Sources of gains in allocative efficiency

l g g- 2 E RESEARCH PAPER SERIES JutJ Ig 9 3 ENTERPRISE BEHAVIOR AND ECONOMIC REFORMS: A COMPARATiE STUDY IN CENTRAL AND EASTERN EUROPE AND INDUSTRIL REFORM AND PRODUcIvrIy iN CHINESE ENTERPRISES RESEARCH PROJECTS OF THE WORLD BANK CHINA NUMBER CH-RPS #3 JANUARY 1991 (REVISED JUNE 1993) Sources of Gains in Allocative Efficiency Gary Jefferson Brandeis University and Harvard Institute of International Development Harvard University Transition and Macro Adjustment Division Policy Research Department World Bank Washington, D.C.   CONTENTS ACKNOWLEDGEMENT . 1 ABSTRACT ................................. ii INTRODUCTION ................................. 1 II. A CONVERGENCE ACCOUNTING FRAMEWORK ....... ............... 3 III. WORLD OIL PRICE SHOCK ................................. 5 IV. CHINA'S INDUSTRiAL REFORMS. 7 VI. CONCLUSIONS. 9 REFERENCES .. 13 APPENDIX ........................... 14 TABLES TABLE 1: SOURCES OF CONVEREGENCE/DIVERGENCE ................ 5 TABLE 2: INDEX OF RELATIVE MARGINAL PRODUCT OF LABOR IN PETROLEUM PRODUCTION AND TOTAL MANUFACTURING ...... 6 TABLE 3: U.S. MANUFACTURING: TEE OIL SHOCK LABOR'S MARGINAL REVENUE PRODUCT .................. 10 TABLE 4: NOMINAL MARGINAL REVENUE PRODUCTS: COMPARISON OF CHNA'S STATE AND COLLECTIVE INDUSTRY ..... 11 TABLE 5: SOURCES OF CONVERGENCE OF FACTOR RETURNS (ANNUAL RATES OF GROWTH) .................. 12   ACKNOwLEDGEMENT The research projects on 'Enterprise Behavior and Economic Reforms: A Comparative Study in Central and Eastern Europe", and "Industrial Reforms and Productivity in Chinese Enterprises" are research initiatives of the Transition and Macro Adjustment Division (PRDTM) of the World Bank's Policy Research Department and managed by I.J. Singh, Lead Economist. These projects are being undertaken in collaboration with the following institutions: The London Business School (LBS); Reforme et Ouvertures des Systemes Economiques (post) Socialistes (ROSES) at the University of Paris; Centro de Estudos Aplicados da Universidade Cat6lica Portuguesa (UCP) in Lisbon; The Czech Management Center (CMC) at Celakovice, Czech Republic; The Research Institute of Industrial Economics of the Janus Pannonius University, Peds (RILE) in Budapest, Hungary; and the Department of Economics at the University of L6dI, in Poland. The research projects are supported with funds generously provided by: The World Bank Research Committee; The Japanese Grant Facility; The Portuguese Ministry of Industry and Energy; The Ministry of Research and Space; The Ministry of Industry and Foreign Trade, and General Office of Planning in France; and the United States Agency for International Development. 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The series is also possible thanks to the contributions of Donna Schaller, Vesna Petrovic, Cecilia Guido-Spano and the leadership of Alan Gelb. i   ABSTRACT This paper formulates a framework for analyzing the gains in allocative efficiency through the convergence of factor returns. Sources of convergence may include: (i) factor reallocations, (ii) differential rates of productivity growth, (iii) changes in production technologies, and (iv) changes in inter-sectoral prices, both product prices and factor input prices. Significant differences among factor retums may arise due to: (i) shocks that create temporary disequilibria, such as oil price shocks and regulatory changes, and (ii) uncompetitive markets, including, in the extreme, the allocation of factors through central planning rather than through the market. The paper applies its framework to an analysis of the convergence of factor returns following: (i) the oil shocks of the 1970s and (ii) the introduction of China's industrial reforms.   Sources of Gains in Allocative Efficiency 1 I. INTRODUCTION In market economies, we find a persistent tendency for factor returns to equalize, an important property of market economies which contributes to productive efficiency. Significant differences among two or more sectors to factor returns may arise due to the following conditions: (i) shocks that create temporary disequilibria, such as oil price shocks, changes in trade regimes and new product or process innovations, and (ii) uncompetitive markets, including, in the extreme, the allocation of factors through central planning rather than through the market. In the first case, the passage of time, such as the years following the oil price shocks of the 1970s, should lead to a set of adjustments that reduce differences in returns to factors between the energy and non-energy sectors. In the case of central planning, economic system reform, such as that underway in China and E. Europe should lead to a convergence of factor returns. Following price or regulatory shocks or the introduction of new product or proceess innovation in market economies or following the creation of markets by reform-minded governments, factor returns