i=1 Equations (51) and (54) lead to a system of unknowns i and 2n Pj . 24 equations that can be solved for the 2n B Sucient statistics for welfare in the trade model with imperfect labor markets Dening real income as Wj ≡ ỹj /Pj and taking the log-derivative leads to d ln Wj = d ln ỹj − d ln Pj . yj is given by yj = wj (1 − uj )Lj . Hence, the log-derivative of yj can be written as uj uj d ln uj = − d ln uj , 1 − uj 1 − uj = d ln wj − d ln yj (55) where the second expression on the right-hand side follows by choice of numéraire. Noting that ỹj = yj (1 + dj ) dj hP and taking The log-derivative of Pj = as constant, it holds that n 1−σ i=1 (βi pi tij ) i 1 1−σ d ln ỹj = d ln yj . is given by ! n X βi pi tij 1−σ βi pi tij 1−σ = d ln pi + d ln tij . Pj Pj d ln Pj i=1 Using xij = βi pi tij Pj 1−σ ỹj λij = xij /ỹj = and dening d ln Pj = n X βi pi tij Pj 1−σ , we can simplify to λij (d ln pi + d ln tij ) . (56) i=1 p = 1−γξii+ξi wi , it also holds that d ln pi = d ln wi . Pn i d ln Pj = i=1 λij (d ln wi + d ln tij ). Combining terms leads to Noting that Hence, we can also write: n d ln Wj = d ln yj − d ln Pj = − X uj d ln uj − λij (d ln wi + d ln tij ) . 1 − uj (57) i=1 Taking the ratio of λij and λjj we can write λij = λjj Noting that dtjj = 0 βi pi tij βj pj tjj by assumption and that 1−σ wj . is the numeraire, so that dwj = dpj = 0, the log-change of this ratio is given by: d ln λij − d ln λjj = (1 − σ) (d ln tij + d ln pi ) . Combining this with equation (56) leads to: d ln Pj = 1 1−σ n X λij d ln λij − d ln λjj i=1 n X ! λij . i=1 Pn Pn Pn Pn , it follows that i=1 λij = 1 and d i=1 λij = i=1 dλij = 0. Pn ỹj = i=1 xijP n dλ = 0 . Using these facts, the above expression simplies Hence, λ d ln λ = ij ij i=1 i=1 ij Noting that to: d ln Pj = − 1 d ln λjj . 1−σ 25 The welfare change can than be expressed as follows d ln Wj = − uj 1 d ln uj + d ln λjj . 1 − uj 1−σ Integrating between an initial situation and a counterfactual situation we end up with ln Ŵj = ln eˆj + 1 1−σ ln λ̂jj . Taking exponents leads to 1 Ŵj where ej = 1 − uj 1−σ = êj λ̂jj , is the share of employed people. When we move from any observed level of trade to autarky, λcjj = 1, which simplies the expression to 1 = êj (λjj )− 1−σ . Ŵj Note, however, that unequal to the case with perfect labor markets considered in Arkolakis et al. (2012), even this expression needs information about counterfactual GDP or at least, with balanced trade, employment levels. C Minimum wages within the search and matching framework In this appendix we show how minimum wages can be introduced in our search and matching framework. Basically, a binding minimum wage will replace the bargaining of workers and rms that are matched. We rst consider the bounds for a binding minimum wage. A minimum wage below the wage that a rm and a worker would bargain is not binding, hence not relevant. The wj , is therefore given by the wage ξj pj . 1 + γ j ξj − γ j (58) lower bound for a binding minimum wage, denoted by curve (12) w j = wj = The upper bound for a minimum wage, denoted by wj , is given by the job's output, as w j = pj . wj < w̃j < wj . longer relevant. ϑj can be rms would not be able to recover vacancy posting costs. Hence, A well dened equilibrium with binding minimum wage With a given binding minimum wage, the wage curve is no w̃ exists if solved by using the job creation curve given in (9) Pj cj ⇒ mj ϑ−µ j pj − w̃j 1/µ cj −1/µ ϑj = , Pj mj w̃j = pj − which corresponds to equation (13). GDP in country j (59) can be derived by replacing uj using equations (8) and (59): yj = w̃j mj pj − w̃j Pj 1−µ 26 µ cj mj µ−1 µ Lj , (60) which corresponds to equation (14). Counterfactual employment can be calculated using the denition of tion (8). Then, replacing mj cj mj µ−1 µ and ϑ ui given in equa- by the expression given in equation (59) and dening ˆ j = Ξ̃c /Ξ̃j , κ̃ j Ξ̃j = we get 1 − uci ˆj = κ̃ 1 − ui pci − w̃j pi − w̃j 1−µ µ Pi Pic 1−µ µ . (61) Assuming that nominal minimum wages are indexed to prices, we can express it as share of prices, i.e. w̃j = ξj pj . Then the last expression simplies to 1 − uci ˆj = κ̃ 1 − ui pci pi 1−µ µ Pi Pic 1−µ µ , (62) which exactly corresponds to equation (20) besides the replacement of κ̂j by ˆj . κ̃ Hence, when assuming that labor market institutions do not change, we can proceed as with bargained wages to calculated employment eects. Note that in the case of binding minimum wages, all GDP changes are due to employment changes. Hence, counterfactual GDP changes correspond to employment changes. Counterfactual trade ows and welfare can be calculated as in the case with bargained wages. D Eciency wages within the search and matching framework In this appendix we show how eciency wages in the spirit of Stiglitz and Shapiro (1984) can be introduced in our search and matching framework. Basically, the no-shirking condition will replace the bargaining of workers and rms that are matched. We rst derive the asset value for a shirker earns wage wj with eort ej . ns and a non-shirker s. The non-shirker ns Hence, the asset value in our one-shoot framework is given by Ejns = wj − ej . A shirker s also earns wage wj (63) but does not show any eort ej . However, a share of dj of shirkers is detected by rms and gets red, which leads to unemployment. Noting that in unemployment the worker earns γ j wj , the asset value for a shirker can be written as Ejs = wj + d(Uj − Ejs ) ⇒ Ejs = The no shirking-condition E ns ≥ E s wj + dj γj wj . 1 + dj leads in equilibrium to E ns = E s . (64) Hence, using Equations (63) and (64), the wage can be written as: wj = 1 + dj ej . 1 − γj Hence, as in the case of bargaining, wages can be solved without knowledge of (65) ϑj . ϑj can be solved by using the job creation curve given in (9) 1 + dj Pj cj ej = pj − ⇒ 1 − γj mj ϑ−µ j mj 1 + dj µ ϑj = pj − ej . Pj cj 1 − γj 27 (66) Now assume that eort ej can be expressed in terms of prices pj as e j = ξj p j . Then we can simplify equation (66) to: ϑj = with Ω̃j = pj Pj 1/µ cj Ω̃j mj −1/µ , (67) 1−γj 1−γj −(1+dj )ξj , which corresponds to equation (13). GDP in country j uj can be derived by replacing using equations (8) and (67), and wj by using equation (65): 1 + dj ej mj yj = 1 − γj pj Pj 1−µ µ cj Ω̃j mj µ−1 µ Lj , (68) which corresponds to equation (14). Counterfactual employment can be calculated using the denition of tion (8), replacing and ui given in equa- ϑ by the expression given in equation (67) and dening Ξ̃j = mj cj mj Ω̃j µ−1 ˆ j = Ξc /Ξj κ̃ j 1 − uci ˆj = κ̃ 1 − ui pci pi 1−µ µ Pi Pic 1−µ µ . (69) which exactly corresponds to equation (20) besides the replacement of κ̂j by ˆj . κ̃ Hence, when assuming that labor market institutions do not change, we can proceed as with bargained wages to calculated employment eects. Counterfactual GDPs can be calculated by using again 1 + dj yj = ξj pj mj 1 − γj Dening Ξj = mj cj mj Ω̃j µ−1 µ pj Pj Now take the ratio of counterfactual GDP, parameters and constants, like yj where κ̂j = Ξcj /Ξj . µ cj Ω̃j mj which leads to: µ−1 µ Lj , (70) , we can write : 1 + dj yj = ξj p j 1 − γj yjc 1−µ ej = ξj pj , = κ̂j yjc ξj , γj , dj , Ξj pcj pj pj Pj 1−µ µ Ξj Lj , and observed GDP and Lj , pc 1−µ j µ Pjc pj Pj 1−µ = κ̂j µ (71) pcj pj yj , while noting that all stay constant: µ1 Pj Pjc ! 