Inter-Firm and Intra-Firm Efficiency Measures

Journal of Productivity Analysis, 15, 185–199, 2001

c 2001 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. °

Inter-Firm and Intra-Firm Efficiency Measures ALFONS OUDE LANSINK Wageningen University ELVIRA SILVA Faculty of Economics of Porto SPIRO STEFANOU Pennsylvania State University

Abstract Intra-firm efficiency involves computing a particular firm’s efficiency degree over time relative to the firm-specific production frontier. Inter-firm efficiency reveals a particular firm’s performance over time relative to the “best practice frontier” among the set of comparable firms. These efficiency measures are related by an inter-firm catch-up component reflecting differences in technology across firms. Those measures are estimated for Dutch pot-plant firms using the Generalized Maximum Entropy formalism. The empirical results suggest the inter-firm catch-up component is the major determinant of inter-firm efficiency. Keywords: intra-firm efficiency, inter-firm efficiency, inter-firm catch-up, Generalized Maximum Entropy.

1.

Introduction

Production efficiency has been the subject of numerous theoretical and empirical studies for several decades since Farrell’s (1957) seminal work. The parametric frontier approach to efficiency measurement involving the specification and estimation of a parametric representation of the technology (frontier production, cost or profit function) has been applied extensively in many industries, including agriculture. Førsund, Lovell and Schmidt (1980), Schmidt (1986), Lovell and Schmidt (1988) and Bauer (1990) each provide a valuable overview of the modelling and estimation of parametric frontier functions and their relationship to efficiency measurement. In addition, Battese (1992) provides a survey of empirical applications of the parametric frontier production approach to technical efficiency measurement in the agricultural sector. The parametric frontier approach has been refined over the last two decades with significant improvements in panel data models opening some new directions for empirical analysis. Important contributions to the refinement of the parametric frontier approach to efficiency measurement for a panel data series include those of Pitt and Lee (1981), Cornwell, Schmidt and Sickles (1990), Kumbhakar (1990), and Battese and Coelli (1992).1 This paper refines the parametric frontier approach to efficiency measurement. The parametric frontier approach to technical efficiency measurement employed here differs from

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previous studies by modelling and estimating a firm-specific frontier production function. The estimation of a firm-specific production frontier is an example of an ill-posed problem, since the number of parameters to be estimated easily exceeds the number of observations. Consequently, least squares or Maximum Likelihood methods cannot be used, unless parametric restrictions are imposed across firms. A frequently made assumption in previous studies on the measurement of technical efficiency is that all slope parameters are equal for all firms while the intercept is firm-specific. A notable exception to this is presented by Kalirajan et al. (1995) who use a random coefficients approach to estimate a production frontier with varying slope parameters. Clearly, assuming constant slopes is a very restrictive assumption, since there is no reason to believe a priori that the intercept is the only firm-specific parameter. The estimation of a production frontier presenting firm-specific intercept and slope parameters is enabled by using Generalised Maximum Entropy estimation (Golan et al., 1996). Output technical inefficiency is modelled as a time- and firm-specific scaling parameter and estimated using a primal specification of the firm’s profit maximization problem. Firm-specific production frontiers, and time- and firm-specific efficiency parameters permit derivations of intra- and inter-firm technical efficiency measures. Intra-firm technical efficiency involves computing a particular firm’s efficiency degree over time taking the firmspecific production frontier as the reference frontier. Inter-firm technical efficiency for a particular firm involves choosing the “best practice frontier” at each time period among the set of comparable firms and then evaluating the firm’s technical efficiency relative to that frontier. Therefore, intra-firm efficiency reveals a specific firm’s performance over time relative to its own technology, while inter-firm efficiency reveals that firm’s performance over time relative to the best available technology in the industry. Inter-firm efficiency is decomposed into intra-firm efficiency and inter-firm catch-up components. The inter-firm catch-up component for a given time period may incorporate differences in technology across firms arising from differences in the rate of adoption of innovations by firms in a specific industry, or input quality differences, or both.2 The remainder of the paper is organized as follows. The concepts of inter- and intra-firm efficiency as well as the notion of inter-firm catch-up are illustrated in the next section followed by the theoretical model used to derive those measures. The data obtained from a stratified sample of Dutch glasshouse firms over the time period 1975–1995 are then discussed, followed by the presentation of the empirical model and the Generalized Maximum Entropy estimation procedure. Finally, the empirical results and conclusions are presented in the last two sections. 2.

