Asset Prices and Armageddon: Do Evangelicals’ ‘End Times’Beliefs A¤ect U.S. House Prices? Christopher Crowe Research Department, International Monetary Fund 700 19th Street NW, Washington, DC 20431. ccrowe@imf.org. March 31, 2008 Abstract According to surveys, around a quarter of Americans expect the world to end as prophesied by the Bible during their own lifetime. This paper undertakes the …rst test of whether these ‘end times’ beliefs a¤ect economic behavior, using a 10-year panel of house price data across 363 Metropolitan Statistical Areas (MSAs). It identi…es a causal e¤ect by interacting a time-varying proxy for the perceived probability of the ‘end times’occurring soon with a geographically-varying proxy for the proportion of believers in Biblical prophecy, both of which are exogenous with respect to changes in house prices, controlling for time and area …xed effects. The paper uncovers a signi…cant positive e¤ect that is robust across samples, speci…cations, and alternative data sources. One explanation for this positive e¤ect is that believers in Biblical prophecy face a tension – between their belief that the end of the world is imminent and Biblical injunctions to behave responsibly in the meantime – that could be reduced by holding illiquid or ‘commitment’ assets to lock in responsible behavior, generating a premium on such assets. Data on mortgage applications support this interpretation. The paper therefore supports models –such as Laibson’s (1997) ‘golden eggs’model of hyperbolic discounting – that incorporate time inconsistent preferences and predict a commitment premium. JEL Classi…cations: E21, R21, Z12. This work re‡ects the views of the author alone and does not re‡ect the views of the IMF, its Executive Board or Management. The author would like to thank Marcos Chamon, Julian Di Giovanni, Andre Faria, Rodney Ramcharan and Romain Ranciere for helpful discussions; Giovanni Dell’Ariccia, Deniz Igan and Luc Laeven for making their mortgage application data available; and Paul S. Boyer and participants at the IMF Research Department’s Brown Bag seminar for comments on an earlier draft of the paper. All remaining errors are my own. 1 1 Introduction According to opinion surveys, half of Americans believe that the world will end as prophesied in the Bible. Around a quarter expect the end to come in their own lifetime. Dispensational Premillenialism, a once-obscure nineteenth century interpretation of Biblical prophecy centered on the ‘rapture’or accession of true believers to heaven, is now the dominant eschatological (end times) framework amongst evangelical Protestants, who make up around one-quarter of the U.S. population.1 These beliefs appear to be becoming more widespread, promulgated by both traditional and new media, and entering both the political realm and mainstream secular culture.2 End times beliefs might be expected to have a profound impact on economic decision-making, particularly with respect to intertemporal choices. Perhaps of greater interest to economists, tracing their impact could also provide insights into how discounting behavior incorporates beliefs about the future and shapes economic outcomes more generally. However, up to now there has been no study of the economic impact of these beliefs. This paper has two goals. First, it attempts to test whether ‘end times’beliefs have any measurable impact on households’intertemporal choices. Second, it argues that any e¤ect could shed light on theories of portfolio choice, and in particular the demand for assets with di¤erent liquidity characteristics. This study faces a number of empirical and conceptual hurdles. The …rst is to identify a suitable dependent variable. Asset prices seem the obvious candidate, since they are inherently forward-looking and should therefore respond to changes in beliefs about the future. Housing assets are the most signi…cant and widely-held 1 Dispensational premillenialism has deep roots among American conservative Protestants, but its interpretation of the Bible’s account of the ‘end times’was not always in the ascendancy (Boyer, 1992; Grenz, 2004; Kilde, 2004). However, global events since the second world war, including in particular the dropping of the atomic bombs on Japan, the creation of the state of Israel, and the Cold War, lent credence to this belief system. Premillenialism (or dispensationalism) is now the dominant eschatological viewpoint for conservative evangelical Christians (Grenz, 2004). Central to the dispensationalist philosophy is the belief, based on a literal reading of the Bible’s book of Revelation, that a period of ‘tribulation’ – a time of extreme and terrible events during which the Antichrist will rule on earth – will commence with the ‘rapture’ or physical ascension of true believers to heaven. The tribulation will end after seven years with the ‘Battle of Armageddon’in which Jesus Christ will return to earth, vanquish the forces of evil in concert with Israel (whose Jewish population will convert to Christianity), and establish a 1,000-year earthly kingdom. A …nal battle between good and evil and judgement day will follow (Grenz, 2004). 2 A 1999 poll for Newsweek found that 40 percent of Americans believed that the world would end in the Battle of Armageddon (Newsweek, October 24, 1999). Of these, 47 percent expected it to occur in their lifetime, while 15 percent expected it to occur within the next year. A 2004 poll for Newsweek found an apparent uptick in these beliefs, with 55 percent of the population reportedly believing that the faithful would be taken to heaven in the ‘rapture’ (Denver Post, April 10, 2005). A popular series of novels set during the ‘tribulation,’the Left Behind series (authored by Tim LaHaye and Jerry B. Jenkins), had sold a total of 65 million copies as of 2007. This …gure includes the 16 books making up the series as well as a number of related titles (source: http://www.leftbehind.com). The tenth title in the series was the best-selling …ction title in the United States in 2001, while a May, 2001 poll found that 9 percent of U.S. adults had read at least one of the books in the series (Forbes, 2004). 