Trade, geography and the skill premium in U.S. manufacturing.

Francis, John ; Zheng, Yuqing

I. INTRODUCTION

The discernible increase in wage inequality in developed countries over the past several decades has been a topic of considerable interest in both the international trade and labor economics literatures. A number of studies have identified at least some role for international trade in these increasing wage disparities. (1) Recent contributions to the New Economic Geography literature by Head and Mayer (2006), Hanson (2005), Mion (2004), and Redding and Venables (2004) have emphasized the influence of the geography of trade on wages, suggesting that countries (or regions) with access to larger markets have higher wages. In this paper, we unite these two strands of the literature by developing a model that examines whether the wage increases attributed to access to larger markets are non-neutral.

Redding and Venables (2004), henceforth RV, develop a structural model of trade relating access to larger markets to per capita incomes. They estimate a generalized gravity equation using world trade data to construct empirical proxies for market and supplier access. These are trade cost weighted measures of export demand and import supply, respectively, that take into account the geographical distribution of trade flows. Market access measures the size of the market that can be reached by firms positioned in a given country. Supplier access measures the ease at which firms in a given country can acquire intermediate inputs. RV show that per capita incomes are increasing in both of these measures. Their model, however, does not differentiate between labor types and therefore does not address the issue of whether market access has different influences on skilled workers and unskilled workers. There is a good reason to believe that the wage increases attributed to market and supplier access would be non-neutral across both skill groups and industries. First, a number of recent theoretical contributions demonstrate a positive relationship between market size and the skill premium. Epifani and Gancia (2006, 2008) show that in the context of a new trade model scale itself is skilled biased under very reasonable assumptions, and they provide supporting empirical evidence. In addition, the New Economic Geography models of Epifani (2005) and Amiti (2005), which explicitly account for factor endowment differences between countries, suggest that the forward and backward linkages provided by agglomeration exacerbate the Stolper-Samuelson Effect, leading to relative wages that overshoot the values that would be observed in the absence of such linkages. Second, Redding and Schott (2003) provide empirical evidence, suggesting that in countries with higher values of market and supplier access individuals have greater incentive to invest in skills, leading to a higher return to education and a larger skill premium. And third, as Feenstra and Hanson (1999), henceforth FH, demonstrate, if production is fragmented, changes in the parameters of the production function over time can shift the composition of activities that are performed abroad in a given industry, leading to non-neutral effects on productivity and factor prices. Countries and industries with better access to overseas production activities, that is, larger levels of supplier access, would be more likely to observe such changes.

In this paper, we augment the methodology in RV to examine the relationship between market and supplier access and the skill premium in U.S. manufacturing industries. Our analysis differs from RV in two principal ways. First, we develop a model that relates market and supplier access to value added prices rather than to wages. This is the natural generalization to a model with more than one internationally immobile factor of production. Second, we use industries as our unit of analysis rather than countries. An industry-level analysis allows us to gauge the effects of market and supplier access on industry value added prices which we can then decompose into mandated factor price adjustments.

Our empirics apply a three-stage estimation procedure. In the first stage, we use a generalized gravity specification to generate proxies for changes in market and supplier access for a cross section of U.S. manufacturing industries between 1984 and 1996. In the second and third stages, we employ the FH mandated wage method to account for the role that these changes have on relative factor returns. We find that changes in market and supplier access have positively impacted value added prices leading to an increase in the skill premium. Growth in these measures can account for around 5% of the increase in the skill premium over the sample period.

The paper is organized as follows. Section II presents a model relating market and supplier access to value added prices. Section III develops our empirical framework. Section IV discusses our empirical results. Section V concludes.

II. THE MODEL

Consider a world that has many industries indexed by i and many countries indexed by j. Final products are differentiated and are produced using internationally immobile primary inputs (e.g., skilled labor, unskilled labor, capital) and intermediates, some of which are imported, in a monopolistically competitive environment. All consumers are assumed to have identical homothetic preferences over aggregates of the varieties available in each industry. Each industry's aggregate takes the constant elasticity of substitution (CES) form

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [n.sub.ik] is the number of industry i varieties produced in country k, [x.sub.ikj] is country j's demand for a single industry i variety produced in country k, and [sigma] > 1 is the elasticity of substitution between varieties. (2) Because there is a CES between varieties and all consumers have identical preferences, the output and price of each variety will be identical in equilibrium. Let [p.sub.ik] be the price of an industry i variety produced in country k. The price of an industry i variety produced in country k and consumed in country j is [p.sub.ik][T.sub.ikj], where [T.sub.ikj] > 1 is the iceberg trade cost of shipping the good from country k to country j; in order for one unit of the good to arrive at its destination more than one unit must be shipped as part of the good melts away in transport. This results in the following price index over industry i varieties in country j

(2) [G.sub.i]j = [[summation over (k)][n.sub.ik][([p.sub.ik][T.sub.ikj]).sup.1-[sigma]]].sup.1/(1 - [sigma]]

In most models of trade, expenditure is considered to be endogenous and depends on the structure of preferences, technology, and endowments in each country. Following RV, we take expenditure to be exogenous to facilitate our empirics. Given the CES aggregate in each industry, country j demand for individual industry i varieties produced in country k is

(3) [x.sub.ikj] = [p.sub.ik.sup.-[sigma]][E.sub.ij] [G.sub.ij.sup.[sigma]-1][T.sub.ikj.sup.1-[sigma]]

where [E.sub.ij] is country j expenditure on industry i products. Equation (3) gives the quantity of bilateral trade for a particular variety. It will be more useful to express bilateral exports as values rather than quantities. The value of industry i exports from country k to country j satisfy

(4) [n.sub.ik][p.sub.ik][x.sub.ikj] = [n.sub.ik][p.sub.ik.sup.1-[sigma]][T.sub.ikj.sup.1-[sigma]][E.sub.ij] [G.sub.ij.sup.[sigma]-1].

We can simplify this expression by first defining the market capacity of industry i in country j as

(5) [m.sub.ij] = [E.sub.ij] [G.sub.ij.sup.[sigma]-1].

Market capacity identifies the position of the demand curve facing an industry i firm in country j. Second, define the supply capacity of industry i in country k as

(6) [s.sub.ik] = [n.sub.ik][p.sub.ik.sup.1-[sigma]].

Supply capacity captures the number of firms and their competitiveness as measured by prices. Combining Equations (4)-(6) gives

(7) [n.sub.ik][p.sub.ik][x.sub.ikj] = [s.sub.ik][T.sub.ikj.sup.1-[sigma]][m.sub.ij].

