Technological inefficiency and the skewness of the error component in stochastic frontier analysis
|
|
- Paul Hamilton
- 5 years ago
- Views:
Transcription
1 Economcs Letters 77 (00) locate/ econbase Technologcal neffcency and the skewness of the error component n stochastc fronter analyss Martn A. Carree a,b, * a Erasmus Unversty Rotterdam, Rotterdam, The Netherlands b Faculty of Economcs and Busness Admnstraton, Maastrcht Unversty, P.O. Box 616, 600 MD Maastrcht, The Netherlands Receved 0 August 001; accepted 0 March 00 Abstract Ths paper concentrates on negatvely skewed one-sded dstrbutons as an explanaton of the occurrence of postve (negatve) skewness n the case of stochastc producton (cost) fronter analyss. It takes as an example the bnomal dstrbuton that can have negatve or postve skew and derves the method-of-moments estmators. 00 Elsever Scence B.V. All rghts reserved. Keywords: Producton fronter; Cost fronter; Skewness; Bnomal dstrbuton JEL classfcaton: C1; D4 1. Introducton A popular econometrc technque to estmate the extent of frm neffcency s stochastc fronter analyss. A poneerng publcaton on the econometrc estmaton of stochastc fronters s Agner et al. (1977). They suggest an estmaton procedure n whch a producton fronter s estmated along wth a two-part composed error term. The frst part of the error term conssts of conventonal statstcal nose and s usually assumed to be normally dstrbuted. The second part represents frm neffcency and s assumed to follow a one-sded dstrbuton. Several dstrbutons have been proposed for the one-sded dstrbuton ncludng the half-normal dstrbuton, the truncated normal dstrbuton, the exponental dstrbuton and the two-parameter gamma-dstrbuton (Greene, 1990). Each of these one-sded dstrbutons has a postve skewness. L (1996) consders the case of the symmetrc one-sded unform dstrbuton. *Tel.: ; fax: E-mal address: m.carree@mw.unmaas.nl (M.A. Carree) / 0/ $ see front matter 00 Elsever Scence B.V. All rghts reserved. PII: S (0)00119-
2 10 M.A. Carree / Economcs Letters 77 (00) A common problem n the use of the stochastc producton fronter analyss s that the estmated skewness of the resduals s postve. Green and Mayes (1991) report that for a sample of 151 UK ndustres, % showed a postve skewness of the combned resdual and that for a sample of Australan ndustres a smlar problem was encountered n 5% of the cases. A postve skewness s consdered problematc because t cannot be reconcled wth a one-sded dstrbuton of neffcences that s postvely skewed. Green and Mayes argue that, apart from possble msspecfcaton of the producton functons, ths ether ndcates super effcency (all frms n the ndustry are effcent) or the napproprateness of the technque of fronter producton functon analyss to measure neffcences. They overlook one mportant addtonal possblty: that of negatvely skewed one-sded dstrbutons of neffcences. In ths paper we consder ths possblty and show that t has mportant consequences for the nterpretaton of the skewness of the error term as a measure of technologcal neffcency.. The model of stochastc producton fronter analyss We consder the followng producton fronter model for a sample of N frms: y5 a 1 x9 b 1 5 1,...,N (1) wth 5 v u beng the composte error term. The commonly made assumpton for the statstcal nose term v s that t s..d. N(0, s ). The u $ 0 represents the technologcal neffcency of frm. The two parts of the error term are assumed to be ndependently dstrbuted. The y and the x-vector stand for the output and the nputs used n the producton process, respectvely. The composte error term has an expected value equal to E 5Eu and a thrd central moment equal to: E( E ) 5 E(v u 1 Eu ) 5E(u Eu ). () Therefore, a postvely skewed dstrbuton of the neffcences u mples that the adjusted error term E has a negatve skewness. Now t has been common practce to use a postvely skewed one-sded dstrbuton. In fact, n case one wants the one-sded error u to have an unbounded range, then most well-known dstrbutons are n fact postvely skewed. Examples nclude the gamma dstrbuton (ncludng the exponental dstrbuton), the Posson dstrbuton, the negatve bnomal dstrbuton, the truncated normal dstrbuton and the half-normal dstrbuton. But there s at least one well-known dstrbuton defned on [0, `) that may show negatve skewness: the Webull dstrbuton. In case one allows for the one-sded error to have a bounded range, a longer lst of 1 Another example s Mester (1997) who apples the stochastc cost fronter analyss and fnds that out of 1 US bank dstrcts three have negatvely skewed resduals. She carefully remarks that her fronter model wth normal half-normal error term does not ft the data n these dstrcts (p. 8). Although we concentrate upon the producton fronter case, the arguments are smlar for the cost fronter model n whch the costs of frm are determned by the cost fronter and an error term of the form 5 u1 v wth the one-sded error term u $ 0 capturng cost neffcences. Johnson et al. (1994, p. 6) show that a Webull dstrbuton has a postve skewness for parameter values up to.60 and a negatve coeffcent of skewness for hgher parameter values. L (1996, p. ) does not recognze ths possblty and argues that a one-sded error component wth unbounded range always has a postve skewness.
