Impoverishing Capital Movements:

Transcription

1 Impoverishing Capal Movements: a Two Country Lucas-Uzawa Model Hyunseok Shim Yonsei Universy 29/11/16 Abstract: This paper uses a standard two sector Lucas-Uzawa model, and applies to include two countries. The two countries have differing inial stock of human capal but are otherwise symmetric. I show that once capal mobily is introduced, there is one time transfer of capal from the country wh smaller inial human capal to the country wh larger inial human capal. Consequently, the country wh small human capal is deprived of consumption and capal in the short run. In the long run, the countries converge to steady state growth, just like in autarky. Wh alternative assumptions for inial stocks of capal and human capal, the model is consistent wh the Lucas Paradox, and also explains the brain drain phenomenon.

2 I. Introduction: Using human capal as a component in economic growth models was first introduced into mainstream economic lerature by classic articles such as Arrow (1962), Uzawa (1965), Romer (1986) and Lucas (199). While human capal is unobservable and immeasurable, nevertheless is important in explaining sustained economic growth. The non-diminishing returns to scale in the human capal sector is the driver of economic growth in many twosector growth models. Using human capal models also explains the Lucas Paradox. Neoclassical growth theory predicts that in the long run, marginal product of capal will converge across the world. When a country wh low stock of capal opens up s capal market, foreign capal should rush in. In the real world, we do not observe such phenomena. The Lucas-Uzawa model is a commonly used two sector growth model, in which human capal exhibs constant returns to scale. I will extend the standard Lucas-Uzawa model framework to include two economies. First, I will show that if capal is the only mobile factor of production, the human capal poor country will experience a capal outflow. Then, I will change some of the basic assumptions to explain the brain drain phenomenon and the Lucas Paradox. This is in part to predict the international flow of capal, migration of skilled labor, and the Lucas Paradox in a general equilibrium setting, and also in part to offer policy implications to countries contemplating opening up their capal markets.

3 II. Relation to earlier work: The model presented in this paper is drawn from a variety of earlier works. The production function for human capal derives mainly from Uzawa (1965), and is linear for simplicy. Other aspects of the model come from what is widely known as the Lucas-Uzawa model, formulated by Uzawa (1965) and Lucas (1988). This model poss two sectors in an economy, and specifies constant returns in the human capal sector as the engine of growth. Model specification details and notation are borrowed from Barro and Sala-i-Martin (23). Unlike previous models of this type that were primarily concerned wh economic growth in a single country, the model presented in this paper examines two countries, and how capal and human capal would move between the two countries. Stiglz(197) explored the two-country, two-sector model, but focused on factor price equalization through international trade of goods. The Lucas Paradox was discussed extensively in Lucas (199). Contrary to neoclassical economic theory, real world capal did not flow to capal poor countries. The usual explanations, as discussed in Alfaro, elemli-ozcan, and Volosovych (28), are differences in fundamentals and international capal market imperfections. The differences in fundamentals, while abstract, can be loosely aggregated into the term human capal. Human capal can encompass anything from worker motivation, education level, government instutions and policies, to social infrastructure. While this, admtedly, is a gross simplification, nevertheless allows for a clear cut analysis.

4 III. The model: 1) Setup The model is a 2-country, 2-factor, 2-sector model Assumptions 1. Capal exhibs diminishing returns wh respect to capal and human capal. 2. Production goods can be used for eher consumption or capal investment. 3. Human capal exhibs constant returns. 4. Human capal uses only human capal for production. 5. Production functions are identical in both countries. Only inial human capal endowment differs. 6. Only capal is mobile internationally. 7. Markets of factors of production are perfectly competive. 8. There is no movement of goods between the countries. Assumptions 3 and 4 follow from Uzawa (1965) and Lucas (1988) C: consumption : capal H: human capal Y: output T: capal transfer < < 1, < v < 1, < δ = δ = δ < 1 H

5 Home is described by the following equations. = ( vh ) C δ + T H t + δ Ht = (1 vh ) t Y = C + + δ + T t t t t t t t t t t t Foreign is symmetric. = ( vh ) C δ T H * t + δ H* t = (1 vh ) * t Y = C + + δ T * t * t * t * t * t t * t * t * t * t t From these, we get, MP vh = Eq. (1) H = H (1 v δ ). Eq. (2) MPH 1 = (1 ) v H Eq. (3) Using a typical Ramsey consumer, the economy is described by three differential equations. c 1 = ( r ρ ) c θ k h c = v δ k k k h = 1 v δ h, where c, k, h denote consumption, capal, and human capal per capa, respectively.

