World Bank Reprint Series: Number 245

Mieko Nishimizu and John M. Page, Jr.

Total Factor Productivity Growth,Technological Progress, andTechnical Efficiency Change

Dimensions of Productivity Changein Yugoslavia, 1965-78

Reprinted with permission from Thle Econiomic Journial, vol. 92 (December 1982),pp. 920-36.

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The Economic Journal, 92 (December I982), 920-936

Printed in Great Britain

TOTAL T 'ACTOR PRODUCTIVITY GROWTH,TECHNOLOGICAL PROGRESS ANDTECHNICAL EFFICIENCY CHANGE:

DIMENSIONS OF PRODUCTIVITY CHANGEIN YUGOSLAVIA, 1965-78*

Alieko Nishimizu and John M Page, Jr.

The economic theory of production has provided the analytical framework formost empirical research on productivity. The cornerstone of the theory is theproduction function which postulates a well-defined relationship between avector of maximum producible outputs and a vector of factors of production.Historical analyses of total factor productivity change, whether the non-parametric index number approach or the parametric approach, identify thechange in total factor productivity as the change in output levels controllingfor input levels, i.e. the vertical shift of the production function. All kinown andusual criticisms notwithstaniding, the resulting estimates have proven to beuseful policy parameters. There is, however, an important weakness in theconventional approach. It does not permit the distinction between technologicalchange and changes in the efficiency with which known technology is appliedto production. More often than not, in fact, the concept of total factor produc-tivity change is used synonymuasly with technological change in the productivityliterature.'

Following Farrell's (I957) contribution to the analysis of production, sub-stantial empirical and methodological interest has focused on the concept of afrontier or 'best practice' production function which defines for any set ofobservations the outer boundary of possible input-output combinations. Muchof this work seeks to measure and explain variations in the total factor pro-ductivity of observations relative to the frontier. The amount by which measuredtotal factor productivity is less than the potential, based on best practice, isconventionally defined as technical inefficiency.

Although technological change and technical efficiency share a commonmethodological basis in the production function, applied work in these fieldshas evolved largely independently. The objective of this paper is to propose amethodology that decomposes total factor productivity change into technologi-

* WVe are grateful to Suman Bery, Laurits C:hristensen, Mark Gersovitz, Larry Westphal, JeffreyWilliamson and Adrian WVood for their valuable comments on an earlier draft. We are indebtedto the Federal Statistical Office of Yugoslavia for making available the unpublished statisticalmaterials used in this tudy, and to Kathleen Jordan and Deborah Bateman for research assistance.The views and interpretations in this paper are the authors' and should not be attributed to the WNorldBank.

I For relevant discussions see, for example, Jorgenson and Nishimryizu (1978, g979) who proposeda methodology for bilateral total factor productivity comparisons, and applied it to aggregate as wellas disaggregate United States Japan comparisons. Caves et al. (ig8x, 1982) and Denny and Fuss( 1980, I98 I) have examined the property of index numnbers and structure of production in multilateralor interspatial and intertemporal output, input arid total factor productivity comparisons.

[ 920 ]

[DECEMBER I982] PRODUCTIVITY CHANGE IN YUGOSLAVIA 92I

cal progress and changes in technical efficiency. We define technologicalprogress as the change in the best practice production frontier, and establishits rate by direct estimation of a deterministic frontier production function.'We then refer to all other productivity change - for example learning by doing,diffusion of new techinological knowledge, improved managerial practice aswell as short run adjustment to shocks exterinal to the enterprise - as technicalefficiency change.

In studying the productivity performance of developing economies, the dis-tinction between teclhnological progress and changes in technical efficiency isparticularly relevant. Given a level of technology, explicit resource allocationmay be required to reach the 'best-practice' level of technical efficiency overtime. There is accumulating evidence that the productivity gain due to such'technological mastery' is substantial in developing economies, and may out-weigh gains from technological progress. It is therefore important to knowhow far one is off the technological frontier at any point in time, and howquickly one can reach the frontier.

The analysis of productivity change in Yugoslavia provides a useful illus-tration of the distinction drawn above. Considerable attention has recentlybeen directed at the sources of the slowdowvn in Yugoslav economic grox th inthe I970s. (See for example Tyson (I980) and Sapir (I980).) The principalfinding of this paper is that changes in technical efficiency dominated tech-nological progress in Yugoslavia tlhroughout the period 1965-70 and that theimpact of deteriorating technical efficiency was particularly acute in theperiod I970-5.

In section I of the paper we outline our methodological framework fordecomposing total factor productivity growth into technological progress andchanges in technical efficiency. Section II discusses specification and estimationof the deterministic frontier production function. We specify a translog produc-tion frontier, which is estimated by the programming technique of Aigner andChu (I968) and Timmer (I970, I97I). To our knowledge this is the firstempirical application of the programming approach to the estimation of aflexible functional form of the production frontier. 2 -ection III presents anapplication of the technique to social sector panel data of Yugoslavia byindustry and region for the period I965-78, and discusses main empiricalresults. Section IV offers some concluding remarks including some policyimplications of our results.

1 For an excellent survey of the literature on the frontier production function see Forsund et al. (1980).A few applications of the frontier production function have been made to the study of technologicalchange. Forsund and Hjalmarsson 1979) lhave eniployed a generalised Cobb-Douglas frontier toexamine technological clhange in the Swedish dairy industry, Greene (ig8ob) has applied a frontiercost function to measure technical change in aggregate U.S. manufacturing. WNe know of no empiricaleffort, hlowever, that exaniines changes in techlnical efficiency simultaneously Wvith technological change,although Timmer (I97o; presented a theoretical discussion of the relationship between them usingFarrell's (I957j unit isoquant.

