Robert H. Edelstein and Konstantin Magin

Transcription

1 U s i n g t h e C C A P M w i t h S t o h a s t i Ta x a t i o n a n d M o n e y S u p p l y t o E x a m i n e U. S. R E I Ts P r i i n g B u b b l e s A u t h o r s Robert H. Edelstein and Konstantin Magin A b s t r a t We examine three issues relating to U.S. real estate investment trust (REIT) priing. First, using a modified apital onsumption asset priing model (CCAPM) with stohasti taxation and money supply, we ompute the fundamental values for REITs for our sample period, Seond, for publily traded equity REITs, we define a bubble to be the differene between the atual stok market prie and the fundamental value derived from our theoretial model. U.S. REITs have, among other orporate strutural features, speial rules governing dividend distributions and orporate taxation that make them an espeially attrative and preferred vehile for testing for the presene of priing bubbles. Our findings suggest that during our sample period, U.S. REITs experiened many prie bubbles, some of whih were quite large. Third, our results imply that monetary poliy, in the short run, plays a role in the formation of these priing bubbles. Eonomists and others have toiled and luubrated for literally hundreds of years attempting to identify, analyze, and explain asset market bubbles, booms, and busts. From these efforts have emerged numerous studies and substantial and substantive aademi and pratitioner debates. We use the infinite horizon apital onsumption asset priing model (CCAPM) with stohasti taxation and money supply derived in Magin (016) and the relatively idiosynrati orporate strutural features of the U.S. equity real estate investment trust (REIT) market to identify and statistially analyze bubbles for U.S. equity REITs between 197 and 013. As employed in this study, an eonomi bubble ours when signifiant trading ours at pries that appear to be inonsistent with intrinsi fundamental value. Our results suggest that during our sample period, , U.S. equity REITs experiened many prie bubbles (i.e., observed REIT pries differed from theoretial fundamental values), some of whih were quite large. We disuss plausible explanations for these bubbles. In partiular, our results indiate that hanges in the real money supply play a statistially signifiant role for aentuating U.S. equity REIT priing bubbles. J R E R V o l. 3 9 N o

2 4 4 E d e l s t e i n a n d M a g i n Of ourse, statistial analyses of priing bubbles are joint tests of the theoretial fundamental value metri and deviations of the observed market pries from this metri. So in order to examine bubbles, it is important to reate a trustworthy measure of fundamental value. Our statistial strategy to perform the joint test, therefore, is to divide the analyses into two sequential parts. First, we test the statistial reliability of the fundamental value, whih serves as the preursor to the seond test. Then we analyze deviations of the observed market pries from fundamental values (i.e., priing bubbles). We employ two separate but related models for deriving fundamental, intrinsi REIT values based on two variants of the CCAPM. The first value model is the CCAPM with stohasti taxation; and the seond value model is the CCAPM with stohasti taxation and money supply. 1 As explained below, we believe these two theoretial models provide reasonable estimates for fundamental value. How and why is this priing bubble study different from the multitude of predeessors? First, while it should almost go without saying, orporate managing, organizing, and planning, as well as shareholder-investor deision-making tend to be tax sensitive. Any analysis of stok pries that does not take into aount the impats and effets of orporate and investor taxation is likely to be ignoring an important explanatory element for market behavior. Our analysis attempts to take into aount that taxation is both stohasti and important; we integrate stohasti taxation into an asset priing model employing the CCAPM framework. Seond, publily traded equity REITs vis-à-vis publily traded C-orporations provide a natural laboratory for analyzing asset priing and evaluating bubbles for the following reasons: (1) REITs, if they follow regulatory requirements, effetively do not pay taxes on net inome at the orporate level; and () REITs are required to pay at least 90% of net inome in the form of dividends. In essene, REITs distribute a substantial amount of ash flow in the form of dividends, and do not pay dividends from after-tax earnings, unlike normal profitable C- orporations. While orporations and shareholders-investors are typially arefully planning and monitoring taxation, in the ase of REITs, orporate taxes de fato are inonsequential. These fators obviate our need to develop a priing model for both orporate and investor taxation. Instead our models will be able to fous on taxation at the shareholder-investor level only. Third, in order to identify and evaluate asset prie bubbles, one needs to have a reliable fundamental theory of value (prie) to ompare with the observed market value (prie). It is the differene between the observed ontemporaneous market value and the theoretial, fundamental value that is the measure for the magnitude of the asset prie bubble. Many asset bubble priing studies either do not provide an expliit theory of prie (value) and/ or simply ompare market pries to data related to general eonomi fundamentals. For example, several studies of housing prie bubbles simply ompare the rates of hange of observed housing sales pries to hanges in household inomes and so forth. In ontrast, we alibrate fundamental theoretial value for U.S. REITs by employing modified existing CCAPM with stohasti taxation. These models have been able to explain a