6 2) Transfer of Capal Inially, the assumption that H > H* and = * imply MP > MP*, which implies T>. If capal is mobile, will move to equate MP in both countries. T H H Eq. (4) 1 1 *1 a *1 1a = > H1 + H*1 Subscribt a denotes autarky. After capal movement, MP1 = MP*1 Using equation (1) and H1 > H*1, we see that 1 > *1 We reach steady state equilibrium in second period, wh no further capal transfers. Because production function of H is CRS, H is always larger than H *. 3) Steady State Equilibrium In steady state equilibrium, H H C = = = > 1 H H C * * * * Also, in equilibrium, marginal product of capal must equal marginal product of human capal. eq 1 eq Y Y = v = = (1 ) v eq eq H H H eq = H Eq. (5) 1 Solved in Appendix A.1

7 4) Factor Prices In competive equilibrium, r t vh t = MPt = t and, 1 t wt = MPHt = (1 ) v Ht Because of posivet, r < r, r*1 f > r*1 a, w1f > w1 a, w*1 f < w*1 1f 1a a Eventually, factor prices will converge to a steady state value. H eq = from equation (5) eq eq eq eq = * = = (1 ) = = * = (1 ) r r v v w w v Dynamics indicate that under capal mobily, the country inially rich in human capal will experience a decrease in rental price of capal due to the inflow of capal and an increase in wages. Factor price equalization is achieved across countries and across sectors.

8 IV. Alternative Environments: 1) Lucas Paradox: H If we assume =, then T= by equation (4). There will no no transfer of H * * capal between the two countries. The model is consistent wh the Lucas paradox. Capal does not flow from rich to poor countries because the difference in human capal negates the difference in capal. 2) Brain Drain: Now suppose H = H*, and > *, and mobily condions reversed. Now, human capal is mobile, and capal is immobile. Let I denote the number of immigrants to home. Human capal will flow as to equate the MPH in both countries. I H H 1 1a 1 *1a = > 1 + *1 In the period in which human capal is allowed to migrate, the model predicts a outflow of human capal from the capal poor country. Thus, in a two-country setting wh identical inial human capal, freedom of human capal movement will incur a brain drain suation. As in Section III. 4), factor prices can be analyzed as follows:

9 r > r, r*1 f < r*1 a, w1f < w1 a, w*1 f > w*1 1f 1a a The signs are oppose. In the short run, the country experiencing brain gain will see an increase in rental price of capal, and a decrease in wages. The country experiencing brain drain will see the oppose. Equilibrium results are same wh those in III. V. Conclusion: The one time transfer of capal T which occurs in the first period impoverishes Foreign. Home has higher inial human capal, and therefore higher MP. When capal is allowed to move, will flow from Foreign to Home until MP is equal in both countries. Foreign s consumption and capal stock is reduced compared to autarkic path in the short run, but eventually catches up. MP in both countries converge to a nonnegative number. Analysis of factor price shows that compared to the autarkic path, the free capal movement path exhibs lower rental price of capal and higher wages in the short run in Home, and vice versa. In the long run, factor prices are equalized across countries and across sectors. Using alternative specifications, the model also explains the Lucas Paradox and the brain drain phenomenon.

10 VI. Policy implications: If a country wh low human capal opens s capal market, will experience a capal outflow, and will lose short term economic growth, although growth will eventually catch up. This finding gives some policy implications. If a country has low human capal compared to other countries, would be more advisable to keep the capal market closed and instute policies to encourage human capal formation. In the Lucas Paradox case, if the country wh less capal and human capal is somehow able to increase human capal and upset the inial human capal ratio, would be able to receive capal inflows from abroad. Capal mobily also has consequences for distribution of income. The country experiencing an inflow of factor of production will experience a short run decline in the price of that factor, and increase in the price of another.

11 VII. Appendix A.1 - Solving for T and I. 1) Solving for T: MP = vh 1 MP must equal in both countries after transfer a + T *1a T = vh vh 1 *1 Dividing through and rearranging, *1 a T H *1 = 1 a + T H1 Solving for T gives T H H 1 *1 a *1 1a = H1 + H*1 2) Solving for I: MPH 1 = (1 ) v H MPH must equal in both countries after migration. 1 a *1a (1 ) v = (1 ) v H + I H I 1a 1a Dividing through and rearranging, H I = H + I 1a *1a 1a 1a

12 Solving for I gives I H H 1 1a 1 *1a = 1 + *1 VIII. H Appendix A.2 - Solving for equilibrium condion H = * * MP vh = In equilibrium, there are no more transfers of capal. MP must equal in both countries, vh vh * = * Dividing through and rearranging, H H = * *

13 IX. References Alfaro, Laura; elemli-ozcan, Sebnem; Volosovych,Vadym(28), Capal Flows in a Globalized World: The Role of Policies and Instutions, Review of Economics and Statistics Arrow, enneth J.(1962), The Economic Implications of Learning by Doing. Review of Economic Studies 29: Barro, Robert J. and Sala-i-Martin, Xavier(23) Economic Growth, 2 nd Edion, The MIT Press Lucas, Robert E.(1988), On the Mechanics of Economic Development, Journal of Monetary Economics 22: 3-42 Lucas, Robert E.(199), Why doesn t Capal Flow from Rich to Poor Countries?, American Economic Review 8: Romer, Paul M.(1986), Increasing Returns and Long-Run Growth, The Journal of Polical Economy, Vol. 94, No. 5: Stiglz, Joeph E.(197), Factor Price Equalization in a Dynamic Economy, The Journal of Polical Economy, Vol. 78, No. 3: Uzawa, Hirofumi(1965), Optimum Technical Change in an Aggregative Model of Economic Growth. International Economic Review 6: 18-31