یادگیری برای یادگیری و رشد بهره وری : شواهدی از کارخانه جدید مونتاژ خودرو

This paper models learning by experience beyond the experience curve, including the possibility of “learning to learn”: the pace of learning increases over time by building on what has already been learned. We compare the extended deterministic learning model with Jovanovic and Nyarkos' [26] stochastic learning. The theoretical models are tested with data on the total factor productivity of a car-assembly plant in its first months of operation. We find that the deterministic “mixed learning model”, where the speed of learning is equal to a constant plus a learning to learn effect, is the one that best fits the empirical data. The mixed learning model results in a time pattern of total factor productivity growth, first increasing and later decreasing, different from the always decreasing rate of growth of the learning curve, opening new perspectives on the study of learning by experience.

Productivity, or the rate at which input quantities are turned into outputs, has received much attention at the macro (as determinant of differences in the per capita income of countries [43]), at the firm (as explanatory of differences in competitiveness and profitability of firms [6]), and at the operational level (explaining differences in efficiency and costs across production units [35]). The bulk of recent productivity research has concentrated on explaining the observed differences in productivity levels across firms within and between industries and countries (Syverson [42], for a review). Much less is known, however, on what determines the time path of productivity for an individual production unit, even though macro productivity growth comes from the aggregation of efficiency gains at the production unit level. There are two primary explanations of productivity gains at the micro level. One considers productivity growth as the consequence of a general time trend of technological progress that continuously expands output at rates faster than the growth in inputs.1 The other explanation is rooted in the learning curve, where the rate of productivity growth is positive but decreases over time (Zangwill and Kandor [48], for a formal generalization of the learning curve). The first explanation implicitly assumes “Schumpeterian” innovation, constantly reinventing the production technology as well as the products and services sold in the market. The second takes the production technology and product attributes as constant, seeing productivity gains as the result of continuous and gradual improvements in the way things are done in the production process. This paper advances the explanation of productivity growth, proposing a general model of learning by experience. The model includes unlimited technical progress and the learning curve as particular cases, but it covers two additional forms of “deterministic” learning. The model is formulated at the level of an operating unit, i.e. a production plant, and it is applied to the learning process underlying the observed productivity growth in a car-assembly plant in the first years of operations. The measure of productivity used in the analysis is invariant to the intensity of capital and labor inputs used in production, i.e. it captures the total factor productivity (TFP) of the plant. We do not observe the specific actions taken by managers and workers to improve the efficiency of the production process; rather, we postulate a relationship between the underlying process of discovery and application of better ways of doing things, and the observed track of improvement in terms of measured TFP. In addition, our paper includes a comparison between the proposed class of deterministic models with the “stochastic” learning model of Jovanovic and Nyarko [26]. We find that the learning model that best fits the empirical data is what we call mixed learning, i.e., workers and managers of the plant combine a fixed rate of learning with a “learning to learn” capability as more knowledge is acquired. The mixed learning model implies that the results of learning translate into a first period of accelerated productivity growth, followed by another period of decelerated growth, until the maximum level of operating efficiency is attained. This is precisely what we observe in the data. Other learning models, such as the exponential version of the learning curve, and Jovanovic and Nyarko's [26] stochastic learning model, do not capture the S shape in the evolution of TFP over time. Although the evidence is obtained from a single plant, the results of the paper suggest that existing explanations of TFP growth, such as generalized technical progress and the learning curve, are incomplete, and other forms of deterministic learning such as learning to learn or mixed learning should also be considered. As for the relation of the paper to the existing literature, the theory section of the paper is in line with Zangwill and Kandor [48], who model the process of continuous improvement compatible with the learning curve [4] and [47] as evidence of such improvement. Our paper is different in that we model the process of learning without limiting the results of the process to those compatible with the evidence of the learning curve. In fact, as mentioned earlier, the pattern of performance improvement of the learning curve is one of four possible results in the class of “deterministic” learning models. The learning curve, and in general, learning by doing, has been applied to units of varying complexity, from single machines (especially scheduling problems, [9], [24] and [45]) to plants [1], [5] and [39] and firms [46], [31], [32] and [6]. The performance measures considered in prior research include cost [47], [48] and [39], productivity [1], [6] and [21], and quality [15], as well as complex measures such as overall equipment effectiveness [46]. This paper is unique in that the learning unit is a start-up assembly plant, enabling us to study learning at the moment in time when it can be expected to be particularly important. The plant produces a homogeneous output and we have monthly data on the number of cars assembled. The time interval between measurements of performance is short and the effects of learning on performance are observed shortly after management decisions, spurred by what has been learned, are implemented. The monthly frequency of observations assures sufficient observations to estimate the learning model for a total time period when the car model assembled in the plant remained unchanged, as well as the main parameters of the production function different from the TFP parameter. The parameters of the production function are estimated jointly with those that capture the features of the learning process, using the Error Correction Mechanisms [17], which is another innovation of the paper. TFP has been used before as an indicator of the results of the learning process at the firm and industry level, but not often, if at all, at the plant level. The rest of the paper is organized as follows. Section 2 presents a description of the theories of learning and their respective analytical formulations for empirical estimation purposes. Section 3 contains the application of the theory to the case study of the assembly plant. Finally, in Section 4, we present the discussion of our results and the main conclusions of our paper.

