Decomposition of Labor Productivity Growth: A Multilateral Production Frontier Approach

Transcription

1 Decomposition of Labor Productivity Growth: A Mutiatera Production Frontier Approach Konstantinos Chatzimichae and Vangeis Tzouveekas (Dept. of Economics, University of Crete, GREECE) ABSTRACT This paper deveops a parametric decomposition framework of abor productivity growth reaxing the assumption of abor-specific efficiency. The decomposition anaysis is appied to a sampe of 5 deveoped and deveoping countries from A generaized Cobb-Dougas functiona specification is used taking into account differences in technoogica structures across group of countries to approximate aggregate production technoogy using Jorgenson and Nishimizu (1978) biatera mode of production. Measurement of abor efficiency is based on Kopp s (1981) orthogona non-radia index of factor-specific efficiency modified in a parametric frontier framework. The empirica resuts indicate that the weighted average annua rate of abor productivity growth was 1.43 per cent over the period anayzed. Technica change was found to be the driving force of abor productivity, whie improvements in abor efficiency and human capita account approximatey for the per cent of that productivity growth. Keywords: abor efficiency and productivity growth, mutiatera production frontier. JEL Cassification: J4, O40, C3-0-

2 DECOMPOSITION OF LABOR PRODUCTIVITY GROWTH: A MULTILATERAL PRODUCTION FRONTIER APPROACH INTRODUCTION The productivity fa observed in many deveoped and deveoping countries during the 60 s and eary 70 s triggered an intense pubic debate aimed to unrave the interna mechanism of productivity growth. This heated debate had resuted to an enormous theoretica and empirica iterature directed to the investigation of the proximate causes of the observed differences in per-capita income across deveoping and deveoped countries. Most researchers used the cross-sectiona version of the famiiar growth accounting framework of Soow (1957) to decompose country variations in the eves of output per worker into parts attributed to the variation in the factors of production and productivity growth. The resuts ead to the concusion that the residua productivity rather than factor accumuation accounts for most of the income and growth differences across nations (see Casei (005) and the references cited therein). This finding athough it uncovers the proximate causes of income differentias is unsatisfactory in the sense that the utimate causes that ead to different eves of productivity are not expained. If we accept that productivity differences are arge, then we are eft with a shortage of convincing expanation for this resut. The ater is important as different sources of productivity differentias require different poicy measures to enhance economic growth either in deveoped or deveoping nations (Prescott, 1988). Since much of these productivity variations represents differences in technoogica structures, then there shoud be an adequate expanation why non-riva innovations do not -1-

3 diffuse across borders. And if they do, then why we sti observe differences in measured productivity rates. If there is a uniform wordwide production frontier, then a of the observed differences in productivity refect a gap from this frontier. Obviousy there are strong barriers to adoption across countries reated to the institutiona and cutura environment preventing many countries from using that common technoogica structure. Oson (198) and Kruse and Rios-Ru (1996) argue, that vested interest groups are obbying for market power, protection from competition, imiting factor mobiity and then bocking adoption of riva technoogies through a poitica process. Parente and Prescott (1999) provide a theoretica mode where the existence of monopoy power extend beyond the traditiona deadweight oss affecting the adoption of new technoogies as we as the appropriate use of technoogies aready adopted. Reative recenty economic growth iterature questions the above perspective, recognizing that the technoogy frontier is not uniform. In other words, it admits that not every country face the same technoogica conditions. According to this perception countries choose the best production technoogies avaiabe to them given their interna economic and structura conditions. Obviousy factor endowments as we as the institutiona and cutura environment affect these choices as some technoogies may be ess productive than others. For instance, ICT technoogies enhance socia wefare through structura transformation in production networks and socia customs but at the same time require human capita, i.e., high iteracy rates, to function propery. Basu and Wei (1998) and Acemogou and Ziibotti (001), expored the appropriateness of technoogy paradigm to expain differences in income eves and economic convergence. They both concude that deveoped countries invent new technoogies that are compatibe --

4 with their own resource endowments and these technoogies do not work appropriatey in deveoping countries with a different input mix. This impies that the adoption of a modern technoogy by poor countries do not raise their productivity eves as it is inappropriate to them. So the assumption of the same technoogica structure may not be adequate to expain productivity variations and empirica work shoud take that into account. Under both paradigms, one woud expect a countries to operate on their own or to the common technoogica frontier being thus fuy efficient. Empirica evidence though suggest that rather the opposite is true. Severa authors suggest that rarey countries are exporing fuy the potentia of the existing technoogy operating far from their respective production frontier (e.g., Färe et a., 1994; Kumar and Russe, 00; Los and Timmer, 005; Badunenko et a., 008). Theoretica modes of expaining inefficiency in resource utiization, focus on the roe of institutions and socia structures to expain why the common or country-specific production technoogy is not utiized appropriatey by individua countries. Apart of the avaiabiity of the technoogy, other factors must be present such as strong investment, a we trained work force, R&D activity, trading reationships, a receptive poitica structure that Abramovitz (1986) summarizes under the term socia capabiity. However, a these eements of efficiency determination are not affecting the efficient use of a inputs in the same manner. For instance, ack of working experience affects rather more intensivey abor efficiency than capita utiization. Nevertheess empirica studies, besides anayzing abor productivity differentias, they utiize an aggregate output or input inefficiency index. Important information, vauabe -3-

