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

Economics of Planning 25: 219-236, 1992 �9 1992 Kluwer Academic Publishers. Printed in the Netherlands.

Estimation of Output Loss from Allocative Inefficiency: A Comparison of the Soviet Union and the U.S. 1

HUMBERTO BARRETO Wabash College, CrawfordsviUe, Indiana, U.S.A.

ROBERT S. WHITESELL Williams College, Williamstown, Massachusetts, U.S.A.

Abstract

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.

I. Introduction

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, additional 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

220 HUMBERTO BARRETO AND ROBERT S. WHITESELL

II. Data

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, however, 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.

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.

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

III. Theoretical analysis

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 inefficiency 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 inefficiency .5

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

OUTPUT LOSS AND ALLOCATIVE INEFFICIENCY 221

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

Since both inputs are being reduced equiproportionately, a simple measure of the efficiency gain is

Proportional /2 /( - 1 - 1 ,7 ( 1 )

Factor Savings L* K* Gain

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.

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.

The measure of efficiency is:

Single Pi f', + Pj Y~ - 1 ( 2 )

Output Augmenting = P i~ + Pj I?j Gain

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) measure, its inclusions does provide a full description of the allocative efficiency analysis and a more complete empirical picture.

IV. E m p i r i c a l e s t i m a t i o n

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


change. The functional forms are:

C D A I : In y~(t) = In % + Ait +/xit 2 + ai In ki(t ) + ei(t) ,

C D I : In y~(t) = In ~,~ + A~t + txi t2 + ai In ki(t ) + ui ( t ) ,

(3)

(4)

where i

yi(t) ki(t) % h i + 21xit Ol i

1 - - Ol i

u i t

= sector i = ou tpu t - l abor ratio in year t = capi ta l - lab0r ratio in year t = an efficiency paramete r = 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.

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 count ry)

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 capi ta l - labor ratio constant. We began by calculating the imputed MRSs for each sector of industry from the product ion function estimates:

f / 1 MRS i ~ k i i = 1, 9 (5)

f K O/i

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 capi ta l - labor ratio for each sector was then calculated, given this new MRS* as

&/MRS* k * - ~ _---~ (6)

Opt imal labor use was then calculated f rom this capi ta l - labor ratio and the predicted level of output 9 as

L* ~ -xi'-#i'2"*si = =- e K i . (7) Yi

From (6) and (7), the optimal amount of capital is


K* * * = k i L i . (8)

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

MRS* = MRS*(/~/k*) , (9)

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.

The iterative procedure described above generates M R S * - t h e MRS which rules in every sector. Fur thermore, 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.

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

kr =Kc/Lc, (10)

and

MRS c = [(1 - &c)kr (11)

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 proport ional gain in output that could be achieved was calculated as the Single Output Augmenting Gain in Equation 2. l~

V. Discussion of results

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


Table 1. Percent inefficiency Soviet Union, 1960-1984.

YEAR FGAIN POWER FUEL FMET CHEM MBMW CONST WOOD LIGHT FOOD

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

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.

using bo th the factor savings and p ropor t iona l ou tpu t augment ing mea-

sures. Tab les 3 and 4 give the op t imal M R S , the impu ted initial sectoral

M R S s and the factor rea l locat ions using the factor savings approach. 11

Tab les 5 and 6 give the se lec ted p roduc t ion funct ion es t imates for each

industr ia l sector for the Sovie t U n i o n and the U n i t e d States, respect ively .

Final ly , F igure 1 compares the US and Sovie t factor savings inefficiency measu re .

A rev iew of the factor savings es t imates yields some in teres t ing results.

F igure 1 shows that inefficiency is lower in the U n i t e d States than in the

Sovie t U n i o n in the 1960s and early 1970s, but this d i f ference appears

small - cer ta inly much smal ler than most scholars of the Sovie t e c o n o m y

would have expec ted . Since inefficiency is rising ra ther sharply in the

U n i t e d States and falling slowly in the Soviet U n i o n dur ing the late 1970s,

the d i f fe rence b e c o m e s smal ler over t ime and vir tual ly disappears by the 1980s.