3 M.A. Carree / Economcs Letters 77 (00) well-known dstrbutons wth (possble) negatve skewness becomes avalable. In the current paper we wll examne the bnomal b(n, p)-dstrbuton. There s no partcular reason to choose ths dstrbuton apart from that t allows for both postve and negatve skewness. A smple method-of-moments (MM) estmator for the bnomal one-sded dstrbuton can be derved by usng the corrected OLS approach (see e.g. Greene, 1990; Olson et al., 1980). Ths approach mples that frstly the parameters of the producton functon (1) are estmated usng least squares and that secondly the estmated resduals are used to estmate the parameters of the dstrbutons of u and v. The corrected OLS procedure leads to consstent estmators of the 4 parameters of the producton functon and of the composed error term dstrbuton. Frst defne j k j k r 5 u Eu so that Er 5 0. Because r and v are ndependent, we have that Er v 5 Er Ev wth j k and k postve ntegers. In addton, because v s dstrbuted symmetrcally we have Ev 5 0fk s an odd postve nteger. From the error decomposton E 5 v r we fnd: E( E ) 5 Ev 1 Er E( E ) 5Er () (4) E( E ) 5 Ev 1 6Ev Er 1 Er. (5) 4 4 For a normally dstrbuted v we nsert Ev 5 s and Ev 5 s. By combnng Eqs. () and (5) we have: 4 4 E( E ) (E( E )) 5 Er (Er ). (6) From Eqs. (4) and (6) an MM-estmator for a two-parameter dstrbuton can be derved n analogue to Greene (1990). For the bnomal dstrbuton we have that Er 5 np(1 p), Er 5 np(1 4 5 p)(1 p) and Er 5 (np(1 p)) 1 np(1 p)(1 6p 1 6p ). From the thrd central moment t s obvous that the bnomal dstrbuton has a postve skewness for p between zero and one half and a negatve skewness for p between one half and unty. After replacng the kth central moments of k wth the sample analogues mk 5 o e /N we have the followng two equatons that determne MM-estmates for n and p: m 5np(1 p)(1 p) m m 5 np(1 p)(1 6p 1 6p ). (7) 4 That s, the values of p determne the sgns of the sample moments m (kurtoss adjusted for the value for normalty). Assume that m ± 0 and defne x 5 (m m )/m. (skewness) and m4 m 4 4 The method-of-moment estmators for the two parameters of the bnomal dstrbuton are derved usng the second, thrd and fourth sample moments. The use of hgher-order moments makes the estmators vulnerable to outlers and may lead to poor small sample propertes. Greene s (1990) MM-estmators for the two-parameter Gamma-dstrbuton suffer from ths problem as well. Hoskng (1990) proposes to use L-moments nstead of the standard measures of skewness and kurtoss to acheve relatvely small senstvty to outlers. However, the dervaton of estmators based upon L-moments s beyond the scope of the present paper. 5 See for example Johnson et al. (199, p. 107).
4 104 M.A. Carree / Economcs Letters 77 (00) Fg. 1. Method-of-moments estmator p as a functon of x 5 (m m )/m. Accordng to Eq. (7) ths should be equal to (6p 6p 1 1)/(p 1). From ths we derve the two possble values of p as a functon of x: 1 1 1Œ ]] 1 1 1Œ ]] p15] 1] x 1] x 1 p5] 1] x ] x 1. (8) For values of x less than 1 only the p1-soluton s allowed. For values of x n excess of 11 only the p-soluton s allowed. For values of x n between 1 and 11 the sgns of m and m4 m determne whch of the two solutons s approprate. That s, f skewness s postve (m. 0) then the p1-soluton wll be chosen otherwse the p-soluton. In Fg. 1 the graphs of p1 and p as a functon of x are gven. Not all combnatons of the emprcal values for m and m4 m allow for MM-estmates. In fact, n case m m. m. 0or m m. m. 0 there are no vald MM-estmates for p. To 4 4 derve the MM-estmator for Ev 5 s usng Eq. () we also requre that m should not be less than np(1 p) after nsertng the MM-estmates of p and n. It s a queston of emprcs whether these volatons, whch would ndcate the mplausblty of the one-sded dstrbuton to be of a bnomal type, are encountered.. What do negatve and postve skewnesses actually measure? Emprcal studes usng the producton fronter approach have been assumng postvely skewed one-sded dstrbutons (and, hence, negatvely skewed adjusted composte error terms). As a consequence, when a postve value of m was found, the only logcal concluson could be that there had been unfortunate samplng from a dstrbuton that had n fact a populaton skewness below zero. As Monte Carlo studes have shown, ths s a possblty that may occur relatvely frequently n case the one-sded dstrbuton has a small varance n comparson wth the symmetrc error dstrbuton (see e.g. Fan et al., 1996; Green and Mayes, 1991). Waldman (198) showed that resortng to a maxmum lkelhood procedure nstead of a corrected OLS procedure does not resolve the problem. In
5 M.A. Carree / Economcs Letters 77 (00) Fg.. Probabltes of b(0, 0.5). fact, he has shown that, n case of a postve m, the ML estmator for the stochastc fronter model s smply OLS for the slope vector and the absence of any effcences (varance of u s zero). When an ndustry showed postve skewness of the resduals t was therefore assumed that there were lttle f any neffcences. Green and Mayes (1991) argue that a postve skew mples that establshments n the ndustry are super effcent, rather than neffcent (p. 58). In contrast to the concluson of super effcency n case of a postve skewness, the example of the bnomal dstrbuton shows that a postve skewness suggests a one-sded dstrbuton that has low probabltes for small neffcences and hgh probabltes of large neffcences. For the bnomal dstrbuton t ndcates that p s between one half and one. Hence, only a small fracton of the frms or plants attan a level of productvty close to the fronter whle a large fracton attans consderable neffcences. See Fg. n whch we have n equal to 0 (neffcency categores) and p equal to The case of a negatve skewness mples that only a small fracton of frms are laggng behnd. See Fg. n whch we have p equal to 0.5. Fgs. and can also be nterpreted as two stages n an ndustry characterzed by the cycle of Fg.. Probabltes of b(0, 0.75).
