Further Advances in Forecasting Day-Ahead Electricity Prices Using Time Series Models

Transcription

1 KIEE Inernaional Transacions on PE, Vol. 4-A No. 3, pp. 59~66, Furher Advances in Forecasing Day-Ahead Elecriciy Prices Using Time Series Models Hany S. Guirguis* and Frank A. Felder Absrac - Forecasing prices in elecriciy markes is criical for consumers and producers in planning heir operaions and managing heir price risk. We uilize he generalized auoregressive condiionally heeroskedasic (GARCH) mehod o forecas he elecriciy prices in wo regions of New York: New York Ciy and Cenral New York Sae. We conras he one-day forecass of he GARCH agains echniques such as dynamic regression, ransfer funcion models, and exponenial smoohing. We also examine he effec on our forecasing of omiing some of he exreme values in he elecriciy prices. We show ha accouning for he exreme values and he heeroskedacic variance in he elecriciy price ime-series can significanly improve he accuracy of he forecasing. Addiionally, we documen he higher volailiy in New York Ciy elecriciy prices. Differences in volailiy beween regions are imporan in he pricing of elecriciy opions and for analyzing marke performance. Keywords: forecasing, elecriciy prices, GARCH, volailiy, exreme values. Inroducion In many pars of he world, he elecric power indusry is using compeiive markes o mee consumers demand for elecriciy. Accurae forecass of prices are criical for producers and consumers in planning heir operaions and managing heir price risk. Recen work summarized he lieraure on elecriciy forecasing and in paricular he use of ime-series analysis and provided some accurae and efficien price forecasing ools such as dynamic regression model (DRM) and ransform funcion approach (TFA) []. We exend his work by employing he generalized auoregressive condiionally heeroskedasic (GARCH) mehod, among ohers, o forecas elecriciy prices in New York Ciy (NYC) and Cenral New York Sae (CNYS). Addiionally, we incorporae prices for oil and naural gas, wo fuels used by marginal generaion unis, ino our forecasing models. Finally, we calculae volailiy esimaes, which are imporan in pricing elecriciy opions and have imporan implicaions for analyzing marke performance. Price volailiy is one of several inpus in calculaing he value of an opion, e.g., by using he Black-Scholes equaion. In addiion, differences in volailiy in subregions may indicae wo separae elecriciy markes, perhaps due o ransmission consrains and resuling higher producion coss. * Dep. of Economic and Finance, School of Business, Manhaan College. (hany.guiriguis@manhaan.edu) Corresponding Auhor: Cener for Energy, Economics & Environmenal Policy, Edward J. Blousein School of Planning and Public Policy, Rugers, The Sae Universiy of New Jersey. (ffelder@ rci.rugers.edu) Received May 3, 004 ; Acceped Augus 3, 004 Being able o idenify when such separaions occur is imporan because he separaion of a generally compeiive marke ino smaller markes provides he necessary bu no sufficien condiions o exercise marke power. We seleced wo regions of New York Sae for analysis o compare our forecasing and volailiy resuls beween a subregion of he sae ha is ransmission-consrained and may be subjec o he exercise of marke power (NYC) wih a subregion of he sae ha has surplus generaion and where he exercise of marke power is no a serious concern (CNYS). Convenionally, he economeric modeling such as DRM and TFA assumes a consan one-period forecas variance. Mos of he economic ime-series, however, violae he classical assumpion of consan variance (homoskedasiciy). Many ime-series exhibi periods of large volailiy followed by periods of relaive ranquiliy. Thus, he variance a ime migh depend on pas informaion. As a resul, if addiional informaion from he pas were allowed o affec he forecas variance, one migh expec beer forecas inervals []. In 98, a new model wih mean 0, and serially uncorrelaed wih nonconsan variances condiional on he pas bu wih consan uncondiional variance, was inroduced []. Linear auoregressive condiional heeroskedasic (ARCH(q)) models consis of wo equaions. The firs equaion fis he ime series o he bes auoregressive moving average (ARMA) specificaion, whereas he second equaion models he condiional variance as an AR(q) process where q is he square of esimaed residuals calculaed from he firs equaion. Since ARCH(q) requires long lags in he modeling of many applicaions, Bollerslev