2 assets on household balance sheets (Bucks and others, 2006). Housing has the additional bene…t of being location-speci…c, which is exploited in the paper’s identi…cation strategy. It also has speci…c liquidity characteristics compared to other widely-held household assets, allowing the paper’s …ndings to shed light on the second empirical question identi…ed above. This paper therefore focuses on the house price index published quarterly by the O¢ ce of Federal Housing Enterprises Oversight (OFHEO) for 363 Metropolitan Statistical Areas (MSAs). The second challenge is …nding suitable proxies for end times beliefs that are exogenous to the dependent variable and therefore o¤er convincing identi…cation of a causal relationship. The identi…cation strategy employed in this paper exploits the panel dimension of the house price data, focusing on the interaction between two exogenous variables. The …rst is a geographically-varying proxy for the share of those holding ‘end times’beliefs, and the second a time-varying proxy for the intensity of the beliefs. Controlling for area and time …xed e¤ects, any relationship between the resulting interaction term and house prices should then re‡ect a causal one. The exogeneity of the population share of ‘believers’ relies on the fact that population characteristics change only slowly over time, so that the proportion of the population that holds ‘end times’beliefs is, at …rst approximation, constant over the short- to medium-term, and hence uncorrelated with within-area variation in house prices over the ten-year time horizon studied here. The exogeneity of the ‘belief intensity’proxy relies on the fact that the information set available to ‘believers’(including the eschatological framework through which information is …ltered) is common across areas. In both cases, the actual data proxies used strengthen this claim of exogeneity, since the proxy for the geographically-varying proportion of believers is available for only one relevant year, and the proxy for the belief intensity measure is taken from an internet source which is by de…nition common across areas. To proxy for the proportion of believers in premillenialism in each area, the paper uses the share of evangelical Protestants, derived from the 2000 Religious Congregations and Membership Study, obtained from the Association of Religion Data Archive (ARDA). While premillenialism is most strongly associated with the most conservative, or ‘fundamentalist’, evangelical denominations, polling evidence suggests that its view of the ‘end times’is the majority one for evangelicals as a whole. For instance, a 1999 poll for Newsweek found that around 71 percent of evangelical Protestants believed that the world would end exactly as prophesied in the Bible, compared to only 28 percent of nonevangelical Protestants and just 18 percent of Catholics (Newsweek, October 24, 1999). Figure 1 shows the geographical distribution of evangelical Protestants across MSAs. [Figure 1 about here] To proxy for the intensity of ‘end times’beliefs this paper employs the Rapture Index (RI), a well-known “prophetic speedometer”published on a popular premillenialist website.3 The RI embodies what Grenz (2004) describes as “the 3 The RI’s creator, Todd Strandberg, describes it as a “prophetic speedometer. The higher the number, the faster we’re moving towards the occurrence of pre-tribulation 3 dispensationalist admonition to read the newspaper in one hand and the Bible in the other,”interpreting current events in light of premillenialist beliefs –notably with respect to Israel and the Middle East, but also with respect to Russia and Iran (who are interpreted as modern manifestations of biblical entities), the European Union and United Nations (associated with ‘world government’and hence the Antichrist), and natural disasters (seen as precursors of the tribulation). The index consists of an unweighted sum of 45 subcomponents which are each scored from 1 to 5 depending on the scorer’s subjective assessment of the current degree of ‘prophetic activity’ with respect to each category. Figure 2 presents a snapshot of the index in December, 2007, including the 45 categories. The index is updated regularly in response to domestic and world events. For instance, following the events of 9/11 – that were interpreted by some fundamentalists and premillenialists as “indications that Christ’s return is imminent” (Kilde, 2004) – the Rapture Index reached a record high. Figure 3 shows the evolution of the index over time. [Figures 2 & 3 about here] As a …rst step, the paper conducts an event study centered on 9/11. Comparing house price growth in the second quarter and fourth quarter of 2001 (immediately before and after the attacks), there is a clear di¤erential e¤ect on areas depending on their population share of evangelicals. Controlling for area and time …xed e¤ects, there is a marked increase in house price growth in areas with large shares of evangelicals in the fourth quarter, compared to the second quarter. By contrast, no di¤erential e¤ect is visible in 2000. The paper then uses a ten-year panel of annual data (1997-2006) covering all 363 MSAs to test whether the interaction of the two proxies has any impact on house prices. The preferred speci…cation analyzes the relationship in lagged …rst di¤erences, with geographic and time …xed e¤ects and some economic controls. In line with the event study evidence, the paper uncovers a positive and highly statistically signi…cant e¤ect (with a t-statistic of around 15). A one standard deviation change in the Rapture Index in MSAs with the average share of evangelicals is estimated to generate a 0.8 percentage point increase in house prices (compared to MSAs with no evangelicals). To place this in context, the average annual real increase in prices over the period was 3.4 percentage points. This result is then subjected to a battery of robustness checks. First, the baseline regression is run without lags and in levels rather than …rst di¤erences. Second, the RI is interacted with State dummies to focus on within-State interactions. Third, the share of evangelicals is interacted with a series of macroeconomic variables, in case the RI is simply picking up cyclical or macroeconomic factors. Fourth, the baseline regression is run for a number of di¤erent subsamples (with the sample cut across areas, time periods and area characteristics). Fifth, the baseline regression is run using di¤erent data proxies for house prices and the share of ‘believers’. Finally, the paper attempts to control for possible rapture.” http://www.raptureready.com/rap2.html. The RI has featured in Time magazine (July 1, 2002), and appears to enjoy some currency, with the website receiving more than 250,000 visits per month in 2003 (Christianity Today, March 2003: http://www.christianitytoday.com/ct/2003/marchweb-only/3-24-43.0.html.). 