6 106 M.A. Carree / Economcs Letters 77 (00) nnovaton and mtaton. Assume that the productvtes n an ndustry are characterzed by Fg.. In case one frm acheves an mportant nnovaton by whch t can ncrease productvty, t becomes domnant (n terms of productvty), and Fg. may emerge. Other frms wll then seek to mtate the successful frm and Fg. may be restored. Ths process of transent domnance n an ndustry would lead to a cyclcal tme seres pattern of postve and negatve skewness of resduals of the stochastc producton fronter analyss: nnovaton leads to postve skew, mtaton leads agan to negatve skew. What s the more lkely nterpretaton of a postve skewness of the composte error term n stochastc producton fronter analyss? On the one hand, t may be an unfortunate draw and the ndustry may be characterzed by super effcency (or at least, the symmetrc error term v domnates the one-sded dstrbuted u ). On the other hand, the large majorty of frms may be qute neffcent (lke n Fg. ). The two nterpretatons are completely dfferent, ether ndcatng no effcences or large neffcences. An argument aganst the frst nterpretaton s that relatve productvtes of plants are persstent over tme (e.g. Baley et al., 199). In case there would have been no neffcences (.e. the error term s determned completely by statstcal nose 5 v ) one would not expect such persstence, unless the statstcal nose has strong autocorrelaton. 4. Concluson An mportant methodologcal problem n stochastc fronter analyss has been the occurrence of resduals beng skewed n the wrong drecton. In the case of producton fronters, many tmes postvely skewed resduals have been found, whle n the case of cost fronters, negatve skewnesses have been qute common. The tradtonal soluton to the problem has been to argue that there are no neffcences and to put the varance of the one-sded dstrbuton equal to zero. Ths soluton fals to be convncng. Ths paper suggests a dfferent soluton: the one-sded dstrbuton of neffcences may be negatvely skewed (n case of producton fronters) or postvely skewed (n case of cost fronters). Ths does not mply that the tradtonal soluton argung for unfortunate samplng s mpossble, but that a better approach to the stochastc fronter analyss, n whch a comparson s made of several ndustres (or regons or tme perods), s to use a dstrbuton allowng for postve and negatve skewness. Acknowledgements The author s grateful to the Royal Netherlands Academy of Arts and Scences (KNAW) for fnancal support and to Peter Brouwer for our dscussons on the applcaton of stochastc producton fronter models to Dutch constructon ndustry data. References Agner, D.J., Lovell, C.A.K., Schmdt, P., Formulaton and estmaton of stochastc fronter producton functon models. Journal of Econometrcs 6, 1 7.
7 M.A. Carree / Economcs Letters 77 (00) Baley, M.N., Hulten, C., Campbell, D., 199. Productvty dynamcs n manufacturng plants. Brookngs Papers on Economc Actvty: Mcroeconomcs, Fan, Y., L, Q., Weersnk, A., Semparametrc estmaton of stochastc producton fronter models. Journal of Busness and Economcs Statstcs 14, Green, A., Mayes, D., Techncal neffcency n manufacturng ndustres. Economc Journal 101, Greene, W.H., A Gamma-dstrbuted stochastc fronter model. Journal of Econometrcs 46, Hoskng, J.R.M., L-moments: analyss and estmaton of dstrbutons usng lnear combnatons of order statstcs. Journal of the Royal Statstcal Socety, Seres B 5, Johnson, N.L., Kotz, S., Balakrshnan, N., In: nd Edton. Contnuous Unvarate Dstrbutons, Vol. 1. John Wley, New York. Johnson, N.L., Kotz, S., Kemp, A.W., 199. In: nd Edton. Unvarate Dscrete Dstrbutons. John Wley, New York. L, Q., Estmatng a stochastc producton fronter when the adjusted error s symmetrc. Economcs Letters 5, 1 8. Mester, L.J., Measurng effcency at US banks: accountng for heterogenety s mportant. European Journal of Operatonal Research 98, 0 4. Olson, J.A., Schmdt, P., Waldman, D.M., A Monte Carlo study of estmators of the stochastc fronter producton functon. Journal of Econometrcs 1, Waldman, D.M., 198. A statonary pont for the stochastc fronter lkelhood. Journal of Econometrcs 18,
Economic Design of Short-Run CSP-1 Plan Under Linear Inspection Cost
Tamkang Journal of Scence and Engneerng, Vol. 9, No 1, pp. 19 23 (2006) 19 Economc Desgn of Short-Run CSP-1 Plan Under Lnear Inspecton Cost Chung-Ho Chen 1 * and Chao-Yu Chou 2 1 Department of Industral
More informationMgtOp 215 Chapter 13 Dr. Ahn
MgtOp 5 Chapter 3 Dr Ahn Consder two random varables X and Y wth,,, In order to study the relatonshp between the two random varables, we need a numercal measure that descrbes the relatonshp The covarance
More informationPrice and Quantity Competition Revisited. Abstract
rce and uantty Competton Revsted X. Henry Wang Unversty of Mssour - Columba Abstract By enlargng the parameter space orgnally consdered by Sngh and Vves (984 to allow for a wder range of cost asymmetry,
More informationMode is the value which occurs most frequency. The mode may not exist, and even if it does, it may not be unique.
1.7.4 Mode Mode s the value whch occurs most frequency. The mode may not exst, and even f t does, t may not be unque. For ungrouped data, we smply count the largest frequency of the gven value. If all
More information3/3/2014. CDS M Phil Econometrics. Vijayamohanan Pillai N. Truncated standard normal distribution for a = 0.5, 0, and 0.5. CDS Mphil Econometrics
Lmted Dependent Varable Models: Tobt an Plla N 1 CDS Mphl Econometrcs Introducton Lmted Dependent Varable Models: Truncaton and Censorng Maddala, G. 1983. Lmted Dependent and Qualtatve Varables n Econometrcs.
More informationReal Exchange Rate Fluctuations, Wage Stickiness and Markup Adjustments
Real Exchange Rate Fluctuatons, Wage Stckness and Markup Adjustments Yothn Jnjarak and Kanda Nakno Nanyang Technologcal Unversty and Purdue Unversty January 2009 Abstract Motvated by emprcal evdence on
More informationoccurrence of a larger storm than our culvert or bridge is barely capable of handling? (what is The main question is: What is the possibility of
Module 8: Probablty and Statstcal Methods n Water Resources Engneerng Bob Ptt Unversty of Alabama Tuscaloosa, AL Flow data are avalable from numerous USGS operated flow recordng statons. Data s usually
More information/ Computational Genomics. Normalization
0-80 /02-70 Computatonal Genomcs Normalzaton Gene Expresson Analyss Model Computatonal nformaton fuson Bologcal regulatory networks Pattern Recognton Data Analyss clusterng, classfcaton normalzaton, mss.
