RECENT DEVELOPMENTS IN QUANTITATIVE COMPARATIVE METHODOLOGY:


 Ashley Taylor
 3 years ago
 Views:
Transcription
1 Federco Podestà RECENT DEVELOPMENTS IN QUANTITATIVE COMPARATIVE METHODOLOGY: THE CASE OF POOLED TIME SERIES CROSSSECTION ANALYSIS DSS PAPERS SOC 302
2
3 INDICE 1. Advantages and Dsadvantages of Pooled Analyss... Pag The Estmaton Issue: GLS vs. OLS Tme and Space Effects Poolng Dlemma and Casual Heterogenety Pooled TSCS analyss n STATA software Bblography... 41
4 The frst draft of ths paper has been wrtten at McDonough School of Busness (Georgetown Unversty) n November For ths reason, I would lke to thank Professor Denns Qunn for the opportunty he allowed me.
5 Students of the poltcal economy have tended to nvestgate relatonshp between nsttutons and economc varables by comparng observatons across space or observatons over tme. Untl recently, the space and the tme domans have rarely been combnated n the comparatve research. However, new quanttatve methods stress senstvty to tme as well as space. Pooled tme seres crosssecton analyss (TSCS) s probably the most mportant way to examne smultaneously these dmensons. In ths paper, I wll try to descrbe the state of the art of ths approach dscussng frst the characterstcs of TSCS data and advantages and dsadvantages of ths statstcal technque (Secton 1). Hence, I wll dscuss man ssues that relate to the estmaton method (secton 2). After that, I wll address the most mportant problems that relate to the model specfcaton by concentratng frst on effects of the tme and the space (Secton 3), and then on the poolng dlemma and causal heterogenety ssue (Secton 4). Fnally, I wll present mplementatons and commands n STATA software to analyze TSCS data (Secton 5). Recent Developments n Quanttatve Comparatve Methodology 5
6 1. Advantages and Dsadvantages of Pooled Analyss Pooled analyss combnes tme seres for several crosssectons 1. Pooled data are characterzed by havng repeated observatons (most frequently years) on fxed unts (most frequently states and natons). Ths means that pooled arrays of data are one that combnes crosssectonal data on N spatal unts and T tme perods to produce a data set of N T observatons. Here, the typcal range of unts of analyzed would be about 20 (f we examne developed countres), wth each unt observed over a relatvely long tme perod, lke years. However, when the crosssecton unts are more numerous than temporal unts (N>T), the pool s often conceptualzed as a crosssectonal domnant. conversely, when the temporal unts are more numerous than spatal unts (T>N), the pool s called temporal domnant (Stmson 1985). Gven ths preamble, we can wrte the generc pooled lnear regresson model estmable by Ordnary Least Squares (OLS) procedure k 1 + β k k =2 y t = β xkt + et (1) Where = 1,2,.; N; refers to a crosssectonal unt; t = 1,2,.; T; refers to a tme perod and k = 1,2,.; K; refers to a specfc explanatory varable. Thus, y t and x t refer respectvely to dependent and ndependent varables for 1 Another name of pooled TSCS analyss s panel analyss, but t can be confused wth panel research n survey studes. 6 Recent Developments n Quanttatve Comparatve Methodology
7 unt and tme t; and e t s a random error and β 1 and β k refer, respectvely, to the ntercept and the slope parameters. 2 Moreover we can denote the NT NT varancecovarance matrx of the errors wth typcal element Ε e e t ) by Ω. ( js Estmatng ths knd of model and some of ts varants (see below), solves many problems of tradtonal methods of the comparatve research (.e. tme seres analyss and crosssectonal analyss). Several reasons support ths. The frst reason concerns the small N problem suffered by both tme seres and crosssectonal analyss. The lmted number of spatal unts and the lmted number of avalable data over tme led data sets of these two technques to volate basc assumpton of standard statstcal analyss. Most specfcally, the small sample of conventonal comparsons shows an mbalance between too many explanatory varables and too few cases. Consequently, wthn the contest of the small sample the total number of the potental explanatory varables exceeds the degree of freedom requred to model the relatonshp between the dependent and ndependent varables. In contrast, thanks to pooled TSCS desgns, we can greatly relax ths restrcton. Ths s because, wthn the pooled TSCS research, the cases are countryyear (NT observatons) startng from the country n year t, then country n year t+1 through country z n the last year of the perod under nvestgaton Ths allow us to test the mpact of a large number of predctors of the level and change n the dependent varable wthn the framework of a multvarate analyss (Schmdt 1997, 156). Second, pooled models have ganed popularty because they permt to nqury nto varables that elude study n smple crosssectonal or tme 2 I assume the dependent varable, y, s contnuous. In the case of bnary Recent Developments n Quanttatve Comparatve Methodology 7
8 seres. Ths s because ther varablty s neglgble, or not exstent, across ether tme or space. In practce, many characterstcs of natonal systems (or nsttutons) tend to be temporally nvarant. Therefore, regresson analyss of pooled data combnng space and tme may rely upon hgher varablty of data n respect to a smple tme seres or crosssecton desgn research (Hcks 1994, ). A thrd reason to support pooled TSCS analyss concerns the possblty to capture not only the varaton of what emerges through tme or space, but the varaton of these two dmensons smultaneously. Ths s because, nstead of testng a crosssecton model for all countres at one pont n tme or testng a tme seres model for one country usng tme seres data, a pooled model s tested for all countres through tme (Pennngs, Keman e Klennjenhus 1999, 172). Gven these advantages, n the last decade pooled analyss has became central n quanttatve studes of comparatve poltcal economy. Several authors have utlzed pooled models to answer to classcal questons of ths dscplne. An accumulatng body of research has used ths statstcal technque to test the man hypothess concernng the poltcal and nsttutonal determnants of macroeconomc polces and performances (Alvarez, Garrett, Lange 1991; Hcks 1991; Swank 1992). Most specfcally, regardng the study of publc polcy, we can cte emprcal works on poltcal and socoeconomc causes of the welfare state development (Pampel and Wllamson 1989; Huber Ragn and Stephen 1993; Schmdt 1997). Regardng research on both economc polces and performances, researchers have tred to verfy and characterze a dependent varable, see Beck et al. (1998). 8 Recent Developments n Quanttatve Comparatve Methodology