Productivity growth (increasing output produced, at a higher rate than the rate of increase in the quantity of inputs used in production) is viewed as the main driver of economic prosperity, so there is much ongoing research seeking a better understanding of the sources of productivity growth over time. Solow's [41] ground-breaking paper, pointing to evidence that the aggregate output of an economy tends to grow at a higher rate than growth in aggregated inputs, identified the difference between the two growth rates as a “residual”. Gaining a better understanding of this residual, and of the factors that lead to sustainable growth, has been the concern of a great deal of research since the 1950s. This paper studies productivity and productivity growth in a more limited context than that of the whole economy, namely in a car-assembly plant in its first years of operation. During the time period of the analysis, September 1984 to March 1992, the production technology remained invariant and the plant assembled the same basic model. In this highly controlled and stable production environment, it is most likely that any progress in operating efficiency and productivity will be the result of learning by employees, and plant managers, the best ways of doing things within the constraint imposed by the fixed macro technology. Therefore, by studying the time pattern of operating efficiency in terms of the TFP observed in the plant each month, we are able to discover which of the learning models proposed in the literature is best represented by the empirical evidence. Our results indicate that a deterministic learning model, where the pace of learning combines an exogenous constant term and a time-increasing term as a function of relative cumulative past learning, is the model best represented by the empirical data. This mixed learning implies that TFP will increase over time, first at an increasing rate and, after a certain point in time, at a decreasing rate, so the cumulative value of the TFP parameter is S-shaped over time. The estimated stochastic learning model of Jovanovic and Nyarko, fitted to the same data, did not capture the S-shaped time profile of TFP observed in the data. One tentative explanation of why deterministic learning is closer to the empirical evidence than the stochastic mode is that the assembly plant in this study belongs to a large and experienced world-wide car manufacturer, and the engineers and managers who designed the plant probably were quite conversant with the high standards of performance that would result from operational learning. Notice also that the process of deterministic learning does not mean that there will be no noise around the TFP trend over time; what it does imply is that such noise will not be part of the learning process itself, as it is in the case of the stochastic learning models. Thus, the results of our study do have certain practical implications. First, our findings are consistent with the hypothesis that knowledge acquisition is a gradual process, so that even when workers and managers know the standard of maximum efficiency, that standard may take some time to be attained. Moreover, under production conditions of stable technology and standard product characteristics it can be expected that the potential knowledge acquired by some form of learning by experience will be finite, with counterpart value of efficiency level A* in our analysis. In the particular case of this car-assembly plant, it took between six and seven years to reach the value of A*, which was around 50% higher than the level of operating efficiency at the beginning of the period. In fact, in January of 1992, coinciding with the end of the complete learning cycle, the management of the company began to introduce major changes in the assembly plant, including the use of more robots in place of workers, as well as changes in the model being assembled. Therefore, managers appear to have been aware of the stagnation of productivity growth from operational learning and, once the limit was reached, they introduced major changes in the technology, and in the product itself, among other things by beginning a new cycle of learning and productivity growth. Second, the 50% increase in cumulative TFP does not occur at uniform growth rates over time. Rather, the growth rates vary substantially, first accelerating and later decelerating. In our assembly plant, the maximum monthly growth rate in TFP is estimated to occur in month 40, just in the middle of the period of observation, and its value was 0.45%. We reject perpetual or unlimited learning (constant growth rate in TFP for unlimited time) as a good descriptor of the variable that tracks the results of learning and improving; since most studies of productivity growth with macro data assume constant growth rates in TFP over time, the micro results cast doubt on the macro analysis being able to capture what happens at the micro level. The empirical results also reject the hypothesis of a constant learning rate as the best descriptor of the time evolution of TFP. Since the constant learning rate is a special case of the widely-used learning curve, our results suggest that mixed learning should be considered as a plausible alternative to the learning curve. Third, the econometric methodology used in the estimation of the parameters of the model (ECM) distinguishes between “the speed of learning” and “the speed of adjustment” in the working of the assembly plant. The former is a measure of the pace at which knowledge is acquired, while the speed of adjustment is a measure of how fast what is learned is transformed into higher productive efficiency. The empirical results indicate that, in this plant, it took between five and six months to adjust from current to target production results (speed of adjustment of 0.183). Future research should replicate the empirical test of the learning models derived in this paper with data from other production plants or production processes, including learning in machine-scheduling activities and any possible process-improving environment. In this respect, it will be important to verify to what extent the mixed learning model (implying an S-shaped time pace of the performance indicator resulting from learning and improving) is limited to start-up operations, or not. Future research with data from multiple plants and other industries should also examine whether there is any plant, firm and/or industry characteristic that determines which of the learning models considered in this paper, including the stochastic one, is more likely to occur. An extension closely related to the research done so far would be to examine the cross-model learning spillover within the same assembly plant, as in Levitt et al. [30]; the de-learning or forgetting process, i.e. the rate at which accumulated knowledge depreciates [7] and [44]; and the joint learning of the plant together with the learning of a close external supplier [27]. Finally, another limitation to overcome is to incorporate into the analysis the observation of the actions managers take when they learn in contexts of continuous improvement. We have modeled the presumed cycle of action–performance–action, but the only information used in the modeling is the observed performance. As in many manufacturing plants around the world, during the period of study our assembly plant introduced the methods of continuous improvement of TQM and related techniques that will underlie the observed improvement in operating efficiency. It would be of interest for managers who want to know the effect of their decisions to trace the measurement of improvements in TFP after the introduction of a particular innovation in work organization, human resources management, and so on. Research aimed at explaining differences in productivity (and economic performance in general) across firms from different industries and countries, has grown in recent years [10] and [16]. Differences in productivity are evaluated at a given moment of time, but it would be of interest to investigate the time dynamics of TFP growth rates to infer the underlying learning model, and how this model is related to specific management techniques implemented. Acknowledgment The authors thank two anonymous referees and Professor Adenso Díaz for their comments on an early version of the paper. They also thank the Spanish Ministry of Science and Innovation, Project ECO2009-13158, for financial support.