Inter- and Intra-Firm Efficiency

Assuming one output, Q, and one input, a, Figure 1 presents two hypothetical firm-specific production frontiers for firms A and B at a given point of time. Let a 0 and Q a 0 be the observed input and output quantities for firm A, respectively, and assume B is firm A’s comparable firm. The maximum output firm A can obtain from input quantity a 0 with its own technology is given by Q aA0 with intra-firm technical efficiency, (E AA ), being equal to the ratio Q a 0 /Q aA0 .

INTER-FIRM AND INTRA-FIRM EFFICIENCY MEASURES

187

Figure 1. Intra- and inter-firm efficiency.

Firm B’s production frontier is represented by curve B, and Q aB0 is the maximum output level obtained from the input quantity a 0 . The inter-firm catch up component for firm A, (E CA ), is defined as the ratio of maximum output obtainable from firm A’s production technology given input quantity a 0 to the maximum output level that can be obtained from the same input quantity from firm B’s technology, Q aA0 /Q aB0 . Inter-firm efficiency for firm A, (E AB ), relates observed output level, Q a 0 , to the maximum output obtainable from firm B’s technology, Q aB0 . In this example, inter-firm efficiency for firm A is given by the ratio Q a 0 /Q aB0 . The relation between E AA E CA and E AB is given as E AB = E AA · E CA . 3.

Theoretical Model

Intra-Firm Efficiency The notion of intra-firm efficiency implies a firm that has a firm-specific production frontier and maximum output may not be always obtained due to inefficiencies in the production process. Intra-firm technical efficiency involves computing a particular firm’s technical efficiency degree over time taking the firm-specific production frontier as the reference frontier.

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Intra-firm output technical inefficiency is modelled as a time- and firm-specific scaling parameter and estimated using a primal specification of the firm’s profit maximization problem. This study uses the primal specification rather than the dual value function, since output technical efficiency can be computed directly from the firm-specific production frontier. The firm-specific production frontier is modelled as follows: Q ht = Uht · Fh (X ht ) + εht

(1)

where Q ht is the observed output level for firm h at time period t; Uht ∈ [0, 1] is a firm- and time-specific scaling parameter representing output technical inefficiency for firm h at time t; Fh (.) is the firm-specific frontier function for firm h; X ht is an observed (n × 1) vector of inputs for firm h at time t; and εht is an error term accounting for exogenous random events such as exceptional weather circumstances. Given the production specification in (1), intra-firm efficiency for firm h at time t is determined as the ratio of actual output to the frontier output at time t: E htA =

Uht · Fh (X ht ) = Uht . Fh (X ht )

(2)

A coherent system of n input demand equations at time period t can be derived by using the first-order conditions of firm h’s profit maximization problem: Uht ∂ Fh (·) = cit ∂ X hit

i = 1, . . . , n

(3)

where cit is the ratio of the price of input i to the output price at time t. Inter-Firm Efficiency Inter-firm technical efficiency involves choosing the “best practice frontier” at each time period among the set of comparable firms and then evaluating each firm’s technical efficiency degree relative to that frontier. Consequently, inter-firm efficiency reveals a particular firm’s performance relative to the best available technology in the industry. Assume firm j belongs to the set of comparable firms for firm h. Given the observed input bundle for firm h, X ht , and evaluating firm j’s production frontier at input level X ht yields: Q h j = Fj (X ht )

(4)

where Q h j is the maximum output level firm j could obtain if this firm were using the same input bundle as firm h. Given firm h’s set of comparable firms at time period t, the “best practice frontier” for firm h at time t, Fht∗ (.), is determined as the technology providing maximum obtainable output given the input vector X ht : Fht∗ (X ht ) = max{Fj (X ht )}. j

(5)

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189

Once the “best practice frontier” is identified, inter-firm efficiency of firm h at time t, E htB , is determined as the ratio of firm h’s actual output at time t to the maximum obtainable output at time t in the reference group: E htB =

Uht Fh (X ht ) . Fht∗ (X ht )

(6)

Inter-Firm Catch-Up The inter-firm catch-up component for a particular firm reflects differences between the firm’s production technology frontier and the “best practice frontier.” These differences may be due to several reasons such as input quality differences (e.g., managerial capability, experience, education) or differences in the adoption rate of innovations across firms. Given the “best practice frontier” for firm h in (5), the inter-firm catch-up component is given by: C = E ht

Fh (X ht ) . Fht∗ (X ht )

(7)

This component can be estimated residually since it provides the link between the inter-firm efficiency and intra-firm efficiency. 4.

