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Populat i on G rowth and P roduct i v i ty Di fferences across Nations and the L ong -R un T rade E qu ili br i um. S ERDAR S AYAN serdar sayan .net Department of Economics and Center for Social Policy Research TOBB University of Economics and Technology Yıldırım Beyazıt University
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Population Growth and Productivity Differences across Nations and the Long-Run Trade Equilibrium SERDAR SAYAN serdarsayan.net Department of Economics and Center for Social Policy Research TOBB University of Economics and Technology Yıldırım Beyazıt University Ankara December 24, 2015
Motivation Demographic projections by the UN: Dissimilarities already existing between relative factor endowments of capital-abundant nations (in North America, Europe and East Asia) and the rest of the world are expected to grow in the decades ahead. If marked differences in population growth rates in the relatively capital- and labor-abundant parts of the world are to conform to these projections, greater variations will be observed in the age profiles of populations.
Motivation Changes in the age composition of a nation additional changes in relative factor endowments Demographic differences potentially emerge as major determinants of regional commodity and factor flows. Until recently, very few studies in the literature have investigated the validity of predictions of the standard HO model in a dynamic framework: --possibly due to the fact that trade between two countries that are identical in every respect but the initial capital/labor ratios (relative factor endowments) would last only until these ratios have been equalized as a result of trade itself.
It would still be interesting to study dynamic patterns of trade, if there are differences which would cause factor proportions to evolve independently of trade over time. Differential speed of demographic transition and the resulting differences in population growth rates across countries/regions provide an empirically relevant example to such differences leading to an evolution in relative factor endowments.
DEFINITION OF THE PROBLEM The static 2x2x2 Heckscher-Ohlin model of int’l trade • suggests that differences in relative factor endowments alone would be sufficient for trade (that is Pareto-superior to autarky), • is very useful and has been a very popular basis for many theoretical and empirical studies in a static context, • does not, however, offer any insight s into the dynamics of trade and the nature of any equilibrium to be reached between trading nations or the gains from trade in the long-run.
Literature Some studies in the dynamic trade/growth literature recognized this role of unequal rates of population growth early on (Oniki and Uzawa, 1965; Findlay, 1970) The long-run pattern of comparative advantage depends ultimately on the propensity to save and the growth rate of labor force. Stiglitz (1970): The differences in saving rates could be explained by differences in time preference rates of nations and hence could serve as long-run determinants of comparative advantages. Two-sector growth models in Oniki and Uzawa (1965) and Findlay (1970) are capable of indicating the directions and magnitude of changes in trade flows in response to changes in capital/labor ratios, but they can not show the effects of changes in the age composition of population on relative endowments.
Literature (Cont’d): OLG-GE Trade Models To address these, an overlapping generations general equilibrium (OLG-GE) framework would be needed. An early OLG-GE trade model: Fried (1980) two commodities, two generations, one factor (land) compares steady state solutions under free trade and autarky no population growth Later, Eaton (1987), and Galor and Lin (1997) used OLG-GE models to study trade issues. Galor and Lin (1997) dynamic micro foundations of the HO model on the basis of differences in time preference rates across two nations, OLG GE framework used takes the changes in the savings behavior of individuals over the working and retirement phases of the life cycle into account. [PREFERENCES DIFFERED not an a la-HO set up]
Literature (Cont’d) All these studies, however, have either completely overlooked possible growth of populations in respective nations, or assumed populations growing at identical and constant rates. Numerous applied OLG-GE models have also been constructed following Auerbach and Kotlikoff (1987) to investigate the implications of changes in old-age dependency ratios for labor supply, savings and fiscal balances (see Miles, 1999 for a survey). Yet, due possibly to computational difficulties involved in solving large scale OLG-GE models in multi-country settings, relatively few studies have put this framework into use for studying international commodity and factor flows. Notable examples are Juillard and INGENUE Team (2001) and Kenc and Sayan (2001).
Literature (Cont’d) Sayan (2003) studied the effects of differential speed of population growth and aging on international migration patterns, on the basis of simulation results from a 2x2x2x2 model similar to the one here. Sayan (2005) Numerical solutions to a 2x2x2x2 OLG-GE HO model with constant and time-varying population growth rates. Jelassi and Sayan (2009) Closed form solutions to the model in Sayan (2005). Naito and Zhao (2009) Closed form solutions to the model in Sayan (2005) + A compensaton scheme to make trade Pareto-superior to autarky Yakita (2012) OLG GE HO model with increases in life expectancy in one country
The Model • 2-country, infinite horizon OLG model with perfect foresight. • Each country is populated by 2-period living individuals. • Letting ηt denote the number of individuals born in period t where n denotes the population growth rate. • For country i , the production and household consumption decisions are characterized as follows.
The Model—Production Side • 2 goods indexed by j; constant returns to scale Cobb-Douglas production function technologies using capital (K) and labor (L) as inputs. • Good 1, which is used both for consumption purposes and as capital, is taken as the numeraire. • Good 1 is the relatively more labor intensive good, while good 2 is relatively more capital intensive. • All capital and labor available are divided between the two sectors such that
The Model—Production Side The production functions are defined as: In per worker terms
The Model—Production Side (Cont’d) The production sectors are assumed to be competitive so that the Representative firm producing good 1 maximizes profits, π1t by solving
The Model—Demand Side An individual born at time t has a utility function of the form: where For j=1, 2, Cjyt denotes the amount of good j consumed when young and Cjot+1 denotes the amount of good j consumed when old, all in per capita terms. The representative household solves: subject to he life-time budget constraint
The Model—Demand Side (Cont’d) where rt+1 is the rationally anticipated return to capital in period t+1and pt+1 is the rationally anticipated price of good 2 in period t+1. The Model—Autarky Equilibrium Since olds consume all their wealth in the current period, only capital transferred to the next period is the savings of the current young, implying:
The Model—Autarky Equilibrium Dynamic equilibrium requires clearance of goods’ markets in each period t. Since these two equations imply each other by Walras’ law, we can write A manipulation of these equations enables us to express pt as a function of capital per worker kt.
The Model—Trade Equilibrium We model trade by replacing autarky market clearing conditions in each country, we require that world-wide demand to both goods is equal to the world-wide supply: A natural result of free trade will be the equalization of prices in both countries in each period. So, must also hold
Simulation Scenarios In order to observe the paths that endogenous variables would follow over time, the autarky and trade models described above have been simulated under two different demographic scenarios: Under the first scenario, population growth rates, and , were allowed to start with different initial values and decline at differing speeds across countries, whereas the second scenario considered distinct but constant population growth rates for each region, i.e., The 1950 values of average population growth rates for "more -“ and "less-developed regions" by the UN classification were allowed to serve as the respective(initial) rates for regions Aand B under (Scenario 1) Scenario 2.
Simulation Strategy Simulation of the autarky and trade models requires that a set of common values be chosen for production and utility parameters, and the initial values of capital stock per capita, , and relative price ratio, , that are common to both regions be specified. The simulation strategy adopted here was to start by solving the autarky model under common production and utility parameters selected, and with a population growth rate that is very close to zero (0.01% to be exact). The resulting steady state values of and were then fed as the initial values, and region-specific autarky models and the trade model were solved again under each demographic scenario.
Factor Prices under Autarky and Trade (Left: Scenario 1; Right: Scenario 2)
Per Capita Sectoral Outputs under Autarky and Trade: Efficiency Gains from Trade (Left: Sce. 1; Right: Sce. 2)
Ranking of Long-Run Equilibrium Values of Key Variables under Autarky and Trade in Regions A and B: Scenario 1 and Scenario 2
