Comparing Class Level Chain Drift for Different Elementary Aggregate Formulae Using Locally Collected CPI Data


 Poppy Bennett
 2 years ago
 Views:
Transcription
1 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Gareth Clews 1, Anselma DobsonMcKttrck 2 and Joseph Wnton Summary The Consumer Prces Index (CPI) s a measure of consumer prce nflaton; t s a fxed basket prce ndex constructed from a combnaton of weghted and unweghted arthmetc and geometrc means of prce relatves. The content of the basket s updated every year and so are the weghts; ths s to ensure that the selecton of products n the basket and ther weghts reman representatve of the overall pattern of expendture of households covered by the CPI. These changes lead to a dscontnuty n the ndex seres. To remove ths effect, the ndex seres before and after the change are lnked to produce a contnuous seres and ad comparson of the prce ndex level across years. A prce ndex can be used to measure nflaton n a number of ways. The most common s to look at how the ndex has changed over a year; ths s calculated by comparng the prce ndex for the latest month wth the same month a year ago. Makng ths comparson nvolves crossng a lnk. Comparng ndex numbers across a tme nterval contanng one or more lnks can gve dfferent values to the same comparson wthout a lnk. The dfference between an ndex number calculated wth a lnk and an ndex number calculated over the same perod drectly (wthout a lnk), s known as chan drft 3. If we make a comparson across a lnk where the basket and the weghts are unchanged then whether we see chan drft depends on the type of ndex formula we use. If the ndex s bult from purely geometrc formulae at both elementary aggregate and hgher levels then there s no drft a comparson of ndex number dfferences from a lnked and drect ndex seres wll gve the same answer. However, f some arthmetc formulae are used ether at the elementary aggregate level, or the upper levels, or both, then the drft wll not be zero 4. Measurng chan drft n the CPI s complcated by effects such as the changng of the basket of tems each year and the weghts. What we are nterested n s the dfferences between chaned and drect ndces due to the choce of formula Placement student from the Unversty of the West of England Channg s repeated lnkng usually at regular tme ntervals; f the comparson of ndex numbers s made across a tme perod contanng several lnks then the drft s cumulatve. It s possble for the drft to be zero wth arthmetc formulae, but ths s only n very specal crcumstances Offce for Natonal Statstcs 1
2 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Ths paper nvestgates the magntude of the drft for three choces of elementary aggregate formula; the Carl, Dutot and Jevons, where the lnk occurs at the class level as s the case for the CPI. In all cases, the upper level ndex formula s the Lowe as s used n the CPI. The calculatons are made usng locally collected prce data and magntudes of drft are calculated for each class. It s wdely quoted that the use of the (arthmetc) Carl formula at the elementary aggregate level wll lead to a larger drft than the (geometrc) Jevons. The Dutot formula s expected to behave somewhat smlarly to the Jevons formula despte ts use of an arthmetc mean. These comparsons are complcated by the fact that the lnk s carred out at the class level, so elementary aggregate ndces are combned usng the Lowe ndex formula (a weghted arthmetc average). The emprcal results show that the drft from usng the Carl formula does exceed the drft from the Jevons n most, but not all cases. The average (absolute) drft across all classes n 2009 for the Carl s 0.67, for the Jevons s 0.11 and for the Dutot s The correspondng Fgures for 2010 are 0.47, 0.06 and There are a few classes where the drft of the Jevons exceeds the drft for the Carl 5 out of 65 classes n 2009 and 10 out of 64 n The drft when usng Jevons s often smlar to when usng Dutot and can be hgher or lower. An understandng of the factors that contrbute to the magntude of the drft wll be the subect of further work. Acknowledgements The Authors would lke to thank Natale Weaden, Robert O Nell, Ra Sanderson and Jeff Ralph for ther contrbutons to ths research. 1. Introducton The degree to whch dfferent elementary aggregate (EA) formulae contrbute to chan drft s a topc whch enters the dscusson of whch s the most approprate formula to use at the lowest level of aggregaton for an nflaton measure. One of the crtcsms of the Carl formula s that ts arthmetc nature wll result n a hgher chan drft than the geometrc Jevons formula. Whle ths may seem to be somewhat natural, the actual stuaton s complcated by the fact that chan lnkng doesn t occur at the elementary aggregate level, but at the class level. To reflect the formula used n the CPI, a comparson has to be made wth the dfferent elementary aggregates combned wth the Lowe formula up to class level. The topc of chan drft and the choce of elementary aggregate formula was rased durng the RPI Consultaton; however, there was no resource avalable to nvestgate t at the tme. There appears to have been lttle nvestgaton of ths topc n the lterature. The most elementary scenaro n whch chan drft occurs s a prce bounce stuaton. Ths s where the prce starts at a specfc level before ncreasng (or decreasng) n the next perod and then returnng to ts ntal value n the followng perod. Ths can also be extended across any number of perods wth only the requrement that the start and end prce are equal. We consder the choce of elementary aggregate formula on the chan drft at hgher levels of aggregaton. Offce for Natonal Statstcs 2