1−µ µ , (72) This exactly correspond to equation (23). Hence, we can calculated counterfactual GDP as in the case with bargained wages according to equation (24). Similarly, counterfactual trade ows and welfare can be calculated as in the case with bargained wages. 28 µ E A Ricardian gravity model with imperfect labor markets following Eaton and Kortum (2002) j The representative consumer in country is again characterized by the utility function As in Eaton and Kortum (2002) we assume a continuum of goods of individual goods is denoted by q(k), k ∈ [0, 1]. Uj . Consumption leading to the following utility function Z 1 σ−1 σ σ σ−1 , (73) is the elasticity of substitution in consumption. Again, international trade of Uj = q(k) dk 0 where σ i goods from j to imposes iceberg trade costs tij > 1 for all i 6= j , and tij = 1 for i = j. Countries dier in the eciency with which they can produce goods. We denote country i's k ∈ [0, 1] as zi (k). Denoting input costs in country i as ci , j in country i is then ci /zi (k). account, delivering a unit of good k produced in country i eciency in producing good the cost of producing a unit of good Taking trade barriers into to country j costs pij (k) = Assuming perfect competition, bought good k from country pij (k) i. ci zi (k) tij . (74) is what consumers in country where to buy. Hence, the price they actually pay for good all sources j would pay if they In an international economy, consumers can select from k is pj (k), the lowest price across i: pj (k) = min {pij (k); i = 1, · · · , N } , where n (75) denotes the number of countries. i's Let country k be the realization of an −Ti z −θ , where T distribution Fi (z) = e i eciency in producing good drawn Fréchet random variable with independently is the location parameter (also called state of technology by Eaton and Kortum (2002)) and θ governs the variation within the distribution and thereby also the comparative advantage within the continuum of goods. Fi (z) Plugging in Equation (74) in Noting that the distribution of prices for P r[Pj ≤ p] = 1 − Qn i=1 [1 − Gij (p)], −θ leads to: θ Gj (p) = 1 − e−Φj p , where Φj = θ Gij (p) = P r[Pij ≤ p] = 1 − e−[Ti (ci tij ) ]p . which a country j buys is given by Gj (p) = leads to (76) −θ i=1 Ti (ci tij ) . Pn The probability that country i provides good k at the lowest price to country j is given by (see Eaton and Kortum (2002), page 1748): πij = Ti (ci tij )−θ . Φj (77) With a continuum of goods between zero and one this is also the fraction of goods that country j buys from country that country j i. Eaton and Kortum (2002) show that the price of a good actually buys from any country exact price index is given by Pj = −1/θ γΦj , with function. 29 i is also distributed γ= Γ 1 1−σ θ+1−σ θ Gj (p), where and that the Γ is the Gamma j buys from country i, πij is also the fraction of its i (xij ) due to the fact that the average expenditures The fraction of goods that country expenditures on goods from country per good do not vary by source. Hence, Ti (ci tij )−θ Ti (ci tij )−θ yj = Pn y , −θ j Φj k=1 Tk (ck tkj ) xij = where yj is country j 's (78) total spending. Exporters total sales (including home sales) are equal to exports total spending and are simply given by: n X yi = xij = Ti c−θ i n X t−θ ij j=1 Solving for Ti c−θ i j=1 leads to: Ti c−θ i = Replacing Ti c−θ i yi t−θ ij j=1 Φj yj (79) . (80) Pn in Equation (78) with this expression leads to: xij = Φj − θ1 Pj = γΦj Using yj . Φj to replace Φj xij t−θ ij −θ Pn tij j=1 Φj yi yj . yj in both terms of the denominator leads to: t−θ ij −θ Pn = γ θ Pj yi yj . t−θ ij j=1 γ θ P −θ yj j Dening − 1 θ −θ n X tij Πi = θj , Pj j=1 and noting that we can express Pj = γ −θ Φj − 1 θ = γ Pj also as follows: −θ n X !− 1 θ −θ Ti (ci tij ) = γ −θ i=1 i=1 = n X tij −θ i=1 where θj = yj /y W Πi with −θ by θ , θ θi yW = 1−σ t−θ il l=1 Φl yl Pn − 1 !− 1 , P j yj . xij Replacing t−θ ij yi n X Then we can write: = yi yj yW tij Πi P j −θ . we end up with exactly the same system as in the AvW model. Hence, our approach can be applied to both worlds with the only dierence that the interpretation diers and the roles of θ and σ 30 have to be exchanged. E.1 Counterfactual GDP in the Eaton and Kortum (2002) framework with perfect labor markets Assuming that there are no intermediates and one unit of the nal good is produced with one unit of labor, ci = wi . Noting that yi Ti wi−θ = t−θ ij Pn j=1 Φj Solving for wi yi = wi Li = Pn yj j=1 γ θ θi and using again tij Pj −θ = γ −θ θi Πθi . θj leads to: 1 −1 wi = γTiθ θi θ Π−1 i . yic /yi = wic /wi , Noting that the change in GDP is given by yic yi where 1 1 γTiθ (θic )− θ (Πci )−1 = 1 θ −1 γTi θi θ Π−1 i leads to 1 = (θic )− θ (Πci )−1 −1 θi θ Π−1 i c − 1 θ , = i i i = θi Πθi . E.2 Counterfactual GDP in the Eaton and Kortum (2002) framework with imperfect labor markets We assume that there are no intermediates and with one unit of labor for the rm. zi units of the nal good k are produced For simplicity, we omit the product index following. Denoting the net price earned by the producer by k in the the total surplus zi pi − wi and the worker's by wi − bi . Nash bargaining leads to wi − bi = ξi (zi pi − wi ). Using bi = γi wi and combining leads to wi = ξi /(1 − γi + ξi )zi pi = ξi /(1 − γi + ξi )ci . of a successful match is given by zi pi − bi , pi = pij /tij , while the rm's rent is given by Firms create vacancies until all rents are dissipated. The free entry (zero prot) condition is given by Mi /Vi (zi pi − wi ) = Pi ci . wi = z i p i − Rewriting leads to the job creation curve Pi ci Pi ci . −µ = ci − m i ϑi mi ϑ−µ i (81) Using the job creation and wage curve, labor market thightness ϑi = Noting that yi = wi (1 − ui )Li ci 1/µ ci Ωi mi ca be expressed as: −1/µ . (82) and using again yi Ti c−θ = i Solving for ci Pi ϑ t−θ ij j=1 Φj yj = Pn Pn j=1 γθ θi tij Pj −θ = γ −θ θi Πθi . θj leads to: 1 −1 ci = γTiθ θi θ Π−1 i . c Noting that the change in GDP is given by yi /yi wi by yic yi ξi /(1 − γi + ξi )ci 1 (1 − uci )γTiθ (θic )− θ (Πci )−1 (1 − = (1 − − ui )wi ] and replacing leads to 1 = (83) uci )wic /[(1 1 θ −1 ui )γTi θi θ Π−1 i 1 = (1 − uci ) (θic )− θ (Πci )−1 −1 (1 − ui )θi θ Π−1 i 31 (1 − uci ) = (1 − ui ) c − 1 θ i , i where i = θi Πθi . For the change in employment exactly the same relationship as in the main text holds. Hence, we end up with − 1−µ µθ P 1 −θ t i ci − µθ yic i ij = κ̂i . P −θ yi i c c t i ij i 32 (84) 33 (.1,5] (.005,.1] (.0025,.005] (0,.0025] (-.0025,0] [-.01,-.0025] No data Figure 1: Employment eects of counterfactually incepting PTAs as observed in 2006. 