The production recipes approach to modeling technological innovation: An application to learning by doing

Abstract

We do two things in this paper. First, we put forward some elements of a microeconomic theory of technological evolution. This involves adding nascent (essentially undiscovered) technologies to the existing technologies of neoclassical production theory, and, more importantly, expanding the notion of the production plan to include the recipe – the complete description of the underlying engineering process. Second, we use the recipes approach in constructing a simple microeconomic model of shop-floor learning by doing. We simulate the dynamics of the model and report the effects of changes in the basic parameters on the resulting engineering experience curves. For correctly chosen values of these parameters, the predictions of the model match the observed experience curves.

Introduction

According to neoclassical theory, a production plan is merely a point in input–output space. The neoclassical theory has been extended to accommodate intertemporal features such as the variability over time of factor supplies, uncertainty about the production process, and uncertainty about prices. The neoclassical theory of production is not, however, fully dynamic since it does not provide a microeconomic basis for explaining technological evolution due to (for example) learning by doing, education and training, research and development, or technology transfer.

In this regard, macroeconomics is ahead of its microeconomic foundations. In his celebrated article on learning by doing, Arrow (1962) accounts for the observed fact that unit production costs can fall even in the absence of capital accumulation and R&D effort. Arrow attributes the increased productivity to learning by doing on the shop floor by production workers and managers. Arrow models learning by doing as a positive macroeconomic production externality: increases in ‘manufacturing experience’ – as measured (for example) by cumulative gross investment – lead to increased productivity. Several other macro models of technological progress are based on some production externality. See, for example, Shell (1967), Clemhout and Wan (1970), Stokey (1988), Romer (1990), and Lucas (1993).

Another class of (not unrelated) macro models of technological evolution is based on non-conventional factors of production. Uzawa (1965) introduced in a simple growth model human capital, the stock of which can be increased by devoting resources to education. In the hands of Lucas (1988), Caballe and Santos (1993) and others, this human-capital model (with clearly modelled externalities) has become a staple for analyzing productivity growth. Shell 1966, Shell 1967, Shell 1973 and Romer 1986, Romer 1990 introduced into growth theory the macro variable technological knowledge. The Shell–Romer theory combines technological knowledge (or the stock of patents) with production externalities and increasing returns to scale to analyze the role of industrial organization in growth, the dependence of growth on initial conditions, and other important macro problems.¹

Macroeconomic models based on production externalities and/or nonconventional inputs have been useful in raising important issues about public policy toward technology and in explaining observed increases in aggregate output, but the inadequacy of the microeconomic foundations of these models is a serious problem for the theory of production. In the present paper, we put forward some key elements of a microeconomic theory of technological evolution. To the existing (or currently available) technologies of neoclassical production theory, we add nascent technologies, which include both undiscovered technologies and forgotten technologies.²

The reader might be skeptical about any modeling of undiscovered technologies. While existing technologies can be verified by current engineering practice, undiscovered technologies cannot. On the other hand, practicing production engineers and business managers are not reluctant to base important business decisions on forecasts of technological progress in the firm's manufacturing operations. In fact, one of the most reliable analytic tools in production management is the engineering experience curve (or learning curve), which projects existing unit production costs for a given product into its future unit production costs. Among production engineers, marketing managers, business executives, and even corporate directors, empirical learning curves are far better known and more frequently used than are empirical production functions or empirical cost functions.

The most important new idea in the present paper is in our description of the production plan. To the usual input–output specification, we add a description of the underlying engineering recipe employed. Describing how one recipe is related to another then should allow one to build models that suggest which types of technologies are likely to be uncovered in the course of ordinary shop floor operations (learning by doing), which R&D programs are most likely to be successful, which types of technologies are ripe for transfer from one firm (or economy) to another, and so forth. Inspiration for our production recipes approach can be found in Nelson and Phelps (1966) and Nelson and Winter (1982). Inspiration for the nascent technology approach can be found in the separate and distinct works of Shell (1973) and Kauffman (1988).

We assume that a production recipe is described by a vector of basic production operations such as heating, mixing, stirring, shaping, boxing, internal factory transportation, and so forth. For given outputs, the input requirements for each of the operations depends on the instruction (or setting) given for that operation and the instructions given for some of the other operations. Hence we allow for production externalities within the firm.³ These intrafirm production externalities⁴ are crucial to our analysis.

As a specific application of our (more general) production recipes approach (along with our nascent technology approach), we construct a simple model of shop-floor learning by doing. The modeled interrelationships among the recipes (and hence the technologies) are relatively sophisticated. Other aspects of the model are relatively simple. We assume that the firm employs a single input to produce a single output and that, for a given fixed recipe, this process entails constant returns to scale. We also assume that the firm's output stream is predetermined. We allow for deviations from the currently reigning technology, but we assume that such production trials (or errors) are not directly controlled by the firm. We assume that a newly discovered recipe is either accepted or rejected merely on the basis of current cost efficiency relative to that of the reigning technology.

These strong assumptions allow us to employ a variant of Kauffman's NK model⁵ to analyze the dynamics of manufacturing costs. The NK model was originally designed for analyzing asexual biological evolution. In the evolutionary biology interpretation, it is assumed that the ‘fitness’ of a creature can be represented by a scalar. The corresponding assumptions for learning by doing are the single output, the single input, and constant returns to scale, which together allow the scalar ‘fitness’ to be replaced by the scalar ‘current technological efficiency’ (the inverse of current unit production cost). In the first interpretation, it is assumed that genetic changes occur at random and that fitter creatures immediately replace less fit ones. In the present interpretation, the corresponding assumptions are that shop-floor trials take place at random and that the reigning recipe is replaced by the new recipe if and only if the new recipe is more efficient in the short run, i.e. recipe selection is myopic.

In Section 2, we introduce nascent technologies and production recipes. In Section 3, we use the recipes model to construct a model of learning by doing. In Section 4, we review the existing empirical literature on engineering experience curves. In Section 5, we do the comparative dynamics for the model of learning by doing, and relate the predictions of this model to the observations. By correctly choosing the basic parameters of the model, we are able to match the basic statistics and important qualitative phenomena from observed experience curves – including the mean progress ratios (an inverse measure of the slope of the experience curve) and their standard deviations, plateauing (runs without improvements), curvature bias, and sensitivity to the length of the production run. In Section 6, we provide a summary and our conclusions.