5 from a poicy perspective, can be gained by providing an empirica anaysis focusing excusivey on abor-specific efficiency. Probaby the most important aspect reated with resource utiization and therefore productivity differentias across countries, recognized by many researcher, is the roe of human capita. Inspired by the eary approaches on human capita theory (Schutz, 1961; Becker, 1975), many empirica researchers have focused on the important roe payed by educationa eves in the efficiency of input utiization and hence on the growth process. In these eary theoretica contributions schooing is viewed as an investment in skis having a direct effect on abor productivity as we as an indirect one through the improvement of worker s abiity to work efficienty (Wech, 1970). Griiches (1970) and Jorgenson and Fraumeni (1993) found that a significant portion of differentias is attributed directy to increases in educationa eves. On the other hand, Wech (1970) and Barte and Lichtenberg (1987), among others, found that highy educated workers have a comparative advantage with regard to the impementation of new technoogies exhibiting therefore higher efficiency eves. Recenty the deveopment of detaied educationa data by Barro and Lee (1993; 001) and the formuation of endogenous growth modes by Lucas (1988) and Romer (1990), enabed the empirica anaysis on the roe of education in economic growth. A of these studies on growth accounting again indicated that a significant portion of measured productivity growth is attributed directy to increases in educationa eves of the abor force (e.g., Benhabib and Spiege, 1994; O Nei, 1995; Bis and Kenow, 000). Regardess of the nature and the aims of these studies, they provided unshaken evidence about the important roe payed by human -4-

6 capita in the growth process, suggesting that it is an important eement of any productivity decomposition anaysis and it shoud be incuded in any empirica research. Motivated by the works of Färe et a., (1994), Kumar and Russe (00) and Henderson and Russe (005), we attempt in this paper to contribute in the reevant iterature providing a theoreticay consistent parametric decomposition of abor productivity growth. According to these studies abor productivity is decomposed into the rates of growth of factor intensities and TFP. However, shifts in reative capita-abor prices and the biases of technoogica change are aso important possibiities for changes in the growth rate of factor intensities. Taking that into account, our decomposition framework provides a more detaied anaysis of changes in abor productivity across countries. First, we focus on abor-specific inefficiency rather than an output efficiency measure which is more reevant when abor productivity growth is anayzed. The proposed index for measuring abor-specific technica and aocative efficiency is based on Kopp s (1981) orthogona non-radia index of technica efficiency modified in a parametric frontier framework. Then the derived index of abor-specific efficiency is used to provide a compete decomposition framework of abor productivity growth. Second, we dispense with the assumption of a common wordwide production technoogy in estimated parametricay the aggregate production frontier. Our empirica aggregate production frontier mode is based on the generaized Cobb-Dougas functiona specification suggested by Fan (1991) that accounts for biases in technica change, extended into a mutiatera context in order to take into account differences in technoogica structures among countries in the sampe using Jorgenson and Nishimizu (1978) biatera production structure. In that way forma statistica testing can be used to -5-

7 examine the existence of a common wordwide technoogy utiized by a countries in the sampe. The production frontier was estimated econometricay, incorporating human capita, using Cornwe et a., (1990) fixed effects formuation that aows for country specific time varying inefficiencies. Foowing Griiches (1963), human capita is introduced as an augmenting factor of abor input using Ha and Jones (1999) construction, enabing thus the identification of both its direct and indirect roe on measured abor productivity. Using this genera framework we provide a compete decomposition anaysis of abor productivity growth in a sampe of 5 deveoped and deveoping countries from drawn from Penn Word Tabes. Besides decomposing the growth of output per worker into technoogica change, technoogica catch-up and physica and human capita accumuation, our decomposition anaysis accounts for the existence of variabe returns to scae and for the abor biases of technica change due to changes in reative factor prices. The remaining paper is organized as foows. In the next section, we present the theoretica framework for measuring abor productivity growth in a parametric context. Next section 3 presents data description and describes the empirica mode and estimation procedures. Section 4 discusses the empirica resuts whie, the ast section concudes the paper. THEORETICAL FRAMEWORK Let assume that countries in period t utiize abor, physica and human capita to produce a singe aggregate output y R + through a we-behaved technoogy described by the foowing non-empty, cosed set: -6-

8 {( ε ) ( ε )} t T = k,,,y y f k,,,t : (1) where k R + denotes physica capita, R + abor, ε R + human capita, t R + is a time index, and, ( ) 4 f k,,,t : R R is a stricty increasing, differentiabe concave ε + + production function, representing the maxima output from physica capita and abor use given human capita and technoogica constraints. Using (1) we can define the input correspondence set as a the input combinations capabe of producing y R + as: t { + } ( ) ( ε) 3 : ( ε ) L y = k,, R k,,,y T. Given the assumptions made on f (), the input correspondence set is a cosed convex set satisfying strong disposabiity of abor and physica capita inputs. Aternativey, aggregate production technoogy may be defined by the dua cost function ( ) ( ) 3 1 C w, y,, t : R y R R as: ε ( ε ) = { + k : ( ε )} C w,y,,t min w w k y f k,,,t () k, where R( y) = { y R+ : L( y) }, = { k} R w w,w ++ are the stricty positive effective abor and capita prices. The cost function is differentiabe in a its arguments, nondecreasing in w and y, non-increasing in ε and t, and homogeneous of degree one in w. At this point we may assume that the production of aggregate output may not be technica efficient, i.e., countries are not abe to minimize input use in the production of a given aggregate output in the ight of the prevaiing factor prices. Concentrating in abor -7-

