Long-run Equilibrium and Short-run Adjustment in U.S. Housing Markets

Transcription

1 Long-run Equlbrum and Short-run Adjustment n U.S. Housng Markets Huran Pan Department of Economcs, Calforna State Unversty, Fullerton, Fullerton, CA 92834, USA. Phone: (offce), (fax). Emal: hpan@fullerton.edu Chun Wang Department of Economcs, Brooklyn College, Graduate Center, Cty Unversty of New York, Brooklyn, NY 11210, USA. Emal: cwang@brooklyn.cuny.edu Ths Verson: November 2015 Abstract Ths paper examnes the long-run equlbrum between real house prces and macroeconomc fundamentals n U.S. housng markets, as well as the short-run adjustment of real house prces back to the equlbrum. Pooled mean-group and mean-group estmaton technques developed by Pesaran and Smth (1995) and Pesaran et al. (1999) are appled to a panel of the 51 U.S. states over the perod from 1976Q3 to 2012Q4. Our results suggest a common long-run relatonshp over the sample perod between real house prces and ther economc fundamental determnants n the 51 U.S. states. However, the speed of adjustment of real house prces vares vastly across states, wth a half-lfe estmate of 22 quarters on average, and the devatons of real house prces from the equlbrum range from 30% to 46% across states over tme. JEL classfcaton codes: R21, R31 Key words: house prce, panel unt root, panel contegraton, pooled mean-group estmator, mean-group estmator. Runnng Ttle: Long-run Equlbrum and Short-run Adjustment n U.S. Housng Markets Correspondng author

2 1. Introducton The relatonshp between house prces and key macroeconomc varables s of great concern to polcymakers and researchers, especally after the meltdown of the U.S. housng market startng around 2006 and the subsequent global fnancal crss. In ths context, there are two man streams of lterature. One argues that there s no bubble n the U.S. housng market and that changes n house prces reflect movements n macro fundamentals such as personal ncome, unemployment, mortgage rates, etc. For nstance, Leung (2014) bulds a dynamc stochastc general equlbrum model to justfy that house prces and ncome are co-ntegrated. Courchane and Holmes (2014) fnd that U.S. house prces were closely algned wth economc fundamentals before 2008 when the mortgage markets crashed. Nnej et al. (2013) nvestgate whether ntrnsc bubbles and ratonal speculatve bubbles resulted n devatons n U.S. house prces from economc fundamentals durng Holly et al. (2010) studes the determnants of real house prces n a panel of 49 U.S. states from 1976 to 2007 and concludes that the rsng real house prces were n lne wth real ncome. Other nfluental studes nclude Malpezz (1999), McCarthy and Peach (2004), Hmmelberg et al. (2005), and Smth and Smth (2006). Emprcal studes on the mpact of macroeconomc varables on house prces usng nternatonal data are also rch (e.g., Apergs, 2003; Boroweck, 2009; Deng et al., 2009; Kholodln et al., 2010). The other strand of lterature fnds no evdence of a long-run relatonshp between house prces and macro-fundamentals, mplyng that house prces are not n lne wth fundamentals, and thus, housng bubbles may exst. Stgltz (1990) defnes a house prce bubble as a stuaton n whch house prce growth s not supported by changes n ts fundamentals. For nstance, Peláez (2012) suggests a dsequlbrum exsted between house prces and per capta ncome durng the perod n the U.S. Arshanapall and Nelson (2008) fnd evdence of a U.S. housng 1

3 bubble from 2000 to 2007 wth a contegraton test. Galln (2006) uses both U.S. natonal-level data and a panel of 95 U.S. ctes and concludes that house prces and ncome are not contegrated. Meen (2002) and Shller (2005) use aggregate U.S. data and fnd that changes n fundamentals do not explan the surge n U.S. house prces after In the lterature, the fundamental model of equlbrum house prces s one of the nfluental theores about the evoluton of equlbrum house prces. 1 Ths model compares observed house prces wth ther fundamental values that are estmated based on the long-run relatonshp between house prces and macroeconomc fundamentals (Kaufmann and Mühlesen, 2003; Klyuev, 2008; Holly et al., 2010). In ths paper, we examne the long-run relatonshp between real house prces and macroeconomc fundamentals and the short-run adjustment of real house prces to the equlbrum n the 51 U.S. states over the perod 1976Q3 2012Q4. 2 What dstngushes our work from prevous emprcal studes on the relatonshp between house prces and macroeconomc fundamentals s the followng: (1) Our work apples the pooled mean-group (PMG) and mean-group (MG) estmaton technques developed by Pesaran and Smth (1995) and Pesaran et al. (1999) to study both the long-run and the short-run behavors of real house prces at the U.S. state level and, n partcular, the devatons of real house prces from ther fundamentals and the speed of adjustment of real house prces to macroeconomc dsturbances. The PMG and MG estmatons are mplemented n levels of data and allow for non-statonarty and contegraton across a panel of data well suted to capturng housng market characterstcs. (2) Our study uses the most recent quarterly state-level data, whch better capture the correcton 1 Alternatve theory ncludes the asset prce approach, whch compares observed prce-rent ratos wth tme-varyng dscount factors that are determned by the user cost of ownng a house (Campbell and Shller, 1987; Wang, 2000; Mkhed and Zemčík, 2009a). 2 The Unted States conssts of the 50 states and the Dstrct of Columba, whch are referred to as the 51 states hereafter. 2