9 macroeconomc partsan strategy. In partcular, they have shown that, once n offce, dfferent partes attempt to manage the economc cycle usng the standard fscal and monetary nstruments. However, these same studes have dscovered that the ablty of partes to pursue ther most preferred macroeconomc strateges depends on nsttutonal structures of the domestc labor market (Comptson 1997; Oatley 1998), and ncreasngly nternatonalzed markets (Garrett 1998; Garrett and Mtchell 1999). Fnally, several authors have utlzed TSCS analyss to examne the mpact of poltcal and economc varables on the fnancal openness of domestc markets (Alesna et al. 1994; Qunn and Inclan 1997). Therefore, pooled TSCS analyss s an nalenable nstrument for the development of the comparatve poltcal economy. However, the popularty of ths statstcal technque does not depend only on ts applcaton n substantve research, but also recent papers dscussng methodologcal ssues that t mples (Stmson 1985; Hcks 1994; Beck and Katz 1995; 1996). In partcular, ths latter lterature s more numerous now because pooled TSCS desgns often volate the standard OLS assumptons about the error process. 3 In fact, the OLS regresson estmates, used by socal scentsts commonly to lnk potental causes and effects, are lkely to be based, neffcent and/or nconsstent when they are appled to pooled data. 4 Ths s because the errors for regresson 3 For OLS to be optmal t s necessary that all the errors have the same varance (homoschedastcty) and that all of the errors are ndependent of each other. 4 An unbased estmator s one that has a samplng dstrbuton wth a mean equal to the parameter to be estmated. An effcent estmator s one that has the smallest dsperson, (.e., one that one whose samplng dstrbutonhas the Recent Developments n Quanttatve Comparatve Methodology 9
10 equatons estmated from pooled data usng OLS procedure and pooled data tend to generate fve complcatons (Hcks 1994, ). Frst, errors tend to be no ndependent from a perod to the next. In other terms, they mght be serally correlated, such that errors n country at tme t are correlated wth errors n country at tme t+1. Ths s because observatons and trats that characterze them tend to be nterdependent across tme. For example, temporally successve values of many natonal trats (.e., populaton sze) tend not to be ndependent over tme. Second, the errors tend to be correlated across natons. They mght be contemporaneously correlated, such that errors n country at tme t are correlated wth errors n country j at tme t. As Hcks (1994, 174) notes, we could not expect errors n the statstcal model for Sweden to lack some resemblance to those for the Norway or errors for Canada and the Unted Stated to be altogether ndependent. Instead, we would expect dsturbances for such natons to be crosssectonally correlated. In ths way, errors n Scandnavan economes may be lnked together but reman ndependent wth errors of North Amercan countres. Thrd, errors tend to be heteroschesdastc, such that they may have dfferng varances across ranges or sub sets of natons. In other words, natons wth hgher values on varables tend to have less restrcted and, hence, hgher varances on them. For example, the Unted Stated tends to have more volatle as well as hgher unemployment rates than the Swtzerland. Ths means that the smallest varance). Fnally, an estmator s sad to be consstent f ts samplng dstrbuton tends to become concentrated on the true value of the parameter as sample sze ncreases to nfnte (Kmenta 1986,123). 10 Recent Developments n Quanttatve Comparatve Methodology
11 varance n employment rates wll tend to be greater for bgger natons wth large heterogeneous labor forces than for small, homogeneous natons (Hcks 1994, 172). Moreover, errors of a TSCS analyss may show heteroschesdastcty because the scale of the dependent varable, such as the level of government spendng, may dffer between countres (Beck and Katz 1995, 636). Fourth, errors may contan both temporal and crosssectonal components reflectng crosssectonal effects and temporal effects. Errors tend to conceal unt and perod effects. In other words, even f we start wth data that were homoschedastc and not autocorrelated, we rsk producng a regresson wth observed heteroschestastc and autocorrelated errors. Ths s because heteroschedastcy and autocorrelaton we observe s a functon also of model msspecfcaton. The msspecfcaton, that s pecular of pooled data, s the assumpton of homogenety of level of dependent varable across unts and tme perods. In partcular, f we assume that unts and tme perods are homogeneous n the level (as OLS estmaton requres) and they are not, then least squares estmators wll be a compromse, unlkely to be a good predctor of the tme perods and the crosssectonal unts, and the apparent level of heteroschedastcty and autocorrelaton wll be substantally nflated (Stmson 1985, 919). Ffth, errors mght be nonrandom across spatal and/or temporal unts because parameters are heterogeneous across subsets of unts. In other words, snce processes lnkng dependent and ndependent varables tend to vary across subsets of natons or/and perod, errors tend to reflect some causal heterogenety across space, tme, or both (Hcks 1994, 172). Therefore, ths Recent Developments n Quanttatve Comparatve Methodology 11
