Authors
Department of Economics, Southern Methodist University, Dallas, USA
Abstract
Keywords
1. Introduction
The U.S. economy has witnessed a signiﬁcant increase in volatility and magnitude of international capital ﬂows since 1980, as shown in Figure 1. In addition, while there were moderate net outﬂows of capital prior to 1980, the U.S. economy experienced a strong net inﬂow of foreign direct investment (FDI)[1] between 198090 and then again from 1996 to 2001. Between 2001 and 2005, net FDI ﬂows have become substantially more volatile with large inand outﬂows. One of the interesting implications of this reversal in U.S. international capital ﬂows is its impact on the relative wages between skilled and unskilled workers, i.e. the skill premium. Provided that capital and skilled labor are complementary factors of production[2], net capital inﬂows constitute a positive demand shock for skilled labor causing a rise in the skill premium. Therefore, the reversal of international capital ﬂows in the 80s and the second half of the 90s is a potential culprit for the rise in the U.S. skill premium that began in the early 80s and peaked around 2001 (see Figure 2).
The issue of whether capital ﬂows cause changes in the skill premium has been examined in papers by Feenstra and Hanson [10], [11], [12], Sachs and Shatz [32], Eckel [8], Blonigen and Slaughter [4], Taylor and Driﬃeld [34] and Figini and G¨org [13],[14], among others. Feenstra and Hanson [10] and Sachs and Shatz [32] formulate theoretical models in which they examine the impact of capital outﬂows from a skilled labor abundant economy like the United States. In both papers the capital outﬂow occurs in the form of outsourcing intermediate goods production to an unskilled labor abundant economy. Both papers investigate empirically the relationship between import shares, employment levels, and factor intensity and arrive at similar conclusions: foreign investment is an important factor in explaining relative wage changes. Eckel [8] formulates a 3x2 trade model with eﬃciency wages and demonstrates how capital movements, and not wage rigidities, are responsible for an increase in wage inequality[3]. Feenstra and Hanson [11], Taylor and Driﬃeld [34], and Figini and G¨org [13], using industrylevel data for Mexico, the UK, and Ireland, respectively, ﬁnd that international capital ﬂows aﬀect the wage premium. Blonigen and Slaughter [4], in contrast, do not ﬁnd signiﬁcant eﬀects of FDI on U.S. wage inequality.
The goal of this paper is to study the impact of capital ﬂows on relative wages in the U.S. over the period 19582005, while at the same time taking account of other factors that potentially aﬀect relative wages such as international trade in goods and services, total factor productivity (TFP) growth, factorspeciﬁc technological change, and changes in labor endowments. We formulate a multisector speciﬁc factors (SF) model of a small open economy with perfectly mobile international capital[4]. The speciﬁc factor is skilled labor, while both capital and unskilled labor are mobile across sectors. Exogenous changes in the international interest rate trigger capital outﬂows and inﬂows in this model[5]^{ }. The solution to this multisector SF models yields the
Figure 1: U.S. Inﬂows (+) and Outﬂows () of Net Foreign Direct Investment, 19502010.
Source: BEA. Capital Inﬂows: FDI in the U.S.; Capital Outﬂows: U.S. Direct Investment Abroad (for years prior to 1977, Direct Investment Capital Outﬂows = Equity & Intercompany Accounts Outﬂows + Reinvested Earnings of Incorporated Aﬃliates). Numbers in Billion USD.
Figure 2: Ratio of average nonproduction labor wage to average production labor wage in U.S. manufacturing industries, 19582005
change in the relative wage rate as a function of changes in international interest rates as well as changes in product prices, TFP growth, factorspeciﬁc technological progress, and labor endowment changes. Using estimates of factordemand elasticities and data on the U.S. manufacturing sector from 1958 to 2005, we calculate the change in the skill premium as predicted by the model and compare the predicted with the actual change[6]. We then calculate the contribution to the predicted change by each of the exogenous forces. In addition to the full sample, we consider four subperiods: 195866, 196781, 19822000, and 200105.
Our main results are as follows. First, the net capital outﬂow that U.S. manufacturing industries experienced during the period 195881 had a depressing eﬀect on the skill premium. In contrast, the net capital inﬂows that occurred in the majority of years between 1981 and 2000 had a positive eﬀect on the skill premium. Second, trade eﬀects working through product price changes caused an increase in the skill premium for all periods. Third, increases in nonproduction labor endowments worked towards depressing the skill premium, as did a fall in production labor endowment. Fourth, production labor speciﬁc technical change increased the skill premium, while nonproduction labor speciﬁc technical change had the opposite eﬀect on the skill premium.
In terms of relative contributions, technology played the largest role in aﬀecting the skill premium, followed by changes in interest rates and product prices, which had approximately equal contributions. Labor endowment changes had the least relative impact on skill premium changes.
The ﬁnding of this paper that capital movements played a signiﬁcant role in aﬀecting relative wages in the U.S. provides strong empirical support for the theoretical results of Feenstra and Hanson [10], Sachs and Shatz [32], and Eckel [8]. In addition, our results reﬂect ﬁndings from two distinct strands of the skill premium literature. With the labor economics literature, such as papers by Berman, Bound and Griliches [2] and Berman, Bound and Machin [3], we share the conclusion that (factorspeciﬁc) technological change is likely to be one of the primary forces which increased the skill premium. Like certain papers from the empirical trade literature, such as Sachs and Shatz [31], Leamer [28], and Krueger [26], we concur that product price changes may have strongly contributed to the observed increase in the skill premium.
The paper is organized as follows. The theoretical model is derived in section 2. In section 3 and 4 we discuss model simulation results and data issues, respectively. We present our main results in section 5. Section 6 concludes.
2. The Theoretical Model
Our model is closely related to a class of models based upon the 2x3 SF model derived in Jones [18], which allow for international capital mobility (see, for instance, Thompson [35] and Jones, Neary and Ruane [21]). Our model is similar in this respect. However, it diﬀers signiﬁcantly in that it incorporates the multisectoral feature of an economy following Jones [19]. We consider a small open economy which produces m commodities in as many sectors of production. There are three factors of production in each sector. Two of these factors, capital (K) and production labor (P), are perfectly mobile between sectors, while the third factor, nonproduction labor (NP), is sector speciﬁc, i.e., immobile[7]. Production functions are continuous, twice diﬀerentiable, quasiconcave and exhibit diminishing returns to the variable factors. Domestic prices are exogenous and are assumed to be aﬀected by globalization shocks. Capital is also assumed to be perfectly mobile internationally. Its return is determined in world markets and is exogenous. Production sectors are indexed by j =1, ...., m, and factors of production are indexed by i = K, NP, P . Aggregate factor endowments are denoted by Vi. Thus, there are a total of m + 2 factors of production in the economy. Let aKj,aNPj,aPj denote the quantity of the three factors required per unit of output in the jth sector, i.e., aij denote unit input coeﬃcients. Let pj ,qj represent price and output of the jth sector and r, wNPj,and wP denote factor prices. Here r and wP denote the capital rental price[8] and production labor wages, respectively, while wNPj denotes nonproduction labor wages in the jth sector. The following set of equations represents the equilibrium conditions for this model:
(1) 