34 (.07,2.98] (.04,.07] (.03,.04] (.01,.03] [0,.01] No data Figure 2: Employment eects of a hypothetical labor market reform in the US (κ̂U S = 1.03). 35 Figure 3: Employment eects of counterfactually abolishing the US-Canadian border. Table 1: Summary statistics Mean xij (cur. mn US$) GDP (cur. mn US$) PTA ln(DIST ) CON T IG COM LAN G Std. Dev. Min. Max. N 2,048.991 8,950.166 0 348,420.6 38,313 386,072.995 1,143,571.923 126.99 13,201,819 43,372 0.237 0.425 0 1 44,688 7.863 1.213 4.201 9.880 44,688 0.077 0.266 0 1 44,688 0.074 0.262 0 1 44,688 Notes : Summary statistics for the OECD sample from 1950 to 2006. The 28 countries included are Australia, Austria, Belgium, Canada, Switzerland, Czech Republic, Germany, Denmark, Spain, Finland, France, United Kingdom, Greece, Hungary, Ireland, Iceland, Italy, Japan, Korea, Netherlands, Norway, New Zealand, Poland, Portugal, Slovak Republic, Sweden, Turkey, and United States. Data are taken from Head et al. (2010) which can be downloaded from http://www.cepii.fr/anglaisgraph/bdd/gravity.htm. 36 37 tijτ tijτ 36,945 X 37,741 X X (0.010) (0.023) (0.857) 0.655*** (1.451) 0.663*** 22.734*** (0.019) 20.897*** 0.308*** (0.016) (0.049) 0.274*** 0.769*** (0.019) (0.030) 0.386*** 0.276*** (0.019) (0.027) (0.009) 0.097*** -0.669*** -1.050*** zijτ ln zijτ (3) 37,493 X (0.006) 0.657*** (0.428) 21.198*** (0.017) 0.267*** (0.019) 0.387*** (0.019) 0.116*** (0.010) -1.041*** ln xijτ OLS (4) 38,313 X X (0.021) 0.682*** (1.284) 18.100*** (0.019) 0.332*** (0.017) 0.150*** (0.018) 0.414*** (0.010) -0.816*** xijτ PPML (5) 36,945 X (0.006) 0.663*** (0.405) 20.899*** (0.014) 0.274*** (0.019) 0.386*** (0.019) 0.097*** (0.009) -1.050*** ln zijτ OLS (6) 37,741 X X (0.024) 0.655*** (1.670) 22.719*** (0.016) 0.311*** (0.049) 0.769*** (0.030) 0.275*** (0.027) -0.669*** zijτ PPML (7) 37,493 X (0.006) 0.653*** (0.405) 21.172*** (0.015) 0.276*** (0.019) 0.387*** (0.019) 0.115*** (0.010) -1.040*** ln xijτ OLS (8) 38,313 X X (0.021) 0.683*** (1.353) 18.028*** (0.013) 0.341*** (0.017) 0.151*** (0.018) 0.414*** (0.010) -0.813*** xijτ PPML Results for a gravity model of normalized trade ows between 28 OECD countries between 1950 and 2006 estimated by ordinary least squares (OLS) and Poisson pseudo-maximum-likelihood (PPML). zij are trade ows standardized by importer and exporter GDPs. ln DIST is distance between exporting and importing country, CON T IG is an indicator variable equal to 1 if the exporting and importing countries i and j share a common border, COM LAN G is an indicator variable equal to 1 if the exporting and importing country share a common ocial language, and P T A is an indicator variable equal to 1 if the exporting and importing country have signed a preferential trade agreement. All regressions control for multilateral resistance terms (MRTs) via exporter and importer xed eects. (Robust) standard errors in parentheses, *** p <0.01, ** p <0.05, * p <0.1. Standard errors for σ and µ are bootstrapped using 200 replications. Notes : N asymmetric symmetric zero trade µ σ Estimated elasticities P T Aijτ First stage COM LAN Gij CON T IGij ln DISTij Second stage (2) PPML (1) OLS Table 2: Estimation results for gravity model for the OECD sample, 1950-2006 Table 3: OECD sample, Comparative static eects of PTA inception in 2006 (1) (2) (3) (4) (5) (6) (7) (8) share %GDP SMF SMF SMF AvW SMF AvW SMF %GDP %GDP % ln(p̂) % ln(ê) %ê ∆u %EV %EV Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States 1.27 1.35 1.39 1.72 1.31 1.26 1.19 1.16 1.09 1.17 1.26 1.15 1.22 1.11 0.59 0.60 1.24 0.68 1.22 1.25 1.20 1.29 1.12 1.21 1.42 1.16 0.98 0.62 1.91 2.09 2.16 2.80 2.00 1.90 1.75 1.69 1.57 1.71 1.91 1.68 1.82 1.59 0.53 0.56 1.87 0.72 1.82 1.88 1.78 1.95 1.61 1.80 2.22 1.70 1.34 0.60 65.48 63.98 63.40 59.82 64.68 65.60 67.09 67.77 69.39 67.58 65.53 67.95 66.37 69.06 111.38 108.92 65.84 95.20 66.33 65.79 66.78 65.09 68.74 66.62 63.00 67.71 73.06 103.98 34.52 36.02 36.60 40.18 35.32 34.40 32.91 32.23 30.61 32.42 34.47 32.05 33.63 30.94 -11.38 -8.92 34.16 4.80 33.67 34.21 33.22 34.91 31.26 33.38 37.00 32.29 26.94 -3.98 0.66 0.75 0.79 1.12 0.70 0.65 0.57 0.54 0.48 0.55 0.65 0.53 0.61 0.49 -0.06 -0.05 0.64 0.03 0.61 0.64 0.59 0.68 0.50 0.60 0.82 0.55 0.36 -0.02 -0.62 -0.71 -0.72 -1.05 -0.65 -0.62 -0.53 -0.49 -0.43 -0.50 -0.60 -0.52 -0.58 -0.46 0.06 0.05 -0.61 -0.03 -0.59 -0.55 -0.54 -0.59 -0.46 -0.55 -0.78 -0.50 -0.34 0.02 1.27 1.43 1.51 2.18 1.35 1.24 1.10 1.03 0.91 1.05 1.25 1.03 1.17 0.93 -0.12 -0.10 1.22 0.06 1.17 1.22 1.13 1.30 0.96 1.14 1.57 1.04 0.68 -0.06 1.91 2.18 2.29 3.27 2.05 1.89 1.67 1.58 1.39 1.60 1.90 1.56 1.77 1.43 -0.18 -0.14 1.85 0.10 1.78 1.86 1.71 1.98 1.46 1.74 2.38 1.59 1.04 -0.07 Average 0.89 1.15 87.51 12.49 0.26 -0.24 0.49 0.76 Notes : Counterfactual analysis based on parameter estimates from column (6) of Table 2. AvW gives results assuming perfect labor markets. SMF are results for the gravity model using a search and matching framework for the labor market. 38 Table 4: Heterogeneity of comparative static eects in percent of PTA inception, OECD sample with perfect labor markets in 2006 Heterogeneity of goods trade changes in % Min. 2.50% 25% 50% 75% 97.5% Max. Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States -31.46 -32.65 -33.20 -33.63 -32.01 -31.24 -30.13 -29.65 -28.64 -29.79 -31.30 -29.59 -30.68 -28.85 -20.08 -20.27 -31.03 -21.63 -30.69 -31.09 -30.36 -31.66 -29.05 -30.46 -33.63 -29.72 -26.87 -15.13 -30.62 -31.42 -31.98 -33.55 -30.77 -29.98 -28.85 -28.36 -27.33 -28.51 -30.04 -28.30 -29.41 -27.55 -19.11 -19.20 -29.77 -20.68 -29.42 -29.83 -29.09 -30.41 -27.76 -29.19 -32.41 -28.43 -25.54 -15.03 -24.11 -1.54 -2.14 -31.28 -0.60 0.52 2.15 2.86 4.33 2.64 0.44 3.64 1.34 4.02 -11.69 -11.72 0.83 -13.23 2.03 0.75 1.81 -0.09 3.72 1.66 -1.46 3.45 6.91 -12.03 -23.09 2.15 1.31 -30.36 3.12 4.29 5.89 6.62 8.15 6.39 4.20 6.79 5.05 7.82 -10.46 -10.24 4.52 -12.07 5.13 4.52 5.54 3.66 7.52 5.38 1.17 6.60 10.82 -10.65 -21.48 4.06 3.21 -28.90 5.05 6.25 7.97 8.49 10.05 8.35 6.16 8.80 7.11 9.72 -8.82 -1.01 6.57 -10.23 7.21 6.48 7.61 5.60 9.41 7.45 2.67 8.68 12.77 -8.82 19.36 7.85 6.96 3.34 8.87 10.11 11.89 12.67 14.22 12.43 10.02 21.67 11.01 13.94 2.58 23.42 10.45 15.11 19.77 10.35 11.52 9.44 13.61 11.36 14.70 21.45 14.70 17.65 19.62 8.31 7.42 8.31 9.34 10.58 12.37 13.14 14.76 12.90 10.48 23.46 11.48 14.42 2.67 23.46 10.91 18.13 21.54 10.82 12.00 9.91 14.09 11.83 16.38 23.23 14.76 19.62 Average -29.09 -27.95 -2.39 0.71 2.87 12.87 13.78 Notes : Counterfactual analysis based on parameter estimates from column (6) of Table 2. 39 Table 5: Heterogeneity of comparative static eects in percent of PTA inception, OECD sample with imperfect labor markets in 2006 Heterogeneity of goods trade changes in % Min. 2.50% 25% 50% 75% 97.5% Max. Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States -31.28 -32.60 -33.17 -33.59 -31.96 -31.18 -30.05 -29.59 -28.59 -29.72 -31.24 -29.48 -30.58 -28.79 -19.84 -20.04 -30.98 -21.47 -30.61 -31.02 -30.28 -31.60 -28.98 -30.39 -33.59 -29.63 -26.77 -15.20 -30.48 -31.38 -31.96 -33.51 -30.73 -29.93 -28.79 -28.32 -27.30 -28.45 -29.99 -28.20 -29.32 -27.50 -18.91 -19.02 -29.73 -20.56 -29.35 -29.78 -29.02 -30.36 -27.69 -29.13 -32.38 -28.36 -25.44 -15.11 -24.11 -1.76 -2.38 -31.22 -0.82 0.32 1.96 2.62 4.08 2.44 0.23 3.50 1.20 3.80 -11.54 -11.70 0.60 -13.28 1.83 0.54 1.63 -0.30 3.53 1.46 -1.68 3.27 6.74 -12.08 -23.07 1.93 1.07 -30.28 2.91 4.09 5.72 6.42 7.93 6.23 4.00 6.66 4.93 7.63 -10.42 -10.20 4.32 -12.09 4.94 4.32 5.39 3.44 7.35 5.21 0.99 6.42 10.69 -10.69 -21.48 3.89 3.02 -28.84 4.89 6.09 7.82 8.30 9.84 8.21 6.00 8.71 7.02 9.54 -8.76 -0.88 6.39 -10.27 7.04 6.33 7.48 5.44 9.25 7.30 2.45 8.52 12.65 -8.89 19.50 7.68 6.78 3.57 8.72 9.96 11.76 12.49 14.03 12.29 9.86 21.75 10.92 13.78 2.81 23.53 10.27 15.26 19.80 10.21 11.40 9.28 13.48 11.21 14.66 21.49 14.53 17.80 19.76 8.16 7.24 8.54 9.19 10.44 12.25 12.98 14.59 12.78 10.35 23.57 11.41 14.27 2.91 23.57 10.75 18.27 21.59 10.69 11.89 9.76 13.97 11.70 16.37 23.30 14.59 19.76 Average -29.01 -27.88 -2.54 0.57 2.75 12.81 13.74 Notes : Counterfactual analysis based on parameter estimates from column (6) of Table 2. 40 Table 6: OECD sample, Comparative static eects of a 3% increase of (1) (2) (3) κ in US in 2006 (4) (5) (6) (7) (8) share %GDP SMF SMF SMF AvW SMF AvW SMF %GDP %GDP % ln(p̂) % ln(ê) %ê ∆u %EV %EV Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.05 0.04 0.16 0.05 0.05 0.06 0.05 0.05 0.06 0.05 0.07 0.06 0.05 0.05 0.06 0.05 0.10 0.06 0.05 0.06 0.05 0.06 0.06 0.04 0.06 0.07 2.94 64.21 92.16 97.90 58.87 88.14 86.68 82.17 89.08 88.99 83.22 85.50 74.23 78.21 85.90 84.40 83.34 90.60 67.18 82.30 85.81 80.60 86.12 82.50 83.89 98.41 81.20 74.89 -1.34 35.79 7.84 2.10 41.13 11.86 13.32 17.83 10.92 11.01 16.78 14.50 25.77 21.79 14.10 15.60 16.66 9.40 32.82 17.70 14.19 19.40 13.88 17.50 16.11 1.59 18.80 25.11 101.34 0.04 0.00 0.00 0.07 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.01 0.00 0.03 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.01 0.02 2.98 -0.04 0.00 0.00 -0.06 -0.01 -0.01 -0.01 0.00 0.00 -0.01 -0.01 -0.02 -0.01 -0.01 -0.01 -0.01 0.00 -0.03 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 0.00 -0.01 -0.02 -2.84 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.01 0.00 0.19 0.02 0.02 0.03 0.01 0.01 0.03 0.02 0.05 0.04 0.02 0.02 0.03 0.01 0.09 0.03 0.02 0.03 0.02 0.03 0.02 0.00 0.03 0.05 2.94 Average 0.00 1.12 51.79 48.21 1.11 -1.06 0.00 1.11 Notes : Counterfactual analysis based on parameter estimates from column (6) of Table 2. AvW gives results assuming perfect labor markets. SMF are results for the gravity model using a search and matching framework for the labor market. 41 Table 7: Heterogeneity of comparative static eects in percent of a 3% increase of OECD sample with imperfect labor markets in 2006 Heterogeneity of goods trade changes in % Min. 2.50% 25% 50% 75% 97.5% Max. Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States -1.43 -0.57 -0.50 -1.43 -0.62 -0.64 -0.72 -0.61 -0.61 -0.70 -0.66 -0.92 -0.81 -0.65 -0.68 -0.70 -0.58 -1.23 -0.72 -0.66 -0.75 -0.65 -0.71 -0.69 -0.50 -0.74 -0.90 -1.42 -1.32 -0.46 -0.40 -1.43 -0.51 -0.54 -0.62 -0.50 -0.50 -0.59 -0.55 -0.82 -0.70 -0.55 -0.57 -0.59 -0.48 -1.13 -0.61 -0.55 -0.65 -0.54 -0.61 -0.58 -0.39 -0.63 -0.80 -1.31 -0.15 0.69 0.75 -0.75 0.63 0.61 0.53 0.65 0.64 0.55 0.59 0.37 0.48 0.60 0.57 0.55 0.67 0.06 0.53 0.59 0.50 0.60 0.53 0.56 0.75 0.51 0.39 -0.13 -0.08 0.78 0.85 -0.69 0.73 0.71 0.64 0.74 0.74 0.66 0.69 0.43 0.55 0.69 0.67 0.66 0.76 0.12 0.64 0.69 0.60 0.70 0.64 0.66 0.85 0.62 0.45 -0.07 -0.02 0.84 0.90 -0.62 0.79 0.78 0.70 0.80 0.80 0.72 0.76 0.50 0.61 0.77 0.74 0.72 0.82 0.18 0.70 0.77 0.67 0.77 0.71 0.73 0.91 0.68 0.52 0.00 0.11 0.99 1.04 -0.50 0.93 0.91 0.83 0.95 0.94 0.85 0.89 0.62 0.74 0.90 0.87 0.85 0.97 0.31 0.83 0.90 0.80 0.90 0.84 0.86 1.04 0.81 0.64 0.12 0.11 0.99 1.05 -0.50 0.93 0.91 0.83 0.95 0.95 0.85 0.89 0.62 0.74 0.90 0.87 0.85 0.97 0.31 0.83 0.90 0.80 0.90 0.84 0.86 1.05 0.81 0.65 0.12 Average -0.78 -0.68 0.46 0.55 0.62 0.75 0.75 Notes : Counterfactual analysis based on parameter estimates from column (6) of Table 2. 42 κ in US, Table 8: Estimation results for gravity model of US-CAN trade in the Anderson and van Wincoop (2003) sample ln DIST BORDER (1) (2) (3) (6) OLS PPML PPML OLS PPML PPML zij zij ln zij zij zij -1.252*** -1.328*** -1.353*** -1.411*** -1.934*** -1.942*** (0.0368) (0.0420) (0.0430) (0.0292) (0.0418) (0.0409) -1.551*** -0.981*** -0.962*** -1.562*** -0.807*** -0.804*** (0.0589) (0.0823) (0.0835) (0.0603) (0.122) (0.121) X X zero trade N R2 ln L (5) ln zij internal trade MRTs (4) X X X X X X X X X 1511 1511 1560 1551 1551 1600 0.664 0.898 0.897 0.744 0.999 0.999 -1841 -0.002 -0.002 -1957 -0.014 -0.014 Notes : Results for a gravity model of normalized trade ows between 30 US states and 10 Canadian provinces in 1993 estimated by ordinary least squares (OLS) and Poisson pseudo-maximum-likelihood (PPML) on the sample used in Anderson and van Wincoop (2003). zij are trade ows standardized by importer and exporter GDPs. BORDER is an indicator variable equal to 1 if a trade ow between regions i and j crosses the US-CAN border. Intra-trade indicates whether inter-state/inter-provicincial trade is included. All regressions control for multilateral resistance terms (MRTs) via exporter and importer xed eects. (Robust) standard errors in parentheses, *** p <0.01, ** p <0.05, * p <0.1. 43 Table 9: US-CAN sample, Comparative static eects of erasing the US-CAN border ROW Alabama Arizona California Florida Georgia Idaho Illinois Indiana Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Missouri Montana New Hampshire New Jersey New York North Carolina North Dakota Ohio Pennsylvania Tennessee Texas Vermont Virginia Washington Wisconsin Alberta British Columbia Manitoba New Brunswick Newfoundland Nova Scotia Ontario Prince Edward Island Quebec Saskatchewan Total average US average CAN average Notes : (1) (2) (3) (4) (5) (6) (7) AvW SMF share %GDP SMF SMF AvW SMF %GDP %GDP % ln(p̂) % ln(ê) %ê %EV %EV 1.75 1.16 1.28 1.04 1.11 1.16 1.88 1.17 1.29 1.31 1.13 2.85 1.17 1.28 1.68 1.46 1.20 2.34 1.94 1.32 1.33 1.25 2.11 1.37 1.38 1.23 1.10 2.75 1.27 1.90 1.44 2.42 1.42 1.63 1.19 1.31 1.40 2.63 1.43 1.63 1.67 1.36 4.25 1.43 1.61 2.29 1.94 1.49 3.40 2.72 1.68 1.70 1.57 3.04 1.78 1.79 1.53 1.31 4.05 1.59 2.65 1.89 75.00 88.97 84.59 95.39 91.63 89.31 73.39 88.64 84.45 83.87 90.32 66.47 88.73 84.87 76.08 79.86 87.35 69.29 72.77 83.65 83.39 85.72 70.96 82.11 81.91 86.44 91.66 67.03 85.20 73.27 80.45 25.00 11.03 15.41 4.61 8.37 10.69 26.61 11.36 15.55 16.13 9.68 33.53 11.27 15.13 23.92 20.14 12.65 30.71 27.23 16.35 