9 input it shoud hod that y f ( k, θ, ε,t) = where θ is a measure of abor-specific technica efficiency indicating how much abor shoud be reduced sti being abe to produce the same eve of aggregate output. Formay, θ may be defined according to Kopp s (1981) orthogona non-radia index of input-specific technica efficiency: 1 { θ : θ 0 ( θ ε )} KP LTE min, y f k,,,t θ = > (3) which is bounded between zero and one, i.e., 0 < LTE KP 1. Graphicay, the above definition is presented in Figure 1. Assuming that country i operates at point A in the graph utiizing 0 quantity from abor and 0 k quantity from capita producing y eve of aggregate output. Obviousy the country in question is technicay inefficient as it is possibe to reduce input use moving on the respective isoquant and sti being abe to produce the same eve of aggregate output. If inefficiency arises ony from abor use then an obvious change woud be the movement to point B on the graph, where capita use remains unchanged but abor quantity has been reduced to 1 = θ 0. However, sti at point B country is not fuy efficient. Athough abor use is at its technica efficient point country fais to utiize an appropriate capita-abor mix given the input prices it faces. This is achieved at point C where cost of aggregate production is minimized given factor prices, human capita endowments and production technoogy. A measure of the extent for this aocation error is provided by the foowing ratio: LAE = ( w ε ) *,y,,t θ (4) -8-

10 * where (,y, ε,t) w is the Hicksian constant output demand function for abor obtained from () through Shephard s emma which is non-decreasing in y and w k and nonincreasing in w, ε and t. The above ratio may be viewed as an index of abor aocative efficiency which, contrary to its technica efficiency index, can take positive vaues * beow or above unity and it is equa to one when θ ( w,y, ε,t) =. If it is greater (ess) than one, abor is under- (over-) utiized at its technicay efficient eve given capita and abor prices. In deveoped countries that are abundant in capita input, abor aocative efficiency is expected to be greater than one whereas in deveoping countries that are abundant in abor input ess than one assuming competitive factor prices. Using (3) and (4) we may define overa abor efficiency by the product of abor technica and aocative efficiency or, equivaenty, by the ratio of optima to observed abor use as: KP LOE LTE LAE ( w ε ) ( w ε ) * *,y,,t,y,,t θ = = = θ (5) * which is equa to one when ( w,y, ε,t) =. When LOE > 1, individua country overutiizes abor input at the observed point given the prevaiing factor prices, whereas when LOE < 1 abor is under-utiized. Taking the ogarithms on the ast equaity of (5) and totay differentiating with respect to time we get: -9-

11 ( w ε ) * n,y,,t d LOE = y+ e ( w,y, ε,t) w+ e ( w,y, ε,t) w n y d k k ( w ε ) * n,y,,t d + e ε ( w,y, ε,t) ε+ t (6) where a dot over a function or a variabe indicates its time rate of change, d * n ( w,y, ε,t) d ( w ε ) = and e (,y, ε,t) e,y,,t n w k ( w ε ) * n,y,,t w = are the compensated n w own- and cross-price easticities of abor demand, respectivey and, e d ( w,y,,t) k ε ε = ( w ε ) * n,y,,t nε is the compensated abor demand easticity with respect to human capita. Then, using the conventiona divisia index of abor productivity, i.e., ( ) dn y LP= = y-, the time rate of change of the first equaity in (5), i.e., dt KP LOE = LTE + LAE, and substituting them into (6), we obtain ( w ε ) * KP n,y,,t d LP = LTE + LAE+ 1 y e ( w,y, ε,t) w n y e,y, ε,t w e,y, ε,t ε d ( w ) ( w ) d k k ε ( w ε ) * n,y,,t t (7) decomposing, thus, abor productivity growth into a abor-specific technica and aocative inefficiency effect (first two terms), an output effect (third term), a substitution effect (fourth and fifth terms), a human capita effect (sixth term) and, a technoogica change effect (ast term). Using the cost share equation of abor input, i.e., -10-

12 ( w ε ) nc, y,,t n w ( w ε ) = S,y,,t = * ( w ε ) ( w ε ) w,y,,t C,y,,t, taking ogarithms and sighty rearranging terms we obtain: ( ε ) ( ε ) ( ε ) * n,y,,t = n S,y,,t + nc,y,,t n w w w w (8) Then differentiating (8) with respect to aggregate output and time we can further decompose the output and technoogica change effect as (Kuroda, 1987; 1995): ( w ε ) ( w ε ) ( w ε ) = + n y n y n y * n,y,,t n S,y,,t nc,y,,t ( w ε ) ( w ε ) 1 S,y,,t C = + ε y,y,,t S,y,,t ny ( w ε ) (9) and ( w ε ) ( w ε ) ( w ε ) * n,y,,t ns,y,,t nc,y,,t = + t t t 1 S ( w,y, ε,t) t = + C,y,,t S,y,,t t ( w ε ) ( w ε ) (10) C nc ( w,y, ε,t) t where ε ( w,y, ε,t) = is the output cost easticity and, C ( w,y, ε,t) y n y = ( w ε ) nc,y,,t t is the rate of cost diminution (i.e., dua rate of technica change). Substituting equations (9) and (10) into (7) resuts in -11-

