Free trade and income redistribution in a three factor model of the U.S. economy.
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 manufactured goods npl → manufacturas fpl; bienes mpl manufacturados
manufactured goods npl → produits manufacturés 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 General equilibrium theory is a branch of theoretical microeconomics. It seeks to explain production, consumption and prices in a whole economy.
General equilibrium tries to give an understanding of the whole economy using a bottom-up approach, starting with individual model of production. Factor shares, industry shares, and estimates of substitution for skilled labor, unskilled labor, and capital are used to examine comparative statics Comparative statics is the comparison of two different equilibrium states, before and after a change in some underlying exogenous parameter. As a study of statics it compares two different unchanging points, after they have changed. .
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 com·ple·men·tar·i·ty
1. The correspondence or similarity between nucleotides or strands of nucleotides of DNA and RNA molecules that allows precise pairing.
2. 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 null hypothesis,
n theoretical assumption that a given therapy will have results not statistically different from another treatment.
n . 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 Adv. 1. in other words - otherwise stated; "in other words, we are broke"
put differently , 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 The introduction to this article provides insufficient context for those unfamiliar with the subject matter.
Please help [ improve the introduction] to meet Wikipedia's layout standards. You can discuss the issue on the talk page. 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 inelastic
Of or relating to the demand for a good or service when quantity purchased varies little in response to price changes in the good or service. . This inelasticity in·e·las·tic
Lacking elasticity; unyielding or unadaptable. See Synonyms at stiff.
ine·las·tic 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 Factor price equalization is an economic theory, which states that the relative prices for two identical factors of production in the same market will eventually equal each other because of competition. (NFPE NFPE Non Financial Public Enterprise
NFPE Non-Feedback Proportional Electric Control
NFPE National Fire Protection Engineering ).
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 FPE Final Prediction Error
FPE Floating Point Exception (a computer math error)
FPE Fokker-Planck Equation
FPE Fire Protection Engineering
FPE Free Primary Education (Africa) does not strictly hold.
Cobb-Douglas and constant elasticity of substitution In economics, more specifically econometrics or mathematical economics, there are production functions that describe the output given a certain combination of inputs (e.g. labour and capital). (CES) technologies are also specified. A high degree of similarity is found across model specifications.
II. Summary of the General Equilibrium Model of Production and Trade
The long run competitive model of production developed by Jones and Scheinkman , Chang , and Takayama  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 A group of characters or symbols representing a quantity or an operation. See arithmetic expression. Omitted] (1)
where w represents (a vector of) endogenous endogenous /en·dog·e·nous/ (en-doj´e-nus) produced within or caused by factors within the organism.
1. Originating or produced within an organism, tissue, or cell. factor prices, x endogenous outputs, v exogenous Exogenous
Describes facts outside the control of the firm. Converse of endogenous. factor endowments, p exogenous word prices of outputs facing the open economy, [Sigma] a square matrix of price elasticities Price elasticities
The percentage change in quantity divided by a percentage change in the price. Answers the question: How much will the demand for my product decrease if I raise prices by 10%? 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 TRANSITORY. That which lasts but a short time, as transitory facts that which may be laid in different places, as a transitory action. 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 Price Taker
1. An investor whose buying or selling transactions are assumed to have no effect on the market.
2. A firm that can alter its rate of production and sales without significantly affecting the market price of its product.
1. 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 reciprocity
In international trade, the granting of mutual concessions on tariffs, quotas, or other commercial restrictions. Reciprocity implies that these concessions are neither intended nor expected to be generalized to other countries with which the contracting parties . Factor prices are affected by changes in endowments with prices of goods constant, as described by the [Delta]w/[Delta]v elasticity matrix.
III. Factor Shares, Factor Intensity, and Industry Shares
Figures on employment are taken from a U.S. Census publication . 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 sep·a·ra·ble
Possible to separate: separable sheets of paper.
sep , 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 Attributed vicariously.
