ABSTRACT

Transcription

1 Asymmetrc Causalty and Asymmetrc Contegraton between Income and House Prces n the Unted States of Amerca Mohsen Bahman-Oskooee and Seyed Hesam Ghods* The Center for Research on Internatonal Economcs and Department of Economcs The Unversty of Wsconsn-Mlwaukee bahman@uwm.edu sghods@uwm.edu ABSTRACT When the U.S. house prces were rsng before the Fnancal Crss of 2008, Case and Shller (2003) argued that ncome growth alone explans the pattern of recent home prce ncreases n most states. Can then the declne n ncome after 2008 explan the burst and abnormal decrease n house prces? Alternatvely we ask whether the effects of ncome on house prces are symmetrc or asymmetrc. We employ quarterly data from each of the states n the U.S. and nonlnear modellng approach of Shn et al. (2014) to show that ndeed, household ncome changes do have asymmetrc effects on house prces n most of the states n the U.S. Whle adjustment asymmetry s borne out by the results n all states, short-run mpact asymmetry s evdenced n 18 states and sgnfcant long-run asymmetry n 21 states. JEL Classfcaton: R13 Key words: House Prces, Household ncome, Asymmetry, Approach. *. Valuable comments of an anonymous referee and those of the edtor are greatly apprecated. Any remanng error, however, s our own responsblty. 1

2 I. Introducton Over the last three decades housng market n the U.S. has been subject to abnormal fluctuatons. However, house prces n dfferent states have fluctuated dfferently to changes n overall economc condtons n the Unted States. Whle many factors such as household ncome, nterest rates, stock prces, constructon costs, housng completons, and a measure of polcy uncertanty are sad to determne the house prces, Case and Shller (2003, p. 300) argue that ncome growth alone explans the pattern of recent home prce ncreases n most states. If ncrease n ncome caused house prces to rse pror to 2003, the perod whch was consdered by Case and Shller, dd declne n ncome cause house prces to drop durng post 2008? Furthermore, f the answer s n the affrmatve, dd ncome changes cause house prces symmetrcally or asymmetrcally? Recent studes such as Chen and Patel (1998), Galln (2006), Chen et al. (2007), McQunn and O Relly (2008), Holmes and Grmes (2008), Km and Bhattacharya (2009), Holly et al. (2011), Abbott and De Vta (2012 and 2013), and Katraklds and Tranchanas (2012) have nvestgated short-run causalty or long-run relatonshp between house prces and ncome or some other varables n dfferent countres. 1 Whle none of these studes have consdered asymmetry short-run causalty, Katraklds and Tranchanas (2012) consdered asymmetry contegraton to nvestgate housng prce dynamcs n only Greece. Whle our approach wll be smlar to Katraklds and Tranchanas (2012), we wll modfy ther approach so that we can also nvestgate the short-run asymmetry causalty and engage n perhaps, the most comprehensve study that uses data from each of the 52 states of the Unted States of Amerca. To ths end, we ntroduce the 1 Old lterature s revewed by Malpezz (1999). For detaled revew of recent lterature see Bahman-Oskooee and Ghods (2016). 2

3 model and the method n Secton II. The results are then reported and dscussed n Secton III and a concludng summary s provded n Secton IV. Data defnton and sources are cted n the Appendx. II. The Model and Methods Followng the lterature we begn wth a log-lnear relaton between house prces (HP) and household ncome (HI) as follows: 2 LnHPt a blnhi t t (1) Specfcaton (1) mples that household ncome determnes house prces n the long run. But, do changes n house hold ncome cause house prces to change n the short run? Granger (1969) ntroduced concept of Granger causalty by demonstratng that HI causes HP f after allowng for past hstory of the dependent varable (HP) current and past values of HI are jontly sgnfcant. The concept s appled only to statonary varables and snce most of the tme seres varables are non-statonary, ther frst-dfferences are used n applyng Granger causalty test as below: LnHP t n1 1 LnHP t n2 0 LnHI t t (2) In (2), household ncome s sad to cause house prces f 0 and ths could be establshed ether by the F or Wald test. However, later n 1987 Engle and Granger (1987) argued and demonstrated that f the two varables are adjustng n the short-run n a stable manner, we must make sure they are also convergng toward ther long-run equlbrum values. If ths s to be the 2 Some other studes have assessed the mpact of other varables on house prces wthout engagng n asymmetry causalty detecton. Snce our man goal s to nvestgate asymmetrc causalty between ncome and hose prces, followng Granger (1969) we restrct ourselves to a bvarate model. Example of studes that have ncluded other varables wthout causalty detecton are: Mkhed and Zemck (2007), Chen at al. (2007), Hatzus (2008), Wheaton and Nechayev (2009), Campbell et al. (2011), and Bahman-Oskooee and Ghods (2016). 3

4 case, the gap between two sdes of (1) must declne n ths process. Ths s tested by ncludng lagged error term from (1) nto (2) as follows: LnHP t n1 1 LnHP t n2 0 LnHI t t1 t (3) Specfcaton (3) s called an error-correcton model n whch f adjustment s to be toward longrun, estmate of λ must be negatve and sgnfcant. Three ponts related to equatons 1-3 deserve menton. Frst, accordng to Engle and Granger (1987) f the two varables n (1) are ntegrated of the same order d, f they are to be contegrated, εt should be ntegrated at an order less than d. For example, f both HP and HI are ntegrated of order one, for contegraton εt should statonary. Second, Bahman-Oskooee and Oyolola (2007) have argued that we can stll use (3) to establsh Granger causalty from HI to HP by testng whether 0 n (3). Fnally, Banerjee et al. (1989) have demonstrated that f an estmate of λ n (3) s negatve and sgnfcant, that could be an ndcaton of contegraton between two varables. However, they argue that the t-rato that s used to judge ts sgnfcance has a nonstandard dstrbuton, hence they provde new crtcal values. In case one varable s I(1) and the other one s I(0) n equaton (1) or n any other lnear model, none of the above tests are applcable. Pesaran et al. (2001) then ntroduce a unque procedure known as bounds testng approach. They solve equaton (1) for, εt and lag the soluton by one perod to arrve at: t1 LnHPt 1 b' LnHIt 1 (4) Rght-hand sde of (4) replaces εt-1 n (3) to arrve at another error-correcton specfcaton as follows: 4