13 ( w ) ( w ) ( w ) KP C t d LP = LTE + LAE + 1 εy, y, ε,t y C, y, ε,t e ε, y, ε,t ε Efficiency effect Scae effect Technoogica change effect Human capita effect ( w ε ) ( w ε ) S,y,,t S,y,,t d d 1 e ( w,y, ε,t) w e k ( w,y, ε,t) wk + y S ( w,y, ε,t) t ny Price effect Extended abor biased techoogica change effect (11) which is the fina decomposition formua of abor productivity growth. Specificay, equation (11) attributes abor productivity growth into six sources. The first three terms accounts for changes in TFP which in turn is decomposed into changes in abor efficiency, the effect of scae economies and technoogica change. The first component of the right hand side of (11) indicates changes in abor-specific technica and aocative inefficiency over time. It is positive (negative) as abor technica and aocative efficiency increases (decreases) over time. There is no a priori reason for both types of efficiency to increase or decrease simutaneousy (Schmidt and Love, 1980) nor that their reative contribution shoud be of equa importance for productivity growth. More importanty, what reay matters in productivity growth decomposition anaysis is not the degree of efficiency itsef, but its improvement over time. That is, even at ow eves of overa efficiency, output gains may be achieved by improving either technica or aocative abor efficiency, or both. However, it seems difficut to achieve substantia rates of growth at very high eves of technica and/or aocative efficiency. The second term measures the reative contribution of scae economies to abor productivity growth. Under constant returns-to-scae, i.e., ε C ( w ε ) = 1 y,y,,t, output growth or contraction makes no contribution to abor productivity change and therefore this term vanishes. It is positive (negative) under increasing (decreasing) returns-to-scae as ong as aggregate -1-

14 output increases and vice versa. The third term refers to the dua rate of technica change, which is positive (negative) under progressive (regressive) technica change which can be further decomposed into a neutra and factor biased effect depending on the maintained assumption of the aggregate production technoogy. The fourth term is the effect of human capita accumuation on abor productivity growth. It is positive as an increase (decrease) in human capita affects negativey (positivey) the optima use of abor and it is zero if human capita remains constant over time. 3 The sum of the ast three terms is the tota substitution effect (i.e., changes in factor intensities) which is decomposed into a price effect, a biased technoogica change effect and a non-homotheticity effect. The first term is the price effect of the abor demand due to changes in abor and capita prices. If the technoogy satisfies a neocassica properties the own effect contributes positivey (negativey) to abor productivity growth as ong as the price of abor increases (decreases) over time whereas the cross demand effect is negative (positive) if capita prices increases (decreases). The price effect is zero when both abor and physica capita prices remain constant over time. The second term is the extended abor biased technica change effect (Backorby et a., 1976; Ante and Capabo, 1988). Changes in reative prices of capita and abor induces changes in the individua factor cost shares as production is moved aong the expansion path (first term in the ast bracket). Further if the assumption of input homotheticity is not maintained an additiona output effect is induced atering further factor proportions reative to their initia vaues (second term in the ast bracket). If the technoogy is abor-saving (using) the extended abor biased technica change effect is positive (negative), whereas it is zero when technica change is extended Hicks neutra or if the production technoogy is inear homogeneous. In -13-

15 homothetic technoogies the second term of the extended abor biased technica change effect vanishes as ( w ε ) S,y,,t n y = 0. DATA AND EMPIRICAL MODEL For the quantitative measurement and decomposition of abor productivity growth we utiized a baanced data set of 5 deveoped and deveoping countries covering the period from 1965 to For aggregate output, physica capita and abor input we make use of the Penn Word Tabes (ver. 5.6). 5 For the cacuation of capita and abor prices, foowing the approach suggested by Mamuneas et a., (006), we use the share of empoyee compensation in nationa income pubished by the Tota Economy Growth Accounting Database of the Groningen Growth and Deveopment Centre and Nationa Account Statistics of the United Nations (UN). 6 Human capita was proxied using Barro and Lee (1993; 001) educationa data that are avaiabe for the same group of countries and for the same time period. 7,8 Foowing Henderson and Russe (005), we adopt Ha and Jones (1999) construction where education appears as an augmentation factor for ( ) abor using an exponentia specification, i.e., h( ε ) = e ϕ ε with ( ) ϕ ε being a Mincerian piecewise inear function with zero intercept and sope that varies according to the time span. 9 Foowing Psacharopouos (1994) survey on the evauation of the returns to education, those parameters were defined as being for the first four years, for the next four years and for education beyond the eight year. Our empirica mode for providing measurement of abor productivity growth is based on a Cobb-Dougas type of aggregate production frontier. Specificay, minimizing -14-

16 the cost on the fexibiity of the functiona specification, we adopt a generaized Cobb- Dougas (or quasi-transog) production frontier, proposed by Fan (1991). This functiona specification, athough not enough fexibe ike the transog, it aows for variabe returns to scae, input-biased technica change, and time varying output and demand easticities, but it restricts the atter to be unchanged over countries. It permits statistica testing for various features of the aggregate production technoogy, providing at the same time an anaytica cosed form soution for the corresponding dua cost frontier necessary to identify appropriatey a terms in (11) (Fan and Pardey, 1997). Since both deveoped and deveoping countries are incuded in the sampe we shoud take into account technoogica differences among them. To essen these potentia biases in approximating production technoogy, we extent Jorgenson and Nishimizu (1978) biatera production structure into a mutiatera context within the generaized Cobb-Dougas production frontier mode. Specificay, we distinguish six different groups of countries (i.e., South and Centra America, North America and Oceana, Europe, Asia, Africa and Asian Tigers) assuming that each one of those groups exhibit it s own technoogica structure. In that way, on the one hand, it is possibe to identify differences in a terms appearing in (11) between group of countries that are assumed to exhibit different technoogica conditions, whie on the other, we aow for more fexibe patterns for technoogica features (i.e., returns to scae, technoogica change, production and demand easticities) between groups of countries essened further the cost of choosing a ess fexibe functiona specification for the approximation of the wordwide production technoogy. -15-