Data

Intra- and inter-firm efficiency analysis requires data with cross-section and time series components. Panel data on specialized pot-plant firms covering the period 1979–1995 are obtained from a stratified sample of Dutch glasshouse firms keeping accounts on behalf of the LEI accounting system. Firms typically remain in the panel for a maximum of eight years, resulting in an incomplete panel. Firms rotate in and out the sample to avoid a selection bias which arises when firms improve their performance by their presence in the accounting system. The data set contains 941 observations on 185 firms. One output and three variable inputs (energy, materials and services) are distinguished. Output mainly consists of pot-plants. Other outputs included are fruits, vegetables and flowers. Energy consists of gas, oil and electricity, as well as delivery of thermal energy by electricity plants. Materials consist of seeds and planting materials, pesticides, fertilizers and other materials. Services include services by contract workers and services from storage and delivery of outputs. Fixed inputs are structures (buildings, glasshouses, land and paving), machinery and installations and labour. Labour is measured in constant prices of 1985 and is calculated as the product of quality-corrected man years and the yearly costs of labour in 1985 (LEIDLO/CBS). The quality correction of labour is performed by the LEI. Labour is specified as a fixed input because a large share of labour consists of family labour. Furthermore, the flexibility of hired labour is restricted by the presence of permanent contracts and by the fact that hiring additional people involves search costs for the firm operator. Capital in structures and machinery and installations is measured at constant 1985 prices.

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Tornqvist price indexes are calculated for output and the three composite variable inputs with prices obtained from the LEI-DLO/CBS. The price indexes vary over the years but not over the firms, implying differences in the composition of inputs and output or quality differen- ces are reflected in the quantity (Cox and Wohlgenant, 1986). Implicit quantity indexes are generated as the ratio of value to the price index. Average values and standard deviations of the variables that are used in this study can be found in Table A.1 of the Appendix. 5.

Empirical Model

The firm-specific frontier for each firm in the sample is assumed to follow a Quadratic specification:3 Ã ! 7 7 7 X X X Q t = U t · β0 + βi xit + 0.5 βi j xit x jt + ε0t (8) i=1

i=1 j=1

where xit are input quantities at time t, with i = 1 (energy), 2 (materials), 3 (services), 4 (structures), 5 (machinery and installations), and 6 (labour). A time trend (i = 7) is included in the empirical model to account for neutral exogenous technological change in the estimation period. ε0t is an error term representing specification errors, measurement errors and all variables not accounted for in the specification. In what follows, it is assumed that the error distribution is centered about zero and that the domain of the error distribution is bounded (Golan et al., 1996: 83) Using the first-order conditions for profit maximization, the input demand equations are derived as: Ã ! 7 X 1 cit · − βi − β jt x jt + εit i = 1, . . . , 3. (9) xit = βii Ut j=1, j6=i Equation (8) and the system of equations in (9) are estimated simultaneously using the Generalized Maximum Entropy estimation method. The next section provides a brief exposition of the Generalized Maximum Entropy formalism. 6.

Generalized Maximum Entropy Estimation

The Generalized Maximum Entropy (GME) formalism can address ill-posed problems in economics. Ill-posed problems may arise when the number of unknown parameters exceeds the number of data points implying traditional estimation methods cannot be used (Golan, Judge and Miller, 1996). The Bayesian interpretation of the GME problem is that prior information is added to the sample information in the form of discrete supports for the prior distribution of unknown parameters (Paris and Howitt, 1998). A further discussion of the strengths and weaknesses of GME estimation compared to traditional (e.g. Maximum Likelihood and Leas Squares) methods is given in Paris and Howitt (1998).