2 Greene (xg8oa) has proposed a specification of the translog production function with a twoparameter Gamma distribution which can be estinated by maximum likelihood techniques.

922 THE ECONOMIC JOURNAL [DECEMBER

I. THEORETICAL FRAMEWVORK

The starting point for our analysis is a functional relationship between outputsand inputs which characterises the production processes of a well-definedeconomic entity, for example a firm:

G[x(s, t), z(s, t); s, t] < o, (I)

where x and z are respectively the vector of outputs and inputs of firm s attime t. s and t appear in G to indicate the levels of marginal factor productivitiesof firm s at time t. For brevity of exposition, let us suppose that the outputvector is separable from the input vector, and that there exists an appropriateaggregate index of output. We can then represent the production relationship as

x(s, t) < g[z(s, t), s, t], (2)

where x(s, t) represents the index of aggregate output of firm s at time t. Weassume that the usual regularity conditions are satisfied by g.

For any observed combination of output and inputs of a firm, the inequalityin (2) holds when the observed firm is not employing its inputs with the pro-ductivity level of 'best practice' at the observed input mix. Denoting by s, t,and x the potential or best practice productivity and output levels, we canrewrite (2) for an 'interior firm' operating at less than the best practice:

x(s, t) = g[z(s, t); s, t]< g[z(s, t); ] = (s t). (3)

g is assumed to be well-defined over s and t; and it represents our presumptionthat a firm possesses good technological or economic reasons in operating awayfrom its potential frontier.

Let us define the potential level of total factor productivity relative to theactual observed level of total factor productivity for this firm as the minimumpossible factor of reduction in potential output that can be produced with theobserved inputs employed at the actual productivity levels:

e(s, t) x(s, t) = g[z(s, t); s, t], (o < e < I). (4)

An alternative definition for e(s, t) is the maximum factor of increase in actualoutput that can be produced with the observed input employed at the potentialproductivity levels:' x

x(s, t)/e(s, t) = g[z(s, t); s, t]- (5)

These two definitions are equivalent within our framework, and e is reduced toan output level comDarison between x and x at the observed input mix z(j, t):

e(s, t) = x(s, t)/x(s, t). (6)

From the first equality of (3), the rate of change of total factor productivityobserved for the firm s is

g(Z, s, t) == x 5S, t) -gzf s, t)iz(s, t), ( 7)

1 These definitions are due to Malmquist (1953). See Caves el al. (1g8i, 1982) for discussion of

Malmquist index in productivity comparisons.

i982] PRODUCTIVITY CHANGE IN YUGOSLAVIA 923

where g2(s, t) is the vector of output elasticities of eaclh component of z, andthe dot over variables denotes logarithmic time derivatives. But from (5), wecan rewrite (7) as

gfz, s, t) = g(z, s, I ) + d(s, t) + [gz(s i) -gz( s, t)] z(s, t). (8)

In equation (8), the rate of technological change of the 'best practice'frontier, g( , s, t), represents in a sense the 'true rate of teclhnological progress.Over any given set of firms the frontier production function provides informa-tiorn on the subset of firms which define the technological state of the art. Itsmovement over time, however, must not be confused with changes in the rela-tive efficiency with which known techniques are employed. These effects arecaptured by e(s, t) in equation (8). As we have defined it, es, t) represents therate at which any observed firm is moving toward or away from the bestpractice frontier. We can refer to e as the rate of technical efficiency changein the sense discussed in the introduction.' Finally, at any given level of inputs,an interior firm's effort to reach its potential output may entail changes inoutput elasticities. The last component of observed total factor productivitychange in (8) represents this. Thus, equation (8) represents a decompositionof the conventional measure of total factor productivity change into threecomponents: techn6logical progress, technical efficiency change, and outputelasticity differences between the frontier and the interior.

The relationship between our decomposition of total factor productivitychange and the conventional approach is illustrated for a simplified case inFig. i. g, and g2 represent linear homogeneous, Cobb-Douglas frontier pro-duction functions witlh Hicks neutral technical progress between periods I and2. Points A and C are the observed levels of output xI, x2 (in logarithms) at timei and 2 with corresponding potential levels xl, A2 at points a and c.2 The linesegment AB represents the projectioni of the input contribution to the change inoutput, based upon the actual output elasticities of the interior firm.3 Thedistances Aa and Cc are el and e2, respectively

The conventional measure of total factor productivity change is BC, thechange in output net of the input contribution to that change, A'B. The usualinterpretation is that BC represcnts the increase in output due in some senseto technological progress. Our method posits that the contribution of techno-logical progress is given directly by the displacement of the frontier productionfunction, bc. If the observed firm had employed the best practice technologiesembodied in g, and g2, the difference between its potential outputs a'c and theamount of the change attributable to the increase in input, a'b, would equal bc.The increase in output predicted from the frontier production function is BC'

1 By definition, e for a firm that sustains best-practice over time must be zero. For others it will bepositive (negative) as the firm experiences a decreasing (increasing) gap between its potential toactual productivity levels. Of course it is possible for a firm to be on the frontier at one time periodand off it at another. In such cases e will take on the value anid signi appropriate to the direction ofmovement relative to the shifting frontier.

' All variables in the text referring to Fig. I will be defined in logarithms unless specifically noted.The reader nmay think of x as oUtptut per capita and z as capital labour ratio.

I AB is drawn parallel tog,. We assume the equality between actual and potential output elasticitiesof z for brevity of exposition.