2 60 Furher Advances in Forecasing Day-Ahead Elecriciy Prices Using Time Series Models inroduced a GARCH(p,q) model in which boh auoregressive (p) and moving average componens (q) in he heeroskedasic variance are included in he curren condiional variance equaion o allow for a more flexible lag srucure [3]. More precisely, he ARCH model allows limied number of lagged shocks o affec he condiional variance, whereas he GARCH model allows all he lags o affec he condiional variance by incorporaing boh he lagged values of he squared errors and he lagged condiional variance. Engle, Lilien, and Robins exended he basic ARCH and GARCH model o allow he mean of a sequence o depend on is own condiional variance and is called ARCH-M and GARCH-M [4]. Since he inroducion of ARCH and is variaions, here have been many applicaions uilizing such models in differen economic and finance seings. Readers no familiar wih ARCH, GARCH, and relaed variaions are referred o [] and [3].. Time-Series Analysis A general descripion of he assumpions used in imeseries models and he ime-series modeling approach as applied o elecriciy markes is provided in Nogales e al., 00.. The New York Sae Elecriciy Markes New York Sae implemened wholesale elecric markes on November 8, 999. I has a day-ahead marke and a real-ime marke for energy based on locaional marginal pricing. The New York Independen Sysem Operaor (NYISO) collecs sar-up, no-load, and up o en energy bids in dollars per megawa-hours ($/MWh) ha span he oupu of each generaion uni. The NYISO performs uni commimen based on hese day-ahead bids and clears for each hour for he nex day (he day-ahead locaional prices), which will be paid o seleced generaors and charged o day-ahead load. A real-ime marke occurs wihin he day o accommodae any sysem changes. Power flows are generally wes o eas and norh o souh as lower cos generaion unis ouside of he greaer New York Ciy region expor power o New York Ciy and Long Island. The NYISO defines he NYC and CNYS zones. Differences in spo elecriciy prices beween hese wo regions of he sae are due primarily o ransmission consrains ha limi he abiliy o expor cheaper elecriciy locaed in upsae New York o he load cener in New York Ciy. The New York Sae power sysem is summer-peaking, bu also has a subsanial winer peak. New York Ciy accouns for approximaely 30% of he energy usage and 33% of he peak energy demand (NYISO, 999). The CNYS zone consumes approximaely 0% of he sae s elecrical demand; for example, on Augus 9, 003 a 3 pm (according o publicly available daa on he NYISO webpage), CNYS demand was 073 megawa-hours and oal demand in New York Sae was 3,036 megawahours. This power sysem has he expeced hourly, daily, and seasonal rends wih respec o demand and prices common o ypical U.S. power sysems in he Norheas and elsewhere.. Daa We consruced ime-series of day-ahead, zonal, wholesale elecriciy prices in New York Ciy and for Cenral New York Sae for pm along wih six inpu fuel prices (hree oil and hree naural gas price sreams a differen locaions). Oil or naural gas is likely o be he marginal fuel a pm. Fuel coss are he major componen of a fossil fuel uni s variable coss. Given ha elecriciy prices in New York Sae are he marginal cos of providing one addiional megawa-hour of elecriciy and he marginal megawa is ypically a fossil fuel uni, we would expec a priori a posiive relaionship beween he prices of fossil fuels and elecriciy prices. However, due o ransmission consrains, which may require he backing down of inexpensive unis and he ramping up of expensive unis, locaional elecriciy prices are also affeced by congesion. None of he oil price sreams, and only one naural gas price sream, are saisically significan. The naural gas price sream ha is saisically significan is denoed TRNY o indicae he Transconinenal Gas Pipe Line Corporaion daily prices repored by DRI/McGraw Hill. The elecriciy price ime-series runs from December 8, 000 hrough March 3, 003. Due o daa limiaions, he inpu fuel price daa series began on December 8, 000 bu ended a he sar of December 00 and were available only for work days (i.e., weekdays ha are no holidays)..3 Forecasing Techniques We begin our empirical sudy by esing wheher our daa ses are nonsaionary wih a sochasic rend. If our daa are difference saionary, we ransform hem ino saionary ses by differencing. To es for saionariy, we conduc he Dickey-Fuller and he Phillips-Perron uni roo ess (wih and wihou ime rend) on he level of NYC, CNYS, and TRNY naural gas prices for he enire sample period. Table displays he resuls of uni roo ess for each variable where he appropriae number of lags in our ess is deermined by Akaike informaion crierion (AIC)