3 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng The structure of ths paper s as follows. Frst we provde a bref overvew of the terms used n ths paper and a descrpton of the constructon of the CPI. We then descrbe the data used followed by a theoretcal analyss of the problem. We nclude our results before concludng. 1.1 Defnng drft To defne chan drft, frst consder three tme perods, t=0, 1 and 2 and an arbtrary ndex formula f( ab, ). The drect ndex, Λ, between t = 0 and t = 2 s defned as applcaton of the ndex formula to the start and end data, ( 0, 2) f ( 0, 2) Λ = (1) A lnked ndex, Λ, across the tme perod [0,2], wth a lnk at tme perod t = 1 s gven by: ( 0, 2) f ( 0,1) f ( 1, 2) * Λ = (2) In ths paper, chan drft s defned as the dfference Λ (0,2) Λ(0,2). The lmted lterature on drft ncludes the rato of a lnked and drect ndex and defnes ths as a drft factor; however, the rato and dfference are related so there s no ssue n consderng a dfference[1]. 1.2 Structure of the CPI The CPI measures the change n prces for goods and servces purchased by households over tme. It s a measure of nflaton based on average household expendture on tems n a fxed basket. In an deal stuaton the CPI would be calculated usng the prces for all transactons occurrng throughout the UK. However, ths s not avalable so there are two approxmatons made. The frst s to collect prces for tems on shelves and consder ths as a proxy for the prces pad by consumers for tems. Secondly only a sample of all avalable tems from a sample of locatons s taken. Ths sample forms the basket. The tems n the basket are classfed based on the nternatonal classfcaton system for household consumpton expendtures, known as Classfcaton of Indvdual Consumpton by Purpose (COICOP). Ths s a herarchcal structure. Each level s an aggregaton of somewhat homogeneous subgroups. For example, the alcohol class s made up of separate subclasses for beer, wne and sprts, each of whch s also an aggregate of more detaled types of alcohol. Fgure 1, below, provdes a dagrammatc example of ths construct. The basket remans fxed, leadng to use of the term fxed basket, for one calendar year and s updated to reflect changes n consumer spendng habts every February. Offce for Natonal Statstcs 3
4 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Fgure 1: Dagrammatc explanaton of the structure of the COICOP classfcaton system Prces are collected for tems n the basket and are used, alongsde weghts  from a varety of sources  whch descrbe expendture on those tems, to calculate prce ndces at each level of the COICOP structure. These weghts are calculated from expendture shares for the classfcaton and are avalable at all levels other than the stratum level (see Fgure 2 below). At the most detaled level of descrpton weghts are not avalable. Hence, some unweghted averages are used n the CPI. These are referred to as elementary, or unweghted, aggregates. Wthn the CPI ths form of aggregate s calculated only where weghtng nformaton s not avalable. In practce the formula used where weghts are not avalable s the Jevons prce ndex or n some cases the Dutot prce ndex. The Jevons prce ndex s an unweghted geometrc mean of a group of prce relatves, where a prce relatve for a gven product s the rato of the prces n the current perod to the prces n the base perod. The Dutot prce ndex s the rato of the arthmetc mean of prces n the current perod to the arthmetc mean of prces n the base perod. At hgher levels, where we have weghts for each component, a weghted arthmetc mean s used. Ths s often descrbed as beng of Laspeyres type and s known as a Lowe ndex, where the weghts are calculated from expendture nformaton n a perod before the prce reference (base) perod. Fgure 2 provdes a dagrammatc nterpretaton of the structure of the CPI. Ths Fgure s a smplfed verson of the structure descrbed n the CPI Techncal Manual [2] whch provdes more nformaton on the structure and weghts used at each level. Dfferent weghts wthn the CPI are updated at dfferent tmes n the year. In January, the class weghts are updated. Followng ths, n February, the basket tself s updated as descrbed above, along wth the assocated tem weghts. As a result of ths the CPI s chan lnked twce every year. Ths s done by calculatng a January based ndex based on the prces for the December n the prevous year. We then multply ths by the ndex for the precedng years from the base perod (2005) and the newly calculated ndex n the current month wth prces based n January. Ths means that January ndces contan only one chan lnk whlst those for the rest of the year have two. The formula used for ths calculaton s ncluded n the Annex. Offce for Natonal Statstcs 4
5 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Fgure 2. The structure of the CPI, ndcatng where weghts are appled 2. Data The data used n ths analyss are the locally collected prce quotes used n the calculaton of the CPI 5. To obtan these data, prce collectors n the feld vst shops and outlets wthn sampled locatons. These data do not comprse the whole coverage of prces used and account for around 57% of the total weght. In the CPI the prce quotes collected from stores s supplemented by data collected centrally for products that are not bought from shops; for such thngs as TV lcences whch are unformly prced across the country; and for products for whch local collecton s dffcult. Fgure 3 shows a comparson between the month on same month n prevous year growths (commonly referred to as the twelve month growth) n the publshed CPI and the CPI calculated usng only the locally collected data. All locally collected elementary aggregates are constructed usng the Jevons prce ndex. 5 Avalable from the ONS webste: Offce for Natonal Statstcs 5
6 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Fgure 3: Twelve month growth rates of the CPI when calculated usng only locally collected data and the full CPI 3. Methodology Measurng chan drft n the CPI s complcated by effects such as the changng of the basket of tems each year and the weghts. The dfferences between chaned and drect ndces caused by updatng weghts and the basket are a necessary result of those changes whch are made to ensure that the CPI remans relevant. The element of chan drft that we are most nterested n s the dfferences between chaned and drect ndces due to the choce of formula. Ideally, f lnkng occurs wthout a change to weghts or basket composton then there wll be no chan drft. To measure only the effect of the choce of formula on chan lnkng the ndces, wthout other contrbutng factors t s necessary to mantan the same basket of tems and assocated weghts. We have chosen to use an artfcal lnk durng the calendar year, whch mantans the fxed basket and weghts. Our three tme perods are May, June and July usng data for both 2009 and Offce for Natonal Statstcs 6