Equation (7) states that the value of bilateral exports from country k to country j in a given industry is a function of the supply capacity of the exporting country, trade costs, and the market capacity of the importing country. This relationship is similar to a gravity equation in that trade flows depend on three empirically viable factors. [F.sub.i]rst, they depend on exporting country effects (supply capacity) which can be empirically captured by an exporter dummy variable. Second, they depend on importing country effects (market capacity) which can be empirically captured by an importing country dummy variable. And third, they depend on trade costs which can be captured using standard gravity model variables, for example, bilateral distances, border effects.

Production of industry i varieties in country j requires the use of a composite input of primary factors and intermediates. Let [Z.sub.ij] be a vector of primary inputs, that is, skilled labor, unskilled labor, capital, and let [F.sub.i]([Z.sub.ij]) be a linearly homogeneous, industry-specific production function. Production of industry i varieties in country j follows

(8) f + [m.sub.xij] = [[F.sub.i]([Z.sub.ij])].sup.1-[sigma]][Q.sub.ij.sup.[alpha]]

where f, m >0, [x.sub.ij] is output and 0 < [alpha] < 1. The right-hand side of Equation (8) is a Cobb-Douglas composite input of primary inputs and intermediates where [alpha] is the intermediate expenditure share. We assume that the composite input is purchased in a perfectly competitive factor market. Equation (8) states that production requires a fixed (f) and a marginal (m) input of the composite.

Note that by assumption there are no interindustry input linkages in production. Both FH and Hijzen (2007) identify two potential types of outsourcing: narrow outsourcing occurs within industries and differential outsourcing occurs between industries. Both studies find little effect of differential outsourcing on the skill premium and significant effects of narrow outsourcing. Our assumption of no interindustry linkages is more in line with narrow outsourcing. Furthermore, it has been shown in the New Economic Geography literature that interindustry linkages have little effect on the model's outcome as long as intraindustry linkages are stronger than interindustry linkages. (3) It is also important to note that the [F.sub.i](x) in Equation (8) can be interpreted as value added as [Q.sub.ij] represents intermediate goods in production. (4) As a result, the unit cost associated with [F.sub.i](x) is the value added price in industry i and country j.

Equation (8) implies that the total cost function for an industry i firm in country j is

(9) [TC.sub.ij] = [c.sub.ij.sup.1-[alpha]][G.sup.[alpha].sub.ij](f + [mx.sub.ij])

where [c.sub.ij] is the country j unit cost function associated with the production composite [F.sub.i](x). Note that this unit cost function depends on the prices of the primary factors [Z.sub.ij]; this dependence is omitted from the notation for simplicity. Because competition is monopolistically competitive, firms will maximize profits by setting prices ([sigma] - 1)/[sigma] over marginal cost. After choosing units of measurement such that m = ([sigma] - 1)/[sigma] the price of an industry i variety produced in country j is

(10) [p.sub.ij] = [c.sub.ij.sup.1-[alpha]][G.sub.ij.sup.[alpha]]

New firms will enter the market until profits equal zero. Setting price equal to average cost and solving for the firm's output shows that each firm will have the same fixed scale of production

(11) [bar.x] = f [sigma]

We can now characterize market clearing for industry i varieties in each country. Using Equations (3) and (11), the total demand for all sector i varieties in country j satisfies

(12) [c.sub.ij.sup.(1-[alpha])[sigma]][G.sub.ij.sup.[alpha][sigma]] f [sigma] = [summation over (k)][E.sub.ik] [G.sub.ik.sup.[sigma]-1][T.sub.ijk.sup.1-[sigma]]

Equation (12) has become known in the New Economic Geography literature as the wage equation as so named by Fujita, Krugman, and Venables (1999). However, in this more general model it is more a relationship of value added prices than of wages. Equation (12) can be simplified with two additional definitions. The market access of industry i in country j is defined as the distance weighted sum of the market capacities of all countries

(13) M [A.sub.ij] = [summation over (k)][m.sub.ik][T.sub.ijk.sup.1-[sigma]]

A larger value for market access reflects larger demand for country j's industry i output. Market access, then, can be considered a measure of the size of the market for country j firms. Similarly, supplier access is defined as the distance weighted sum of the supply capacities of all countries

(14) S [A.sub.ij] = [summation over (k)][s.sub.ik][T.sub.ijk.sup.1-[sigma]]

= [summation over (k)] [G.sub.ik.sup.[sigma]-1]

A larger value for supplier access reflects greater supply of industry i inputs from the rest of the world. (5) Combining Equations (12)-(14) and rearranging allow the wage equation to be written as:

(15) [c.sub.ij] = [(f [sigma]).sup.[sigma]/[alpha]-1] S[A.sub.ij.sup.[alpha]/(sigma]-1)(1-[alpha]) M[A.sub.ij.sup.1/[sigma](1-[alpha])

Equation (15) states that industries with higher values of market and supplier access have higher value added prices. For our empirical work it is more useful to express the wage equation in log differences over time. Assuming that the elasticity of substitution and the expenditure share on intermediates is constant over time, differentiating Equation (15) with respect to time yields

(16) [DELTA] ln [c.sub.ij] = [[beta].sub.1] [DELTA] ln S[A.sub.ij] + [[beta].sub.2][DELTA] ln M[A.sub.ij]

where [[beta].sub.1] = [alpha]/(1 - [alpha])(1 - [sigma]) and [[beta].sub.2] = 1/[sigma](1 [alpha]) are positive constants. This equation suggests that industries with higher growth in market and supplier access have higher growth in value added prices. If changes in market and supplier access affect value added prices then the Stolper-Samuelson Theorem, working through the [F.sub.i](x), predicts that factor prices will also be affected. This equation is the basis for the second and third stages of the empirical estimation in the following.

III. EMPIRICAL FRAMEWORK

In order to gauge the effects that growth in market and supplier access have on factor returns we must relate Equation (16) to primary factor prices. FH propose a two-step estimator to accomplish this goal. Once a set of structural variables that are purported to affect value added prices is identified, their procedure allows one to obtain estimates of the factor price adjustments mandated by changes in each structural variable over time. Equation (16) motivates the inclusion of market and supplier access as structural variables in such an estimation.