924 TIUE ECONOMIC JOURNAI [DECEMBER

(equals bc). In Fig. I, this is less tlhan the actual clhange BC. The distance C'C

is the change in output attributed to technical effic'i. c-i gain, e. The observed

production point has moved closer to the frontier in period 2 than in period i.Conventional measures of total factor productivity change cannot distinguish

between technological progress and changes in teclhnical efficiency, yet the

two are analytically distinct and may lave quite different policy implications.Technological progress, as Nwe definie it, is the consequence of innovation or

~92

- gt

-1 (-

dg'a

l - B

- X 2

Fig. i. Alternative interl)retations of produ tivity (hange.

adoption of new technology by lest practice firms. Total factor productivity

change, however, is the sum of the rate of teclhnological progress and changes

in technical efficiency. Higlh rates of teticHitlogi,.lM progress can co-exist with

deteriorating technical efficiency - perhaps due to failures in achieving tech-

nological mastery or due to slhort-runi cost-minimising behaviour in the face of

quasi-fixed vintage capital - and thus wvitlh low or the often observed negative

overall rates of total factor productivity change. O(n the otlher hiand, relatively

low rates of techllological progress cani co-exist with rapidly improving technical

efficiency. Policy actions intended to improve the rate of total factor produc-

tivity growtlh miglht be badly misdirected if focusecl on accelerating the rate of

innovation for example in circumstances where the cause of lagging total

factor productivity clhanige is a low rate of mastery or diffusion of best practice

technology.

1982] PRODUCTIVITY CIIANGE IN YUGOSLAVIA 925

II. SPECIFICATION AND ESTIMATION OF FRONTIER

PRODUCTION FUNCTIONS

In the estimation of frontier production models, the conventional approach hasbeen to impose rather strong restrictions on the properties of the technology.Most empirical estimates of the production frontier have employed variants ofthe Cobb-Douglas form (Timmer (197I), Forsund and Hjalmarsson (1979))wllich despite its many attractive prcp :rties remains quite restrictive in itsability to approximate the nature of factor substitution possibilities and thecharacteristics of technological change. Flexible functional forms of the pro-duction function impose relatively fewer a priori restrictions on the structureof production. One such flexible form which has been frequently used inrecent empirical literature is the transcendental logarithmic forrm (Christensenet al. I97I, I973), whiclh is a second-order Taylor-series approximation to atwice-differentiable arbitrary production function.1

We can write the translog production function corresponding to (3) as:

In x(4, t) = a0(s, I) + am (s, t) In z,.(s, t) + 2- E E /n In z. (s, t) In z? (s, t),I2 17^ 7b

(9)wherea< ) - aO (s9) + at (;s) t+ -2-13tt (S) t2, (IO

an(S, t) = n (s) + 13.t(S) t. (Io)

The output elasticity of eaclh factor input is:

I in x(s, t) = a(s) + ±ft(S) t + > /mn, In z,, (s, t), (m = I, ... , N) (i 2)l n zm(s, t) I

All differences in marginal factor productivities across (s, t) are assumed to becaptured in {ajn} and {/?,l.t}; thus the structure of factor substitution possibilitiesdescribed by {I?ml} is invariant across (s, t). The rate of total factor productivitychange is the change in output with respect to time holding all factor inputsconstant:

a In x(s, t) = at(s) +fltt(s) t+E flint(S) In Zm(S, t). (13)

For the subset of firms who perAbrm the 'best-practice' at different points intime, the translog frontier production function is

ln X(s, t) = (o+at t + [tt2) +E (,m±+/mtt) In Zm(S, t)

+ I z flmn in Zm(S, t) In z,,(s, t), (14)7it n

for which the frontier equivalent of (I2) and (I3) also applies.For the frontier firms, wve can interpret the technological progress coefficients

as follows: at is the rate of technological progress at a frontier point around

l The structure of production specified by a chosen functional form directiy implies the propertyof index numbers used to measure output, inputs, and productivity. See Diewert (I976), Caves et al.(1981, i982), Denny and Fuss (i980, ig81) for detailed discussion of various index number propertiesand the structure of production.

926 THE ECONOMIC JOU'RNAL [DECEMBER

which the I'aylor-series expansion approximates tne frontier. Unnder normaleconomic conditions, it should be non-negative; itt is the rate of change ofteclhological progress, and takes on a positive, negative, or zero value depend-ing on wlhether there is acceleration, deceleration or constancy of the rate oftechnological progress; l,,,,t is tlle change in the output elasticity of each factorinput over time, so that it takes on a positive, negative, or zero value dependingon whether the Wias of technological change is rn-th factor using, m-th factorsaving, or neutral.

Three general approaches to the estimation of frontier production functionsare found in the literature. T'hese may be characterised as deterministic,probabilistic, and stochastic estimation techlniques. (For a tllorough recentsurvey of the estimation problem and an empirical application see van denBroek et al. (i980o.) The deterministic approach utilises the whole sample ofobservations but constrains all observed points in output space to lie on orbelow the frontier. Although this technique corresponds most closely to thetheoretical concept of the frontier as an outer boundary onI the production set,empirically it is sensitive to errors in observations. The probabilistic and sto-chastic approaches basically attempt to reduce the sensitivity of the estimatedfrontier to truly random errors. The probabilistic approach (Timmer, I971)

accomplishes this by allowiing a pre-specified percentage of the most efficientobservations to lie above the frolntier. Stoclhastic frontiers (Aigner et al. (I977),

Mecusen aind van dein Broek (I977), van den Broek et al. (i 9806) specify bothan efficiency distribution and pure random v-ariations in the error structure ofthe estimated frontier. In the present context we have chosen to estimate adeterministic frontier by restricting the observed points in output-iniput spaceto lie on or below the production surface. Hence, we specify a one-sided erroradded to 4 such that it enforces the on-or-below the frontier constraint.