(2) 
The above equations are factor market clearing conditions for labor inputs. Notice that a similar condition does not hold for capital inputs. With perfect capital mobility, the small open economy facing exogenous capital returns faces an inﬁnitely elastic supply curve of capital. Demand conditions determine the amount of capital employed. Sectoral unit input coeﬃcients are variable and are subject to technological change. In particular, changes in these coeﬃcients can be decomposed as in Jones [20][9]:
(3) 
Here, denotes changes in input coeﬃcients as a result of changes in relative factor prices, while denotes exogenous technological progress (i.e., the reduction in the amount of factor i required to produce one unit of output j). Note that is a function of returns to sector speciﬁc factors as well as returns to the mobile factor:
(4) 

(5) 

(6) 
Next, zeroproﬁt conditions are given by:
(7) 
Using hatcalculus and denoting factor shares by , Equation (7) can be written as:
(8) 
where is a measure of TFP in sector j. To derive equation (8) we made use of the WongViner Envelope Theorem, which implies that:
(9) 
From the factor market clearing equations (1)(2) we get:
(10) 

(11) 
where represent the reduction in the use of production labor across all sectors. Note that is deﬁned as . Thus, we refer to in equation (8) as sectorspeciﬁc technological change (TFP) and to as factorspeciﬁc technological change. Note that both these terms measure technological change holding factor prices constant. Replacing in equation (11) with (10) we get:
(12) 
From equations (4)(6) we get:
(13) 

(14) 

