R. Robert Russell

Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence

We decompose labor-productivity growth into components attributable to (1) technological change (shifts in the world production frontier), (2) technological catch-up (movements toward or away from the frontier), and (3) capital accumulation (movement along the frontier). The world production frontier is constructed using deterministic methods requiring no specification of functional form for the technology nor any assumption about market structure or the absence of market imperfections. We analyze the evolution of the cross-country distribution of labor productivity in terms of the tripartite decomposition, finding that technological change is decidedly nonneutral and that both growth and bipolar international divergence are driven primarily by capital deepening. (JEL O30, O47, D24)

Measures of technical efficiency

Abstract Fare and Lovell (J. Econom. Theory 19 (1978), 150–162) suggest four properties that a measure of technical efficiency should satisfy; the commonly employed Debreu-Farrell measure fails three of them. Necessary and sufficient conditions for a measure to satisfy the four conditions are provided and recently proposed measures are analyzed in the light of this result. Also, it is argued that the Debreu-Farrell measure has several desirable properties when one takes account of (1) (perhaps unknown) market prices and the relationship between technical and economic efficiency and (2) its characterization as a measure of economic efficiency using the shadow prices implicit in the production technology.

On testing separability restrictions with flexible functional forms

Abstract In this paper, we examine the implications of imposing separability on the translog and three other flexible forms. Our results imply that the Berndt-Christensen ‘nonlinear’ test for weak separability tests not only for weak separability, but also imposes a restrictive structure on the macro and micro functions for all currently known ‘flexible’ functional forms. For example, testing for weak separability using the translog as an exact form is in fact equivalent to testing for a hybrid of strong (additive) separability and homothetic weak separability with Cobb-Douglas aggregator functions. Our results show that these ‘flexible’ functional forms are ‘separability-inflexible’. That is, they are not capable of providing a second-order approximation to an arbitrary weakly separable function in any neighbourhood of a given point.

On the Axiomatic Approach to the Measurement of Technical Efficiency

Efforts to axiomatize the measurement of technical efficiency were stimulated by the Fare/Lovell [1987] suggestion that (input) efficiency measures should satisfy three conditions: (I) indication of efficient input vectors (the measure is equal to one if and only if the input bundle is techically efficient in the sense of Koopmans El 9511), (M) manotonicity (increasing one input quantity while holding all other inputs and all outputs constant lowers the measure), and (H) homogeneity of degree minus one (e.g., doubling all input quantities while holding all outputs constant cuts the measure in half).

Continuity of Measures of Technical Efficiency

Abstract The paper introduces continuity—in “technologies” as well as input and output quantities—into the axiomatic structure of the measurement of technical efficiency. Impossibility results show that continuity rules out other axioms (including indication of efficient input/output combinations), as well as some specific measures. Possibility results suggest that the natural choice for the measurement of technical efficiency is the extended Debreu/Farrell measure (the inverse of the distance function defined on the free-disposal hull of the upper level set).

Distance Functions in Consumer and Producer Theory

Although nobody seems to have recognized it at the time, 1953 was a banner year for duality theory, which in turn facilitated a veritable revolution in the application of consumer and producer theory some two decades later.1 Sten Malmquist (1953) and Ronald W. Shephard (1953) independently introduced the notion of a distance function (also called a gauge function and a transformation function2) to economists.3 In production theory, the (input) distance function is simply the maximal radial contraction (equivalently, the minimal radial expansion) of an input vector consistent with the technological feasibility of producing a given output vector. In utility theory, it is the maximal radial contraction (or minimal radial expansion) of a consumption vector consistent with the attainment of a particular utility level.

Functional Structure and the Allen Partial Elasticities of Substitution: An Application of Duality Theory

In a recent paper in this journal, Berndt and Christensen [1] provided a sufficient condition for the equality of pairs of Allen partial elasticities of substitution (AES). Russell [13] provided weaker sufficient conditions for this equality to hold. The purpose of this paper is to provide a condition which is necessary as well as sufficient. By exploiting the powerful theorems of duality theory, Diewert [7] has provided a simpler and more elegant proof of Russells result. Using duality and results on functional structure, we provide in Section 3 the complete characterization which is needed to equate pairs of AES. The results of Russell and of Berndt and Christensen are then generated in a compact fashion as special cases; this highlights the interrelationships between the various assumptions which have been used. In Section 4 a stronger equality condition on the AES is examined. Again exploiting the theorems of duality and functional structure, we provide a necessary and sufficient condition for this stronger equality condition to hold. The results due to Russell and to Berndt and Christensen are again generated as special cases by appealing to duality. Before proceeding to these tasks, we present in Section 2 those duality and functional structure results which are essential to the argument which follows.

Evaluating the Effects of Aromatics Content in Gasoline on Gaseous and Particulate Matter Emissions from SI-PFI and SIDI Vehicles.

We assessed the emissions response of a fleet of seven light-duty gasoline vehicles for gasoline fuel aromatic content while operating over the LA92 driving cycle. The test fleet consisted of model year 2012 vehicles equipped with spark-ignition (SI) and either port fuel injection (PFI) or direct injection (DI) technology. Three gasoline fuels were blended to meet a range of total aromatics targets (15%, 25%, and 35% by volume) while holding other fuel properties relatively constant within specified ranges, and a fourth fuel was formulated to meet a 35% by volume total aromatics target but with a higher octane number. Our results showed statistically significant increases in carbon monoxide, nonmethane hydrocarbon, particulate matter (PM) mass, particle number, and black carbon emissions with increasing aromatics content for all seven vehicles tested. Only one vehicle showed a statistically significant increase in total hydrocarbon emissions. The monoaromatic hydrocarbon species that were evaluated showed increases with increasing aromatic content in the fuel. Changes in fuel composition had no statistically significant effect on the emissions of nitrogen oxides (NOx), formaldehyde, or acetaldehyde. A good correlation was also found between the PM index and PM mass and number emissions for all vehicle/fuel combinations with the total aromatics group being a significant contributor to the total PM index followed by naphthalenes and indenes.

Functional Separability and Partial Elasticities of Substitution

Theorems 3 and 4 of the recent paper by Berndt and Christensen [1] relate weak and strong separability [14] of a production function to certain equality restrictions on the partial elasticities of substitution. Both theorems are local. Also, homotheticity of the production function is a condition of both theorems but is not included in either set of necessary conditions. This note extends and strengthens the Berndt-Christensen results. First, Theorem 1 and Corollary 1 generalize Theorems 3 and 4 of Berndt and Christensen by showing that the relations hold globally (once certain details regarding differentiability are taken into account). Second, Theorem 2 and Corollary 2 strengthen the Berndt-Christensen results by showing that homotheticity of the specific aggregator functions (homothetic separability [2, 10]), but not necessarily of the production function itself, is sufficient for separability to induce the appropriate restrictions on the partial elasticities of substitution. Third, Theorem 3 and Corollary 3.1 show that homotheticity of the specific aggregator functions is a necessary condition for weak, and hence strong, separability together with equality restrictions on the partial elasticities of substitution. Finally, three additional corollaries (1.2, 2.2 and 3.2) of this note relate the partial elasticity of substitution restrictions to homothetically recursive production functions [3].

Two-stage budgeting: An extension of Gorman's theorem

SummaryThis note extends Gormans [1959] classic result on two-stage budgeting to encompass the two-group cases that he assumed away. The proof, which exploits unpublished and recently published results not available to Gorman in 1959, makes it apparent that the entire structure needed for two-stage budgeting is, in fact, imbedded in the two-group case.