4 of real house prces across the 51 U.S. states after the recent collapse of the housng market n the U.S. 3 Our analyss ams to provde dsaggregate perspectves of U.S. housng markets and to show the common characterstcs of such markets across the entre U.S. Recent emprcal lterature has extensvely nvestgated the relatonshp between house prces and economc fundamentals. The fndngs vary wth the econometrc models and the data used. For nstance, Mkhed and Zemčík (2009a) confrm the exstence of housng bubbles n 23 U.S. MSAs from the frst half of 1978 to the second half of 2006, usng the panel unt root test by Pesaran (2007) and the panel contegraton test by Pedron (1999, 2004) to account for crosssectonal dependence. Mkhed and Zemčík (2009b) use aggregate quarterly U.S. data for 1980Q2 to 2008Q2 and annual data on 22 U.S. MSAs from 1978 to 2007 to show that house prces do not algn wth fundamentals n sub-samples before 1996 and from 1997 to Clark and Coggn (2011) apply unt root tests and contegraton tests to the U.S. both naton-wde and dvded nto four regons over the perod from 1975Q1 to 2005Q2, snce these tests are techncally mmune to the cross-sectonal dependence problem and explctly allow for structural breaks. They fnd that U.S. house prces and fundamental economc varables are unt root varables that are not contegrated. Vector error correcton models (VECMs) have recently been appled to handle both the non-statonarty and endogenety problems n the study of house prce determnants. Such models also dstngush between long-run relatonshps and short-run adjustments. For nstance, Wheaton et al. (2014) estmate VECMs separately for 68 U.S. MSAs usng quarterly data for house prces and resdental constructon permts from 1980Q1 to 2012Q2. Panel error correcton models, whch are combnatons of panel data and error correcton models, have also been 3 We do not consder MSA-level data n ths study because MSAs correspond to labor market areas wthn whch workers are wllng to commute, and thus they cannot represent the entre U.S. housng market. For example, Pan and Wang (2013) fnd that a common postve long-run relatonshp among house prces, personal ncome, and labor force growth does exst n 286 U.S. MSAs but not n U.S. non-msas. 3

5 appled to study housng markets (e.g., Hendershott et al., 2002; Brounen and Jennen, 2009; Ott, 2014). In ths paper, to nvestgate the possble long-run relatonshp between real house prces and ther macroeconomc fundamental varables, we frst conduct three panel unt root tests those by Im et al. (2003), Maddala and Wu (1999), and Pesaran (2007) to verfy the order of ntegraton for each varable n level and n frst dfference (quarter-to-quarter change). Then, we apply Westerlund s (2007) panel contegraton tests to nvestgate the exstence of a long-run relatonshp between real house prces and ther economc fundamental varables. In contrast to prevous studes, whch have used the resdual-based contegraton tests by Engle and Granger (1987), Phllps and Oulars (1990), or Pedron (1999, 2004), our study uses Westerlund s tests, whch are based on structural (rather than resdual) dynamcs, have good sze accuracy, and are more powerful than the resdual-based tests. Moreover, Westerlund s tests accommodate ndvdual specfc short-run dynamcs and allow for cross-sectonal dependence. Three out of four tests reject the null hypothess of no panel contegraton for the full sample from 1976Q3 to 2012Q4, suggestng the exstence of a long-run relatonshp between real house prces and ther fundamental values over the full sample perod. Ths result provdes emprcal justfcaton for applyng the PMG and MG estmatons to real house prces and economc fundamentals. The PMG and MG estmators are two mportant methodologes for estmatng non-statonary dynamc panels, whle allowng for heterogeneous parameters across groups. Compared to methodologes used n prevous studes, the PMG and MG estmatons are conducted n levels and take nto account any non-statonarty and contegraton n panel data. The PMG estmator mposes a homogenety restrcton on the long-run relatonshp between varables, whle the MG estmator does not (Koetter and Poghosyan, 2010). These estmators have been prevously used 4

6 to study house prce determnants n varous countres. For example, Kholodln et al. (2010) analyze house prce determnants n an nternatonal sample of countres, Stepanyan et al. (2010) study selected countres from the former Sovet Unon, and Koetter and Poghosyan (2010) focus on regonal housng markets n Germany. In ths paper, we employ the PMG and MG estmators to examne real house prce determnants n the U.S., usng a panel of the 51 U.S. states over the perod from 1976Q3 to 2012Q4. Our results show that the PMG estmator s preferable, whch suggests a common long-run relatonshp among real house prces, real personal ncome per worker, populaton growth, unemployment rates, and the net cost of borrowng across the 51 U.S. states. However, there s substantal heterogenety n the speed of the short-run adjustment of real house prces and n the devatons of real house prces from ther long-run equlbrum across states. In addton, the devatons of real house prces from fundamentals n the post-crss perod (2010Q4) are greater than the devatons durng the peak (2007Q1), mplyng that the economc fundamentals deterorated even more rapdly than real house prces n the post-crss perod. Ths s consstent wth the fndng of Stepanyan et al. (2010) for the former Sovet Unon countres. Overall, our results can provde mportant emprcal nsght nto modelng house prce dynamcs. The remander of ths paper s organzed as follows. Sectons 2 and 3 descrbe the emprcal methodologes and data, respectvely. The emprcal results are presented n Secton 4. Fnally, Secton 5 concludes and sheds lght on some polcy mplcatons. 2. Econometrc Model and Technques 2.1 Testng for Panel Unt Roots and Contegraton 5