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The GME formalism reveals a powerful tool when firm-specific frontiers need to be estimated. In this case, the number of parameters is usually very large, leading to negative degrees of freedom. Rewriting the production frontier in (8) in a matrix form yields Yt = Ut · X t β + ε0t

(10)

where β is a Kx1-vector of parameters to be estimated. Estimating this model using GME econometrics requires all βk to be expressed as the sum of the product of M probabilities and support values βk =

M X

pkm z km

(11)

m=1

where pkm are probabilities and z km are the corresponding support values. Support values for all parameters of the production frontiers are [−10, −5, 0, 5, 10]. Inspection of the average values of the variables used in the estimation shows that the average values of all inputs and prices are smaller than 10, whereas the average value of output is slightly larger than 10. Therefore, it is expected a priori that the parameters will lie in the specified interval [−10, 10]. Similarly, the error terms in the frontier production function and input demand equations are expressed as the sum of the product of N probabilities (witn ) and support values (vitn ) εit =

N X

witn vitn

i = 0, 1, . . . , 3

(12)

n=1

Support values of the error terms are determined using the 3σ rule, where σ is the empirical standard deviation of the dependent variable (Golan, Judge and Miller, 1996). It is assumed that the error distribution is bounded, symmetric and centered about zero, which is reflected in a symmetric support for the error terms, i.e. vit1 = −vitN , for each i and t. GME estimation comprises the maximization of the following entropy function: H ( p, w) = −

M K X X

pkm ln( pkm ) −

k=1 m=1

T X N I X X

witn ln(witn )

(13)

i=0 t=1 n=1

subject to the model or consistency constraints: Yt = U t

M K X X

pkm · z km · X kt +

k=1 m=1

N X

w0tn · v0tn

(14)

n=1

and X it =

Ki X M X k=1 m=1

pkm · z km · Vkt +

N X n=1

witn · vitn

(15)

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the additivity constraints: M X

pkm = 1

for all k

witn = 1

for all i, t

m=1 N X

(16)

n=1

and the constraint on Ut : 0 ≤ Ut ≤ 1

for all t

(17)

where X kt = [1x1t · · · x7t 0.5x1t x1t 0.5x1t x2t · · · 0.5x7t x7t ], Vkt = [cit /Ut − 1 − x1t · · · − xi−1t − xi+1t · · · − x7t ], and K i is a subset of K . Curvature conditions of the production frontier impose non-negative marginal products and concavity in variable and fixed inputs. Non-negative marginal products of the variable and fixed inputs is ensured by adding the following set of restrictions during estimation: βi +

7 X

βi j X j ≥ 0

i = 1, . . . , 6.

(18)

j=1

Concavity of the production frontier in variable and fixed inputs is imposed by using the necessary condition that the diagonal elements of the matrix of second order of input quantity derivatives are negative and the sufficient but not necessary condition that the row and column elements corresponding to the off-diagonal element are smaller in absolute terms than the absolute value of the diagonal element. This results in a set of additional restrictions that are imposed during estimation: βii ≤ 0 |βi j | ≤ |βii |

i = 1, . . . , 6 i, j = 1, . . . , 6

(19)

where βii , βi j are diagonal and off-diagonal elements of the matrix of second order derivatives of the production frontier to input quantities. This GME problem provides the optimal probability vectors that can be used to form point estimates of the unknown parameter vector and the unknown disturbances (Golan, Judge and Miller, 1996). The GME objective function is strictly concave in the interior of the additivity constraint set implying uniqueness of the optimal solution. The existence of a unique solution is assured if the intersection of the consistency and additivity constraint set is non- empty and if supports are specified correctly. The reader should note that the estimator that is used here does not account explicitly for the endogeneity of the variable input quantities in the system of output supply and input demand equations in (14)–(15). Nevertheless, as Golan et al. (1996) state: ‘this formulation may lead to parameter estimates that are slightly biased but have excellent precision.’ Also, it should be noted that error terms may be correlated across equations and that this information is not used here during estimation.

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Table 1. Annual mean value and growth rates of intra-firm efficiency, catch up and inter-firm efficiency by group of firms. Intra-Firm Time Period

Catch-Up

Inter-Firm

Mean

Growth Rate

Mean

Growth Rate

Mean

Growth Rate

1975–1980 1981–1985 1986–1990 1991–1995

0.891 0.893 0.957 0.926

−0.087 0.039 0.015 −0.002

0.683 0.497 0.675 0.778

0.117 −0.147 −0.071 −0.011

0.598 0.429 0.643 0.716

0.013 −0.117 −0.061 −0.016

1975–1995

0.910

−0.013

0.638

−0.023

0.577

−0.046

1975–1980 1981–1985 1986–1990 1991–1995

0.911 0.895 0.901 0.836

−0.090 −0.009 −0.002 −0.020

0.462 0.526 0.573 0.567

−0.067 0.022 −0.063 0.003

0.416 0.468 0.516 0.471

−0.153 0.012 −0.067 −0.014

1975–1995

0.887

−0.027

0.530

−0.022

0.467

−0.049

1975–1980 1981–1985 1986–1990 1991–1995

0.871 0.844 0.849 0.765

−0.137 −0.063 −0.067 −0.013

0.703 0.596 0.487 0.401

−0.082 0.041 −0.020 0.125

0.611 0.495 0.406 0.283

−0.215 −0.026 −0.091 0.113

1975–1995

0.822

−0.052

0.510

0.045

0.411

−0.008

Small Firms

Medium Firms

Large Firms

7.

