کارایی بلند مدت و کوتاه مدت در یک کارخانه خودروسازی: یک مطالعه موردی اقتصاد سنجی Long- and short-term efficiency in an automobile factory: An econometric case study

۱٫ Introduction This paper models and econometrically estimates the production technology of an automobile assembly plant in its first years of operation. The production technology involves two functional relationships: one, the long-term relationship, is the standard economic production function that gives the maximum output produced per period of time from a given combination of labour and capital services. The second functional relationship, the shortterm, models the month-by-month changes in production, matched with changes in current and past output and input services, with planned management decisions, and with unplanned stochastic shocks. The two relationships are jointly estimated using the Error Correction Mechanism (ECM) of Engle and Granger (1987), with monthly data on output and inputs in the early years of the plant operation. The paper is an econometric case study (Jones et al., 2006) on the estimation of a production function, including the measurement of the growth rate in total factor productivity (TFP), as an indicator of improvements over time in the efficiency of the assembly operations.1 The automobile plant in question belongs to a multinational corporation with long experience in the industry. The results of the kind of research presented in this paper provide plant and company managers with valuable information for production planning and control. First, for budgetary purposes, management will want to know the number of hours and total cost of labour and capital services estimated for the planned capacity of the plant. Second, the initial years of operation of the plant are those when the efficiency gains from learning-by-doing and the like are expected to be higher; ignoring these initial efficiency gains may lead to over-staffing in the years of steady state operation. Third, in the short-term operations of the plant, the management team will want to distinguish the effects of changes in production due to stochastic shocks from those perturbations of the normal functioning of the production process that can be controlled through management actions. They will also want to be sure that deviations from the technological possibilities frontier of the assembly plant that inevitably result from day-to-day perturbations are transitory, and that the production process continues on a convergence path to the frontier. Our paper argues that the ECM is a valid econometric technique to aid management in the planning and control of plant operations. The automobile industry has been acknowledged as the more innovative of the 20th century (Womack et al., 1990), with innovations in production technology, work organization, and human resources policies that have been later adopted by firms in other industries. Not surprisingly, there is a body of research on the measurement of management innovations and their effects on the productivity of plants and firms, in the automobile and in other industries. In fact, most of the management practices and innovations examined in insider and case study econometrics (team production, TQM, continuous improvement, pay for performance.) were first introduced in the automobile industry (see Hayes and Clark, 1986; Gunasekaran et al., 1994 for early work in the performance of production plants). Productivity, i.e. the ratio between output produced in a period of time and volume of production inputs, has been and continues to be a common measure of performance for researchers in economics, management, and operations, since it has well known implications for the competitiveness of firms and countries (see Syverson, 2011 for a review of productivity research). Papers on productivity related to ours include research on the production function estimation (Lieberman et al., 1990; Lieberman and Dhawan, 2005), and the measurement of the productivity (the inverse of) of automobile assembly plants as hours per vehicle, HPV (Weyer, 2011).2 Our work differs in that we model and estimate the economic production function of a plant producing a single car model that remains practically unchanged throughout the period of study. We use monthly observations of inputs and output data, and measure output in physical units. Prior papers on production functions estimation use annual company data from firms that produce several differentiated car models, and output is measured in monetary units. Ichniowski and Shaw (2009) in their methodological paper alert us to the aggregation bias that may result when using firm level data to examine the performance of process and plant operations, as well as the limitations of using monetary units of output in efficiency measurement, when output prices reflect the market power of firms. Moreover, we take advantage of our monthly data to model the production process as two interrelated input–output relationships, one a long-run relationship and the other short-term. Gabaix (2011) shows the errors in estimating parameters of functional relationships using macroeconomic aggregates that hide the heterogeneity and variability of input–output relationships at the firm level. The time series econometric estimation used in our paper gives the estimated parameters of the long-term relationship, controlling for the dynamics in output and input relationships resulting from short-term shocks and perturbations, thus minimizing aggregation bias of the kind pointed out by Gabaix. The measure of operating efficiency used in this paper is the TFP parameter of the economic production function, which differs from the (inverse) partial-labour productivity measure of HPV, used by industry analysts and managers. Steward (1983) and Ghobadian and Husband (1990) pointed out time ago the relevance of multi-factor productivity measures in operations management. The operating efficiency of a production unit measures the capabilities of transforming inputs into outputs. Productivity, on the other hand, is simply a ratio between output and input quantities. Greater labour productivity (lower HPV) will not necessarily be an indicator of superior operating efficiency if, for example, the unit with greater productivity produces with a more capital-intensive technology than the less productive one. If the production process of a plant is modelled with the economic production function, the measure of operating efficiency is the TFP term of the production function; variations in labour productivity are indicative of variations in TFP if the capital-to-labour ratio remains unchanged, and the technology shows constant returns to scale. Our paper is also related to research on insider and case-study econometrics. For example, Ichniowski et al. (1997) study the effect of the application of certain human resource practices on the productivity of steel finishing plants; Lazear (2000) investigate the impact on productivity of the introduction of performance-related pay; Hamilton et al. (2003) study team work and productivity, and Jones et al. (2010) produce a time series econometric study on the effects on worker productivity of a wide range of changes in compensation. Our paper is novel in that it models the production process in two interrelated functional relationships, one that captures the production technology embedded in the plant, and the other that accounts for the day-to-day operating conditions that cause deviations from the technological frontier. As part of this short-term relationship, we include interventions at different moments in time, such as a change in the number of production shifts, the schedule of vacation times, and a labor strike that – although these are not properly the managerial innovations examined by insider and case-study econometrics – from an econometric point of view, they are treated as if they were. Thus, ECM econometrics could also be a useful econometric tool in studies that deal with managerial innovations. In this paper, we estimate the long- and short-run relationships with a one-step ECM (Stock, 1987) applied to time series data generated by the assembly plant. The estimation mechanism corrects for spurious correlations that may appear when the economic variables in levels follow a common time trend (as often happens with inputs and outputs of a production process). It also corrects for omitted variable biases that can occur when the estimation of the long-term relationship (economic production function) ignores the correlation between inputs and outputs caused by short-term perturbations in the production process. The estimation will indicate whether the production process converges to the long-term relationship or not. If convergence is not rejected, then the estimation provides consistent and efficient estimates of the parameters of the production function (output-toinput elasticity and the growth rate in TFP). At the same time, from the short-term estimation, we obtain the deviations from the long-term output growth rate caused by the perturbations of the production process. The remainder of the paper is organised as follows: Section 2 offers a description of the automobile assembly plant and the data collected for the research study. In Section 3, we formulate the theoretical and econometric models of the production technology. Section 4 presents the results of our econometric estimation of the parameters that summarize the production technology. In Section 5, we compare the results of our research with other published papers on the automobile industry. Section 6 presents our conclusions and summarizes our main findings.