3 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y substantial portion of the equity premium puzzle in real estate. The obverse side for explaining the puzzle is related to estimating reliable fundamental value priing. Fourth, many well-respeted analyses of the booms and busts (and bubbles) laim that debt (often assoiated with the growth in the money supply) frequently plays a paramount role in the generation of these asset boom, bust, bubble yles. To address possible effets of monetary poliy on the real asset pries, we use a new modified infinite horizon CCAPM with stohasti taxation and real money supply derived in Magin (016). Thus, by inorporating the real money supply into our prie model, we provide a benhmark for the theoretial asset prie, taking into aount the real money supply. Fifth, why do we use the modified CCAPM versus the simpler CAPM (apital asset priing model) to perform our statistial analysis? The CAPM is a one time period analysis that identifies the risk of any seurity as the ovariane between the seurity s rate of return and the rate of return of the market portfolio. Aording to the simple CAPM, the unertainty assoiated with the market portfolio is the sole soure of risk in the eonomy, but this model does not provide a theoretial intertemporal struture that allows one to identify what auses the market portfolio to be risky. In ontrast, maroeonomis does provide a theoretial struture that enables us to identify various soures of aggregate unertainty over time, as well as to understand the mehanisms by whih these maroeonomi variables affet seurity returns and pries. The intertemporal asset priing model that is embedded in stohasti models of maroeonomis is the CCAPM. The name derives from the fat that the equations that desribe the behavior of asset pries and returns in the CCAPM devolve from the intertemporal onsumption/ savings and asset hoie deisions of households. Hene, the CCAPM provides a preferred maroeonomi intertemporal stohasti asset priing framework. As indiated, we use the modified CCAPM that inorporates stohasti taxation and money supply. The remainder of the paper is organized as follows. We provide a seletive review of the voluminous booms, busts, bubbles, and debt literature, as well as that for stohasti taxation and the equity premium puzzle, and how these subjet areas relate to this paper. We then review the theoretial foundations of this paper the CCAPM with stohasti taxation and real money supply. Employing a set of reasonable parametri values for key variables, we next quantify and statistially test the theoretial priing equations derived in Magin (016). We then use the theoretial values (pries) for REITs implied by the CCAPM with stohasti taxation and the real money supply to identify and analyze possible asset priing bubbles. The paper loses with a brief onlusion and summary. L i t e r a t u r e R e v i e w This researh paper spans, interfaes, and extends several well-developed, extensive and expansive finanial eonomi researh subjet areas. Our paper is J R E R V o l. 3 9 N o

4 4 4 4 E d e l s t e i n a n d M a g i n influened by several interesting and important analyses pertaining to real estate market booms and busts. Our researh is, also, intertwined with asset priing models with onomitant issues, suh as the equity premium puzzle, the oeffiient of relative risk aversion for investors, and the impats of stohasti taxation on investment deision-making. We next provide a brief review of pertinent prior researh. B o o m s, B u s t s B u b b l e s, a n d D e b t As a starting point for understanding bubbles, one should aknowledge the ontribution made by Aliber and Kindleberger (011) in their book, Manias, Panis and Crashes. They trae and analyze various bubble episodes aross history in whih eonomi outomes are speulative, and in no way refletive of the underlying fundamental eonomi values. Their analyses of the northern European tulipmania in and the English South Seas bubble in the early 1700s are aptivating and reminisent of alleged bubbles throughout history. During the peak of tulipmania in Marh 1637, tulip bulbs were transating for values that were about 10 times the annual inome of a skilled raftsman. Suddenly, in 1637 the tulip bulb values started to deline preipitously to levels of % to 5% of their peak. The South Sea Company, a British stok ompany founded in 1711, was a publi-private partnership that was granted a monopoly for British trade with South Ameria. However, England was at war with Spain, and Spain ontrolled South Ameria. Hene, there were little real prospets that trade would take plae for the ompany in South Ameria. However, the ompany stok skyroketed as it expanded its transations in British government debt. The ompany s value peaked in 170, before ollapsing to approximately the original flotation prie; hene, the so-alled South Sea Bubble. Beause of the publi outry, Britain in 170 passed the Bubble At, whih forbade the reation of suh stok ompanies without royal hartering. Friedman and Shwartz (1965), in their study of the Great Depression, demonstrate that the inept mis-management of monetary poliy exaerbated an eonomi downturn, reating a downward spiral bubble for the monetary system, as well as the real eonomy. They laim that a moderately informed understanding of them (the monetary eonomis of the banking pani) would have ut short the liquidity risis before it had gone very far, and perhaps before the end of 1930 (p. 11). They also aver that bubbles/ ollapses an sometimes be readily avoided, but one underway are diffiult to ontrol and retify: Eonomi ollapse often has the harater of a umulative proess. Let it go beyond a ertain point, and it will tend to for a time to gain strength from its own development as its effets spread and return to intensify the proess of ollapse. Beause no great strength would be required to hold bak the rok that starts a landslide, it does not follow that the landslide will not be of major proportions (p. 13). Friedman (1968) onludes that monetary poliy annot affet real variables in the long run. He writes that It annot use its ontrol over nominal quantities to

5 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y peg a real quantity the real rate of interest, the rate of unemployment, the level of real national inome, the real quantity of money, the rate of growth of real national inome, or the rate of growth of the real quantity of money. More reently, in a 01 speeh, Ben Bernanke, Federal Reserve Chairman, iting researh by Fuster and Willen (010), Hanok and Passmore (011), Krishnamurthy and Vissing-Jorgensen (011), and Wright (01), laims early skeptis of balane sheet (monetary) poliies worried that any effets on Treasury yields would not be transmitted to other interest rates and asset pries. The evidene reported in these papers refutes this onern. In the same speeh, he reognizes that stimulative monetary poliy may have potential for reating risks to finanial stability. Swanson (015) indiates that monetary poliy, and espeially large-sale asset purhases, during had large effets on orporate yields (raising orporate bond pries) and stok market asset pries. Swanson suggests that these monetary poliy impats may not be persistent (i.e., generate short-run asset prie effets). In sum, more reent researh suggests that monetary poliy has the potential to play a substantive part in the genesis of bubbles, booms, and busts. Reinhardt and Rogoff (009) explore the interrelationship between speulative bubbles, inflation, debt, and monetary rises over the last 800 years. As in Aliber and Kindleberger (011), they examine several historial episodes of speulative bubbles, and attribute many of the bubbles to unrealisti expetations, speulative behavior, and over leverage. They onlude that publi and private setor mishandling of debt is frequently the ause of these speulative bubbles. Mian and Sufi (014) examine how the Great Reession of 008 and the housing market were intertwined with the finanial setor, espeially beause of overzealous mortgage debt issuane. Shiller (009) in his book, Irrational Exuberane, a phrase oined by a now infamous quote from then Federal Reserve hieftain Alan Greenspan, develops several arguments demonstrating how the stok market was overvalued. He also suggests that the U.S. real estate market at the time (005) was likely to be a bubble, a bubble that was puntured three or four years after the book. It is often thought that bubbles are relatively short-term phenomena, and quikly ome down to earth. The U.S. residential real estate bubble ommened in 001, and did not reah its peak until 006. This real estate bubble was repliated in many parts of the world, oming to a rashing halt in 007 (see Bardhan, Edelstein, and Kroll, 01). In fat, bubbles an last deades, as doumented by Ambrose, Eihholtz, and Lindenthal (01). In their study of 300 years of housing prie behavior in Holland, they find that bubbles an have elongated lives, lasting 70 or 80 years where housing pries systematially do not reflet the underlying eonomi rental fundamentals. While there are many explanations, ranging from overleverage loose monetary poliy, rowd herding, animal spirits, and heterogeneous expetations the upshot J R E R V o l. 3 9 N o