The following outlines our application of the FH procedure. The unit cost function associated with the composite of primary factors, that is, the value added price, is

(17) [c.sub.i] = [summation over (z)] [a.sub.iz][w.sub.iz]

where [a.sub.izj] is the unit factor z requirement in industry i, and [w.sub.izj] is the wage paid to factor z in industry i. Note that the country j (subscript) has been removed because our application of the second and third stages uses only U.S. data. Changes in prices over time reflect not only changes in factor prices but also changes in productivity. Furthermore, factors are mobile across industries over time so factor prices will equate across industries. The empirical implementation of Equation (17) expressed in log differences is

(18) [DELTA] ln [c.sub.ij] = -[TFP.sub.i] + [summation over (z)] [V.sub.iz][bar.[DELTA] ln [w.sub.z]] + [[epsilon].sub.i]

where [[epsilon].sub.i] is an i.i.d, error term, [V.sub.iz] is the factor z cost share in industry i, [TFP.sub.i] is the total factor productivity in industry i, and the overbar represents an economy-wide average. This equation relates the changes in value added prices to the changes in economy-wide factor prices. Equation (18) suggests that changes in value added prices are affected not only by the changes in factor prices but also by productivity growth. (6) FH examine the error term in this equation more closely and show that the proper specification of Equation (18) is

(19) [DELTA] ln [c.sub.ij] = [ETFP.sub.ij] = [summation over (z)][V.sub.iz][bar.[DELTA] ln [w.sub.z]]

where total factor productivity has been replaced with effective total factor productivity ([ETFP.sub.i]) and moved to the left-hand side of the estimating equation. (7) Note that Equation (19) is an identity. Hence, estimation of Equation (19) has no meaningful empirical application. To address this problem FH suggest a two-step procedure. The assumption that changes in value added prices and productivity over time are driven by a set of structural variables, [H.sub.i], gives a first step regression

(20) [DELTA] ln [c.sub.ij] = [ETFP.sub.ij] = [[beta].sub.0] + [[beta].sub.1][H.sub.i] + [[mu].sub.i]

where [[mu].sub.i] is an i.i.d, error term. The estimated coefficients from Equation (20) determine the predicted contribution of each structural variable to growth in value added price plus ETFP. If improvements in productivity as a result of the changes in the structural variables are perfectly passed through to prices the coefficient [[beta].sub.1] in Equation (20) should not be significantly different from zero. A positive coefficient suggests that changes in the [H.sub.ij] have a further impact on prices over and above their impact on total factor productivity. Hence, the estimation of Equation (20) is a test of whether the structural variables have a non-neutral effect on prices and productivity.

In the second step, the predicted values from stage 1 are regressed on factor cost shares to determine the factor price changes mandated by the price changes attributed to each structural variable. Let [[??].sub.1] be the estimated coefficient from the estimation of Equation (20). The second step is

(21) [[??].sub.1][H.sub.ij] = [[gamma].sub.zj][summation over (z)][V.sub.zj] + [[zeta].sub.ij]

where [[zeta].sub.i] is an i.i.d, error term. The estimated coefficients from Equation (21) give the mandated factor price adjustments resulting from the price and productivity changes attributed to each structural variable.

A. Three-Stage Estimation Procedure

To test whether growth in market and supplier access have non-neutral effects on factor prices we apply a three-stage estimation. In stage 1, following RV, we estimate a generalized gravity equation to generate proxies for market and supplier access at two points in time. Our second and third stages then apply the FH two-step procedure. In stage 2, changes in value added prices plus ETFP are regressed on changes in market and supplier access. In stage 3, the predicted values from stage 2 are regressed on factor cost shares to determine how changes in market and supplier access have contributed to changes in factor returns over the sample period.

The first stage of the estimation is to obtain empirical estimates consistent with Equation (7). We perform this estimation using data from two different time periods, which allows us to construct empirical proxies for market and supplier access at two points in time. Time subscripts are omitted for simplicity. The empirical implementation of Equation (7) is

(22) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [X.sub.ijk] is the value of country j's industry i exports to country k, [rep.sub.j] is an exporting country fixed effect, [part.sub.k] is an importing country fixed effect, [distj.sub.k] is the distance between the capital cities of country j and country k, [bordj.sub.k] is a dummy variable indicating whether country j and country k share a common border, [colony.sub.jk] is a dummy variable indicating a colonial link between country j and country k, [legal.sub.jk] is a dummy variable indicating whether country j and country k share a common legal system, and [v.sub.ijk] is a stochastic error term. Note that Equation (22) is very similar to a gravity specification where importer and exporter gross domestic product (GDP) are replaced with importer and exporter dummy variables. Equation (22) differs from RV in that all coefficients vary across industries. We follow Bergstrand (1989), and estimate a separate regression for each industry.

The coefficients resulting from the estimation of Equation (22) provide empirical proxies for market and supplier access

(23) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(24) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where "hats" represent estimated coefficients. The first terms in brackets in both Equations (23) and (24) are the domestic portions of market and supplier access and include an internal measure of trade costs ([T.sub.ijj]). We follow RV using [dist.sub.ijj] = 0.67 [(area/[pi])].sup.1/2] to proxy internal distances. This gives the average distance between two points within a country assuming that the country is circular. We then proxy internal trade costs as:

(25) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Note that relative to external distances the coefficient on internal distance is halved. This is meant to capture that internal trade costs are lower than external trade costs.

The second and third stages of the estimation procedure take the log changes of market and supplier access from stage 1 and apply them to the estimation of Equations (20) and (21). The second stage estimating equation is then

(26) [DELTA] ln [c.sub.i] + [ETFP.sub.i] = [[beta].sub.0] + [[beta].sub.1][DELTA] ln [[??].sub.i] + [[beta].sub.2][DELTA] ln [[??].sub.i] + [[beta].sub.2][[LAMBDA].sub.i] + [[mu].sub.i]

where [[LAMBDA].sub.i] is a vector of additional controls. In RV, market and supplier access are highly collinear with a correlation coefficient between the two proxies of 0.88. For this reason they estimate two separate regressions, one for market access and one for supplier access. While this seems reasonable at the aggregate level of analysis it is not apparent that the same collinearity would exist at a more disaggregated level. However, our data show that the log changes in our proxies for market and supplier access are still significantly collinear. (8) For this reason we follow their methodology and estimate two separate stage 2 regressions.

In the third stage, we regress the implied price changes attributed to each structural variable on factor cost shares

(27) [[??].sub.1][[??].sub.i] = [[gamma].sub.z][summation over (z)][V.sub.iz] + [[zeta].sub.i]

(28) [[??].sub.2][[??].sub.i] = [[theta].sub.z][summation over (z)][V.sub.iz] + [[xi].sub.i]

The estimated coefficients from Equations (27) and (28) give the mandated factor price responses to the price and productivity changes attributed to growth in market and supplier access.

B. Data and Estimation Issues

Our data span from 1984 to 1996. For the stage 1 gravity equation we use trade data for 103 countries from the NBER World Trade Flows Database which gives bilateral exports for each country by 4-digit Standard International Trade Classification (SITC), Revision 2. Table 1 shows a list of the countries included in our analysis. We chose 1984 as our initial period because the trade data is more complete from 1984 onward which gives a larger number of usable observations. Recent empirical works by Helpman, Melitz, and Rubinstein (2008), Manova (2006), and Melitz and Cunat (2007) suggest that trade flows are volatile over time. To account for this we smooth trade flows by averaging over 3-year intervals. Our initial time period averages trade flows over the period from 1984 to 1986, and our later time period averages trade flows over the period from 1994 to 1996. All of our trade data were deflated using the U.S. GDP deflator.