12 complcaton, lke the prevous one, could be nterpreted as a functon of msspecfcaton. If we estmate constantcoeffcents models, we cannot capture the causal heterogenety across tme and space. In the last decade, several models have been developed to deal wth these complcatons and dfferent solutons have been jonted because problems usually do not appear alone. However, for reasons of the clearness, I wll present the dfferent models tryng to separate varous solutons utlzed to deal wth sngle problems. In the next secton, I wll dscuss ParksKmenta method and Beck and Katz s (1995; 1996) proposal. They represent two dfferent approaches to tackle the complcatons of seral correlaton, contemporaneous correlaton and heteroschedastcty (respectvely problem 1, 2 and 3). After that, I wll address specfcaton problems by dstngushng between the ssue of tme and space effects (problem 4) and causal heterogenety (problem 5). 12 Recent Developments n Quanttatve Comparatve Methodology
13 2. The Estmaton Issue: GLS vs. OLS ParksKmenta method has been the most utlzed approach for TSCS analyss n comparatve poltcal economy untl the mdnnetes (see for example, Pampel and Wllamson 1989; Alvarez, Garrett, Lange 1991; Hcks 1991; Swank 1992; Huber, Ragn, and Stephen 1993). Nevertheless, from those years, when the two papers of Beck and Katz (1995; 1996) suggested an alternatve approach to the ParksKmenta method, ths latter proposal has probably became the one most utlzed by socologsts and poltcal scentsts (see for example, Qunn and Inclan 1997; Oatley 1998; Garrett 1998; Garrett and Mtchell 1999). Accordng to an hstorcal reason, let me start by dscussng the Parks Kmenta method. Ths method frst elaborated by Parks (1967) and then dscussed by Kmenta (1971; 1986) (here referred to as ParksKmenta method) uses an applcaton of the generalzed least squares (GLS) estmaton. The regresson equaton for ths method may be wrtten n the same form of the equaton 1: k 1 + β k k =2 y t = β xkt + et (2) Thus, t s an equaton where a sngle ntercept and slope coeffcent are constant across unts and tme ponts. However, accordng to ParksKmenta method, ths equaton must be estmated by GLS because ths estmaton procedure s based on less restrctve assumptons concernng the behavor of Recent Developments n Quanttatve Comparatve Methodology 13
14 regresson dsturbance and, thus, concernng the varancecovarance matrx, Ω, than the classcal regresson model (Kmenta 1986, 607). Therefore, the GLS estmaton has a specal nterest n connecton wth tme seres and crosssecton observatons. Regardng the problem of estmatng parameters β of the generalzed lnear regresson model, we can wrte the followng expresson: ' 1 1 ' 1 ( x Ω x) x Ω y (2.1) Ths estmaton s based on the assumpton that the varancecovarance matrx of the errors, Ω, s known. However, snce n many cases the varancecovarance matrx s unknown, we cannot use GLS but feasble generalzed least squares (FGLS). It s feasble because t uses an estmate of varancecovarance matrx, avodng the GLS assumpton that Ω s known. Consequently, we need to fnd a consstent estmate of Ω, say, Ω ), to substtute Ω ) for Ω n the formula to get a coeffcent estmator β (Kmenta 1986, 615). Thus we denote the FGLS estmates of β by β ). Let me now consder the problem of error complcatons. The Parks Kmenta method combnes the assumptons concernng seral correlaton, contemporaneous correlaton and panel heteroschedastcty of errors. The partcular characterzaton of these assumptons are (Kmenta 1986, 622): 2 t Ε ( e ) = σ (2.2) Ε ( e ) = σ (2.3) t e jt j 14 Recent Developments n Quanttatve Comparatve Methodology
15 e t = ρ e 1 + ν (2.4) t t In the other words, ths approach deals wth errors complcatons by specfyng respectvely a model for heteroschedastcty (equaton 2.2), a model for contemporaneous correlaton (equaton 2.3), and a model for seral correlaton so called AR(1) (I.e., frstorder autoregressve model), where ρ s a coeffcents of frstorder autoregressveness. In ths model we allow the value of the parameter another(equaton 2.4). ρ to vary from one crosssecton unt to 2 We now need to fnd consstent estmators of ρ and σ (.e., elements of the varancecovarance matrx of the errors). Accordng to ths am, Parks Kmenta method conssts of two sequental FGLS transformatons. Frst, t elmnates seral correlaton of the errors then t elmnates contemporaneous correlaton of the errors. 5 Ths s done by ntally estmatng equaton 2 by OLS. The resduals from ths estmaton are used to estmate the untspecfc seral correcton of the errors, whch are then used to transform the model nto one wth serally ndependent errors. Resduals from ths estmaton are then used to estmate the contemporaneous correlaton of the errors, and the data s once agan transformed to allow for the OLS estmaton wth now errors wthout any complcatons. 5 As Beck and Katz (1995, 637) note, accordng to ParksKmenta method the correcton for the contemporaneous correlaton of the errors automatcally corrects for any panel heteroschedastcty. Consequently we need only consder correctons for contemporaneous correlaton and seral correlaton of errors. Recent Developments n Quanttatve Comparatve Methodology 15
16 2 Havng obtaned consstent estmators of ρ and σ, we have completed the task of dervng consstent estmators of elements of the Ω. Hence, by substtutng Ω ) for Ω, we can obtan desred estmates of coeffcents and of ther standard errors (Kmenta 1986, 620). From ths pont Beck and Katz revew the ParksKmenta method. They (1995, 694) clam that, whle GLS are optmal propretes for TSCS data, the really appled FGLS does not do the same. Ths s because, although FGLS uses an estmate of the error process, the FGLS formula for standard errors assumes that the varancecovarance matrx of the errors s known, not estmated. Ths s a problem for TSCS models because the error process has a large number of parameters. Ths oversght causes estmates of standard errors of the estmated coeffcents to understate ther true varablty. In partcular, Beck and Katz show that the overconfdence n the standard errors makes the ParksKmenta method unusable unless where there are more tme ponts than there are crosssecton unts. In other words, t he problem of the ParksKmenta method s most evdent for the types of TSCS data typcally analyzed by poltcal scentsts and socologsts. Here, Beck and Katz propose to use a less complex method. Ths because t s well known that even though OLS estmates of TSCS model parameters may not be optmal, they often perform well n practcal research stuatons. If the errors meet one of more of the TSCS error assumptons, the OLS estmates of β wll be consstent but neffcent. Moreover, t s well known that the OLS estmates of the standard errors may be hghly naccurate n such stuatons. Consequently, Beck and Katz propose to retan OLS parameter estmators but replace OLS standard errors wth panelcorrected standard errors (PCSEs) that 16 Recent Developments n Quanttatve Comparatve Methodology