6 4 4 6 E d e l s t e i n a n d M a g i n is that asset pries an differ signifiantly, sometimes for prolonged periods, from intrinsi underlying fundamental eonomi value. This said, it is sometimes diffiult to determine what is the underlying intrinsi fundamental eonomi value, irrespetive of the mehanism ausing the speulative bubble. M a r o P o l i y a n d S t o k M a r k e t P r i e s R e t u r n s Many earlier studies trae the interrelationships between and among various aspets of maro poliy, espeially monetary poliy, and their impats on stok market pries and returns. Fama and Frenh (1989), Shwert (1990), and Chen (1991), among others, indiate that the term struture, affeted by monetary poliy, an explain variations in expeted stok returns. The findings in Fama and Frenh (1989) imply that monetary poliy strongly influenes the equity market required rate of return. Jensen and Johnson (1995) laim that there is a diret link between Federal Reserve disount rate hanges and stok market returns. Patelis (1997) suggests that monetary poliy variables an be used to foreast stok market returns. Thorbeke (1997) provides empirial evidene that the various forms of monetary poliy, measured by federal fund rates and so forth, impat stok market returns. Jensen, Merer, and Johnson (1996) find that the impats of monetary poliy over the business yle affet expeted seurity returns asymmetrially. Jensen and Merer (006) find that turning points and monetary poliy are important preditors of future seurity market behavior. More reent studies, suh as Bjournland and Leitemo (009) and Ozdagli and Yu (01), among others, suggest that monetary poliy hanges do not affet stok market returns uniformly. The effets of monetary poliy on the expeted returns and priing of individual stoks appear to depend on both the eonomi yle and the miro irumstanes of individual firms. Several studies (e.g., Darrat and Glasok, 1989; Mueller and Pauley, 1995; Chen, Peng, Shyu, and Zeng, 011) also indiate that the rates of return for REITs are sensitive to hanges in monetary poliy. In summary, the empirial evidene strongly suggests that monetary poliy is intertwined in the eonomi proess for determining stok market expeted rates of returns. F u n d a m e n t a l A s s e t P r i e s, S t o h a s t i Ta x a t i o n, a n d t h e E q u i t y P r e m i u m P u z z l e Paradoxially, almost no researh has been onduted on the effets of stohasti taxes on asset pries and alloations. The researh that has been done was primarily motivated by the equity premium puzzle. The equity premium puzzle was originally identified by Mehra and Presott (1985), using historial data for the stok market portfolio 1. The traditional CCAPM, with an isoelasti onstant relative risk aversion (CRRA) utility funtion and an expeted equity risk premium of 6% for the S&P 500, using average historial stok returns, produes a oeffiient of relative risk aversion of roughly This unbelievably high oeffiient of relative risk aversion onstitutes the so-alled equity premium

7 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y puzzle. There have been many attempts to resolve the equity premium puzzle. See DeLong and Magin (009), for example, for a review and analysis of various attempts to resolve the equity premium puzzle. The introdution of taxation into the standard maroeonomi models seemed to pave one of the most promising ways to approah the puzzle. MGrattan and Presott (005) and Sialm (006, 009) were among the first to introdue taxation into the general equilibrium models. However, their work does not resolve or diretly address the puzzle. Magin (016) derives the infinite horizon CCAPM with stohasti dividend taxation and monetary poliy. He finds that under reasonable assumptions on assets dividends and probability distributions of the future dividend taxes and onsumption, the model implies the onstant prie/ after-tax dividend ratios. He also suggests that the higher urrent and expeted dividend tax rates imply lower urrent asset pries. Finally, he derives that, ontrary to popular belief, monetary poliy is neutral, in the long run, with respet to the real equilibrium asset pries. Magin (015a) proves the existene of equilibria in the infinite horizon general equilibrium with inomplete markets (GEI) model with inseure property rights. Inseure property rights ome in the form of the stohasti taxes imposed on agents endowments and assets dividends. He finds that under reasonable assumptions, finanial market (FM) equilibria exist for most of the stohasti tax rates. Moreover, suffiiently small hanges in stohasti taxation preserve the existene and ompleteness of FM equilibria. Magin (015b), reognizing that taxation unertainty plays a major role for investors, introdued a modified CCAPM with a stohasti tax rate t imposed on the inome and apital wealth of stok holders. Using this modified model, he finds that for a typial investor, who realizes after-tax dividend inome as well as short-term and long-term gains in aordane with historial patterns, the oeffiient of relative risk aversion is Sine earlier studies by Mehra (003) and Mehra and Presott (003) suggest that a oeffiient of relative risk aversion,, between and 4 would seem reasonable, the Magin estimate for 3:76 is believable. The risk premium puzzle for asset lasses other than 1 stok market portfolios has been largely unexplored. The known exeptions for real estate assets are Shilling (003) and Edelstein and Magin (013, 014). In his study, Shilling (003) deploys the CCAPM and two different real estate value data sets; however, he does not take into aount the possible impats of taxation. He onfirms the existene of the equity premium puzzle for real estate assets, and onludes that the puzzle is even more pronouned for real estate than for the general stok market. In ontrast, employing a novel modeling twist by applying the CCAPM with stohasti taxation derived in Magin (015b) to NAREIT data, Edelstein and Magin (013) demonstrate that, for a range of reasonable stohasti tax burdens, the oeffiient of relative risk aversion for U.S. equity REIT shareholders is likely J R E R V o l. 3 9 N o