3 Hany S. Guirguis and Frank A. Felder 6 specified as follows: AIC = T ln(residual sum of squares) + n () where n = number of parameers esimaed (p + q + possible consan erm); and T = number of useable observaions. Table shows ha our daa se is saionary as indicaed by Dickey-Fuller and Phillips-Perron ess a he 5% significance level. Table Dickey-Fuller and Phillips-Perron for Uni Roo Tes (December-8-00 o November-5-0) NYC CNYS TRNY Dickey-Fuller Trend No-Trend Phillips-Perron Trend No-Trend Nex, we adop four differen esimaion echniques o forecas he elecriciy prices in NYC and CNYS where he esimaed parameers are allowed o vary over ime:.. Dynamic Regression Model (DRM) The mos parsimonious specificaion (i.e., he model wih he leas number of esimaed coefficiens) wih significan coefficiens can be saed as follows: P = α + α P + α 3 TRNY - + ε () where he elecriciy price (P ) is relaed o he values of is firs lag and o he firs lag of he naural gas prices (TRNY - ). We find oher fuel prices and lagged elecriciy prices o be saisically insignifican a he 5% significance level... Transfer Funcion Approach (TFA) The ransfer funcion is an exension of he ARMA model, where he process of he dependen variable (P ) is allowed o depend on oher independen variables such as he energy prices. The mos parsimonious specificaion wih significan coefficiens can be saed as follows: P = α + α P +[(w 0 + w L+..+ w n L n )/ (-δ L- -δ m L m )]TRNY -d + ε (3) where (L) is he lag operaor indicaing he number of lags for each variable, he number of numeraor lags (n) is zero, he number of denominaor lags (m) is zero, and he delay period for he series (d) is one...3 Exponenial Smoohing (ES) wih Trend and Seasonaliy Presenaion We employ he exponenial smoohing mehod. For each period, we perform nine exponenial smoohing echniques ha exploi all he available combinaions from rends (no, linear, exponenial) and seasonal rends (none, addicive, muliplicaive). For example, one of he combinaions is a linear rend and a seasonal addiive rend. We hen choose he bes-fiing model ha minimizes he in-sample squared one-sep forecas errors based on Schwarz crierion [5]...4 The Generalized Auoregressive Condiional Heeroskedasic (GARCH) Mehd Here we invesigae wheher elecriciy prices can be modeled o capure he volailiy variaions in he elecriciy marke. We run Lagrange muliplier es for ARCH and GARCH disurbances [6]. The purpose of his es is o deermine wheher ARCH or GARCH are appropriae by evaluaing he correlaion of he square of he residuals (variance) by regressing he square of he residuals on a consan and on one lag value. Firs, we esimae he residuals from he DRM for he whole ime series. Second, we regress he squared residuals on a consan and on heir firs lagged value. Wih a sample of T residuals, under he null hypohesis of no ARCH errors, he es TR converges o a χ disribuion wih one degree of freedom. Table Lagrange Muliplier Tes for ARCH of GARCH Errors (December-8-00 o November-5-0) NYC CNYS Lagrange Muliplier Significance Level As indicaed by Table, he null hypohesis ha he squared disurbances are uncorrelaed is rejeced in favor of he alernaive hypohesis of ARCH or GARCH errors for he elecriciy prices in NYC a he 5% significance level. In conras, he Lagrange muliplier es does no indicae he presence of he ARCH or GARCH errors in case of he elecriciy prices in CNYS. However, as shown laer, modeling he condiional variance of he elecriciy prices in CNYS ends o improve significanly he forecasing performance of our models. We begin our analysis by searching for he mos parsimonious ARMA specificaion of he elecriciy price equaion where he energy prices are included. Nex, we explore modeling he volailiy of he elecriciy prices as an auoregressive condiional heeroskedasiciy (ARCH) process, a generalized auoregressive condiional heeroskedasiciy (GARCH) process or GARCH in mean (GARCH-M). We