More informationSpatial Variations in Covariates on Marriage and Marital Fertility: Geographically Weighted Regression Analyses in Japan
Spatal Varatons n Covarates on Marrage and Martal Fertlty: Geographcally Weghted Regresson Analyses n Japan Kenj Kamata (Natonal Insttute of Populaton and Socal Securty Research) Abstract (134) To understand
More informationTCOM501 Networking: Theory & Fundamentals Final Examination Professor Yannis A. Korilis April 26, 2002
TO5 Networng: Theory & undamentals nal xamnaton Professor Yanns. orls prl, Problem [ ponts]: onsder a rng networ wth nodes,,,. In ths networ, a customer that completes servce at node exts the networ wth
More informationIdentification of climatic effect on crop yield of Marathwada region by using multiple linear regression & stochastics frontier approach
016; (5): 841-848 ISSN Prnt: 94-7500 ISSN Onlne: 94-5869 Impact Factor: 5. IJAR 016; (5): 841-848 www.allresearchjournal.com Receved: 11-0-016 Accepted: 1-04-016 Satyvan Yashwant Research Scholar, Department
More informationII. Random Variables. Variable Types. Variables Map Outcomes to Numbers
II. Random Varables Random varables operate n much the same way as the outcomes or events n some arbtrary sample space the dstncton s that random varables are smply outcomes that are represented numercally.
More informationA Comparison of Statistical Methods in Interrupted Time Series Analysis to Estimate an Intervention Effect
Transport and Road Safety (TARS) Research Joanna Wang A Comparson of Statstcal Methods n Interrupted Tme Seres Analyss to Estmate an Interventon Effect Research Fellow at Transport & Road Safety (TARS)
More informationECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE)
ECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE) May 17, 2016 15:30 Frst famly name: Name: DNI/ID: Moble: Second famly Name: GECO/GADE: Instructor: E-mal: Queston 1 A B C Blank Queston 2 A B C Blank Queston
More informationTHE VOLATILITY OF EQUITY MUTUAL FUND RETURNS
North Amercan Journal of Fnance and Bankng Research Vol. 4. No. 4. 010. THE VOLATILITY OF EQUITY MUTUAL FUND RETURNS Central Connectcut State Unversty, USA. E-mal: BelloZ@mal.ccsu.edu ABSTRACT I nvestgated
More informationTests for Two Ordered Categorical Variables
Chapter 253 Tests for Two Ordered Categorcal Varables Introducton Ths module computes power and sample sze for tests of ordered categorcal data such as Lkert scale data. Assumng proportonal odds, such
More informationMidterm Exam. Use the end of month price data for the S&P 500 index in the table below to answer the following questions.
Unversty of Washngton Summer 2001 Department of Economcs Erc Zvot Economcs 483 Mdterm Exam Ths s a closed book and closed note exam. However, you are allowed one page of handwrtten notes. Answer all questons
More informationElements of Economic Analysis II Lecture VI: Industry Supply
Elements of Economc Analyss II Lecture VI: Industry Supply Ka Hao Yang 10/12/2017 In the prevous lecture, we analyzed the frm s supply decson usng a set of smple graphcal analyses. In fact, the dscusson
More informationLikelihood Fits. Craig Blocker Brandeis August 23, 2004
Lkelhood Fts Crag Blocker Brandes August 23, 2004 Outlne I. What s the queston? II. Lkelhood Bascs III. Mathematcal Propertes IV. Uncertantes on Parameters V. Mscellaneous VI. Goodness of Ft VII. Comparson
More informationInterval Estimation for a Linear Function of. Variances of Nonnormal Distributions. that Utilize the Kurtosis
Appled Mathematcal Scences, Vol. 7, 013, no. 99, 4909-4918 HIKARI Ltd, www.m-hkar.com http://dx.do.org/10.1988/ams.013.37366 Interval Estmaton for a Lnear Functon of Varances of Nonnormal Dstrbutons that
More informationFinancial Risk Management in Portfolio Optimization with Lower Partial Moment
Amercan Journal of Busness and Socety Vol., o., 26, pp. 2-2 http://www.ascence.org/journal/ajbs Fnancal Rsk Management n Portfolo Optmzaton wth Lower Partal Moment Lam Weng Sew, 2, *, Lam Weng Hoe, 2 Department
More informationLinear Combinations of Random Variables and Sampling (100 points)
Economcs 30330: Statstcs for Economcs Problem Set 6 Unversty of Notre Dame Instructor: Julo Garín Sprng 2012 Lnear Combnatons of Random Varables and Samplng 100 ponts 1. Four-part problem. Go get some
More informationProblem Set 6 Finance 1,
Carnege Mellon Unversty Graduate School of Industral Admnstraton Chrs Telmer Wnter 2006 Problem Set 6 Fnance, 47-720. (representatve agent constructon) Consder the followng two-perod, two-agent economy.
More informationOPERATIONS RESEARCH. Game Theory
OPERATIONS RESEARCH Chapter 2 Game Theory Prof. Bbhas C. Gr Department of Mathematcs Jadavpur Unversty Kolkata, Inda Emal: bcgr.umath@gmal.com 1.0 Introducton Game theory was developed for decson makng
More informationWhich of the following provides the most reasonable approximation to the least squares regression line? (a) y=50+10x (b) Y=50+x (d) Y=1+50x
Whch of the followng provdes the most reasonable approxmaton to the least squares regresson lne? (a) y=50+10x (b) Y=50+x (c) Y=10+50x (d) Y=1+50x (e) Y=10+x In smple lnear regresson the model that s begn
More informationInformation Flow and Recovering the. Estimating the Moments of. Normality of Asset Returns
Estmatng the Moments of Informaton Flow and Recoverng the Normalty of Asset Returns Ané and Geman (Journal of Fnance, 2000) Revsted Anthony Murphy, Nuffeld College, Oxford Marwan Izzeldn, Unversty of Lecester
More informationSpurious Seasonal Patterns and Excess Smoothness in the BLS Local Area Unemployment Statistics
Spurous Seasonal Patterns and Excess Smoothness n the BLS Local Area Unemployment Statstcs Keth R. Phllps and Janguo Wang Federal Reserve Bank of Dallas Research Department Workng Paper 1305 September
More informationChapter 5 Student Lecture Notes 5-1
Chapter 5 Student Lecture Notes 5-1 Basc Busness Statstcs (9 th Edton) Chapter 5 Some Important Dscrete Probablty Dstrbutons 004 Prentce-Hall, Inc. Chap 5-1 Chapter Topcs The Probablty Dstrbuton of a Dscrete
More informationRandom Variables. b 2.