8 4 4 8 E d e l s t e i n a n d M a g i n to fall within the interval of 4.3 to 6.9, values signifiantly lower than those reported in most prior studies for real estate and other asset markets. These results imply that the CCAPM with stohasti taxation will generate reasonable fundamentally determined REIT asset pries. D e v e l o p i n g a n d Te s t i n g C C A P M f o r R E I Ts P r i i n g In this setion, we delineate two related models for omputing the fundamental value of REITs. We then examine statistially for eah of our REIT fundamental values how well the theory fits atual, observed REIT market pries. In this way, by presenting a theory for asset priing first and then testing it empirially, we are following the time honored reommended praties advoated by eonomists, suh as Koopmans (1947) and Luas (1976). Sine the CCAPM with stohasti taxation generates a reasonable oeffiient of risk aversion, a first natural appliation is to use this model to reate theoretial REIT asset pries. We dub this first theoretial prie to be the fundamental REIT value, without money. The money supply, as disussed above, is believed by many to have a speial impat on asset pries. Hene, we use a seond extension of the CCAPM with stohasti taxation and money supply to derive a seond measure for REIT fundamental value. We dub this seond theoretial prie to be the fundamental REIT value, with money. C C A P M w i t h S t o h a s t i D i v i d e n d Ta x a t i o n a n d w i t h o u t M o n e t a r y P o l i y Aording to Magin (016), CCAPM with stohasti dividend taxation and without monetary poliy implies: 1/ e p (1 ) d k {1,..., n}, (1) kt 1/ 1 e t kt where p kt is the prie per share of an asset k at period t, d kt is the dividend per share paid by an asset k at period t, and t is the dividend tax at period t, (1a) E ln b tl1, tl (1a) VAR ln b tl1. tl

9 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y Taking logarithms of both sides, we obtain: 1/ e ln[p kt] ln 1/ 1 e () ln[(1 t) d kt] k {1,..., n}. Let us quantify now this theoretial model. Historially, Mehra (003) and Mehra and Presott (003) find that: tl1 tl E ln 0.0, tl1 tl VAR ln Set: 1 1 b R 1.01 ƒ Therefore, we estimate: ln(0.99) (1 a) 0.0, (1 a) Thus, 1 1 ln(0.99) (1 a) 0.0 (1 a) J R E R V o l. 3 9 N o

10 4 5 0 E d e l s t e i n a n d M a g i n Hene, 1/ ln(0.99)(1a)0.001/ (1a) e e. Edelstein and Magin (013) estimated that for equity REITs holders: 4.3 a 6.9. Therefore, it is reasonable for the purposes of our analyses to set: 5. So: 1/ ln(0.99)(15) 0.01/ (15) e e 1/ ln(0.99)(15) 0.01/ (15) e 1 e and ln 1/ ln(0.99)(15) 0.01/ (15) e e ln 1/ ln(0.99)(15) 0.01/ (15) e 1 e.647. As in Edelstein and Magin (013, 014), we are assuming that the typial investor in REITs, who has below average ordinary inome tax rates, pays an overall effetive dividend tax rate d of half of that of an investor in general stoks. rekt Therefore, using equation (), we obtain the following expression for alulating theoretial pries of equity REITs: d ln[p ] ln[(1 ) d ] k {1,..., n}. (3) kt rekt kt

11 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y Thus, equation (3) represents the resultant of applying the CCAPM with stohasti taxation, with our parametri assumptions, to REITs. In order to test the empirial validity of our theory, we regress, using OLS, the logarithm of the annual NAREIT real prie index ln[ p kt] for equity REITs against the logarithm of the annual after-tax real REIT dividend payout ln[(1 d rekt) d kt] for the period. 3 We obtain the following OLS regression for : ln[ p ] ln[(1 ) d ]. (4) kt t kt (0.9) (0.13) Adjusted R 0.55, F-statisti 49.98, DW-statisti 0.98 Equation (4) is the regression output, analogous to the theoretial REIT priing model equation (3). The results are partially onsistent with the theoretial model. In partiular, the oeffiient for after-tax REIT dividend payouts is statistially different from zero, but not statistially different from unity (both at the 1% onfidene levels). On the other hand, the estimated value of the interept term is statistially different from zero (at the 1% signifiane level) and statistially different (at the 5% level) from the theoretial model interept value. The adjusted R is Hene, the model explains a little more than half of the REIT prie variation, during an era with several signifiant pereived bubbles in real estate markets. Unfortunately, the Durbin-Watson statisti assoiated with the OLS estimation for equation (4) indiates that there is signifiant autoorrelation. 4 Thus, the estimated oeffiients are likely to be biased. In order to address this problem, we adopt a modified error orretion model (ECM). This method reates indiretly unbiased oeffiient estimators for the long-run equilibrium relation between the prie (value) of REITs and the after-tax dividends. See the Appendix for the derivation of the modified ECM. The form of the ECM is as follows: ln[ p ] ln[(1 ) d ] kt 0 1 t kt ln[ p ] ln[(1 ) d ] kt1 3 t1 kt1 (DPRE 1989) (D 008) (D 009), 1 3 J R E R V o l. 3 9 N o