We use data on bilateral distances, border classifications, and colonial links from the CEPII distance file. (9) The common legal system variable comes from Helpman et al. (2008). (10) For the second- and third-stage regressions we use averaged data for the same years listed earlier from the NBER Industry Productivity Database, (11) which has data on factor payments and prices by 4-digit 1987 SIC categories. These data terminate in 1996, which is why we chose this as the final year in our sample. The production data were deflated using the appropriate deflators provided with the data. If an appropriate deflator was not available we used the U.S. GDP deflator. It is important to note that FH do not deflate their production data. Hence, their estimation predicts changes in nominal factor prices while our estimation predicts changes in real factor prices. The trade and production data use different industry coding systems. In order to match up the first-stage estimation with the latter two stages we follow Melitz and Cunat (2007) and concord the trade data to 1987 export SIC codes. (12) We then concord the NBER Productivity Data to match the export SICs and perform all of our analysis at this level of disaggregation. After dropping industries for which there was either missing or incomplete data, we have a sample of 1,876,621 trade flows for 387 export SIC sectors for each of the two time periods.

In our control variables we include other factors that may have contributed to increases in value added price plus ETFP. We include the log change in the R&D intensity to account for technological change. These data are available from the National Science Foundation. (13) Union coverage may also affect productivity and prices. (14) To capture these potential effects we also include data on union coverage densities by industry from Hirsch and MacPherson (2003). These data are available by the CIC codes used in the Current Population Survey. These, as well as our other control variables, were concorded to the export-based SIC codes using the value of shipments in the NBER Productivity Database as weights.

Following FH and Hijzen (2007) we also include a set of interactions to capture the heterogeneity of changes in the structural variables across industries. The elasticity of substitution, [sigma], may differ across industries. As this can be interpreted as an inverse indicator of market power, we interact all variables with the industry's four-firm concentration ratio to allow the effects of each variable to affect prices and productivity in highly concentrated industries differently than in less concentrated industries. These data are from the 1987 Census of Manufactures at the U.S. Census Bureau; 1987 is roughly the midpoint of our data. Following Hijzen (2007) we also include interactions of all variables with a measure of factor intensity to capture that changes in each variable may affect unskilled labor intensive industries differently than skilled labor intensive industries. We define factor intensity as the ratio of the average share of unskilled workers to that of skilled workers over the two time periods in the sample. This is readily calculated using the NBER data. Table 2 shows summary statistics for the variables used in the second- and third-stage regressions.

Recent contributions to the literature on estimation of the gravity equation have shown that ignoring the problem of zero trade observations can result in severely biased estimates. As our data are relatively disaggregated we have a large proportion of zero observations making this problem of special concern. (15) To deal with this problem we present three sets of results for our first-stage estimation. First, we estimate in logs by ordinary least squares (OLS) using the log of 0.1 plus the trade flow as our dependent variable; second we estimate using Poisson pseudo maximum likelihood (PPML) as suggested by Santos-Silva and Tenreyro (2007); and finally we estimate the Eaton and Tamura (1994) Tobit model (henceforth ET Tobit).

There are a number of observations in the trade data for which there is zero trade for one of the two time periods and positive trade for the other. In order for our estimates from the 1984-1986 period to be comparable to the estimates from the 1994-1996 period we must have the same number of observations and the same vector of regressors within each industry. Including observations for which there are zero trade flows in one period but not the other would mean including a different set of importer and exporter dummies across time rendering market and supplier access proxies incomparable over time. We include only those observations that are either positive or zero in both time periods.

As the second-stage regressions involve generated regressors, standard OLS errors are invalid. To correct this problem we bootstrap the standard errors using 1,000 bootstrap replications. (16,17) The third-stage regressions contain generated regressands, and, again, OLS errors are invalid. FH suggest a procedure to correct the standard errors in this situation. However, Dumont et al. (2005) suggest that this correction is negatively biased and propose an unbiased correction. We present results using both corrections.

IV. ESTIMATION RESULTS

We estimated the first-stage gravity equation for each of the 387 industries in both time periods by each of the three estimation techniques described earlier. All were estimated with robust standard errors. Table 3 reports the average coefficients across all industries weighted by each industry's share of world trade. In parentheses below each average coefficient is a pair indicating respectively the proportion of the coefficients in all 387 regressions that were positive and statistically significant at the 10% level and the proportion of the coefficients that were negative and statistically significant at the 10% level. Table 3 also shows the average predicted log change in market and supplier access for each specification; standard deviations are shown in parentheses below each average. These are weighted by the value of shipments in each industry from the NBER Productivity Database. The final row shows the correlation between growth in market access and growth in supplier access for each specification.

The results of the first-stage estimates are largely as expected. Nearly all of the distance coefficients are negative and statistically significant. The border, colonial tie, and common legal system coefficients are primarily positive and statistically significant. However, the magnitude of the coefficients and their trends over time vary from specification to specification. The estimates of the distance coefficient are significantly smaller in absolute value in the PPML specification compared to either the OLS or ET-Tobit models. This is consistent with the findings by Santos-Silva and Tenreyro (2007) using aggregate trade data. The OLS and ET-Tobit estimates suggest that the average distance coefficient is getting more negative over time. This is consistent with the evidence in the study by Berthelon and Freund (2008). The average border coefficient is at least slightly increasing over time in all three specifications. However, the magnitude of the estimates is considerably smaller with the ET-Tobit model. The average colonial link coefficient is decreasing over time in all three specifications, suggesting that colonial ties are becoming less important for trade. However, the average PPML estimate is considerably smaller compared to the other two specifications. The average legal system coefficient is decreasing over time using the PPML and ET-Tobit results while the OLS results predict the opposite. In addition, the PPML coefficients are significantly smaller than the other two specifications. Finally, all three specifications predict an increase in the average constant term over time. The evidence by Buch, Kleinert, and Toubal (2004) suggests that this is indicative of distance becoming more important over time. All three specifications predict significant growth in both market and supplier access over time with somewhat higher growth in supplier access compared to market access.

The tables that follow present the second- and third-stage estimates using the proxies of market and supplier access from all three sets of first-stage regressions. The results are similar across specifications so we will confine our discussion to those generated using the first-stage ET-Tobit estimates (columns (5) and (6) in each table). Tables 4 and 5 show the results from our second-stage regressions. Table 4 presents the results of the stage 2 estimation involving market access while Table 5 presents the results involving supplier access. In each of these tables we present two sets of results. The odd numbered columns show the second-stage results omitting control variables, whereas the even numbered columns include all controls.