Although it is possible to estimate the parameters of the production frontierby single cquatioin methlods, recent applications of the translog form haveemployed joiInt estimatioin of the production fuInctioin and the set of factorshare equatioIns I2, to olbtain more precci.e cstiuiatecs. Use of the system of

share equations, however, is usually predicted on the assumption of profitmaximisation in competitive product and factor markets wlhich leads toequality between ol)served factor imcomiie shares and output elasticities. Thereis a substanitial bocly of evidence to indicate that this equtality does not hold

in the case of self-m uagacd enterprises in the Yugoslav social sector. (See, forexample. Sapir I980 and IS()Id T 97 .; It is therefore impossible to knowif the ( ,linitred parameters are those oftlie production fronitier or a spuriousset arisinig out of mis-spr( ificatioll of th( inlput share equations For this reasonwve are coii,traiuiecd to use at siniglec equationl metlhod to estimate the production

frontier.Choice of a procedure to estimate the parameters of the prodluction frontier

dcpendsN crucially onl the asstumptioni made w-ith regard to the distribution ofthe errors. If oine is wsillinig to impose a sl)ecific disturbanc e model, pirocedures

have been suggested for the maxinilum likelihood estimationi of the productionfunction parameters '.Schmidt I97() , Greene 1'i98oa ,. The statiltical

i982] PRODUCTIVITY CHANGE IN YUGOSLAVIA 927properties of the maximum likelihood estimators are not straightforward in allcases, however, and there is little guidance as to the appropriate specificationof the distribution of the errors (Schmidt (I976), van den Broek et al. (I980)).An alternative is to minimise the sum of the deviations from the frontier, subjectto the constraint that all observations lie on or below the frontier (Aigner andChu (i968), Timmer (197i), Forsund and Hjalmarrsson (I979)). Given thisspecification the estimation procedure we adopt is an application of linearprogramming,

The objective function to be minimised is linear in the unknown parameters:T S

min: z [(o'+,att+ -1ttt2) + s; (2im + ± t t) ln Zm(S, t)t-ls-=1

+2 I An zn Z(s, t) In zR,,(s, t)- In x(s, t)] (I 5))In ii

The constraints of the model are imposed by the restrictions on the obser-vations securing the observed input-output combinations to lie on or belowthe frontier:

(,Zo + t + -1t tt) + E (a' + &t t) In z. (s, t)VI

+1 ZE fI.,mn ln Z17 1 (s) t) ln z,,(s, t) > ln x(s, t), (s = I, ... , S;it n

t = )...)T) . (6)We assume that the translog frontier is characterised by constant returns toscale, and therefore impose the following restrictions:

E 2 "r = I,

EA.mn = 0, (n = I, ... , N), (I7)

in£m = 0°

In addition to differentiability, we maintain monotonicity and concavity to bethe minimum irreducible properties of the frontier. The translog frontier isneither monotonic nor concave for any arbitrary set of its domain. To imposemonotonicity, we restrict {&m} and {xt} to be non-negative. These are necessarybut not sufficient conditions for monotonicity, so that we also restrict the outputelasticity of each factor input and the rate of technological progress to be non-negative:

am _+ &t t+ In zn Z(s, t) > o, (m = In .. . N),n

aSt +tt t + Am,t In zm (S, t) > o. ( I 8)

Under monotonicity and constant returns to scale, the necessary and sufficientconditions for concavity can be expressed as the non-positivity of own shareelasticities (see Lau (1978)). Thus, we impose concavity on the frontier by therestriction, {/Al....} < o for m = I, ... , N.

We estimate the frontier gross production function by sector where factor

928 THE ECONOMIC JOURNAL [DECEMJSER

inputs are capital, labour, and material inputs. Gross output and materialinput series are in constant producer prices of I972. Capital input series are netcapital stocks at replacement cost in I972 prices. Labour input series are thenumber of persons employed. For each of twenty-six social sectors of Yugoslavia,our panel data consist of a i965-78 time series by eight regional cross sections,where the regions are six republics (Bosnia, Croatia, Macedonia, Montenegro,Serbia, Slovenia) and two autonomous provinces (Kosovo and Vojvodina). Adescription of data sources is given in the Appendix.

A short note on normalisation is required here. Recall that the translogproduction function is a second-order Taylor-series approximation to an arbi-trary production function. Choice of a normalisation point around which theTaylor-series is expanded becomes important, since we know that the sum ofthe early terms in the series provides a good approximation in the neighbour-hood of the chosen normalisation point. In the present context the normalisa-tion point should represent a production point that closely approximates thefrontier, and therefore the choice of the normalisation point with respect to ourregional dimension is an important issue. In this respect, we choose the Republicof Slovenia as it is generally considered to be the most developed region inYugoslavia.

The estimated translog frontier parameters for each sector are presented inTable 2 in the Appendix. The rate of technological progress for each region ineach sector is computed by comnbining these frontier parameters with observedinput levels as in (13) for each year, and taking simple averages of consecutivepairs. The level of technical efficiency as defined in (6) can be obtained as theantilog of the slack variables in our linear programming constraints (i6). Therate of change in technical efficiency is approximated by taking the log differ-ences of successive time periods. WVe then compute the rate of total factor pro-ductivity chang( the rate of technological progress plus the rate of change intechnical efficienc, T- TcreCfore, our total factor productivity change estimatesfor Yugoslavia are not adjusted for the effect due to difference between un-observed interior output elasticities and estimated frontier elasticities (seeequation (8)).