7 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng For the CPI structure we compared equaton (1) wth equaton (2) usng the formulae ( 0, 2) w ( 0,1) w ( 1, 2) * Λ = Ε Ε (3) And ( 0, 2) w ( 0, 2) Λ = Ε (4) where w s the weght for product up to the class level 6, Ε ( 0, 2) s the elementary aggregate for product n perod 2 based on perod 0, that s, ths s the stratum ndex for stratum. We are comparng three elementary aggregate formulae, the Jevons, Dutot and the Carl: 1 n p ( b) J Ε ( ab, ) = [Jevons] p ( a) D ( ab, ) Ε = p ( b) p ( a) [Dutot] Ε 1 p ( b) C ( ab, ) = n p a [Carl] Pror to calculatng the ndces, a cleanng process was appled to the locally collected prce data. The process ncluded removng mssng or zero prce relatves and also those prce relatves larger than a threshold value of 10. Ths follows the CPI methodology used by ONS. The process of calculatng prce ndces and aggregatng these to hgher levels followed that used n the CPI. The approach usng the Carl or Dutot elementary aggregates s dentcal to the constructon of the CPI wth only the formula used for the stratum level ndces changed. The stratum ndces ndces were then aggregated usng the assocated weghts and the Lowe formula 7 gven n (3) and (4). Ths resulted n drect and chaned class level ndces, and thus the value of the chan drft, for each of the elementary aggregate formulae. The comparson s made at the class level as ths s the frst level where ndces are chaned n the CPI. The chan drft was calculated for each class for both of the elementary aggregate formulae for each of the years 2009 and Ths s n effect a compound weght; we have flattened the structure of the CPI so that nstead of aggregaton across the homogenous groups we consder the sum across all stratum ndces. Ths greatly reduces the complexty of the formulae we present wthout changng the result. A Laspeyrestype (arthmetc) ndex wth weghtng nformaton taken from expendture data dated pror to the prce reference perod. Offce for Natonal Statstcs 7
8 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng 4. Analyss In ths secton, we use equatons (3) and (4) to make theoretcal conclusons about the relatve sze and drecton of the chan drft that can be expected from each elementary aggregate formula. Λ Λ as defned by equatons (3) and (4). We have the followng * Consder ( 0, 2) ( 0, 2) 0, 2 0, 2 w 0,1 w 1, 2 w (0, 2) * Λ Λ = Ε Ε Ε (, ) = wwε 0,1 Ε 1, 2 wε (0, 2) 2 = w Ε 0,1 Ε 1, 2 + wwε 0,1 Ε 1, 2 wε (0, 2) (, ) (5) Ths formula does not, at ths pont, have any dependence on the choce of elementary aggregate formula. By consderng the elementary aggregate beng one of Jevons, Dutot or Carl, n turn, we can somewhat smplfy equaton (5) for each stuaton. We should note here that ths formula also apples to any level of aggregaton. The dfference between each level s the weght appled to each elementary aggregate. In any numercal applcaton the weghts should be handled carefully. 4.1 Chan drft when usng a Jevons elementary aggregate J ab, ab, Ε J 0,1 Ε J 1, 2 =Ε J 0, 2 If Ε s a geometrc mean of prce relatves, Ε then equaton (5) becomes * 2 J J J (, ) J J J = ww Ε ( 0,1) Ε ( 1, 2) w( 1 w) Ε (0, 2) (, ) J J J = ww Ε ( 0,1) Ε ( 1, 2) ww Ε ( 0, 2) (, ) (, ) (, ) Λ 0, 2 Λ 0, 2 = w Ε 0, 2 + wwε 0,1 Ε 1, 2 wε (0, 2) J J J = ww Ε 0,1 Ε 1, 2 Ε 0, 2. Ths equaton s nether postve nor negatve defnte (or ndeed semdefnte). I.e. a pror the chan drft can be ether postve or negatve. 8 and 4.2 Chan drft when usng a Dutot elementary aggregate Ε D 0,1 Ε D 1, 2 =Ε D 0, 2 9. Hence, the equaton for chan drft when usng It s easly seen that the Dutot formula at the elementary aggregate level s gven equaton (6) wth the Jevons J D ab, Ε ab,. It s also elementary aggregate Ε replaced by the Dutot elementary aggregate (6) 8 9 A short proof of ths equalty can be found n Annex B A short proof of ths equalty can be found n Annex B Offce for Natonal Statstcs 8
9 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng the case, a pror, that the chan drft resultng n the use of Dutot at the elementary aggregate level may be postve or negatve and s not necessarly larger or smaller than that of the Jevons or Carl formulae. 4.3 Chan drft when usng a Carl elementary aggregate The use of an unweghted arthmetc mean of prce relatves, the Carl formula, at the elementary aggregate level provdes a more complcated problem than both the Jevons and Dutot elementary aggregate formulae. Here C C 1 p 1 1 p 2 E ( 0,1) E ( 0,1) = n p 0 n p 1 1 p 1 p 2 = 2 n p 0 p 1 1 p 1 pk 2 = 2 n k p 0 pk 1 (7) Ths formula does not easly smplfy to the drect ndex plus or mnus some other term as t does for the other formulae and so no smple argument for the consderaton of the chan drft n the hgher level s possble. Let ε be the chan drft n the elementary aggregates ε : = E 0,1 E 1, 2 E 0, 2 C C C There s no a pror condton whch means that ths chan drft must be postve, negatve, greater than that usng any other elementary aggregate formula n the report or less than t 10. We can, C C C however, wrte E ( 0,1) E ( 1, 2) = E ( 0, 2) + ε and then C 2 C C ( w w wε ) ww (8) Λ 0, 2 Λ 0, 2 = 1 E 0, E 0,1 E 1, 2 Equaton (8) can then be used to provde a condton on the sgn of the chan drft n the hgher level ndex n terms of weghts, elementary aggregates and the chan drft at the lowest level. Ths formula s a good deal more complcated and features more terms than the other formulae. It s plausble to compare the chan drft theoretcally usng ths formula and those for the other aggregates; however, ths only provdes theoretcal condtons and can only represent what happens n practce once we use the collected prces. We shall then provde emprcal evdence to make statements on whch aggregates cause greater or lesser chan drft gven the dstrbutons of prce relatves. (, ) 10 Ths s a typcal argument aganst the Carl elementary aggregate, whch theoretcally s not true. It s, however, backed up by emprcal evdence where the dstrbuton of prces s known. Offce for Natonal Statstcs 9
