Estimation of output loss from allocative inefficiency: A comparison of the Soviet Union and the U.S.

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<ul><li><p>Economics of Planning 25: 219-236, 1992 9 1992 Kluwer Academic Publishers. Printed in the Netherlands. </p><p>Estimation of Output Loss from Allocative Inefficiency: A Comparison of the Soviet Union and the U.S. 1 </p><p>HUMBERTO BARRETO Wabash College, CrawfordsviUe, Indiana, U.S.A. </p><p>ROBERT S. WHITESELL Williams College, Williamstown, Massachusetts, U.S.A. </p><p>Abstract </p><p>This paper presents two different estimates of the output loss resulting from allocative inefficiency in the Soviet Union and the United States. Surprisingly, the evidence from our examination of nine industrial sectors during the period 1960-1984 shows only small differences in measured allocative inefficiency between the United States and Soviet economies. Instead of immediately rejecting this result as the product of unreliable data and insurmountable methodological difficulties, we present a plausible explanation for the unexpectedly strong performance of Soviet-type economies in the allocation of labor and capital across sectors. If true, the finding of relatively low levels of resource misallocation implies that the source of poor economic performance in Soviet-type economies must be due to technical inefficiency, slow technological change, and/or production of the wrong mix of outputs. </p><p>I. Introduction </p><p>In 1983 Padma Desai and Ricardo Martin published a paper which calculated the output loss caused by an interbranch misallocation of inputs in Soviet industry. This paper extends their work in two important respects. First, although three methods of measuring 'efficiency loss' were discussed in their paper, only one was actually calculated. Thus, addition- al information, which would be helpful in understanding the ability of the Soviet system to allocate resources efficiently, is foregone. Calculation of the alternative methods would be useful in order to estimate the range of possible variation in the measures. Second, the estimates are given without a comparative context. Since no similar estimates have been made for market economies, it is impossible to know whether their estimates imply large or small levels of allocative inefficiency for the Soviet economy. This paper addresses these issues by calculating several different measures of output loss for both the Soviet Union and the United States. 2 </p></li><li><p>220 HUMBERTO BARRETO AND ROBERT S. WHITESELL </p><p>II. Data </p><p>The data are output, capital and labor for nine branches of industry (see Table 7) for the period 1960-1984. In an attempt to make the branches as comparable as possible, sectors for the US were chosen on the basis of their similarity to the Soviet branches. Perfect commensurability, how- ever, proved impossible. Gas and sanitary services are not included in the Soviet electric power sector. The Soviet fuel branch and the US mining sector are not the same because the latter includes the mining of nonfuels. The US metallurgy branch includes nonferrous metals, while its Soviet counterpart does not. Perhaps the greatest dissimilarity lies in the construction materials sector. The US data do not include a category equivalent to the Soviet construction materials branch. As an imperfect substitute, furniture and fixtures has been used instead. </p><p>The Soviet output data are the CIA estimates of value-added by sector of origin in 1970 prices. 3 The capital data are gross productive fixed capital in 1973 prices derived from official Soviet statistics. The labor data are the total number of hours worked derived by Feshbach and Rapawy (1976) for 1960-1974, extended by Rosefielde (1983) to 1980, and extended by us to 1984. </p><p>The U.S. data are from the Bureau of Economic Analysis. The output data are value-added by sector of origin in 1982 prices, the capital data are gross fixed capital stock in 1982 prices, and the labor data are the total number of hours worked. 