5 LnHP t n1 1 LnHP t n2 0 LnHI t LnHP 0 t1 LnHI 1 t1 t (5) Pesaran et al (2001) then propose to apply the F test to establsh jont sgnfcance of lagged level varables n (5) as a sgn of contegraton. However, the F test n ths context has new crtcal values that they tabulate. Snce ther crtcal values do account for ntegratng propertes of varables n a gven mode, there s no need for pre-unt root testng and ndeed, varables could be combnaton of I(0) and I(1). 3 Once contegraton s establshed, long-run effects of household ncome on house prces are establshed by normalzng estmate of λ1 on λ0. The short-run effects are judged by the estmates of δ s. Followng Bahman-Oskooee and Oyolola (2007) we apply the Wald test to determne whether 0 as a sgn of short-run causalty. One man assumpton n estmatng (5) s that changes n household ncome has symmetrc effects on house prces. However, t s possble that the effects could be asymmetrc. When household ncome rses, more people are workng and they are more optmstc about the future, hence demand for housng ncreases, pushng the prces hgher. However, when house hold ncome falls due to loss of a job, ths could be consdered a short-run phenomenon and some may contnue fnancng ther house usng ther savng rather than sellng ther houses and depressng house prces, hence asymmetry response of house prces to changes n household ncome. In order to assess asymmetry effects of changes n household ncome, we follow Shn et al. (2014) and frst form ΔLn HI as changes n household ncome. We then use partal sum of postve changes (denoted by ΔLn HI + ) to generate a varable, POS, whch ndcates only ncreases n household ncome. Smlarly, we use partal sum of negatve changes (denoted by ΔLn HI - ) and generate a varable, NEG, whch reflects only the declne n ncome as follows: 3 Indeed, we have made sure that there s no I(2) varable. 5

6 POS t t j1 LnHI j t j1 max( LnHI j,0), NEG t t j1 LnHI j t j1 mn( LnHI j,0) (6) Shn et al. (2014) then recommend replacng Ln HI n (5) by POS and NEG varables to arrve at the followng specfcaton: LnHP t n1 1 LnHP t n2 0 POS t n3 0 NEG t LnHP 0 t1 POS 1 t1 NEG 1 t1 t (7) Snce method of constructng the two varables,.e., POS and NEG ntroduce nonlnearty nto the model, Shn et al. (2014) label ths specfcaton a model whereas, model (5) s referred to as the lnear model. They show that Pesaran et al s (2001) method and crtcal values are equally applcable to specfcaton (7). Once (7) s estmated usng a set crteron such as AIC to select an optmum model, we shall engage n a few hypothess testng. Frst, we shall nfer short-run adjustment asymmetry f number of lags obtaned for ΔPOS varable are dfferent than those obtaned for ΔNEG varable. Second, n terms of the sze of the mpact we wll establsh short-run mpact asymmetry f. Ths s done by applyng the Wald test. Thrd, we wll establsh short-run asymmetry Granger causalty f ether 0 or 0. If the frst condton holds but the second condton does not, then we shall conclude that ncrease n ncome causes house prces but decrease n ncome does not. Smlarly, f the second condton s proven to hold but not the frst one, we wll conclude that a declne n ncome causes house prces but not an ncrease. Agan the Wald test wll be used to test these hypothess. Fourth, contegraton between Ln HP, POS and 6

7 NEG varables wll be establshed by applyng the F test and usng upper bound crtcal values from Pesaran et al. (2001). Note that here Shn et al. (2014, p. 291) recommend treatng POS and NEG as one varable and usng the crtcal values for the case of k=1. Ths s mostly due to dependency between POS and NEG and the fact that crtcal values are hgher for the case of one exogenous varable (k=1) compared to when k=2. Alternatve test for contegraton wll be based Banerjee et al. (1998). Wthn the lnear or nonlnear approach, Pesaran et al. (2001) propose usng the long-run normalzed estmates and long run model n ether case to generate the error tem. Denotng ths error term by ECM, the lnear combnaton of lagged level varables are then replaced by ECMt-1 and the new specfcaton s estmated at optmum lags. Lke the F test, the t-statstc that s used to judge sgnfcance of ECMt-1 wthn approach has an upper bound and a lower bound crtcal value that Pesaran et al. (2001, p. 303) supply. Fnally, once contegraton s establshed, long-run asymmetry effects of household ncome changes s tested by usng the Wald test to determne f estmate of III. The Results The lnear model (5) and nonlnear model (7) are both estmated usng quarterly data over the perod 1975I-2014III from each of states n the Unted States of Amerca. Detals of the data are provded n the Appendx. We mpose a maxmum of eght lags on each-frst dfferenced varable and use Akake s Informaton Crteron (AIC) to select the optmum lags. We then report the results from each optmum lnear and nonlnear models and for each state n Table 1. For each model, after excludng the short-run estmates for the dependent varable, we report the short-run 4 For some other applcaton of the lnear model see Bahman-Oskooee and Tanku (2008), and De Vta and Kyaw (2008). For nonlnear model see Apergs (2003), Apergs and Mller (2006), Bahman-Oskooee and Bahman (2015), Bahman-Oskooee and Fardtavana (2016), and Verheyen (2013). 7

8 estmates n Panel A and long-run estmates n Panel B. All dagnostc statstcs are then reported n Panel C. For ease of exposure and readng a sgnfcant coeffcent or statstc at the 10% (5%) level s ndcated by one * (two **). These sgnfcant statstcs are dentfed by usng the crtcal values reported at the bottom of Table 1. Table 1 goes here We begn revewng the results for the state of Alaska, the frst state n Table 1 and then summarze the results for the remanng states. In the lnear model snce household ncome carres two sgnfcant coeffcents we can say that household ncome n Alaska has short-run effects on house prces. Sum of these short-run effects are sgnfcant, mplyng short-run causalty form household ncome to house prces. However, these short-run effects does not seem to last nto the long run snce the long-run coeffcent obtaned for LnHI s nsgnfcant. No wonder why contegraton s not supported nether by the F test nor by ECMt-1. Nether s sgnfcant n ths lnear model. The Lagrange Multpler (LM) statstc s also nsgnfcant, mplyng autocorrelaton free resduals but the coeffcent estmate are unstable once the CUSUM (denoted by QS) and CUSUMSQ (denoted by QS 2 are appled to the resduals of the optmum model. Whle unstable estmates are denoted by U, stables ones are denoted by S. How do our fndngs change f we shft to the estmate of the nonlnear model n Alaska? From the nonlnear model we gather that both ncome ncreases (ΔPOS) and ncome decreases (ΔNEG) have short-run effects on house prces snce each carres at least one sgnfcant coeffcent. These short-run effects do last nto the long run snce both POS and NEG varables carry sgnfcant long-run coeffcents as evdenced from panel B. The long-run estmates are also meanngful due to the fact that contegraton s establshed at least by ECMt-1. Snce the nonlnear model produces evdence of contegraton between house prces and household ncome, ths s 8