In Table 4, the coefficient on market access is positive and significant at the 5% level or better in both regressions. The interaction between the log change in market access and the four-firm concentration ratio is positive in column (5) and negative in column (6). However, the magnitude of the estimates is very small and neither shows statistical significance. These results suggest that there is very little evidence that market access affects prices and productivity in highly concentrated industries differently than in unconcentrated industries. The interaction between the log change in market access and factor intensity is negative and statistically significant at the 5% level or better in both specifications. These results suggest that growth in market access has a more profound effect on prices and productivity in skilled labor intensive industries relative to unskilled labor intensive industries. The coefficients on growth in R&D intensity are positive and significant at the 1% level. And there is some evidence that these effects are smaller in concentrated industries, but very little evidence that growth in R&D intensity affects value added prices and productivity differently based on factor intensity. Finally, the union coverage density coefficients are, in general, insignificant.

In Table 5, the coefficient on supplier access is positive and significant at the 1% level in both regressions. The interaction between the log change in supplier access and the four-firm concentration ratio is again very small and in general insignificant. These results suggest that, as with market access, there is little evidence that supplier access affects prices and productivity in highly concentrated industries differently than in unconcentrated industries. The interaction between the log change in supplier access and factor intensity is negative and statistically significant at the 1% level in both specifications. These results provide strong evidence that growth in supplier access has a more profound effect on prices and productivity in skilled labor intensive industries relative to unskilled labor intensive industries. The coefficients on growth in R&D intensity are positive and significant at the 5% level. And there is evidence that these effects are smaller in concentrated industries given that the interactions between growth in R&D intensity and the four-firm concentration ratio are negative and significant at the 10% level. There is very little evidence that growth in R&D intensity affects value added prices and productivity differently based on factor intensity as the interactions of growth in R&D intensity with factor intensity are insignificant. Finally, the union coverage density coefficients are, in general, insignificant with the exception of their interaction with the four-firm concentration ratio, which are negative and significant at the 1% level.

The results in Tables 4 and 5 suggest that growth in access to larger markets, whether it be in product markets or input markets, has non-neutral effects on value added prices and productivity. This is largely consistent with the model presented in Section II. This would then suggest that, via the Stolper-Samuelson Effect, changes in market and supplier access should have effects on the skill premium. Although our estimation is somewhat different from RV, it is evident that our coefficients on market and supplier access are significantly smaller in magnitude compared to their study. One possible explanation for this is that RV use cross-country data on wages which, in general, have greater variation than cross-industry wage data from a single country, resulting in larger estimates. Furthermore, it is likely that market and supplier access have less variation across industries than across countries as in the work by RV. The final stage of the estimation takes the changes in value added prices and ETFP attributed to growth in market and supplier access and decomposes them into their mandated factor price changes to give an estimate of how access to larger markets has affected the skill premium over the sample period.

Tables 6 and 7 show the results from the stage 3 regressions. Table 6 shows the stage 3 results using the predicted values from the market access regressions summarized in Table 4, and Table 7 shows the stage 3 results using the predicted values from the supplier access regressions summarized in Table 5. Each column in Tables 6 and 7 use the results from the corresponding columns in Tables 4 and 5. Errors shown in parentheses use the Dumont et al. (2005) correction, and errors in brackets use the FH correction. All regressions are weighted by the average value of shipments in each industry between the two time periods. The difference in the coefficients on the skilled and unskilled factor cost shares represents the percentage increase in the wage gap caused by each structural variable. The final two rows show the predicted change in the skill premium and the percentage of the actual change in the skill premium over the sample period explained by each structural variable.

First consider the stage 3 market access regressions in Table 6. Both regressions suggest that the changes in prices plus ETFP resulting from growth in market access mandates an increase in the skilled wage at the 5% level or better. Both specifications suggest that growth in market access has increased the skill premium. The estimates suggest that growth in market access can explain up to 5.25% of the growth in the skill premium over the sample period. Next consider the supplier access results in Table 7. Both specifications suggest that the changes in prices plus ETFP resulting from growth in supplier access mandate an increase in the skilled wage and a decrease in the unskilled wage at the 10% level of significance or better. Both specifications predict that growth in supplier access has increased capital returns at the 5% level of significance. These results are then somewhat stronger than the market access results in that there are no mandated factor price adjustments that are statistically insignificant. Both specifications then suggest that growth in supplier access has increased the skill premium. The estimates suggest that growth in market access can explain up to 5.28% of the growth in the skill premium over the sample period.

V. CONCLUSION

Recent contributions to the literature in trade and geography have demonstrated that access to larger markets has a positive effect on wages. However, very little work has been performed to examine whether these increases are neutral across skill groups. In this paper, we develop a model that relates industry-level growth in access to larger markets to industry-level growth in value added prices and then empirically test whether increased access to larger markets has non-neutral effects on prices and productivity and, therefore, has an impact on the skill premium. Following RV, we develop a theoretical model suggesting that both market access, a measure of the size of the market facing a firm located in a given country, and supplier access, a measure of the ease of acquiring inputs for a firm located in a given country, are positively correlated with value added prices. We then combine this with empirical mandated wage approach to determine whether changes in these measures mandate a statistically significant change in the skill premium over the period from 1984 to 1996.

Our results suggest that growth in both market and supplier access has positive and primarily statistically significant effects on prices plus ETFP over the sample period. We find evidence that these effects are more pronounced in skilled labor intensive industries; however, we find little evidence that market concentration influences these effects. Because market and supplier access growth is collinear we performed two separate sets of mandated wage estimates. We find that growth in market access mandates an increase in the skilled wage across all of our econometric specifications and a decrease in the unskilled wage across most of our specifications. We find that growth in supplier access mandates an increase in the skilled wage and a decrease in the unskilled wage across all of our econometric specifications. The mandated increase in the skill premium resulting from growth in market and supplier accesses is up to 5.25% and 5.28% respectively of the actual change in the skill premium over the sample period. It is important to note that as growth in market and supplier access is highly collinear it is difficult to separate the impact of each on inequality. Hence, it would be inappropriate to conclude that growth in market and supplier access each explain around 5% of the change in the skill premium over the sample period. However, our results do suggest that growth in access to larger markets, whether those be in final goods or input markets, does have a significant impact on the skill premium.