4 </p><p>III. Theoretical analysis </p><p>The analysis is based on the idea that whenever factor marginal rates of substitution (MRS) diverge, gains can be realized through an efficient reallocation of resources among sectors. The allocative inefficiency or foregone gains in output caused by unequal MRSs can be expressed in three different ways. The single output augmenting measure of inefficien- cy produces the initial amounts of n - 1 different sectoral outputs and more of an arbitrarily chosen nth output. The proportional output augmenting method reallocates labor and capital such that equipropor- tional increases of each output are produced with the initial total factor endowment. Finally, the factor savings method produces the initial output vector with fewer factors of production. Because these last two measures are equivalent, this paper will present empirical estimates only for the factor savings and single output augmenting measures of allocative inef- ficiency .5 </p><p>The factor savings method consists of measuring the gains to be realized from a reallocation of inputs that equalizes marginal rates of substitution and thereby produces the observed output vector with a </p></li><li><p>OUTPUT LOSS AND ALLOCATIVE INEFFICIENCY 221 </p><p>smaller factor endowment. Since there are many possible ways to reduce inputs, it is necessary to choose a particular MRS which production in each sector must meet. This is done by choosing the MRS which preserves the original global capital-labor ratio. 6 </p><p>Since both inputs are being reduced equiproportionately, a simple measure of the efficiency gain is </p><p>Proportional /2 /( - 1 - 1,7 (1 ) </p><p>Factor Savings L* K* Gain </p><p>where /2, /( are original amounts and L*, K* are efficient amounts of labor and capital. This measure represents either the potential gain from an efficient reallocation of resources or the loss from the inefficient allocation. </p><p>A second strategy for measuring the potential gains from an efficient allocation, the single output augmenting approach, involves generating the same output in all sectors except one, then allocating the savings of factors in the n - 1 sectors to the nth output. The increase of output in that one sector is a measure of the gain from the proper reallocation of resources, or the loss from a misallocation. </p><p>The measure of efficiency is: </p><p>Single Pi f', + Pj Y~ - 1 (2 ) </p><p>Output Augmenting = Pi~ + Pj I?j Gain </p><p>where I?j is the original amount of output produced by sector j and Y~ is the efficient amount of sector j's output. Since resources are reallocated differently in the single output augmenting approach from the factor savings approach, these measures will not be the same. This measure will also vary according to which sector's output is expanded. Although the single output augmenting measure does not have the same neat, intuitive appeal of the factor savings (and proportional output augmenting) mea- sure, its inclusions does provide a full description of the allocative efficiency analysis and a more complete empirical picture. </p><p>IV. Empi r i ca l es t imat ion </p><p>In order to estimate the production gain that could be achieved from an efficient reallocation of resources, aggregate production functions were estimated for the nine industrial branches in each country. Eight forms of the Cobb-Douglas production function were estimated. All production functions assume constant returns to scale and Hicks neutral technical </p></li><li><p>222 HUMBERTO BARRETO AND ROBERT S. WHITESELL </p><p>change. The functional forms are: </p><p>CDAI : In y~(t) = In % + Ait +/xit 2 + ai In ki(t ) + ei(t), </p><p>CDI : In y~(t) = In ~,~ + A~t + txi t2 + ai In ki(t ) + ui(t), </p><p>(3) </p><p>(4) </p><p>where