9 preferred to the lnear model. Addtonally, the nonlnear model clearly produces evdence of asymmetrc effects of ncome changes on house prces. Frst, snce number of lags are dfferent, there s evdence of short-run adjustment asymmetry. Second, snce sze and sgn of some of the coeffcents attached to ΔPOS are dfferent than those attached to ΔNEG, there s also evdence of short-run asymmetry effects. However, sum of these coeffcents do not seem to be statstcally dfferent because the Wald statstc for testng whether 9 s nsgnfcant, mplyng lack of short-run mpact asymmetry. However, ths s not the case for long-run asymmetry due to the fact that the Wald statstc for testng long-run asymmetry s hghly sgnfcant. Fnally, snce s sgnfcant but s not, we can say that n Alaska ncreases n ncome causes house prces but decreases n ncome does not, supportng short-run asymmetry causalty. We are now n a poston to summarze our fndngs for all states. Frst, n the lnear model, household ncome carres at least one short-run sgnfcant coeffcent n all states except n Mssour and Nevada. The sum of these coeffcents s sgnfcantly dfferent from zero,.e., 0 by the Wald test n 36 states. Thus, n most states household ncome causes house prces. Second, these short-run effects translate nto the long run sgnfcant effects only n 34 states and these long run effects are meanngful n only 24 states snce contegraton s supported ether by the F or ECMt-1 test. How do the result change f we ntroduce nonlnear adjustment of household ncome and shft to the estmates of nonlnear models? From the estmates of nonlnear optmum models we gather that: Frst, ncome ncreases (ΔPOS) and ncome decreases (ΔNEG) have short-run effects n almost all states. However, number of lags on ΔPOS are dfferent than those on ΔNEG n 35 states, supportng adjustment asymmetry. Second, n almost all models ether the sze or sgn of these short-run estmates are dfferent, supportng short-run asymmetry effects. Thrd, sum of the short-run coeffcent estmates

10 attached to ΔPOS) are sgnfcantly dfferent than the sum of coeffcents attached to ΔNEG,.e., n 18 states, supportng short-run mpact asymmetry. The lst ncludes Arkansas, Arzona, Calforna, Colorado, Florda, Indana, Lousana, Massachusetts, Msssspp, Oho, Oklahoma, Oregon, South Carolna, South Dakota, Utah, Washngton, Wsconsn, and West Vrgna. Fourth, stayng wth short-run results we also learn that ncrease n ncome causes house prces n 21 states but decrease n ncome causes house prces only n 15 states. The 21 states n whch 0 that s supported by sgnfcant Wald statstc are: Alaska, Arzona, Colorado, Connectcut, Florda, Hawa, Idaho, Massachusetts, Maryland, Mssour, Montana, North Dakota, New Jersey, Oklahoma, South Dakota, Texas, Utah, Vrgna, Vermont, Wsconsn, and West Vrgna. In the 15 states n whch 0 s supported by sgnfcant Wald statstc are: Arkansas, Arzona, Calforna, Colorado, Connectcut, Florda, Indana, Lousana, Massachusetts, Msssspp, Oho, Oregon, South Carolna, South Dakota, and Wsconsn. Once agan we ask n how many states short-run asymmetry effects last nto the long run? From Panel B we gather that ether the POS or NEG varable carry a sgnfcant long-run coeffcent n 41 states. The comparable fgure from the lnear model was 34 where household ncome carred a sgnfcant long-run coeffcent. Thus, ntroducng nonlnear adjustment yelds more sgnfcant results. These sgnfcant long-run estmates are meanngful n 33 states snce ether the F statstc or ECMt-1 s sgnfcant. The comparable fgure for contegraton n the lnear model was 24. Agan, ths s an ndcaton of superorty of the nonlnear specfcaton. It yeld more support for contegraton between house prces and household ncome. Fnally, we ask 10

11 whether long-run asymmetrc effects are sgnfcantly dfferent. Here we test f 1 1. The Wald test appears to be sgnfcant n 21 states only. 5 IV. Summary and Concluson The fnancal crss of 2008 that shook the world n general and the Unted States n partcular was mostly attrbuted to the real estate bubble that burst n the Unted States. Specfcally, house prces that rose abnormally n the Unted States pror to 2008, declned abnormally after However, changes were dsproportonate and dffered from one state to another. Whle there are many factors contrbutng to fluctuatons n house prces, Case and Shller (2003, p. 300) argued that ncome growth alone explans the pattern of recent home prce ncreases n most states. If ncome ncrease explans most of the ncrease n housng prces pror to 2008, does declne n ncome explan most of the declne n housng prces durng post 2008? In other word, do ncome changes have symmetrc or asymmetrc effects on house prces? The man purpose of ths paper was to nvestgate whether changes n household ncome have symmetrc or asymmetrc effects on the housng prces n each state of the Unted States. Indeed, prevous research assumed the effects are asymmetrc and ncluded household ncome n ther model and estmated a lnear model. Followng the recent trend n appled research we separate household ncome ncreases from decreases usng partal sum concept. We then estmate the lnear model usng Pesaran et al. (2001) bounds testng approach frst and Shn et al. (2014) nonlnear approach next. The latter approach allows us also to test f changes n 5 Note that just lke the lnear model n whch the LM statstc was sgnfcant n 14 states, t s stll sgnfcant n 14 states n the nonlnear model. Thus, autocorrelaton does not seem to be an ssue n most models. Estmated coeffcents are also stable, at least ether by the CUSUM or CUSUMSQ tests n most models. 11

12 ncome have symmetrc or asymmetrc effects on house prces. We do ths usng quarterly data over the perod 1975I-2014III from each and every states of the Unted States. Our fndng could be best summarzed by sayng that nonlnear model performs better than the lnear model n that t provdes more support for contegraton between house prces and household ncome. Gven that prevous studes have not been able to fnd much support for contegraton, nonlnear model that even ncludes other factors should be gven serous consderaton. Second, we fnd support for the adjustment asymmetry n almost all states, mplyng that the speed wth whch ncrease n ncome affects house prces s dfferent than the speed wth whch decrease n ncome affects. Thrd, snce the sze and sgn of short-run effects were dfferent due to ncrease n ncome as compared to decrease n ncome, short-run effects of ncome changes were asymmetrc n almost all states. However, short-run mpact asymmetry was found only n 18 states. Fnally, whle the short-run asymmetry effects lasted nto the long-run n 41 states, only n 21 states the long-run effects were sgnfcantly asymmetrc. These asymmetrc effects could be attrbuted to reacton of the households to an ncrease n ther ncome as compared to a decrease n ther ncome. When household ncome rses, ther demand for housng rses too, pushng the prces up. However, when ther ncome declnes, f ths s consdered a short-run phenomenon they may fnance ther mortgages usng savng rather than sellng. All n all, our fndngs are statespecfc and show mportance of usng dsaggregated data state by state. 12