OUTPUT LOSS AND ALLOCATIVE INEFFICIENCY

Table 2. Percent inefficiency United States, 1960-1984.

225

YEAR FGAIN MIN POWER METAL MBMW CHEM FURN WOOD LIGHT FOOD

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 3.2 2.3 1.9 5.7 1982 6.0 14.4 5.5 4.8 6.1 7.2 3.4 2.5 1.9 6.1 1983 5.4 13.3 5.0 4.2 5.6 6.5 3.1 2.2 1.7 5.5 1984 5.1 12.2 4.5 3.9 5.5 6.2 3.0 2.1 1.6 5.3

T h e s e resu l t s a r e s t r ik ing in t h r e e respec t s . F i r s t , t h e y p r e s e n t e v i d e n c e

t h a t t h e r e m a y be no s ign i f ican t d i f f e r e n c e in t h e a l l oca t i ve e f f i c i ency o f a

m a r k e t e c o n o m y a n d a S o v i e t - t y p e e c o n o m i c sy s t em. 12 M o s t e c o n o m i s t s

w o u l d h a v e e x p e c t e d t h a t t h e S o v i e t U n i o n w o u l d be a g r e a t d e a l m o r e

i ne f f i c i en t t h a n t h e U S ; b u t o u r resu l t s s h o w t h a t such an e x p e c t a t i o n m a y

b e i n c o r r e c t . S e c o n d , t h e i n c r e a s e in a l l o c a t i v e e f f i c i ency in t h e S o v i e t

U n i o n d u r i n g t h e l a t e 1970s a n d ea r ly 1980s runs c o u n t e r to o t h e r

a n a l y s e s - i n c l u d i n g t h o s e o f t h e Sov i e t s t h e m s e l v e s - w h i c h h a v e a r g u e d

t h a t e f f i c i ency was d e c r e a s i n g in t h e 1970s and 1980s. F ina l ly , t h e

a b s o l u t e l e v e l o f i ne f f i c i ency e s t i m a t e d fo r t h e S o v i e t e c o n o m y s e e m s

smal l . T h i s c o n f i r m s t h e resu l t s o f D e s a i a n d M a r t i n (1983) , w h o f o u n d

e v e n s m a l l e r l eve l s o f ine f f i c i ency . 13 In c o n c l u s i o n , c o n t r a r y to p o p u l a r

b e l i e f , w e f a i l ed to f ind e v i d e n c e o f m a s s i v e a l l oca t i ve i ne f f i c i ency in t h e

S o v i e t U n i o n .

B e f o r e w e a t t e m p t to i n t e r p r e t t h e s e resu l t s it m u s t be r e e m p h a s i z e d

t h a t t h e s e e s t i m a t e s c a l c u l a t e o n l y losses in o u t p u t f r o m a l l o c a t i v e

i n e f f i c i e n c y in p r o d u c t i o n . A l l o c a t i v e i ne f f i c i ency f r o m a m i x o f o u t p u t s

t h a t is w r o n g f r o m t h e v i e w p o i n t o f c o n s u m e r d e m a n d is n o t b e i n g t a k e n

i n t o a c c o u n t in th is analys is . B y n o t us ing p r i ces , t h e analys is a v o i d s

i n s u r m o u n t a b l e d a t a p r o b l e m s a n d soc ia l w e l f a r e f u n c t i o n c o n s i d e r a t i o n s ;


Table 3. Factor reallocations Soviet Union, 1960-1984. Factor savings method.