may converge through a variety of channels. These include: (i) factor reallocations, (ii) differential rates of productivity growth, (iii) changes in production technologies, and (iv) changes in inter-sectoral prices, both product prices and factor input prices. This paper develops an accounting framework for measuring the contribution of each of these sources to changes in relative factor returns between two sectors. In market economies, profit-seeking behavior on the part of sellers and buyers tends to erode intersectoral and interregional differences in returns to labor, capital or materials. Studies conducted within industrial market economies concerning the costs of allocative inefficiency resulting from impediments to optimal resource allocation show that these costs are relatively small.' Nonetheless, transitory shocks can create disequilibria which require periods of time for adjustment. The oil price shocks of the 1970s, for example, by shifting back the energy supply curve, caused substantial increases in returns to petroleum products relative to other goods in the U.S. economy. Over time, however, these quasi-rents were eroded. By 1986, the initial increase in returns to labor employed in the petroleum products industry relative to returns in overall manufacturing had been eliminated. The question addressed by this paper is the nature of the adjustment mechanism. What combination of price adjustments, quantity adjustments or technological change led to the restoration of equilibrium in labor markets following the oil price shock? Prepared for the Fourth International Economics Conference on U.S.-PRC Cooperation in Beijing, November 10-12, 1992. Research support provided by the National Science Foundation and the Henry Luce Foundation is gratefully acknowledged. 1. See Leibenstein's (1976) review of this literature in which he concludes that in mature industrial economies, potential gains from allocative efficiency are trivial.  2 Sources of Gains in Allocauve Efficiency In China, Eastern Europe, and the former Soviet Union, economic reform initiatives seek to increase efficiency by introducing market-oriented policies and institutions into economies formerly dominated by state planning. Ecornomic system reform has also been an important policy thrust in many developing countries in which bureaucracy has dominated pricing and resource allocation decisions or within which product and factor markets are undeveloped. An important potential source of efficiency gain, in both socialist and developing economies, is price reform coupled with the introduction of factor markets to facilitate the deployment of labor, investment resoruces, and intermediate inputs toward activities where these inputs can generate their highest marginal social return and thereby improve allocative efficiency. At the outset of China's economic reforms in 1978, the industrial sector consisted of a core and a relatively small periphery. The core, consisting of state-owned enterprises, was relatively intensive in capital and materials, while the periphery, consisting of urban collectives and rural commune industry, was relatively intensive in labor. These patterns of factor intensity created and sustained substantial differences in factor returns. By the late 1980s, following a decade of reform, evidence was beginning to emerge that returns to capital, labor and materials were beginning to converge between the state-owned industrial core and the periphery. What combination of price adjustments, quantity adjustments or structural change was driving this converg;ence of factor returns? The restoration of market equilibrium among energy and non-energy sectors following oil price shocks in the 1970s and the convergence of factor returns within the industrial sector following the introduction of incentive and market reforms in China are but two examples of situations involving adjustment within a two-sector setting. Lewis (1954), Fei and Ranis (1964), and Yorgenson (1966) each modeled the dynamics of changing returns to labor between agriculture and industry within developing coluntries. Harris (1970) looked at the problem from a rural-urban perspective. The state and non-state, agriculture-industry, and rural-urban distinctions are but examples of a large number of dichotomous distinctions that warrant attention. Intuitively, changes in relative factor returns or marginal revenue products across two or more sectors result from two types of conditions. The first, affecting physical marginal products, consists of changes in relative factor intensities, differential rates of productivity growth, and technological changes that affect factor output elasticities. The second leaves physical products unaffected but, by changing relative prices, affects marginal revenue products. This 'latter source of change in factor returns includes both changes in relative product prices and changes in inter-sectoral factor input