17 take nto account the contemporaneous correlaton of the errors and perforce heteroschedastcty. 6 However, any seral correlaton of the errors must be elmnated before PCSEs are calculated. Seral correlaton may be modeled by ncludng a lagged dependent varable n the set of ndependent varables or corrected by estmatng a model for autoregressveness as proposed by Parks Kmenta method. Beck et al. (1993, 946) revew ths latter soluton. Ths s because t s hart to see why the parameters of the equaton 2 should be constant across crosssecton unts, whle the nusance seral correlaton parameters should vary from unt to unt. In a recent paper, Beck and Katz (1996) argue that seeng the seral correlaton as a nusance that obscures the true relatonshp and transformng the data to remove seral correlaton, many approaches to pooled TSCS data analyss can be msleadng. In other words, they argue that overtme persstence n the data consttutes substantve nformaton that should be ncorporated n the model. Therefore, they argue that t s best model dynamcs va a lagged dependent varable rather than va seral correlaton errors. Incorporatng a lagged value of the dependent varable on the rght hand sde of the equaton yelds an explct estmate of the extent of stckness or persstence n the dependent varable. Ths allows us to stay closer to the orgnal data than transformed data would. Consequently, we can develop the equaton 1 n the followng form: 6 Beck and Katz (1995, 634) argue that snce s not possble to provde analytcal formula for the degree of overconfdence ntroduced by the Parks Kmenta method, they provde evdences from Monte Carlo experments usng smulated data. At the same tme, by usng Monte Carlo analyss they show that OLS wth PCSEs allow for accurate estmaton of varablty n the presence n the presence of the TSCS errors structures Recent Developments n Quanttatve Comparatve Methodology 17
18 k 1 + β 2 y t 1+ β k k = 3 y t = β xkt + et (3) Where y t 1 stands for the frst lag of the dependent varable and β 2 stands for ts slope coeffcent. Once the dynamcs are accounted for, TSCS analysts can estmate model parameters by OLS and ther standard errors by PCSEs n order to take nto account contemporaneous correlaton of the errors and heteroschedastcty. The correct formula for the samplng varablty of OLS estmates s gven by the roots of the dagonal term of the followng expresson (Beck and Katz 1995, 638): ' 1 ' ' 1 Cov( β v ) = ( x x) ( x Ωx)( x x) (3.1) The mddle term of ths equaton contans the correcton for the panel data. Under the condtons that the resduals are contemporaneously correlated and heteroschedastc, the matrx of covarance of the errors Ω s an NT NT block dagonal matrx wth an N N matrx of the contemporaneous covarance, Θ along the dagonal. Thus, to estmate equaton 3.1 we need a consstent estmate of Θ. Snce the OLS estmates of the equaton 1 are consstent, we can use OLS resduals from that estmaton to provde a consstent estmate of Θ. The dea of usng OLS wth PCSEs s fne and smple and has been known to have numerous applcatons n comparatve poltcal economy. However, as Maddala (1997, 3) argues, Beck and Katz s prescrptons are not, strctly 18 Recent Developments n Quanttatve Comparatve Methodology
19 speakng, correct. They suggest OLS estmaton wth panel corrected covarance matrx estmaton, as suggested n ther earler paper (Beck and Katz 1995) for a model wth no lagged dependent varables. Wth lagged dependent varables, t s well known that OLS estmators are nconsstent n the presence of seral correlaton n errors. Thus the problem s not merely gettng the correct standard errors but also to get consstent estmates of the parameters. In other words, the soluton offered by Beck and Katz can be categorzed n the what not to do f there are lagged dependent varables. Accordng to Maddala ther crtcsm of the ParksKmenta method s vald but not ther suggested soluton. Therefore, although the BeckKatz approach has been heavly appled n comparatve research, the estmaton debate could not be conclusve yet. However, snce BeckKatz argument addresses the problem of standard error nflaton and, hence, to avod callng somethng sgnfcant when t mght not be, let me now dscuss the nference ssue n comparatve research. Tests of statstcal sgnfcance are generally used n regresson analyss to evaluate the relablty of estmaton results. These tests calculate the probablty that a random sample n whch the regresson coeffcents are as estmated could be drawn from a parent populaton n whch the regresson coeffcent was zero. However, for TSCS data sets,used n comparatve research, the countres and years under nvestgaton are not a representatve sample of a larger populaton of countres and years. They are the populaton. Ths means that regresson estmate of the populaton regresson s a coeffcent of tself. Therefore, once we have carry out the regresson therefore we know whether the populaton parameter s zero (or not) wthout the need for recourse Recent Developments n Quanttatve Comparatve Methodology 19