16.61 14.28 29.04 17.89 18.09 13.56 8.34 32.97 14.80 26.73 19.55 0.60 0.16 0.25 0.05 0.11 0.15 0.69 0.16 0.25 0.27 0.13 1.40 0.16 0.24 0.54 0.39 0.19 1.03 0.73 0.27 0.28 0.22 0.87 0.32 0.32 0.21 0.11 1.32 0.23 0.70 0.37 1.75 0.43 0.70 0.15 0.30 0.41 2.04 0.45 0.71 0.76 0.36 4.25 0.45 0.69 1.58 1.10 0.52 3.07 2.17 0.78 0.80 0.63 2.55 0.90 0.92 0.58 0.29 4.00 0.67 2.07 1.05 2.42 0.62 1.00 0.22 0.44 0.60 2.80 0.65 1.01 1.07 0.52 5.74 0.64 0.97 2.19 1.56 0.75 4.19 2.97 1.10 1.12 0.89 3.54 1.27 1.29 0.83 0.44 5.37 0.94 2.83 1.48 8.87 5.67 14.54 11.65 14.76 8.68 9.49 12.98 6.77 13.50 14.20 8.91 23.59 18.74 23.92 13.89 15.22 20.92 10.74 21.84 58.59 60.59 57.25 57.78 57.23 58.67 58.37 57.51 59.68 57.42 41.41 39.41 42.75 42.22 42.77 41.33 41.63 42.49 40.32 42.58 5.65 3.42 9.47 7.52 9.61 5.52 6.08 8.41 4.20 8.78 18.46 10.79 32.81 25.37 33.38 17.99 20.00 28.76 13.39 30.10 24.60 14.41 43.63 33.65 44.34 23.98 26.61 38.11 17.88 40.00 1.86 1.28 8.72 2.58 1.60 13.95 82.93 86.49 58.88 17.07 13.51 41.12 0.66 0.24 5.54 2.05 0.68 18.18 2.79 0.96 24.21 Counterfactual analysis based on parameter estimates from column (1) of Table 8. We set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5. AvW gives results for the Anderson and van Wincoop (2003) estimates assuming perfect labor markets. SMF are results for the gravity model using a search and matching framework for the labor market. 44 Table 10: Heterogeneity of comparative static eects in percent of erasing the US-CAN border, US-CAN sample with perfect labor markets Heterogeneity of goods trade changes in % Min. 2.50% 25% 50% 75% 97.5% Max. ROW Alabama Arizona California Florida Georgia Idaho Illinois Indiana Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Missouri Montana New Hampshire New Jersey New York North Carolina North Dakota Ohio Pennsylvania Tennessee Texas Vermont Virginia Washington Wisconsin -11.51 -8.90 -9.43 -8.33 -8.63 -8.86 -12.07 -8.93 -9.46 -9.55 -8.75 -15.69 -8.93 -9.42 -11.17 -10.24 -9.07 -14.00 -12.31 -9.60 -9.64 -9.29 -13.03 -9.84 -9.88 -9.19 -8.62 -15.69 -9.37 -12.12 -10.13 -11.27 -8.65 -9.19 -8.09 -8.39 -8.62 -11.83 -8.68 -9.22 -9.31 -8.51 -14.85 -8.69 -9.17 -10.93 -9.99 -8.83 -13.77 -12.08 -9.35 -9.40 -9.05 -12.79 -9.60 -9.64 -8.95 -8.38 -14.62 -9.13 -11.88 -9.89 -5.04 -2.42 -3.00 -1.82 -2.14 -2.39 -5.63 -2.46 -3.03 -3.13 -2.27 -10.01 -2.46 -2.98 -4.67 -3.67 -2.61 -7.71 -5.89 -3.17 -3.22 -2.85 -6.66 -3.43 -3.48 -2.74 -2.13 -9.52 -2.93 -5.69 -3.61 -4.23 -1.50 -1.98 -0.89 -1.21 -1.46 -4.83 -1.53 -2.02 -2.11 -1.34 -9.24 -1.54 -1.96 -3.86 -2.85 -1.68 -6.92 -5.10 -2.16 -2.20 -1.87 -5.87 -2.42 -2.47 -1.82 -1.20 -8.76 -1.91 -4.89 -2.74 68.98 73.97 72.95 74.89 74.48 74.04 67.92 73.91 72.89 72.72 74.25 60.14 73.90 72.98 69.63 71.42 73.64 64.23 67.46 72.64 72.56 73.21 66.09 72.17 72.10 73.41 74.50 61.00 73.07 67.82 71.61 255.21 265.70 263.54 267.97 266.76 265.84 252.98 265.57 263.42 263.06 266.28 236.62 265.55 263.62 256.58 260.33 265.00 245.22 252.00 262.89 262.73 264.10 249.13 261.92 261.75 264.52 266.80 238.42 263.81 252.77 260.74 264.38 275.14 272.93 277.47 276.22 275.28 262.09 275.01 272.80 272.44 275.74 245.31 274.99 273.00 265.78 269.63 274.43 254.13 261.09 272.26 272.09 273.50 258.14 271.26 271.09 273.93 276.27 247.15 273.20 261.88 270.05 Alberta British Columbia Manitoba New Brunswick Newfoundland Nova Scotia Ontario Prince Edward Island Quebec Saskatchewan -63.50 -57.64 -71.68 -67.82 -71.68 -63.17 -64.53 -69.67 -59.77 -70.36 -63.32 -57.43 -70.88 -67.66 -71.02 -63.00 -64.36 -69.52 -59.58 -70.21 198.33 246.23 131.42 163.03 129.22 200.97 189.91 147.89 228.80 142.27 219.30 270.57 147.69 181.53 145.33 222.13 210.30 165.32 251.92 159.30 222.01 273.71 149.79 183.91 147.42 224.86 212.93 167.57 254.91 161.50 224.73 276.87 151.90 186.31 149.50 227.61 215.57 169.83 257.90 163.71 225.24 277.47 152.30 186.76 149.90 228.13 216.07 170.26 258.47 164.13 Total average US average CAN average -23.94 -10.34 -65.98 -23.65 -10.05 -65.70 40.37 -3.92 177.81 45.83 -3.01 197.34 102.52 71.19 199.86 245.73 259.85 202.39 252.86 269.14 202.87 Notes : Counterfactual analysis based on parameter estimates from column (1) of Table 8. We set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5. 45 Table 11: Heterogeneity of comparative static eects in percent of erasing the US-CAN border, US-CAN sample with imperfect labor markets Heterogeneity of goods trade changes in % Min. 2.50% 25% 50% 75% 97.5% Max. ROW Alabama Arizona California Florida Georgia Idaho Illinois Indiana Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Missouri Montana New Hampshire New Jersey New York North Carolina North Dakota Ohio Pennsylvania Tennessee Texas Vermont Virginia Washington Wisconsin -11.91 -9.10 -9.70 -8.44 -8.80 -9.06 -12.50 -9.14 -9.72 -9.82 -8.94 -16.25 -9.13 -9.66 -11.56 -10.58 -9.30 -14.55 -12.75 -9.85 -9.90 -9.53 -13.59 -10.12 -10.16 -9.43 -8.80 -16.25 -9.61 -12.54 -10.45 -11.63 -8.81 -9.42 -8.16 -8.52 -8.77 -12.22 -8.85 -9.44 -9.54 -8.66 -15.40 -8.84 -9.37 -11.29 -10.30 -9.02 -14.29 -12.47 -9.57 -9.62 -9.25 -13.33 -9.85 -9.88 -9.14 -8.51 -15.14 -9.32 -12.27 -10.18 -5.07 -2.27 -2.92 -1.57 -1.95 -2.23 -5.70 -2.31 -2.94 -3.04 -2.10 -10.31 -2.30 -2.87 -4.69 -3.64 -2.49 -7.92 -5.97 -3.08 -3.13 -2.73 -6.89 -3.37 -3.41 -2.62 -1.95 -9.75 -2.82 -5.75 -3.57 -4.19 -1.23 -1.79 -0.52 -0.91 -1.19 -4.83 -1.27 -1.81 -1.91 -1.06 -9.48 -1.26 -1.74 -3.81 -2.75 -1.45 -7.07 -5.10 -1.95 -2.00 -1.64 -6.02 -2.25 -2.29 -1.59 -0.90 -8.91 -1.69 -4.88 -2.61 67.86 73.21 72.07 74.27 73.78 73.29 66.74 73.14 72.02 71.84 73.51 58.60 73.16 72.15 68.52 70.39 72.83 62.82 66.26 71.78 71.69 72.39 64.64 71.26 71.19 72.59 73.79 59.58 72.25 66.65 70.63 251.64 262.86 260.46 265.46 264.05 263.02 249.29 262.70 260.36 259.99 263.48 232.23 262.75 260.63 253.03 256.93 262.05 241.08 248.30 259.84 259.67 261.14 244.91 258.76 258.61 261.55 264.06 234.30 260.83 249.11 257.44 260.99 272.51 270.04 275.18 273.73 272.68 258.58 272.35 269.95 269.56 273.15 241.07 272.39 270.22 262.41 266.42 271.67 250.15 257.56 269.41 269.23 270.74 254.08 268.30 268.15 271.16 273.74 243.19 270.42 258.40 266.95 Alberta British Columbia Manitoba New Brunswick Newfoundland Nova Scotia Ontario Prince Edward Island Quebec Saskatchewan -64.25 -58.39 -72.23 -68.44 -72.23 -63.93 -65.25 -70.23 -60.55 -70.94 -64.09 -58.21 -71.46 -68.30 -71.58 -63.77 -65.10 -70.10 -60.37 -70.81 193.96 242.13 128.31 159.51 126.34 196.56 185.70 144.79 224.40 138.96 215.80 267.55 145.28 178.79 143.15 218.59 206.92 162.98 248.50 156.72 218.73 270.95 147.55 181.38 145.41 221.54 209.77 165.42 251.73 159.10 221.74 274.46 149.89 184.04 147.73 224.59 212.70 167.93 255.06 161.55 222.36 275.18 150.37 184.59 148.20 225.21 213.30 168.45 255.75 162.05 Total average US average CAN average -24.33 -10.64 -66.64 -24.02 -10.31 -66.38 39.50 -3.88 174.07 45.22 -2.86 194.43 101.13 70.23 197.16 242.69 256.63 199.97 250.00 266.11 200.55 Notes : Counterfactual analysis based on parameter estimates from column (1) of Table 8. We set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5. 