III. EMPIRICAI, RESULTS

The most important finding of this paper is that the change in technicalefficiencv dominated technological progress in their relative importance in sec-toral total factor productivity growtth of Yugoslavia. Table I preseints our resultsin terms of average annual rates of total factor productivity change, technologicalprogress and technical efficiency change based on the translog frontier estimatesfor twenty-six social sectors (columns ' i), i2) and (3)). In Table i, the sectorsare classified according to the average signs of these three estimates for theperiod I965-78. These average annual growth rates are also presented for threesub-periods corresponding roughly to Yugoslav Economic Plan periods. Onehalf of the sectors (groups I and II) show no technological progress estimatedat the frontier. The otlher half (groups III, IV and V) show technological

Table i

Classification of Economic Activities by Nature of Total Factor Productivity Change: Yugoslavia Social Sector, i965-78

I 965-78 1965 7o(I 2) (3) (4) (5) () ( (3) (4) (5)

I + 0 +Printing and publisliing o-67 0°0( o-67 -062 005 0-14 0°00 0-14 7- 11 0-03 FChemical products 0-1o o0oo -0-1 (0-55 o-65 o-og o-oo -o 09 1-03 094 PPetroleum and gas* 0-56 0°0o o-56 1-85 1-29 0-55 o0oo o055 1-15 -o-6o 0Shipbuilding o 18 oon o-I8 -1-55 -1-37 4-88 000 4-88 -2A49 2-39Eleclricit) 1-87 000 1-87 - 1-00 °-87 3-67 ° °° 3-67 -I -07 2-59 c:II- 0 - oAgriculture -O-o8 o 00 -o-o8 0-95 0.87 -1-63 0-00 -1-63 2-01 o-38 iGoiistruction -o-46 0-00 -0-46 o033 -0-13 o-45 0-00 0-45 1-35 i-8o ,Food processing *-0-57 00oo -0-57 0-o0 -0-56 -0oog o-00 -0o9 °0°7 -0-02 <Tobacco -I 6V o00 -i-6o -2-26 -3-86 0-72 0o00 0°72 -5-78 -5-o6 ^Textile products -o017 o0o -(o17 0-00 -017 -o0-56 0-00 -0-56 0-58 Oo02Lumber and Wood products -o-6o o-oo -o-6o 0-55 -0°(5 -o 20 000o -0 20 o(98 0-78 >Ferrous .netals* -o-19 o-oo -0-19 -0-71 -090 0o20 00 0o20 -°49 -0-29Trade and Catcringt -o-8i o-oo -o-8i -2-24 -3 05 -0-19 0-00 -o0-g -3-61 -3-80III + + + -

Forestry 1-21 0-43 o.78 -1 0l 0o20 2-75 0o52 2-23 - 121 1-54 ZCoal and coal products* 1-87 1-58 0P9 -3-14 - 127 395 2-21 173 -439 -o-44 <Rtubber products 4-70 o-56 4 13 -5 43 -(073 2-55 0 47 2-05 -2-95 -0-40 <Metal products+ O-54 0-31 0-23 -0 22 0-32 0-48 0-40 o-o8 0-29 O-77 oMiscellaneous Mfg. 3-88 0-37 3-51 -4-12 -0-24 9 62 O-35 9 62 -5-1t 4-52 mTransport and Communications 1-94 o-8i 1P12 -2-16 -0-22 4'45 0-91 3-54 -3-19 1-26 rIN + + -

Paper prodtucts 0-48 o-67 -o20 -0-46 002 0-72 i-o6 -033 -0-31 0-41 >Leather products 0-07 0-22 -0-15 -o-82 -O-75 0-38 O-20 o-x8 -0-78 -0-40Non-metallic minerals* 2-20 339 -1-19 -1-75 0o45 303 3-98 -o-96 - I'l 1-92Electrical machinery 0-25 o-28 -0-03 o-og o034 0-15 0-39 -0-23 1-12 1-27V - + -

Building inaterials§ -o-o0 o-o6 -0-10 o-8S o-8o o-68 o-og o059 1-82 2-50Non-ferrous metals* -o-70 1 44 -2-14 -0-51 -1-21 0o00 1-22 - 122 -0-36 -0-36Arts and CraftsII -0-32 0-75 - i-o6 OOI -0-3I 0-55 0-53 0-02 -4-03 -3-48 (

1970-5 1975-81) () (3) (4) (S)()5) (3) (4) (5) q

(0I o'Printing and piiblisliiiig - 0O02 0-00 -0-02 - i6 - i-i8 2-71 0-00 2-71 - o-6o 2-1 IChemical products - O075 0(00 -0-75 o-6o -0-15 1-83 o0oo i-83 - O033 I-S5Petroleum anid Gas* - 2-85 00oo -2-85 -0-70 - 355 6-26 oo 6-26 - 4,92 1-34Shipbuiilding - 6-29 0o00 -6-29 3-77 -2-52 3T15 W0oo 3 l5 -8-88 -5-73Hectrictiv 143 o00o I-43 - 1-92 - 0-49 -0O39 0-00 -039 o-65 0-26