20 to probablty theory (Comptson 1997, 7412). Nevertheless, as Western and Jackman (1994, 4123) suggest, we can adopt a Bayesan approach of statstcal nference rather than the conventonal statstcal nference to address ths problem. In fact, the comparatve researchers dscomfort wth frequentstc nference s well founded because s not applcable to a no stochastc settng. It s smply rrelevant for ths problem to thnk of observatons as drawn from a random process when further realzatons are mpossble n practce, and lack meanng even as abstract propostons. In contrast, the Bayesan model of the statstcal nference s a vald soluton to ths problem of the comparatve research. Ths s because the probablty s conceved subjectvely as characterzng a researcher s uncertanty about the parameters of statstcal model rather than a fact characterzng an object n the external world. Consequently, for the Bayesan approach t s not relevant that data are not generated by a repeatable mechansm such as con flp. 20 Recent Developments n Quanttatve Comparatve Methodology
21 3. Tme and Space Effects As we argued above, error complcatons can be also caused by model msspecfcatons. If we assume that the level of the dependent varable s homogeneous across tme perods and unts, we rsk that error contans both temporal and crosssecton components reflectng, respectvely, tme effects and crosssecton effects. In partcular, f dfferent tme perods and crosssecton are consstently hgher or lower on the dependent varable, the common ntercept β 1 estmated n OLS regresson wll be a average of all tme perod and unts that may not be representatve for any one of the sngle groups of observatons. To deal wth ths problem, we can use ether the covarance model or the error component model. Both these models use a varyng ntercept term n order to capture the dfferences n behavor over tme and space (Judge et al. 1985, 519). Consequently, for both models, we can wrte the followng equaton: k t = 1 + µ + λt ) + k =2 y ( β β x + e (4) k kt t Wth ntercept β + 1 t = β 1 + µ λt. Where 1 β s the mean ntercept, µ represents the unt effects and λ t represents tme effects. However, f we are nterested n stable dfference across crosssecton unts only, we use the µ term and drop the λ t from the equaton. Alternatvely, f we are nterested n change over tme only, we use λ t and drop the µ term from the equaton. Recent Developments n Quanttatve Comparatve Methodology 21
22 If the term µ and λ t are fxed, the equaton 4 s a covarance model (or a dummy varable model). Conversely, when they are random, t s an error component model. In other words, n the case of covarance model, the specfc characterstc of a crosssecton unts and of a tme perod are parameters; but, usng error component model the specfc characterstc of a crosssecton unts and of a tme perod are normally dstrbuted random varables. Thus, n the statstcal lterature, the error component model s kwon as a random effect model, and the covarance model s referred to as a fxed effect model. The reasonng underlyng the covarance model s that n specfyng the regresson model we have faled to nclude relevant explanatory varables that do not change over tme and/or others that do not change across crosssecton unts, and hence the ncluson of dummy varables s a coverup of our gnorance (Kmenta 1986, 633). Conversely, the reasonng underlyng the error component model s that the relevant explanatory varables that we have omtted random varables and, thus, µ and/or λ t are drawn from a normal dstrbuton. Regardng the covarance model as one wth a varyng ntercept appears reasonable because we address the unt and/or the perod effects through the ad hoc addton of dummy varables for crosssecton unts and/or tme perods. On the other hand, regardng error component model as one wth a varyng ntercept could appear arbtrary (Judge et al 1985, 522). In fact, t could also be vewed as one where all coeffcents are constant and the regresson dsturbances are composed by three ndependent models (one component assocated wth the tme, one component assocated wth the space and the thrd assocated wth both dmensons) (Kmenta 1986, 633). Consequently, for the 22 Recent Developments n Quanttatve Comparatve Methodology
23 error component model we can reparameterze the equaton 4 n the followng form: k 1 + β k k =2 y t = β xkt + e t t (4.1) Where et = µ + λt + ω t and µ are random over crosssecton, λ t are random over tme and ω t are random over space and tme. The three components, µ, λ t, and ω t are normally dstrbuted and each has propertes lke those assumed for OLS regresson. Each component also has a constant error varance such that the varance for the summary error e t s constant, or homoschedastc. Thus, ths model cannot deal wth the heteroschedatc error complcaton (Hcks 1994, 177). Moreover, each component s also free of autocorrelaton. However, despte to ths apparent neglect of problem of autoregressveness, a coeffcent of correlaton between of a gven crosssecton unt at two dfferent pont of tme (between e t and e s ) s mpled by the formulaton of ths model At the same tme, the error component model address the contemporaneous correlaton of the error by ncludng a coeffcent of correlaton between the dsturbance of two dfferent crosssectonal unts at a gven pont of tme (between e t and e s ) (Kmenta 1986, ). Therefore, usng ths knd of unrestrctve assumpton concernng the dsturbance, the most approprate estmaton procedure for the error component model s the GLS (and most specfcally FGLS) method recommended by ParksKmenta approach. In contrast, the alternatve method prescrbng the Recent Developments n Quanttatve Comparatve Methodology 23
