همگرایی و رشد بهره وری کل عوامل در صنعت نفت:ارزیابی تجزیه و تحلیل تجربی برای همگرایی

While economic theory acknowledges that some features of technology (e.g., indivisibilities, economies of scale and specialization) can fundamentally violate the traditional convexity assumption, almost all empirical studies accept the convexity property on faith. In this contribution, we apply two alternative flexible production technologies to measure total factor productivity growth and test the significance of the convexity axiom using a nonparametric test of closeness between unknown distributions. Based on unique field level data on the petroleum industry, the empirical results reveal significant differences, indicating that this production technology is most likely non-convex. Furthermore, we also show the impact of convexity on answers to traditional convergence questions in the productivity growth literature.

Indivisibility implies that inputs and outputs are not necessary perfectly divisible and also that scaling up or down the entire production process in infinitesimal fractions may not be feasible. Start-up and shut-down cost in electricity generation are just one good example (O’Neill et al., 2005). Scarf, 1986 and Scarf, 1994 stresses the importance of indivisibility in selecting among technological options. Economies of scale and specialization (implied by the presence of indivisibilities and other forms of non-convexities in production) entail that higher per-capita production increases the extent of the market, facilitates the division of labor, and increases the efficiency of production.1 These economically important features of technology, together with the well-known case of externalities, fundamentally violate the convexity of the production possibility set (see Farrell, 1959, for an overview). However, in traditional empirical analysis (e.g., traditional parametric production analysis, or even nonparametric production analysis), these features are dismissed through the imposition of the convexity axiom. In reality, it is clear that non-convexities in production are sufficiently important to explain behavior in some industries and are critical in the development of the new growth theory (see, e.g., Romer, 1990, on nonrival inputs). In a similar vein, McFadden (1978) already recognized that the importance of convexity in production analysis lies in its analytic convenience rather than its economic realism. Therefore, given its relevance to both economic theory and associated empirical analysis, one cannot ignore the potential impact of non-convexity.2 However, almost no previous studies have directly tested for the existence of non-convexity in production using rigorous statistical techniques. Nevertheless, non-convexities in production play an important role in the theoretical micro-economic literature and have been studied for decades (see, e.g., Frank, 1969 and Villar, 1999). For instance, the general equilibrium theory of non-convex technologies has been thoroughly analyzed (e.g., Bobzin, 1998 and Joshi, 1997, or more recently, Chavas and Briec, 2012). Recently, operational methods to derive linear prices supporting a competitive equilibrium in markets with non-convexities based on mixed integer programming have been devised (e.g., O’Neill et al., 2005). In this contribution, we apply two alternative flexible production models using nonparametric specifications of technology and test the validity of the non-convexity assumption in production. One non-convex specification of production technology (NCP) is the Free Disposable Hull model (initiated by Deprins et al. (1984)). It only imposes the assumption of strong or free disposability of both inputs and outputs. Another more common technology specification adds convexity to these strong disposability axioms to form a convex nonparametric production model (CP) (see, e.g., the seminal article of Farrell, 1957, Afriat, 1972 and Färe et al., 1994, among others). Based on distance functions as representations of technology (and their interpretation as efficiency indicators) computed relative to both these non-convex and convex nonparametric specifications of technology, following Briec et al. (2004), we test the significance of the differences using Li’s (1996) nonparametric test of closeness between two unknown distributions resulting from independent or dependent observations. Obviously, if convexity of technology is questionable, then also the more specific assumption of convexity of either input or output sets separately is doubtful. Simar and Wilson (2008) develop a complementary view on the statistical properties of these convex and non-convex non-parametric frontier estimators that highlights a kind of asymmetry in imposing both assumptions. If the true production possibility set is convex, then CP and NCP estimators are consistent and should yield approximately the same estimates for large datasets, though the NCP model normally has a slower rate of convergence. However, if technology is non-convex, then the NCP model remains consistent while the CP model offers an inconsistent approximation. These nonparametric specifications require large data sets for production technologies to avoid the small sample error problem. Furthermore, to avoid any aggregation bias, the analysis should ideally focus on firm-level data with sufficient detail regarding the production process. Here, we apply this test of convexity to unique field-level data from the petroleum industry in the US Gulf of Mexico over the period from 1947 to 1998. Although the production possibility set of oil and gas development and exploitation is acknowledged to be non-convex in part of the literature (see, e.g., Devine and Lesso, 1972 and further arguments below), we are unaware of there being previous economic studies that put this assumption to an empirical test. Hence, whether the above NCP methodology yields a relevant reference technology in this industry becomes a most interesting empirical question for testing. Furthermore, a topic that has received widespread attention with the appearance of endogenous growth theories is the question of convergence in productivity levels (see Islam, 2003 for a survey). In view of the importance of non-convexities for growth theory (Romer, 1990), we consider the suggestion by Bernard and Jones (1996, p. 1043) that “future work on convergence should focus much more carefully on technology”. In particular, we investigate the issue of convergence/divergence in total factor productivity change using a recent discrete time Luenberger productivity indicator (Chambers, 2002) computed relative to nonparametric technology specifications, while testing for the significance of the eventual differences between the CP and NCP models. The very length of the observation period provides ample scope to test the impact of the convexity assumption on the eventual convergence of total factor productivity growth rates. The choice between non-convexity and convexity in measuring total factor productivity change relates to the nature of technical change. The NCP model has the advantage of eventually allowing for local instead of global technical change (see, e.g., the discussion in Tulkens, 1993, and infra). Note that we believe this is the first paper defining local and global technological change precisely. While this distinction between local and global technological change plays a role in some theoretical work (see, e.g., Atkinson and Stiglitz, 1969, among others), we are aware of only few empirical works raising this issue. If NCP is the true representation of technology, then previous empirical work on the convergence issue might not be reliable. Anticipating one of the key results, this study only finds convergence for the NCP model. This contribution is structured as follows. Section 2 reviews the background literature. Section 3 presents the Luenberger productivity indicator as well as its underlying distance functions, the distinction between local and global technical change in our analysis, and the econometric models employed to test for convergence. Section 4 introduces the sample of petroleum field data from the Mexican Gulf. The next section presents the empirical results and provides the outcomes of the statistical tests. The final section offers some concluding remarks.