Random Varables Generally the object of an nvestgators nterest s not necessarly the acton n the sample space but rather some functon of t. Techncally a real valued functon or mappng whose doman s the sample
More informationLecture Note 2 Time Value of Money
Seg250 Management Prncples for Engneerng Managers Lecture ote 2 Tme Value of Money Department of Systems Engneerng and Engneerng Management The Chnese Unversty of Hong Kong Interest: The Cost of Money
More informationCHAPTER 9 FUNCTIONAL FORMS OF REGRESSION MODELS
CHAPTER 9 FUNCTIONAL FORMS OF REGRESSION MODELS QUESTIONS 9.1. (a) In a log-log model the dependent and all explanatory varables are n the logarthmc form. (b) In the log-ln model the dependent varable
More informationAppendix - Normally Distributed Admissible Choices are Optimal
Appendx - Normally Dstrbuted Admssble Choces are Optmal James N. Bodurtha, Jr. McDonough School of Busness Georgetown Unversty and Q Shen Stafford Partners Aprl 994 latest revson September 00 Abstract
More informationRaising Food Prices and Welfare Change: A Simple Calibration. Xiaohua Yu
Rasng Food Prces and Welfare Change: A Smple Calbraton Xaohua Yu Professor of Agrcultural Economcs Courant Research Centre Poverty, Equty and Growth Unversty of Göttngen CRC-PEG, Wlhelm-weber-Str. 2 3773
More informationA Utilitarian Approach of the Rawls s Difference Principle
1 A Utltaran Approach of the Rawls s Dfference Prncple Hyeok Yong Kwon a,1, Hang Keun Ryu b,2 a Department of Poltcal Scence, Korea Unversty, Seoul, Korea, 136-701 b Department of Economcs, Chung Ang Unversty,
More informationNotes on experimental uncertainties and their propagation
Ed Eyler 003 otes on epermental uncertantes and ther propagaton These notes are not ntended as a complete set of lecture notes, but nstead as an enumeraton of some of the key statstcal deas needed to obtan
More informationMeasures of Spread IQR and Deviation. For exam X, calculate the mean, median and mode. For exam Y, calculate the mean, median and mode.
Part 4 Measures of Spread IQR and Devaton In Part we learned how the three measures of center offer dfferent ways of provdng us wth a sngle representatve value for a data set. However, consder the followng
More informationInternational ejournals
Avalable onlne at www.nternatonalejournals.com ISSN 0976 1411 Internatonal ejournals Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 MODELING AND PREDICTING URBAN MALE POPULATION OF BANGLADESH:
More informationA Bootstrap Confidence Limit for Process Capability Indices
A ootstrap Confdence Lmt for Process Capablty Indces YANG Janfeng School of usness, Zhengzhou Unversty, P.R.Chna, 450001 Abstract The process capablty ndces are wdely used by qualty professonals as an
More informationEDC Introduction
.0 Introducton EDC3 In the last set of notes (EDC), we saw how to use penalty factors n solvng the EDC problem wth losses. In ths set of notes, we want to address two closely related ssues. What are, exactly,
More informationUsing Cumulative Count of Conforming CCC-Chart to Study the Expansion of the Cement
IOSR Journal of Engneerng (IOSRJEN) e-issn: 225-32, p-issn: 2278-879, www.osrjen.org Volume 2, Issue (October 22), PP 5-6 Usng Cumulatve Count of Conformng CCC-Chart to Study the Expanson of the Cement
More informationECONOMIC ANALYSIS OF FISHERY IN THE NORTHERN PERSIAN GULF
ECONOMIC ANALYSIS OF FISHERY IN THE NORTHERN PERSIAN GULF ABDOULKARIM ESMAEILI Department of Agrcultural Economcs, College of Agrculture, Shraz Unversty, Shraz, Iran Tel: +989171612327 Fax: +987112273517
More informationParallel Prefix addition
Marcelo Kryger Sudent ID 015629850 Parallel Prefx addton The parallel prefx adder presented next, performs the addton of two bnary numbers n tme of complexty O(log n) and lnear cost O(n). Lets notce the
More informationThe Integration of the Israel Labour Force Survey with the National Insurance File
The Integraton of the Israel Labour Force Survey wth the Natonal Insurance Fle Natale SHLOMO Central Bureau of Statstcs Kanfey Nesharm St. 66, corner of Bach Street, Jerusalem Natales@cbs.gov.l Abstact:
More informationSimple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSIO THEORY II Smple Regresson Theory II 00 Samuel L. Baker Assessng how good the regresson equaton s lkely to be Assgnment A gets nto drawng nferences about how close the regresson lne mght
More informationMultifactor Term Structure Models
1 Multfactor Term Structure Models A. Lmtatons of One-Factor Models 1. Returns on bonds of all maturtes are perfectly correlated. 2. Term structure (and prces of every other dervatves) are unquely determned
More informationCalibration Methods: Regression & Correlation. Calibration Methods: Regression & Correlation
Calbraton Methods: Regresson & Correlaton Calbraton A seres of standards run (n replcate fashon) over a gven concentraton range. Standards Comprsed of analte(s) of nterest n a gven matr composton. Matr
More informationIncorrect Beliefs. Overconfidence. Types of Overconfidence. Outline. Overprecision 4/15/2017. Behavioral Economics Mark Dean Spring 2017