4 6 Furher Advances in Forecasing Day-Ahead Elecriciy Prices Using Time Series Models ry differen specificaions and reach he final preferred model specified by GARCH(,) and ARMA(,0) wih one lag of naural gas prices (TRNY) whose coefficien is significan for values beween 0. and Our joinly esimaed specificaion can be saed as follows: P = α + α P + α 3 TRNY - + ε (4) h = β + β h 3 + β ε (5) where he appropriae log likelihood funcion of equaions 4 and 5 can be defined as follows: T log L = ln( π ) 05. ln h 05. T = T = ( ε ) h Then, we uilize he BFGS (Broyden, Flecher, Goldfarb, and Shanno) algorihm o maximize he log likelihood funcion wih respec o he α i s and β i s for i = o 4. We iniially esimae he elecriciy prices over he firs 00 days exending from December 8, 000 o May, 00 using he four esimaion echniques. Then, he oneday ou-of-sample forecasing performance of he four esimaion echniques is evaluaed. Nex, we add one day a a ime o he ending dae, and repea he process of esimaing and forecasing he elecriciy prices over he nex weekdays exending from May 3, 00 o November, 00. The main advanage of such rolling window esimaes is ha our forecass are more sensiive o including observaions from he daase, which helps in locaing any exreme observaions ha migh mask he causaliy beween he elecriciy prices and heir deerminans. 3. Numerical Resuls We use four measures of he performance of he four forecasing echniques: mean forecasing error (MFE), mean absolue forecasing error (MAFE), roo mean squared forecasing error (RMSFE), and he Theil U saisics. These measures are expressed in he following equaions: i= (6) f MFE = ( P P ) (7) i= i MAFE = ( P P i ) (8) i f i U = i= f RMSFE = ( P P ) (9) i i RMSFE f [ Pi ] + [ Pi ] (0) i= i= where P f is he one-day forecasing price. Tables 3 and 4 repor he MFE, MAFE, RMSFE, and he Theil U saisics a a one-sep for New York Ciy and Cenral New York, respecively. The resuls reveal ha he forecass of he rolling GARCH ouperform he forecass of he oher esimaion echniques for he days. Addiionally, our rolling forecass locae four exreme observaions on Augus 7-0, 00. The exreme observaions were idenified by he significan deerioraion in he forecasing abiliy of our echniques and he unprecedened increase in he elecriciy prices. (We are no correcing for all he exreme values, which would require adoping a formal echnique ha is beyond he scope of his paper.) Exremely high prices in elecriciy markes can occur for a variey of reasons. During he Augus 7-0, 00 period, he prices reached levels of $04.9 and $ for NYC and CNYS, respecively. The elecriciy markes in New York Sae have a bid cap of $000/MWh. Generaion unis canno submi bids for energy above his cap, bu elecriciy prices may reach higher levels due o locaional marginal pricing. During hese periods, here was eiher insufficien energy and reserves o mee load or here was an unusually pronounced abiliy o exercise marke power. Alhough such observaions are of imporan value, heir naure and he probabiliy of heir occurrence seem o be unique and non-repeiive. Therefore, including hese observaions wih such unusual high values may produce bias in parameer esimaes and hence may deeriorae he efficiency of our forecass. There is a growing body of evidence suggesing ha he efficiency of boh parameers esimaes and ou-of-sample forecass can be improved if exreme values are accouned for in GARCH. For example, [7] aribue he excess kurosis of he esimaed residuals from GARCH models o he addiive ouliers in he sock marke reurns. When hey accoun for such ouliers, he adjused daa are normally disribued and he ou-ofsample forecass of he GARCH improve significanly. Thus, we accoun for he four exreme observaions by replacing hem wih he elecriciy price on Augus 6, 00 (omiing he four observaions presens similar forecasing resuls). The GARCH model (he one mos preferred from he previous sep) is hen re-esimaed afer replacing hese exreme values. As Tables 3 and 4 indicae, he four saisics reveal a significan improvemen when we accoun