7 Before nvestgatng the possble long-run relatonshp between real house prces and ther macroeconomc fundamental varables, we begn wth three panel unt root tests: Im et al. (2003), Maddala and Wu (1999), and Pesaran (2007), to verfy the order of ntegraton for each varable n level and n frst dfference. The null hypothess for all three tests s that all panels contan unt roots. Specfcally, the Im-Pesaran-Shn (IPS) unt root test s based on the ndvdual augmented Dckey-Fuller (ADF) regresson: y t t y p, t1 jy, t j t j0, (1) where and t ndcate state and tme, respectvely, and y denotes real house prces. The IPS t statstc s the average of the t-statstcs (denoted as ) for s n the ndvdual ADF regressons: t IPS N ( t E t 0 ) N(01, ) vart 0, (2) where t 1 N N t 1. P 2 The Maddala and Wu (MW) test statstc s obtaned by N 1 ln p, and combnes the p- values from the ndvdual ADF tests. Both the IPS and MW tests assume no cross-sectonal dependence n the panel data. However, house prces and macroeconomc fundamentals show strong cross-sectonal dependence (Mkhed and Zemčík 2009a, b; Holly et al., 2010), whch should be taken nto account n testng for unt roots and contegraton. Pesaran (2007) proposes a panel unt root test robust to cross-sectonal dependence, known as the CIPS test. It s based on the cross-secton augmented Dckey-Fuller (CADF) regresson: y t t y p p, t1 yt 1 jy, t j jyt j t j0 jq, (3) 6

8 ~ y where t s the cross-secton mean of y t. The CIPS statstc s the cross-secton average of t t CIPS 1 N N 1 ~ t ( N, T ), (4) ~ t where s the t-statstc for n the ndvdual CADF regresson. If the varables were found to be non-statonary based on the unt root tests, then we would have needed to further examne whether they were contegrated. Accordng to the economc theory, f real house prce developments are n lne wth economc fundamentals, non-statonary real house prces should be contegrated wth other non-statonary economc varables wth the same order of ntegraton. We apply Westerlund s (2007) panel contegraton tests to nvestgate the exstence of a long-run relatonshp between real house prces and other key economc fundamental varables. The tests allow for a large degree of heterogenety, both n the long-run contegratng relatonshp and n the short-run dynamcs, and dependence wthn as well as across the cross-sectonal unts. The null hypothess s that of no contegraton n the panel. In partcular, the data-generatng process for the error-correcton tests s: : y t ' d t, t1, t1 j1, t j ' ( y x ) y x p j p j jq, t j e t, (5) where d contans the determnstc components and x represents economc fundamental varables. Westerlund (2007) proposes four tests based on the least squares estmate of and ts t-rato. 4 The group-mean statstcs are calculated as n Eq.5 G 1 N N 1 SE( ˆ ) ˆ and G 1 N N 1 ˆ (1) T ˆ, (6) 4 Detals of the test procedures are provded n Westerlund (2007). 7

9 where SE( ˆ ) s the conventonal standard error of ˆ. The panel statstcs are computed as P ˆ SE( ˆ) and P ˆ T. (7) 2.2 PMG and MG Estmatons To further study the long-run equlbrum between real house prces and macroeconomc fundamentals n U.S. housng markets, as well as the short-run adjustment of real house prces, we apply the PMG and MG estmators to a panel of the 51 U.S. states over the perod 1976Q3 2012Q4. The PMG and MG estmators have been proposed to estmate non-statonary dynamc panels n whch the parameters are heterogeneous across groups. The man dfference between the two estmators s that the PMG estmator mposes a homogenety restrcton on the long-run relatonshp between varables whle the MG estmator does not. Such homogenety restrctons mposed by the theory can be tested emprcally usng the Hausman test. The house prce determnants frequently studed n the housng lterature nclude real ncome per capta, populaton growth, unemployment rates, and real nterest rates (e.g., Muellbauer and Murphy, 1997; Meen, 2002; Barker, 2005). 5 Holly et al. (2010) provde a theoretcal model that justfes the exstence of contegraton between real house prces and real ncome per capta, as well as a role for the real nterest rate and demographc factors. 6 Compatble wth the long-run 5 Other factors have also been consdered n the lterature, such as buldng costs (Shller, 2005), ownng costs of housng (Hmmelberg et al., 2005), and rent (Mkhed and Zemčík, 2009a, b). However, data for these varables are not avalable for the 51 U.S. states at quarterly frequency, therefore, we do not nclude them n our study. 6 In ther theoretcal model, the house prce-ncome rato, also known as the affordablty ndex, s statonary. Ths mples that the log of the real house prce ndex wll be contegrated wth the log of real ncome per capta wth the contegratng vector gven by (1, 1), f the log of the real house prce ndex s an ntegrated varable of order 1,.e., I(1). In the long run, therefore, the elastcty of real house prces to real ncome s unty. In addton, they also consder the possble effect of populaton growth rates on the log of the real house prce ndex at the state level. In aggregate tme-seres analyss, t s dffcult to dentfy the effects of slowly movng varables such as populaton growth on real house prces. However, n the panel context, the cross-secton dmenson can be used to dentfy such 8