IIAgriculture -0-48 o00o -0-48 O-17 -0-.31 3T17 000 317 0°49 3-66Construction - ivo6 0-00 - i-o6 -o-69 - 1-75 -o-98 0o00 -0-98 0-32 -o-66Foocl processing - 1-20 0-00 - 1*20 -0-01 - 1-21 -0-30 0-00 -0o30 -o-o6 -0-36Tobacco -0-7 0-07 - O(74 -4-56 - 5-30 -6-88 o-oo -6-88 7-43 O055Textile products 0-24 0-00 0-24 -o-58 - O034 -0-20 0-00 - 0O20 -0-02 -0-22Lumber and WNood products - i-6o ( -0 - 1-60 - -01( - i-6i 0-40 o-oo 0-40 O-75 1-15Fecrrous metals* - 2-20 000 - 2-20 o-i6 - 2-04 2-53 000 -2-53 -2-56 -0-03 MTrade and Cateringt - 1-37 0i10 - 137 -- 94 - 3-31 -0-90 (-00 -o-9o - 0-45 - 135 pIII0Forestrv - O-54 0-41 -0-95 -o-8I - I35 1-59 0-34 1-25 -1-04 0-55 0Coal and coal products* - 1-74 I-40 -3.14 - 1-03 - 2-77 4-43 o-81 3-62 -4-60 -0-17 0Rubber products 5-72 0o56 5-16 -6-93 - 1-21 6-5/ 0-72 5-85 - 7-o6 - 0-49 xMetal prnollucts, o-56 0-29 0-27 -o-58 -0-02 o-60 o-19 -0-46 -0-46 0-14 QMIiscellanieous Mfg. 5-00 O-39 4-62 -4-36 0-64 -7-51 0-37 - 7 94 -2-15 -9-66Transport and Communications - 0°49 o-76 - 1-25 -o-28 -0-77 i-8o O075 i-o6 -3-56 - 1-76 0

IV'Paper products - 0-47 o-58 - 1-05 -0-28 -0-75 1-65 O-I9 I-46 -0-99 o-66 zLeatlher produicts o-64 0-24 0-40 -0-78 -0-1I4 -1-40 0-22 -I-6I -I-14 - 2-34 >Non-metallic minerals* 2-30 3-21 -0-91 -2-81 -0-51 o-64 2-69 -2-05 -i-o6 -0-42Electricil machliniery - o-77 0-24 - 1-0l 0-03 -074 2-10 0O14 195 - I-52 o-58

Building materials§ - o075 0-05 - o-8o o-8o b-05 -0-07 0-01 -o-og -0-70 - 0-77Non-ferrous metals* - 2-2J ) 1-72 - 3-92 -0-46 -2-66 o-62 1.34 -0-72 -0-84 -0-22Arts and Craftslj 0-04 0-81 - 0-77 I-24 1-28 - 2-36 1-00 -3-36 2-05 -0-31

Columns: Notes:(i) Total factor productivity change [(2) + (3)]. * Include mining activities in each category. 0(2) Techlnological progress. t Retail and Wholesale Trade and Hotels and Restaurants.(3) Technical eflicienc) change (I). + Fabricated metal products, non-electrical machinery and transport(4) Input contribution difference due to frontier and observed factor share equipment other than ships.

difference. § Stone, clay and glass products and processed construction materials.Equals [g,,(s, t)-g,(S, t)] i(s, t). Small-scale industrial activities and services n.e.c.

(5) Total factor productivity change (using observed factor shares).

I982] PRODUCTIVITY CHANGE IN YUGOSLAVIA 93I

progress, of whiclh only in six sectors (the sectors in group IV and two sectorsin group III) the rate of technological progress dominates technical efficiencychange on average for the period I965-78.

In order to facilitate a comparison of our method with the conventionalmeasure of total factor productivity change wve provide in column (5) of rable I

index number estimates of average annual total factor productixity changebased on factor iricome shares observed in our data base. The differencebetween our parametric frontier estimates of total factor productivity changeand those derived by the index number method should equal the differencebetween;the estimated input contributions to growth based on frontier outputelasticities and interior output elasticities (the last term in equation (8)).Hence, we also provide in column (4) the magnitude of these differences,using observed factor income shares for 'interior' output elasticities. The' sumof columns (2), (3) and (4) equals the index number estimate of total factorproductivity change iri column (5), and is flher-Fboe an exact decompositionof the index number estimate.

As we discussed in Section II, it is difficult to interpret the index numberestimates of total factor productivity change in Yugoslavia in view of thefailure of obserxed income shares to reflect actual output elasticities of factorinputs. The magnitude of the clifThrel(cs in input contributions is as likely toreflect biases introduced by incorrect specification of the indices for factorinputs in the conventional mcthod, as differecccs in the underlying structureof production between the frontier and the interior observations. For i965-78,

in seventeen of the twenty six sectors the estimiiated input contribution usingobserved shares exceeds that based oIn the parameters of the production frontier,and hence, our estimates of total factor productivity clhange exceed thosederived by the conventional method. In three sectors the estimated inputcontributions are approximately equal, and in six sectors the estimate of totalfactor productivity change based on the frontier parameters is less than thatbased on observed shares. For the period i965-78 we identify eleven sectorswith negative average total factor productivity clhange by the parametricfrontier method and sixteen sectors based on the index number approach.There are nine cases in whiclh the two sets of estimates differ in sign; in sevenof the nine the index number method yields a negative rate of total factorproductivity change.

The additional information provided by our decomposition is most clearlyillustrated by the results for those sectors shlowing technological progress(groups III, IV and V). Of the thirteen sectors identified in Table I as showingtechnological progress at the frontier, seven are clharacterised by negative totalfactor productivity growth during the period I965-78 based on the indexnumber method. In eaclh of these cases the conv-entional metlhod would yieldthe incorrect conclusion that teclhnological progress had been absent in thesector. In groups IV ani( V technological progress is accompaniied by deteriorat-ing technical efficiency, a result wlhichl could not be inferred from the conven-tional approach.