17 In particuar, the mutiatera generaized Cobb-Dougas production frontier mode, expressed in natura ogarithms, has the foowing form: ϕε ( ) ( ) ϕε ( it ) ( ) n y t. t n e 0 t tt it it = it it + nk + n e t + nk t + v k t kt it it it it (1) where i = 1, K,N are the countries in the sampe, t = 1, K,T are the time periods, = 1, K,J are the group of countries defined in the mutiatera structure of the production technoogy, v it depicts a symmetric and normay distributed error term, it ( 0 v ) v ~ N,σ, (i.e., statistica noise), which represents eft-out expanatory variabes and measurement errors in the dependent variabe and, = D, k k = D, t t = D and, kt kt = D with D being a dummy variabe indicating the groups of countries, i.e., D = 1 for country beonging in group and D = 0 for every other country beonging to other groups. The above specification considers the data on inputs and aggregate output for each one of the countries in the sampe beonging into different groups as a separate set of observations which are assumed to be generated by mutiatera modes of production. Hence, the presence of D as an argument in the production function above aows for different production technoogies to be assigned into the different groups of countries. Finay, = ξ are country- and period-specific intercepts introduced into 0 0 it it (1) in order to capture tempora variations in output technica efficiency foowing -16-

18 Cornwe et a., (1990) fixed effects specification. According to this formuation output technica inefficiency is assumed to foow a quadratic pattern over time, i.e., ξ it = ζ i0 + ζ i1 t + ζ i t (13) where, ζ i0, ζ i1 and i ζ are the ( 3) N unknown parameters to be estimated. If ζ i1 ζ i 0 = = i, then output technica efficiency is time-invariant, whie when ζ i1 = ζ1 and ζ i = ζ i then output technica efficiency is time-varying foowing, however, the same pattern for a countries in the sampe. 10 The mode in (1) and (13) can be estimated foowing either an one or a two step procedure by singe-equation methods under the assumption of expected profit maximization. When NT is reativey sma, one can adopt an one-step procedure where ξ it is incuded directy in (1) using dummy variabes. However, in this case it is not possibe to distinguish between technica change and time-varying technica efficiency if both are modeed via a simpe time-trend (as in our case). In the two-step procedure, OLS estimates on the within group deviations are obtained for s and then the residuas for each producer in the pane are regressed against time and time-squared as in (13) to obtain estimates of ζ s for each country in the sampe. In both cases time-varying output technica inefficiency is obtained foowing the normaization suggested by 0 Schmidt and Sickes (1984). Specificay, define max{ ξ } t = as the estimated intercept of the production frontier in period t. Then output technica efficiency of each O country in period t is estimated as TE exp( ξ ) it 0 = it, where ξit ( ˆ ˆ t it ) i it =. 11 The -17-

19 advantages of this specification are its parsimonious parameterization regardess of functiona form, its straightforward estimation, its independence of distributiona assumptions, and that it aows output technica inefficiency to vary across countries and time. Moreover, since the expression in (13) is inear to its parameters, the statistica properties of individua country-effects are not affected. Under price uncertainty, expected profit maximization impies cost minimization aowing us to go back and forth between the production and cost functions in a theoreticay consistent way (Batra and Uah, 1974). Thus, soving the optimization probem in () using (1) we obtain the foowing dua to (1) cost function in a ogarithmic form: 0 t tt y wit ncit = δ t + δ t δ t + δ n y + δ n ϕε e ( it ) k t wit kt + δ n wkit + δ n t + δ ( it ) n wkitt ϕε e (14) where k kt E 0 1 k kt + t 0 δ t = n t ( + t) n t +, + t E + t E = + + t + kt, t t y δ = δ, δ k t t = δ, (15) tt tt y δ = δ, δ y = δ, δ k k y = δ, δ t t y = δ, δ y = 1 kt kt y E Then, using (14) we can derive the optima demand function for abor input as: -18-

20 t δ + δ t * 0 t tt y k nit = n + δ t + δ t δ t + δ n y + δ n w kit w it wit t wit kt + δ n δ ( it ) n t δ ( it ) n wkitt ϕε + + ϕε e e (16) From (16) we can derive the compensated own- and cross-price easticities of abor demand, i.e., e * nit = = δ + δ t 1 n w d t it (17) and e n * d it k kt k = = δ + δ n wkit t (18) which are necessary for the estimation of the fifth term in (11). These demand easticities are both group and time-specific. Simiary the abor demand easticity with respect to human capita is obtained from: e n ( t) ( ) ϕ ε * d it t it ε = = δ + δ εit nεit εit (19) that provides estimates of the fourth term in (11). The output cost easticity necessary for the estimation of the scae effect is obtained from: -19-

21 ε C y nc n y it = = it δ y (0) The hypothesis of constant returns-to-scae can be statisticay tested by imposing y the restriction that δ = 1, which is equivaent with imposing inear homogeneity in k the aggregate production frontier given the restrictions in (15), i.e., + = 1 and t kt + = 0. If this hypothesis cannot be reected then the underying technoogy exhibits constant returns-to-scae and the second term in (11) vanishes. For the estimation the technoogica change effects (third and ast terms in (11)) we need to compute the rate of cost diminution and the abor share equation. The former under the mutiatera generaized Cobb-Dougas specification in (14) is obtained, nc w C = = δ + δ t + δ n + δ n w ( it ) t e ϕε t it t tt t it kt it kit (1) The hypothesis of Hicks-neutra and zero technica change invoves the foowing t kt parameter restrictions in (1): δ = δ = 0 and δ t = δ tt = δ t = δ kt = 0, respectivey. 1 Accordingy, using the optima abor share equation, i.e., S nc = = δ + δ t it t it n wit () we can compute the extended abor biased technica change effect as: -0-