10 theory and the contegratng relatonshp among the varables of nterest, we descrbe the longrun relatonshp between real house prces and ther fundamentals n the followng log-lnear form 7 : RHP t 0 1 RINC t 2POPt 3 URt 4RMORT t1 D t, (8) where and t ndcate state and tme, respectvely; RHP s the (log) real house prce ndex; and RINC s the (log) real personal ncome per worker. Based on the theory n Holly et al. (2010), the elastcty of real house prces to real ncome s unty n the long run. In addton to real ncome per capta, other factors such as changes n demographcs, unemployment rates, and the net cost of borrowng also play a role n the determnaton of real house prces at the state level. POP represents the rate of change n populaton, UR s the unemployment rate, and RMORT s the net cost of borrowng defned by the real long-term mortgage rate net of real house prce apprecaton or deprecaton as n Holly et al. (2010) and Kholodln et al. (2010), whch s ncluded n Eq.8 wth a lag to avod smultanety. 8 A pror we would expect a rse n populaton growth and a fall n the unemployment rate would be assocated wth hgher real house prces, whle a rse n the net cost of borrowng would negatvely nfluence real house prces. Fnally, s the state-specfc fxed effect and D represents the vector of dummy varables that capture the mpact of polcy nterventons 9 and common shocks to the economy (e.g., the Interstate effects. For a gven level of real ncome per capta, real house prces are expected to be hgher n states wth a hgher populaton growth rate. 7 Ths s a sem-loglnear specfcaton for real house prces and the fundamentals, whch s commonly used n the emprcal lterature on the long-run relatonshp between house prces and the determnants (see, e.g., Terrones and Otrok, 2004; Ahearne et al., 2005; Almeda et al., 2006; Égert and Mhaljek, 2007; Iossfov et al., 2008, and Stepanyan et al., 2010). Ths specfcaton reflects the fact that populaton growth s consdered statonary n the steady state of the economy, and the level of economc development (approxmated by the level of real ncome per capta), combned wth other determnants, nfluence the level of real house prces n the long run. 8 The appendx defnes the varables used n more detal. 9 There have been sgnfcant polcy market nterventons and bank deregulaton durng the sample perod, for nstance, the Communty Renvestment Act of 1977 (October 12, 1977), the Regle-Neal Interstate Bankng and Branchng Effcency Act of 1994 (September 29, 1994), and the Fnancal Servces Modernzaton Act of 1999 (November 12, 1999). 9

11 Bankng and Branchng Deregulaton Index developed by Rce and Strahan, 2010, and the recent fnancal crss). One feature of the model n whch we are nterested s the extent to whch real house prces are drven by fundamentals such as real ncome per capta, populaton growth, unemployment rate, and the net cost of borrowng. If the varables are ntegrated of order one (.e. I(1)) and co-ntegrated, then the error term t s statonary (.e. I(0)) for all. The autoregressve dstrbuted lags, ARDL(p,q,q,q,q), dynamc panel representaton of the long-run Eq.8 s: RHP t p j1 RHP j q q q q t j j RINC t j j POP t j jur t j j RMORT t j D, (9),,,,, t j0 j0 j0 j1 The model specfcaton n the error-correcton form of Eq.9 s as follows: RHP ( RHP p1 j1 t RHP j t j t1 q1 j0 RINC 1 j 0 1 RINC t j 1 q1 j0 POP UR 2 j 2 t POP t j 3 q1 j0 t 3 j RMORT 4 UR t j q j1 t1 4 j ) RMORT t j, t (10) where (1 ), p j j1 0, q 1 j j0 1, q 2 j j0 2, q 3 j j0 3, and q 1 4 j j1 4. The error-correcton term ( RHP ˆ ˆ ˆ ˆ ˆ t1 0 1 RINC t 2POPt 3 URt 4RMORT t1 ) represents the temporary devatons of real house prces from ther fundamental values at the state level. The homogenety restrcton mposed by the PMG estmator s on the coeffcents of long-run real house prce determnants 1, 2, 3, and 4, restrctng all the long-run parameters to be the same across states. Ths restrcton can be relaxed to restrctng only the subset of the long-run parameters to be the same across states. The ntercept, the speed of the adjustment parameter and the short-run adjustment coeffcents 1 j, 2 j, 0 3 j, and 4 j vary across states. We expect a negatve speed of adjustment parameter, whch suggests that real house prces 10