Our results highlight that geography not only shapes aggregate national incomes but also has consequences for the distribution of income. While better access to larger markets is positively correlated with overall incomes as shown by RV we demonstrate that access to larger markets is also positively correlated with income inequality. However, the increase in inequality attributed to access to larger markets is rather small relative to the overall increase in income inequality and is not much different than many estimates of trade's overall effect on inequality. While geography plays some role in shaping inequality it is by no means a primary role.

ABBREVIATIONS

CES: Constant Elasticity of Substitution

ETFP: Effective Total Factor Productivity

GDP: Gross Domestic Product

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(1.) See Baldwin and Cain (2000), Baldwin and Hilton (1984), Feenstra and Hanson (1999), Haskel and Slaughter (2001), Hijzen (2007), Learner (1998), and Sachs and Shatz (1994).

(2.) It is possible that [sigma] may vary across industries. We address this possibility in the empirics in the following.

(3.) See Fujita et al. (1999) and Krugman and Venables (1996).

(4.) See Sims (1969).

(5.) Note that both market and supplier access have domestic components as country j is included in the sums in Equations (14) and (15).

(6.) This specification has been at the heart of a number of empirical studies linking trade and wage inequality. For example, see Baldwin and Cain (2000), Baldwin and Hilton (1984), Feenstra and Hanson (1999), Haskel and Slaughter (2001), Hijzen (2007), Learner (1998), and Sachs and Shatz (1994).

(7.) Effective total factor productivity is defined as [ETFP.sub.ij] = [summation over (z)][V.sub.iz][bar.[DELTA] ln [w.sub.zj]] - [DELTA] ln [c.sub.ij], where the over-bar signifies the economy wide average. For more on this see FH.

(8.) The correlation between the log changes in market and supplier access differs depending on our first-stage specification but is as high as 0.813. To further explore collinearity we ran auxiliary regressions of the log change in market access on the other explanatory variables which generated [R.sup.2] significantly larger than that of our second-stage regression containing both variables indicating that collinearity is present.

(9.) These data is available at www.cepii.fr.

(10.) These data are available at www.economics.harvard. edu/faculty/helpman.

(11.) Bartlesman, Becker, and Gray (2000).

(12.) The export SIC codes differ from the standard SIC codes because some SIC classifications cannot be observed at the border. See Feenstra, Romalis, and Schott (2002) for a detailed discussion.

(13.) These data are available on the web from the NSF's Industrial Research & Development Information System (IRIS), www.nsf.gov/statistics/iris. Specifically, we use the data from Table H-2, Company R&D funds as a percent of net sales in R&D-performing companies, by industry and size of company: 1956-1998.

(14.) See Doucouliagos and Laroche (2003).

(15.) The proportion of zeros in our data varies by industry but ranges from 75% to 91%. Overall 80% of our observations are zero. For a discussion of the issue of zero trade flows in the gravity equation see Helpman et al. (2008), Martin and Pham (2008), Martinez-Zaroso, Nowak-Lehman, and Vollmer (2009), and Santos Silva and Tenreyro (2007, 2009).

(16.) RV, following Pagan (1984), use a more complex bootstrapping method. They resample trade flow observations from the first stage, calculate market and supplier access based on the resample, and then perform the second-stage regression. This is feasible because there is a single first-stage regression. Our market and supplier access calculations combine the results of 774 first-stage regressions making this more complex procedure infeasible.

(17.) We used Stata to perform the second-stage regressions which does not permit weights with the bootstrap option. We manually weighted the data and then ran a bootstrap estimation on the manually weighted data.

JOHN FRANCIS and YUQING ZHENG *

* The authors would like to thank seminar participants at the University of Arkansas, the 2007 Annual Meeting of the Southern Economic Association and the Fall 2008 Meeting of the Midwest International Economics Group for their valuable input. We would also like to thank Otis Gilley for his insight in working through some nontrivial economic issues.

Francis: Assistant Professor, Department of Economics & Finance, College of Business, Louisiana Tech University, Ruston, LA 71272. Phone 318-257-2917, Fax 318-257-4253, E-mail [email protected]

Zheng: Research Associate, Department of Applied Economics and Management, Cornell University, Ithaca, NY 14853. Phone 607-592-9955, Fax 607-254-4335, E-mail [email protected]

doi: 10.1111/j.1465-7295.2010.00351.x

TABLE 1
List of Countries Used in the First-Stage Gravity Estimation

Albania
Algeria
Angola
Argentina
Australia
Austria
Bangladesh
Belgium-Luxembourg
Bolivia
Brazil
Bulgaria
Burkina Faso
Cameroon
Canada
Central African Rep.
Chad
Chile
China
China HK SAR
Colombia
Congo
Costa Rica
Cote D'Ivoire
Cyprus
Dem. Rep. Congo
Denmark
Dominican Rep
Ecuador
Egypt
El Salvador
Ethiopia
Finland
France
Gabon
Gambia
Germany
Ghana
Greece
Guatemala
Guinea Bissau
Guyana
Haiti
Honduras
Hungary
India
Indonesia
Iran
Ireland
Israel
Italy
Jamaica
Japan
Jordan
Kenya
Korea Rep.
Madagascar
Malawi
Malaysia
Mali
Mauritania
Mauritius
Mexico
Mongolia
Morocco
Mozambique
Nepal
The Netherlands
New Zealand
Nicaragua
Niger
Nigeria
Norway
Pakistan
Panama
Paraguay
Peru
Philippines
Poland
Portugal
Romania
Saudi Arabia
Senegal
Sierra Leone
Singapore
South Africa
Spain
Sri Lanka
Sudan
Sweden
Syria
Taiwan
Tanzania
Thailand
Trinidad and Tobago
Tunisia
Turkey
The United Kingdom
The United States
Uganda
Uruguay
Venezuela
Zambia

Notes: Germany was not yet reunified in the 1984-1986 time period.
For comparison to the later time period we aggregated
the 1984-1986 trade flows for East and West Germany.

TABLE 2
Summary Statistics for Stages 2 and 3
Variables

 Standard
Variable Mean Deviation

[DELTA]log real unskilled wage -0.0037 --
[DELTA]log real skilled wage 0.1050 --
[DELTA]log value added prices + ETFP 0.1432 0.0681
[DELTA]log R&D intensity -0.0118 0.2753
[DELTA]log union coverage density -0.2614 0.2288
Four-firm concentration ratio 40.2249 22.4791
Factor intensity 1.8830 1.2135
Average skilled labor share 0.0694 0.0470
Average unskilled labor share 0.0933 0.0494
Average capital share 0.2836 0.1368

Note: All averages are weighted by the average value of
shipments between the two time periods in each industry.