In the legal sense, the term imputed is used to describe an action, fact, or quality, the knowledge of which is charged to an individual based upon the actions of another for whom the individual is responsible rather than on the individual's yearly wages are $16,833 for skilled labor and $9,971 for unskilled labor. The residual of national income is allotted al·lot
tr.v. al·lot·ted, al·lot·ting, al·lots
1. To parcel out; distribute or apportion: allotting land to homesteaders; allot blame.
2. to capital. Depreciable depreciable
Of, relating to, or being a long-term tangible asset that is subject to depreciation. 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 is described by ratios of these factor shares, since
[Mathematical Expression Omitted] (5)
where [a.sub.ij] represents the cost minimizing amount of factor i used per unit of output in sector j. Factor intensity must be analyzed bilaterally across all three pairs of industries. The three sets of factor intensity rankings are:
[Mathematical Expression Omitted] (6)
Capital, which implicitly includes land, is consistently used most intensively in agriculture, and least intensively in manufacturing. Skilled labor is the least intensive input in agriculture. The service sector uses both skilled labor and capital intensively.
Industry shares [[Lambda].sub.ij] are defined as [v.sub.ij]/[v.sub.i], representing the portion of factor i employed in sector j. These industry shares are calculated as
[[Lambda].sub.ij] [equivalent to] [W.sub.ij]/[Y.sub.i], (7)
where [Y.sub.i] is the total income of factor i. Factors are assumed to be freely mobile and have equal prices across sectors. The model's derived industry share matrix [Lambda] in (1) is
[Mathematical Expression Omitted] (8)
Although agriculture is consistently capital intensive, it employs only 10.3% of the capital stock. Agriculture employs very small percentages of labor. In the 3 x 2 model, agriculture is dropped from the specification. Services is the largest sector, employing more than 65% of every productive factor. The service sector employs about three times as much capital and skilled labor as does manufacturing, and about twice the unskilled labor.
IV. Translog Estimates of Technical Substitution
Estimates of aggregate factor price elasticities in the matrix a complete specification of the model in (1). Little such technical work has been done in services, the predominant and growing sector of the U.S. economy.
Each sector's production function is specified as a translog Taylor series expansion,
[Mathematical Expression Omitted] (9)
where x is output, [v.sub.i]'s are inputs, [Alpha]'s and [Gamma]'s are technical coefficients, and i, h = k, s, u.
A system of factor share equations is derived directly from (9),
[S.sub.i] = [[Alpha].sub.i] + [summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) over i] [[Gamma].sub.ij] ln [v.sub.k] + [[Delta].sub.i]x (10)
This system of factor share equations is estimated using iterative it·er·a·tive
1. Characterized by or involving repetition, recurrence, reiteration, or repetitiousness.
2. Grammar Frequentative.
Noun 1. Zellner generalized least squares. Allen elasticities of substitution ([S.sub.ih]) are found by inverting the bordered Hessian matrix In mathematics, the Hessian matrix is the square matrix of second-order partial derivatives of a function. Given the real-valued function
Berndt and Christensen  point out that the estimation of the system in (10) assumes CRS CRS Course
CRS Certified Residential Specialist (real estate certification)
CRS Central Reservation System
CRS Can't Remember Stuff (polite form)
CRS Cost Reduction Strategy
CRS Consumer Relations Specialist and Hicks Hicks , Edward 1780-1849.
American painter of primitive works, notably The Peaceable Kingdom, of which nearly 100 versions exist. neutral technical change. As output expands along a linear expansion path, factor payments, unit inputs, and factor shares would all be unchanged, given homotheticity and constant returns. These assumptions can be tested by including an output coefficient in the estimation. The system
[S.sub.i] = [[Alpha].sub.i] + [summation over i] [[Gamma].sub.ij] ln [v.sub.k] + [[Delta].sub.i]x (11)
is estimated, and the null hypothesis [[Delta].sub.i] = 0 is tested. A Chi square chi square (kī),
n a nonparametric statistic used with discrete data in the form of frequency count (nominal data) or percentages or proportions that can be reduced to frequencies. test reveals that this null hypothesis cannot be rejected in any sector at a 90% confidence level.