Empirical Results

Inter-firm efficiency for a particular firm involves choosing the “best practice frontier” at each time period among the set of comparable firms and then evaluating the firm’s technical efficiency relative to that frontier. Based on the average area of greenhouses in the sampling period, firms are classified into small, medium and large size categories. Small firms are those with an average area less than 1/3 of the sample mean. Medium firms have an average area in the range 1/3–4/3 of the sample mean, while large firms have an average area of greenhouses larger than 4/3 of the sample mean. Given those three groups of firms, the set of comparable firms for a particular firm h in each year is defined as all firms in the same size class. The set of comparable firms for each firm is used for computing the inter-firm catch-up and inter-firm efficiency ratios consistent with (7) and (6), respectively. A solution to the GME estimation problem is found for all firms in the sample.4 Using the GME results, estimates of intra-firm and inter-firm efficiency as well as estimates of the inter-firm catch-up component are generated for each firm in the sample at each time period. Table 1 presents information on the annual mean value and growth rates of intra- and inter-firm efficiency as well as the inter-firm catch-up component for each group of firms. Small firms have higher means of the intra-firm efficiency measure during all time periods

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Table 2. Sensitivity analysis of mean values and growth rates of intra-firm efficiency, catch-up and inter-firm efficiency. Intra-Firm

Catch-Up

Inter-Firm

Time Period

Mean

Growth Rate

Mean

Growth Rate

Mean

Growth Rate

Small Firms 1975–1995

0.894

−0.003

0.592

0.013

0.528

−0.004

Medium Firms 1975–1995

0.879

−0.016

0.480

−0.014

0.418

−0.031

Large Firms 1975–1995

0.834

−0.041

0.515

−0.016

0.417

−0.059

than medium and large firms. Also, small firms exhibit the highest (although negative) annual growth rates of intra-firm efficiency in the whole period 1975–1995. The catch-up component is highest on average in the whole period 1975–1995 for small firms, followed by medium and large firms. However, small and medium firms have lower annual growth rates of the catch-up component during the time period 1975–1995 than large firms. The annual growth rates indicate positive overall growth of the catch-up component for large firms and negative overall growth rates for small and medium firms. Analysis of the annual mean value and annual growth rates of the intra-firm efficiency measure and inter-firm catch-up component indicates behavioral differences across groups of firms. Small firms have a larger growth rate for the intra-efficiency measure than for the catch-up component (in absolute terms); i.e., they have been more concerned in exploring their current production potential than in adopting new technologies. Large firms, on the other hand, have been more aggressive in terms of adopting new technologies. This may be the result of large firms having better access to credit than small firms to finance the implementation of new technology or because new technologies (e.g., computers) are more profitable when implemented on a larger scale. Table 2 provides the results of a sensitivity analysis of the results to multiplying the support values of the parameters only by a factor two.5 It can be seen that the mean values of intra-firm efficiency, catch-up and inter-firm efficiency are fairly robust to increasing the support values. The growth rates are more sensitive to increasing the support values. This is especially the case for the large firms; for the small and medium firms, the growth rates are marginally greater. However, most of the conclusions suggested by the results in Table 2 are the same as those of the original results in Table 1. Variation in growth of the intra-firm efficiency measure and the catch-up component are regressed on several exogenous variables (using OLS) capturing the effect of the energy crises (in 1974 and 1982), household and demographic characteristics, location and investment in physical capital (Table 3).6 Five of the eleven parameter estimates are found to be statistically significant at the critical 10% level in the intra-firm efficiency growth regression, while two of the eleven parameter estimates are found to be statistically significant at the critical 10% level in the catch-up growth regression.