10 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng 5. Results 5.1 Chan drft Before we provde the results of the comparson of the values for chan drft when usng the dfferent formulae t s worth notng the assumptons and condtons for whch these results hold. The weghts for all perods n the chan are the same because they are chosen wthn the year; n the producton of the CPI these wll change across the lnks. Ths means that for the actual ndex our equatons do not apply exactly, but refer to a smplfed stuaton. A closed form formula for the chan drft, as n equatons (6), (7) and (8) can be obtaned for varable weghts. As noted n secton 2, the data used are locally collected prce data for 2009 and 2010 only; ths does not cover the entrety of the CPI collecton. The mplementaton of the channg used s also artfcal n order to remove the effect of updatng weghts and the basket. Ths means that the results do not relate drectly to any chan drft present n the CPI but rather provde a comparson of the relatve sze of the chan drft from usng dfferent formulae on CPI prce data. In practce the chan drft s also compounded year on year as the ndces are chan lnked twce a year from the base year of Ths has not been consdered as t makes the formulae more complcated and ntroduces other effects due to problems such as changes to the basket and weghts. We do not suggest that a drect ndex should be the target measure for nflaton as chan lnkng s necessary to ensure that the ndex remans relevant through basket and weght updates. Ths report only descrbes the effect that the chan lnkng procedure has on the value compared to the case where chan lnkng was not performed and focuses on dfferences n chan drft arsng from the choce of formula used to calculate elementary aggregates. These assumptons do not nvaldate the research; however, any numbers gven here are not drectly equal to any chan drft wthn the CPI. The results we present n ths paper should not be nterpreted as any knd of bas n the CPI, but only taken to show the effect of the chan lnkng procedure on the hgher level Laspeyres type ndex formula usng CPI data. Fgure 4 shows comparson of the chaned vs. drect ndces for each elementary aggregate n 2009 and There s a postve correlaton between drect and chaned ndces usng all three elementary aggregates, whch s to be expected. The dotted lne on the graph corresponds to those values for whch the chaned ndex concdes exactly wth the drect. We see that n most nstances the class ndces are above ths lne, meanng that the chaned ndex s larger than the drect. Ths s an artefact of usng an arthmetc mean at the hgher level and occurs for all choces of elementary aggregate. The effect s notceably larger n the ndces whch use the Carl formula at the lower level. It s worth notng that there are occasons where the chan drft n the class ndex usng a Jevons elementary aggregate s larger than that of the ndex number makng use of the Carl formula. Ths s rare, occurrng n only 15 nstances out of 129 across the dataset; where ths s the case, the drft s also small: the average absolute drft usng the Jevons n these cases s In the 114 cases where the absolute drft s greater n the Carl than the Jevons, the average absolute drft usng the Carl s Offce for Natonal Statstcs 10
11 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Fgure 4: A comparson of the chaned vs. drect class level ndces for each of the elementary aggregate formulae for 2009 and 2010 Offce for Natonal Statstcs 11
12 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng The chan drft values are compared n Fgure 5. Fgure 5 shows that for all three elementary aggregates, the chan drft s postve n the maorty of cases (96%, 73% and 72% postve for Carl, Jevons and Dutot respectvely). Ths s most strkng for Carl whch often has large values of drft; Fgure 5 shows that the values of drft are clustered around zero for Dutot and Jevons but are often large for Carl. It s also notceable that the use of a Jevons and Dutot elementary aggregates n the CPI structure causes a suffcent proporton of classes to exhbt negatve chan drft, where the drect ndex s n fact larger than that when chan lnked. The use of a Carl elementary aggregate can be seen to create negatve chan drft for some classes but ths effect s seen far less frequently. Fgure 5 ndcates that there s no drect relatonshp between the ndex level tself and the amount of chan drft. We note here that one value for whch the chaned ndex exceeded 120 and the drect ndex was 105 was removed from the 2009 data; ths ndex used the Carl formula at the elementary aggregate level. The datum was removed to provde clarty of the behavour of the rest of the ndces n the Fgure and has been omtted throughout. Fgure 5. Chan drft vs. chaned ndex number for all classes Offce for Natonal Statstcs 12
13 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Fgure 6 shows that the use of the Carl formula at the lowest level does not always cause larger absolute chan drft than the use of ether of the other two formulae, though when ths s the case the drft from the Carl s often much larger than the drft from ether Jevons or Dutot. Fgure 6 also shows that the chan drft from usng the Jevons formula at the elementary aggregate level s often very smlar to the chan drft from the Dutot. Fgure 6: Chan drft by class for each choce of elementary aggregate n 2009 and 2010 It s expected n the lterature that a Carl elementary aggregate wll nduce larger chan drft than the use of ether of the other choces of formula n the CPI at the class level. Fgure 6 supports ths clam. The average of the absolute values of the chan drft s gven n the table below. Offce for Natonal Statstcs 13