12 react to dsequlbrum n the real estate market: Real house prces decrease followng postve devatons from the long-run equlbrum n the real estate market, whle real house prces ncrease followng negatve devatons from the long-run equlbrum. 3. Data The data for house prces and macroeconomc varables at the U.S. state level cover the 50 states and the Dstrct of Columba over the perod 1976Q3 2012Q4. We obtan the quarterly house prce all-transactons ndex (estmated usng sales prces and apprasal data) from the Federal Housng Fnance Agency (FHFA). The ndex s based on transactons and apprasals, and then s adjusted for apprasal bas. 10 Followng prevous lterature, we use personal ncome per worker, populaton growth, and unemployment rates as house prce determnants to estmate the house prce devatons. The U.S. state-level data on personal ncome are obtaned from the U.S. Bureau of Economc Analyss (BEA). To obtan the real house prce ndex and real personal ncome, the house prce ndex and personal ncome are dvded by the consumer prce ndex (CPI), whch s avalable for four census regons n quarterly frequency from the U.S. Bureau of Labor Statstcs (BLS). 11 States n a partcular census regon share the same CPI. Inflaton rates are calculated based on the CPI as well. 12 State populaton data are obtaned from the U.S. Census Bureau. 13 Cvl labor force and unemployment rates at the state level are taken from the BLS. 14 Mortgage 10 The FHFA house prce ndex ncludes only homes wth mortgages that conform to Fredde Mac and Fanne Mae gudelnes. Jumbo loans over $417,000 are not ncluded. Ths ndex s equally weghted regardless of the value of the house. 11 The U.S. Census Bureau groups the 50 states and the Dstrct of Columba nto four census regons, namely, Northeast, Mdwest, South, and West regons. 12 We do census X12 multplcatve seasonal adjustment for the CPI, and then calculate the annual rate of nflaton based on the CPI. 13 Raw populaton data s avalable n yearly frequency and we convert the annual data to quarterly frequency usng constant match n EVews. 14 Cvl labor force and unemployment rates are reported n monthly frequency and we convert monthly to quarterly frequency usng the average method n EVews. 11

13 rates are avalable for four census regons n quarterly frequency from the Federal Reserve Bank of St. Lous (FRED). States n a partcular census regon share the same mortgage rates. Followng Holly et al. (2010) and Kholodln et al. (2010), we construct the net cost of borrowng as the real long-term mortgage rate net of real house prce apprecaton or deprecaton. The long-term nterest rate s adjusted usng the housng prce ndex and not the CPI based on the consderatons of a household, whch makes a decson about the long-term nvestment of buyng a housng asset. Ths rate compares the nterest ncome from a bank depost wth captal gans from changes n housng prces. A detaled descrpton of the data s provded n the appendx. [Table 1 here] Table 1 reports the summary statstcs. We observe that the real house prce ndex (1980=100) vared across the states over tme, wth a mnmum of 52 (Hawa, 1981Q4), a maxmum of 345 (Massachusetts, 2005Q3), and an average of 135. The macroeconomc varables are more dspersed. Specfcally, real personal ncome per worker vared from US$18,179 (Msssspp, 1980Q2) to US$60,802 (Dstrct of Columba, 2010Q4), wth an average of US$30,254. Unemployment rates ranged from 2.1% (New Hampshre, 1987Q1) to 18% (West Vrgna, 1983Q1), wth an average of 6%. 4. Emprcal Results 4.1 Panel Unt Root and Contegraton Test Results Table 2 summarzes the panel unt root results based on the full sample from 1976Q3 to 2012Q4. To conduct the testng, we nclude tme trends for the real house prce ndex and real personal ncome per worker, snce both varables exhbt a clear upward trend over tme n the sample. 12

14 The number of lags for each varable n each state s chosen automatcally usng the Bayesan nformaton crteron (BIC) wth a maxmum of four lags 15. Boldface values denote samplng evdence n favor of unt roots. For the full sample, all three panel unt root tests suggest that the real house prce ndex and real personal ncome per worker are ntegrated of order one, or I(1), and that the remanng four varables are statonary, or I(0), at the 5% sgnfcance level. [Table 2 here] Gven the panel unt root test results for the full sample, we proceed to conduct Westerlund s (2007) panel contegraton tests on the two I(1) varables (.e., real house prce ndex and real personal ncome per worker). Table 3 reports the results. Three of the four statstcs and the correspondng p-values suggest rejectng the null of no panel contegraton. Therefore, our results confrm the exstence of a long-run relatonshp between real house prces and ther fundamental values over the perod from 1976Q3 to 2012Q4, whch satsfes the assumptons n the followng PMG and MG estmatons. [Table 3 here] 4.2 Long-run Equlbrum between Real House Prces and Macroeconomc Fundamentals Table 4a reports the estmaton results of the PMG and MG specfcatons of Eq.10. The upper panel reports the average long-run coeffcent estmates n Eq.10 for the log of the real house prce ndex. As a benchmark, Model I ncludes the log of real personal ncome per worker, populaton growth rates, unemployment rates, and the net cost of borrowng as the macroeconomc fundamentals for the log of the real house prce ndex. 16 Notably, the Hausman 15 Results are consstent when eght lags are used as the maxmum. 16 We also consdered nflaton rates as an explanatory varable n the PMG and MG estmatons. However, we ran nto convergence problems when we added nflaton rates to the general specfcatons. 13