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Table 3. Coefficient estimates from regression of intra-firm efficiency growth and catch-up growth on exogenous variables. Growth Intra-firm Efficiency Variables Constant Successora Locationb Family Labourc Age of Firm Operator Modernity Structuresd Modernity Machinery and Installationsd D1e D2 D3 D4

Growth Catch-up

Coefficient Estimates

t-value

Coefficient Estimates

t-value

0.03 0.00 0.01 0.05 −0.00

0.99 0.03 1.12 2.42 −1.69

−0.03 0.04 0.04 −0.05 0.00

−0.39 1.22 2.02 −1.12 0.82

0.06

1.57

0.04

0.56

−0.19

−5.04

−0.10

−1.33

0.10 0.01 −0.09 0.01

4.14 0.54 −5.29 −0.42

−0.05 −0.01 0.01 −0.10

−1.09 −0.22 0.16 −2.58

a Successor

is 1 for successor available. b Location is 1 for location in glass district. c Family labour is the share of family labour in the firm’s total labour. d ratio of the balance value to the new value. e D1–D4 indicate the number of years after the oil crisis (1974 and 1982). For example, D1 is 1 for 1975 and 1983.

The availability of a successor for the firm has no impact on the intra-efficiency growth, but positively affects catch-up (although the parameter is not significant in both cases). This implies that firms with a successor are more aggressive in terms of keeping up with new technologies than firms without a successor. Results also suggest that firms in the greenhouse district are more aggressive in keeping up with new technologies and exploring the existing production potential than firms at other locations.7 The presence of many similar firms in the neighborhood may be one of the reasons why competition among them is stronger in the greenhouse district. Clearly, competitive pressure can affect management quality and the adoption of new technologies. Moreover, the speed of adoption and diffusion of new technologies may be affected positively by the presence of many similar firms in the neighborhood allowing experiences to be exchanged more rapidly. The presence of study groups of similar firms in regions with a high pot-plant firm density may be another factor explaining the importance of location in the growth of the intra-firm efficiency and catch-up component. The study groups act as a means of exchanging experiences with existing and new production technologies and are often used by agricultural extension personnel as a venue to inform firm operators about new developments. Family labour has a significant positive impact on the growth rate of intra-firm efficiency and a negative impact on the growth rate of the catch-up component. This suggests that firms operated by family labour are better at improving the efficiency of the existing production potential than in keeping up with new technologies. However, these results may actually

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reflect a size effect that appears in Table 1, since small firms are usually operated by a larger share of family labour than large firms. Modernity of structures has a positive impact on the growth of the intra-firm efficiency and catch-up component. In addition, modernity of machinery and installations has negative impacts on the intra-firm efficiency growth and on the catch-up growth. These results indicate that modernity of structures plays a more important role in the catch-up growth than modernity of machinery and installations, implying firm operators obtain a competitive advantage by continuously modernizing their greenhouses. The results also indicate that firms with obsolete machinery and installations have more potential for intra-firm efficiency and catch-up growth than firms with up-to-date machinery and installations. That is, firms with up-to-date machinery and installations are on average closer to the firm-specific and sector frontier than firms with obsolete machinery and installations.8 The oil crisis has a positive impact on the growth rates of intra-firm efficiency and a negative impact on the growth rates of the catch-up component in the two years immediately following the year of the crisis. The positive impact on intra-firm efficiency growth rate suggests that the firm’s first reaction after a sharp energy price increase is to explore the existing technology to its full potential (i.e., pursue intra-firm efficiency). The negative (although insignificant) impact on the catch-up component indicates that investments in new technologies are hampered in the first and second year after the crisis. The third year after the crisis yields a significant negative impact on the intra-firm efficiency growth measure and a positive impact on the catch-up component. This may indicate that firms (slowly) start to invest in new technologies, which require some experience before they are used to their full potential. Table 4 provides the results of a sensitivity analysis of the regression of growth rates of the intra-firm efficiency measure and the catch-up component on several exogenous variables results to multiplying the support values of the parameters only by a factor two. The growth in intra-firm efficiency estimates across Tables 3 and 4 are virtually identical. The same coefficient estimates remain statistically significant and take on the same relative magnitude across the two cases presented in these tables. For the most part, the growth catch-up estimates do not differ across the two cases. In Table 3, the estimates for the growth catch-up equation are not stable with only the coefficients on location and the fourth year after the 1974 and 1982 oil crises offering significant coefficient estimates. When the support values of the parameters are multiplied only by a factor of two in Table 4, none of the coefficient estimates present t-values significantly different from zero. The growth catch-up regression estimates present only one coefficient estimate changing sign (the dummy for the second year post oil crises) but both remain statistically insignificant. Therefore, most of the conclusions obtained from the results in Table 4 are the same as those of the original results in Table 3. 8.