4 patterns of correlation, temporal and spatial, either in the dependent variable or in the error term. The results remain signi…cant in all speci…cations. This positive e¤ect may appear counterintuitive. According to the basic asset pricing equation, the price of an asset should re‡ect the expected product of its return and the stochastic discount factor (SDF) (Campbell, 2000). An increase in the expected probability of the world ending should lower the SDF, and therefore have a negative impact on house prices in areas with a large share of evangelicals (assuming some trading frictions across areas). However, housing’s particular asset characteristics –speci…cally its relative illiquidity –could account for the observed positive interaction e¤ect. In particular, illiquidity allows agents to commit to a particular consumption stream when their preferences are time-inconsistent (Harris and Laibson, 2002; Laibson, 1997; Strotz, 1956). Illiquid assets that facilitate commitment will therefore trade at a higher price, re‡ecting the premium placed on the ability to commit (Kocherlakota, 2001). The appendix outlines a simple 3-period model with time-inconsistent preferences, based on Kocherlakota (2001), in which such a commitment premium is shown to increase in response to a higher perceived probability of the world ending, with the e¤ect stronger in areas with higher shares of ‘believers’ (Proposition 1 in the appendix). For premillenialists, a potential source of time inconsistency is the tension between the belief that the ‘end times’are imminent, and Biblical injunctions to act prudently in the time remaining. For instance, ‘end times’writers quote Jesus’s parable (Luke 19: 12-26) cautioning his followers to “occupy till I come.” The parable describes a nobleman who entrusts his savings to his servants ahead of a foreign trip, and on his return praises those servants who have invested the money and are able to return it with interest, while castigating the servant who simply holds the original sum for safe-keeping. The parable has been interpreted by end times writers as indicating the need to behave wisely in all spheres of life (including the economic) even while expecting Jesus’s return.4 Hence, although believers may initially intend to behave as suggested by the parable, and save for the future regardless of their beliefs about the end times, they may later be tempted to renege on this commitment, in response to their end times beliefs, and save less. This temptation is less easy to act upon if agents save using relatively illiquid assets, such as by paying into a 401(k) account or by tying themselves to large monthly mortgage payments. This account of the positive interaction e¤ect uncovered in the data is not the only potential explanation. Others include the possibility that concerns about the ‘end times’prompt a general ‡ight to (perhaps safer) real assets such as housing. However, the general equilibrium model outlined in the Appendix provides a number of additional predictions which can be taken to the data to shed light on the relative merit of the particular channel proposed here. In particular, the model makes two predictions concerning borrowing behavior that can be tested against data on mortgage applications (using the Home Mortgage Disclosure Act (HMDA) Loan Application Registry data collected and aggre4I am grateful to Paul Boyer for bringing this point to my attention. 5 gated to the MSA level by Dell’Ariccia, Igan and Laeven, 2008).5 The model predicts that (1) the volume of mortgage lending (the total number of loans) among believers falls, and (2) the average loan size increases, as the perceived probability of the world ending increases. Both predictions are supported by the data, lending further credence to this channel. This paper touches on a number of previously unrelated literatures. It contributes to a growing literature on the economic e¤ects of religion (Iannaccone, 1998 provides an early survey, while recent contributions include those by Barro and McCleary, 2003; Scheve and Stasavage, 2006; and Guiso, Sapienza and Zingales, 2003). The results are also in line with an earlier empirical literature that found that fear of a nuclear holocaust adversely a¤ected savings during the Cold War, consistent with it depressing the discount factor (Russert, Cowden, Kinsella and Murray, 1994; Russert and Slemrod, 1993; Russert and Lackey, 1987; and Slemrod, 1986). The empirical results contribute to a growing literature on recent house price trends that stress non-standard psychological factors (Shiller, 2007) and geographical heterogeneity (Gyurko, Mayer and Sinai, 2006). The results also provide evidence consistent with the existence of a commitment premium on illiquid assets. This paper can therefore be thought of as a positive response to Kocherlakota’s (2001) argument that the prediction of a commitment premium provides the key means of testing whether models with time-inconsistent preferences are valid.6 The rest of the paper is organized as follows. Section 2 provides an overview of the paper’s empirical strategy and the data employed. Section 3 presents the 9/11 event study. Section 4 gives the panel estimation results for the house price data, including the baseline results, robustness checks and an interpretation of the results. Section 5 tests the model’s additional predictions using the mortgage application data, while section 6 o¤ers some conclusions. 