15 tests wth p-values greater than 0.05 suggest that the PMG estmator s preferable, snce we fal to reject the null hypothess that the dfference between the PMG and MG models s not systematc. Ths suggests a common long-run relatonshp among real house prces, real personal ncome per worker, populaton growth, unemployment rates, and the net cost of borrowng across the 51 U.S. states. In the PMG estmatons restrctng common long-run coeffcents across states, we fnd a statstcally sgnfcant postve long-run relatonshp between the log of the real house prce ndex and the log of real personal ncome per worker, and the ncome elastcty of house prces s The mpact of populaton growth on real house prces s also sgnfcantly postve. In lne wth our expectatons, unemployment rates and the net cost of borrowng have a sgnfcantly negatve effect on real house prces n the long run. Overall, our results confrm that the long-run equlbrum real house prces ncrease wth rsng demand due to hgher ncome and populaton growth, but lower unemployment rates and the net cost of borrowng. Dagnostc tests confrm the valdty of our model specfcaton. Specfcally, the standard error of regresson vares from 0.01 n North Carolna to 0.07 n Hawa, wth an average of The formal statstcal tests of heteroscedastcty reject the null hypothess of equalty of error varances at the 5% level n 28 states. At the 5% level, there s no evdence of resdual seral correlaton n the equatons for 33 states. Ramsey s RESET tests for functonal form show no evdence of msspecfcaton n 29 states. 17 [Table 4a here] Prevous emprcal studes ndcate that bank deregulaton led to nter and ntra-state mergers and acqustons, as well as a general broadenng of the geographc scope of bankng operatons, 17 If the sample s larger than the 30, one can gnore the normalty ssue f t exsts, per the central lmt theorem. 14

16 whch enabled banks to dversfy depost collecton across locatons, and to lower the cost of fundng. Rce and Strahan (2010) constructed a tme-varyng ndex of nterstate branchng deregulaton that captured dfferences n bankng regulatory constrants between 1994 and Favara and Imbs (2015) use the Rce Strahan deregulaton ndex to evaluate the consequences of deregulaton on mortgage credt and house prces and fnd that U.S. branchng deregulaton between 1994 and 2005 affected the supply of mortgage loans, and va the effect on credt, the ncrease n house prces. Therefore, n Model II, we nclude the ndex of nterstate branchng deregulaton constructed by Rce and Strahan (2010). Ths ndex captures the mpacts of the Regle Neal Interstate Bankng and Branchng Effcency Act of 1994 and the Fnancal Servces Modernzaton Act of It s shown that bank deregulaton plays a postvely nsgnfcant role n the adjustment of real house prces. 20 The fndngs for the other macroeconomc varables reman unchanged. The meltdown of the U.S. housng market around 2006 trggered the subsequent global fnancal crss. In Model III, we add a tme dummy varable (Dummy08q3) to control for the mpact on the U.S. housng markets durng the recent fnancal crss. 21 The tme dummy s nsgnfcant because ts mpact on real house prces s partally captured by other macroeconomc fundamentals. [Table 4b here] Snce economc fundamentals could have varyng mpact on real house prces n the long run versus the short run, we examne alternatve model specfcatons n Table 4b, whch allow for 18 The ndex ranges from 0 (most restrcted) to 4 (least restrcted). 19 We consdered the Communty Renvestment Act of 1977 n the estmatons. It turns out to be nsgnfcant. 20 Bank deregulaton remans nsgnfcant when sub-samples 1994Q1 2015Q4 or 1994Q1 2012Q4 are used. 21 The recent fnancal crss was trggered by Lehman Brothers flng for bankruptcy on September 15,

17 dfferent economc fundamentals n the long-run equlbrum versus the short-run adjustment of real house prces. Specfcally, Model IV ncludes real personal ncome per worker and populaton growth, Model V consders real personal ncome per worker and the unemployment rate, and Model VI ncorporates real personal ncome per worker, populaton growth, and the net cost of borrowng n the long run. The lags of real house prces and all four economc fundamentals n Eq.10 are consdered n the short run. Consstent wth the results n Table 4a, the Hausman tests suggest that the PMG estmator s preferred n all model specfcatons. All longrun coeffcents are statstcally sgnfcant wth the expected sgns. 4.3 Short-run Adjustments of Real House Prces to the Long-run Equlbrum The lower panels of Tables 4a and 4b report the short-run coeffcent estmates of the PMG and MG specfcatons. In the short run, the lags of real house prces are ncluded to allow for momentum n real house prces, followng Case and Shller (1989) and most recently Favara and Imbs (2015). The coeffcent s negatvely sgnfcant, mplyng that hgher real house prces n the prevous perods could lead to a subsequent reverse of real house prces to the equlbrum. The speed of the adjustment of real house prces to the long-run equlbrum s measured by the coeffcent n Eq.10. All model specfcatons of the PMG estmatons show a sgnfcantly negatve speed of adjustment, rangng from to Ths fndng ndcates real house prces adjust to the long-run equlbrum n response to a shock: Followng postve devatons from the long-run equlbrum n the real estate market, real house prces decrease, and vce versa. Followng the lterature, the half-lfe of the adjustment s approxmated by ln(2)/ln(1+ ), ndcatng the tme necessary for a devaton from the long-run equlbrum s halved. For the benchmark Model I, the coeffcent of suggests that roughly 3% of the 16