(15) 
where for k = K, NP, P is deﬁned as the elasticity of cij with respect to changes in w_{k}, holding all other factor prices constant[10].
To solve this model for mobile factor prices, substitute equations (14) and (15) in equation (12). This yields:
(16) 
where . With Equation (16) can be rewritten as[11]:
(17) 
Equation (17) together with equation (8) can be used to solve for and . To do so, rewrite Equation (8) as:
(18) 
Using the above in equation (17) we get:
(19) 
That gives us:
(20) 
Using equation (20) we can solve for :
(21) 
Using this solution in equation (18) we can solve for :
(22) 

(23) 
Before proceeding to the next section, certain characteristics of the above solution in equation (23) should be considered. First, changes in sectoral skill premiums are functions of interest rate changes, product price changes, changes in labor endowments, and factorspeciﬁc as well as sectorspeciﬁc technological change. Second, changes in the skill premium also depends on factor intensities ( ) and factor elasticities (λ) in all sectors. Third, without making unreasonable ad hoc assumptions about these intensities and elasticities, it is not possible to determine the sign of the partial derivatives of the sectoral skill premium ( ) with respect to the exogenous variables.
3. Simulation Results
In this paper, we are interested in how the changes in the skill premium ( ) respond to changes in interest rates, product prices, TFP growth, factorspeciﬁc technological change, and changes in labor endowments. Since the analytical partial derivatives of the sectoral skill premium with respect to the exogenous parameters cannot be signed without strong assumptions, we compute instead a numerical solution for a simpliﬁed version of the above model. Based on these simulations, it is straightforward to ﬁnd the sign and magnitude of the skill premium change with respect to the diﬀerent parameter changes.
For the numerical simulations, we reduce the number of sectors to two, denoted by 1 and 2. For the two sectors, zeroproﬁt conditions are given by:
(24) 

(25) 
where p, q denote prices and quantity respectively; K denotes the endogenously determined quantity of capital; denotes the ﬁxed quantity of sector speciﬁc nonproduction labor; and denotes the mobile factor. r, w_{P} ,w_{NP}j denote returns to the factors of production. Market clearing for the mobile factor is given by:
(26) 
Output in the two sectors is determined via a ‘nested’ CES production function as proposed by Krusell et al [23]. The advantage of using such a speciﬁcation is that it allows for varying elasticity of substitution between factors of production:
(27) 

(28) 
Here A_{1} and A_{2} are the sector speciﬁc (neutral) technological change parameters, while represents factor speciﬁc (skillbiased) technical change. µ and denote the share parameters. In this speciﬁcation the elasticity of substitution between and K is identical to the elasticity of substitution between and . This is given by The elasticity of substitution between K and is given by . Here , . If then we have a CobbDouglas in 3 factors. As these parameters approach 1 we get greater substitutability than in the CD case. Thus, for > we get capitalskill complementarity. In both sectors, wages of mobile factors equal the value of their marginal product:
(29) 

(30) 
Finally, in both sectors the marginal product of capital must equal the exogenously determined interest rate:
(31) 

(32) 
Table 1: Parameter Values
.33 
.20 
270 
1 
1 

.66 
.55 
100 
1 
1 

.55 
.50 
100 
1 
1 
Source: Authors
The parameter values used in the simulated models are given in Table 1. These values were chosen to mimic the values of relative prices and quantities for the U.S. manufacturing industries for average values over the period 195805. For example, the average ratio of production to nonproduction workers in U.S. manufacturing industries for this period is 2.7, which is the number we use in our simulations. The revenue share for production labor in sector 1 is assumed to be 55%, while that for nonproduction labor in sector 2 is 40%. Thus, production labor is used most intensively in sector 1, while nonproduction labor is used most intensively in sector 2(Factor intensity is deﬁned as follows: sector 1 uses factor P intensively and sector 2 uses factor NP intensively iﬀθ_P1⁄(θ_P2>θ_NP1⁄θ_NP2 )). The elasticities of substitution among factors were chosen following Johnson [17] such that they reﬂect capitalskill complementarity. Table 2 presents the simulation results.
Table 2: Simulation Results