12 4 5 E d e l s t e i n a n d M a g i n where: 1 if t 1989 DPRE otherwise, 1 if t 008 D otherwise, 1 if t 009 D otherwise. Equation (4) represents the statistial estimation of the ECM, with the addition of fixed time effets for pre-1989, 008, and 009: ln[ p ] ln[(1 ) d ] kt t kt (0.30) (0.11) 0.37 ln[ p ] 0.41 ln[(1 ) kt1 (0.07) (0.07) t (DPRE 1989) 0.36 (D 008) (0.05) (0.11) 0.55 (D 009). (0.15) Adjusted R 0.69 (4) In turn, equation (4) an be employed to generate the unbiased oeffiient estimates for the long-term relation for our model: ln[ p ] ˆ ˆ ln[(1 ) d ] k {1,..., n}, kt t kt 0 ˆ.64 (s.e. 0.69), 3 ˆ 1.11 (s.e. 0.44). The derived statistial results for ˆ and ˆ imply that eah of these oeffiients are statistially different from zero and statistially onsistent with the eonomi theory personified in equation (3). Put somewhat differently, the results suggest

13 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y that the relation desribed by equation (3) is an appropriate measure of fundamental long-run equilibrium value for REITs at eah point in time. It is laimed that monetary poliy may have had a signifiant influene on the priing of real estate assets at various times during our sample period, In order to examine the influene of the real money supply on REIT pries, we apply the CCAPM to inlude both stohasti taxation and real money supply. C C A P M w i t h S t o h a s t i D i v i d e n d Ta x a t i o n a n d w i t h M o n e t a r y P o l i y Aording to Magin (016), CCAPM with stohasti dividend taxation and monetary poliy implies: 1/ e 1/ pkt e dkt k {1,..., n}. (5) 1/ 1 e Taking logarithms of both sides, we obtain: 1/ e 1/ ln[p kt] ln e 1/ 1 e ln[d ] k {1,..., n}, (6) kt where: E[ln[1 ]], t VAR[ln[1 t]]. We also know that: , J R E R V o l. 3 9 N o

14 4 5 4 E d e l s t e i n a n d M a g i n So 1/ e 1/ e 1/ 1 e e / e 1 e / e 13.8 ln(0.99)(15) 0.01 / (15) ln(0.99)(15) 0.01 / (15) and 1/ e 1/ ln e 1/ 1 e e / ln e 1 e ln(0.99)(15) 0.01 / (15) ln(0.99)(15) 0.01 / (15) Using equation (6), we obtain the following expression for alulating theoretial pries of equity REITs: ln[p kt] ln[d kt] k {1,..., n}. (7) Thus, equation (7) represents the resultant of applying the CCAPM with both stohasti taxation and monetary poliy, with our parametri assumptions, to REITs. In order to test the empirial validity of our theory represented by equation (7), we regress, using OLS, the logarithm of the annual NAREIT real prie index [ p kt] for equity REITs against the logarithm of the annual real REIT dividend payout ln[(d kt ] for the period. We obtain the following OLS regression for : ln[ p ] ln[d ]. (8) kt (0.43) (0.16) kt Adjusted R 0.47, F-statisti 36.81, DW-statisti 0.95

15 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y Analogous to equation (4), equation (8) is the OLS regression we use to test the validity of the REIT priing model, inlusive of the real money supply, equation (7). In equation (8), the values of the regression interept and the oeffiient for the REIT real annual dividend payouts are statistially different from zero (at the 1% level), but not statistially different from the theoretial values omputed in equation (7). That is, the results are onsistent with the REIT priing model, with the inlusion of the real money supply. The overall fit for the OLS regression is However, the Durbin-Watson statisti assoiated with the OLS estimation for equation (8) suggests that there is a signifiant autoorrelation problem. In suh irumstanes, the estimated oeffiients for equation (8) are likely to be biased. In order to address this issue, as we have done for equation (4) for the stohasti taxation model, we employ a modified ECM for the stohasti taxation money supply theoretial model. The ECM will permit us to derive unbiased oeffiient estimators for the long-run equilibrium relation between the prie (value) of REITs and the dividends (for the stohasti taxation/ money supply theoretial model). The form of the ECM is as follows: ln[ p ] ln[d ] ln[ p ] kt 0 1 kt kt1 ln[d ] (DPRE 1989) 3 kt1 1 (D 008) (D 009). 3 Equation (8) represents the statistial estimation of the ECM, with the addition of fixed time effets for pre-1989, 008, and 009: ln[ p ] ln[d ] 0.36 ln[ p ] kt kt kt1 (0.4) (0.09) (0.06) 0.49 ln[d ] 0.04 (DPRE 1989) kt1 (0.07) (0.05) 0.33 (D 008) 0.56 (D 009). (0.10) (0.13) Adjusted R 0.76 (8) Equation (8) an be utilized to reate the unbiased oeffiient estimates for the long-term relation for our model: J R E R V o l. 3 9 N o

16 4 5 6 E d e l s t e i n a n d M a g i n ln[ p kt] ˆ ˆ ln[d kt] k {1,..., n}, 0 ˆ 1.61 (s.e. 0.55), 3 ˆ 1.36 (s.e. 0.50). The derived statistial results for ˆ and ˆ imply that eah of these oeffiients are statistially different from zero and statistially onsistent with the oeffiients in equation (7), the priing model with stohasti taxation and money supply. Put somewhat differently, the results suggest that the relation desribed in equation (7) is an appropriate measure of the fundamental long-run equilibrium value for REITs at eah point in time. These overall results (derived by using the ECM s to estimate equations (4) and (8)) imply that the long-run equilibrium prie/dividend relations from equations (3) and (7) provide reasonable measures for REIT fundamental values over time. A n a l y z i n g R E I T B u b b l e s We analyze REIT bubbles in this setion. Conventionally, the asset priing bubble for an asset k at time t is defined as the differene p kt p kt between the atual market prie of an asset and its fundamental, p kt. p kt To provide a visual sense for REIT bubbles during the period, Exhibits 1 and trak atual market pries p kt versus theoretial pries p kt. The atual (market) REIT prie index in Exhibits 1 and is set to be 100 for 197. Exhibit 1 harts theoretial REIT pries p kt generated by the CCAPM with stohasti taxation t and without the real money supply M t /P t, i.e., equation (1), and atual market pries for equity REITs for the period. p kt Similarly, Exhibit harts theoretial REITs pries p kt generated by the CCAPM with stohasti taxation t and with real money supply M t /P t, i.e., equation (5), and atual market pries for equity REITs for the period. p kt Exhibits 1 and provide a pitorial vision of REIT booms, busts, and bubbles in A areful examination of these figures indiates that the positive and negative bubbles suggested by our models are onsistent with regulatory hanges and eonomi events. For example, the negative bubble (i.e., the market undervaluation for REITs vis-à-vis our theoretial fundamental valuations) during 1973 and 1974 reflets the fat that real estate markets, in general, and REITs, in partiular, were in substantial deline aused, at least in part, by the reessionary eonomy. The hange in the tax law in 1986 made REITs more attrative to real estate investors versus publi and private syndiation vehiles. These tax hanges