24 OLS wth PCSEs s not especally approprate for the error component model. In fact, gven that the error component model s heavly used n crosssectonal domnant data set, Beck and Katz (1995, 645) do not consder ths model. Ther proposal s lmted to temporally domnant models. Alternatvely, for the covarance model, we can use ether BeckKatz approach or ParksKmenta method. In ths case the dsturbance e t s supposed to satsfy the assumpton of the classcal lnear regresson model. Moreover, as Beck and Katz (1995, 645) note, ths model presents no specal problems, especally when t s utlzed n a temporally domnant model and t s allowed ntercepts to vary by unt only. Ths s because the number of untspecfc dummy varables requred s not large and, thus, the fxed effects do not use an absurd number of degree of freedom. However, we could allow e t to be autoregressve and heteroschedastc, and then use the GLS (FGLS) estmaton procedure for a covarance model (Kmenta 1986, 630). In other words, the ParksKmenta method can be made to address the unt and perod effects through the ad hoc addton of dummy varables for crosssecton unts, tme perods, or both (Hcks 1994, 175). Fnally, let me brefly dscuss the problem of the choce between these models. Snce assumng unt and/or tme perod effects to be fxed or random s not obvous, the estmaton procedure could not be chosen accordngly (Judge et al.1985, 527). For example, consder a research where the dependent varable, n addtonal to explanatory varables, s affected by a varable whch vares across unts yet remans constant over tme (as usually happens n poltcal economy research). Here, the nference concernng coeffcents of relevant explanatory varables could be uncondtonal wth the respect to other 24 Recent Developments n Quanttatve Comparatve Methodology
Can 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 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 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 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 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 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 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 informationInternational University of Japan Public Management & Policy Analysis Program
Internatonal Unversty of Japan Publc Management & Polcy Analyss Program Practcal Gudes To Panel Data Modelng: A Step by Step Analyss Usng Stata * Hun Myoung Park, Ph.D. kucc65@uj.ac.jp 1. Introducton.
More informationThe Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15
The Analyss of Covarance ERSH 830 Keppel and Wckens Chapter 5 Today s Class Intal Consderatons Covarance and Lnear Regresson The Lnear Regresson Equaton TheAnalyss of Covarance Assumptons Underlyng the
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 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 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 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 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 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 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 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 informationAn 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 informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More informationExhaustive Regression. An Exploration of RegressionBased Data Mining Techniques Using Super Computation
Exhaustve Regresson An Exploraton of RegressonBased Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The
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 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 informationStatistical Methods to Develop Rating Models
Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, 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 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 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 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 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 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 informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationDiagnostic Tests of Cross Section Independence for Nonlinear Panel Data Models
DISCUSSION PAPER SERIES IZA DP No. 2756 Dagnostc ests of Cross Secton Independence for Nonlnear Panel Data Models Cheng Hsao M. Hashem Pesaran Andreas Pck Aprl 2007 Forschungsnsttut zur Zukunft der Arbet
More informationH 1 : at least one is not zero
Chapter 6 More Multple Regresson Model The Ftest Jont Hypothess Tests Consder the lnear regresson equaton: () y = β + βx + βx + β4x4 + e for =,,..., N The tstatstc gve a test of sgnfcance of an ndvdual
More informationLatent Class Regression. Statistics for Psychosocial Research II: Structural Models December 4 and 6, 2006
Latent Class Regresson Statstcs for Psychosocal Research II: Structural Models December 4 and 6, 2006 Latent Class Regresson (LCR) What s t and when do we use t? Recall the standard latent class model
More informationA Probabilistic Theory of Coherence
A Probablstc Theory of Coherence BRANDEN FITELSON. The Coherence Measure C Let E be a set of n propostons E,..., E n. We seek a probablstc measure C(E) of the degree of coherence of E. Intutvely, we want
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 informationCHAPTER 7 THE TWOVARIABLE REGRESSION MODEL: HYPOTHESIS TESTING
CHAPTER 7 THE TWOVARIABLE REGRESSION MODEL: HYPOTHESIS TESTING QUESTIONS 7.1. (a) In the regresson contet, the method of least squares estmates the regresson parameters n such a way that the sum of the
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 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 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 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 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 informationThe Current Employment Statistics (CES) survey,
Busness Brths and Deaths Impact of busness brths and deaths n the payroll survey The CES probabltybased sample redesgn accounts for most busness brth employment through the mputaton of busness deaths,
More informationLecture 10: Linear Regression Approach, Assumptions and Diagnostics
Approach to Modelng I Lecture 1: Lnear Regresson Approach, Assumptons and Dagnostcs Sandy Eckel seckel@jhsph.edu 8 May 8 General approach for most statstcal modelng: Defne the populaton of nterest State
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 informationCriminal Justice System on Crime *
On the Impact of the NSW Crmnal Justce System on Crme * Dr Vasls Sarafds, Dscplne of Operatons Management and Econometrcs Unversty of Sydney * Ths presentaton s based on jont work wth Rchard Kelaher 1
