International Capital Movements and Relative Wages: Evidence from U.S. Manufacturing Industries

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 1980-90 and then again from 1996 to 2001. Between 2001 and 2005, net FDI flows have become substantially more volatile with large in-and 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 industry-level 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 1958-2005, 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, factor-specific technological change, and changes in labor endowments. We for­mulate a multi-sector 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 multi-sector SF models yields the

Figure 1: U.S. Inflows (+) and Outflows (-) of Net Foreign Direct Investment, 1950-2010.

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 non-production labor wage to average production labor wage in U.S. manufacturing industries, 1958-2005

change in the relative wage rate as a function of changes in international interest rates as well as changes in product prices, TFP growth, factor-specific technological progress, and labor endow­ment changes. Using estimates of factor-demand 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: 1958-66, 1967-81, 1982-2000, and 2001-05.

Our main results are as follows. First, the net capital outflow that U.S. manufacturing industries experienced during the period 1958-81 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 non-production 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 non-production 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 (factor-specific) 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 multi-sectoral 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, non-production labor (NP), is sector specific, i.e., immobile[7]. Production functions are continuous, twice differentiable, quasi-concave 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 non-production labor wages in the jth sector. The following set of equations represents the equilibrium conditions for this model:

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]:

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:

Next, zero-profit conditions are given by:

Using hat-calculus and denoting factor shares by , Equation (7) can be written as:

where  is a measure of TFP in sector j. To derive equation (8) we made use of the Wong-Viner Envelope Theorem, which implies that:

From the factor market clearing equations (1)-(2) we get:

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 sector-specific technological change (TFP) and to  as factor-specific technological change. Note that both these terms measure technological change holding factor prices constant. Re­placing  in equation (11) with (10) we get:

From equations (4)-(6) we get:

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:

where . With  Equation (16) can be rewritten as[11]:

Equation (17) together with equation (8) can be used to solve for  and . To do so, rewrite Equation (8) as: 

Using the above in equation (17) we get:

That gives us:

Using equation (20) we can solve for :

Using this solution in equation (18) we can solve for :

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 factor-specific as well as sector-specific 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, factor-specific 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, zero-profit conditions are given by:

where p, q denote prices and quantity respectively; K denotes the endogenously determined quantity of capital;  denotes the fixed quantity of sector specific non-production labor; and  denotes the mobile factor. r, w_P ,w_NPj denote returns to the factors of production. Market clearing for the mobile factor is given by:

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:

Here A₁ and A₂ are the sector specific (neutral) technological change parameters, while  represents factor specific (skill-biased) 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 Cobb-Douglas in 3 factors. As these parameters approach -1 we get greater substitutability than in the C-D case. Thus, for >  we get capital-skill complementarity. In both sectors, wages of mobile factors equal the value of their marginal product:

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

Table 1: Parameter Values

  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 1958-05. For example, the average ratio of production to non-production 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 non-production labor in sector 2 is 40%. Thus, production labor is used most intensively in sector 1, while non-production 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 capital-skill complementarity. Table 2 presents the simulation results.

Table 2: Simulation Results

  Source: Authors

For the benchmark simulation, we set the inter-industry capital ratio between sector 1 and 2 to .93, which implies an average non-production 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 non-production and production workers for a 10% increase in endowments, product prices, factor-specific 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; non-production labor specific technological progress; TFP growth in sector 1; a higher price of good 1; an increase in interest rates; and larger endowment of non-production 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 skilled-labor 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 Stolper-Samuelson 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):

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 NBER-CES Manufacturing Database [29]. This database contains annual information on all U.S. manufacturing industries from 1958 to 2005. At the 4-digit 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 factor-demand 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

                         Source: Authors

Several issues need to be discussed at this point. First, we use the production and non-production 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 non-production 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 cost-shares 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 1-6) presents estimates for changes in the proportion of the work force from 1973-88 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 co-movement 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 sector-specific 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 industry-specific 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, 1958-200

Source: Economic Report of the President, 2011. Table B-73.

Fourth, the empirical implementation of equation (33) requires data on international interest rates. An obvious choice, the 1-year 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 1982-05. 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 value-added 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 cost-shares 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 factor-demand elasticities (see Appendix A), we derive an estimate of  using the following equations[14]

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 zero-profit conditions so that all factor returns are indexed by j:

Rewriting the last equation yields:

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:

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 1958-05 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, 1958-66, 1967-81, 1982-2000, and 2001-05, correspond to different trends in the skill-premium.

Table 4: Observed and Predicted Average Annual Skill Premium Growth Rates

     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 sub-periods. Only for the 2001-05 subperiod does the model predict a further rise in the skill premium, while the actual skill premium declined. In terms of magnitudes, the model over-predicts 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 co-movement 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, 1958-2005

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 sub-periods, 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 sub-periods as well as the entire period.

Table 5: Decomposition of the Predicted Skill Premium Growth Rate

                             Source: Authors

Table 6: Decomposition of Individual Effects

     Source: Authors

Table 7: Contributions by Factor (in %) and Residual

                            Source: Authors