Incorrect Belefs Overconfdence Behavoral Economcs Mark Dean Sprng 2017 In objectve EU we assumed that everyone agreed on what the probabltes of dfferent events were In subjectve expected utlty theory we
More informationData Mining Linear and Logistic Regression
07/02/207 Data Mnng Lnear and Logstc Regresson Mchael L of 26 Regresson In statstcal modellng, regresson analyss s a statstcal process for estmatng the relatonshps among varables. Regresson models are
More informationQuiz on Deterministic part of course October 22, 2002
Engneerng ystems Analyss for Desgn Quz on Determnstc part of course October 22, 2002 Ths s a closed book exercse. You may use calculators Grade Tables There are 90 ponts possble for the regular test, or
More informationSkewness and kurtosis unbiased by Gaussian uncertainties
Skewness and kurtoss unbased by Gaussan uncertantes Lorenzo Rmoldn Observatore astronomque de l Unversté de Genève, chemn des Mallettes 5, CH-9 Versox, Swtzerland ISDC Data Centre for Astrophyscs, Unversté
More informationPivot Points for CQG - Overview
Pvot Ponts for CQG - Overvew By Bran Bell Introducton Pvot ponts are a well-known technque used by floor traders to calculate ntraday support and resstance levels. Ths technque has been around for decades,
More informationA MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME
A MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME Vesna Radonć Đogatovć, Valentna Radočć Unversty of Belgrade Faculty of Transport and Traffc Engneerng Belgrade, Serba
More informationEXPORT GROWTH, CAPACITY UTILIZATION, AND PRODUCTIVITY GROWTH: EVIDENCE FROM THE CANADIAN MANUFACTURING PLANTS
bs_bs_banner Revew of Income and Wealth Seres 59, Number 4, December 2013 DOI: 10.1111/row.12028 EXPORT GROWTH, CAPACITY UTILIZATION, AND PRODUCTIVITY GROWTH: EVIDENCE FROM THE CANADIAN MANUFACTURING PLANTS
More informationECE 586GT: Problem Set 2: Problems and Solutions Uniqueness of Nash equilibria, zero sum games, evolutionary dynamics
Unversty of Illnos Fall 08 ECE 586GT: Problem Set : Problems and Solutons Unqueness of Nash equlbra, zero sum games, evolutonary dynamcs Due: Tuesday, Sept. 5, at begnnng of class Readng: Course notes,
More informationEXAMINATIONS OF THE HONG KONG STATISTICAL SOCIETY
EXAMINATIONS OF THE HONG KONG STATISTICAL SOCIETY HIGHER CERTIFICATE IN STATISTICS, 2013 MODULE 7 : Tme seres and ndex numbers Tme allowed: One and a half hours Canddates should answer THREE questons.
More informationFinance 402: Problem Set 1 Solutions
Fnance 402: Problem Set 1 Solutons Note: Where approprate, the fnal answer for each problem s gven n bold talcs for those not nterested n the dscusson of the soluton. 1. The annual coupon rate s 6%. A
More informationApplications of Myerson s Lemma
Applcatons of Myerson s Lemma Professor Greenwald 28-2-7 We apply Myerson s lemma to solve the sngle-good aucton, and the generalzaton n whch there are k dentcal copes of the good. Our objectve s welfare
More information3: Central Limit Theorem, Systematic Errors
3: Central Lmt Theorem, Systematc Errors 1 Errors 1.1 Central Lmt Theorem Ths theorem s of prme mportance when measurng physcal quanttes because usually the mperfectons n the measurements are due to several
More informationUnderstanding price volatility in electricity markets
Proceedngs of the 33rd Hawa Internatonal Conference on System Scences - 2 Understandng prce volatlty n electrcty markets Fernando L. Alvarado, The Unversty of Wsconsn Rajesh Rajaraman, Chrstensen Assocates
More informationTests for Two Correlations
PASS Sample Sze Software Chapter 805 Tests for Two Correlatons Introducton The correlaton coeffcent (or correlaton), ρ, s a popular parameter for descrbng the strength of the assocaton between two varables.
More information4. Greek Letters, Value-at-Risk
4 Greek Letters, Value-at-Rsk 4 Value-at-Rsk (Hull s, Chapter 8) Math443 W08, HM Zhu Outlne (Hull, Chap 8) What s Value at Rsk (VaR)? Hstorcal smulatons Monte Carlo smulatons Model based approach Varance-covarance
More informationThree Approaches to the Analysis of Cost Function in Health Care
Ekonomcký časops, 55, 2007, č. 1, s. 69 78 69 Three Approaches to the Analyss of Cost Functon n Health Care Martn DLOUHÝ Lenka FLUSSEROVÁ* Abstract In ths paper, we descrbe three methods of cost-functon
More informationSTOCHASTIC FRONTIER ANALYSIS OF PRODUCTION FUNCTION AND COST FUNCTION ESTIMATION METHODS. STUDY OF EFFICIENCY AT INDUSTRY LEVEL
Abstract. Ths paper analyses the effcency or productvty at the level of a producton unt, but also at ndustry level, resortng for ths purpose to both parametrc and non-parametrc technques. Cost functon
More information>1 indicates country i has a comparative advantage in production of j; the greater the index, the stronger the advantage. RCA 1 ij
69 APPENDIX 1 RCA Indces In the followng we present some maor RCA ndces reported n the lterature. For addtonal varants and other RCA ndces, Memedovc (1994) and Vollrath (1991) provde more thorough revews.