5 Hany S. Guirguis and Frank A. Felder /4/00 6/4/00 7/4/00 8/4/00 9/4/00 0/4/00 /4/00 /4/00 /4/00 $/MWh /4/00 3/4/00 4/4/00 5/4/00 6/4/00 7/4/00 8/4/00 9/4/00 0/4/00 Dae Price Forecas Fig. Acual Versus Forecas Day-Ahead New York Ciy Elecriciy Prices (May 4, 00 Through November, 00) Using GARCH, Omiing Exreme Values /4/00 6/4/00 7/4/00 8/4/00 9/4/00 0/4/00 /4/00 /4/00 /4/00 $/MWh /4/00 3/4/00 4/4/00 5/4/00 6/4/00 7/4/00 8/4/00 9/4/00 0/4/00 Dae Price Fig. Acual Versus Forecas Day-Ahead Cenral New York Sae Elecriciy Prices (May 4, 00 Through November, 00) Using GARCH, Omiing Exreme Values Forecas Table 3 Comparison of Rolling One-Sep Ou-of-Sample Forecass for New York Ciy (May 3, 00 o November, 00) MFE MAFE RMSFE U Theil Dynamic Regression Transfer Funcion Exponenial Smoohing GARCH GARCH, Omiing Exreme Values for he exreme values in he elecriciy prices beween Augus 7, 00 and Augus 0, 00. Table 4 Comparison of Rolling One-Sep Ou-of-Sample Forecass for Cenral New York Sae (May 3, 00 o November, 00) MFE MAFE RMSFE U Theil Dynamic Regression Transfer Funcion Exponenial Smoohing GARCH GARCH, Omiing Exreme Values Figs. and (locaed a he end of he paper) show he forecass of rolling GARCH as compared o acual

6 64 Furher Advances in Forecasing Day-Ahead Elecriciy Prices Using Time Series Models elecriciy prices a a horizon of one day for New York Ciy and Cenral New York Sae, respecively. Elecriciy prices ($/MWh) are ploed on he y axis and he sample days on he x axis. The conen of he figures reveal he high accuracy of our forecass, which capure he main movemens in he elecriciy prices when accouning for he price volailiy and he exreme values. 4. Comparison Of Price Volailiy In New York Ciy And Cenral New York Sae Volailiy is imporan in he elecriciy marke for several reasons. Firs, i is criical in pricing elecriciy opions, an imporan risk-managemen device commonly used by all ypes of marke paricipans. Since he value and herefore he price of an opion depend direcly and significanly on volailiy, accurae measures of volailiy are criical. Second, comparisons of volailiy beween subregions of a marke are imporan no only for pricing elecriciy opions wih differen delivery poins bu also for deermining wheher here are muliple markes wihin a region. Subregions wih differen levels of volailiy indicae separae markes, which is criical informaion in a marke power analysis. We es wheher he sum of he GARCH variance of he elecriciy prices in NY Ciy (GV NY ) is saisically greaer han ha of Cenral New York Sae (GV CNYS ). In line wih [8], [9], and [0] we use randomizaion ess o avoid making assumpions abou he normaliy and saisical properies of he variance series. Our randomizaion es can be described as follows. Firs, we calculae he GARCH variance from equaion (4) for New York Ciy and Cenral New York Sae for he enire sample period exending from December 8, 000 o November 5, 00. We hen calculae he hisorical raio beween he sum of GV NY and GV CNYS. Second, we perform a complee shuffle of all of he elemens of a vecor combining GV NY and GV CNYS. We hen calculae he randomized raio. Third, we repea second and hird seps 999 imes. Finally, we calculae he p value of he hisorical raio as he fracion of he randomized raios greaer han he original raio. To accoun for he difference in he magniude of elecriciy prices beween he wo regions, we define a normalized measure of he GARCH variance as follows: and ( NGV ) NY ( NGV ) CNYS ( GVNY ) = () ( P ) NY ( GVCNYS ) = () ( P ) CNYS where P NY and P CNYS are he elecriciy prices in New York Ciy and Cenral New York Sae, respecively. Figs. 3 and 4 (also locaed a he end of he paper) depic he GARCH variance and he normalized GARCH variance for he New York Ciy and Cenral New York Sae for he enire period. The figures reveal he higher level of volailiy in New York Ciy. Addiionally, Table Volailiy //00 //00 3//00 4//00 5//00 6//00 7//00 8//00 9//00 0//00 //00 //00 //00 //00 3//00 4//00 5//00 6//00 7//00 8//00 9//00 0//00 //00 Fig. 3 Comparison of he Volailiy of he Elecriciy Prices in New York Ciy and Cenral New York Sae for he Period of January, 00 o November, 00) NYC Dae CNYS

