Economics Research International

Volume 2014, Article ID 376486, 8 pages

http://dx.doi.org/10.1155/2014/376486

## Technical Efficiency and Technical Change in Canadian Manufacturing Industries

Department of Economics, University of Regina, 3737 Wascana Parkway, Regina, SK, Canada S4S 0A4

Received 26 July 2014; Revised 5 December 2014; Accepted 17 December 2014; Published 31 December 2014

Academic Editor: Jean Paul Chavas

Copyright © 2014 Samuel Gamtessa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study applies the “true fixed effects” panel stochastic frontier methodology to the Canadian KLEMS data set to estimate technical change and technical efficiency in the Canadian manufacturing sector. To account for the endogeneity of capital inputs as well as the possible problems related to omitted variables, a two-stage residual inclusion method is pursued. The first stage is estimated using the dynamic panel GMM method. The results show that Canadian manufacturing industries experienced significant declines in technical efficiencies during the last ten years. This suggests that the observed slowdown in TFP growth during the recent past is partly due to declining technical efficiency.

#### 1. Introduction

Canadian labour productivity growth lags behind other countries, particularly that of USA. Slow or no growth in TFP appears to explain this trend [1]. Gordon [2] observes that the TFP index in 2011 was at the same level as its early 1970s levels. According to the Canadian productivity data set used in this study, TFP growth in the manufacturing sector, the best performing sector, was 1.8% per year during the period 1961–1997. However, most of these growth rates were the result of the increases before 1990. TFP stagnated during the 1990s and has been declining since 2000. There is no clear explanation as to why TFP is not growing. The gap between Canada and US TFP growth may be explained by the gap in materials and equipment intensity [1]. Lee and Tang [3] link the productivity gap in the manufacturing sector relative to that of USA to capacity utilization, labour quality, and & gaps. Most recently, the most common view appearing in newspaper headlines is that lagging in innovations is the main culprit.

TFP is commonly interpreted as the index of technical change, suggesting that Canada’s anemic growth in labour productivity is largely caused by lack of technological progress. This interpretation seems to have contributed to the puzzle about the productivity growth problem in Canada given that Canada seems to be doing fine in terms of the factors underlying technical change. In reality, TFP change is entirely attributable to technical change only when production technology is characterized by constant returns to scale and when there is no technical inefficiency [4]. This suggests that it is possible for deterioration of technical efficiency, assuming constant returns to scale (the Statistics Canada data on productivity used in this study preimposes constant returns to scale), to be the main reason for the slowdown or decline in TFP growth even though technical change is positive.

In this study, we provide a parametric decomposition of TFP growth in the Canadian manufacturing sector using the stochastic frontier (SF) method. The SF method, which was developed by Aigner et al. [5] and was mainly used in the analysis of microdata, is more recently used for higher level aggregations as well as for panel data. For example, Sharma et al. [6] employ the SF method to decompose TFP growth across the states in the United States. The decomposition is based on the observation that producers improve their TFP not only by pushing the production frontier (an upward shift in their production functions) or through technical change. In fact, most producers exhibit technical inefficiency or are not operating on the production frontiers such that they could improve their productivities without an improvement in technologies. The stochastic frontier method for panel data has also evolved from assuming that technical efficiency is time-invariant to various specifications that allow it to vary across time [7–10]. However, all of these approaches attributed any panel-specific individual effects to the inefficiency term, thereby leading to biased estimates. The approach adopted in this study is the recently developed true fixed effect framework [11]. This method allows the individual effects to be distinct from inefficiency terms. Another problem in estimating frontier parameters is endogeneity of some or all of the inputs and the omitted variables problem resulting from the fact that the underlying factors for inefficiency, not included in the regressions, may be correlated to the variables that enter in the frontier model. In this study, we adopted a newly developed method known as the two-stage residual inclusion approach [12] in order to address the endogeneity of capital inputs and the omitted variables problem. The first stage estimation is used to predict the residuals that are to be used in the second stage. The Arellano and Bover [13] system dynamic panel GMM method is used to model capital as a function of input prices and output as well as its own lags and the time dummies. This method is well suited as one of the explanatory variables, output, is endogenous and it is treated as endogenous. The second stage estimation follows the true fixed effect method with residual inclusion.

The data used are drawn from Statistics Canada’s KLEMS data set, which provides total factor productivity, labour productivity, input prices, output prices, gross domestic product (GDP), and gross output by 4-digit NAICS aggregation (NAICS stands for North American Industry Classification System). The 21 manufacturing industries, based on NAICS aggregation, have enjoyed much better TFP growth than the overall business sector average.

Comparing the trends in decade average growth rates of TFP and labour productivity (LP) in the manufacturing sector reveals continuous slowdown in productivity. During the most recent years (2001–2007), average TFP growth was negative whereas the average growth rate in LP was dramatically lower than all the averages observed during the previous periods.