2 2.1 Empirical Strategy and Data Basic Speci…cation The basic relationship we are interested in identifying is given as: ln pit = b ( i L (! t )) + BL (Xit ) + "it (1) 5 The author is grateful to the authors for sharing this data. See Dell’Ariccia, Igan and Laeven (2008) for details of the variables. 6 Other work in this area has provided some evidence in support of time-inconsistent preferences. Angeletos and others (2001) argue that a calibrated consumption model with this preference speci…cation can better account for observed phenomena such as consumptionincome comovement and the relatively low share of liquid assets in total household assets. Huang, Liu and Zhu (2006) …nd evidence that agents who are subject to self-control problems (similar to having time-inconsistent preferences) are more likely to invest in human capital, which they argue is a commitment asset. They also …nd that holdings of two di¤erent commitment assets – pensions and education – appear to be positively correlated, as predicted by the model. However, Kocherlakota (2001) argues that average aggregate returns on these same two commitment assets appear to be above the return on liquid assets, contradicting the theory. 6 where pit gives the house price index in area i at time t, i gives the population share of believers, ! t gives the time-varying probability attached to the world ending by believers, L () is a general lag function and Xit gives a vector of controls (including area and time …xed e¤ects and area-speci…c linear time trends). Equation (1) with b 0 can be derived from the general equilibrium model with time-inconsistent preferences outlined in the Appendix (equation 52). 2.2 Data Proxies This paper uses house price data from repeated sales at the level of Metropolitan Statistical Areas (MSAs) available from the O¢ ce of Federal Housing Enterprise Oversight.7 The data is based on conventional conforming mortgage transactions obtained from Freddie Mac and Fannie Mae and is available at a quarterly frequency, although annual averages are used for most of the analysis. The principal advantage of this data over other similarly constructed and widely-used indices (such as the Case-Shiller index) is that it is available for a large and disaggregated set of geographical areas.8 As a robustness check the baseline speci…cation is also estimated using the Case-Shiller data, albeit with coverage therefore limited to only 196 observations over 20 MSAs. The baseline is also estimated using real house price indices, de‡ated by MSA-speci…c consumer price indices obtained from the Bureau of Labor Statistics. Figure 4 presents the average of the change in log house prices across MSAs (using the OFHEO data and weighted by 2000 populations) for 1996-2006. [Figure 4 about here] Data on the share of various religious denominations is obtained from the 2000 Religious Congregations and Membership Study, which provides estimates of adherents at the county level for 149 Christian denominations (including Latter-day Saints), two groups of independent Christian churches, and nonChristian congregations including Jews and Muslims.9 Denominations were coded as Evangelical Protestant denominations following Campbell (2006); in addition, independent (charismatic and non-charismatic) churches were also coded as Evangelical.10 As a robustness check two alternative evangelical measures are compiled and compared to the preferred measure: the ARDA’s own coding, and a narrower measure including only those denominations which explicitly profess to believe in premillenialism (based on the description of individ7 See Table A1 for information on all variables and data sources employed in the paper. individual house prices within each MSA are aggregated geometrically to arrive at the overall index. See Calhoun (1996) for an overview of the underying methodology and data. 9 A description of the data is available at http://www.thearda.com/Archive/Files/Descriptions/RCMSCY.asp. See Jones and others (2002) for more information. 1 0 Campbell follows the ARDA researchers’own coding of White Evangelical denominations, with the exception of the Community of Christ (see the Appendix to Campbell, 2006). We also include the two independent churches groupings in our preferred evangelical measure following Mead, Hill and Atwood (2005, p. 318) who note that ‘the theology and doctrine of [these churches] ... vary according to the beliefs of the pastor, but in general they may be termed conservative evangelical.’ 8 Implicitly, 7 ual denominations in Mead, Hill and Atwood and a reading of their statements of faith and other information on their individual websites). The broader measure seems preferable since the polling and anecdotal evidence suggests that premillenialist beliefs are widely held among the broader evangelical population, and not only among the relatively small ‘fundamentalist’and other denominations for which premillenialist beliefs are central to their faith. Data on the Rapture Index was assembled from several internet sources that provide archived information on past values of the index or information on its current value. Only a subset of the observations of the index and its subcomponents is available (the index is updated approximately weekly). However, because each update of the index provides information on maxima and minima for several past years alongside the current value of the index and its subcomponents, we were able to reconstruct annual observations covering 1995-2006 by taking the midpoint between the reported annual low and high as a proxy for the annual average. Demographic data at the county level – including the population shares of Hispanics and non-Hispanic whites and blacks (respectively sH , sW and sB ) – is obtained from 2000 census data and aggregated to the level of MSAs. Annual data on per capita personal income and population at the MSA level is obtained from the Bureau of Economic Analysis. Annual unemployment data at the MSA level is obtained from the Bureau of Labor Statistics. Macroeconomic controls are obtained from the Federal Reserve Board and the IMF’s World Economic Outlook dataset. 