TABLE 3
Summary of First-Stage Estimations

 OLS OLS
 1984-1986 1994-1996

In distance -1.2517 -1.4152
 (0.0, 99.2) (0.0, 99.5)

Border 0.6406 0.6767
 (78.6, 0.0) (76.2, 0.0)

Colony 1.5497 1.5434
 (95.1, 0.0) (95.6, 0.0)

Legal system 0.4228 0.4569
 (84.8, 0.3) (85.0, 0.0)

Constant 16.2424 18.2943
 (99.2,0.3) (99.2, 0.3)

Observations 5,969 5,969

Number of industries 387 387

[DELTA] ln market access 0.9589 (0.5107)

[DELTA] ln supplier access 1.2032 (0.6040)

Corr [DELTA] In MA--A ln SA 0.6069

 PPML PPML
 1984-1986 1994-1996

In distance -0.8492 -0.8414
 (0.0, 97.9) (1.0, 96.9)

Border 0.6503 0.6644
 (87.6, 0.5) (91.7, 0.3)

Colony 0.1018 -0.1081
 (39.5, 1.8) (20.2, 8.5)

Legal system 0.2484 0.1753
 (61.2, 3.1) (58.4, 2.8)

Constant 14.0658 14.9695
 (98.2, 0.0) (98.4, 0.0)

Observations 5,969 5,969

Number of industries 387 387

[DELTA] ln market access 0.7652 (0.8711)

[DELTA] ln supplier access 0.9963 (1.7233)

Corr [DELTA] In MA--A ln SA 0.5384

 ET-Tobil EX-Tobil
 1984-1986 1994-1996

In distance -1.3874 -1.4020
 (0.0, 100.0) (0.0, 100.0)

Border 0.2357 0.2779
 (53.7, 0.5) (64.1, 0.5)

Colony 1.2203 1.0221
 (97.4, 0.0) (97.9, 0.0)

Legal system 0.5371 0.4959
 (94.6, 0.0) (94.1, 0.0)

Constant 19.2486 20.3960
 (100.0, 0.0) (100.0, 0.0)

Observations 5,969 5,969

Number of industries 387 387

[DELTA] ln market access 0.8699 (1.1412)

[DELTA] ln supplier access 1.0967 (1.1850)

Corr [DELTA] In MA--A ln SA 0.9049

Notes: Dependent variable is equal to the value of bilateral
exports. All regressions include fixed exporter and importer
effects. The coefficients reported in each cell are mean
coefficients weighted by each industry's share of world trade. In
parentheses below each average coefficient are respectively the
proportions of industries for which the coefficient was positive
and significant and negative and significant at the 10% level.
ET-Tobit coefficients are elasticities. The average log changes
in market and supplier access are weighted by each industry's
share in the value of shipments in the NBER Productivity
Database.

TABLE 4
Stage 2 Estimation for Market Access

Independent Variable (1) (2)

[DELTA] ln MA 0.0640 *** 0.0716 ***
 (0.0207) (0.0234)

[DELTA] ln MA x four-firm 0.0006 ** 0.0005
 (0.0002) (0.0003)

[DELTA] ln MA x F-Int. -0.0285 *** -0.0309 ***
 (0.0064) (0.0075)

[DELTA] ln R&D 0.1505 ***
 (0.0521)

[DELTA] ln R&D x four-firm -0.0016 *
 (0.0009)

[DELTA] ln R&D x F-Int. -0.0226
 (0.0170)

[DELTA] ln Cov Den 0.0546
 (0.0521)

[DELTA] ln Cov Den x four-firm -0.0010
 (0.0010)

[DELTA] ln Cov Den x F-Int. -0.0111
 (0.0187)
Constant 0.1107 *** 0.1114 ***
 (0.0192) (0.0197)

First stage OLS OLS

Observations 387 387

[R.sup.2] 0.3476 0.4121

Independent Variable (3) (4)

[DELTA] ln MA 0.0583 *** 0.0571 **
 (0.0196) (0.0232)

[DELTA] ln MA x four-firm 0.0000 -0.0002
 (0.0004) (0.0005)

[DELTA] ln MA x F-Int. -0.0196 *** -0.0155 *
 (0.0063) (0.0080)

[DELTA] ln R&D 0.1335 **
 (0.0552)

[DELTA] ln R&D x four-firm -0.0021 **
 (0.0011)

[DELTA] ln R&D x F-Int. -0.0050
 (0.0184)

[DELTA] ln Cov Den 0.0340
 (0.0545)

[DELTA] ln Cov Den x four-firm -0.0015
 (0.0012)

[DELTA] ln Cov Den x F-Int. 0.0260
 (0.0215)
Constant 0.1231 *** 0.1338 ***
 (0.0118) (0.0149)

First stage PPML PPML

Observations 387 387

[R.sup.2] 0.2629 0.3261

Independent Variable (5) (6)

[DELTA] ln MA 0.0371 *** 0.0389 **
 (0.0157) (0.0169)

[DELTA] ln MA x four-firm 0.0000 -0.0002
 (0.0002) (0.0003)

[DELTA] ln MA x F-Int. -0.0192 *** -0.0139 **
 (0.0064) (0.0070)

[DELTA] ln R&D 0.1426 ***
 (0.0535)

[DELTA] ln R&D x four-firm -0.0018 *
 (0.0010)

[DELTA] ln R&D x F-Int. -0.0114
 (0.0184)

[DELTA] ln Cov Den 0.0650
 (0.0577)

[DELTA] ln Cov Den x four-firm -0.0022 *
 (0.0010)

[DELTA] ln Cov Den x F-Int. 0.0329
 (0.0223)
Constant 0.1394 *** 0.1525 ***
 (0.0107) (0.0142)

First stage ET-Tobit ET-Tobit

Observations 387 387

[R.sup.2] 0.1547 0.2454

Notes: Dependent variable is equal to the log change in value
added price plus effective total factor productivity. All
regressions performed by ordinary least squares. Bootstrapped
standard errors (1,000 replications) are shown in parentheses.
All regressions are weighted by the average value of shipments in
each industry over the two time periods.

The symbols *, **, *** represent significance at the 1%, 5%, and
10% levels respectively.