There are two key contributions of this paper. The first is the application of new econometric methods. The true fixed effect method is a new and important advancement in stochastic frontier regression methods. The two-stage residual inclusion method is also a new approach that has been proposed to deal with endogeneity problems in nonlinear settings. This paper utilizes both of these advancements in empirical methods in a unique way to obtain precise and consistent estimates for technical efficiency. The comparison of the results from these new methods to the time-decay model indicates that the methods adopted here better explain the data. The second contribution is new insight of the Canadian productivity problems. So far, the discussion is based on the perception that TFP slowdown, the main force behind the slowdown in labour productivity, has been caused by inadequate technical changes and thus the recommended policy prescriptions were largely aimed at research and development, training, investments in capital equipment, and the like. The results in this paper point to another unexplored aspect, deterioration in technical efficiency in many of the manufacturing subsectors which have been significant, particularly during the period after 2000. For the manufacturing sector as a whole, we find that the average technical efficiency for the most recent years is much less than the average for the period 1961–1970. This begs the question, why this has been the case and how we might improve it.

The rest of the paper is organized as follows. We discuss TFP and its decomposition into its components in the next section followed by a presentation of the stochastic frontier specifications and its application to decomposition of TFP. Estimation methods are discussed in Section 4 followed by presentation of the results in Section 5. Section 6 provides some concluding remarks.

#### 2. Decomposition of TFP into Its Components

Suppose the production function is given by , where is observed output, is a vector of observed inputs used in production, and is time index. Assuming no inefficiency and constant return to scale, TFP growth is defined as where ; ; given that is the observed use of the th input; and is the cost share of the input (), where is the unit cost of and .

Define the production frontier as , where is the maximum amount of output that can be produced with the input vector at time . In other words, this reflects the technological frontier that producers can achieve only when they are technically efficient. The output-based measure of technical efficiency is defined as , where is actual output and . Taking natural log of both sides, equation and differentiating with respect to time give us which can be written as Given that is the elasticity of frontier output with respect to change in , (3) can be rearranged using the definition of TFP growth in (1) as and noting that growth rate in technical change (TC) is given as , we get Equation (5) is similar to what is seen in Nishimizu and Page Jr. [14]. That is, growth in TFP is equal to the sum of technical efficiency changes, technical changes, and the factor accounting for the effect of input growth. The last term has impact only if the estimated elasticities are different from the corresponding cost shares and if the input quantity is changing.

#### 3. Panel Stochastic Production Model and Decomposition of TFP Growth

The stochastic frontier framework is well suited to empirically implement the above decomposition. Start with the production function: where is the output of the th subsector () in period , is the production technology which represents the frontier, is a vector of inputs, is the time trend variable that serves as a proxy for technical change, and is output-oriented (Farell) technical inefficiency.

Technical inefficiency, , measures the proportion by which actual output () falls short of the maximum possible (frontier) output (given by ). Technical inefficiency is then defined by . Taking log-linearity of both sides of (6), we get Taking the derivative with respect to time gives us By substituting this in (1), we get where is the elasticity of industry th output with respect to the th input and is the cost share of the th input in the th industry. Equation (9) is identical to (5) except that we are defining the relationships for longitudinal data and that the is replaced by . This is because technical efficiency is defined as , which implies that and . Readers are referred to Kumbhakar et al. [10] for more detailed and advanced presentations on this subject.

The discrete time counterparts of these expressions are computed using , where stands for TFP, TC, TE, or .

#### 4. Estimation Method

In its early development, the panel data stochastic frontier framework was based on the assumption that technical inefficiency is estimated by the individual heterogeneity effect or the fixed effect term [8, 15], which implies that it is time-invariant. Cornwell et al. [16], Kumbhakar [17], and Battese and Coelli [18] proposed panel stochastic frontier models with a time-varying inefficiency term, each proposing different specifications of the time-varying inefficiency term. That is, Schmidt and Sickles [8] proposed estimation of a fixed effect model: and they suggest estimation of inefficiency of the th producer using the deviation of the value of the individual specific intercept from the estimated maximum within the sample; that is, (we specify if cost inefficiency is analyzed). Apart from attributing all individual heterogeneity to inefficiency, this method does not permit estimation and evaluation of the evolution of technical efficiency over time.

Cornwell et al. [16], Kumbhakar [17], and Battese and Coelli [18] suggest models in which the individual-heterogeneity effects are time-varying using the specification where is natural logarithm of GDP for the production efficiency model and is the natural logarithm of costs for the cost efficiency model, are the natural logarithm of the input quantities for the production efficiency model and the natural logarithm of the input prices for the cost efficiency model, and In (11), is the idiosyncratic error and is a time-varying panel specific term.

Cornwell et al. [16] assume a quadratic specification of the inefficiency term: which is simply an individual-specific slope variable. In addition to requiring us to estimate large number of parameters (, this specification does not allow decomposition of TFP into TC and TE when technical change is also captured by the time trend. Given that our objective is to decompose TFP growth into its components, this specification is inappropriate for this analysis. Kumbhakar [17], on the other hand, proposed that , where Depending on the values of the parameters, and , lies between zero and one and could be monotone decreasing (increasing) or convex (or concave). The alternative proposed by [18] is where is the last period in the th panel, is the decay parameter, , , and and are distributed independently of each other and are the covariates in the model. When , the degree of inefficiency decreases over time and when , the degree of inefficiency increases over time. Because is the last period, the last period for firm contains the base level of inefficiency for that firm. If , the level of inefficiency decays toward the base level. If , the level of inefficiency increases to the base level.