After reviewing traditional theoretical arguments for non-convexities in production, this study raises doubts regarding the ability of traditional convex production technologies to explain the real-world phenomenon of industrial production. We examine data on the petroleum industry using unique field-level data. We find that the traditional convex production model fits our data rather poorly and that the shape of the technology is likely non-convex. The existing evidence suggests that non-convexities may exist in petroleum fields as well as in some other industries (such as electricity generation, car assembly among others). In the light of this preliminary empirical evidence presented in this study, there is no good reason to take the convexity of production possibility sets for granted in general. Therefore, more studies are called for that explicitly test for the validity of the convexity of technology. The whole issue of testing for convexity raises a host of challenges. Just to mention one, it is important to recall that the shape of the production technology is a crucial determinant of the properties of value functions summarizing optimal economic behavior. For instance, it affects the property of the cost function with respect to changes in outputs: while in general the cost function is non-decreasing in outputs, cost functions estimated on convex (non-convex) technologies are convex (non-convex) in the outputs (Jacobsen, 1970). This could have consequences regarding tests of regularity conditions for traditional parametric estimation approaches. While substantial progress has been made in the development of flexible functional forms (see, e.g., Gallant and Golub, 1984 and Tishler and Lipovetsky, 1997) and the testing of monotonicity and curvature properties (also in a frontier estimation context: see Michaelides et al., 2010 and O’Donnell and Coelli, 2005), it could be a challenge to combine flexible functional forms allowing for eventual convexity or not in outputs and the testing of traditional regularity conditions. If in some distant future these results invalidating convex technologies would be replicated in other industries, then serious implications for standard micro-economic theory could follow. This is because the equilibrium of the firm and the existence of competitive markets normally depend on the convexity of technology. It is therefore necessary for researchers to explicitly test for the assumption of convexity when the true empirically estimated technology may well be non-convex (e.g., according to engineers).