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 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 informationAn Empirical Study of Search Engine Advertising Effectiveness
An Emprcal Study of Search Engne Advertsng Effectveness Sanjog Msra, Smon School of Busness Unversty of Rochester Edeal Pnker, Smon School of Busness Unversty of Rochester Alan RmmKaufman, RmmKaufman
More informationEvaluating credit risk models: A critique and a new proposal
Evaluatng credt rsk models: A crtque and a new proposal Hergen Frerchs* Gunter Löffler Unversty of Frankfurt (Man) February 14, 2001 Abstract Evaluatng the qualty of credt portfolo rsk models s an mportant
More informationTime Series Analysis in Studies of AGN Variability. Bradley M. Peterson The Ohio State University
Tme Seres Analyss n Studes of AGN Varablty Bradley M. Peterson The Oho State Unversty 1 Lnear Correlaton Degree to whch two parameters are lnearly correlated can be expressed n terms of the lnear correlaton
More informationAnalysis of Covariance
Chapter 551 Analyss of Covarance Introducton A common tas n research s to compare the averages of two or more populatons (groups). We mght want to compare the ncome level of two regons, the ntrogen content
More informationPrediction of Disability Frequencies in Life Insurance
Predcton of Dsablty Frequences n Lfe Insurance Bernhard Köng Fran Weber Maro V. Wüthrch October 28, 2011 Abstract For the predcton of dsablty frequences, not only the observed, but also the ncurred but
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 informationRiskbased Fatigue Estimate of Deep Water Risers  Course Project for EM388F: Fracture Mechanics, Spring 2008
Rskbased Fatgue Estmate of Deep Water Rsers  Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
More informationPrediction of Disability Frequencies in Life Insurance
1 Predcton of Dsablty Frequences n Lfe Insurance Bernhard Köng 1, Fran Weber 1, Maro V. Wüthrch 2 Abstract: For the predcton of dsablty frequences, not only the observed, but also the ncurred but not yet
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 informationChapter XX More advanced approaches to the analysis of survey data. Gad Nathan Hebrew University Jerusalem, Israel. Abstract
Household Sample Surveys n Developng and Transton Countres Chapter More advanced approaches to the analyss of survey data Gad Nathan Hebrew Unversty Jerusalem, Israel Abstract In the present chapter, we
More informationThe Probit Model. Alexander Spermann. SoSe 2009
The Probt Model Aleander Spermann Unversty of Freburg SoSe 009 Course outlne. Notaton and statstcal foundatons. Introducton to the Probt model 3. Applcaton 4. Coeffcents and margnal effects 5. Goodnessofft
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 informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationTraditional versus Online Courses, Efforts, and Learning Performance
Tradtonal versus Onlne Courses, Efforts, and Learnng Performance KuangCheng Tseng, Department of Internatonal Trade, ChungYuan Chrstan Unversty, Tawan ShanYng Chu, Department of Internatonal Trade,
More informationEconomic Interpretation of Regression. Theory and Applications
Economc Interpretaton of Regresson Theor and Applcatons Classcal and Baesan Econometrc Methods Applcaton of mathematcal statstcs to economc data for emprcal support Economc theor postulates a qualtatve
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 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 informationThe Application of Fractional Brownian Motion in Option Pricing
Vol. 0, No. (05), pp. 738 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qngxn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com
More informationx f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60
BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true
More informationMarginal Benefit Incidence Analysis Using a Single Crosssection of Data. Mohamed Ihsan Ajwad and Quentin Wodon 1. World Bank.
Margnal Beneft Incdence Analyss Usng a Sngle Crosssecton of Data Mohamed Ihsan Ajwad and uentn Wodon World Bank August 200 Abstract In a recent paper, Lanjouw and Ravallon proposed an attractve and smple
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 informationAn Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services
An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsnyng Wu b a Professor (Management Scence), Natonal Chao
More informationOn the correct model specification for estimating the structure of a currency basket
On the correct model specfcaton for estmatng the structure of a currency basket JyhDean Hwang Department of Internatonal Busness Natonal Tawan Unversty 85 Roosevelt Road Sect. 4, Tape 106, Tawan jdhwang@ntu.edu.tw
More informationProject Networks With MixedTime Constraints
Project Networs Wth MxedTme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σalgebra: a set
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 informationPortfolio Loss Distribution
Portfolo Loss Dstrbuton Rsky assets n loan ortfolo hghly llqud assets holdtomaturty n the bank s balance sheet Outstandngs The orton of the bank asset that has already been extended to borrowers. Commtment
More informationThe Racial and Gender Interest Rate Gap. in Small Business Lending: Improved Estimates Using Matching Methods*
The Racal and Gender Interest Rate Gap n Small Busness Lendng: Improved Estmates Usng Matchng Methods* Yue Hu and Long Lu Department of Economcs Unversty of Texas at San Antono Jan Ondrch and John Ynger
More informationSensitivity Analysis in a Generic MultiAttribute Decision Support System
Senstvty Analyss n a Generc MultAttrbute Decson Support System Sxto RíosInsua, Antono Jménez and Alfonso Mateos Department of Artfcal Intellgence, Madrd Techncal Unversty Campus de Montegancedo s/n,
More informationEstimation and Robustness of Linear Mixed Models in Credibility Context
Estmaton and Robustness of Lnear Mxed Models n Credblty Context by Wng Kam Fung and Xao Chen Xu ABSTRACT In ths paper, lnear mxed models are employed for estmaton of structural parameters n credblty context.