YEAR 1960 1965 1970 1975 1980 1984 TOTAL % GAIN 5.9 6.7 6.8 6.4 5.9 5.5 MRS* 2.2 3.3 4.3 6.1 8.3 10.4

MRS KCHANG (millions of Rubles) LCHANG (millions of hours worked) POWER 6.6 9.5 12.9 17.5 21.9 24.8

-3493 -6366 -10491 -14786 -18699 -21049 941 1167 1439 1457 1412 1329

FUELS 0.7 1.1 1.5 2.2 3.0 3.6 1838 2685 3578 4924 7103 10517

- 1523 - 1507 - 1473 - 1385 - 1471 - 1785

METAL 4.4 6.7 9.2 13.1 17.6 21.9 -2646 -4637 -7350 -10687 -14502 -18199

852 996 1167 1190 1200 1206

MBMW 1.4 1.8 2.3 3.3 4.8 6.3 4528 10901 17903 28900 39519 48358

-2613 -4561 -5687 -6411 -6269 -5976

CONST 2.6 4.9 6.2 9.2 12.6 15.1 - 4 5 6 -2032 -2681 -4700 -6690 -7488

192 506 516 623 655 597

CHEM 3.9 5.6 8.3 12.3 17.2 22.6 -1277 -2748 -5855 -10215 -16418 -23310

438 641 977 1173 1373 1518

WOOD 2.5 4.4 6.0 9.2 12.6 15.9 - 447 - 1584 - 2444 - 4373 - 6209 - 8118

192 420 480 581 606 628

LIGHT 1.0 1.5 1.9 2.9 3.8 4.9 2814 4372 6874 9444 13546 16371

-1890 -1967 -2362 -2217 -2395 -2279

FOOD 8.4 13.3 16.4 22.3 29.8 36.4 -5359 -9436 -13239 -18264 -24020 -29522

1191 1363 1499 1493 1464 1456

b u t s u c h a m o v e m e a n s w e m u s t f o r e g o e x a m i n i n g w h e t h e r o r n o t t h e

c h o s e n v e c t o r o f o u t p u t is e f f i c i en t w i t h r e s p e c t to c o n s u m e r d e m a n d s .

T h e c h o s e n b u n d l e o f o u t p u t s m a y b e ' w r o n g ' f r o m t h e c o n s u m e r s ' p o i n t

o f v i e w , b u t th is t y p e o f i n e f f i c i e n c y is n o t a d d r e s s e d in th is p a p e r . 14

O u r e x a m i n a t i o n o f i n t e r b r a n c h r e s o u r c e m i s a l l o c a t i o n a lso i g n o r e s

f o r e g o n e o u t p u t f r o m t e c h n i c a l i ne f f i c i ency . In fac t , t h e ana lys i s impl i c i t ly


Table 4. Factor reallocations United States, 1960-1984. Factor savings method.

227

YEAR 1960 1965 1970 1975 1980 1984 TOTAL % GAIN 4.0 3.4 3.6 4.3 5.1 5.1 MRS* 140 155 198 240 253 294

MRS KCHANG (millions of Dollars) LCHANG (millions of hours worked) POWER 79 90 100 124 127 131

43694 47364 73915 89728 108750 140008 -420 -403 -530 -525 -614 -725

MINING 44 57 65 57 50 68 55830 56199 69526 95570 132761 146355

74i -617 -636 -869 -1274 -1098

METAL 220 220 309 401 459 624 -25089 -23441 -37708 -48225 -61519 -76837

142 126 151 154 178 177

MBMW 161 170 234 286 315 394 -18281 -14409 -34921 -46390 -69440 -107497

122 89 162 177 245 315

FURN 955 888 1186 1734 1812 1809 -3661 -3819 -5179 -7070 -8251 -8686

9 9 9 9 10 10

CHEM 459 472 556 689 759 831 -75118 -83137 -104400 -129593 -165171 -178288

283 295 304 308 362 349

WOOD 29 31 40 58 64 6i 29455 33345 39882 43511 50879 63814 -445 -459 -427 -358 -386 -458

LIGHT 790 811 1036 1407 1577 1777 -69491 -74992 -95231 -116215 -137359 -149110

186 190 189 177 191 182

FOOD 101 112 122 150 168 194 21636 23316 40657 44379 43626 49137 -182 -177 -260 -233 -210 -205

assumes that t he re is no technical inefficiency since use of p roduc t ion

funct ions impl ies es t imat ion of the m a x i m u m outpu t that can be p r o d u c e d

with g iven levels of inputs. 15 Much , though not all, of the cri t icism of the

eff ic iency of the Sovie t - type system has to do with technical efficiency.

