Free trade and income redistribution in a three factor model of the U.S. economy.

• Author: Thompson, Henry

1. Introduction

   The move toward free trade promises to alter the distribution of income in the U.S. Labor groups generally do not favor the move toward free trade, which can be characterized by the continuing decline in the price of manufactured goods relative to business services. The present study predicts that unskilled labor in the U.S. will lose under a program of free trade, using a general equilibrium model of production. Factor shares, industry shares, and estimates of substitution for skilled labor, unskilled labor, and capital are used to examine comparative statics.

   The interplay of factor intensity and factor substitution in the three factor production structure has proven a considerable analytical challenge. Building on the textbook production model with two factors, the third productive factor allows technical complementarity and creates a more complex pattern of factor intensity. Both factor intensity and factor substitution affect the qualitative nature of the comparative statics. Little is known about the model's quantitative properties. A 3 x 3 model with outputs of the three major sectors (agriculture, manufacturing, services) is specified, and a 3 x 2 model without agriculture is also examined.

   Factor substitution is estimated with production function across states. Skilled labor separated by various Census categories cannot be aggregated with unskilled labor in any sector, and constant returns to scale cannot be rejected as a null hypothesis. Additionally, the three inputs (capital, labor, skilled labor) are all technical substitutes.

   Comparative static results follow a pattern suggested by factor intensity. Changing prices of goods generally have elastic effects on factor prices. Stolper-Samuelson results, in other words, have a quantitative weight. Price changes due to a program of free trade will significantly affect income distribution. Similarly, Rybczynski type results are quantitatively significant in that factor endowment changes have elastic effects on outputs. The implication is that output patterns will differ significantly across freely trading partners.

   Elasticities of factor prices with respect to endowment changes, on the other hand, are very inelastic. This inelasticity suggests that there would only be small long run effects of international migration, capital flows, or endowment differences on the international pattern of factor income. This inelasticity is called near factor price equalization (NFPE).

   Under NFPE, freely trading countries will experience a vector of factor prices nearly equal to each other. NFPE suggests that the qualitative effects of changing or different factor endowments will be quantitatively trivial in the long run when there is competition, full employment, and flexible output adjustment. Factor prices will be nearly equal even when FPE does not strictly hold.

   Cobb-Douglas and constant elasticity of substitution (CES) technologies are also specified. A high degree of similarity is found across model specifications.

2. Summary of the General Equilibrium Model of Production and Trade

   The long run competitive model of production developed by Jones and Scheinkman [14], Chang [9], and Takayama [24] assumes constant returns to scale, full employment, nonjoint production, competitive pricing, cost minimization, and perfect factor mobility across sectors. The model is summarized in matrix form by

   [Mathematical Expression Omitted] (1)

   where w represents (a vector of) endogenous factor prices, x endogenous outputs, v exogenous factor endowments, p exogenous word prices of outputs facing the open economy, [Sigma] a square matrix of price elasticities of the aggregate factor demand functions, [Theta] a matrix of factor shares paid each factor from the revenue of each industry, [Lambda] a matrix of industry shares of each factor employed in each industry, 0 a null matrix, and ^ percentage changes.

   The top equation in (1) is derived from the full employment condition for each of the three productive factors. Full employment captures the long run after transitory adjustments have occurred. The bottom equation in (1) is derived from competitive pricing and cost minimization. The economy is assumed to be a price taker in the international markets for finished goods. At the high level of aggregation in the present study, this assumption is warranted even for an economy as large as the U.S.

   Comparative static results are local in nature and apply to small changes around an original equilibrium. The [Delta]w/[Delta]p Stolper-Samuelson elasticities and the [Delta]x/[Delta]v Rybczynski elasticities are symmetric in their signs due to Samuelson's reciprocity. Factor prices are affected by changes in endowments with prices of goods constant, as described by the [Delta]w/[Delta]v elasticity matrix.

3. Factor Shares, Factor Intensity, and Industry Shares

   Figures on employment are taken from a U.S. Census publication [27]. Skilled labor is specified as the two highest paid Census groups: managers and professionals, along with precision production, craft, repair. Translog estimation, tests of separability, and comparative static results of the model are insensitive to adding or deleting a Census group from the skilled labor category.

   The yearly wage of each group of labor is found by dividing its portion of national income by the number of workers in the group. Imputed yearly wages are $16,833 for skilled labor and $9,971 for unskilled labor. The residual of national income is allotted to capital. Depreciable capital stock figures for manufacturing and agriculture are taken from U.S. Census publications [28; 29]. Based on the total capital stock, capital is paid an average of 15.2%.

   Inputs and outputs are valued in dollars. Factor input is the dollar value of factor i used in sector j,

   [W.sub.ij] [equivalent] [W.sub.i][V.sub.ij], (2)

   where [W.sub.i] is the price of factor i and [V.sub.ij] is the quantity of factor i used in sector j. Index i runs across the three inputs capital (k), unskilled labor (u), and skilled labor (s). The share of factor i in sector j is calculated as

   [[Theta].sub.ij] [equivalent] [W.sub.ij]/[Y.sub.j] (3)

   where [y.sub.j] is the total revenue of sector j.

   Let g represent agricultural output, m manufacturing, and c services. The derived factor share matrix [Theta] is

   [Mathematical Expression Omitted] (4)

   Factor intensity...