Another preliminary test concerns the separability of inputs. A consistent aggregator function for any pair of the three inputs across sectors would indicate that the model could be simplified by reducing the number of inputs. The null hypothesis of nonlinear separability is, however, rejected at a 99% level of confidence except for (i) skilled labor and labor in services, and (ii) capital with both types of labor in agriculture. There is no evidence of separability in manufacturing, where the data is more detailed and estimation results strongest.
Because of a lack of data in the service sector, a Department of Commerce  estimate of the total capital stock in services is split among states assuming each employs the same ratio of capital to labor in services as in manufacturing. Estimates of each sector's factor share equations in (10) are presented in Table I. Factor share equations for skilled labor and unskilled labor are estimated in each of the three sectors. Capital's factor share equation is redundant since [[Gamma].sub.ik] = [[Gamma].sub.ki], [summation over k] [[Gamma].sub.ik] = 0, and [summation over k] [[Alpha].sub.k] = 1.
Estimated technical coefficients along with observed factor shares and industry shares are used to construct Allen elasticities and aggregate cross price elasticities. Jones and Easton  summarize properties of aggregate "super bowl" factor price elasticities [[Sigma].sub.ih], which represent the percentage change across the economy in the input of factor i for a 1% increase in the price of factor h. A positive (negative) [[Sigma].sub.ih] indicates aggregate technical substitution (complementarity).
The [[Sigma].sub.ih] are derived from the Allen elasticities of substitution [S.sub.ih]. Let [Mathematical Expression Omitted] represent the factor [TABULAR DATA FOR TABLE I OMITTED] cross price elasticity in sector j. Sato and Koizumi  show that cost minimizing behavior implies
[Mathematical Expression Omitted] (12)
Sectoral elasticities are weighted by industry shares to derive the super bowl elasticities in matrix [Sigma]:
[Mathematical Expression Omitted] (13)
The degree to which items are similar. implies that rows of the negative semidefinite matrix [Sigma] sum to zero. Estimated own elasticities [[Sigma].sub.ii] in the present data turn out to be negative, which means the undering cost functions are concave Concave
Property that a curve is below a straight line connecting two end points. If the curve falls above the straight line, it is called convex. in factor prices.
Three sets of sectoral elasticities are calculated from Table I using (12). In agriculture, the derived factor price elasticities are
[Mathematical Expression Omitted] (14)
The matrix of factor price elasticities in manufacturing is
[Mathematical Expression Omitted] (15)
and in services
[Mathematical Expression Omitted] (16)
There is noticeably less substitution between unskilled and skilled labor in agriculture than in the other two sectors. There is no complementarity in any sector. The largest own elasticities consistently occur for skilled labor, and the smallest for capital. Weighting these sectoral factor cross price elasticities as in (13) leads to the estimated matrix [Sigma] of aggregate super bowl translog elasticities:
[Mathematical Expression Omitted] (17)
V. Comparative Statics in the 3 x 3 Model
The 3 x 3 model, constructed from (4), (8), and (17), has the same number of productive factors and exogenous prices. The FPE result thus holds: [Delta]w/[Delta]v = 0.
Changing prices of goods affect factor prices in the 3 x 3 Stolper-Samuelson matrix:
[Mathematical Expression Omitted] (18)
These [Delta]w/[Delta]p effects follow a pattern suggested by the underlying factor intensity. The comparative static effects of a changing price run down each column. Every 1% increase in service prices, for instance, would create a 0.58% increase in the return to capital, a 9.95% increase in the wage of skilled labor, and a 7.02% decrease in unskilled wages. Every 1% decrease in manufacturing prices would raise skilled wages by 7.35%, while lowering unskilled wages by 7.85%.
Wages are very sensitive to changing prices in manufacturing and services. The large wage elasticities suggest that the move toward free trade in the U.S., characterized by a falling price of manufactured goods relative to business services, will noticeably hurt unskilled labor and help skilled labor. The return to capital would rise to a much smaller degree in the move toward free trade.