18 prevous quarter s real house prce devatons from the equlbrum are adjusted ths quarter, and the half-lfe estmate s around 22 quarters or 5.5 years, larger than the half-lfe of 3.5 years obtaned by Holly et al. (2010), who used annual data for U.S. states (excludng Alaska and Hawa) from 1975 to Fgure 1 plots the speed of adjustment coeffcents for the 51 U.S. states from the PMG estmaton of the benchmark Model I. The reference lne ndcates the average speed of adjustment ( 0.031) over the sample. We observe large varatons n the speed of adjustment across the 51 U.S. states, rangng from for South Dakota to for Tennessee. There are 23 states wth faster speeds of adjustment than the average. [Fgure 1 here] 4.4 Real House Prce Devatons from the Long-run Equlbrum Based on the benchmark Model I, we nvestgate the magntude of real house prce devatons from ther fundamental values n the U.S., calculated by the error correcton term n Eq.10. Fgure 2 presents the average devaton of real house prces from ther fundamental values across the states over the sample perod 1976Q3 2012Q4. We observe that real house prces postvely devated from ther long-run equlbrum by more than 30% between 1982Q1 and 1983Q3, whch concded wth the ol prce shocks and economc recessons n the early 1980s. Ths suggests that the U.S. housng markets were overheated compared to the undesrable macroeconomc condton n the early1980s. Real house prce devatons gradually reversed to the equlbrum after peakng n1982q4. A smlar pattern occurred durng the recent fnancal crss. Real house prce devatons substantally surged n after the fnancal crss 22 Koetter and Poghosyan (2010) obtan a half-lfe estmate of 6.79 years for the adjustment of house prces to the long-run equlbrum n Germany. 17

19 trggered by Lehman Brothers bankruptcy. The devaton peaked at 46% n 2010Q1 and then gradually declned. [Fgure 2 here] To further compare the devatons of real house prces from economc fundamentals before, durng, and after the crss, followng the nsght of Stepanyan et al. (2010), we examne three crtcal perods: pre-crss (2005Q1), peak (2007Q1), and post-crss (2010Q4). 23 Table 5 presents the means of the varables across the 51 states for the three perods. We observe larger postve real house prce devatons (37%) durng the post-crss perod than durng the pre-crss and peak perods. Real house prces contnued to declne after the economy peaked ( 1.43% of real house prce changes). Real personal ncome per worker decreased by 0.16%, unemployment rates ncreased to unprecedented levels (8.58%), and the net cost of borrowng reached 4.98%, on average, across the 51 states durng the post-crss perod. Thus, the economc fundamentals deterorated even more rapdly than the declne n real house prces durng the post-crss perod. [Table 5 here] Fgure 3 llustrates real house prce devatons n 10 selected states 24 (Arzona, Calforna, Florda, Hawa, Nevada, Massachusetts, Rhode Island, New Jersey, New York, and Washngton) durng the three perods: pre-crss (2005Q1), peak (2007Q1), and post-crss (2010Q4). One common observaton s that the real house prce devatons durng the post-crss perod are larger than those durng the peak. The large postve real house prce devatons n the post-crss perod mply that, despte the relatvely low current levels, real house prces stll have 23 Lehman Brothers fled for bankruptcy on September 15, 2008, whch marks the start of recent global fnancal crss. Accordng to the busness cycle reference dates from NBER, the most recent recesson started n December 2007 and ended n June We choose 2010Q4 as the post-crss perod. We have also tested other tme perods after 2009Q2, wth no sgnfcant dfference n the conclusons. 24 Due to the space lmt, we report on 10 selected states. Results from other states are avalable upon request. 18

20 some room for downward adjustment. Ths fndng s consstent wth the results of Stepanyan et al. (2010), who analyze the house prce determnants n 11 selected former Sovet Unon countres. [Fgure 3 here] 5. Conclusons Ths paper apples the PMG and MG estmators to examne real house prce determnants n the 51 U.S. states from 1976Q3 to 2012Q4. The emprcal results show that real personal ncome per worker, populaton growth, unemployment rates, and the net cost of borrowng jontly contrbute to real house prce developments n the full sample. Our results confrm that the equlbrum real house prces ncrease wth rsng demand due to hgher ncome and populaton growth, and lower unemployment rates and the net cost of borrowng, provdng evdence of a house prce adjustment to the long-run equlbrum. The short-run adjustment estmate ndcates that about 3% on average of the prevous perod s real house prce devatons from the long-run equlbrum are adjusted durng ths perod. We observe large varatons n house prce devatons from the long-run equlbrum and n the speed of short-run adjustment across the 51 U.S. states, provdng evdence of substantal heterogenety of U.S. housng markets. Moreover, the devatons of real house prces from economc fundamentals n the post-crss perod are greater than those durng the pre-crss and peak perods, mplyng that economc fundamentals have deterorated even more rapdly than real house prces n the post-crss perod whch could lead to a further declne n real house prces. To summarze, our study provdes new evdence of the relatonshp between real house prces and ther economc determnants from the perspectves of both long-run equlbrum and shortrun adjustment and can shed some lght on polcy mplcatons for U.S. housng markets and the 19

21 macro-economy. Frst, we confrm the exstence of a common long-run relatonshp among real house prces, real personal ncome per worker, populaton growth, unemployment rates, and the net cost of borrowng across the 51 U.S. states. When housng markets are undesrable, polces that promote real personal ncome and employment or allevate the net cost of borrowng should help long-run housng market recovery. Second, we show that the heterogenety across the U.S. states n terms of devatons of real house prces from ther fundamentals and the speed of adjustment should be taken nto account when makng polces. Thrd, we beleve these results to be relevant for the theoretcal debate between competng approaches to modelng house prce dynamcs. Fnally, our results, whch are based on the U.S. state-level data for the perod 1976Q3 to 2012Q4, suggest that a long tme seres s requred to better capture the correcton of real house prces after the recent housng market collapse n the U.S. Therefore, the applcaton of longer tme seres to fully capture the effects of the fnancal crss on house prce dynamcs would be of great nterest n future research. Acknowledgements The authors express ther thanks to the edtor and the anonymous referee for nvaluable comments, and for the fnancal support provded by the PSC-CUNY Research Awards (Projects TRADA and TRADA ). All remanng errors are our own. 20