Conclusions

This paper develops intra- and inter-firm measures of technical efficiency. Intra-firm technical efficiency measures the use of the firm’s own production potential and, this, represents an absolute measure of technical efficiency. Inter-firm efficiency is a relative efficiency

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Table 4. Sensitivitya analysis of regression of intra-firm efficiency growth and catch-up growth on exogenous variablesb . Growth Intra-firm Efficiency Variables Constant Successor Location Family Labour Age of Firm Operator Modernity Structures Modernity Machinery and Installations D1 D2 D3 D4

Growth Catch-up

Coefficient Estimates

t-value

Coefficient Estimates

t-value

0.06 0.01 0.01 0.05 −0.00

1.52 0.36 1.19 2.27 −2.23

0.05 0.03 0.03 −0.09 −0.00

0.41 0.57 0.87 −1.39 −0.11

0.04

1.10

0.08

0.61

−0.16

−4.02

−0.18

−1.45

0.11 0.02 −0.08 0.01

4.37 1.02 −4.40 0.60

−0.03 0.04 0.11 −0.08

−0.38 0.76 1.93 −1.25

a After b See

multiplying the support values of the parameters by a factor two. Table 3 for explanation of variables.

measure revealing the performance of a particular firm relative to the “best practice” available in the industry. Inter-firm technical efficiency is the product of intra-firm efficiency and the inter-firm catch-up component and reflects differences in human capital potential such as managerial capability and education as well differences in the rate of adoption of innovations. Consequently, this measure may be more relevant for policy purposes than the intra-firm efficiency measure. Intra-firm and inter-firm efficiency measures as well as the inter-firm catch-up component are estimated for Dutch pot-plant firms using the GME formalism. The empirical results suggest two broad conclusions. First, the inter-firm catch-up component is the major determinant of inter-firm efficiency. Second, there are behavioral differences across groups of firms. Small firms exhibit the highest growth rate of intra-firm efficiency, implying this group of firms is more concerned with exploring its production potential. Large firms present the highest growth rate of the catch-up component, suggesting these firms are more active in keeping up with new technologies rather than exploiting their existing production potential. A regression analysis of socio-economic variables on the intra-firm efficiency and catchup growth rates indicates that family labour has a significant positive effect and modernity of machinery and installations a significant negative effect on the intra-firm efficiency growth rate. Location of the firm in a competitive environment has a significant positive effect on the growth of the catch-up component. The results also suggest that the firm’s first reactions to sharp energy price increases is to explore the existing production technology to its full potential rather than to invest in new energy saving technology.

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Table A.1. Description of data. Variable

Price indexes Energy Materials Services Quantities Outputs Energy Materials Services Structures Mach./Installations Labour Trend

Dimension

Symbol

period: 1975–’95 observations: 941 Mean

Standard Deviation

base year 1985 base year 1985 base year 1985

c1 c2 c3

0.713 1.121 1.074

0.209 0.155 0.049

100.000 guilders 100.000 guilders 100.000 guilders 100.000 guilders 100.000 guilders 100.000 guilders 100.000 guilders first year in sample = 1