Of the thirteen sectors with technological progress, four sectors (coal and

932 THE ECONOMIC JOURNAL [DECEMBER

coal products, transportation and communication, non-metallic minerals, andnon-ferrous metals) have been priority sectors in the Yugoslav Economic Plans.Furthermore, these sectors with the exception of transportation and communi-cation are considered to be the sectors in which Yugoslavia has natural resource-based comparative advantage. Two other sectors (metal products and electricalmachinery) were industries in which substantial efforts were made to acquireforeign technology on a continuing basis (see, for example, The World Bank

(1975).)Cyclical characteristics of technical efficiency change are common across

sectors, and reveal distinct differences in performance among the three periodsI965-70, I970-5 and I975-8.1 The period 1965-70 is characteriscd by generallyimproving levels of technical efficiency, particularly in manufacturing. DuringI970-5, on the other hand, only six sectors (five manufacturing sectors) showpositive rates of technical efficiency change. Twenty sectors show deteriorationin the rate of technical efficiency change between these two periods. Somerecovery is observed in 1975-8. Both I970-5 and I975-8 were marked byquantitative restrictions on imports in the face of foreign exchange shortages,accompanied by deflation of the domestic economy under 'stabilisation'programmes. The impact of these slhocks on the level of technical efficiency isapparent in most industries.

Variations in technical efficiency at the sectoral level are also attributable toproblems of investment planning and implementation, lack of technical ex-perience, and poor management and organisation partictularly in co-ordinatingintermediate input supply, in addition to the general impact of stabilisationpolicies. Four sectors in which these problems were particularly acute (woodproducts, electrical machinery, shipbuilding, and ferrous metals) show rapidrates of decline in the level of technical efficiency during the period 1970-5.

Three manufacturing sectors wlhich are characterised by generally improvinglevels of technical efficiency (metal products, chemicals, rubber products) reflectto some extent the success of explicit policy actions undertaken to improvediffusion of technical information, project implementation, and co-ordinationof input supplies.

IV. CONCLUSIONS

In this paper we have proposed a method for the decomposition of total factorproductivity change into two distinct elements, techniical progress and changesin technical efficiency. In doing so we have brouglht together two largely inde-pendent lines of inquiry which have a common analytical basis in the theoryof production. Our motivation was a belief, particularly in the case of develop-ing economies, that identification of total factor productivity change wsithtechnological progress neglected an important dimension of productivity gainsand losses which can be summarised as changes in the efficienicy With which aknown technology is applied to production.

Clearly, teclhnological progress and technical efficieincy change are notneatly separable either in theory or in practice. In our methodological approach

1 Detailed discussion of the sectors and regional results are available in Nislbiniizu and Page (t1982).

I982] PRODUCTIVITY CHANGE IN YUGOSLAVIA 933we define technological progress as the movement of the best practice orfrontier production function over time. We then refer to all other productivitychange as technical efficiency change. The distinction whiclh wve have adoptedis therefore somewhat artificial, but it offers an important added dimension tothe policy relevance of total factor productivity studies.

Our major empirical findiings are a clear illustration of the relevance of thedistinction. In an economy such as Yugoslavia which borrows technologyextensively from abroad, failures to acquire and adapt technology to newinternational standards will be reflected in lack of technological progress atthe frontier. Our findings indicate that in half of Yugoslavia's social sectorindustries there was no perceptible movement of the frontier during the periodi965-78. Many of these activities arc mature industries, both in Yugoslaviaand internationally, in which rapid movement of the frontier is not expected.In several sectors, however, the lack of technical progress is indicative offailures in investment planning and implementation to allow for acquisitionof new technology. In others, the movement of the frontier reflects the successof explicit policies to facilitate the acquisition of foreign technology.

Similarly, changes in technical efficiency across plan periods and amongindividual sectors indicate the success or failure of a number of importantdimensions of econonmic policy and industrial planning. Considerable attentionhas been focused on the question of the slowdown in economic growth inYugoslavia in the I970S. Our analysis indicates that the slowdown in totalfactor productivity growth was a consequence of both a reduccion in the rateof technological progress and of a deterioration in technical efficiency. Therelative magnitude of the two, however, is such that deteriorating technicalefficiency change clearly dominates technological progress. Indeed the abruptchange in the pattern of technical efficiency change between two majorEconomic Plan periods, from moderately positive in I965-70 to negative inI970-5, points to a major shift in the production environment between the two.

Development Research DepartmentThe Wforld Bank

Date of receipt offina! typescript: April 1982

APPENDIX

Data on gross output and material input in currenit prices and labour com-pensation are obtained from Statisticki Bilten :'No. 773, No. I I75), and DrustveniProizvod i Narodni Dohodak. Producer price indexes for gross output and inter-mediate input are obtained from Stalisticki Godisnjak 'Statistical Yearbooks ofY'ugoslatia). Capital stocks in constant prices are obtained from StatistickiGodisnal, Osnova sSredstra Drus/vene Privred, and worksheets provided by theFederal Statistical Office of Yugoslavia. Data on number of persons employedare obtained from Statistical Yearbooks of Ytugoslavia. All published data sourcesare by the Federal Statistical Office of Yugoslavia.