46 Table 12: OECD sample, Comparative static eects of PTA inception controlling for trade imbalances in 2006 (1) (2) (3) (4) (5) (6) (7) (8) share %GDP SMF SMF SMF AvW SMF AvW SMF %GDP %GDP % ln(p̂) % ln(ê) %ê ∆u %EV %EV Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States 1.43 1.48 1.53 1.91 1.44 1.38 1.30 1.27 1.22 1.27 1.39 1.27 1.35 1.22 0.65 0.66 1.39 0.75 1.36 1.37 1.32 1.42 1.22 1.33 1.56 1.27 1.07 0.69 2.09 2.24 2.33 3.03 2.15 2.04 1.89 1.82 1.71 1.83 2.05 1.81 1.98 1.72 0.59 0.61 2.05 0.79 1.98 2.02 1.92 2.11 1.73 1.93 2.39 1.83 1.43 0.67 67.09 65.41 64.86 61.52 66.07 66.98 68.40 69.05 70.64 68.86 66.88 69.23 67.64 70.27 110.65 108.36 67.25 95.38 67.66 67.15 68.07 66.45 69.97 67.95 64.44 68.99 74.24 103.70 32.91 34.59 35.14 38.48 33.93 33.02 31.60 30.95 29.36 31.14 33.12 30.77 32.36 29.73 -10.65 -8.36 32.75 4.62 32.34 32.85 31.93 33.55 30.03 32.05 35.56 31.01 25.76 -3.70 0.68 0.77 0.81 1.16 0.73 0.67 0.59 0.56 0.50 0.57 0.68 0.55 0.64 0.51 -0.06 -0.05 0.67 0.04 0.64 0.66 0.61 0.70 0.52 0.62 0.84 0.56 0.37 -0.02 -0.65 -0.73 -0.75 -1.08 -0.67 -0.64 -0.55 -0.51 -0.45 -0.52 -0.63 -0.54 -0.61 -0.47 0.06 0.05 -0.64 -0.03 -0.62 -0.57 -0.56 -0.61 -0.47 -0.57 -0.81 -0.51 -0.35 0.02 1.43 1.59 1.68 2.44 1.50 1.38 1.22 1.15 1.02 1.16 1.39 1.14 1.31 1.04 -0.13 -0.11 1.37 0.07 1.31 1.36 1.25 1.45 1.06 1.27 1.74 1.16 0.75 -0.06 2.09 2.35 2.49 3.56 2.22 2.05 1.81 1.71 1.52 1.73 2.07 1.69 1.94 1.56 -0.19 -0.15 2.04 0.11 1.95 2.01 1.86 2.15 1.58 1.88 2.58 1.72 1.12 -0.08 Average 0.98 1.25 87.94 12.06 0.27 -0.25 0.55 0.82 Notes : AvW gives results assuming perfect labor markets. SMF are results for the gravity model using a search and matching framework for the labor market. 47 Table 13: Heterogeneity of comparative static eects in percent of PTA inception, OECD sample with perfect labor markets and controlling for trade imbalances in 2006 Heterogeneity of goods trade changes in % Min. 2.50% 25% 50% 75% 97.5% Max. Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States -31.65 -32.41 -33.05 -33.89 -31.82 -31.04 -29.90 -29.38 -28.65 -29.46 -31.13 -29.37 -30.63 -28.70 -19.90 -20.09 -31.14 -21.60 -30.67 -30.84 -30.14 -31.48 -28.74 -30.27 -33.43 -29.48 -26.50 -15.26 -30.85 -31.17 -31.82 -33.81 -30.57 -29.78 -28.62 -28.09 -27.34 -28.16 -29.86 -28.08 -29.35 -27.40 -18.97 -19.06 -29.88 -20.69 -29.39 -29.57 -28.86 -30.22 -27.44 -28.99 -32.21 -28.19 -25.15 -15.15 -24.52 -1.42 -2.15 -31.52 -0.57 0.57 2.24 2.99 4.06 2.89 0.45 3.75 1.18 3.98 -11.56 -11.71 0.44 -13.43 1.85 0.87 1.88 -0.06 3.93 1.71 -1.40 3.59 7.21 -12.15 -23.53 2.33 1.36 -30.66 3.21 4.39 5.96 6.75 7.86 6.64 4.27 6.92 4.87 7.77 -10.49 -10.28 4.10 -12.29 4.97 4.70 5.60 3.73 7.72 5.41 1.13 6.76 11.11 -10.80 -21.93 4.14 3.15 -29.22 5.04 6.24 8.00 8.58 9.71 8.56 6.11 8.81 6.88 9.62 -8.90 -0.90 6.09 -10.46 6.95 6.55 7.63 5.57 9.57 7.44 2.68 8.74 13.02 -8.94 18.94 7.94 6.92 3.10 8.88 10.12 11.94 12.77 13.87 12.66 9.99 21.79 10.79 13.86 2.64 23.35 9.97 15.16 19.56 10.45 11.56 9.43 13.80 11.36 14.79 21.61 15.03 17.80 19.20 8.39 7.36 8.08 9.33 10.58 12.41 13.24 14.42 13.12 10.45 23.60 11.25 14.33 2.70 23.39 10.43 18.22 21.34 10.90 12.02 9.88 14.27 11.82 16.50 23.41 15.11 19.79 Average -28.95 -27.81 -2.39 0.70 2.81 12.86 13.77 Notes : Counterfactual analysis based on parameter estimates from column (6) of Table 2. 48 Table 14: Heterogeneity of comparative static eects in percent of PTA inception, OECD sample with imperfect labor markets and controlling for trade imbalances in 2006 Heterogeneity of goods trade changes in % Min. 2.50% 25% 50% 75% 97.5% Max. Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States -31.46 -32.36 -33.01 -33.85 -31.77 -30.98 -29.83 -29.34 -28.61 -29.39 -31.07 -29.26 -30.52 -28.65 -19.66 -19.86 -31.09 -21.43 -30.59 -30.78 -30.06 -31.43 -28.67 -30.20 -33.40 -29.40 -26.39 -15.33 -30.70 -31.13 -31.80 -33.77 -30.53 -29.73 -28.56 -28.05 -27.31 -28.10 -29.82 -27.98 -29.26 -27.35 -18.77 -18.87 -29.84 -20.56 -29.33 -29.52 -28.79 -30.18 -27.37 -28.93 -32.19 -28.11 -25.05 -15.23 -24.52 -1.65 -2.39 -31.42 -0.79 0.36 2.03 2.75 3.81 2.68 0.23 3.60 1.03 3.75 -11.53 -11.64 0.20 -13.47 1.65 0.66 1.69 -0.29 3.72 1.50 -1.62 3.40 7.04 -12.20 -23.51 2.10 1.11 -30.58 2.99 4.18 5.79 6.53 7.63 6.46 4.05 6.78 4.75 7.57 -10.45 -10.25 3.89 -12.32 4.78 4.49 5.44 3.51 7.54 5.23 0.98 6.57 10.98 -10.84 -21.93 3.96 2.95 -29.15 4.87 6.08 7.85 8.38 9.49 8.41 5.95 8.72 6.79 9.44 -8.84 -0.77 5.91 -10.51 6.77 6.39 7.49 5.40 9.40 7.28 2.45 8.56 12.90 -9.01 19.09 7.77 6.73 3.34 8.71 9.97 11.80 12.59 13.68 12.51 9.83 21.88 10.70 13.69 2.87 23.45 9.79 15.31 19.59 10.29 11.43 9.26 13.66 11.21 14.75 21.65 14.86 17.96 19.34 8.23 7.18 8.31 9.17 10.44 12.28 13.07 14.23 12.99 10.30 23.72 11.18 14.17 2.95 23.50 10.26 18.36 21.40 10.76 11.90 9.72 14.14 11.69 16.49 23.49 14.93 19.93 Average -28.87 -27.74 -2.55 0.55 2.69 12.80 13.72 Notes : Counterfactual analysis based on parameter estimates from column (6) of Table 2. 49 Table 15: OECD sample, Comparative static eects of a 3% increase of κ in US controlling for trade imbalances in 2006 (1) (2) (3) (4) (5) (6) (7) (8) share %GDP SMF SMF SMF AvW SMF AvW SMF %GDP %GDP % ln(p̂) % ln(ê) %ê ∆u %EV %EV Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.05 0.04 0.17 0.05 0.06 0.06 0.05 0.05 0.06 0.06 0.08 0.07 0.06 0.06 0.06 0.05 0.11 0.06 0.06 0.06 0.06 0.06 0.06 0.04 0.06 0.08 2.93 65.60 92.82 98.49 60.29 88.91 87.44 83.07 89.86 89.76 84.20 86.36 75.36 79.34 86.78 85.34 84.32 91.30 68.48 83.18 86.62 81.63 86.97 83.48 84.73 99.08 82.19 75.97 -1.46 34.40 7.18 1.51 39.71 11.09 12.56 16.93 10.14 10.24 15.80 13.64 24.64 20.66 13.22 14.66 15.68 8.70 31.52 16.82 13.38 18.37 13.03 16.52 15.27 0.92 17.81 24.03 101.46 0.04 0.00 0.00 0.07 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.01 0.00 0.03 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.01 0.02 2.98 -0.04 0.00 0.00 -0.07 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.02 -0.01 -0.01 -0.01 -0.01 0.00 -0.03 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 0.00 -0.01 -0.02 -2.84 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.01 0.00 0.20 0.02 0.02 0.03 0.02 0.02 0.03 0.02 0.06 0.04 0.02 0.02 0.03 0.01 0.10 0.03 0.02 0.03 0.02 0.03 0.03 0.00 0.03 0.05 2.93 Average 0.00 1.13 52.33 47.67 1.11 -1.06 0.00 1.11 Notes : Counterfactual analysis based on parameter estimates from column (6) of Table 2. AvW gives results assuming perfect labor markets. SMF are results for the gravity model using a search and matching framework for the labor market. 50 Table 16: Heterogeneity of comparative static eects in percent of a 3% increase of κ in US controlling for trade imbalances, OECD sample with imperfect labor markets in 2006 Heterogeneity of goods trade changes in % Min. 2.50% 25% 50% 75% 97.5% Max. Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States -1.42 -0.54 -0.47 -1.41 -0.59 -0.62 -0.70 -0.58 -0.58 -0.67 -0.63 -0.91 -0.78 -0.62 -0.67 -0.69 -0.56 -1.22 -0.70 -0.63 -0.72 -0.62 -0.68 -0.67 -0.46 -0.71 -0.89 -1.41 -1.31 -0.43 -0.37 -1.41 -0.49 -0.51 -0.60 -0.47 -0.47 -0.57 -0.53 -0.80 -0.68 -0.52 -0.56 -0.58 -0.45 -1.11 -0.59 -0.52 -0.62 -0.52 -0.58 -0.56 -0.36 -0.61 -0.78 -1.31 -0.15 0.70 0.77 -0.74 0.65 0.62 0.54 0.66 0.66 0.57 0.60 0.37 0.49 0.61 0.57 0.55 0.68 0.05 0.54 0.61 0.52 0.62 0.55 0.57 0.78 0.52 0.39 -0.14 -0.09 0.81 0.87 -0.68 0.75 0.73 0.64 0.77 0.76 0.67 0.71 0.43 0.56 0.72 0.67 0.66 0.79 0.12 0.64 0.71 0.62 0.72 0.66 0.67 0.88 0.63 0.45 -0.08 -0.03 0.85 0.92 -0.62 0.80 0.78 0.70 0.81 0.81 0.73 0.77 0.50 0.62 0.78 0.74 0.72 0.83 0.18 0.71 0.77 0.68 0.78 0.72 0.74 0.93 0.69 0.52 -0.02 0.10 0.99 1.05 -0.50 0.93 0.91 0.82 0.95 0.95 0.85 0.89 0.62 0.74 0.90 0.86 0.84 0.97 0.30 0.83 0.90 0.80 0.90 0.84 0.86 1.05 0.81 0.64 0.10 0.10 0.99 1.06 -0.50 0.94 0.91 0.82 0.95 0.95 0.86 0.89 0.62 0.74 0.90 0.86 0.84 0.97 0.30 0.83 0.90 0.80 0.90 0.84 0.86 1.06 0.81 0.64 0.10 Average -0.76 -0.65 0.47 0.56 0.62 0.75 0.75 Notes : Counterfactual analysis based on parameter estimates from column (6) of Table 2. 51 Table 17: US-CAN sample, Comparative static eects of erasing the US-CAN border controlling for trade imbalances (1) (2) AvW SMF %GDP %GDP % ln(p̂) 1.74 1.15 1.26 1.08 1.05 1.15 1.86 1.20 1.32 1.34 1.11 2.81 1.18 1.18 1.60 1.46 1.21 2.26 1.83 1.36 1.18 1.28 2.11 1.40 1.38 1.25 1.07 2.58 1.24 1.57 1.45 2.39 1.40 1.60 1.25 1.25 1.40 2.60 1.46 1.67 1.70 1.34 4.19 1.43 1.51 2.20 1.94 1.49 3.30 2.60 1.73 1.54 1.59 3.04 1.81 1.79 1.55 1.28 3.86 1.56 2.31 1.91 Alberta British Columbia Manitoba New Brunswick Newfoundland Nova Scotia Ontario Prince Edward Island Quebec Saskatchewan 12.16 5.33 15.57 13.48 15.48 10.10 12.69 14.18 9.99 15.40 Total average US average CAN average 2.02 1.25 11.25 ROW Alabama Arizona California Florida Georgia Idaho Illinois Indiana Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Missouri Montana New Hampshire New Jersey New York North Carolina North Dakota Ohio Pennsylvania Tennessee Texas Vermont Virginia Washington Wisconsin Notes : (3) (4) (5) (6) (7) share %GDP SMF SMF AvW SMF % ln(ê) %ê %EV %EV 75.00 88.84 84.57 95.52 91.36 89.26 73.43 88.82 84.72 84.11 90.18 66.12 88.82 83.93 75.77 79.98 87.46 69.08 71.80 84.06 81.92 85.90 71.11 82.47 82.07 86.53 91.48 66.05 85.15 69.94 80.62 25.00 11.16 15.43 4.48 8.64 10.74 26.57 11.18 15.28 15.89 9.82 33.88 11.18 16.07 24.23 20.02 12.54 30.92 28.20 15.94 18.08 14.10 28.89 17.53 17.93 13.47 8.52 33.95 14.85 30.06 19.38 0.60 0.16 0.25 0.06 0.11 0.15 0.69 0.16 0.26 0.27 0.13 1.41 0.16 0.24 0.53 0.39 0.19 1.01 0.73 0.28 0.28 0.23 0.87 0.32 0.32 0.21 0.11 1.30 0.23 0.69 0.37 1.75 0.43 0.69 0.15 0.30 0.42 2.03 0.45 0.72 0.77 0.36 4.25 0.45 0.69 1.54 1.10 0.52 3.01 2.16 0.79 0.80 0.64 2.55 0.90 0.92 0.59 0.30 3.94 0.66 2.05 1.05 2.41 0.63 1.00 0.23 0.44 0.60 2.78 0.66 1.03 1.09 0.53 5.75 0.64 0.98 2.14 1.56 0.75 4.11 2.96 1.11 1.12 0.90 3.54 1.27 1.29 0.84 0.44 5.30 0.93 2.81 1.49 17.66 8.56 24.60 20.59 24.52 15.32 18.57 22.04 14.04 23.85 65.99 59.14 59.33 61.84 59.06 62.82 65.39 60.41 68.86 60.82 34.01 40.86 40.67 38.16 40.94 37.18 34.61 39.59 31.14 39.18 5.69 3.42 9.37 7.41 9.40 5.45 6.08 8.21 4.18 8.75 18.61 10.78 32.38 24.96 32.56 17.73 20.00 28.01 13.33 29.99 24.79 14.39 43.06 33.10 43.25 23.63 26.62 37.12 17.81 39.86 2.74 1.58 16.58 83.17 86.27 64.82 16.83 13.73 35.18 0.66 0.24 5.53 2.05 0.68 18.14 2.78 0.96 24.15 Counterfactual analysis based on parameter estimates from column (1) of Table 8. We set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5. AvW gives results for the Anderson and van Wincoop (2003) estimates assuming perfect labor markets. SMF are results for the gravity model using a search and matching framework for the labor market. 52 Table 18: Heterogeneity of comparative static eects in percent of erasing the US-CAN border, US-CAN sample with perfect labor markets and controlling for trade imbalances Heterogeneity of goods trade changes in % Min. 2.50% 25% 50% 75% 97.5% Max. ROW Alabama Arizona California Florida Georgia Idaho Illinois Indiana Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Missouri Montana New Hampshire New Jersey New York North Carolina North Dakota Ohio Pennsylvania Tennessee Texas Vermont Virginia Washington Wisconsin -11.48 -8.86 -9.38 -8.57 -8.44 -8.88 -12.00 -9.09 -9.66 -9.73 -8.69 -15.71 -9.00 -9.02 -10.88 -10.29 -9.14 -13.71 -11.88 -9.84 -9.01 -9.45 -13.09 -10.02 -9.93 -9.33 -8.54 -15.07 -9.29 -10.76 -10.23 -11.33 -8.70 -9.23 -8.42 -8.28 -8.73 -11.85 -8.94 -9.51 -9.58 -8.54 -14.72 -8.85 -8.87 -10.73 -10.13 -8.99 -13.57 -11.73 -9.68 -8.86 -9.30 -12.94 -9.86 -9.78 -9.17 -8.38 -13.93 -9.14 -10.61 -10.08 -4.94 -2.20 -2.76 -1.89 -1.74 -2.22 -5.50 -2.44 -3.06 -3.13 -2.02 -9.79 -2.35 -2.37 -4.30 -3.66 -2.50 -7.34 -5.37 -3.24 -2.33 -2.83 -6.67 -3.44 -3.35 -2.70 -1.85 -8.79 -2.66 -4.17 -3.67 -3.95 -1.23 -1.68 -0.92 -0.77 -1.25 -4.52 -1.48 -1.98 -2.06 -1.05 -8.85 -1.38 -1.29 -3.30 -2.66 -1.53 -6.37 -4.38 -2.17 -1.27 -1.82 -5.70 -2.36 -2.27 -1.73 -0.88 -7.84 -1.58 -3.17 -2.60 75.60 80.80 79.76 81.07 81.64 80.76 74.56 80.35 79.21 79.07 81.13 66.65 80.52 80.48 76.79 77.97 80.24 71.18 74.81 78.86 80.50 79.63 72.41 78.51 78.68 79.87 81.44 68.49 79.94 77.03 78.08 276.00 287.14 284.91 288.35 288.93 287.04 273.78 286.16 283.72 283.43 287.84 256.83 286.54 286.44 278.54 281.08 285.95 266.53 274.31 282.99 286.49 284.63 269.18 282.23 282.59 285.15 288.51 260.77 285.30 279.06 281.31 291.37 302.97 300.65 304.23 304.84 302.87 289.07 301.95 299.41 299.11 303.70 271.42 302.34 302.25 294.02 296.66 301.73 281.52 289.62 298.65 302.30 300.36 284.28 297.86 298.23 300.90 304.40 275.52 301.06 294.56 296.90 Alberta British Columbia Manitoba New Brunswick Newfoundland Nova Scotia Ontario Prince Edward Island Quebec Saskatchewan -66.90 -54.68 -71.51 -68.78 -71.14 -63.69 -67.68 -69.72 -63.50 -71.29 -66.75 -54.48 -70.39 -68.64 -70.14 -63.53 -67.54 -69.59 -63.34 -71.17 156.67 251.41 120.95 142.08 121.84 181.54 150.65 134.78 183.04 122.61 175.16 276.72 136.86 159.52 137.83 201.82 168.70 151.69 203.43 138.64 178.03 280.65 139.33 162.23 140.31 204.97 171.50 154.32 206.59 141.13 180.28 283.73 141.27 164.35 142.25 207.43 173.70 156.37 209.07 143.08 181.11 284.87 141.99 165.14 142.97 208.35 174.52 157.14 210.00 143.81 Total average US average CAN average -24.09 -10.25 -66.89 -23.85 -10.04 -66.56 35.37 -3.68 156.56 40.64 -2.67 175.04 102.32 78.01 177.91 256.42 281.19 180.15 268.41 296.78 180.99 Notes : Counterfactual analysis based on parameter estimates from column (1) of Table 8. We set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5. 