i yi(t) ki(t) % h i + 21xit Ol i </p><p>1 - - Ol i </p><p>u i t </p><p>= sector i = output- labor ratio in year t = capital- lab0r ratio in year t = an efficiency parameter = the rate of Hicks-neutral technical change = imputed output share of capital = imputed output share of labor = error term with zero mean and constant variance = u I + piEi -1, this assumes first order autocorrelation. </p><p>Setting /x = 0 results in CDA2 and CD2, setting A = 0 results in CDA3 and CD3, and setting /x = A = 0 results in CDA4 and CD4. These functions are nested and a likelihood ratio procedure is used to choose a best estimate for each branch in each country) </p><p>The factor savings measure of efficiency gain was calculated, for each year, by searching for a MRS* which would produce the initial bundle of outputs efficiently; i.e., forcing equalized MRSs throughout the economy, while holding the global capital- labor ratio constant. We began by calculating the imputed MRSs for each sector of industry from the production function estimates: </p><p>f / 1 MRS i ~ k i i = 1, 9 (5) </p><p>f K O/i </p><p>As a first approximation to MRS*, a weighted average of the initial MRSs was calculated, using the sectoral shares in total output as weights. The optimal capital- labor ratio for each sector was then calculated, given this new MRS* as </p><p>&amp;/MRS* k* - ~ _---~ (6) </p><p>Optimal labor use was then calculated from this capital- labor ratio and the predicted level of output 9 as </p><p>L* ~ -xi'-#i'2"*si = =- e K i . (7) Yi </p><p>From (6) and (7), the optimal amount of capital is </p></li><li><p>OUTPUT LOSS AND ALLOCATIVE INEFFICIENCY 223 </p><p>K* * * =kiL i . (8) </p><p>These sectoral factor usages were then added and the global capital- labor ratio calculated. If this new global capital-labor ratio was not equal to the original global capital-labor ratio, then a new MRS* was chosen and the process was repeated. Each new MRS* was chosen as </p><p>MRS* = MRS*(/~/k*), (9) </p><p>where /~ is the original capital-labor ratio and k* is the most recently calculated capital-labor ratio. This process was repeated until it con- verged; i.e., the new capital-labor ratio was identical to the original. </p><p>The iterative procedure described above generates MRS*- the MRS which rules in every sector. Furthermore, note that intrasectoral capital- labor ratios change, but the global capital-labor ratio remains constant. The percentage gain in output that could be achieved by an efficient reallocation of resources is then calculated as described in Equation (1) above as the Proportional Factor Savings Gain. </p><p>The single output augmenting approach was calculated similarly. As an example we use the case of chemical production. All outputs, except chemicals were produced efficiently given an initial MRS*, as in Equa- tions 5 to 8. This released some capital and labor which were then allocated to the chemical sector. The capital-labor ratio and imputed MRS for chemicals were calculated as </p><p>kr =Kc/Lc, (10) </p><p>and </p><p>MRS c = [(1 - &amp;c)kr (11) </p><p>where the c superscript represents chemicals and K c and Lc represent the released amounts of capital and labor. If MRS~ was unequal to the MRS*, then a new MRS* was chosen and the reallocation process was repeated. This procedure was continued until the MRSs were equal in all sectors; every sector but chemicals producing the original output level, and the actually existing amounts of total capital and labor being used. The proportional gain in output that could be achieved was calculated as the Single Output Augmenting Gain in Equation 2. l~ </p><p>V. Discussion of results </p><p>The results are presented in Tables 1 to 6 and Figure 1. Tables 1 and 2 show the losses in output from resource misallocation in percentage terms </p></li><li><p>224 HUMBERTO BARRETO AND ROBERT S. WHITESELL </p><p>Table 1. Percent inefficiency