22 t 1 S δ it = t S t δ + δ t it (3) Since the mutiatera generaized Cobb-Dougas aggregate production mode is homothetic the second term in the extended abor biased technoogica change effect is zero and therefore it does not contribute in abor productivity growth. If the underying aggregate production technoogy exhibits zero technica change then the third and the ast terms in (11) are zero and abor productivity growth is affected ony from the remaining four terms. If, however, technica progress is Hicks-neutra then ony the extended abor biased technica change effect vanishes. Finay, if the underying technoogy is neutra t with respect to abor use, i.e., δ = 0, then again the fina term in abor productivity decomposition formua vanishes 13. Finay, for the estimation of the first term in (11) we need to compute abor technica efficiency. For doing so we use Reinhard, Love and Thissen (1999) approach in the context of the mutiatera generaized Cobb-Dougas production frontier. 14 Conceptuay, measurement of KP LTE it requires an estimate for the quantity it = θ it % which is not observed. Substituting this into the aggregate production function mode in (1) and by noticing that the abor-specific technica efficient point ies on the frontier, i.e., ξ it = 0, reation (1) may be rewritten as: ( % ϕε ( )) (% ϕε ( it )) n y t. t n e 0 t tt it it = t it + nk + n e t + nk t + v k t kt it it it it (4) -1-

23 Since under weak monotonicity, output technica efficiency shoud impy and must be impied by abor-specific technica efficiency, we can set the input specification in (4) equa to the output-oriented specification in (1). Then, using the parameter estimates obtained from the econometric estimation of the mutiatera generaized Cobb- Dougas production mode and soving for % it, we can derive a measure of Kopp s (1981) non-radia abor-specific technica efficiency from the foowing reation (Reinhard Love and Thissen, 1999): 15 LTE = exp ξ KP it it t + t (5) which is aways different than zero as ong as farms are technicay inefficient from an output-oriented perspective, i.e., ξit 0 or ζ i0 0, ζi 1 0, ζi 0 i. Using (13) and (5) the time rate of change of abor technica efficiency is computed from: LTE KP i1 i it t t ( 0 + 1t+ t ) t ( t) t ζ + ζ t ζ i ζi ζi = (6) It is time-invariant if aso output technica efficiency is time-invariant, i.e., ζ 1 = ζ = 0 t i and biased technica change is abor neutra, i.e., = 0. It s tempora pattern is i i common across countries if ζ 1 ζ1 i =, ζ i ζ = i, = and =. t t --

24 Labor aocative efficiency is then computed using the derived demand for abor input in (16) and the abor technica efficient use, i.e., % = LTE, as: KP it it it * ξ it LAEit = it ( w, y, ε,t) exp t it (7) + t 1 and it s time rate of change is then computed using the time derivative of (16) and reation (6) above as: LAE it KP ( w ε ) n( LTEit it ) * n it, y,,t = t t (8) In effect it remains constant over time under zero technica change and time invariant t abor technica inefficiency, i.e., ζ 1 = ζ = 0 = 0 and i i t tt t = = = kt = 0, whie it s tempora pattern is common across countries if ζ i1 = ζ 1 ζ = ζ i and i =, k k =, t t =, kt kt =. EMPIRICAL RESULTS The fixed effects parameter estimates of the mutiatera aggregate Cobb-Dougas production frontier mode in (1) are presented in Tabe 1 aong with their corresponding standard errors. The maority of the estimated parameters (except of two) were found to be statisticay significant at the 1 or 5 per cent eve. A parameters have the anticipated positive sign, whie their magnitudes are bounded between 0 and 1 indicating that the -3-

25 bordered Hessian matrix of first- and second-order partia derivatives is negative semidefinite. This impies that a reguarity conditions hod at the point of approximation, i.e., positive and diminishing margina productivities. In the ower pane of Tabe 1 are aso reported the country and time specific parameters of Cornwe et a., inefficiency effects mode in (13) for the country with the maximum efficiency score in each one of the six groups. For the maority of the countries in the sampe a parameters were found to be positive (except of some African countries) impying improvements in output technica efficiency over time (this finding is statisticay examined next). 16 Severa hypotheses concerning the mutiatera structure of the aggregate production frontier mode were tested using the generaized ikeihood-ratio test statistic 17 and the resuts are presented in the upper pane of Tabe. First, the hypothesis that the imposed mutiatera structure of the aggregate production frontier mode in (1) is not vaid is reected at the 5 per cent significance eve (first hypothesis in tabe ). Further, the assumption that ony the biases of technica change are simiar across group of countries is aso reected (second hypothesis in tabe ). The same is true for the margina productivities of physica capita and abor inputs (third hypothesis in tabe ). Statistica testing resuts in the same concusion when each one of the estimated coefficients is tested separatey (ast four hypotheses). Hence, indeed data on inputs and aggregate output in our sampe are generated by mutiatera modes of production supporting our initia hypothesis for approximating the wordwide production technoogy. There are significant differences across group of countries in their respective choice of production technoogy which shoud be taken into account in abor productivity growth decomposition. Basu and Wei (1998) and Acemogou and Ziibotti (001), -4-