T h e resul ts p r e sen t ed he re offer no guidance in de t e rmin ing the level of

t echnica l inefficiency. H igh technical ineff iciency is perfec t ly compa t ib l e


Table 5. Best regression results, Soviet Union, 1960-84.

Sector R 2

D - W y A ~ ~ p SE SE SE SE SE t t t t t

POWER -0.8163 0.7282 0.8383 0.9982 0.0655 0.0198 0.1282 1.47 12.46 36.84 6.54

FUELS - 0 . 9 0 0 8 0.8978 1.1481 0.9980 0.1083 0.0590 0.0278 1.96 8.32 15.22 41.35

METAL -0.1015 0.5153 1.1220 0.9962 0.0914 0.0598 0.0468 1.94 1.11 8.62 23.95

CHEM -0.0306 0.4644 0.8900 0.9930 0.0547 0.0325 0.1006 1.70 0.56 14.27 8.85

MBMW 0.0519 0.4736 0.8811 0.9943 0.0227 0.0307 0.1114 1.42 2.28 15.43 7.91

CONST 0.1258 0.3600 0.5528 0.9790 0.0296 0.0203 0.1858 1.89 4.26 17.72 2.97

WOOD 0.0859 0.2713 0.8345 0.9863 0.0169 0.0190 0.1254 2.04 5.08 14.31 6.65

LIGHT -0.1159 0.3738 0.8464 0.9928 0.0133 0.0214 0.1228 1.68 8.72 17.50 6.89

FOOD 0.0937 0.0272 -0.0005 0.1809 0.9852 0.0730 0.0061 0.0001 0.1000

1.28 4.44 4.87 1.81

with a low level of a l locat ive inefficiency, as a l locat ive inefficiency is m e a s u r e d here . 16

A n o t h e r technica l exp lana t ion for the low level of inefficiency esti-

m a t e d focuses on the l imi ted n u m b e r of sectors s tudied. These es t imates

are not for the ent i re e c o n o m y , but only for the manufac tu r ing and

min ing sectors. It has been found that the level of inefficiency is posi t ively

r e l a t ed to the n u m b e r of sectors used in the analysis. 17 Thus, the addi t ion

o f o the r sectors of the e c o n o m y would increase the absolute m easu re of ineff iciency, but it would do so for bo th the Sovie t and U.S . economies , is


Table 6. Best regression results, United States, 1960-1984.

229

Sector R 2

D - W y A /x o~ p SE SE SE SE SE t t t t t

POWER -1.0208 0.0436 -0.0013 0.7806 0.9900 0.8801 0.0061 0.0001 0.1565

1.16 7.17 10.10 4.99

MINING -0.0823 0.8305 1.0447 0.9624 0.6111 0.1138 0.0729 0.90 0.13 7.30 14.34

METAL 2.5115 0.1563 0.5438 0.7073 0.2155 0.0518 0.1789

11.66 3.02 3.04

MBMW 2.5460 0.0009 0.0910 0.6370 0.9491 0.4267 0.0003 0.1480 0.1682

5.97 3.69 0.62 3.79

FURN 0.9780 0.6444 0.8449 0.1281 0.0576

7.64 11.19

CHEM 2.6029 0.0320 - 0.0004 0.1114 0.9753 0.6321 0.0036 0.0002 0.1561

4.12 8.76 2.29 0.71

W O OD 1.2407 0.2960 1.0250 0.9330 0.3858 0.1521 0.0318 1.36 3.22 1.95 32.22

LIGHT 2.0703 0.0161 1.0724 0.9875 0.3140 0.1230 0.0318 1.38 6.95 0.13 77.27

FOOD 2.0218 0.0230 0.2118 0.9829 0.6889 0.0060 0.2116

2.94 3.83 1.00

This is caused by the implici t a ssumpt ion that there is an efficient

a l locat ion of factors within each sector. The re laxat ion of this assumpt ion

is l ikely to increase the measures of inefficiency. These poin ts make it clear tha t our analysis does not examine efficiency

in the Soviet and US economies in a 'g lobal ' or a l l -encompass ing sense. The analysis concerns a par t icular type of e f f i c i e nc y - efficiency in the

a l locat ion of inputs for p roduct ion . A l though other kinds of inefficiency are essent ial ly ' a s sumed away' by the analysis, this does no t affect the compar i son of the two economies in te rms of allocative inefficiency in


Table 7. The data by country and sector.