Table 2

Deterministic Frontier Translog Production Function Coefficients, Yugoslavia 1905-78

Lumber Printing CoalCon- Food Textile and Wood Building Paper and Chemical Petroleum and Coal

Agriculture Forestry struction Processing Tobacco products products materials products Publishing products and Gas products

ao 7-85563 6-54696 8-92599 8.41300 6-07361 8-32452 8-05692 6-90549 7-04443 6-79953 7-94850 5'21999 7-20321ar 0-00598 - - o-ooo6g 9 -'0 13 4 - 0-01879

Tr - -o-os - - - - -00 - - - -0-00247

X 43029 0-11588 0-01458 0-10771 o-64375 0-1924.1 0-02943 0-49879 0o08401 0(13425 - o-o8o85 0-46080a 0-33174 0-55206 0-40902 0-13320 0012502 0-20848 0-2842 0-07888 0-23584 040491 0-21175 0-24981 O073293

M,u 0-23798 0-33385 0-57641 O075909 0-23123 0-59912 o-68636 0-42233 0-68015 0-46083 0-78825 o-66934 0-220981

KK - 0-41 i82 -(j-22065 -- - 0- 15860 -0-20227 -0-39240 - 0-02712 -0 24874 -0-07497 -0-096:3 - - -03-4317

13LL -0-1 1690 -0'021t7 - oo-8496 -0-23836 - 0-10986 -0-30829 -0-04175 -0-07528 -0-03563 - -003593 - -

aoMo -9 - ) 680 - -0-15160 -0-07520 -0-16712 - - -0.03593 - -

Pfl. o-26436 o(P2086 -o000592 0-19848 o-i56o6 0-27454 - 0-00316 0-07832 0-05530 0-04817 - - 0-02159

/,rm 0-14746 O-09979 0-00592 -0-03988 0-04620 0-11785 0-03028 0-17015 0-OI967 0:04817 - 0-02159 M

fALM -0-14746 -t)09979 o-o9o88 0-03988 -0-04620 0-03375 0-04491 -t)00303 - 0-01967 -0-04817 o003593 - -o-02I59 n

iT, - o-oo261 - - - - - -0-00175 - o-oo6i8 zfLT - -0-00299 - - - 0-00218 - - -o-oi i68 o3T - 00038 - - - - - - -0-00043 - - -o55o

Trans- °Miscel- portation 0

Noui- Non- laneous and Trade Arts QIRubber Leathel metallic Ferrous ferrous Metal Electrical Ship- manu- Commu- and and P

products products minerals metals metals products machinery building facturing Electricity nication Catering Crafts Z

a, 6-39872 7-18516 6-47544 8-18623 7.60021 9-14500 7-81879 3-21268 5-72188 7-60716 8-38950 9-36949 7-21128

ap o-oo867 0-00324 0-03593 - 0-01158 0-00404 0-00335 - o-oogo0 - 0-00489 - 0-01051I8rT -O00025 -0-00028 -(000410 - 0-00036 - o-ooo65 -0-00227 - -0-00030 - -0-00007 - -0-00059

XA 0-03583 0-03938 0-32901 - 0-17727 0-07I96 0-16835 0-21999 0-33052 0O11480 0-34135 0-04573 0-07067

ML 0-72866 0-33429 0-39280 0-21053 0-12480 0-29810 0-14532 0-69772 0-35171 0-47974 o-38677 o-62464 0-30520M 023551 o-62634 0-27819 0-78947 o-69794 o-62994 o-68633 0-08229 0-31777 0-40546 0-27188 0-32962 0-62413/i,hK -o-oo684 - - -0-07739 - - o-o8532 - o-1i85I - -0-28951 -0O-II87 -

LL - - -0-18526 - - -0-22120 - - - 0-12105 -0-19776 - 0-07380 - UfiMM - 0-05602 - - - - - 0-11820 - - - - - - M

0KL - -002459 0-09263 - 0-03869 o-iio6o - 0-05910 o-o4266 0-1I978 o-o9888 -0-14475 0-09284

iRM - 0-03143 -0-09263 - 0-03869 -o-iio6o 0-05910 o-o4266 -0-00127 -o-o9888 0-14475 0-01904 -

OL, - 0-02459 0-09263 - -003869 0-11060 0-05910 -0-04266 0-00127 o-o9888 0-14475 -0-01904 -

KrT 0-00717 0-00403 0-00708 - -0-01631 0-00330 -o-ooi66 - -0-00343 - - 0-oi647 - o-o0167 p

fLT -0-00786 -0-00569 -o0-02671 - o-oo688 -o-oo586 o-ooo96 - 0-00132 - 0-01487 - -0-00987

filT o-ooo69 o-oo066 0-01963 - 0-00943 0-00256 0-00071 - 0O00210 - o-ooi6o - -0-00180

I982] PRODUCTIVITY CHANGE IN YUGOSLAVIA 935

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No. 239. J. Michael Finger, "Trade and the Structure of American Industry,"Anniials of the Amitericant Academny of Political anid Social Science

No. 240. David M.G. Newbery and Joseph E. Stiglitz, "Optimal CommodityStock-piling Rules," Oxford EcoZnomic Papers

No. 241. Bela Balassa, "Disequilibrium Analysis in Developing Countries: AnOverview," World Dev)elopment

No. 242. T.N. Srinivasan, "General Equilibrium Theory, Project Evaluation,and Economic Development," The Thleory anid Exl7erience of EconomnicDI9eelopmnent

No. 243. Emmanuel Jimenez, "The Value of Squatter Dwellings in DevelopingCountries," Economnic Dezvelopntent and Cultural Chanige

No. 244. Boris Pleskovic and Marjan Dolenc, "Regional Development in aSocialist, Developing, and Multinational Country: The Case of Yugo-slavia," Inzterznatioinal Regional Science Rezview;

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