Rybcynski effects of changing factor endowments on outputs are
[Mathematical Expression Omitted] (19)
Again, results mirror factor intensities. Capital is strongly and positively tied to agriculture, unskilled labor to manufacturing, and skilled labor to services.
With prices constant, immigration immigration, entrance of a person (an alien) into a new country for the purpose of establishing permanent residence. Motives for immigration, like those for migration generally, are often economic, although religious or political factors may be very important. of unskilled workers amounting to 1% of the current total supply of unskilled workers would raise manufacturing output by 8.45% and agricultural output by 1.17%, while service output would fall 2.87%. Wages would not be affected by immigration of unskilled workers, but these effects are examined in a 3 x 2 model in the next section. Education would presumably pre·sum·a·ble
That can be presumed or taken for granted; reasonable as a supposition: presumable causes of the disaster. convert unskilled workers to skilled workers, raising output of services and decreasing manufacturing output.
A curious property of even models, those with same number of productive factors and exogenous prices is that the [Delta]w/[Delta]p and [Delta]x/[Delta]v elasticities are completely free of influence from the pattern of substitution. This property is not noted in the literature. No matter how the production functions are specified and whether complementarity or substitution dominates, the reported [Delta]w/[Delta]p and [Delta]x/[Delta]v comparative static elasticities would occur. These important comparative static results depend only on factor shares and industry shares.
VI. Near Factor Price Equalization in a 3 x 2 Model
The literature on the 3 x 2 model includes Jones , Burgess [6; 7], Batra and Casas , Ruffin , Suzuki , Jones and Easton , and Thompson . A 3 x 2 model is created by dropping agriculture out of the present 3 x 3 specification. There is some justification for such a move. Agricultural production is also tightly controlled and subsidized by government policy. Labor and capital may not readily move between agriculture and the rest of the economy. Also, agriculture is very small relative to the other sectors in the U.S. economy.
Factor shares in the 3 x 2 model are taken directly from the last two columns of (4). Factor intensity in the 3 x 2 model is exactly that of the last inequality in (6). Unskilled labor is the "extreme" input in manufacturing and capital is the extreme input in services, while skilled labor is the "middle" factor. Ruffin  shows that extreme factors are migration "enemies" in the 3 x 2 model, regardless of the pattern of technical substitution. An increase in the endowment of unskilled labor, in other words, will lower the return to capital, and vice versa VICE VERSA. On the contrary; on opposite sides. . The middle factor skilled labor is a migration "friend" of both extreme factors.
The 3 x 2 industry share matrix can be derived directly from (8) by disregarding the share of inputs employed in agriculture:
[Mathematical Expression Omitted] (20)
The dominance of the service sector is again very apparent. The 3 x 2 system in (1) under the assumption of translog production functions is constructed from (4), (14), (15), (16), and (20). The resulting matrix of substitution elasticities is
[Mathematical Expression Omitted] (21)
The substitution elasticities in (21) are very similar to those in (17), due to the small agriculture industry shares.
The [Delta]w/[Delta]v elasticities of the 3 x 2 model are
[Mathematical Expression Omitted] (22)
These elasticities of factor prices with respect to factor endowments are small, suggesting international capital flows and labor migration have little long run impact on factor prices. The own skilled labor effect, for instance, implies that every 1% increase in the endowment of skilled labor would lower the wage of skilled labor by only 0.305%. A 50% difference in the endowment of unskilled labor between two such freely trading countries would result in an estimated differences of only 0.15% in the wages of unskilled labor, 1.55% in capital returns, and 1.9% in skilled wages.
The inelasticity of these [Delta]w/[Delta]v terms is called near factor price equalization (NFPE). The assumption of complete output adjustment and free factor mobility between sectors contributes to NFPE. In this long run model with full employment, outputs adjust freely with changing factor endowments, while factor prices would be fairly stable due to NFPE. The economy is assumed to be a price taker in international markets, importing any excess demand and exporting any excess supply as factor endowments change.