USSR Sectors US Sectors

Electric power Electric, gas and sanitary services

Fuels Mining Ferrous metallurgy Metallurgy Machine building and Machine building and

metal working metal working Chemicals Chemicals Construction Furniture and fixtures

materials Wood products Wood products Light industry Light industry Food processing Food processing

production. Thus, our finding concerning the unexpectedly low level of Soviet allocative efficiency is still noteworthy given the fact that most economists believe that Soviet-type systems are inferior to market systems in all senses of the term efficiency.

Instead of immediately concluding that unreliable data and methodological difficulties are the source of the surprisingly low allocative inefficiency estimates (a view discussed below), perhaps there are theoretical considerations which would lead one to expect low levels of allocative inefficiency in production in Soviet-type economies. The system has weak incentives for technical efficiency and innovation, but its relative strength is an ability to allocate resources. The system has long

3 1960

I 1

1970 l g 8 0

Y E A R

Fig. 1.

6

=.

2 s 5

" 4

[] USSR

8 US


been considered relatively good at mobilizing investment and labor and having the capacity to rapidly transfer resources in desired directions. Furthermore, the 'second economy' operates as a source of efficient reallocation when the planning system is inadequate. Informal markets, such as those utilizing tolkachi, result in trades which are based directly on the needs of individual firms. Our results provide empirical support for the proposition that resource allocation in production is a relative strength of the Soviet economy and is not a significant source of inefficiency.

Similar considerations provide an explanation for the apparent improvement in allocative efficiency over time. The planning mechanism may be able to improve the efficiency of its resource allocation over time because planners obtain more and better information as the operation of the economy is observed. 19 One would also expect that allocation is easier the slower the growth of the economy and the slower the rate of technological innovation. 2~ Economic growth has been decreasing since the early 1960s and it is likely that the rate of innovation has been decreasing as we l l . 21 Finally, growth in the importance of the second economy would be expected to improve allocative efficiency over time. The rhetoric of the Soviets themselves implies that there has been an expansion of the second economy.

The surprisingly small difference in allocative inefficiency is the most striking result, but a closer examination of the estimates- including the single output augmenting measures of inefficiency- reveals additional information about these alternative economic systems. A review of the factor savings estimates for the Soviet Union over time shows a decrease in allocative efficiency from 1960 to 1962, a constant rate of inefficiency throughout the remainder of the 1960s, and an increase in allocative efficiency beginning sometime in the early 1970s (see FGAIN in Table 1 and Figure 1). For the United States, initially, there is an improvement in efficiency; followed by a decrease in efficiency from the mid-1960s to 1982; and, finally, some improvement in the last two years of the period (see FGAIN in Table 2 and Figure 1). The factor savings measure of inefficiency shows much more volatility for the United States industrial economy.

The U.S. factor savings estimates show sharp increases in inefficiency in 1975 and again in 1979. These changes in allocative efficiency corre- spond to 1974 and 1979 oil price increases. This is evidence of the U.S. economy's sensitivity to dramatic economic changes. The improvement in efficiency in the years following these shocks indicates that the market economy will, after some time, adjust to the changed circumstances and allocative efficiency will improve.