13 Appendx Data Sources and Defntons Quarterly data over the 1975I-2014III perod are used to carry out the emprcal exercse. HP = House Prce. House prce data s House Prce Index (HPI) whch s a weghted repeat sales ndex measurng average prce changes repeat sales or re-fnancngs on the same sngle-famly house. Ths nformaton s obtaned by studyng repeat mortgage transactons on sngle-famly propertes whose mortgages have been securtzed or purchased by Fanne Mae or Fredde Mac snce The HPI provdes as an accurate ndcator of house prce trends at dfferent geographc levels. The breadth of ts sample provdes more nformaton than other house prce ndexes. Ths data s avalable for the nne Census Bureau dvsons, the 50 states and Dstrct of Columba, and for Metropoltan Statstcal Areas and Dvsons. Federal Housng Fnance Agency publshes monthly and quarterly HPI data. In ths study, we use seasonally adjusted real HPI by adjustng the HPI by Consumer Prce Index. HI = Household ncome. It s defned as Total Personal Income publshed by the U.S. Bureau of Economc Analyss. Here we use real Total Personal Income whch s seasonally adjusted fgures deflated by Consumer Prce Index. 13

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17 Table 1: Estmates of Both the and Models for 52 States of the Unted States of Amerca Alaska Alabama Arkansas Arzona Panel A: Short-Run ΔLnHI t 0.44(1.72)* 0.68(3.9)** 0.35(3.7)** 0.55(3.1)** ΔLnHI t (1.05) 0.07(0.38) -0.13(1.37) 0.09(0.56) ΔLnHI t (0.92) -0.15(.84) -0.01(0.12) -0.34(1.9)** ΔLnHI t (0.11) 0.35(2.0)** -0.08(0.82) ΔLnHI t (1.32) 0.14(1.48) ΔLnHI t (2.9)** -0.01(.07) ΔLnHI t (1.48) 0.31(3.4)** ΔLnHI t-7 ΔLnHI t-8 ΔPOS t 0.66(1.64)* 0.03(1.63) 0.02(1.58) 0.61(2.70)** ΔPOS t (1.35) ΔPOS t-2 ΔPOS t-3 ΔPOS t-4 ΔPOS t-5 ΔPOS t-6 ΔPOS t-7 ΔPOS t-8 ΔNEG t 1.18(1.58) 1.27(3.7)** 0.84(4.7)** 0.24(0.52) ΔNEG t (0.51) -0.13(0.34) -0.64(3.4)** -0.82(1.90)* ΔNEG t (1.03) -0.95(2.6)** -0.16(0.86) -1.09(2.34)** ΔNEG t (0.21) 1.09(2.9)* -0.02(0.11) ΔNEG t (2.0)** 0.39(2.00)** ΔNEG t (2.3)** -0.01(0.05) ΔNEG t (2.5)** 0.40(2.2)** ΔNEG t-7 ΔNEG t-8 Panel B: Long-Run Constant 3.07(0.45) 5.94(42.9)** 0.98(0.30) 5.56(90.5)** 4.22(1.17) 5.67(51.9)** 1.73(0.88) 5.19(49.5)** Ln HI t 0.14(0.35) 0.24(1.40) 0.06(0.31) 0.20(1.9)** POS t 1.24(6.49)** 0.41(2.0)** 0.53(1.8)* 0.37(3.04)** NEG t 3.66(6.02)** 1.60(1.36) 2.67(2.0)** 1.75(1.55) Panel C: Dagnostc F ** 6.07** ECM t (1.73) -0.20(3.6)** -0.04(2.48) -0.07(2.75) -0.02(1.67) -0.03(1.83) -0.04(3.4)** -0.05(4.3)** LM ** 12.22** QS (QS 2) U (U) U (U) S (U) S (U) S (U) S (U) S (U) U (U) Adjusted R Wald Tests: δ = ** * * δ + = ** * δ - = * * δ + = δ * * ** * Notes: See end of the Table. 17

18 Calforna Colorado Connectcut Delaware Panel A: Short-Run ΔLnHI t 0.02(3.3)** 0.30(3.3)** 0.43(3.5)** 0.26(1.47) ΔLnHI t (1.8)* ΔLnHI t-2 ΔLnHI t-3 ΔLnHI t-4 ΔLnHI t-5 ΔLnHI t-6 ΔLnHI t-7 ΔLnHI t-8 ΔPOS t 0.02(2.27)** 0.33(2.6)** 0.63(3.9)** 0.04(1.63) ΔPOS t (0.15) ΔPOS t (0.28) ΔPOS t (0.00) ΔPOS t (1.9)** ΔPOS t (1.52) ΔPOS t (2.0)** ΔPOS t (1.36) ΔPOS t-8 ΔNEG t -0.09(0.34) 0.08(0.34) 0.06(1.25) 0.40(0.95) ΔNEG t (1.85)* -0.71(3.0)** 0.33(0.76) ΔNEG t (1.70)* -0.58(1.46) ΔNEG t (0.38) ΔNEG t (1.18) ΔNEG t (2.1)** ΔNEG t (1.9)* ΔNEG t (1.7)* ΔNEG t-8 Panel B: Long-Run Constant (3.9)** 5.33(45.9)** -3.88(1.58) 4.94(24.3)** -1.80(0.47) 5.4(49.7)** -2.59(1.10) 5.76(50.1)** Ln HI t 0.80(6.09)** 0.51(3.8)** 0.40(2.0)** 0.49(3.5)** POS t 0.91(2.9)** 0.66(2.5)** 0.87(2.2)** 0.69(2.2)** NEG t 1.95(1.17) 1.21(0.62) 1.88(1.47) 1.54(1.01) Panel C: Dagnostc F 8.78** 5.11* ECM t (4.2)** -0.03(3.9)** -0.02(2.39) -0.02(3.43)* -0.03(2.86) -0.04(3.37)* -0.04(2.45) -0.05(2.79) LM QS (QS 2) S (S) S (S) S (S) S (S) S (U) S (U) U (U) S (U) Adjusted R Wald Tests: δ = * * * δ + = * * δ - = * * * δ + = δ * *