2.3 Empirical Strategy Taking (1) to the data requires two principal steps. First, a …rst di¤erence transformation is applied to deal with the potential non-stationarity of the house price series. Second, the vector of …rst di¤erenced controls is modeled to include time and area …xed e¤ects, so that the interaction term of interest is strictly exogenous to the remaining variation in the dependent variable. Finally, a simple one-year lag structure is assumed for both the interaction term and the controls. The baseline empirical speci…cation is then given by (2): ln pit = b ( i !t 1) + i + t + Zi;t 1 + uit (2) Area and time …xed e¤ects are given by i and t , respectively, while Zit gives the remaining (…rst di¤erenced) controls and uit is assumed iid. 2.4 Extensions to the Baseline Model House prices are likely to vary in response to a wide set of economic and social conditions, many of which are excluded from our baseline set of controls. In particular, both our main proxies are likely to be correlated with other variables, so that the estimated interaction term could be picking up the e¤ect of these omitted variables. There is also a danger that the baseline results could somehow 8 be an arti…ce due to the assumed dynamic structure, or that any signi…cance level attached to the estimated e¤ect could be over-estimated due to failing to adequately capture spatial or temporal correlation patterns. A number of extensions to the baseline empirical model are therefore also estimated. First, (2) is estimated without lags (in …rst di¤erences and levels): ln pit ln pit = b( = b( ! t ) + i + t + Zit + uit ! t ) + i + t + Xit + uit i i (3) (4) where Xit includes State-speci…c time trends to capture the widely di¤erent time pro…le of house prices in di¤erent parts of the U.S. Second, a set of interaction terms between State dummy variables Ds and the RI is included, to counter concerns that the share of evangelicals in each MSA could be acting as a proxy for any other factors that vary signi…cantly across geographic areas: X ln pit = b ( i !t 1 ) + (Ds ! t 1 ) + i + t + Zi;t 1 + uit (5) s Third, a number of additional interactions with a set of macroeconomic variables m are included, to control for any correlation between the RI and general macroeconomic conditions: ln pit = b ( !t i 1) + d( mt i 1) + i + t + Zi;t 1 + uit (6) Finally, the paper presents estimates of a number of speci…cations that attempt to deal with problems caused by spatial or temporal correlation. One set of speci…cations simply relaxes the iid assumption with respect to uit : assuming a panel AR(1) process, allowing for clustering (within MSAs to capture serial correlation or across State-year clusters to capture spatial correlation), or by explicitly specifying and estimating a spatial correlation structure. A second set of speci…cations attempts to control for spatial and temporal correlation by modifying equation (2). First, a one period lag of ln pit is introduced: ln pit = ln pi;t 1 + b( !t i 1) + i + t + Zi;t 1 + uit (7) The introduction of the endogenous lagged dependent variable renders standard …xed e¤ects estimation inconsistent, so (7) is estimated using panel GMM techniques. Second, a spatial lag model is estimated via MLE: 0 1 X ln pit = @ wij ln pj;t A + b ( i ! t 1 ) + i + t + Zi;t 1 + uit (8) j where wij gives the element of the spatial weight matrix for areas i; j. Finally, a matching exercise is run where each area is matched with its closest geographic neighbor, and (2) is then di¤erenced across the two members of each unique pair i; j: (ln pit ln pjt ) = b ( i j) !t 1+ 9 i;j + t + (Zi;t 1 Zj;t 1 )+ei;jt (9) where i;j denotes the combined …xed e¤ect for the unique area pair i; j and ei;jt the corresponding error term.11 2.5 Sample and Descriptive Statistics Table 1 presents summary statistics for the principal variables used in the paper. The baseline sample consists of 10 years of data for the 363 MSAs de…ned in the O¢ ce of Management and Budget Bulletin number 07-01 (December, 2006).12 [Table 1 about here] 3 9/11 Event Study A Time/CNN poll in 2002 found that interest in the ‘end times’ increased markedly in the wake of the 9/11 attacks: more than one-third of respondents claimed to be paying more attention to how the news might relate to the end of the world, and almost one-quarter believed that the Bible predicted the attacks (Time, July 1, 2002). Some 59 percent claimed to believe that the account of the ‘end times’in the Bible’s book of Revelation would come true (compared to 40 percent in response to a similar question in 1999). This up-tick in interest is also re‡ected in a spike in internet tra¢ c to the Rapture Index site (some eight million visitors in the immediate aftermath of 9/11 according to Time), while the index itself concurrently reached its all-time high. Hence, one means of analyzing the impact of ‘end times’beliefs on behavior is to analyze the evolution of house prices in the run-up to and immediate aftermath of the attacks. An advantage of this exercise is that it does not rely explicitly on the Rapture Index to proxy for end times beliefs, but rather exploits the broader evidence that the attacks were interpreted by many as a sign of the ‘end times.’ One can also exploit the quarterly frequency of the OFHEO data, focusing on the period immediately surrounding the attacks by comparing the behavior of house prices in the second and fourth quarters of 2001. As an additional comparison, one can also compare the behavior of prices in the same two quarters in 2000. Of course, 9/11 had a wide-ranging economic impact via a number of channels, making it hard to disentangle the e¤ect of ‘end times’beliefs, so that the results of this exercise should be taken as merely suggestive. To eliminate common time or area e¤ects, the one-quarter change in the log house price index is …rst regressed on period and MSA dummies. Figure 5 then 1 1 This exercise is somewhat similar to Black (1999) and related studies that test parental valuation of school quality by comparing house prices close to school district boundaries (eliminating geographically-speci…c omitted variables that vary continuously rather than discretely in the region of the boundary). In this study the matching is coarser, re‡ecting the larger unit of analysis (MSAs versus individual homes). This exercise results in 253 unique matched pairs with mean distance 60.8 miles. Note that to the extent that serial correlation enters via common regional house price cycles, then this speci…cation will minimize serial as well as spatial correlation. 