26 appropriateness of technoogy paradigm is verified by the econometric estimation of our aggregate production frontier. The next set of hypotheses testing concerns the structure of technoogy, i.e., returns-to-scae and technica change. The resuts are presented in the midde pane of Tabe. First, it seems that for every country group, the aggregate production technoogy is not characterized by constant returns-to-scae as the reevant hypothesis was reected at k t kt the 5 per cent eve, i.e., + = 1 and + = 0. This impies that the scae effect is present constituting an important source of abor productivity growth. Average country and time estimates of scae coefficients were found to be increasing for South and Centra American (1.095), North America and Oceana (1.041), Asian Tigers (1.080) and Europe (1.0141). On the other hand, African and Asian countries exhibit decreasing returns as the reevant point estimates were found and , respectivey. This impies that ess deveoped countries in these two continents (i.e., Africa and Asia) have gone beyond the potentia capabiities of their aggregate own production technoogy. T TT t kt The hypotheses of zero technica change i.e., = = = = 0 and Hicks- t kt neutra technica change i.e., = = 0, were aso reected at the 5 per cent significance eve. On the average technica change was found progressive in a country groups with the highest vaue being for Asian Tigers, per cent. For North America and Oceania the corresponding figure was , for European countries , for South and Centra American countries , for African countries and for Asian countries The parameters reated with the neutra technica change, i.e., t and tt, were found to be positive and statisticay significant at the 1 per cent eve, impying -5-

27 that technica change was constanty progressive for the time period under consideration. The second order parameters reated with the biased part of technoogica change, i.e., t and kt were found to vary among the different groups of countries. Specificay, technica change was found to be abor using in North America and Oceania and abor saving in South and Centra America, Africa, Asia and Asian Tigers, whie the corresponding parameter was found positive for Europe but statisticay insignificant. On the other hand, technica change was capita using in South and Centra America, Africa, and Asian Tigers and capita saving in Europe and North America and Oceania. The reative parameter for Asia was found statisticay insignificant. We have further examined the hypothesis of abor-neutra technica change using the LR-test. The resuts are in favour of abor-biased technica change reecting the reevant hypothesis (ast hypothesis in the midde pane of tabe ). Thus, the abor biased technica change effect, i.e., first term in the ast parenthesis in reation (11) is present and it shoud be taken into consideration in the decomposition anaysis of abor productivity growth. The fina set of statistica testing refers to the specification of abor technica and aocative efficiency and it s tempora pattern. First, countries in the sampe are indeed not expoiting fu the potentia of their aggregate production technoogy exhibiting inefficiencies in resource utiization. These inefficiencies in abor use shoud be taken into account when abor productivity growth is to be anayzed. Specificay the hypothesis that a ζ parameters are ointy equa to zero is reected at the 5 per cent eve of significance (first hypothesis in the ower pane of tabe ). Further, abor technica efficiency was found to be time varying during the period as the hypothesis that ζ t = ζ = and = 0 is aso reected at the same significance eve ( nd hypothesis in i1 i 0-6-

28 the ower pane). This tempora pattern of abor technica efficiency is not common across countries in the sampe, impying differences between countries in movements towards their respective aggregate production frontier. Specificay the hypothesis that ζ = ζ, ζ = ζ and i1 1 i i = t t = is reected from the generaized LRtest (3 rd hypothesis in the ower pane of the tabe). Concerning abor aocative inefficiency, statistica testing impies that there are time varying abor utiization mistakes at its technicay efficient point. Finay, indeed countries in the sampe are making adustments towards better utiization of abor under the prevaiing factor prices which are not common across countries in the sampe (ast two hypotheses in tabe ). Estimates of both abor technica and aocative efficiency in the form of frequency distribution are reported in Tabe 3 for each group of countries. Estimated mean abor technica efficiency over both countries and time was found to be 66.4 per cent. This figure impies that the same eve of aggregate output coud have been produced on the average, under the current technoogica conditions and physica capita use, if abor use was decreased amost by 34 per cent. There is a notabe difference on the average efficiency scores between rich and poor group of countries. The most abor technicay efficient group was found to be Asian Tigers (87.81 per cent) foowed by North America and Oceania (79.4 per cent), and Europe (68.3 per cent). On the other hand, the ess abor technicay efficient groups were South and Centra America (63.88 per cent), Asia (61.1 per cent) and Africa (44.75 per cent). Some of the Asian Tigers exhibit the highest mean technica efficiency vaues (Thaiand per cent, Korea Rep per cent, Japan per cent and Hong Kong per cent) whereas African countries -7-

29 have the owest ones (Zambia per cent, Zimbabwe per cent, Maawi per cent and Mauritius per cent). On the other hand, estimates of abor aocative efficiency further confirm this divergence among poor and rich countries. In a three groups of deveoped countries mean abor aocative efficiency is greater than unity indicating that abor is underutiized at its technica efficiency point compared with the groups of deveoping countries where the corresponding figure is beow one. Specificay, mean abor aocative efficiency is 1.1 for North America and Oceania, 1.5 for Europe, and 1.3 for Asian Tigers. Contrary, in South and Centra America the corresponding figure is 0.66, 0.57 in Africa and 0.67 in Asia. Israe and most European countries are underutiizing abor at its technica efficient point having mean vaues we above unity (Israe 1.53, Begium 1.56, Ireand 1.40 and Denmark 1.41). On the other hand, India (0.34), Maawi (0.39), Turkey (0.47) and Sri Lanka (0.47) seem to over-utiize extensivey abor input. Concerning the tempora pattern of these efficiency measures, the three ess efficient groups (South and Centra America, Asia and Africa) were found to foow a quite simiar tempora pattern. As far as abor technica efficiency, a three groups were found to foow an ascending path unti 1975, foowed by a constant decrease -except of some sight upward variations- after this year. Ony South and Centra American countries were found to present sma improvements in their abor efficiency score at the end of the period under consideration. The picture is different as regard aocative efficiency scores. A three countries were found to foow an ascending tempora pattern which was constanty sharper for Asian countries. On the other hand, North America and Oceania and Europe were found to foow approximatey a common path unti the second -8-