19 Florda Georga Hawa Iowa Panel A: Short-Run ΔLnHI t 0.29(1.9)* 0.22(1.87)* 4.03(7.9)** 0.12(1.29) ΔLnHI t (0.65) ΔLnHI t (0.63) ΔLnHI t (1.95)* ΔLnHI t (1.40) ΔLnHI t (3.2)** ΔLnHI t (2.3)** ΔLnHI t-7 ΔLnHI t-8 ΔPOS t 0.54(2.9)** 0.25(1.88)* 1.05(1.57) 0.10(0.66) ΔPOS t (0.40) 1.38(2.0)** 0.29(2.0)** ΔPOS t (2.55)** -0.55(3.6)** ΔPOS t-3 ΔPOS t-4 ΔPOS t-5 ΔPOS t-6 ΔPOS t-7 ΔPOS t-8 ΔNEG t -0.30(0.84) 0.04(0.80) 8.6(8.4)** 0.20(1.02) ΔNEG t (0.35) -4.0(3.1)** -0.28(-1.42) ΔNEG t (2.5)** -4.8(3.9)** 0.69(3.56)** ΔNEG t (0.28) 0.19(1.02) ΔNEG t (0.59) 0.33(1.74)* ΔNEG t (0.37) 0.73(3.7)** ΔNEG t-6 4.9(4.3)** -1.11(5.4)** ΔNEG t-7-4.4(4.7)** ΔNEG t-8 Panel B: Long-Run Constant -0.80(0.28) 5.21(39.4)** 3.06(3.0)** 5.5(104)** -14.0(3.9)** 5.3(88.8)** 0.34(0.09) 5.54(42.6)** Ln HI t 0.31(2.2)** 0.13(2.6)** 1.12(5.4)** 0.27(1.39) POS t 0.21(1.56) 0.20(2.2)** 2.15(9.4)** 0.54(1.22) NEG t -0.58(0.47) 0.75(0.88) 4.97(6.0)* 0.96(0.96) Panel C: Dagnostc F ** 8.24** ** ECM t (3.05)* -0.04(4.6)** -0.06(4.9)** -0.05(3.75)** -0.11(2.51) -0.22(4.2)** -0.04(3.02)* -0.04(2.46) LM * 14.79** QS (QS 2) S (U) S (U) S (S) S (S) S (U) S (U) U (U) S (U) Adjusted R Wald Tests: δ = * * * * δ + = * * δ - = * δ + = δ * *

20 Idaho Illnos Indana Kansas Panel A: Short-Run ΔLnHI t 0.31(1.9)* 0.31(2.5)** 0.22(2.6)** 0.07(0.92) ΔLnHI t (1.04) -0.08(1.16) ΔLnHI t (1.34) -0.03(0.35) ΔLnHI t (1.29) 0.16(2.1)** ΔLnHI t (0.63) 0.14(1.9)** ΔLnHI t-5-0.2(2.2)** ΔLnHI t-6 ΔLnHI t-7 ΔLnHI t-8 ΔPOS t 0.09(3.2)** 0.04(1.8)** 0.09(4.5)** 0.03(1.92)* ΔPOS t-1 ΔPOS t-2 ΔPOS t-3 ΔPOS t-4 ΔPOS t-5 ΔPOS t-6 ΔPOS t-7 ΔPOS t-8 ΔNEG t 0.35(0.89) 0.17(0.77) 0.52(3.4)** 0.11(0.83) ΔNEG t (1.10) -0.1(0.6)** -0.15(1.11) ΔNEG t (0.06) 0.59(2.8)** -0.23(1.70)* ΔNEG t (2.4)** -0.33(1.6)* 0.28(2.0)** ΔNEG t (0.23) -0.30(1.55) ΔNEG t (0.17) -0.5(2.5)** ΔNEG t (3.0)** ΔNEG t (2.8)** ΔNEG t-8 Panel B: Long-Run Constant 0.96(0.52) 5.48(76.0)** -6.3(3.5)** 5.5(104)** 3.21(1.32) 5.6(240)** 3.02(0.76) 5.53(60.9)** Ln HI t 0.26(2.4)** 0.60(6.7)** 0.12(0.93) 0.13(0.59) POS t 0.62(6.0)** 0.74(2.7)** 0.79(8.4)** 0.87(2.6)** NEG t 2.09(3.7)** 1.35(1.36) 2.51(8.4)** 3.11(2.5)** Panel C: Dagnostc F 5.01* ** 6.59** ** ECM t (3.18)* -0.12(2.99) -0.06(4.6)* -0.06(4.4)** -0.03(2.51) -0.10(4.7)** -0.02(2.26) -0.03(2.98) LM ** 39.76** QS (QS 2) S (U) S (U) S (U) S (U) S (U) S (U) S (U) S (U) Adjusted R Wald Tests: δ = * * δ + = * δ - = * δ + = δ * * * *

21 Kentucky Lousana Massachusetts Maryland Panel A: Short-Run ΔLnHI t 0.42(5.05)** 0.38(3.7)** 0.23(2.4)** 0.27(1.87)* ΔLnHI t (0.74) 0.07(0.63) ΔLnHI t (0.39) 0.10(0.94) ΔLnHI t (0.63) 0.09(0.92) ΔLnHI t (0.07) 0.23(2.2)** ΔLnHI t (4.05)** 0.05(0.48) ΔLnHI t (2.80)** 0.15(1.49) ΔLnHI t (3.3)** ΔLnHI t-8 ΔPOS t 0.07(2.5)** 0.07(3.7)** 0.38(2.8)** 0.04(0.24) ΔPOS t (5.3)** 0.51(2.6)** ΔPOS t (3.1)** ΔPOS t (3.0)** ΔPOS t (1.49) ΔPOS t (0.06) ΔPOS t (3.5)** ΔPOS t (1.70)* ΔPOS t (2.5)** ΔNEG t 0.68(3.2)** -0.06(0.24) 0.76(1.9)* ΔNEG t-1-0.5(2.3)** -0.97(2.4)** ΔNEG t-2 ΔNEG t-3 ΔNEG t-4 ΔNEG t-5 ΔNEG t-6 ΔNEG t-7 ΔNEG t-8 Panel B: Long-Run Constant -2.17(0.35) 5.63(144)** 0.62(0.13) 5.1(82.5)** -12.0(4.2)** 5.5(55.3)** -5.90(3.0)** 5.47(44.5)** Ln HI t 0.40(1.23) 0.23(0.90) 0.94(6.4)** 0.61(6.0)** POS t 0.70(10.7)** 1.56(6.4)** 0.96(1.9)* 0.83(3.5)** NEG t 2.79(7.08)** 5.42(5.6)** 1.15(0.52) 2.64(1.15) Panel C: Dagnostc F ** ** 4.45 ECM t (1.36) -0.10(2.74) -0.02(2.63) -0.03(3.7)** -0.03(3.8)** -0.02(3.5)** -0.03(3.7)** -0.03(3.6)** LM ** ** 4.01 QS (QS 2) S (U) S (U) U (U) S (U) S (S) S (S) S (U) S (U) Adjusted R Wald Tests: δ = * * * * δ + = * * δ - = * * δ + = δ * * * *