7 Hany S. Guirguis and Frank A. Felder //00 //00 3//00 4//00 5//00 6//00 7//00 Volailiy 8//00 9//00 0//00 //00 //00 //00 //00 3//00 4//00 5//00 6//00 7//00 8//00 9//00 0//00 //00 Dae NYC CNYS Fig. 4 Hisorical Raios of he GARCH Variance of New York Ciy o Cenral New York Sae and heir Significance Level provides a formal es for he variance raio of he wo regions. Table 5 shows ha he probabiliy of obaining a raio es greaer han he hisorical, or unshuffled, raio is.00. Thus, he resuls confirm ha he elecriciy prices in New York Ciy have a higher level of volailiy. Table 5 Hisorical Raios of he GARCH Variance of New York Ciy o Cenral New York Sae and heir Significance Level GVNC NGVNC GVCNCS NGVCNCS Raio Saisics.46.7 Marginal Sign Level I akes slighly less han 60 minues o run he enire analysis jus described on a PC Penium II wih 8 Mb of RAM a GHz. This is a shor enough ime o allow hese echniques o be used in pracice. We used Regression Analysis of Time Series (RATS) sofware o conduc mos of he compuaions. 5. Conclusions In line wih oher sudies such as [], we conclude ha incorporaing volailiy ino price forecasing via he GARCH process significanly improves he forecasing performance over he oher echniques evaluaed. In paricular, he GARCH process performance is a subsanial improvemen over DRM, TFA, and ES. Eliminaion of he few exreme values furher improves he performance of he GARCH process. Exreme values, however, are imporan o esimae in many applicaions. More research is needed ha combines GARCH wih echniques ha forecas exreme values. We also find ha New York Ciy has a larger daily volailiy han does Cenral New York Sae. One possible explanaion is ha he marke for elecriciy in New York Ciy has more marke power han does he upsae region. Higher volailiy can be an indicaor of collusive behavior or higher ransmission consrains. More deailed analysis is required o disinguish beween hese wo possible causes. We also noice ha here are wo peaks and prey sable variance in beween: addiional invesigaion is needed o deermine he cause. Our work can be exended in several direcions. Firs, a formal echnique o idenify and correc for ouliers insead of he use of visual inspecion can be incorporaed ino he analysis. Second, he elecriciy price forecasing and volailiy analysis can be applied o oher hours in he dayahead marke besides pm, o he real-ime marke, and o oher regions wihin New York Sae and elsewhere. References [] F. J. Nogales, J. Conreras, A. J. Conejo, R. Espínola, Forecasing Nex-Day Elecriciy Prices by Time Series Models, IEEE Transacions on Power Sysems, vol. 7, no., 00, pp [] R. Engle, Auoregressive condiional heeroscedasiciy wih esimaes of he variance of U.K. inflaion, Economerica, 50, 98, pp [3] T. Bollerslev, Generalized auoregressive condiional heeroscedasiciy, Journal of Economics, 3, 986, pp [4] R. Engle, D. Lilien, and R. Robins, Esimaing ime varying risk premia in he erm srucure: The ARCH-M model, Economerica, 55, pp , 986. [5] NYISO Repor, New York Power Pool Zone

8 66 Furher Advances in Forecasing Day-Ahead Elecriciy Prices Using Time Series Models Forecasing Models, February 0, 999, p., available a nyiso.com. [6] G. Schwarz, Esimaing he Dimension of a Model, Annals of Saisics 6, pp , 978. [7] E. Waler, Applied Economeric Time Series, New York: John Wiley & Sons, 994, pp & pp [8] P. Franses and H. Ghijsels, 999, Addiive ouliers, GARCH and forecasing volailiy, Inernaional Journal of Forecasing 5, pp.-9. [9] E. W. Noreen, Compuer-Inensive Mehods for Tesing Hypoheses: An Inroducion, New York, NY: John Wiley & Sons, 989. [0] M. Kim, C. Nelson, and R. Sarz. Mean Reversion in Sock Prices? A reappraisal of he Empirical Evidence, Review of Economic Sudies 58, 999, pp [] G. McQueen, Long-Horizon Mean-Revering Sock Prices Revisied, Journal of Financial and Quaniaive Analysis 7, 99, pp.-8. [] H. Guirguis, C. Giannikos and R. Anderson, The US Housing Marke: Asse Pricing Forecass Using Time Varying Coefficiens, Journal of Real Esae Finance and Economics, forhcoming. Hany S. Guirguis He earned his Ph.D. in Economics from he Universiy of Oregon in 995. He is Assisan Professor of Economics and Finance a Manhaan College in Riverdale, New York. His research ineress are in applied economerics. Frank A. Felder He earned his Ph.D. in Technology, Managemen and Policy from he Massachuses Insiue of Technology in 00. He is Assisan Research Professor wih he Cener for Energy, Economic and Environmenal Policy a he Edward J. Blousein School of Planning and Public Policy, Rugers, The Sae Universiy of New Jersey.