Base 

315 
7.7 
9.0 
0.9 
9.0 
0.9 
1.6 
3.4 
6.9 
3.7 
3.4 
6.9 
3.7 

339 
7.9 
1.2 
9.8 
1.2 
9.8 
1.4 
0.3 
0.3 
9.6 
0.3 
0.3 
9.6 

.50 
0.9 
10.3 
0.7 
10.3 
0.7 
0.8 
7.3 
2.3 
3.0 
2.5 
2.3 
2.9 

.55 
3.6 
15.3 
1.4 
15.3 
1.4 
3.6 
5.7 
4.8 
6.0 
5.7 
4.7 
6.0 

.76 
4.1 
2.0 
16.8 
2.0 
16.8 
4.1 
0.5 
0.5 
9.3 
0.5 
0.5 
0.6 

205 
1.2 
2.6 
1.7 
12.8 
1.7 
1.1 
6.7 
4.0 
7.0 
6.7 
4.0 
7.0 

126 
2.4 
2.4 
4.9 
2.4 
15.4 
2.3 
0.7 
0.6 
9.2 
0.7 
0.6 
9.2 

238 
0.2 
2.1 
2.7 
2.1 
2.7 
0.1 
0.7 
0.5 
10.9 
10.7 
0.5 
10.9 

32.2 
1.1 
15.7 
19.8 
15.7 
19.8 
1.0 
5.0 
3.9 
4.7 
4.5 
3.9 
4.7 

1.10 
2.8 
4.6 
2.1 
4.6 
2.1 
2.7 
1.5 
2.5 
8.6 
8.4 
6.8 
8.6 

1.52 
3.3 
11.2 
16.1 
11.2 
16.1 
3.2 
6.3 
2.7 
6.3 
3.1 
2.7 
3.4 

1.31 
3.1 
4.6 
8.4 
4.5 
8.4 
3.0 
4.3 
0.5 
0.2 
5.3 
4.4 
5.7 
Source: Authors
For the benchmark simulation, we set the interindustry capital ratio between sector 1 and 2 to .93, which implies an average nonproduction to production wage ratio of 1.31. This number is close to the actual ratio of 1.61 (the average ratio for U.S. manufacturing industries over the sample period). In Table 2, we present the change in the skill premium (sectoral as well as average) between nonproduction and production workers for a 10% increase in endowments, product prices, factorspeciﬁc technological change, interest rates and TFP growth. The forces that cause an increase in the skill premium are: an increase in the endowment of production labor; an increase in product price of sector 2; TFP growth in sector 2; and capital speciﬁc technological progress. In contrast, the skill premium falls with production labor speciﬁc technological progress; nonproduction labor speciﬁc technological progress; TFP growth in sector 1; a higher price of good 1; an increase in interest rates; and larger endowment of nonproduction labor.
The critical conclusion to be drawn from these results regards the change in the skill premium due changes in the interest rates. We ﬁnd that the average skill premium declines by less than 10%. Thus, for parameters chosen in the benchmark case there is an inverse relationship between interest rate changes and the skill premium. Recalling that interest rate increases are an indicator for capital outﬂows, this decline in the skill premium is expected as with less capital, the demand for skilled workers decline. Also note that an increase in the price of good 2 (the skilledlabor intensive good) causes a rise in the skill premium, while an increase in the price of the unskilled labor intensive good implies a decline in the premium. Therefore, the model predicts StolperSamuelson type eﬀects of product price changes as well.
4. Data
To obtain the equilibrium factor price changes, we ﬁrst write out the full system of equilibrium equations as given in (8) and (20):
(33) 
To calculate the factor price changes, we need data for the elements of the LHS vector and the RHS matrix. The data set we use is the latest version of the NBERCES Manufacturing Database [29]. This database contains annual information on all U.S. manufacturing industries from 1958 to 2005. At the 4digit 1972 SIC level there are 448 industries. Due to missing data, we exclude SIC 2384, 2794 and 3292 from our analysis. Note that all growth rates in period t are deﬁned as the change between period t + 1 and t relative to period t (see Leamer [28] for a similar deﬁnition). Growth rates are thus forward looking. As a result, we lose observations for 2005. The λ variables in the matrix above are functions of factordemand elasticities. These elasticities are not directly observed and must be estimated. A detailed description of how we estimate these elasticities is given in Appendix A. Appendix B contains a brief description of how we construct the remaining variables. Table 3 provides descriptive statistics for the key exogenous variables, and for the actual factor price changes observed in the data. Note that while some of the statistics are computed by pooling over all industries and over the entire sample period, others are computed by pooling over industries only.
Table 3: Descriptive Statistics
variable 
Mean 
S.D. 
Min 
Max 
Obs. 
.015 
.0515 
.7009 
.98 
20492 