While the 3 x 2 model does not lead to the FPE property between freely trading competitive countries, factor prices would not be far apart in the international equilibrium. Furthermore, NFPE is robust under different aggregation schemes. Econometric e·con·o·met·rics
n. (used with a sing. verb)
Application of mathematical and statistical techniques to economics in the study of problems, the analysis of data, and the development and testing of theories and models. studies such as Butcher and Card  and LaLonde and Topel  find little empirical evidence that immigration has any impact on income distribution.
VII. Cobb-Douglas and CES Production
Estimates of aggregate substitution elasticities can be formulated under the assumption of Cobb-Douglas (CD) or constant elasticity of substitution (CES) production using only factor shares and industry shares. These specifications allow a comparison of comparative static properties between the translog model and a production technology with well known properties.
Under the CD assumption, the Allen elasticity of substitution Elasticity of substitution is the elasticity of the ratio of two inputs to a production (or utility) function with respect to the ratio of their marginal products (or utilities). Mathematical definition
Let the utility over consumption be given by [Mathematical Expression Omitted] is equal to 1. Then [E.sub.ih] = [[Theta].sub.hj] from (12), and [[Sigma].sub.ih] = [summation over j] [[Theta].sub.ij][[Lambda].sub.hj] . The derived CD substitution matrix This page is about the concept in bioinformatics. For the economics concept also called the Slutsky matrix, see the article Slutsky equation.
In evolutionary biology, a substitution matrix in the three sector model is
[Mathematical Expression Omitted] (23)
The degree of substitution in the CD model is less than in the translog model in (7), especially for skilled labor and unskilled labor. For capital, the [[Sigma].sub.Ki] (i = k, s, u) terms are about 85% as large as those in the CD model. Similarly, the [[Sigma].sub.iK] elasticities of adjustments to a changing price of capital are 85% to 91% of those in the translog model. In contrast, the skilled and unskilled labor substitution are less than half (36% to 49%) of those in the CD model.
The [Delta]w/[Delta]v elasticities in the 3 x 2 CD model are uniformly slightly larger in absolute magnitude absolute magnitude: see magnitude. than those reported for the translog model in (22). The CD production isoquants are less convex Convex
Curved, as in the shape of the outside of a circle. Usually referring to the price/required yield relationship for option-free bonds. , and changing endowments within the production cone require slightly larger adjustment of the supporting isocost hyperplane.
Arbitrarily reducing the degree of substitution further with CES production increases the size of the [Delta]w/[Delta]v elasticities proportionately. For instance, an Allen elasticity of substitution of 0.5 causes the [Delta]w/[Delta]v terms to increase [(0.5).sup.-1] = 2 times. Over short time periods when there is little opportunity for substitution among factors, migration and international capital flows may thus have elastic effects on factor prices.
The [Delta]w/[Delta]p and [Delta]x/[Delta]v elasticities in the 3 x 2 CD model are also similar to those reported in the 3 x 3 translog model. Under CES or CD technology, these elasticities are identical in any model with one more type of factor than good. The [Delta]x/[Delta]v CES elasticities are similar in value to those in the 3 x 3 translog model, except for larger effects associated with skilled labor. In the CD model, there are more convex production isoquants and more output adjustment with changes in the endowment of skilled labor. Comparative static effects associated with a changing capital endowment are about 60% as large as those in the translog model. All models are generally insensitive in the comparative static adjustments associated with unskilled labor.
As the U.S. economy opens to free international trade with newly industrializing and developing countries, the relative price of manufactures will fall. The U.S. economy will continue its shift toward specialization in business services. Unskilled labor can expect to suffer in this move toward free trade, with capital and skilled labor projected winners. Learner  makes this point quite clearly.
There is some disagreement in the literature over the empirical issue of free trade and falling wages. Lawrence and Slaughter , Krugman and Lawrence , and Bhagwati and Dehejia  attribute most of the recent wage decline to changing technology rather than increasing trade. On the other hand, Sachs and Shatz , Batra and Slottje , and Learner  believe increasing trade is significantly contributing to falling wages in the U.S.
