Testing for Catching-up: Statistical Analysis of DEA Efficiency Estimates

To prevent spurious sparks from arising at a spark plug (6) connected to the secondary (3) of an ignition coil upon sudden current rise through the primary (2) when a switching transistor (4) serially connected with the primary becomes conductive, the primary (2) of the ignition coil is serially connected with another resistor (7) to form one branch of a bridge circuit, the other branch being formed by two resistors (8, 9) connected in parallel with said first branch. The diagonal terminals (11, 11') are connected to a source of reference voltage (Uref), formed for example by a Zener diode (12) and the emitter-base path of a control transistor (13), the collector of which is connected to the base of a driver transistor (14) which is controlled from an ignition control source (i) either to conduction or non-conduction to, in turn and 180 DEG out of phase, control non-conduction and conduction of the switching transistor (4). Current from the collectro of the control transistor to the base of the driver transistor (14) modifies the current to the base of the switching transistor (4) by branching current flow to the base under control of the driver transistor. Preferably, the resistor (7) in series with the primary (2) of the ignition coil is either of a value somewhat in excess of the ohmic resistance of the primary (2) of the ignition coil or the resistance value can be controlled as a function of an operating parameter of the engine of which the ignition system forms a part, for example decreasing in value as the pressure of compression within the cylinder, of which the spark plug is a part, increases.

[1]  Leâ Opold Simar,et al.  A general methodology for bootstrapping in non-parametric frontier models , 2000 .

[2]  M. Farrell.  The Measurement of Productive Efficiency , 1957 .

[3]  H. Leibenstein,et al.  Empirical Estimation and Partitioning of X-Inefficiency: A Data-Envelopment Approach , 1992 .

[4]  C. I. Jones,et al.  Why Do Some Countries Produce so Much More Output Per Worker than Others? , 1998 .

[5]  P. Schmidt,et al.  Confidence statements for efficiency estimates from stochastic frontier models , 1996 .

[6]  M. Abramovitz.  Catching Up, Forging Ahead, and Falling Behind , 1986, The Journal of Economic History.

[7]  Danny Quah,et al.  Twin peaks : growth and convergence in models of distribution dynamics , 1996 .

[8]  G. Psacharopoulos.  Returns to investment in education: A global update , 1994 .

[9]  R. Shepherd.  Theory of cost and production functions , 1970 .

[10]  Steven N. Durlauf,et al.  Multiple regimes and cross‐country growth behaviour , 1995 .

[11]  Peter Schmidt,et al.  Multiple comparisons with the best, with economic applications , 2000 .

[12]  M. C. Jones,et al.  A reliable data-based bandwidth selection method for kernel density estimation , 1991 .

[13]  P. Schmidt,et al.  Production Frontiers and Panel Data , 1984 .

[14]  G. Debreu.  The Coefficient of Resource Utilization , 1951 .

[15]  A. U.S.,et al.  FORMULATION AND ESTIMATION OF STOCHASTIC FRONTIER PRODUCTION FUNCTION MODELS , 2001 .

[16]  R. R. Russell,et al.  Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence , 2002 .

[17]  B. Park,et al.  A NOTE ON THE CONVERGENCE OF NONPARAMETRIC DEA ESTIMATORS FOR PRODUCTION EFFICIENCY SCORES , 1998, Econometric Theory.

[18]  P. W. Wilson,et al.  Asymptotics for DEA estimators in non-parametric frontier models , 2003 .

[19]  R. Färe,et al.  Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries , 1994 .

[20]  R. Russell,et al.  Human Capital and Convergence: A Production-Frontier Approach , 2005 .

[21]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[22]  Yasmina Reem Limam,et al.  The components of output growth: A stochastic frontier analysis , 2002 .

[23]  R. Barro,et al.  International Data on Educational Attainment Updates and Implications , 2000 .

[24]  L. R. Christensen,et al.  THE ECONOMIC THEORY OF INDEX NUMBERS AND THE MEASUREMENT OF INPUT, OUTPUT, AND PRODUCTIVITY , 1982 .