14 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Table 1. Average of the absolute values of the chan drft across all classes n each year for each choce of elementary aggregate formula. Average absolute chan drft values Year Carl Jevons Dutot At ths pont t s worth consderng how the class ndces usng Jevons and Dutot elementary s the absolute value of aggregates compare. Fgure 7 shows exp{ d }, where the chan drft when usng the Jevons formula at the stratum level and the use of Dutot. Fgure 7. d s that correspondng to Exponentaton of the dfference n absolute chan drft at the class level between the Jevons and Dutot elementary aggregates. Offce for Natonal Statstcs 14
15 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng The ponts to the left of the the vertcal lne at 1 correspond to the nstances where the chan drft usng a Dutot elementary aggregate exceeds that when usng Jevons. Those ponts to the rght of 1 are the classes for whch chan drft when usng a Jevons formula exceeds that when usng Dutot. We see that there are more nstances where the chan drft usng a Jevons elementary aggregate formula s larger than that when usng a Dutot, and consstently so over the two years, but the dfference s usually of smaller magntude than those ponts to the left of the lne. 5.2 Prce Bounce Ths work explored the prevalence of prce bouncng across the classes. In the context of ths research a prce bounce corresponds to prces beng at a set level n May, before changng value n June and then returnng to ther ntal level n July. Ths s the smplest case of the phenomenon and the prce bounce occurs over the chan lnk. Cases where the prce vares for more months before returnng to ther ntal level, asymmetrc comparsons around the chan lnk perod or prces returnng to nearby ther ntal level are out of scope of ths work and further complcate the matter. There s some evdence that there s greater chan drft n classes wth a hgher proporton of prce bounce, however ths s not the only reason for chan drft. Further nvestgaton of prce bounce and the relaton of prce bounce to chan drft s needed to understand ths more. Fgure 8. Proporton of Prce Bounce aganst absolute Chan Drft from the Carl formula at the elementary aggregate per Class, 2009 and 2010 Offce for Natonal Statstcs 15
16 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng 6. Conclusons Ths work has used the locally collected prce data and an artfcal, mdyear lnk to explore the relatve magntudes of chan draft n class level ndces when usng varous elementary aggregate formulae. It shows that the use of a Carl formula at the elementary aggregate level does lead to greater chan drft than usng a Jevons or Dutot formula for most classes. There are a number of areas where addtonal work could be carred out. Frstly, tryng to dentfy what factors contrbute to the dfferent szes of the drft for dfferent classes would be nterestng and why there are nstances where the Jevons drft exceeds the Carl. The actual stuaton of the real CPI s, of course, more complcated wth a double lnk; t would be nterestng to see the effect of a second lnk. It would also be nterestng to see the compound effect of multple lnks and lnks over longer perods. References [1] Peter von der Lppe, 2005, Index Theory and Prce Statstcs, Peter Lang, ISBN [2] ONS, 2014, Consumer Prces Techncal Manual, [3] Bert Balk, 2008, Prce and Quantty Index Numbers, Cambrdge Unversty Press, ISBN Offce for Natonal Statstcs 16
17 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Annex A. Chan lnkng n the CPI The Consumer Prce Index ncorporates changes to weghts and a change to the basket every year n January (hgher level weghts) and February (basket and tem weghts). Ths forces the requrement of a chan lnk for each change so that the ndex s chan lnked twce for each ndex n y n year y wth a base perod of January n year c Λ ( bx, ) the double chan lnked ndex b = ( basemonth,baseyear ) s. Usng the same notaton as n the man text, x = ( month,year ) for wth base perod n c Λ (( Jan, y n),( t, y) ) = Λ( ( Jan, y v),( Dec, y v) ) Λ( ( Dec, y v),( Jan, y ( v 1 ))). v= 1 Λ (( Jan, y),( t, y) ) The square bracket denotes the compoundng of the chan lnks over tme so as to create a contnuous seres from the base perod to the current month n the current year. In essence the chan lnk uses the last value from the prevous year along wth a specal ndex calculated usng January prces aganst a prevous December base perod to translate the current year s seres so that there are no level shfts. Ths process s a pure translaton of the seres and does not affect the behavour. Offce for Natonal Statstcs 17
18 Comparng Class Level Chan Drft for Dfferent Elementary Aggregate Formulae Usng Annex B. Relatonshp between Drect and Chaned elementary Aggregates B1. Jevons Prce Index 1 1 n n p p (1) (2) J J Ε ( 0,1) Ε ( 1, 2) = p( 0) p( 1) B2. Dutot Prce Index 1 1 n n (1) (2) (1) (2) p p p p = = p( 0) p( 1) p( 0) p( 1) 1 n p (2) = = Ε p ( 0) J ( 0, 2) p (1) p (2) D D Ε ( 0,1) Ε ( 1, 2) = p(0) p(1) p(1) p (2) p(2) = p(0) p(1) = = Ε p(0) D ( 0, 2) Offce for Natonal Statstcs 18
An Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationMoment of a force about a point and about an axis
3. STATICS O RIGID BODIES In the precedng chapter t was assumed that each of the bodes consdered could be treated as a sngle partcle. Such a vew, however, s not always possble, and a body, n general, should
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationQuality Adjustment of Secondhand Motor Vehicle Application of Hedonic Approach in Hong Kong s Consumer Price Index
Qualty Adustment of Secondhand Motor Vehcle Applcaton of Hedonc Approach n Hong Kong s Consumer Prce Index Prepared for the 14 th Meetng of the Ottawa Group on Prce Indces 20 22 May 2015, Tokyo, Japan
More informationSolutions to First Midterm
rofessor Chrstano Economcs 3, Wnter 2004 Solutons to Frst Mdterm. Multple Choce. 2. (a) v. (b). (c) v. (d) v. (e). (f). (g) v. (a) The goods market s n equlbrum when total demand equals total producton,.e.