53 Table 19: Heterogeneity of comparative static eects in percent of erasing the US-CAN border, US-CAN sample with imperfect labor markets and controlling for trade imbalances Heterogeneity of goods trade changes in % Min. 2.50% 25% 50% 75% 97.5% Max. ROW Alabama Arizona California Florida Georgia Idaho Illinois Indiana Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Missouri Montana New Hampshire New Jersey New York North Carolina North Dakota Ohio Pennsylvania Tennessee Texas Vermont Virginia Washington Wisconsin -11.90 -9.09 -9.68 -8.79 -8.62 -9.11 -12.46 -9.34 -9.96 -10.03 -8.91 -16.27 -9.22 -9.27 -11.28 -10.66 -9.40 -14.27 -12.31 -10.13 -9.27 -9.72 -13.68 -10.33 -10.23 -9.60 -8.74 -15.62 -9.55 -11.21 -10.58 -11.71 -8.89 -9.49 -8.59 -8.43 -8.92 -12.27 -9.15 -9.77 -9.84 -8.72 -15.27 -9.03 -9.08 -11.09 -10.47 -9.21 -14.09 -12.13 -9.94 -9.07 -9.53 -13.49 -10.14 -10.04 -9.41 -8.54 -14.43 -9.36 -11.02 -10.39 -4.97 -2.02 -2.66 -1.70 -1.52 -2.04 -5.58 -2.29 -2.96 -3.04 -1.83 -10.06 -2.17 -2.22 -4.30 -3.63 -2.36 -7.53 -5.42 -3.14 -2.21 -2.70 -6.89 -3.36 -3.26 -2.57 -1.64 -8.98 -2.52 -4.23 -3.63 -3.90 -0.97 -1.48 -0.64 -0.46 -0.99 -4.51 -1.24 -1.79 -1.86 -0.77 -9.05 -1.12 -1.04 -3.22 -2.55 -1.31 -6.49 -4.35 -1.97 -1.03 -1.61 -5.84 -2.19 -2.09 -1.52 -0.59 -7.96 -1.34 -3.15 -2.46 74.48 80.05 78.87 80.27 80.97 80.00 73.36 79.55 78.32 78.18 80.40 65.13 79.77 79.68 75.70 76.93 79.42 69.77 73.66 77.98 79.69 78.79 70.96 77.58 77.77 79.03 80.74 67.11 79.13 75.84 77.08 272.18 284.06 281.56 285.33 286.03 283.97 269.81 282.99 280.37 280.07 284.81 252.24 283.47 283.27 274.80 277.42 282.72 262.14 270.43 279.66 283.30 281.39 264.67 278.80 279.21 281.90 285.54 256.46 282.10 275.09 277.74 286.96 299.31 296.72 300.63 301.37 299.22 284.50 298.21 295.48 295.17 300.10 266.23 298.70 298.50 289.69 292.41 297.92 276.53 285.14 294.74 298.53 296.54 279.16 293.85 294.27 297.07 300.85 270.62 297.28 289.99 292.75 Alberta British Columbia Manitoba New Brunswick Newfoundland Nova Scotia Ontario Prince Edward Island Quebec Saskatchewan -67.54 -55.49 -72.06 -69.38 -71.71 -64.43 -68.30 -70.29 -64.17 -71.84 -67.41 -55.32 -70.98 -69.26 -70.74 -64.30 -68.18 -70.17 -64.03 -71.73 153.10 247.03 117.87 138.79 118.86 177.32 147.15 131.69 179.37 119.57 172.43 273.52 134.51 157.02 135.57 198.49 166.02 149.38 200.70 136.34 175.50 277.73 137.15 159.91 138.23 201.86 169.02 152.19 204.08 139.00 178.08 281.27 139.37 162.35 140.46 204.69 171.54 154.55 206.93 141.24 179.09 282.66 140.24 163.30 141.33 205.80 172.53 155.47 208.05 142.12 Total average US average CAN average -24.50 -10.58 -67.52 -24.24 -10.33 -67.21 34.57 -3.62 153.08 40.11 -2.52 172.40 101.00 77.06 175.47 253.27 277.71 178.05 264.85 292.72 179.06 Notes : Counterfactual analysis based on parameter estimates from column (1) of Table 8. We set σ = 5 as in Anderson and van Wincoop (2003) and µ = 0.5. 54 Table 20: US-CAN sample, Comparative static eects in percent of erasing the US-CAN border for various parameter values µ σ 0.2 average %GDP average %ê average %EV total US CAN total US CAN total US CAN 5 10 15 11.82 4.73 2.94 6.63 2.27 1.32 71.26 33.14 21.69 9.42 3.79 2.36 4.34 1.52 0.89 67.58 30.01 19.41 12.28 4.84 2.99 5.46 1.90 1.11 91.00 38.91 24.87 0.5 5 10 15 4.08 1.73 1.10 2.32 0.90 0.55 24.37 11.39 7.44 2.05 0.88 0.56 0.79 0.31 0.19 16.64 7.53 4.88 4.32 1.81 1.14 1.58 0.62 0.39 36.25 15.68 10.02 0.75 5 10 15 2.58 1.11 0.71 1.60 0.65 0.41 13.95 6.51 4.25 0.66 0.29 0.19 0.24 0.10 0.06 5.54 2.52 1.63 2.79 1.19 0.75 0.96 0.39 0.25 24.21 10.48 6.69 0.9 5 10 15 2.10 0.91 0.58 1.38 0.57 0.36 10.47 4.88 3.18 0.22 0.10 0.06 0.08 0.03 0.02 1.84 0.84 0.54 2.29 0.98 0.63 0.77 0.32 0.20 20.19 8.74 5.58 0.99 5 10 15 1.88 0.82 0.52 1.28 0.54 0.34 8.88 4.13 2.70 0.02 0.01 0.01 0.01 0.00 0.00 0.17 0.08 0.05 2.07 0.89 0.57 0.69 0.29 0.18 18.36 7.95 5.07 Notes : Table reports average changes in nominal GDP, employment, and the equivalent variation for the gravity model using a search and matching framework for the labor market with varying elasticity of substitution σ and the elasticity of the matching function µ. 55 Table 21: US-CAN sample, Comparative static eects of erasing the US-CAN border controlling for trade imbalances for various parameter values µ σ 0.2 average %GDP average %ê average %EV total US CAN total US CAN total US CAN 5 10 15 12.14 4.82 2.99 6.69 2.25 1.30 75.02 34.77 22.73 9.50 3.80 2.36 4.42 1.52 0.88 67.53 30.19 19.57 12.37 4.85 2.99 5.57 1.90 1.10 90.93 39.15 25.08 0.5 5 10 15 4.26 1.80 1.14 2.31 0.88 0.54 27.19 12.68 8.27 2.05 0.88 0.56 0.79 0.31 0.19 16.61 7.58 4.92 4.32 1.81 1.14 1.59 0.62 0.38 36.18 15.77 10.10 0.75 5 10 15 2.74 1.18 0.75 1.58 0.63 0.39 16.58 7.72 5.03 0.66 0.29 0.18 0.24 0.10 0.06 5.53 2.53 1.64 2.78 1.18 0.75 0.96 0.39 0.24 24.15 10.54 6.75 0.9 5 10 15 2.26 0.98 0.62 1.36 0.55 0.35 13.03 6.06 3.95 0.22 0.10 0.06 0.08 0.03 0.02 1.84 0.84 0.55 2.29 0.98 0.62 0.77 0.32 0.20 20.14 8.79 5.63 0.99 5 10 15 2.04 0.89 0.57 1.26 0.52 0.33 11.41 5.30 3.46 0.02 0.01 0.01 0.01 0.00 0.00 0.17 0.08 0.05 2.07 0.89 0.57 0.69 0.29 0.18 18.32 8.00 5.12 Notes : Table reports average changes in nominal GDP, employment, and the equivalent variation for the gravity model using a search and matching framework for the labor market with varying elasticity of substitution σ and the elasticity of the matching function µ. 56 Table 22: OECD sample, Comparative static eects in percent of PTA inception for various parameter values µ σ average %GDP average %ê average %∆u average %EV 0.2 5 10 15 16.76 7.13 4.53 11.90 5.00 3.16 -11.05 -4.63 -2.92 15.23 6.33 3.98 0.5 5 10 15 7.60 3.35 2.15 2.75 1.20 0.77 -2.55 -1.11 -0.71 5.66 2.44 1.55 0.75 5 10 15 5.75 2.55 1.64 0.90 0.40 0.25 -0.83 -0.37 -0.24 3.71 1.61 1.03 0.9 5 10 15 5.15 2.28 1.47 0.30 0.13 0.08 -0.27 -0.12 -0.08 3.07 1.34 0.85 0.99 5 10 15 4.89 2.16 1.39 0.03 0.01 0.01 -0.02 -0.01 -0.01 2.78 1.21 0.78 Notes : Table reports average changes in nominal GDP, employment, and the equivalent variation for the gravity model using a search and matching framework for the labor market with varying elasticity of substitution σ and the elasticity of the matching function µ. 57 Table 23: OECD sample, Comparative static eects in percent of PTA inception controlling for trade imbalances for various parameter values µ σ average %GDP average %ê average %∆u average %EV 0.2 5 10 15 16.68 7.11 4.51 11.91 5.00 3.16 -10.94 -4.61 -2.91 15.25 6.33 3.98 0.5 5 10 15 7.54 3.32 2.13 2.75 1.20 0.77 -2.54 -1.11 -0.71 5.67 2.44 1.55 0.75 5 10 15 5.69 2.52 1.62 0.90 0.40 0.25 -0.83 -0.37 -0.23 3.71 1.61 1.03 0.9 5 10 15 5.10 2.26 1.45 0.30 0.13 0.08 -0.27 -0.12 -0.08 3.07 1.34 0.85 0.99 5 10 15 4.83 2.14 1.37 0.03 0.01 0.01 -0.02 -0.01 -0.01 2.78 1.21 0.78 Notes : Table reports average changes in nominal GDP, employment, and the equivalent variation for the gravity model using a search and matching framework for the labor market with varying elasticity of substitution σ and the elasticity of the matching function µ. 58