1 2 However, house price data is unavailable for the Hinesville-Fort Stewart, GA MSA prior to 2001, so that our baseline sample size is 3,625 observations. 10 plots the …tted relationship between the residuals obtained from this …rst stage and the share of evangelicals in each MSA.13 [Figure 5 about here] Figure 5 suggests that 9/11 had a di¤erential impact on house price growth across MSAs depending on the proportion of evangelicals in their population. Between the second and fourth quarters of 2001 there was a statistically significant upward shift in house price growth for areas with a high share of evangelicals, compared to areas with a low share. This pattern is not discernible in 2000.14 4 Panel Estimation 4.1 Baseline Speci…cation and Macroeconomic Interactions This section presents the main results as well as some robustness checks with respect to speci…cation and omitted variables. Table 2 presents the principal panel regression results. The baseline speci…cation (equation (2), shown in column I) is in …rst di¤erences and includes as controls the MSA unemployment rate and the change in (log) MSA per-capita income and the change in (log) population. All explanatory variables, including the interaction term, are lagged one period. The regression includes year dummies and MSA …xed e¤ects. The interaction term is highly statistically signi…cant (with a t-statistic of around 15) and is also economically signi…cant: a one standard deviation change in the Rapture Index for an MSA with the average share of evangelicals in the population, other things being equal, would lead to a 0.8 percentage point increase in house prices compared to an MSA with no evangelicals. [Table 2 about here] Columns II and III assess whether the imposed dynamic structure is giving ‡attering results, by presenting results for speci…cations without lags: column II retains the …rst di¤erenced speci…cation (equation 3) while column III presents results for a speci…cation in levels (equation 4; this speci…cation also includes state-speci…c deterministic time trends to help control for the large geographical variations in house price growth over the period; note that the unemployment rate is included in levels in all speci…cations). Column IV replicates column I but models the geographic e¤ects as random disturbances rather than parameters to be estimated (GLS random e¤ects). Columns V and VI are also estimated via GLS but additionally drop the year dummies (column VI also includes a deterministic time trend to control for the upward trend in house price growth over the period apparent in Figure 4). The estimated interaction term is stable across speci…cations, and remains highly statistically signi…cant. Note that the estimated e¤ect of increases in the Rapture Index, for MSAs with a zero 1 3 One obtains almost identical results using the raw data rather than residuals. p-value of the test that the slope coe¢ cient is the same in quarters 2 and 4 in 2001 is 0.000; for 2000 the p-value is 0.538. 1 4 The 11 evangelical population, is negative in columns V and VI, which is also in line @pN com with the theory since it is demonstrated in the appendix that @! 0.15 Column VII includes State dummies interacted with ri 1 (as in equation 5) and hence estimates the within-State interaction e¤ect. This controls for the fact that the share of evangelicals varies considerably across States along with other factors that might be driving the estimated interaction e¤ect (particularly if the Rapture Index were itself correlated with some other time-varying factor whose e¤ects might di¤er across di¤erent types of areas, such as a common macroeconomic shock). Because a considerable amount of information is lost by looking only at within-State variation, one would expect the estimated e¤ect to be smaller. However, it remains statistically signi…cant at the 1 percent level even when this large quantity of information is dropped. While the results of Table 2 appear to be robust across speci…cations, a potential criticism of the results is that the change in the Rapture Index over time might be proxying for other factors, such as the macroeconomic environment, that might impact on house prices in di¤erent MSAs according to their demographic or economic characteristics in a way that would mimic the interaction e¤ect we uncover in the data. Table 3 therefore jointly estimates interaction e¤ects for both the Rapture Index and a range of macroeconomic variables to see whether the former e¤ect stands up to the inclusion of the latter (equation 6). The variables (GDP growth, in‡ation, the national unemployment rate, the change in the world oil price and the average federal funds rate) are included both individually (columns I-V) and jointly (column VI). Finally, column VII includes the share of evangelicals interacted with a linear deterministic time trend, to proxy for any macroeconomic factors (or …nancial variables, such as a loosening of lending standards associated with mortgage securitization) that may have changed monotonistically over time and might have di¤erential e¤ects on di¤erent areas (perhaps depending on some variable correlated with the share of evangelicals). [Table 3 about here] Only the inclusion of the federal funds rate has any major e¤ect on the coe¢ cient estimate of the interaction term (column V), but the latter remains highly statistically signi…cant. Quantitatively, using the results in column VI and comparing one standard deviation changes in each time-varying variable, only changes in the federal funds rate have a larger di¤erential impact on house prices according to the share of evangelicals in the population. Only the interaction e¤ect with respect to growth (and only in column VI) has a higher t-statistic than the interaction e¤ect with respect to the Rapture Index. When a deterministic time trend is included (interacted with the share of evangelicals, in column