17 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y Exhibit 1 Theoretial and Market Pries for Equity REITs for reated a boom/ positive bubble for REITs between 1986 and 1989, refleted in Exhibit 1, and to a lesser extent, in Exhibit. Exhibits 1 and identify signifiant negative REIT bubbles during the general deline in real estate markets and a onomitant elongated reession in For most of the subsequent 1990s, there was a robust market for REITs, and an emergene of many REIT IPOs and seondary offerings. During this time period, there was a pronouned REIT market ebulliene. Exhibit 1 and espeially Exhibit suggest a prolonged REIT market positive bubble. The REIT positive bubbles delined as the dot-om boom peaked around 000. The dot-om boom was preipitously followed by the dot-om bust. In this dot-om bust environment, investors preferenes hanged, and were seeking ash flowing investments. Thus, REITs beame a market favorite for investing during the early 000s. This set of irumstanes is refleted by a series of positive bubbles for REITs between 000 and 007 in Exhibits 1 and. The REIT industry began struggling in 007 as the Global Finanial Crisis (GFC) affeted most asset markets. REIT values plunged during the (GFC), and, as many believe, REIT pries delined to levels that were substantially below their fundamental value. Exhibits 1 and are onsistent with these notions about the (GFC), with a negative bubble for REIT priing ourring in 008. Beause of J R E R V o l. 3 9 N o

18 4 5 8 E d e l s t e i n a n d M a g i n Exhibit Theoretial and Market Pries for Equity REITs for the (GFC), many listed equity REITs responded by deleveraging and inreasing their equity positions. As equity REITs beame solvent and interest rates delined, investors were attrated bak to REITs. The REIT market experiened a boom in ; in fat, aording to our models for fundamental value, many stok analysts, and as refleted in Exhibits 1 and, REITs have been in a period of positive bubbles. Hene, we believe our models provide reasonable methods for deteting asset priing bubbles in the REIT market. As disussed above, a large prevalent quantum of earlier researh indiates that, in the short run, a driving fore for the generation of asset prie bubbles is the unantiipated rapid growth in debt instruments, in general, and the money supply, in partiular. Given the log-linear nature of the CCAPM, as is evident by Equations (3) and (7), it is natural then to reate a simple test to examine the empirial impat of the log of the money supply, ln[m t /P t ], upon the differential ln[ p kt] ln[p kt ]. Therefore, for the purposes of this analysis, it makes sense to define the asset priing bubble as ln[ p kt] ln[p kt ]. Equations (9) and (10) represent partial tests for the effet of hanges in the log of the U.S. real money

19 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y supply, ln[m t /P t ], upon U.S. REIT bubbles ln[ p kt] ln[p kt ] during the period: M t P (0.66) (0.0) t ln[ p ] ln[ p ] ln. (9) kt kt Adjusted R 0.30, F-statisti In equation (9), using OLS, the dependent variable is ln[ p kt] ln[p kt ], where ln[p kt ] is given by equation (3), i.e., it is derived from the CCAPM with stohasti taxation but without money supply. The independent variable is ln[m t /P t ]. This regression suggests that inreases in the real money supply explain, in part, the U.S. REIT prie bubbles; the oeffiient for the money supply is statistially signifiant at the 1% level. The positive oeffiient for the money supply implies that the differene between the observed atual REIT market prie and the theoretial REIT prie inreases as the money supply grows. Put somewhat differently, eteris paribus, inreases in the real money supply explain a portion of the variation in ln[ p kt] ln[ p kt ]. The adjusted R implies that, in the short run, the money supply explains 30% of the variation in ln[ p ] ln[ p kt ]. Similar to equation (9), in equation (10), using OLS, the dependent variable is ln[ p kt] ln[p kt ], where ln[p kt ] is now given by equation (7), i.e., it is derived from the CCAPM with both stohasti taxation and money supply. Again, the independent variable is ln[m t /P t ]: M t P (0.65) (0.0) t ln[ p ] ln[p ] ln. (10) kt kt Adjusted R 0.36, F-statisti 4.31 kt The results from equation (10) are similar to those found for equation (9). The oeffiient for the log money supply is signifiantly positive at the 1% level. The overall fit for equation (10) explains 36% of the variation between the REIT market prie and the model REIT prie. Taken together, the results from equations (9) and (10) are onsistent with the notion that, in the short run, the money supply (monetary poliy) an have a signifiant impat on the magnitude of U.S. REIT priing bubbles. While the findings are for a partiular market, the U.S. REIT market during a relatively short time horizon, they do provide new onfirming evidene for earlier researh that laims that the money supply is an important determinant of the magnitude of asset priing bubbles. J R E R V o l. 3 9 N o