TABLE 5
Stage 2 Estimation for Supplier Access

Independent Variable (1) (2)

[DELTA] In SA 0.0525 *** 0.0689 ***
 (0.0192) (0.0251)

[DELTA] In SA x four-firm 0.0002 -0.0001
 (0.0003) (0.0005)

A In SA x F-Int -0.0209 *** -0.0211 ***
 (0.0061) (0.0071)

[DELTA] In R&D 0.1475 ***
 (0.0515)

[DELTA] In R&D x four-firm -0.0019 *
 (0.0010)

[DELTA] In R&D x F-Int. -0.0143
 (0.0178)

[DELTA] In Cov Den 0.0974
 (0.0601)

4 In Cov Den x four-firm -0.0025 *
 (0.0134)

[DELTA] In Cov Den x F-Int. 0.0045
 (0.0183)

Constant 0.1171 *** 0.1210 ***
 (0.0216) (0.0207)

First stage OLS OLS

Observations 387 387

[R.sup.2] 0.2905 0.3715

Independent Variable (3) (4)

[DELTA] In SA 0.0442 ** 0.0430 *
 (0.0243) (0.0222)

[DELTA] In SA x four-firm 0.0003 0.0001
 (0.0003) (0.0002)

A In SA x F-Int -0.0210 *** -0.0171 ***
 (0.0065) (0.0067)

[DELTA] In R&D 0.1216 ***
 (0.0466)

[DELTA] In R&D x four-firm -0.0017 **
 (0.0009)

[DELTA] In R&D x F-Int. -0.0054
 (0.0151)

[DELTA] In Cov Den 0.0505
 (0.0465)

4 In Cov Den x four-firm -0.0017 *
 (0.0009)

[DELTA] In Cov Den x F-Int. 0.0228
 (0.0190)

Constant 0.1285 *** 0.1385 ***
 (0.0122) (0.0140)

First stage PPML PPML

Observations 387 387

[R.sup.2] 0.2398 0.2992

Independent Variable (5) (6)

[DELTA] In SA 0.0341 *** 0.0448 ***
 (0.0111) (0.0162)

[DELTA] In SA x four-firm 0.0002 -0.0002
 (0.0002) (0.0003)

A In SA x F-Int -0.0176 *** -0.0152 ***
 (0.0048) (0.0057)

[DELTA] In R&D 0.1225 **
 (0.0500)

[DELTA] In R&D x four-firm -0.0016 *
 (0.0009)

[DELTA] In R&D x F-Int. -0.0057
 (0.0161)

[DELTA] In Cov Den 0.0942
 (0.0579)

4 In Cov Den x four-firm -0.0029 ***
 (0.0010)

[DELTA] In Cov Den x F-Int. 0.0258
 (0.0198)

Constant 0.1362 *** 0.1450 ***
 (0.0120) (0.0129)

First stage ET-Tobit ET-Tobit

Observations 387 387

[R.sup.2] 0.2132 0.3074

Note: See Table 4 notes.

TABLE 6
Stage 3 Estimation for Market Access

 (1) (2) (3)

Skilled labor share 0.4896 *** 0.5510 *** 0.3816 ***
 (0.1215) (0.1470) (0.1164)
 [0.1184] [0.1446] [0.1140]

Unskilled labor share -0.3603 *** -0.3778 *** -0.2072 **
 (0.0822) (0.1038) (0.0859)
 [0.07901 [0.10131 [0.0836]

Capital share 0.0847 *** 0.0857 *** 0.0623 **
 (0.0227) (0.0261) (0.0261)
 [0.0208] [0.0245] [0.0250]

Constant 0.0081 0.0042 -0.0047
 (0.0126) (0.0115) (0.0058)
 [0.0122] [0.0110] [0.0051]

First stage OLS OLS PPML

Observations 387 387 387

[R.sup.2] 0.5766 0.6422 0.5888

Predicted change in skill 0.8499 0.9289 0.5151
 premium

Proportion explained 7.82% 8.54% 5.42%

 (4) (5) (6)

Skilled labor share 0.3216 ** 0.3549 *** 0.2898 **
 (0.1426) (0.1194) (0.1350)
 [0.1402] [0.1183] [0.1339]

Unskilled labor share -0.1517 -0.2153 *** -0.1349
 (0.1039) (0.0808) (0.0835)
 [0.1015] [0.0796] [0.0822]

Capital share 0.0536 ** 0.0130 0.0094
 (0.0274) (0.0104) (0.0094)
 [0.0260] [0.0089] [0.0074]

Constant -0.0048 -0.0045 -0.0053
 (0.0061) (0.0053) (0.0051)
 [0.0052] [0.0049] [0.0047]

First stage PPML ET-Tobit ET-Tobit

Observations 387 387 387

[R.sup.2] 0.4264 0.4591 0.3996

Predicted change in skill 0.4733 0.5703 0.4247
 premium

Proportion explained 4.35% 5.25% 3.91%

Notes: Dependent variable is equal to the predicted change in
prices plus effective total factor productivity caused by
changes in market access. Standard errors in parentheses are
adjusted by the methodology in the study by Dumont et al.
(2005). Standard errors in brackets are adjusted by the
methodology by Feenstra and Hanson (1999). All regressions are
weighted by the average value of shipments in each industry over
the two time periods.

The symbols *, **, *** represent significance at the 1%, 5%, and
10% levels respectively.

TABLE 7
Stage 3 Estimation for Supplier Access

 (1) (2) (3)

Skilled labor share 0.4881 *** 0.5526 *** 0.3265 ***
 (0.1285) (0.1561) (0.1257)
 [0.1247] [0.1527] [0.1216]

Unskilled labor share -0.2813 *** -0.2398 ** -0.2048 **
 (0.0931) (0.1136) (0.0804)
 [0.0894] [0.1103] [0.0757]

Capital share 0.0568 *** 0.0516 ** 0.0606 **
 (0.0216) (0.0230) (0.0289)
 [0.0190] [0.0204] [0.0269]

Constant 0.0023 -0.0044 -0.0060
 (0.0145) (0.0143) (0.0065)
 [0.0140] [0.0138] [0.0053]

Stage 1 estimation OLS OLS PPML

Observations 387 387 387

[R.sup.2] 0.5805 0.5546 0.4019

Predicted change in skill 0.7694 0.7924 0.5314
 premium

Proportion explained 7.08% 7.29% 4.89%

 (4) (5) (6)

Skilled labor share 0.2870 * 0.3576 *** 0.3761 ***
 (0.1670) (0.1050) (0.1424)
 [0.1625] [0.1035] [0.1409]

Unskilled labor share -0.1527 * -0.2169 *** -0.1477 *
 (0.0864) (0.0753) (0.0809)
 [0.0801] [0.0738] [0.0790]

Capital share 0.0508 * 0.0418 ** 0.0357 **
 (0.0300) (0.0171) (0.0174)
 [0.0272] [0.0161] [0.0161]

Constant -0.0058 -0.0094 -0.0137
 (0.0080) (0.0067) (0.0087)
 [0.0066] [0.0064] [0.0084]

Stage 1 estimation PPML ET-Tobit ET-Tobit

Observations 387 387 387

[R.sup.2] 0.3869 0.4317 0.3871

Predicted change in skill 0.4398 0.5744 0.5238
 premium

Proportion explained 4.04% 5.28% 4.82%

Note: See Table 6 notes.