prices. At the national level, productivity growth may originate from any of three sources. These are: (a) productivity growth (technical change or realization of scale economies) within the firm, (b) increases in production efficiency resulting from the convergence of factor returns across sectors or firms, and (c) allocative efficiency in the general equilibrium sense in which prices reflect relative scarcities and consumer plus producer welfare are maximized. This paper  Sources of Gains in Allocative Efficiency 3 evaluates the contribution of greater production efficiency to measured productivity growth and formulates an approach for decomposing the sources of growing (or declining) production efficiency. II. A CONVERGENCE AcCOUNTING FRAmEWORK As described in Section 1, changes in relative nominal factor returns between two or more sectors can originate from several sources. To see this formally for the general case, assume a twice-differentiable sectoral production function with scale economies of the general form: Q, = Atf(St, Xi), (1) where Q is real sectoral output, A is a measure of technical efficiency, S represents firm-level scale economies (e.g. average firm size, Q/N, where N is the number of firms in the sector),2 X is a vector of factor inputs, and t represents time. Equation (1) is homogeneous of degree one in the Xs,3 but the technology is constant-returns only if aQI&S = 0. Totally differentiating Equation (1) gives: dQt = dAtf( . ) + (aQIaS)4St + rj(aQ/aXI)^dXk,. (2) Dividing Equation (2) by Equation (1) and multiplying the second term on the right-hand side by S/S and the subsequent terms by X,/Xi yields: 0 0 0 q = a + j s + Eaj xj (3) where q, s and x represent rates of change in Q, S and X, aiga = 1, ai = (aQ/aXi)(XJIQ), B = (aQIaS)(S/Q)4 and ai and B are elasticities of output with respect to input i and scale. Total factor productivity growth (tfp) is represented by the sum of technical change (a) and scale effects (-Bs) in Equation (3). Equation (3) represents a relationship between physical inputs and prices. Now we add prices. The marginal revenue product of factor i can be represented as: MRPk = adRPqV0/(X-)d (4) 2. The scale variable could also be summarized by higher moments of Q/N. 3. That is, if firm scale (S) is unchanged, a uniform change in the Xs will result in a proportional change in output. For the Cobb-Douglas case used in this paper, the relationship between S and Q is shown in the Appendix. 4. In all fixed-weight calculations in this paper, the weights are averages of the initial and terminal values.  4 Sources of Gains in Allocaive Efficiency where P, and Pi are the prices of output and factor input i in period t. The coefficient a, is factor i's output elasticity, measured as a, = /(1-B).5 For the case in which the technology is constant returns to scale (i.e. B = 0), al = ui. Taking a logarithmic time derivative, Equation (4) can be transformed into a rate-of-change version as follows: 0 0 0 0 0 0 m rpi = a, + pq + q - P - xi (5) 0 where a, represents the growth, if any, of thie coefficient a,. Substituting Equation (3) into Equation (5) yields an expression for the rate of change of factox i's marginal revenue product in terms of its component changes: 0 0 0 0 0 0 0 m rp= + ( p -P.) + x + s s +a(x- x;). (6) The right-hand side of Equation (6) decomposes changes in factor i's marginal revenue product into tie folloning sources: (i) changes in the output price ( pq), (ii) changes in ie relevant input price, (pj),6 (iii) tectnicaI0change (ca), (iv) growth due scale economies (B s), (v) changes irfactor input ratios [aj( xj - x;)], and (vi) a shift in the own factor's output elasticity (ar). Equation (6) is the basic accounting relationship that can be used to decompose the sources of change in factor returns within a single sector. Within each sector there are i such relationships, corresponding to each factor. ][n order to investigate the sources of convergence or divergence for returns to factor i between two sectors, Equation (6) can be written for each of the sectors and appropriately differencecl to account for the sources of convergence or divergence. Designating the two sectors A and B and differencing yields the following terms: 00 0 0 5. This can be shown by substituting (q - n) for s in Equation (3) and solving for q, where n is the rate of growth in the number of firms. 6. Note that only changes in the own price of tlhe relevant fiLctcr affect its nominal return. Changes in the prices of other factor inputs have no direct effects on the marginal revenue product of the own factor.  Sources of Gains in Alocative Efficiency 5 TABLE 1: SOURCES OF CONVERGENCE/DIVERGENCE 0 0 1. relative growth of marginal revenue products m rpi - m rp of which: 2. differential total factor productivity growth t' - t %pB of which: a. technical progress - aB 0 0 b. scale economies (B sA) - (B SB) 0 0 0 3. differential rates factor deepening a4( x -