The Soviet economy, on the other hand, appears to be much less sensitive to economic disturbances. This is due to the stability of prices and the allocative mechanism. Shocks to the system that radically change


supply, demand and equilibrium prices have little effect on the allocation of factors in the Soviet economy because equilibrium prices do not guide allocation decisions. Furthermore, the internal economy is shielded from external economic shocks by the separation of internal and foreign markets; i.e., changes in the foreign trade market have no direct, and only a very minor indirect, influence on the operation of the domestic economic mechanism) 2

VI. Conclusion

Estimation of the factor savings and single output augmenting measures of inefficiency for the Soviet Union and the United States confirmed some 'stylized' facts, but also yielded some unexPected , interesting results. Weak evidence is presented that the Soviet Union suffered from a greater degree of allocative inefficiency than the United States. This conclusion is reached, not only by a comparison of the factor savings measure, but also by the generally lower levels of single output augmenting inefficiency in the United States. Surprisingly, the differences are much smaller than might have been expected, and we have argued that this indicates that allocative inefficiency in production is not a significant source of inefficiency in the Soviet economy. In addition, the Soviet economy appears to maintain a much more stable level of inefficiency, and it actually may have been improving over time in the pre-Gorbachev era. This can be seen in both the factor savings and the single output augmenting measures of inefficiency.

Several caveats, in addition to those already mentioned, need to be emphasized. First, well known objections to aggregate production functions are relevant. Second, it could be argued that factor MRSs should not be equal because labor is not homogeneous, so we could be estimating spurious inefficiency. These are potentially serious problems that cannot be corrected without more disaggregated data. Since more disaggregated data on the Soviet economy are unavailable, there is little alternative other than to rely on aggregate indicators. Third, it could be argued than to rely on aggregate indicators. Third, it could be argued that this analysis supplants the market mechanism by not using prices and is, therefore, not relevant for the U.S. market economy. An attempt was made to make the analysis of the two countries as comparable as possible. Since the relevant price data are not available for the Soviet Union, and would not be equilibrium prices anyway, this method yields a better comparison than one which included market prices. 23 Fourth, it could be argued that the reallocations presented are illegitimate because factors are not substitutable across sectors. Since factors are malleable in the long run, this does not appear to be an important criticism. Gross allocative inefficiencies would be expected to lead to long-run changes in


investment and production decisions that would tend to eliminate them. Short-run fixedness of inputs is part of the cause of the inefficiencies that are being measured. Finally, although we have attempted to make the estimates as comparable as possible, deficiencies and dissimilarities in the data could certainly bias the results. Because of these potential problems the results must be considered suggestive but not conclusive.

The purpose of this paper is to place previous research on the allocative efficiency of the Soviet economy into a comparative perspective and to test the variability of the estimates using different methods of estimation. The results indicate a generally higher level of allocative efficiency in the United States than in the Soviet Union, but the difference is much less than most students of the Soviet economy would have expected. The implication is that resource allocation problems may be a less important explanation of poor performance in a Soviet-type economic system than other problems, such as technical inefficiency, lack of technological innovation, and a poor product mix.

Notes

1. We would like to thank Abram Bergson, Joe Berliner, Joe Brada, Padma Desai, Ed Hewett, David Kemme, Peter Murrell and several referees who have made helpful comments on various versions of this paper. A stronger than usual caveat is in order that none of these people should be associated with the errors or conclusions contained in this paper.

2. This paper follows the method used by Desai and Martin (1983). Toda (1986) used fixed-point methods of calculating efficiency loss, as suggested by Whalley (1976), and found losses not much different from Desai and Martin.

3. Sources are Block (1979), 137; CIA (1984), 69; and Joint Economic Committee (1986), 78.

4. The Bureau of Economic Analysis publishes a capital input series which takes into account variations in the utilization of capital. Although clearly superior, this series was not used in order to maintain comparability with the available data from the Soviet Union.

5. It can be shown that the proportional output augmenting measure is equivalent to the factor savings measure if there are constant returns to scale.

6. See Desai and Martin (1983b) for a more detailed description of this procedure. 7. Desai and Martin use a different measure, i.e.,

MRS*/~ + / ( - 1 ,

MRS*L* + K*

but it can be shown that their measure and ours are equivalent. We would like to thank Peter Murrell for pointing out this equivalence.