20 4 6 0 E d e l s t e i n a n d M a g i n C o n l u s i o n We identify U.S. REIT prie bubbles using NAREIT data for the period. For this analysis, a bubble is defined for publily traded REITs to be the differene between the log of the atual, observed stok prie and the log of the intrinsi, fundamental value at a point in time. We employ two similar models to estimate fundamental value. The first fundamental, intrinsi value is alulated by utilizing the CCAPM with stohasti taxation and reasonable parametri assumptions. Sine the money supply (and other debt instruments) is believed by many to play a ruial role in the generation of asset bubbles, we extend our earlier analysis to alulate a seond measure of fundamental value by utilizing the CCAPM with both stohasti taxation and money supply. For analytial purposes, REITs provide a preferred natural laboratory experiment for bubble testing beause of the rules governing net inome taxation and dividend distributions; in essene, REITs basially are pass-through vehiles without taxation at the entity level, permitting our modeling to fous on the inlusion of shareholder-investor taxation, without the additional ompliations of investment vehile taxation. Taken together, the two modified CCAPM fundamental value measures we use and the speial struture of REITs reate a setting for streamlined analyses for testing for the presene of asset prie bubbles. Our analysis and findings suggest that REIT prie bubbles are omnipresent and statistially signifiant during our sample period. Moreover, hanges in the money supply appear to play a role in generating REIT bubbles. While we provide plausible maroeonomi rationales for the various sequenes of bubbles, our researh should be haraterized as identifying but not neessarily explaining the root auses, the intensities, and/ or the persisteny of these bubbles. We leave the determination of ausal explanations and the intensity-persisteny relationships between REIT bubbles and other variables as a task for future researh. A p p e n d i x The error orretion model (ECM) is designed to reate statistially unbiased oeffiient estimators in the presene of autoorrelation. The ECM is desribed by equation (A1): ln[ p ] B B ln[x ] B ln[x ] kt 0 1 t t1 B ln[ p ] k {1,..., n}, (A1) 3 kt1

21 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y where: X (1 ) d t t kt k {1,..., n}. The underlying long-term relation from the model for REIT priing an be desribed as equation (A): ln[ p ] ln[x ] k {1,..., n}, kt t (A) In long-run equilibrium, it is assumed that: ln[ p ] ln[ p ] k {1,..., n} and ln[x ] ln[x ]. (A3) kt kt1 t t1 Therefore, B0 B1 B and. 1 B 1 B 3 3 Subtrating ln [ p kt1] from both sides of equation (A1) and adding and subtrating B 1 ln[x t1] from the right-hand side of equation (A1) produes: ln[ p ] (B 1) B ln[x ] kt 3 1 t (B 1) ln[ p ] 3 kt1 (1 B ) ln[x ] k {1,..., n}. (A4) 3 t1 Equation (A4) an be rewritten for onveniene as: ln[ p ] ln[x ] ln[ p ] kt 0 1 t kt1 ln[x ] k {1,..., n}, (A4) 3 t1 J R E R V o l. 3 9 N o

22 4 6 E d e l s t e i n a n d M a g i n suh that: (1 B ), 0 3 B, 1 1 B 1, 3 (1 B ). 3 3 Equation (A4) beomes the statistial relation to be estimated to orret for the oeffiient estimation biases reated by autoorrelation. Equation (A4), with fixed time effets added, is the relation estimated above as equation (4). Using a similar approah for the ECM, equation (8) an be derived to generate oeffiient estimates for ˆ and ˆ for the fundamental REIT priing model with both stohasti taxation and money supply. E n d n o t e s 1 See Magin (015b) for the original derivation of the CCAPM with stohasti taxation. See Magin (016) for the derivation of the infinite horizon CCAPM with stohasti taxation and money supply. See Edelstein and Magin (013) for our prior analysis of REITs. Effetive dividend tax rates for investors in general stoks an be found at users.nber.org/taxsim/marginal-tax-rates/af.html. 3 Calulations are based on monthly NAREIT All Equity REITs Index data for equity REIT pries and dividends. 4 It is not surprising that there exists autoorrelation for the NAREIT rate of return (log prie) data series. This empirial issue of autoorrelation in REIT stok data has been identified by several researhers. It is the other side of the oin for researh that finds momentum in stok market returns. See Hung and Glasok (010) and Goebel, Harrison, Merer, and Whitby (013) for examples. R e f e r e n e s Aliber, R.Z. and C.P. Kindleberger. Manias, Panis and Crashes: A History of Finanial Crises. Sixth edition. Palgrave Mamillan, 011. Ambrose, B., P. Eihholtz, and T. Lindenthal. House Pries and Fundamentals: 355 Years of Evidene. Working Paper, Pennsylvania State University, Maastriht University, and Maastriht University, 01. Bardhan, A., R. Edelstein, and C. Kroll. Global Housing Markets. Wiley Press, 014. Bjournland, H.C. and K. Leitemo. Identifying the Interdependene Between U.S. Monetary Poliy and the Stok Market. Journal of Monetary Eonomis, 009, 56:, 75 8.