30 haf of 70 s when European countries experienced a decrease in their abor technica efficiency score. In the beginning of 80 s, North America and Oceania countries overcame sighty the corresponding technica efficiency score of the European countries, foowing however approximatey a common path after this year. The resuts for the two groups are simiar, regarding abor aocative efficiency. Finay, Asian Tigers were found to experience an increase in their abor technica efficiency score unti 1975 which is though ower than those of Europe and North America and Oceania. After a sma decrease in the second haf of 70 s, Asian Tigers experienced an increase in abor technica efficiency which was about two times higher than those of the other two deveoped country-groups. As far as aocative efficiency, Asian Tigers were found to foow a sighty descending path during the first five years, foowed by a constant increase unti the end of the period. The highest rates of these improvements are observed in the second haf of 80 s. Deveoping countries with ow capita-abor mix seems to utiize more inefficienty abor input compared with deveoped countries not exporing fu the advantage of their technoogica conditions. The appropriate technoogy paradigm of Basu and Wei (1998) expains differences in the gap from the frontier among deveoped and deveoping countries, but in a competitive economic environment exchange rate misaignments, institutiona features (e.g., rigidities in product and abor markets) and competitive pressures affect the overa performance of individua economies. Further, the abundance of abor input in deveoping countries resuts in over-utiization of its use in the production process creating further inefficiency probems (e.g., India, Turkey and Maawi). Finay, it is notabe the fact that the variation on average abor technica -9-

31 efficiency is higher for the groups of deveoping countries. It seems that some rich deveoping countries have passed over some factor ratios and improved the technoogies specific to these ratios enhancing the utiization of their stock of abor (i.e., Mexico, Coombia, Paraguay). This is aso indicated by estimated mean abor aocative efficiency vaues in Africa and South and Centra America. Tabe 4, reports the average vaues over countries and time of abor productivity growth and it s decomposition using reation (11). These figures are the weighted averages computed foowing Oey and Pakes (1996) aggregation scheme. This is actuay a weighted average measure of wordwide abor productivity growth, using countries output shares as weights. During the time period, the weighted average abor productivity growth was per cent annuay. The greatest part of that abor productivity growth was due to TFP growth (75.76 per cent) and to a esser extent due to changes in factor intensities (15.45 per cent) and human capita accumuation (8.79 per cent). This finding is in accordance with the reevant iterature that aso attributes the greatest share of productivity changes to TFP growth. Concerning the sources of TFP growth, changes in the avaiabe technoogy (48.83 per cent) driven mainy by neutra technica changes (45.04 per cent) and to a esser extent due to factor biases (3.40 per cent) are the most important factor accounting for that productivity growth. The effect of scae economies and efficiency changes on abor productivity growth was found to be of equa importance accounting for the and per cent of it, respectivey. Improvements in abor technica efficiency were more important indicating a trend towards the respective technoogica frontier in each country. Sti, however, the maority -30-

32 of countries experienced a shift of the frontier rather than growth of their efficiency scores. In tota, substitution effects (i.e., changes in capita-abor mix) were the second highest source of that productivity growth accounting for the per cent of it. Shifts in reative capita-abor prices and the biases of technoogica change are important possibiities for changes in the growth rate of factor intensities and the accumuation of physica capita. The abor price effect (5.66 per cent) and the biased abor saving effect (7.33 per cent) are dominant. The bias of technoogica change towards saving abor and using capita is associated with the rising trend of abor price and the decine in the price of capita. In this sense, the bias of technoogica change is consistent with the induced innovation hypothesis (Hayami and Ruttan, 1970). Finay, human capita accumuation accounts on the average for the 8.79 per cent of measured productivity growth. This is mainy due to the high rates of growth in educationa eves during 70 s in both deveoped and deveoping countries. Besides these average vaues it is aso important to see the decomposition resuts for each group of countries separatey. Tabes 5a and 5b present the decomposition of abor productivity growth per group of country for the five sub-periods. The vaues reported therein are the within groups weighted average for each sub-period. According to these resuts Asian Tigers experienced the higher abor productivity growth during time period,.564 per cent, that is amost two times higher than the next two groups of deveoped countries, namey North America and Oceania (1.35 per cent) and Europe (1.18 per cent). South and Centra America aso experienced a high average annua abor productivity growth, 1.3 per cent, driven mainy by scae economies and -31-

33 technoogica improvements. On the other tai of the productivity distribution are African and Asian countries that exhibit significant ower vaues, and 1.004, per cent respectivey. Concerning the composition of these average vaues, productivity changes rather than changes in factor intensities seems to dominate measured abor productivity growth. There is ony the exception of African countries where the contribution of productivity changes accounts for the 5.60 per cent of that growth. Changes in reative factor prices resuted to significant abor-saving technoogica improvements in these countries given their input-mix which was abundant in abor input. Thus, the percentage contribution of the extended abor saving technoogica change effect was the highest among a groups of countries accounting for the.1 per cent of abor productivity growth. In Asian Tigers TFP accounts approximatey for the per cent of tota abor productivity changes whereas substitution effect ony for the per cent. The contribution of human capita changes was the owest among a groups of countries, 3.63 per cent (this figure is higher in Taiwan and Korea Rep.). These high TFP growth was due to technoogica advances, per cent, and the effect of scae economies, per cent, (that was the highest scae effect among a groups). Korea Rep. and Taiwan exhibit a very strong scae effect, whereas technoogica changes were significant in Thaiand, Japan and Korea Rep (see tabes 6a and 6b). Given their factor endowments, Asian Tigers seems to benefit a ot from exporing further the potentia of their technoogica conditions. They operate far beow their minimum efficient size where the average productivity of their resource endowments is maximized. Efficiency improvements payed an important roe ony in Japan, Taiwan and Thaiand indicating -3-