More informationNasdaq Iceland Bond Indices 01 April 2015
Nasdaq Iceland Bond Indces 01 Aprl 2015 Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes
More information9. PPI Calculation in Practice
9. PPI Calculaton n Practce A. Introducton 9.1 Ths chapter provdes a general descrpton of the ways PPIs are calculated n practce. The methods used n dfferent countres are not exactly the same, but they
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More information10. XMPI Calculation in Practice
10. XMPI Calculaton n Practce A. Introducton 10.1 Ths chapter provdes a general descrpton wth examples of the ways n whch XMPIs are calculated n practce. The methods used n dfferent countres are not exactly
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationIntroduction: Analysis of Electronic Circuits
/30/008 ntroducton / ntroducton: Analyss of Electronc Crcuts Readng Assgnment: KVL and KCL text from EECS Just lke EECS, the majorty of problems (hw and exam) n EECS 3 wll be crcut analyss problems. Thus,
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationEditing and Imputing Administrative Tax Return Data. Charlotte Gaughan Office for National Statistics UK
Edtng and Imputng Admnstratve Tax Return Data Charlotte Gaughan Offce for Natonal Statstcs UK Overvew Introducton Lmtatons Data Lnkng Data Cleanng Imputaton Methods Concluson and Future Work Introducton
More informationDescribing Communities. Species Diversity Concepts. Species Richness. Species Richness. SpeciesArea Curve. SpeciesArea Curve
peces versty Concepts peces Rchness pecesarea Curves versty Indces  mpson's Index  hannonwener Index  rlloun Index peces Abundance Models escrbng Communtes There are two mportant descrptors of a communty:
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationb) The mean of the fitted (predicted) values of Y is equal to the mean of the Y values: c) The residuals of the regression line sum up to zero: = ei
Mathematcal Propertes of the Least Squares Regresson The least squares regresson lne obeys certan mathematcal propertes whch are useful to know n practce. The followng propertes can be establshed algebracally:
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationWill the real inflation rate please stand up overlooked quirks of a favoured chainlinking technique
Wll the real nflaton rate please stand up overlooked qurks of a favoured chanlnkng technque Dr Jens Mehrhoff*, Head of Secton Busness Cycle, Prce and Property Market Statstcs * Jens Ths Mehrhoff, presentaton
More informationStudy on CET4 Marks in China s Graded English Teaching
Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes
More informationChapter 3 Group Theory p. 1  Remark: This is only a brief summary of most important results of groups theory with respect
Chapter 3 Group Theory p.  3. Compact Course: Groups Theory emark: Ths s only a bref summary of most mportant results of groups theory wth respect to the applcatons dscussed n the followng chapters. For
More informationGraph Theory and Cayley s Formula
Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll
More informationII. PROBABILITY OF AN EVENT
II. PROBABILITY OF AN EVENT As ndcated above, probablty s a quantfcaton, or a mathematcal model, of a random experment. Ths quantfcaton s a measure of the lkelhood that a gven event wll occur when the
More informationSIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA
SIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA E. LAGENDIJK Department of Appled Physcs, Delft Unversty of Technology Lorentzweg 1, 68 CJ, The Netherlands Emal: e.lagendjk@tnw.tudelft.nl
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationMAPP. MERIS level 3 cloud and water vapour products. Issue: 1. Revision: 0. Date: 9.12.1998. Function Name Organisation Signature Date
Ttel: Project: Doc. No.: MERIS level 3 cloud and water vapour products MAPP MAPPATBDClWVL3 Issue: 1 Revson: 0 Date: 9.12.1998 Functon Name Organsaton Sgnature Date Author: Bennartz FUB Preusker FUB Schüller
More informationWorld Economic Vulnerability Monitor (WEVUM) Trade shock analysis
World Economc Vulnerablty Montor (WEVUM) Trade shock analyss Measurng the mpact of the global shocks on trade balances va prce and demand effects Alex Izureta and Rob Vos UN DESA 1. Nontechncal descrpton
More informationCapital asset pricing model, arbitrage pricing theory and portfolio management
Captal asset prcng model, arbtrage prcng theory and portfolo management Vnod Kothar The captal asset prcng model (CAPM) s great n terms of ts understandng of rsk decomposton of rsk nto securtyspecfc rsk
More information9 Arithmetic and Geometric Sequence
AAU  Busness Mathematcs I Lecture #5, Aprl 4, 010 9 Arthmetc and Geometrc Sequence Fnte sequence: 1, 5, 9, 13, 17 Fnte seres: 1 + 5 + 9 + 13 +17 Infnte sequence: 1,, 4, 8, 16,... Infnte seres: 1 + + 4
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationMultivariate EWMA Control Chart
Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant
More informationPrediction of Wind Energy with Limited Observed Data
Predcton of Wnd Energy wth Lmted Observed Data Shgeto HIRI, khro HOND Nagasak R&D Center, MITSISHI HEVY INDSTRIES, LTD, Nagasak, 8539 JPN Masaak SHIT Nagasak Shpyard & Machnery Works, MITSISHI HEVY INDSTRIES,
More informationQuestions that we may have about the variables