More informationOCR Statistics 1 Working with data. Section 2: Measures of location
OCR Statstcs 1 Workng wth data Secton 2: Measures of locaton Notes and Examples These notes have sub-sectons on: The medan Estmatng the medan from grouped data The mean Estmatng the mean from grouped data
More informationModule Contact: Dr P Moffatt, ECO Copyright of the University of East Anglia Version 2
UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PG Examnaton 2012-13 FINANCIAL ECONOMETRICS ECO-M017 Tme allowed: 2 hours Answer ALL FOUR questons. Queston 1 carres a weght of 25%; Queston 2 carres
More informationA Set of new Stochastic Trend Models
A Set of new Stochastc Trend Models Johannes Schupp Longevty 13, Tape, 21 th -22 th September 2017 www.fa-ulm.de Introducton Uncertanty about the evoluton of mortalty Measure longevty rsk n penson or annuty
More informationIntroduction. Chapter 7 - An Introduction to Portfolio Management
Introducton In the next three chapters, we wll examne dfferent aspects of captal market theory, ncludng: Brngng rsk and return nto the pcture of nvestment management Markowtz optmzaton Modelng rsk and
More informationComparison of Singular Spectrum Analysis and ARIMA
Int. Statstcal Inst.: Proc. 58th World Statstcal Congress, 0, Dubln (Sesson CPS009) p.99 Comparson of Sngular Spectrum Analss and ARIMA Models Zokae, Mohammad Shahd Behesht Unverst, Department of Statstcs
More informationAn Application of Alternative Weighting Matrix Collapsing Approaches for Improving Sample Estimates
Secton on Survey Research Methods An Applcaton of Alternatve Weghtng Matrx Collapsng Approaches for Improvng Sample Estmates Lnda Tompkns 1, Jay J. Km 2 1 Centers for Dsease Control and Preventon, atonal
More informationMaturity Effect on Risk Measure in a Ratings-Based Default-Mode Model
TU Braunschweg - Insttut für Wrtschaftswssenschaften Lehrstuhl Fnanzwrtschaft Maturty Effect on Rsk Measure n a Ratngs-Based Default-Mode Model Marc Gürtler and Drk Hethecker Fnancal Modellng Workshop
More informationThe Mack-Method and Analysis of Variability. Erasmus Gerigk
The Mac-Method and Analyss of Varablty Erasmus Gerg ontents/outlne Introducton Revew of two reservng recpes: Incremental Loss-Rato Method han-ladder Method Mac s model assumptons and estmatng varablty
More informationMonetary Tightening Cycles and the Predictability of Economic Activity. by Tobias Adrian and Arturo Estrella * October 2006.
Monetary Tghtenng Cycles and the Predctablty of Economc Actvty by Tobas Adran and Arturo Estrella * October 2006 Abstract Ten out of thrteen monetary tghtenng cycles snce 1955 were followed by ncreases
More informationσ may be counterbalanced by a larger
Questons CHAPTER 5: TWO-VARIABLE REGRESSION: INTERVAL ESTIMATION AND HYPOTHESIS TESTING 5.1 (a) True. The t test s based on varables wth a normal dstrbuton. Snce the estmators of β 1 and β are lnear combnatons
More informationIn the 1990s, Japanese economy has experienced a surge in the unemployment rate,
Productvty Growth and the female labor supply n Japan Yoko Furukawa * Tomohko Inu Abstract: In the 990s, Japanese economy has experenced a surge n the unemployment rate, and ths s due partly to the recent
More informationAC : THE DIAGRAMMATIC AND MATHEMATICAL APPROACH OF PROJECT TIME-COST TRADEOFFS
AC 2008-1635: THE DIAGRAMMATIC AND MATHEMATICAL APPROACH OF PROJECT TIME-COST TRADEOFFS Kun-jung Hsu, Leader Unversty Amercan Socety for Engneerng Educaton, 2008 Page 13.1217.1 Ttle of the Paper: The Dagrammatc
More informationCOMPARISON OF THE ANALYTICAL AND NUMERICAL SOLUTION OF A ONE-DIMENSIONAL NON-STATIONARY COOLING PROBLEM. László Könözsy 1, Mátyás Benke 2
COMPARISON OF THE ANALYTICAL AND NUMERICAL SOLUTION OF A ONE-DIMENSIONAL NON-STATIONARY COOLING PROBLEM László Könözsy 1, Mátyás Benke Ph.D. Student 1, Unversty Student Unversty of Mskolc, Department of
More informationChapter 3 Student Lecture Notes 3-1
Chapter 3 Student Lecture otes 3-1 Busness Statstcs: A Decson-Makng Approach 6 th Edton Chapter 3 Descrbng Data Usng umercal Measures 005 Prentce-Hall, Inc. Chap 3-1 Chapter Goals After completng ths chapter,
More informationREFINITIV INDICES PRIVATE EQUITY BUYOUT INDEX METHODOLOGY
REFINITIV INDICES PRIVATE EQUITY BUYOUT INDEX METHODOLOGY 1 Table of Contents INTRODUCTION 3 TR Prvate Equty Buyout Index 3 INDEX COMPOSITION 3 Sector Portfolos 4 Sector Weghtng 5 Index Rebalance 5 Index
More information2) In the medium-run/long-run, a decrease in the budget deficit will produce:
4.02 Quz 2 Solutons Fall 2004 Multple-Choce Questons ) Consder the wage-settng and prce-settng equatons we studed n class. Suppose the markup, µ, equals 0.25, and F(u,z) = -u. What s the natural rate of
More informationProblems to be discussed at the 5 th seminar Suggested solutions
ECON4260 Behavoral Economcs Problems to be dscussed at the 5 th semnar Suggested solutons Problem 1 a) Consder an ultmatum game n whch the proposer gets, ntally, 100 NOK. Assume that both the proposer
More informationSolutions to Odd-Numbered End-of-Chapter Exercises: Chapter 12
Introducton to Econometrcs (3 rd Updated Edton) by James H. Stock and Mark W. Watson Solutons to Odd-Numbered End-of-Chapter Exercses: Chapter 1 (Ths verson July 0, 014) Stock/Watson - Introducton to Econometrcs
More information4: SPOT MARKET MODELS
4: SPOT MARKET MODELS INCREASING COMPETITION IN THE BRITISH ELECTRICITY SPOT MARKET Rchard Green (1996) - Journal of Industral Economcs, Vol. XLIV, No. 2 PEKKA SULAMAA The obect of the paper Dfferent polcy
More informationAsset Management. Country Allocation and Mutual Fund Returns
Country Allocaton and Mutual Fund Returns By Dr. Lela Heckman, Senor Managng Drector and Dr. John Mulln, Managng Drector Bear Stearns Asset Management Bear Stearns Actve Country Equty Executve Summary
More informationA FRAMEWORK FOR PRIORITY CONTACT OF NON RESPONDENTS
A FRAMEWORK FOR PRIORITY CONTACT OF NON RESPONDENTS Rchard McKenze, Australan Bureau of Statstcs. 12p36 Exchange Plaza, GPO Box K881, Perth, WA 6001. rchard.mckenze@abs.gov.au ABSTRACT Busnesses whch have
More informationarxiv:cond-mat/ v1 [cond-mat.other] 28 Nov 2004
arxv:cond-mat/0411699v1 [cond-mat.other] 28 Nov 2004 Estmatng Probabltes of Default for Low Default Portfolos Katja Pluto and Drk Tasche November 23, 2004 Abstract For credt rsk management purposes n general,
More informationNotes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator.
UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PG Examnaton 2016-17 BANKING ECONOMETRICS ECO-7014A Tme allowed: 2 HOURS Answer ALL FOUR questons. Queston 1 carres a weght of 30%; queston 2 carres
More informationClearing Notice SIX x-clear Ltd
Clearng Notce SIX x-clear Ltd 1.0 Overvew Changes to margn and default fund model arrangements SIX x-clear ( x-clear ) s closely montorng the CCP envronment n Europe as well as the needs of ts Members.
More informationProductivity Growth in the Canadian Broadcasting and Telecommunications Industry: Evidence from Micro Data
Catalogue no. 11F0027M No. 089 ISSN 1703-0404 ISBN 978-1-100-23158-7 Research Paper Economc Analyss (EA) Research Paper Seres Productvty Growth n the Canadan Broadcastng and Telecommuncatons Industry:
More informationPreliminary communication. Received: 20 th November 2013 Accepted: 10 th December 2013 SUMMARY
Elen Twrdy, Ph. D. Mlan Batsta, Ph. D. Unversty of Ljubljana Faculty of Martme Studes and Transportaton Pot pomorščakov 4 632 Portorož Slovena Prelmnary communcaton Receved: 2 th November 213 Accepted:
More informationWork, Offers, and Take-Up: Decomposing the Source of Recent Declines in Employer- Sponsored Insurance
Work, Offers, and Take-Up: Decomposng the Source of Recent Declnes n Employer- Sponsored Insurance Lnda J. Blumberg and John Holahan The Natonal Bureau of Economc Research (NBER) determned that a recesson
More informationElton, Gruber, Brown, and Goetzmann. Modern Portfolio Theory and Investment Analysis, 7th Edition. Solutions to Text Problems: Chapter 9
Elton, Gruber, Brown, and Goetzmann Modern Portfolo Theory and Investment Analyss, 7th Edton Solutons to Text Problems: Chapter 9 Chapter 9: Problem In the table below, gven that the rskless rate equals
More informationAn Empirical Study on Stock Price Responses to the Release of the Environmental Management Ranking in Japan. Abstract
An Emprcal Study on Stock Prce esponses to the elease of the Envronmental Management ankng n Japan Fumko Takeda Unversy of Tokyo Takanor Tomozawa Unversy of Tokyo Abstract Ths paper nvestgates how stock
More informationEconomics 1410 Fall Section 7 Notes 1. Define the tax in a flexible way using T (z), where z is the income reported by the agent.
Economcs 1410 Fall 2017 Harvard Unversty Yaan Al-Karableh Secton 7 Notes 1 I. The ncome taxaton problem Defne the tax n a flexble way usng T (), where s the ncome reported by the agent. Retenton functon:
More informationJeffrey Ely. October 7, This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.
October 7, 2012 Ths work s lcensed under the Creatve Commons Attrbuton-NonCommercal-ShareAlke 3.0 Lcense. Recap We saw last tme that any standard of socal welfare s problematc n a precse sense. If we want
More informationFinal Exam. 7. (10 points) Please state whether each of the following statements is true or false. No explanation needed.
Fnal Exam Fall 4 Econ 8-67 Closed Book. Formula Sheet Provded. Calculators OK. Tme Allowed: hours Please wrte your answers on the page below each queston. (5 ponts) Assume that the rsk-free nterest rate
More informationCenter for Policy Research Working Paper No. 121
ISSN: 1525-3066 Center for Polcy Research Workng Paper No. 121 ALTERNATIVE TECHNICAL EFFICIENCY MEASURES: SKEW, BIAS, AND SCALE QU FENG AND WILLIAM C. HORRACE Center for Polcy Research Maxwell School of
More informationThe Effects of Industrial Structure Change on Economic Growth in China Based on LMDI Decomposition Approach
216 Internatonal Conference on Mathematcal, Computatonal and Statstcal Scences and Engneerng (MCSSE 216) ISBN: 978-1-6595-96- he Effects of Industral Structure Change on Economc Growth n Chna Based on
More informationChapter 3 Descriptive Statistics: Numerical Measures Part B
Sldes Prepared by JOHN S. LOUCKS St. Edward s Unversty Slde 1 Chapter 3 Descrptve Statstcs: Numercal Measures Part B Measures of Dstrbuton Shape, Relatve Locaton, and Detectng Outlers Eploratory Data Analyss
More informationWages as Anti-Corruption Strategy: A Note
DISCUSSION PAPER November 200 No. 46 Wages as Ant-Corrupton Strategy: A Note by dek SAO Faculty of Economcs, Kyushu-Sangyo Unversty Wages as ant-corrupton strategy: A Note dek Sato Kyushu-Sangyo Unversty
More information