.0064 
.0405 
.9321 
1.7659 
20492 

.0065 
.0379 
.9262 
1.7382 
20492 

.0357 
.0317 
.0397 
.112 
47 

.0354 
.0464 
.0947 
.1453 
47 

.0044 
.0396 
.1017 
.0589 
47 

.002 
.0265 
.065 
.0491 
47 

.0478 
.056 
.5859 
1.4518 
20492 

.0543 
.1553 
.9250 
12.22 
20492 

.011 
.0965 
.1831 
.2788 
47 
Source: Authors
Several issues need to be discussed at this point. First, we use the production and nonproduction labor classiﬁcation from the NBER data set as a proxy for unskilled and skilled workers. This approximation has been criticized on the grounds that production worker category may include workers with high education levels or skills, while the group of nonproduction workers may include workers with low education levels or skills. However, we maintain this classiﬁcation since it is a reasonable approximation used widely in the literature. In addition, results by Kahn and Lim [22] show a high correlation between costshares based on the two classiﬁcation schemes indicating that the two schemes are close substitutes. Second, due to the lack of (manufacturing) sector speciﬁc data on labor endowments, we use growth rates of observed labor employment instead. Kosters [25] (Table 16) presents estimates for changes in the proportion of the work force from 197388 for workers with 12 years of education or less, and for workers with 16 or more years of education. Translated into annual growth rates, his estimates show that the endowment of skilled and unskilled workers grew at a rate of .0076 and .0048, respectively. The corresponding growth rates for skilled and unskilled workers using average manufacturing employment data are .0078 and .0104, respectively. The substantial comovement between the change in labor endowments and the change in employment indicates that the approximation error is likely to be small. Third, capital factor shares are computed as 1 minus labor and materials factor shares, i.e., as a residual. This implies that our deﬁnition of capital factor shares includes payments to other sectorspeciﬁc assets as well and is thus larger than the true capital share. Similarly, since we do not have data on the quantity of these other assets or on industryspeciﬁc depreciation rates and consumption of ﬁxed capital, we compute the ex post rental price of capital as value added less total labor compensation divided by the capital stock ( Errors in the NBER dataset resulted in a negative rental price of capital for a few industries. These values were arbitrarily ﬁxed at an uniform rate of 10%.). Compared to the true rental price of capital, our computed one is upward biased.
Figure 3: Moody’s Baa rate, 1958200
Source: Economic Report of the President, 2011. Table B73.
Fourth, the empirical implementation of equation (33) requires data on international interest rates. An obvious choice, the 1year London Interbank Oﬀer Rate on U.S. Dollar Deposits (LIBOR), is not available for the entire sample period. We therefore use a close proxy (see Figure 3), the Moody’s Baa series[12], which is also used by Feenstra and Hanson [12][13]. This measure yields a positive average annual growth rate of 1.1% over the sample period and a negative average growth rate of 3.3% during 198205. According to the international capital ﬂow mechanism outlined earlier, these growth rates are consistent with observed ﬂows for the manufacturing sector, i.e., net outﬂows prior to 1982 and mostly net inﬂows in subsequent years. Fifth, our theoretical model does not include intermediate inputs. In the empirical analysis, we account for the impact of intermediate inputs on product prices by deriving a valueadded price change measure. This is done, as in Leamer [28], by subtracting from the vector of product price changes the inner product of a diagonal matrix with material costshares on its main diagonal and a vector of growth rates of material deﬂators. Sixth, according to equation (3), changes in unit input coeﬃcients can be decomposed into changes due to factor price variations (holding technology constant) and changes due to technological progress (holding factor prices constant). Since we only observe in the data, we proceed by constructing an estimate for and then use (3) to construct a measure of ^{ }Using the estimated factordemand elasticities (see Appendix A), we derive an estimate of using the following equations[14]
(34) 

(35) 