Soviet Union, 1960-1984. </p><p>YEAR FGAIN POWER FUEL FMET CHEM MBMW CONST WOOD LIGHT FOOD </p><p>1960 5.9 3.7 4.9 5.8 6.0 6.5 6.6 6.4 5.2 6.8 1961 6.3 4.1 5.6 6.2 6.4 7,0 7.0 6.7 5.6 7.2 1962 6.8 4.5 6.3 6.7 6.9 7.5 7.5 7.0 5.9 7.7 1963 6.8 4.6 6.4 6.7 6.9 7.5 7.4 6.9 5.9 7.8 1964 6.8 4.6 6.5 6.7 6.8 7.5 7.3 6.8 5.8 7.8 1965 6.7 4.6 6.6 6.6 6.7 7.4 7.2 6.7 5.7 7.7 1966 6.7 4.7 6.7 6.6 6.7 7.4 7.1 6.6 5.7 7.8 1967 6.7 4.7 6.8 6.6 6.6 7.3 7.0 6.4 5.6 7.7 1968 6.7 4.7 6.9 6,6 6.7 7.3 7.0 6.4 5.6 7.8 1969 6.8 4.9 7.2 6.7 6.8 7.4 7.1 6.4 5.6 7.9 1970 6.8 4.9 7.4 6.7 6.7 7.4 7.0 6.3 5.5 7.8 1971 6.6 4.9 7.5 6.6 6.5 7.2 6.7 6.0 5.4 7.6 1972 6.6 4.9 7.6 6.5 6.4 7.1 6.7 5.8 5.2 7.4 1973 6.5 5.0 7.7 6.4 6.3 7.0 6.4 5.7 5.1 7.2 1974 6.5 5.1 7.9 6.4 6.3 6.9 6.3 5.6 5.1 7.2 1975 6.4 5.0 8.0 6.3 6.2 6.8 6.2 5.4 5.0 7.0 1976 6.5 5.2 8.3 6.4 6.3 6.9 6.2 5.4 5.0 7.0 1977 6.3 5.! 8.2 6.2 6.0 6.7 6.0 5.2 4.8 6.7 1978 6.2 5.1 8.3 6.1 6.0 6.6 5.9 5.0 4.7 6.6 1979 6.0 5.0 8.3 6.0 5.8 6.4 5.6 4,8 4.5 6.3 1980 5.9 5.0 8.3 5.9 5.7 6.3 5.5 4.7 4.4 6.1 1981 5.8 5.0 8.4 5.8 5.5 6.1 5.3 4.5 4.3 5.9 1982 5.8 5,0 8,5 5.7 5.5 6.1 5.3 4.4 4.2 5.8 1983 5.7 4.9 8.5 5.6 5.4 5.9 5.1 4.3 4.1 5.6 1984 5.5 4.9 8.4 5.4 5.2 5.8 4.9 4.1 4.0 5.4 </p><p>Note: In Tables 1, 2 FGAIN = factor savings gain method. The others are the single output augmenting method with the given sector's output increased. POWER= electric power, FUEL = fuel industry, FMET = ferrous metallurgy, CHEM = chemicals, MBMW = machine building and metal working, CONST = construction materials, WOOD = wood-working and wood products, LIGHT=light industry (non-durable consumer goods), FOOD =food processing. </p><p>using both the factor savings and proport ional output augmenting mea- </p><p>sures. Tables 3 and 4 give the optimal MRS, the imputed initial sectoral MRSs and the factor real locations using the factor savings approach. 11 </p><p>Tables 5 and 6 give the selected product ion function estimates for each industrial sector for the Soviet Un ion and the Uni ted States, respectively. </p><p>Finally, Figure 1 compares the US and Soviet factor savings inefficiency measure. </p><p>A review of the factor savings estimates yields some interesting results. F igure 1 shows that inefficiency is lower in the Un i ted States than in the Soviet Un ion in the 1960s and early 1970s, but this difference appears small - certainly much smaller than most scholars of the Soviet economy would have expected. Since inefficiency is rising rather sharply in the Un i ted States and falling slowly in the Soviet Un ion during the late 1970s, the dif ference becomes smaller over t ime and virtually disappears by the 1980s. </p></li><li><p>OUTPUT LOSS AND ALLOCATIVE INEFFICIENCY </p><p>Table 2. Percent inefficiency United States, 1960-1984. </p><p>225 </p><p>YEAR FGAIN MIN POWER METAL MBMW CHEM FURN WOOD LIGHT FOOD </p><p>1960 4.0 9.3 2.7 4.9 4.1 4.6 2.2 2.3 2.2 3.6 1961 3.9 9.3 2.8 4.7 4.0 4.6 2.1 2.2 2.1 3.6 1962 3.7 8.8 2.8 4.4 3.7 4.4 2.1 2.1 2.0 3.4 1963 3.6 8.6 2.8 4.2 3.6 4.4 2.0 2.0 1.9 3.4 1964 3.5 8.4 2.8 4.1 3.5 4.3 2.0 1.9 1.8 3.3 1965 3.4 7.9 2.7 3.8 3.3 4.2 1.9 1.8 1.7 3.2 1966 3.2 7.6 2.7 3.6 3.2 4.1 1.9 1.7 1.6 3.1 1967 3.3 7.9 2.9 3.6 3.2 4.2 1.9 1.7 1.6 3.2 1968 3.3 8.0 3.0 3.6 3.2 4.2 1.9 1.7 1.6 3.2 1969 3.4 8.3 3.1 3.6 3.3 4.4 2.0 1.8 1.6 3.3 1970 3.6 9.2 3.5 3.8 3.5 4.7 2.1 1.9 1.7 3.6 1971 3.9 10.0 3.9 4.0 3.7 5.0 2.2 2.0 1.7 3.9 1972 3.9 9.8 3.9 3.9 3.7 5.1 2.3 2.0 1.7 3.9 1973 3.6 9.1 3.6 3.7 3.6 4.8 2.2 1.8 1.6 3.7 1974 3.7 9.3 3.7 3.7 3.6 4.9 2.2 1.8 1.6 3.8 1975 4.3 11.0 4.4 4.0 4.I 5.5 2.5 2.0 1.7 4.4 1976 4.3 10.9 4.3 4.0 4.2 5.6 2.5 2.0 1.7 4.4 1977 4.4 10.9 4.3 4.0 4.3 5.7 2.6 2.0 1.7 4.5 1978 4.3 10.5 4.2 3.9 4.4 5.7 2.6 2.0 1.6 4.5 1979 4.6 10.8 4.3 4.0 4.7 5.9 2.8 2.0 1.7 4.8 1980 5.1 12.2 4.8 4.3 5.2 6.5 3.0 2.2 1.8 5.3 1981 5.5 12.8 5.0 4.5 5.6 6.8 3....</p></li></ul>

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