22 Mane Mchgan Mnnesota Mssour Panel A: Short-Run ΔLnHI t 0.56(2.0)** 0.15(1.25) 0.01(2.54)** 0.15(1.54) ΔLnHI t (1.91)* ΔLnHI t (1.30) ΔLnHI t (2.4)** ΔLnHI t-4 ΔLnHI t-5 ΔLnHI t-6 ΔLnHI t-7 ΔLnHI t-8 ΔPOS t 0.15(2.4)** 0.13(3.5)** 0.04(2.0)** 0.35(3.1)** ΔPOS t-1 ΔPOS t-2 ΔPOS t-3 ΔPOS t-4 ΔPOS t-5 ΔPOS t-6 ΔPOS t-7 ΔPOS t-8 ΔNEG t 1.37(2.1)** 0.23(3.2)** 0.10(1.34) 0.06(1.45) ΔNEG t (0.48) ΔNEG t (1.81)* ΔNEG t-3 ΔNEG t-4 ΔNEG t-5 ΔNEG t-6 ΔNEG t-7 ΔNEG t-8 Panel B: Long-Run Constant -6.21(2.5)** 5.54(69.9)** (1.38) 5.4(109)** -2.86(1.20) 5.4(68.0)** 2.43(1.04) 5.49(74.8)** Ln HI t 0.73(4.7)** 0.83(2.09)** 0.45(3.5)** 0.17(1.34) POS t 1.48(3.5)** 1.58(6.5)** 0.91(2.6)** 0.53(2.3)** NEG t 3.87(2.2)** 2.85(5.3)** 2.45(1.55) 1.94(1.8)* Panel C: Dagnostc F ** 5.44* ECM t (2.66) -0.10(3.15) -0.02(2.01) -0.08(4.4)** -0.03(3.3)** -0.04(3.6)** -0.03(2.9)* (3.2)* LM 12.33** ** QS (QS 2) S (U) S (U) S (U) U (U) S (U) S (U) S (U) S (U) Adjusted R Wald Tests: δ = * * δ + = * δ - = δ + = δ * *

23 Msssspp Montana North Carolna North Dakota Panel A: Short-Run ΔLnHI t 0.60(2.9)** 0.70(5.24)** 0.30(3.47)** 0.10(1.11) ΔLnHI t (0.58) -0.17(1.10) -0.01(0.07) ΔLnHI t (0.03) 0.32(2.17)** 0.25(2.7)** ΔLnHI t (2.4)** 0.10(0.68) -0.15(1.60) ΔLnHI t (0.45) 0.28(1.88)* -0.03(0.28) ΔLnHI t (0.64) 0.13(0.83) -0.11(1.22) ΔLnHI t (1.27) 0.24(1.64)* -0.10(1.10) ΔLnHI t (4.7)** -0.21(1.40) 0.22(2.3)** ΔLnHI t-8 ΔPOS t 0.02(1.23) 0.74(4.6)** 0.20(1.74)* 0.17(4.6)** ΔPOS t-1-0.5(3.0)** 0.04(0.32) ΔPOS t (2.8)** 0.19(1.81)* ΔPOS t (0.46) 0.04(0.32) ΔPOS t (2.7)** -0.21(1.9)* ΔPOS t (4.0)** ΔPOS t (0.83) ΔPOS t-7-0.3(2.0)** ΔPOS t-8 ΔNEG t 1.32(3.7)** 0.51(2.0)** 0.35(1.64)* 0.17(1.15) ΔNEG t (0.33) 0.42(1.7)* -0.40(1.8)* -0.40(2.6)** ΔNEG t (2.0)** -0.27(1.19) 0.38(2.4)** ΔNEG t (2.0)** -0.13(0.61) -0.44(3.0)** ΔNEG t (0.34) 0.22(0.96) -0.15(1.08) ΔNEG t (1.58) -1.1(4.7)** -0.29(2.0)** ΔNEG t (2.7)** 0.91(3.9)** -0.23(1.64)* ΔNEG t (4.4)** 0.49(3.1)** ΔNEG t-8 Panel B: Long-Run Constant -4.49(0.37) 5.51(26.0)** -5.39(1.44) 5.2(28.6)** 1.67(1.74)* 5.47(99)** -8.32(1.21) 0.08(68.4)** Ln HI t 0.51(0.81) 0.63(2.8)** 0.20(4.1)** 0.82(2.0)** POS t 0.77(1.01) 0.93(5.5)** 0.29(2.9)** 0.79(9.05)** NEG t 2.62(0.84) 1.15(2.2)** 0.71(0.80) 1.12 (8.0)** Panel C: Dagnostc F * ** ** ECM t (2.04) -0.03(1.73) -0.05(2.36) -0.10(3.8)** -0.04(3.08)* -0.07(4.52) -0.06(2.63) -0.21(4.43)** LM ** 15.89** 9.14* QS (QS 2) U (U) U (U) S (U) S (U) S (U) S (U) S (U) S (U) Adjusted R Wald Tests: δ = * * * δ + = * * δ - = * δ + = δ * *

24 Nebraska New Hampshre New Jersey New Mexco Panel A: Short-Run ΔLnHI t -0.12(1.61) 0.39(2.9)** 0.27(2.7)** 0.32(2.0)** ΔLnHI t (1.92)* 0.15(0.97) ΔLnHI t (1.30) -0.09(0.58) ΔLnHI t (1.41) 0.30(1.92)* ΔLnHI t (0.73) ΔLnHI t (3.17)** ΔLnHI t-6 ΔLnHI t-7 ΔLnHI t-8 ΔPOS t 0.01(0.40) 0.35(2.1)** 0.2(1.97)** 0.01(0.90) ΔPOS t (1.10) ΔPOS t (0.71) ΔPOS t-3-0.3(1.9)** ΔPOS t-4 ΔPOS t-5 ΔPOS t-6 ΔPOS t-7 ΔPOS t-8 ΔNEG t -0.33(2.3)** -0.01(0.27) -0.03(0.77) 0.04(0.37) ΔNEG t (2.00)** ΔNEG t (2.7)** ΔNEG t (2.7)** ΔNEG t (0.66) ΔNEG t (2.7)** ΔNEG t (2.9)** ΔNEG t (2.4)** ΔNEG t-8 Panel B: Long-Run Constant 2.75(1.00) 5.52(25.6)** -3.92(2.1)** 5.5(23.2)** -10.9(4.0)** 5.6(47.5)** 1.42(0.69) 5.48(57.7)** Ln HI t 0.15(0.98) 0.55(5.2)** 0.86(6.1)** 0.2(1.9)** POS t 0.23(0.52) 0.17(0.36) 0.26(0.63) 0.23(0.92) NEG t 0.44(0.30) -0.52(0.27) -1.16(0.72) 0.86(0.36) Panel C: Dagnostc F ** ** 4.99* ECM t (2.50) -0.03(1.92) -0.05(4.1)** -0.03(3.6)** -0.03(3.8)** -0.03(3.8)** -0.04(2.55) -0.04(2.43) LM * ** 42.38** QS (QS 2) S (U) S (U) S (U) S (U) S (U) S (S) U (U) U (S) Adjusted R Wald Tests: δ = * * * δ + = * δ - = δ + = δ