Y X1 X2 X3 X4 X5 X6 X7

12.093 2.151 2.811 1.044 6.859 3.533 3.804 3.311

11.389 2.001 3.239 1.121 7.233 4.223 2.687 1.877

Notes 1. Pitt and Lee (1981) consider a stochastic frontier production function for a panel data series. Cornwell, Schmidt and Sickles (1990) and Kumbhakar (1990) propose panel data models with time-varying firm effects. Battese and Coelli (1992) suggest a time-varying effects model for incomplete panel data. 2. The inter-firm catch-up component is similar to the catch-up component defined in cross- country productivity growth studies. However, the catch-up component in those studies incorporates only technical change (e.g., F¨are, Grosskopf, Norris and Zhang, 1994). The inter- firm catch-up involves changes in the “best practice frontier” (technical change) and/or quality input differences (e.g., managerial capability, education, experience). 3. The quadratic specification is employed here because it allows for imposing concavity and monotonicity through a set of linear restrictions. Other popular flexible functional forms, such as the Leontief and Translog do not allow for imposing such restrictions through linear constraints. 4. GAMS (Brooke et al., 1998) was used for estimating the models. Estimation results are not given in this paper due to space limitations, but they can be obtained from the authors upon request. 5. The results are not sensitive to multiplying the intervals for the parameters and error term by a factor larger than one. However results change when multiplying the interval of the parameters (leaving everything else unchanged) with a factor larger than one. This is consistent with a basic result in Generalised maximum entropy estimation discussed in Golan et al. (1996, p. 140) and Golan et al. (1997). 6. In traditional stochastic frontier production estimation a ‘two stage approach’ where growth rates of efficiency are regressed on exogenous variables is inconsistent (see Battese and Coelli (1995)). This is because the exogenous variables of the efficiency regression are implicitly omitted from the frontier regression. In the GME approach that is used in this paper, the inconsistency is introduced in the regression of the intra-efficiency growth rates on exogenous variables. There is no inconsistency in the regression of the catch-up term growth rates because a frontier is estimated for each firm separately. 7. The glassdistrict is the area between Rotterdam and the Hague where 51% of all pot-plant firms are located. 8. This may provide some evidence of the presence of adjustment costs which can result in a reduction in productivity which occurs when more of quasi-fixed factors of production such as durable equipment is absorbed (or released) too quickly. Many of the internal costs of adjustment can be viewed as learning costs.

INTER-FIRM AND INTRA-FIRM EFFICIENCY MEASURES

199

References Battese, G. E. (1992). “Frontier Production Functions and Technical Efficiency: A Survey of Empirical Applications in Agricultural Economics.” Agricultural Economics 7, 185–208. Battese, G. E., and T. J. Coelli. (1992). “Frontier Production Functions, Technical Efficiency and Panel Data: Application to Paddy Farmers in India.” Journal of Productivity Analysis 3, 153–169. Battese, G. E., and T. J. Coelli. (1995). “A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data.” Empirical Economics 20, 325–332. Bauer, P. W. (1990). “Recent Developments in the Econometric Estimation of Frontiers.” Journal of Econometrics 46, 39–56. Brooke, A., D. Kendrick, and A. Meeraus. (1988). GAMS, A Users’s Guide. San Francisco: The Scientific Press. Cornwell, C., P. Schmidt, and R. C. Sickles. (1990). “Production Frontiers with Cross-Sectional and Time-Series Variation in Efficiency Levels.” Journal of Econometrics 46, 185–200. Cox, T. L., and M. K. Wohlgenant. (1986). “Prices and Quality Effects in Cross-Sectional Demand Analysis.” American Journal of Agricultural Economics 68, 908–919. F¨are, R., S. Grosskopf, M. Norris, and Z. Zhang. (1994). “Productivity Growth, Technical Progress and Efficiency Change in Industrialized Countries.” American Economic Review 84, 66–83. Farrell, M. J. (1957). “The Measurement of Productive Efficiency.” Journal of Royal Statistical Society A 120, 253–281. Førsund, F., C. A. K. Lovell, and P. Schmidt. (1980). “A Survey of Frontier Production Functions and of their Relationship to Efficiency Measurement.” Journal of Econometrics 13, 5–25. Golan, A., G. Judge, and D. Miller. (1996). Maximum Entropy Econometrics. New York: John Wiley and Sons. Golan, A., G. Judge, and J. Perloff. (1997). “Estimation and Inference with Censored and Ordered Multinomial Response Data.” Journal of Econometrics 79, 23–51. Kalirajan, K. P., M. B. Obwona, and S. Zhao. (1996). “A Decomposition of Total Factor Productivity Growth: The Case of Chinese Agricultural Growth Before and After Reforms.” American Journal of Agricultural Economics 78, 331–338. Kumbhakar, S. C. (1990). “Production Frontiers, Panel Data and Time-Varying Technical Inefficiency.” Journal of Econometrics 46, 201–211. Lovell, C. A. K., and P. Schmidt. (1988). “A Comparison of Alternative Approaches to the Measurement of Productive Efficiency.” In Ali Dogramaci and Rolf F¨are (eds.), Applications of Modern Production Theory: Efficiency and Production. Boston: Kluwer Academic Publishers. Paris, Q., and R. E. Howitt. (1998). “An Analysis of Ill-Posed Production Problems Using Maximum Entropy.” American Journal of Agricultural Economics 80, 124–138. Pitt, M. M., and L. F. Lee. (1981). “Measurement and Sources of Technical Inefficiency in the Indonesian Weaving Industry.” Journal of Development Economics 9, 43–64. Schmidt, P. (1986). “Frontier Production Functions.” Econometric Review 4, 289–328.