23 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y Chen, M., C. Peng, S. Shyu, and J. Zeng. Market States and the Effet on Equity REIT Returns Due to Changes in Monetary Poliy Stane. Journal of Real Estate Finane and Eonomis, 011, 41:1, Chen, N.F. Finanial Investment Opportunities and the Maroeonomy. Journal of Finane, 1991, 46:, Darrat, A. and J. Glasok. Real Estate Returns, Money and Fisal Defiits: Is the Real Estate Market Effiient? Journal of Real Estate Finane and Eonomis, 1989, :3, DeLong, J.B. and K. Magin. The U.S. Equity Return Premium: Past, Present, and Future. Journal of Eonomi Perspetives, 009, 3:1, Edelstein, R., and K. Magin. The Equity Risk Premium for Seuritized Real Estate: The Case for U.S. Real Estate Investment Trusts. Journal of Real Estate Researh, 013, 35:4, Stohasti Taxation and Priing of CMBS REITs. Paper presented at the Maastriht- NUS-MIT (MNM) Real Estate Finane and Investment Symposium held by Maastriht University s European Center for Corporate Engagement, Maastriht, The Netherlands, August 31 September, 014 and at the AsRES onferene held by the Asian Real Estate Soiety, Brisbane, Australia, July 14 16, 014 and at a onferene held by the Weimer Shool for Advaned Studies in Real Estate and Land Eonomis, North Palm Beah, FL, May 16 18, 014. Fama, E.F. and K.R. Frenh. Business Conditions and Expeted Returns on Stoks and Bonds. Journal of Finanial Eonomis, 1989, 5, Friedman, M. The Role of Monetary Poliy. Amerian Eonomi Review, 1968, 58:1, Friedman, M. and A. Shwartz. The Great Contration: Prineton University Press, Fuster, A. and P. Willen. $1.5 Trillion is Still Real Money: Some Fats About the Effets of the Federal Reserve s Mortgage Market Investments. Publi Poliy Disussion Papers 010, Federal Reserve Bank of Boston, 010. Goebel, P.R., D.M. Harrison, J.M. Merer, and R.J. Whitby. REIT Momentum and Charateristi-Related REIT Returns. Journal of Real Estate Finane and Eonomis, 013, 47:3, Hanok, D. and W. Passmore. Did the Federal Reserve s MBS Purhase Program Lower Mortgage Rates? Journal of Monetary Eonomis, 011, 58:5, Hung, S. and J. Glasok. Volatilities and Momentum Returns in Real Estate Investment Trusts. Journal of Real Estate Finane and Eonomis, 009, 41:, Jensen, G.R. and J.M. Merer. Seurity Markets and the Information Content of Monetary Poliy Turning Points. The Quarterly Review of Eonomis and Finane, 006, 46, Jensen, G.R., J.M. Merer, and R.R. Johnson. Business Conditions, Monetary Poliy, and Expeted Seurity Returns. Journal of Finanial Eonomis, 1996, 40:, Jensen, G.R. and R.R. Johnson. Disount Rate Changes and Seurity Returns in the U.S., Journal of Banking and Finane, 1995, 19:1, Koopmans, T.C. Measurement Without Theory. Review of Eonomis and Statistis, 1947, 9:3, J R E R V o l. 3 9 N o

24 4 6 4 E d e l s t e i n a n d M a g i n Krishnamurthy, A. and A. Vissing-Jorgensen. The Effets of Quantitative Easing on Interest Rates: Channels and Impliations for Poliy. Brookings Papers on Eonomi Ativity, 011, Luas, R. Eonometri Poliy Evaluation: A Critique. In The Phillips Curve and Labor Markets, K. Brunner and A. Meltzer (eds.). Carnegie-Rohester Conferene Series on Publi Poliy. New York, NY: Amerian Elsevier, 1976, 1:1, Magin, K. Equity Risk Premium and Inseure Property Rights. Eonomi Theory Bulletin, 015a, 3:, 13.. Generi Existene of Equilibria in Finite Horizon Finane Eonomies with Stohasti Taxation. Working Paper, The Center for Risk Management Researh, 015b.. Infinite Horizon CCAPM with Stohasti Taxation and Monetary Poliy. Working Paper, The Center for Risk Management Researh, 016. MGrattan, E.R. and E.C. Presott. Taxes, Regulations, and the Value of U.S. and U.K. Corporations. Review of Eonomi Studies, 005, 7:3, Mehra, R. The Equity Premium: Why Is It a Puzzle? Working Paper 951, National Bureau of Eonomi Researh, 003. Mehra, R. and E.C. Presott. The Equity Premium: A Puzzle. Journal of Monetary Eonomis, 1985, 15:, The Equity Premium in Retrospet. Working Paper 955, National Bureau of Eonomi Researh, 003. Mian, A. and A. Sufi. House of Debt: How They (and You) Caused the Great Reession and How We Can Prevent It From Happening Again. Chiago University Press, 014. Mueller, G. and K. Pauley. The Effet of Interest-Rate Movements on Real Estate Investment Trusts. Journal of Real Estate Researh, 1995, 10:3, Ozdagli, A.K. and Y. Yu. Monetary Poliy Shoks and Stok Returns: Identifiation Through Impossible Trinity. Working Paper, Federal Reserve Bank of Boston, 01. Patelis, A.D. Stok Returned Preditability and the Role of Monetary Poliy. Journal of Finane, 1997, 5:5, Reinhart, C.M. and K.S. Rogoff. This Time Is Different: Eight Centuries of Finanial Folly. Prineton University Press, 009. Rubinstein, M. The Valuation of Unertain Inome Streams and the Priing of Options. The Bell Journal of Eonomis, 1976, 7:, Shwert, G.W. Stok Returns and Real Ativity: A Century of Evidene. Journal of Finane, 1990, 45:4, Shiller, R. Irrational Exuberane. Prineton Press, 009. Shilling, D.J. Is There a Risk Premium Puzzle in Real Estate? Real Estate Eonomis, 003, 31:4, Sialm, C. Tax Changes and Asset Priing. Amerian Eonomi Review, 009, 99:4, Stohasti Taxation and Asset Priing in Dynami General Equilibrium. Journal of Eonomi Dynamis and Control, 006, 30:3, Swanson, E.T. Measuring the Effets of Unonventional Monetary Poliy on Asset Pries. Working Paper 1816, National Bureau of Eonomi Researh, 015. Thorbeke, W. On Stok Market Returns and Monetary Poliy. Journal of Finane, 1997, 5:,

25 S t o h a s t i T a x a t i o n a n d M o n e y S u p p l y Wright, J.H. What does Monetary Poliy do to Long-Term Interest Rates at the Zero Lower Bound? Working Paper 17154, National Bureau of Eonomi Researh, 011. This researh was supported by a grant from the Center for Risk Management Researh. We are very grateful to Bob Anderson for his enouragement and kind support. The authors espeially wish to thank Ko Wang and two anonymous referees for important suggestions that signifiantly improved our paper. We also thank Grae Deng for her dediated and exemplary researh assistane. Robert H. Edelstein, University of California at Berkeley, Berkeley, CA or edelstei@haas.berkeley.edu. Konstantin Magin, University of California at Berkeley, Berkeley, CA or magin@berkeley.edu. J R E R V o l. 3 9 N o