25 Nevada New York Oho Oklahoma Panel A: Short-Run ΔLnHI t 0.08(1.57) 0.07(3.3)** 0.26(2.8)** 0.24(3.1)** ΔLnHI t (0.21) ΔLnHI t (1.31) ΔLnHI t (2.7)** ΔLnHI t-4 ΔLnHI t-5 ΔLnHI t-6 ΔLnHI t-7 ΔLnHI t-8 ΔPOS t 0.01(1.08) 0.34(1.58) 0.11(0.63) 0.25(2.0)** ΔPOS t (0.63) -0.18(1.56) ΔPOS t (1.49) 0.08(0.80) ΔPOS t (2.6)* 0.24(2.4)** ΔPOS t (2.3)** ΔPOS t (1.28) ΔPOS t (1.35) ΔPOS t-7 ΔPOS t-8 ΔNEG t 0.002(0.03) 0.002(0.03) 0.66(3.2)** 0.39(2.0)** ΔNEG t (0.67) ΔNEG t (0.28) ΔNEG t (2.0)** ΔNEG t (2.2)** ΔNEG t (2.38)** ΔNEG t (1.53) ΔNEG t-7 ΔNEG t-8 Panel B: Long-Run Constant 4.07(3.7)** 5.45(53.5)** -13.3(5.2)** 5.71(93)** 1.66(0.34) 5.6(137)** 8.05(1.9)* 5.28(50.1)** Ln HI t 0.08(1.34) 0.95(7.7)** 0.19(0.80) -0.16(0.73) POS t 0.12(1.23) 0.63(1.33) 1.24(6.2)** 0.61(2.4)** NEG t 0.65(0.63) 1.04(0.03) 3.39(5.8)** 2.43(2.9)** Panel C: Dagnostc F 10.55** 6.50** 9.68** 6.72** ** ** ECM t (4.6)** -0.05(4.4)** -0.06(4.4)** -0.06(4.5)** -0.02(2.10) -0.07(4.2)** -0.02(2.87) -0.05(4.3)** LM ** 2.10 QS (QS 2) S (U) S (U) S (U) S (U) S (U) S (U) U (U) U (U) Adjusted R Wald Tests: δ = * * δ + = * δ - = * δ + = δ * * * *

26 Oregon Pennsylvana Rhode Island South Carolna Panel A: Short-Run ΔLnHI t 0.65(3.6)** 0.24(2.4)** 0.05(3.8)** 0.31(2.8)** ΔLnHI t (2.4)** ΔLnHI t (0.28) ΔLnHI t (0.84) ΔLnHI t (0.53) ΔLnHI t (1.29) ΔLnHI t (2.3)** ΔLnHI t (2.1)** ΔLnHI t-8 ΔPOS t 0.07(2.8)* 0.02(1.50) 0.38(1.47) 0.04(2.4)** ΔPOS t (0.09) ΔPOS t (2.2)** ΔPOS t (0.99) ΔPOS t-4-0.4(1.8)* ΔPOS t-5 ΔPOS t-6 ΔPOS t-7 ΔPOS t-8 ΔNEG t 1.53(3.2)** -0.01(0.10) 0.25(0.68) 1.12(4.3)** ΔNEG t (3.4)** 0.54(1.44) -0.49(1.82)* ΔNEG t (0.91) -0.9(2.3)** ΔNEG t (0.49) ΔNEG t (1.9)** ΔNEG t (2.0)** ΔNEG t (3.0)** ΔNEG t (4.0)** ΔNEG t-8 Panel B: Long-Run Constant -11.3(3.8)** 5.20(43.1)** -5.91(3.2)** 5.49(69)** -11.3(4.8)** 5.4(48.9)** 1.75(1.05) 5.57(148)** Ln HI t 0.92(5.8)** 0.59(6.4)** 0.10(7.4)** 0.21(2.3)** POS t 1.27(6.04)** 0.44(1.68)* 2.1(4.5)** 0.67(3.7)** NEG t 3.25(2.14)** -0.09(0.10) 5.40(3.0)** 3.98(2.7)** Panel C: Dagnostc F 5.69* ** ** ECM t (3.3)** -0.05(3.34)* -0.06(4.2)** -0.05(3.7)** -0.05(4.1)** -0.05(3.7)** -0.04(2.60) -0.07(3.47)* LM * QS (QS 2) S (S) S (U) S (U) S (S) S (U) S (U) S (U) S (U) Adjusted R Wald Tests: δ = * * δ + = δ - = * * δ + = δ * * * *

27 South Dakota Tennessee Texas Utah Panel A: Short-Run ΔLnHI t 0.17(1.11) 0.23(1.61) 0.19(2.2)** 0.55(3.7)** ΔLnHI t (2.2)** 0.03(0.22) -0.12(1.39) ΔLnHI t (0.90) 0.02(0.16) 0.11(1.29) ΔLnHI t (0.92) 0.15(2.4)** 0.25(2.94)** ΔLnHI t (0.30) 0.12(1.45) ΔLnHI t (0.15) ΔLnHI t (2.0)** ΔLnHI t (5.5)** ΔLnHI t-8 ΔPOS t 0.49(2.3)** 0.02(1.32) 0.06(0.54) 0.38(2.0)** ΔPOS t (1.37) 0.22(1.20) ΔPOS t (0.85) 0.42(2.5)** ΔPOS t (1.64) 0.27(1.55) ΔPOS t-4 0.3(2.9)** ΔPOS t (1.46) ΔPOS t-6 ΔPOS t-7 ΔPOS t-8 ΔNEG t -0.07(0.30) 0.93(2.9)** 0.32(1.34) 0.55(1.38) ΔNEG t (0.99) -0.05(0.16) -0.17(0.70) -0.80(1.95)* ΔNEG t (0.16) -0.35(1.10) 0.18(0.77) ΔNEG t (.013) 1.17(3.7)** 0.5(2.1)** ΔNEG t (1.36) -0.7(2.2)** -0.44(1.8)* ΔNEG t (0.12) -0.6(1.9)** -0.39(1.63) ΔNEG t (2.6)** 0.52(1.60) ΔNEG t (7.0)** ΔNEG t-8 Panel B: Long-Run Constant 1.32(0.34) 6.09(27.9)** 1.38(0.77) 5.4(78.9)** 1.13(0.16) 4.7(10.2)** -1.22(0.71) 5.00(32.9)** Ln HI t 0.24(1.04) 0.22(2.3)** 0.19(0.56) 0.38(3.9)** POS t 0.90(5.4)** 0.24(1.67)* 0.50(0.87) 0.64(4.6)** NEG t 2.23(4.2)** 0.59(0.46) 2.43(0.66) 3.39(1.9)** Panel C: Dagnostc F ** * 3.50 ECM t (1.39) -0.17(4.35)** -0.05(2.55) -0.07(2.87) -0.01(1.83) -0.02(2.84) -0.04(3.1)* -0.04(3.2)* LM 10.14** 30.89** ** 11.22** QS (QS 2) S (U) U (U) S (U) S (U) S (S) S (U) S (S) S (U) Adjusted R Wald Tests: δ = * * * * δ + = * * * δ - = * δ + = δ * * * *