More informationThe impact of hard discount control mechanism on the discount volatility of UK closedend funds
Investment Management and Fnancal Innovatons, Volume 10, Issue 3, 2013 Ahmed F. Salhn (Egypt) The mpact of hard dscount control mechansm on the dscount volatlty of UK closedend funds Abstract The mpact
More informationIs There A Tradeoff between EmployerProvided Health Insurance and Wages?
Is There A Tradeoff between EmployerProvded Health Insurance and Wages? Lye Zhu, Southern Methodst Unversty October 2005 Abstract Though most of the lterature n health nsurance and the labor market assumes
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 informationBERNSTEIN POLYNOMIALS
OnLne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful
More informationRegression Models for a Binary Response Using EXCEL and JMP
SEMATECH 997 Statstcal Methods Symposum Austn Regresson Models for a Bnary Response Usng EXCEL and JMP Davd C. Trndade, Ph.D. STATTECH Consultng and Tranng n Appled Statstcs San Jose, CA Topcs Practcal
More informationControl Charts for Means (Simulation)
Chapter 290 Control Charts for Means (Smulaton) Introducton Ths procedure allows you to study the run length dstrbuton of Shewhart (Xbar), Cusum, FIR Cusum, and EWMA process control charts for means usng
More informationECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management
ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C Whte Emerson Process Management Abstract Energy prces have exhbted sgnfcant volatlty n recent years. For example, natural gas prces
More informationNuno Vasconcelos UCSD
Bayesan parameter estmaton Nuno Vasconcelos UCSD 1 Maxmum lkelhood parameter estmaton n three steps: 1 choose a parametrc model for probabltes to make ths clear we denote the vector of parameters by Θ
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 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 informationPRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB.
PRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB. INDEX 1. Load data usng the Edtor wndow and mfle 2. Learnng to save results from the Edtor wndow. 3. Computng the Sharpe Rato 4. Obtanng the Treynor Rato
More informationStatistical algorithms in Review Manager 5
Statstcal algorthms n Reve Manager 5 Jonathan J Deeks and Julan PT Hggns on behalf of the Statstcal Methods Group of The Cochrane Collaboraton August 00 Data structure Consder a metaanalyss of k studes
More informationTHE DETERMINANTS OF THE TUNISIAN BANKING INDUSTRY PROFITABILITY: PANEL EVIDENCE
THE DETERMINANTS OF THE TUNISIAN BANKING INDUSTRY PROFITABILITY: PANEL EVIDENCE Samy Ben Naceur ERF Research Fellow Department of Fnance Unversté Lbre de Tuns Avenue Khéreddne Pacha, 002 Tuns Emal : sbennaceur@eudoramal.com
More informationPRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION
PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIIOUS AFFILIATION AND PARTICIPATION Danny CohenZada Department of Economcs, Benuron Unversty, BeerSheva 84105, Israel Wllam Sander Department of Economcs, DePaul
More informationForecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network
700 Proceedngs of the 8th Internatonal Conference on Innovaton & Management Forecastng the Demand of Emergency Supples: Based on the CBR Theory and BP Neural Network Fu Deqang, Lu Yun, L Changbng School
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 informationAbstract. 260 Business Intelligence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING
260 Busness Intellgence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING Murphy Choy Mchelle L.F. Cheong School of Informaton Systems, Sngapore
More informationThe Effects of Tax Rate Changes on Tax Bases and the Marginal Cost of Public Funds for Canadian Provincial Governments
The Effects of Tax Rate Changes on Tax Bases and the Margnal Cost of Publc Funds for Canadan Provncal Governments Bev Dahlby a and Ergete Ferede b a Department of Economcs, Unversty of Alberta, Edmonton,
More informationThe program for the Bachelor degrees shall extend over three years of fulltime study or the parttime equivalent.
Bachel of Commerce Bachel of Commerce (Accountng) Bachel of Commerce (Cpate Fnance) Bachel of Commerce (Internatonal Busness) Bachel of Commerce (Management) Bachel of Commerce (Marketng) These Program
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More informationSingle and multiple stage classifiers implementing logistic discrimination
Sngle and multple stage classfers mplementng logstc dscrmnaton Hélo Radke Bttencourt 1 Dens Alter de Olvera Moraes 2 Vctor Haertel 2 1 Pontfíca Unversdade Católca do Ro Grande do Sul  PUCRS Av. Ipranga,
More informationL10: Linear discriminants analysis
L0: Lnear dscrmnants analyss Lnear dscrmnant analyss, two classes Lnear dscrmnant analyss, C classes LDA vs. PCA Lmtatons of LDA Varants of LDA Other dmensonalty reducton methods CSCE 666 Pattern Analyss
More information