Antono Olmos, 01 Multple Regresson Problem: we want to determne the effect of Desre for control, Famly support, Number of frends, and Score on the BDI test on Perceved Support of Latno women. Dependent
More informationI. SCOPE, APPLICABILITY AND PARAMETERS Scope
D Executve Board Annex 9 Page A/R ethodologcal Tool alculaton of the number of sample plots for measurements wthn A/R D project actvtes (Verson 0) I. SOPE, PIABIITY AD PARAETERS Scope. Ths tool s applcable
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationSimon Acomb NAG Financial Mathematics Day
1 Why People Who Prce Dervatves Are Interested In Correlaton mon Acomb NAG Fnancal Mathematcs Day Correlaton Rsk What Is Correlaton No lnear relatonshp between ponts Comovement between the ponts Postve
More informationPROFIT RATIO AND MARKET STRUCTURE
POFIT ATIO AND MAKET STUCTUE By Yong Yun Introducton: Industral economsts followng from Mason and Ban have run nnumerable tests of the relaton between varous market structural varables and varous dmensons
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More informationU.C. Berkeley CS270: Algorithms Lecture 4 Professor Vazirani and Professor Rao Jan 27,2011 Lecturer: Umesh Vazirani Last revised February 10, 2012
U.C. Berkeley CS270: Algorthms Lecture 4 Professor Vazran and Professor Rao Jan 27,2011 Lecturer: Umesh Vazran Last revsed February 10, 2012 Lecture 4 1 The multplcatve weghts update method The multplcatve
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationPassive Filters. References: Barbow (pp 265275), Hayes & Horowitz (pp 3260), Rizzoni (Chap. 6)
Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called
More informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationBrigid Mullany, Ph.D University of North Carolina, Charlotte
Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte
More informationAn InterestOriented Network Evolution Mechanism for Online Communities
An InterestOrented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng 100872, P.R. Chna {chsun,yang}@ruc.edu.cn Abstract. Onlne
More information1.1 The University may award Higher Doctorate degrees as specified from timetotime in UPR AS11 1.
HIGHER DOCTORATE DEGREES SUMMARY OF PRINCIPAL CHANGES General changes None Secton 3.2 Refer to text (Amendments to verson 03.0, UPR AS02 are shown n talcs.) 1 INTRODUCTION 1.1 The Unversty may award Hgher
More informationMultiplePeriod Attribution: Residuals and Compounding
MultplePerod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens
More informationState function: eigenfunctions of hermitian operators> normalization, orthogonality completeness
Schroednger equaton Basc postulates of quantum mechancs. Operators: Hermtan operators, commutators State functon: egenfunctons of hermtan operators> normalzaton, orthogonalty completeness egenvalues and
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationNonparametric Estimation of Asymmetric First Price Auctions: A Simplified Approach
Nonparametrc Estmaton of Asymmetrc Frst Prce Auctons: A Smplfed Approach Bn Zhang, Kemal Guler Intellgent Enterprse Technologes Laboratory HP Laboratores Palo Alto HPL200286(R.) November 23, 2004 frst
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationHYPOTHESIS TESTING OF PARAMETERS FOR ORDINARY LINEAR CIRCULAR REGRESSION
HYPOTHESIS TESTING OF PARAMETERS FOR ORDINARY LINEAR CIRCULAR REGRESSION Abdul Ghapor Hussn Centre for Foundaton Studes n Scence Unversty of Malaya 563 KUALA LUMPUR Emal: ghapor@umedumy Abstract Ths paper
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationEE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN
EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson  3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson  6 Hrs.) Voltage
More informationExpected Value. Background
Please note: Before I slam you wth the notaton from Chapter 9  Secton, I want you to understand how smple Mathematcal Expectaton really s. My frst smplfcaton: I wll refer to t as Expected Value (E )from
More informationOnline Learning from Experts: Minimax Regret
E0 370 tatstcal Learnng Theory Lecture 2 Nov 24, 20) Onlne Learnng from Experts: Mn Regret Lecturer: hvan garwal crbe: Nkhl Vdhan Introducton In the last three lectures we have been dscussng the onlne
More informationNonlinear data mapping by neural networks
Nonlnear data mappng by neural networks R.P.W. Dun Delft Unversty of Technology, Netherlands Abstract A revew s gven of the use of neural networks for nonlnear mappng of hgh dmensonal data on lower dmensonal
More informationEvaluating the Effects of FUNDEF on Wages and Test Scores in Brazil *
Evaluatng the Effects of FUNDEF on Wages and Test Scores n Brazl * Naérco MenezesFlho Elane Pazello Unversty of São Paulo Abstract In ths paper we nvestgate the effects of the 1998 reform n the fundng
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy Scurve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy Scurve Regresson ChengWu Chen, Morrs H. L. Wang and TngYa Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More informationIntroduction to Regression
Introducton to Regresson Regresson a means of predctng a dependent varable based one or more ndependent varables. Ths s done by fttng a lne or surface to the data ponts that mnmzes the total error. 