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25 Shller, R. J. (2005). Irratonal Exuberance, Prnceton Unversty Press, Prnceton. Smth, M. H., & Smth, G. (2006). Bubble, bubble, where s the housng bubble? Brookngs Papers on Economc Actvty, Stepanyan, V., Poghosyan, T. and Bbolov, A. (2010). House prce determnants n selected countres of the former Sovet Unon, IMF Workng Paper WP/10/104. Stgltz, J. E. (1990). Symposum on bubbles, Journal of Economc Perspectves, 4, Terrones, M. and Otrok, C. (2004). The Global House Prce Boom, IMF World Economc Outlook, September (Washngton: Internatonal Monetary Fund). Wang, P. (2000). Market effcency and ratonalty n property nvestment, Journal of Real Estate Fnance and Economcs, 21, Westerlund, J. (2007). Testng for error correcton n panel data, Oxford Bulletn of Economcs and Statstcs, 69, Wheaton, W., Chervachdze, S. and Nechayev, G. (2014). Error correcton models of MSA housng supply elastctes: mplcatons for prce recovery, Massachusetts Insttute of Technology, Department of Economcs, Workng Paper

26 Fgure 1 Speed of adjustment coeffcents from PMG estmaton South Dakota Vermont Montana Delaware Georga Idaho New York New Hampshre Connectcut Mane Iowa Kansas Illnos North Dakota Pennsylvana Rhode Island Vrgna Utah Alaska Colorado Massachusetts Mchgan New Jersey New Mexco Hawa Dstrct of Columba Florda Mssour South Carolna Texas Nebraska Wsconsn Wyomng Maryland Msssspp North Carolna Oklahoma Oregon Lousana Nevada Oho Washngton West Vrgna Alabama Arzona Arkansas Calforna Mnnesota Indana Kentucky Tennessee speed of adjustment Note: Each bar shows the average of speed of adjustment coeffcents over the sample perod 1976Q3 2012Q4 n each state. 25

27 Fgure 2 Average real house prce devatons from PMG estmaton q1 1980q1 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 Note: the sold black lne plots the average of real house prce devatons across 51 U.S. states for each tme perod n the sample. 26

28 Fgure 3 Real house prce devatons n 10 selected states durng the pre-crss, peek, and post-crss perods Arzona Calforna Florda Hawa Massachusetts Nevada New Jersey New York Rhode Island Washngton house prce devatons Pre-crss Peek Post-crss Note: Each bar shows real house prce devatons n a selected state for a specfc perod of tme. Pre-crss s 2005Q1; Peek represents 2007Q1; and Post-crss s 2010Q4. 27

29 Table 1 Summary statstcs State varables Mean Sd Mn Max Real house prce ndex Real personal ncome per worker Populaton 5,190,000 5,760, ,000 38,000,000 Unemployment rate (%) Net cost of borrowng (%) Inflaton rate (%) Log of real house prce ndex Log of real personal ncome per worker Growth rate of populaton (%) Speed of adjustment House prce devatons (%) Note: The sample contans 7,446 observatons n the 51 U.S. states over the perod 1976Q3 2012Q4. Real house prce ndex (1980=100). Personal ncome per worker s deflated by the consumer prce ndex (base year s1980). We do Census X12 multplcatve seasonal adjustment for the consumer prce ndex (CPI), then calculate annual rate of nflaton based on the CPI. 28

30 Table 2 Panel unt root tests Varables Levels Frst dfference IPS MW Pesaran IPS MW Pesaran Real house prce ndex (log) (0.32) (0.21) (0.85) (0) (0) (0) Real personal ncome per worker (log) (0.47) (0.12) (0.79) (0) (0) (0) Populaton growth (0) (0) (0) (0) (0) (0) Unemployment rate (0) (0) (0.04) (0) (0) (0) Net cost of borrowng E (0) (0) (0) (0) (0) (0) Inflaton rate E (0) (0) (0) (0) (0) (0) Note: The sample contans the 51 U.S. states over the perod 1976Q3 2012Q4. P-values are reported n the parenthess. Boldface values denote samplng evdence n favor of unt roots. The null hypothess s that of a unt root. The lags are chosen automatcally usng the BIC wth maxmum four lags. Trend opton s ncluded n the testng for the real house prce ndex and real personal ncome per worker n level. IPS represents the Im-Pesaran-Shn (2003) unt root test; MW denotes Maddala and Wu (1999) unt root test; and CIPS stands for Pesaran (2007) unt root test. 29

31 Table 3 Westerlund s panel contegraton tests on the real house prce ndex and real personal ncome per worker Statstc Value Crtcal value P-value G G P P Note: The sample contans the 51 U.S. states over the perod 1976Q3 2012Q4. The null hypothess s that of no contegraton n the panel. The lags are chosen automatcally usng the BIC wth maxmum four lags. 30