VII) the point estimate for the interaction coe¢ cient with respect to 1 5 Proposition 2 in the Appendix proves this result in the region of ! = 0, although the result would appear to be more general. The empirical evidence should be interpreted with some caution since there only 10 independent observations of ri 1 and many other factors will cause mean house prices to change over time, not only changes in ri. On the other hand, the negative coe¢ cient is robust to the inclusion of macroeconomic controls, as for the inclusion of the time trend in column VI. 12 the Rapture Index is reduced somewhat, but remains highly statistically significant.16 4.2 Alternative Samples and Data Sources The baseline results could be driven by outliers rather than re‡ecting a widely occurring pattern. Table 4 tests for this possibility by re-running the baseline speci…cation for ten subsamples. The …rst two subsamples (I and II) bifurcate the sample by time period, breaking it up into 1997-2001 and 2002-06. The interaction e¤ect appears to have strengthened over time (which is in keeping with the apparently increasing salience of ‘End Times’ beliefs) but is highly statistically signi…cant in both subsamples. Columns III-VI present respective results dropping one of each of the four census divisions (North East, Midwest, South and West). One might expect that dropping the South would decrease the estimated interaction e¤ect if it were spurious, since the South di¤ers significantly from the rest of the country in its share of evangelicals but also along a number of other dimensions for which the share of evangelicals might be acting as a proxy. In fact, the coe¢ cient estimate is higher when the South is excluded. The results remain highly statistically signi…cant in all four samples. [Table 4 about here] The share of evangelicals tends to be somewhat higher in MSAs with high black populations and much lower in MSAs with high Hispanic populations. Hence, the interaction e¤ect might be picking up some idiosyncrasies relating to racial composition or heterogeneity. Columns VII-IX therefore drop some MSAs which are outliers in terms of their racial composition or are particularly racially diverse, based on 2000 census data. Column VI restricts the sample to the most racially homogeneous MSAs (which are all majority-white), including only those where whites account for more than 90 percent of the population, which reduces the sample size from 363 to 73 MSAs. The estimated interaction e¤ect is somewhat reduced but remains statistically signi…cant at the 1 percent level even in this restricted and homogeneous sample. Columns VIII and IX drop two groups of outliers, MSAs whose (respectively) black or Hispanic population is greater than 10 percent, and again the results are robust. Finally column X drops MSAs with shares of evangelicals above the 90th percentile, in case the results are skewed by variation among this small group of MSAs with a particularly high share of evangelicals. In fact the opposite result holds, with the interaction e¤ect somewhat stronger in the sample with relatively low shares of evangelicals.17 1 6 The author also included interaction terms with respect to the yield di¤erential between 10-year and 3-month treasury bills (to capture the yield curve), the change in the (log) gold price, and the OECD’s composite leading indicator for the U.S., in case the Rapture Index is simply a measure of ‘bad news’and therefore acting as a proxy for forward-looking economic indicators (sources: Fedeal Reserve, IMF’s WEO database; OECD). The inclusion of the yield di¤erential has a similar quantitative impact on the coe¢ cient of interest to including the federal funds rate; the other variables have essentially no impact. 1 7 This result might have been expected given the result from dropping the South (column V), the region with the highest share of evangelicals. 13 A second concern is that the baseline results could be particular to the data proxies chosen. The event study in Section 3 provides some evidence that the positive interaction e¤ect does not depend on the use of the Rapture Index to capture variations in the intensity of ‘end times’beliefs. Tables 5 and 6 present evidence using alternative proxies for the share of believers and house prices, respectively. Table 5 presents data on the baseline coding of adherents as evangelical and two alternatives: the ARDA’s own coding and a narrower de…nition that focuses speci…cally on denominations whose doctrinal beliefs appear to explicitly include premillenialism. The ARDA evangelical de…nition is almost identical to the baseline, and hence yields the same results. The narrower de…nition yields a higher coe¢ cient estimate (as one might expect) which remains highly statistically signi…cant. [Table 5 about here] The underlying data coverage of the OFHEO house price index could be biasing the results. For instance, the index does not cover all sales, particularly at the high end, and includes re…nancing as well as actual sales, so could incorporate biased valuations. Table 6 (columns I and II) compares results from the Case-Shiller index and the OFHEO index. The sample coverage is limited to the 20 MSAs for which Case-Shiller indices are available, giving a total of only 196 observations (5 percent of the OFHEO sample). The two indices are highly correlated (the correlation coe¢ cient for log changes is .96). The signi…cance level associated with the interaction e¤ect drops to 10 percent for the CaseShiller index, although the point estimate increases somewhat. The principal reason for the drop in signi…cance appears to be the smaller sample size: the signi…cance level using the OFHEO index for the same sample is also sharply reduced (to the 5 percent level).18 [Table 6 about here] A related concern is the use of nominal house prices in the empirical work, whereas real prices may be of greater interest.19 MSA-speci…c consumer price indices to use as de‡ators are available from the BLS for only 27 MSAs. Columns III and IV compare results for real and nominal indices for this limited sample. Columns V and VI compare results using nominal and real house price changes for all 363 MSAs, where the CPI from the nearest of the 27 MSAs covered by the BLS index is used to proxy for the missing de‡ators.20 The results are robust in both cases. 