The present line of investigation can be extended to include more types of labor as well as energy inputs. Clark, Hofler, and Thompson  find that none of the nine labor skill groups in manufacturing can be aggregated, and studies with disaggregated Broken up into parts. labor yield more detailed results. Complementarity between energy and capital has been uncovered in some applied studies, at least over periods of falling energy prices. An important long term issue will be the shifting pattern of international production and trade due to rising energy prices.
Analysis is greatly simplified if all factors are weak substitutes. Qualitative comparative static results can then largely be anticipated from the pattern of factor intensity. Quantitative results in the general equilibrium economics of production are relatively insensitive to the degree of substitution.
The inelasticity of the effects of changing factor endowments on factor prices, near factor price equalization, emerges as a powerful conceptual tool. Factor prices would not differ much between competitive trading economies, even if some of the conditions leading to complete factor price equalization do not hold. Just as importantly, changes in the prices of goods are found to have elastic effects on factor prices.
There are two important quantitative lessons in this paper. First, the move toward free trade in the U.S. has the potential to substantially distribute income away from unskilled labor. Second, free trade will serve as a strong substitute for international migration and investment.
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3. Batra, Raveendra and David J David J. Haskins (b. April 24, 1957, in Northampton, England) is a British alternative rock musician. He was the bassist for the seminal gothic rock band Bauhaus. Life and work . Slottie, "Trade Policy and Poverty in the United States Poverty in the United States refers to people whose annual family income is less than a "poverty line" set by the U.S. government. Poverty is a condition in which a person or community is deprived of, or lacks the essentials for, a minimum standard of well being and life. : Theory and Evidence." Review of International Economics, October 1993, 189-208.
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7. -----, "Tariffs and Income Distribution: Some Empirical Evidence for the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. ." Journal of Political Economy, February 1976, 17-45.
8. Butcher, Kristin and David Card David Edward Card is a Canadian labor economist and professor at the University of California, Berkeley.
Card earned his B.A. from Queen's University in 1978 and his Ph.D. in Economics in 1983 from Princeton University. , "Immigration and Wages: Evidence from the 1980s." American Economic Review, May 1991, 292-96.
9. Chang, Winston W., "Some Theorems This is a list of theorems, by Wikipedia page. See also
10. Clark, Don P., Richard Hofler, and Henry Thompson, "Separability of Labor in US Manufacturing." Economics Letters Economics Letters is a scholarly peer-reviewed journal of economics that publishes concise communications (letters) that provide a means of rapid and efficient dissemination of new results, models and methods in all fields of economic research. Published by Elsevier. , No. 2, 1985, 197-201.
11. Hamermesh, Daniel and James Grant There have been several people named James Grant.
12. Jones, Ronald W. "A Three-Factor Model in Theory, Trade, and History," in Trade, Balance of Payments, and Growth, edited by Jagdish Bhagwati et al. Amsterdam: North Holland, 1971, pp. 3-21.
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14. ----- and Jose A. Scheinkman, "The Relevance of the Two-Sector Production Model in Trade Theory." The Journal of Political Economy, May 1977, 909-35.
15. Krugman, Paul and Robert Lawrence Robert Lawrence is the name of:
U.S. monthly magazine interpreting scientific developments to lay readers. It was founded in 1845 as a newspaper describing new inventions. By 1853 its circulation had reached 30,000 and it was reporting on various sciences, such as astronomy and , April 1994, 44-49.
16. La Londe, Robert and Robert Topel, "Immigrants in the American Labor Market labor market A place where labor is exchanged for wages; an LM is defined by geography, education and technical expertise, occupation, licensure or certification requirements, and job experience : Quality, Assimilation, and Distributional Effects." American Economic Review, May 1991, 297-302.
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Study of the economic behaviour of individual consumers, firms, and industries and the distribution of total production and income among them. It considers individuals both as suppliers of land, labour, and capital and as the ultimate consumers of the final , No. 2, 1993, 161-210.
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