8. See WhiteseU (1983) and Mizon (1977) for a more detailed description of the selection procedure.

9. Predicted output from the production function estimates was used rather than actually observed levels of output. This choice is necessitated by the fact that interest is focused on allocative inefficiency. If actual output levels were used then the measure of inefficiency would be biased upward (downward) whenever observed output was less


(more) than predicted output. This is the case because the production function estimates would allow production of the observed output level with less (more) of both inputs without any reallocation among industries.

10. It must be stressed that this procedure results in nine different estimates of inefficiency. The estimated MRS* is different in each of the nine cases. The amounts of capital and labor that are reallocated are different in each case, and since they are applied to different outputs with different production functions, the effect on production is different in each case.

11. Note that, as we would expect, when the observed MRS is greater than the optimal MRS*, that sector is allocated more labor and less capital. On the other hand, MRS < MRS* implies a decrease in labor and an increase in capital. In addition, note that the exact same vector of outputs is produced with less total input use.

12. No confidence intervals were calculated because of the complicated functional form involved in the calculation of the inefficiency estimates. Given the standard errors of the estimates there is no doubt that confidence intervals would result in no statistically significant difference between the two countries and might even imply no statistically significant inefficiency in either country.

13. Though our estimates show a slightly higher level of inefficiency, they are well within their confidence levels. The discrepancy is probably caused by the difference in time period, 1960-1984 versus Desai and Martin's 1955-1975. Thornton (1971) and Toda (1986) also get similarly low estimates of allocative inefficiency for the Soviet Union using somewhat different methods.

14. Thus, we estimate the gains in output that could be achieved from an efficient reallocation of resources, but make no claims about the social welfare optimality of the solution. As is well known, there are many efficient allocations possible. There is no way of knowing which is the social welfare optimum. This is particularly true because the analysis is entirely production based; no reliable information about consumer demands or output prices is available. This information cannot be used or estimated because Soviet prices are not determined by supply and demand, and therefore, do not convey the appropriate information.

15. Alternatively, one could argue that there is technical inefficiency, but its effect is Hicks-neutral. If this were the case, the capital coefficients would not be affected, and thus, the factor MRSs would remain unchanged. Thus, one could argue that allocative inefficiency is calculated, given some unknown level of technical inefficiency. Essential- ly, What the analysis amounts to is that if, for example, a worker works only 1 hour for each 8 hours on the job, then that worker will work only 1 hour for each 8 hours regardless of where he/she works. So we are calculating relative sectoral factor productivities, given some fixed level of technical inefficiency.

16. It might be argued that the technical efficiency question could be answered by estimating frontier production functions. However, this would not be sufficient to compare technical efficiency across countries. See Kemme and Whitesell (1992) for a discussion of the limitations of frontier production function for a cross-country comparison. Furthermore, technical inefficiency, as measured in Kemme and Whitesell (1992), is very small- less than 5 percent.

17. See Whitesell (1987 and 1989). These results indicate, however, that the trends over time, the variability in the single output augmenting measure across sectors, and the comparison between the countries are not affected.

18. Table 2 indicates that the single output augmenting estimate for the mining sector in the U.S. results in a greater level of inefficiency than any other estimate. This created the suspicion that much of the U.S. inefficiency was caused by this sector. This could occur, perhaps, because the exclusion of land as an input is more important in this sector than in others. Therefore, the factor savings method was recalculated without mining, but inefficiency was reduced by less than one percent.


19. See, for example, Weitzman (1970) and Manove (1971). 20. See Whitesell (1990) for an expanded version of this argument. 21. The production function estimates presented here are evidence that factor productivity

growth, part of which is technological innovation, has been virtually nonexistent. 22. See Rosefielde (1980). 23. Note also that the levels of inefficiency calculated for the U.S. are consistent with

earlier estimates of the welfare loss from monopoly. See Bergson (1973), Harberger (1954), Kamerschen (1966), and Schwartzman (1960). Although these estimates are not comparable to ours they are alternative estimates of allocative inefficiency.

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