28 Vrgna Vermont Washngton Wsconsn Panel A: Short-Run ΔLnHI t 0.32(2.50)** 1.00(2.0)** 0.03(3.5)** 0.35(2.2)** ΔLnHI t (0.33) -0.03(0.19) ΔLnHI t (0.63) 0.05(0.33) ΔLnHI t (2.9)** 0.30(2.0)** ΔLnHI t (1.93)* 0.01(0.04) ΔLnHI t (1.36) ΔLnHI t (2.7)** ΔLnHI t (2.4)** ΔLnHI t-8 ΔPOS t 0.47(2.4)** 1.18(1.85)* 0.11(1.02) 0.08(0.37) ΔPOS t (2.2)** -0.62(2.8)** ΔPOS t (1.49) 0.12(0.54) ΔPOS t (2.3)** ΔPOS t (1.9)** ΔPOS t (0.40) ΔPOS t (2.4)** ΔPOS t-7 ΔPOS t-8 ΔNEG t -0.11(0.34) 0.71(2.2)** 0.24(1.17) 0.76(2.0)** ΔNEG t (4.4)** -0.5(2.8)** 0.52(1.41) ΔNEG t (0.16) -0.47(1.26) ΔNEG t (2.2)** 1.54(4.0)** ΔNEG t (3.5)** 0.69(2.0)** ΔNEG t (2.1)** ΔNEG t (3.3)** ΔNEG t-7 ΔNEG t-8 Panel B: Long-Run Constant -4.62(2.0)** 5.26(37.5)** -5.53(2.1)** 5.31(44)** -7.13(5.3)** 5.2(60.8)** -6.97(1.14) 5.59(71.4)** Ln HI t 0.54(4.5)** 0.67(4.4)** 0.68(9.6)** 0.65(2.0)** POS t 0.54(1.6)* 1.66(2.4)** 0.66(3.4)** 0.98(6.68)** NEG t 0.11(0.04) 5.24(1.6)* 0.69(0.81) 2.53(3.17)** Panel C: Dagnostc F ** ECM t (2.80) -0.03(3.17) -0.12(2.59) -0.13(3.62)** -0.04(3.5)** -0.04(3.24)* -0.02(1.69) -0.08(3.06) LM ** ** QS (QS 2) S (S) S (S) S (U) U (U) S (S) S (S) S (U) U (S) Adjusted R Wald Tests: δ = * * δ + = * * * δ - = * δ + = δ * * * *

29 West Vrgna Wyomng Dstrct of Columba Panel A: Short-Run ΔLnHI t 0.81(3.7)** 0.02(0.17) 0.19(1.38) ΔLnHI t (1.49) 0.24(2.0)** 0.27(1.98)** ΔLnHI t (0.47) 0.27(2.3)** ΔLnHI t (0.09) 0.24(2.0)** ΔLnHI t (0.22) 0.30(2.5)** ΔLnHI t (2.6)** -0.10(0.82) ΔLnHI t (2.1)** 0.23(2.0)** ΔLnHI t-7 ΔLnHI t-8 ΔPOS t -0.05(0.13) 0.11(3.1)** 0.06(2.38)** ΔPOS t (0.96) ΔPOS t (2.2)** ΔPOS t (2.4)** ΔPOS t (3.3)** ΔPOS t-5 ΔPOS t-6 ΔPOS t-7 ΔPOS t-8 ΔNEG t 1.64(4.3)** 0.13(0.68) -0.37(1.17) ΔNEG t (0.48) 0.37(1.8)* 1.26(4.21)** ΔNEG t (0.87) -0.19(0.94) -0.67(2.1)** ΔNEG t (2.6)** 0.03(0.13) (0.01) ΔNEG t (2.5)** 0.47(2.4)** 0.40(1.35) ΔNEG t (1.08) -0.93(3.2)** ΔNEG t (1.45) 0.99(3.4)** ΔNEG t-7-0.5(2.5)** ΔNEG t-8 Panel B: Long-Run Constant 2.23(0.23) 5.72(68.7)** -2.86(0.94) 5.1(116)** -19.4(8.7)** 5.43(24.4)** Ln HI t 0.16(0.29) 0.48(2.6)** 1.47(11.3)** POS t 1.09(6.4)** 0.9(14.3)** 1.23(4.22)** NEG t 2.76(7.3)** 1.90(7.9)** 0.63(0.72) Panel C: Dagnostc F * 5.09* 5.86** 4.07 ECM t (1.80) -0.20(3.5)** -0.03(-3.2)** -0.12(3.9)** -0.07(4.1)** -0.05(3.46)* LM 14.05** ** QS (QS 2) S (U) S (U) U (U) U (S) S (U) U (S) Adjusted R Wald Tests: δ = * * δ + = * δ - = δ + = δ * * * Notes: a. Numbers nsde the parentheses next to coeffcent estmates are absolute value of t-ratos. *, ** ndcate sgnfcance at the 10% and 5% levels respectvely. 29

30 b. The upper bound crtcal value of the F-test for contegraton when there s on exogenous varable (k=1) s 4.78 (5.73) at the 10% (5%) level of sgnfcance. These come from Pesaran et al. (2001, Table CI, Case III, p. 300). c. The upper bound crtcal value of the t-test for sgnfcance of ECM t-1 s (-3.22) at the 10% (5%) level when k =1. The comparable fgures when k = 2 n the nonlnear model are and respectvely. These come from Pesaran et al. (2001, Table CII, Case III, p. 303). d. LM s the Lagrange Multpler statstc to test for autocorrelaton. It s dstrbuted as χ 2 wth 4 degrees of freedom. The crtcal value s 7.78 (9.48) at the 10% (5%) level. e. All Wald tests are dstrbuted as χ 2 wth one degree of freedom. The crtcal value s 2.71 (3.84) at the 10% (5%) level. 30