In these time-varying panel SF models, is the same across all units. The underlying assumption is similar to that of Schmidt and Sickles [8] in implying that time-invariant individual effects, if present, will be picked up by the time-varying inefficiency effect. This assumption is plausible in studies of firms within the same industry. However, individual heterogeneity is likely when we compare different subsectors.

Greene [11] proposes a model that brings the above two frameworks together, suggesting the following model known as the “true” fixed effect: where . In this specification, both time-invariant individual-heterogeneity (the fixed effect) and the time-varying inefficiency effects are included. Greene [11] suggests that this can actually be estimated by including individual dummies along with the preferred specifications for the time-varying inefficiency term as suggested in (13)–(15), a method termed maximum likelihood dummy variable method (MLDV). This specification enables us to disentangle the time-varying efficiency and the time-invariant unit-specific heterogeneity effects and is feasible given that we have a few cross-section units (21) compared to time periods (47) in our data. However, in short panels, this approach may produce inconsistent variance estimates due to the incidental parameters problem. This has a critical impact on the SF analysis since an accurate estimation of inefficiency scores relies on the precision of these estimates. Belotti and Ilardi [19] show that the incidental variable problem vanishes in long panel (.

If the likelihood function is based on the assumption of the half-normal distribution of the inefficiency term, given , the conditional expected values of the inefficiency terms are computed as , where ; ; , and . On the other hand, if the exponential distribution is assumed, ; ; . Given , technical efficiency, , is defined either as following Jondrow et al. [20] or as following Battese and Ceolli [15].

In our case, there is a reason to suspect that capital is endogenous. Capital is accumulated through investments, which depends on the level of output. Furthermore, the omitted determinants of technical efficiency could be related to these inputs. This usually implies correlations between the inputs and the composite error term [21]. This is similar to the problem caused by endogenous regressors suggesting that both problems can be addressed simultaneously. In such cases, a two-stage procedure in which the first stage estimation is carried out using the generalized method of moments (GMM), which enables us to address the endogeneity problem and the omitted variables problems, should be pursued. GMM is preferred because one of the explanatory variables for capital, output, is endogenous. The second stage follows the residual inclusion (RSI) method discussed in Terza et al. [12]. In this method, residuals estimated from the first stage regressions of the endogenous inputs will be included in the second stage regression which seeks to estimate (16).

The panel GMM method is well suited to handle this type of regression because output is an endogenous variable in the first stage regression. Following Anderson and Hsiao [22], the panel dynamic specification for capital that we seek to estimate is given as where shows that all variables are first differences. In this specification, and are correlated. To overcome this problem, Anderson and Hsiao [22] proposed instrumental variable approach in which , and so on are used to instrument given that is uncorrelated to . Arellano [23] shows, on the other hand, that using the lagged difference as an instrument results in estimators that have a very large variance and obtains results that suggest efficiency of estimators based on lagged levels as instruments instead. Arellano and Bond [24] confirm the superiority of using lagged levels as an instrument with simulation results, leading to the development of the Arellano and Bond [24] and Arellano and Bover [13] GMM methods. The system GMM method proposed by Arellano and Bover [13], which allows simultaneous estimation of the levels and differenced models, actually enables us to estimate dynamic panel data without differencing.

The estimation is based on identification of instruments forming a vector that satisfies the following orthogonality condition: Any exogenous variables in that are not expected to be correlated with the error would be immediate candidates for inclusion in the vector. The endogenous inputs with 2 or more lags can be used as instruments [13, 24]. The GMM estimator is the parameter vector that solves where is an optimal weighting matrix given by , where are parameter estimates from a consistent preliminary GMM estimator using the identity matrix as the weighting matrix [23]. Arellano and Bond [24] derive the corresponding one-step estimator along with the robust variance-covariance estimates (VCE). If the two-step estimator is applied, a finite-sample correction for VCE proposed by Windmeijer [25] should be used to resolve the unreliability of the usual asymptotic approximations, particularly in the presence of heteroskedasticity, because the weighting matrix depends on the estimated parameters. The orthogonality condition is tested using the Hansen -test. Rejection of the null hypothesis would mean that the instruments do not satisfy the orthogonality condition.

The second step of the RSI approach is to estimate (16) by including the residual computed from first stage estimation as a regressor: where are the residuals from the first-step estimation. Equation (19) is estimated by ML using the algorithm proposed in Belotti and Ilardi [19].

#### 5. Data and Estimation Results

##### 5.1. Data

Statistics Canada’s KLEMS (capital, labour, energy, materials, and services) data set provides input, output, prices, and productivity indexes for Canadian industries for the period 1961–2007. In this analysis, we focus on the manufacturing industries. The industries included in the study are listed in Table 1.