(36) 
^{ }
where is the predicted value of [15].
Finally, the assumption of perfect mobility of procij bduction labor (and capital, for our second model) across sectors is a potential source of error when we apply our model to the data. This is due to the fact that in the data, returns for these two factors of production vary across sectors. To adjust for this empirical fact, we proceed as in Feenstra and Hanson [12] and modify the zeroproﬁt conditions so that all factor returns are indexed by j:
(37) 
Rewriting the last equation yields:
(38) 
Equation (38) is identical to equation (8) except for the extra term on the RHS[16]. Following Feenstra and Hanson we add these two terms to and call the resulting expression eﬀective TFP, . Thus we have:
(39) 
With these caveats in mind, we calculate the predicted skill premium growth rate as the manufacturing sector average of diﬀerences between and , followed by a decomposition of the total eﬀect into the changes caused by globalization, endowment, and technological change. To calculate the impact of a particular factor, say product price change, we set all other exogenous variables in the LHS vector of (33), i.e., , and to zero.
5. Model Predictions and Decomposition
Our main results are presented in Table 4. All numbers are averages of annual growth rates. Over the sample period from 195805 the skill premium in U.S. manufacturing industries grew at a modest rate of .11% per year. The skill premium growth rates reported for the four subperiods, 195866, 196781, 19822000, and 200105, correspond to diﬀerent trends in the skillpremium.
Table 4: Observed and Predicted Average Annual Skill Premium Growth Rates
Years 
Observed 
Predicted 
Correlations 
195805 
.0011 
.0279 
.1017 
195866 
.0049 
.0493 
.1268 
196781 
.005 
.0331 
.1158 
198200 
.0072 
.0555 
.1867 
200105 
.0133 
.0777 
.5136 
Source: Authors
Comparing the actual growth rates with the growth rates predicted by our model, we ﬁnd that the model correctly predicts the direction of changes for the entire sample period and for three of the four subperiods. Only for the 200105 subperiod does the model predict a further rise in the skill premium, while the actual skill premium declined. In terms of magnitudes, the model overpredicts for the entire period (2.8% predicted growth as compared to .11% actual growth) as well as for each of the subperiods. The correlation coeﬃcients reported in the last column of Table 4 reveal that the comovement between the predicted and actual growth rates is fairly low except for the ﬁnal subperiod. Figure 4 depicts the observed and predicted growth rates for the entire period. The diﬀerence in magnitude between the volatile predicted values and the rather smooth observed skill premium values is clearly visible from this ﬁgure.
Figure 4: Actual and Predicted Skill Premium Growth Rates in U.S. Manufacturing
Industries, 19582005
Source: Authors
Table 5 contains the decomposition of the predicted skill premium growth rates. Globalization (i.e., product price changes and interest rate changes) had a positive eﬀect on the skill premium for the entire period as well as for the periods after 1981. The impact of technological change mirrors that of globalization, while endowment changes, for the entire period and for all subperiods, caused a decline in the skill premium.
To better understand the impact of changes of these three broad categories on the skill premium, we further decompose each category into their constituent parts (see Table 6). The striking result which emerges from this decomposition is that interest rate changes had a positive eﬀect on the skill premium from 1982 onward. As mentioned earlier, this is exactly the period when capital inﬂows started to become the norm. Globalization working through product price changes had a positive eﬀect on the skill premium for all subperiods as well as the entire period.
Table 5: Decomposition of the Predicted Skill Premium Growth Rate
Years 
Globalization 
Technology 
Endowments 
195805 
.0368 
.0071 
.0159 
195866 
.0231 
.0748 
.0023 
196781 
.0048 
.0044 
.0327 
198200 
.076 
.0154 
.0051 
200105 
.1413 
.0287 
.0349 
Source: Authors
Table 6: Decomposition of Individual Eﬀects

Globalization 
Technology 
Endowments 

Years 
Price 
Interest rate 
TFP 
P specific 
NP specific 
P labor 
NP labor 
195805 
.0436 
.0068 
.0101 
.0567 
.0395 
.0072 
.0087 
195866 
.0059 
.0249 
.0639 
.0651 
.0543 
.0303 
.0327 
196781 
.0613 
.0662 
.0232 
.0306 
.003 
.012 
.0207 
198200 
.0435 
.0325 
.0271 
.064 
.0523 
.007 
.0018 
200105 
.0718 
.0696 
.0473 
.1014 
.0829 
.0748 
.0399 
Source: Authors
Table 7: Contributions by Factor (in %) and Residual