More informationMultiple discount and forward curves
Multple dscount and forward curves TopQuants presentaton 21 ovember 2012 Ton Broekhuzen, Head Market Rsk and Basel coordnator, IBC Ths presentaton reflects personal vews and not necessarly the vews of
More informationTrafficlight a stress test for life insurance provisions
MEMORANDUM Date 006097 Authors Bengt von Bahr, Göran Ronge Traffclght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationEnhancing the Quality of Price Indexes A Sampling Perspective
Enhancng the Qualty of Prce Indexes A Samplng Perspectve Jack Lothan 1 and Zdenek Patak 2 Statstcs Canada 1 Statstcs Canada 2 Abstract Wth the release of the Boskn Report (Boskn et al., 1996) on the state
More informationConversion between the vector and raster data structures using Fuzzy Geographical Entities
Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,
More informationSection B9: Zener Diodes
Secton B9: Zener Dodes When we frst talked about practcal dodes, t was mentoned that a parameter assocated wth the dode n the reverse bas regon was the breakdown voltage, BR, also known as the peaknverse
More informationDescriptive Statistics (60 points)
Economcs 30330: Statstcs for Economcs Problem Set 2 Unversty of otre Dame Instructor: Julo Garín Sprng 2012 Descrptve Statstcs (60 ponts) 1. Followng a recent government shutdown, Mnnesota Governor Mark
More informationNotes on Engineering Economic Analysis
College of Engneerng and Computer Scence Mechancal Engneerng Department Mechancal Engneerng 483 lternatve Energy Engneerng II Sprng 200 umber: 7724 Instructor: Larry Caretto otes on Engneerng Economc nalyss
More informationStress test for measuring insurance risks in nonlife insurance
PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n nonlfe nsurance Summary Ths memo descrbes stress testng of nsurance
More informationDECOMPOSING ALLOCATIVE EFFICIENCY FOR MULTIPRODUCT PRODUCTION SYSTEMS
DECOMPOSING ALLOCATIVE EFFICIENCY FOR MULTIPRODUCT PRODUCTION SYSTEMS EKONOMIKA A MANAGEMENT Tao Zhang Introducton Data envelopment analyss (DEA, the nonparametrc approach to measurng effcency, was frst
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationHOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*
HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt
More informationThe covariance is the two variable analog to the variance. The formula for the covariance between two variables is
Regresson Lectures So far we have talked only about statstcs that descrbe one varable. What we are gong to be dscussng for much of the remander of the course s relatonshps between two or more varables.
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationTHE TITANIC SHIPWRECK: WHO WAS
THE TITANIC SHIPWRECK: WHO WAS MOST LIKELY TO SURVIVE? A STATISTICAL ANALYSIS Ths paper examnes the probablty of survvng the Ttanc shpwreck usng lmted dependent varable regresson analyss. Ths appled analyss
More informationTrade Adjustment and Productivity in Large Crises. Online Appendix May 2013. Appendix A: Derivation of Equations for Productivity
Trade Adjustment Productvty n Large Crses Gta Gopnath Department of Economcs Harvard Unversty NBER Brent Neman Booth School of Busness Unversty of Chcago NBER Onlne Appendx May 2013 Appendx A: Dervaton
More informationErrorPropagation.nb 1. Error Propagation
ErrorPropagaton.nb Error Propagaton Suppose that we make observatons of a quantty x that s subject to random fluctuatons or measurement errors. Our best estmate of the true value for ths quantty s then
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationTo manage leave, meeting institutional requirements and treating individual staff members fairly and consistently.
Corporate Polces & Procedures Human Resources  Document CPP216 Leave Management Frst Produced: Current Verson: Past Revsons: Revew Cycle: Apples From: 09/09/09 26/10/12 09/09/09 3 years Immedately Authorsaton:
More informationOn some special nonlevel annuities and yield rates for annuities
On some specal nonlevel annutes and yeld rates for annutes 1 Annutes wth payments n geometrc progresson 2 Annutes wth payments n Arthmetc Progresson 1 Annutes wth payments n geometrc progresson 2 Annutes
More informationSCALAR A physical quantity that is completely characterized by a real number (or by its numerical value) is called a scalar. In other words, a scalar
SCALAR A phscal quantt that s completel charactered b a real number (or b ts numercal value) s called a scalar. In other words, a scalar possesses onl a magntude. Mass, denst, volume, temperature, tme,
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationThe Analysis of Outliers in Statistical Data
THALES Project No. xxxx The Analyss of Outlers n Statstcal Data Research Team Chrysses Caron, Assocate Professor (P.I.) Vaslk Karot, Doctoral canddate Polychrons Economou, Chrstna Perrakou, Postgraduate
More informationwhere the coordinates are related to those in the old frame as follows.
Chapter 2  Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of noncoplanar vectors Scalar product
More informationSolution of Algebraic and Transcendental Equations
CHAPTER Soluton of Algerac and Transcendental Equatons. INTRODUCTION One of the most common prolem encountered n engneerng analyss s that gven a functon f (, fnd the values of for whch f ( = 0. The soluton
More information