Explained Variation: Contribution by Factor 
Residual 

Years 
Price 
Interest Rate 
Technology 
Endowments 

195805 
25.5 
27.2 
31.2 
16.0 
49.5 
195866 
23.5 
19.5 
36.8 
20.2 
49.5 
196781 
28.5 
27.7 
29.3 
14.5 
51.4 
198200 
29.0 
28.3 
30.9 
11.8 
47.9 
200105 
40.0 
20.4 
28.9 
10.7 
42.8 
Source: Authors
As expected, the observed decrease in the endowment of production workers had a negative eﬀect on the predicted skill premium over the full sample period, as did the increase in the number of nonproduction workers[17]. Similar changes in the supply of production and nonproduction workers for the various subperiods explain the pattern of skill premium changes shown in the last two columns of Table 6. Production labor speciﬁc technological change had a positive eﬀect on the skill premium for the full sample as well as during each subperiod, while nonproduction labor speciﬁc technical change lowered the skill premium in all periods. Interestingly, except for one subperiod (195866), TFP growth always contributed to a decline in the skill premium.
Table 7 presents the relative contribution to the explained variation by each factor as well as the residual (unexplained variation)[18]. While we report shares for price and interest rate changes separately, the shares for technology and endowments are reported as an aggregate over their components. The numbers for the residual shares show that for the entire sample period, as well as most subperiods, approximately 50% of the observed variation in the skill premium is explained by the model. The explained variation breaks down as follows. Interest rate and product price changes each account for roughly a quarter of the predicted changes in the skill premium. Technology accounts for 31%, while labor endowment changes account for 16%. These relative contributions do not vary drastically over the four subperiods. However, the impact of product price changes appears to increase over time, while that of labor endowment changes seems to decline[19].
6. Summary and Conclusions
This paper contributes to the globalization and wage inequality literature in two ways. First, by assuming that interest rates are determined in the world market, we allow for capital to be an endogenous variable that is mobile internationally. Thus, we provide direct empirical evidence on the eﬀects of international capital movements on relative wages. Second, by using a multisector speciﬁcfactors model which we apply to U.S. manufacturing data, we avoid the ‘factorprice’ insensitivity result of the HeckscherOhlin model. Therefore, we are able to provide evidence on the relative impact of globalization, technological progress (sector and factorspeciﬁc), and labor endowment changes on movements in the U.S. skill premium.
Several results emerge from our analysis. First, the net capital outﬂow that occurred during the period 195882 had a depressing eﬀect on the skill premium. In contrast, the net capital inﬂows that were prevalent between 1981 and 2001 had a positive eﬀect on the skill premium. Second, globalization eﬀects working through product price changes caused an increase in the skill premium for all periods. Third, increases in nonproduction labor endowments worked towards depressing the skill premium, as did the decline in the supply of production workers. Fourth, production labor speciﬁc technical change increased the skill premium, while nonproduction labor speciﬁc technical change and TFP growth reduced the skill premium. Finally, in terms of relative contributions, globalization eﬀects, working through changes in interest rates and product prices, had the biggest impact on the skill premium, followed by technology, while labor endowment changes had the least relative impact on skill premium changes.
There are two possible explanations for the large diﬀerences in magnitude between the actual and predicted skill premium growth rates. First, our model does not take into account capital market imperfections, impediments to capital mobility, and risk and uncertainty with respect to foreign direct investment. This may lead to biased predictions. Second, in some sectors such as autos and chemicals, the U.S. may be considered a large economy with potential market power. For these sectors the user cost of capital is likely to be determined in domestic markets rather than being set on world markets as assumed in our model.
The analysis presented in this paper lends itself to several extensions. The model could be easily applied to data for other countries, just as ‘mandatedwage regression’ analysis of U.S. industries was later applied to wage inequality issues in countries such as the UK and Sweden. Another extension would be to include service sector industries in the empirical analysis, as U.S services sectors have witnessed signiﬁcant capital inﬂows since the early ’80s as well.
Appendix A
To calculate the predicted skill premium in equation (33), we need values for . Since ,we can use equations (3) for . Since , we can use equation (3) and (13)(15) to write the following:
(40) 
Moving the term to term to the right, holding technology constant, i.e., , and indexing factor returns to labor by sector j, we get:
(41) 
The on the RHS of this equation are factor demand elasticities. Following the labor demand literature, summarized in Hamermesh [16], we estimate these elasticities with the following model[20]:
(42) 
where is the error term. As noted in the literature (see Roberts and Skouﬁas [30]) equation (42) must be estimated in long timediﬀerences to avoid the potential errorsinvariables problem. Accordingly, we estimate (42) using 10year time diﬀerences. We consider two diﬀerent speciﬁcations. In the ﬁrst speciﬁcation, we use crosssectional data and estimate the elasticities for each year from 196894. In the second speciﬁcation, we use a panel data approach and estimate the above equation with time and industry dummies. For both speciﬁcations, we impose two constraints: and . Since the second speciﬁcations yields implausible results for some own price elasticities, we use the ﬁrst speciﬁcation. Averaging the yearly estimates from the ﬁrst speciﬁcation yields the following values for the demand elasticities [21]:
(43) 
As predicted by theory, all own price elesticities re negative. However, the symmetry condition does not hold. We did not impose this restriction in our elasticity estimations since it has been noted in the literature that such restrictions do not necessarily improve the eﬃciency of the estimates.
Appendix B
Here we describe the construction of the variables used in our analysis.
: Nonproduction labor wages = PAY PRODW
: Nonproduction employment = EMP PRODE
: User cost of capital for jth industry = (VADDPAY)/CAP
r : Nominal interest rate on corporate bonds (Moody’s Baa, from ERP, 2011.)
: Growth rate of total production employment = growth rate of
: Growth rate of nonproduction employment in jth industry
: Share of jth industry in total production labor force = PRODE/ PRODE
: equal to 1 by deﬁnition
: Revenue share of production labor for jth industry = PRODW/VSHIP
: Revenue share of nonproduction labor for jth industry = /VSHIP
: Materials revenueshare for jth industry = MATCOST/VSHIP
: growth rate of real valueadded
: growth rate of production laborinput coeﬃcient for industry j =( )
: growth rate of nonproduction laborinput coeﬃcient for industry j =( ) 
: growth rate of capitalinput coeﬃcient for industry j =( ) 
: Total factor productivity growth in jth industry = .
: Measure of factorspeciﬁc technological change for ith factor =
: growth rate of PIMAT for industry j
: adjustment term for intermediate inputs = product of an m*m matrix with materials revenueshare on its main diagonal with the m*1 vector of
: growth rate of PISHIP for industry
[1] Throughout this paper the terms FDI and capital ﬂows are used interchangeably
[2] See Griliches [15], amongst others, for empirical evidence supporting the capitalskill complementarity hypothesis
[3] De Loo and Ziesmer [7] formulate a speciﬁc factors model with international capital mobility. Two forms of globalization are examined: exogenous product price changes and exogenous changes in interest rates. However, the model does not classify labor inputs as skilled or unskilled and thus does not address the skill premium issue
[4] For a discussion of why the SF model is an appropriate framework for analyzing the globalization and relative wage issue, see Engerman and Jones [9]. Also note that Kohli [24] contrasts the predictive capability of a SF model with a HO model and ﬁnds the former better suited to analyze U.S. data.
[5] In particular, an increase (decrease) in the world interest rate leads to an instantaneous outﬂow (inﬂow) of capital from the economy.
[6] The literature on globalization and wage inequality deals primarily with U.S. manufacturing industries, mainly due to the unavailability of disaggregated wage data for skilled and unskilled workers in nonmanufacturing industries. As Figure 1 reveals, the manufacturing sector has experienced, by and large, similar net capital ﬂows as the overall economy.
[7] Here nonproduction workers are assumed to be skilled, while production workers are assumed to be unskilled labor. Note that an alternative modeling strategy would have been to assume capital to be sector speciﬁc as well. We do not pursue this approach as accurate data on sector speciﬁc capital rental rates are not available.
[8] The terms ‘interest rate’, ‘user cost of capital’, and ‘capital rental price’ are used interchangeably in this paper.
[9] Here .
[10] Note that due to the zerohomogeneity of , and Further, by symmetry,
[11] Note that is the change in due to a change in the factor price of input i.
[12] Annual percent yield on corporate bonds (Moody's Baa: Economic Report of the President, 2011. Table B73). Note that this is an ex ante measure of the rental price of capital.
[13] For a small open economy, the domestic interest rate must be equated to the world interest rate. Therefore, changes in the domestic interest rate triggers off capital ows similar to those due to changes in the world interest rate.
[14] Note that there are two diﬀerences between (13)(15) and (34)(36). First, the returns to mobile factors are industryspeciﬁc in equations (34)(36). Second, the elasticities are now identical across industries. Both changes are necessary to be consistent with the estimation described in Appendix B.
[15] Note that for estimating elasticities, as well as for calculating use a sectoral usercost of capital measure.
[16] We construct wbP as the growth rate of average manufacturing factor returns to production labor
[17] The actual annual growth rates for production and nonproduction workers for the entire sample period are .4% and .2%, respectively.
[18] Note that the four contribution shares add up to 100. The contribution by each factor i is deﬁned as: . The residual share is deﬁned as: . This gives us the % of actual growth rate that is unexplained.
[19] The results shown in Table 7 are along the lines of those in Dasgupta and Osang [6]. However, that paper does not consider the effects of international capital flows.
[20] In the context of international trade and wage inequality, Slaughter [33] has estimated constantoutput factor demand elasticities using the same dataset that we use. However, he does not report these manufacturingwide elasticity estimates in his paper.
[21] Using time averaged instead of yearly estimates entails a tradeoff. It allows us to use a larger dataset to calculate (27), i.e., we avoid losing the years 195867. The cost is that we need to assume that the actual elasticites we are trying to estimate are timeinvariant, i.e., .