4.3 Correcting for Temporal and Spatial Correlation A further criticism of the results is that they might over-state the statistical signi…cance of the estimated e¤ect because they fail to adequately take into 1 8 When the non-lagged speci…cation (as in Table 2, column II) was run for both samples, the signi…cance pattern was reversed, with the interaction e¤ect using the OFHEO index signi…cant only at the 10 percent level, but at the 5 percent level using the Case-Shiller index. 1 9 In the model in the Appendix, the e¤ect of interest is on real prices, with the period 1 consumption good as the numeraire). 2 0 All distances are calculated using MSAs’ latitude and longitude, where these are population-weighted means of the latitude and longitude of each constituent county. 14 account correlation patterns in the data, either over time or across areas. Table 7 presents several attempts to control for serial correlation, by estimating, respectively, a FE model with MSA-speci…c AR(1) residuals or with residuals clustered at the MSA level, and the dynamic price growth equation (7). Column I presents results from the AR(1) model. The coe¢ cient estimate on the interaction e¤ect is somewhat reduced but remains statistically signi…cant at the 1 percent level. Column II presents results for the baseline FE model with residuals clustered at the MSA level; reported standard errors are somewhat higher, but the e¤ect remains highly statistically signi…cant.21 [Table 7 about here] Columns III-VI present estimates of the dynamic price equation (7). Since the lagged dependent variable violates the exogeneity assumption required for FE estimation, these speci…cations are estimated via consistent GMM (Arellano and Bond’s (1991) …rst di¤erenced estimator).22 Columns III and IV present results from the one-step and two-step Arellano-Bond estimator (all results are presented in …rst di¤erences).23 The speci…cation tests proposed by Arellano and Bond (1991) –both the Arellano-Bond test for AR(2) residuals and Hansen’s over-identi…cation test –suggest that the orthogonality conditions required for consistency are not met. To overcome this, columns V and VI present results from applying GMM to a speci…cation in second di¤erences, where the additional di¤erencing should minimize residual serial correlation. The speci…cation tests suggest that the residual correlation problem is eliminated by seconddi¤erencing, and the Arellano-Bond estimators (both one-step and two-step) meet the conditions for consistency. The estimated interaction e¤ect remains positive and statistically signi…cant even in these second-di¤erenced speci…cations (where a signi…cant amount of information has been discarded).24 Table 8 presents the results of robustness checks with respect to spatial correlation in house price growth. As a …rst pass, column I presents results with residuals clustered jointly by State and year (this requires the MSA …xed e¤ects to be dropped, and the equation therefore includes the share of evangelicals and State dummies). The estimated interaction e¤ect is essentially unchanged and remains statistically signi…cant at the 1 percent level. Columns II-IV present 2 1 Bertrand et al. (2004) argue that clustering is a superior technique for addressing panel autocorrelation than …tting a model with AR(1) errors. 2 2 Estimation is undertaken using the xtabond2 Stata command developed by Roodman (2006). I focus on contemporaneous e¤ects from the exogenous variables (rather than oneperiod lags, as in the baseline) since any lagged impact should already be captured via the lagged dependent variable. 2 3 Note that the baseline speci…cation (equation 2) is estimated in …rst di¤erences (the dependant variable is the change in log house prices). When we refer to …rst di¤erences in the context of the GMM estimates, we are referring to …rst di¤erences with respect to this baseline, and hence second di¤ erences (in terms of log house prices). When we come to estimate the baseline in second di¤erences (columns V and VI) to eliminate residual serial correlation, the results from the GMM estimates are therefore derived from third di¤ erences. 2 4 The author also estimated both …rst- and second-di¤erenced speci…cations using Blundell and Bond’s (1998) system GMM estimator, but speci…cation tests suggested that the results remained inconsistent even with the second-di¤erenced speci…cation and so they are not reported here. 15 results from a matching exercise, in which each MSA is matched with its nearest geographic neighbor and the baseline speci…cation is then di¤erenced across each pair to eliminate common geographic e¤ects (equation 9). Column II presents results for the full matched sample; column III and IV present results for more limited subsamples with ‘better’(closer) matches. Despite a signi…cant loss of information in this exercise (re‡ected in much lower R2 s and reduced coe¢ cient estimates), the estimated interaction e¤ect remains positive and statistically signi…cant. Finally, columns V and VI present results from MLE estimation of speci…cations with, respectively, a spatial lag (equation 8) and spatially correlated errors. The models assume that spatial correlation is inversely related to the distance between MSAs for concurrent observations (and zero otherwise).25 In both speci…cations the estimated interaction e¤ect is somewhat reduced, but remains positive and highly signi…cant. [Table 8 about here] 4.4 Interpretation The results presented above suggest that ‘end times’ beliefs have a signi…cant e¤ect on asset holding decisions. Anecdotal evidence lends support to this view. Kilde, 2004, presents historic evidence of these beliefs leading people to make economically signi…cant decisions, including selling all their possessions (the “Millerites” of the 1840s) or risking death in confrontation with the authorities (the followers of David Koresh in 1993). Contemporary press accounts include examples of people selling their houses or cutting short their education (Christian Science Monitor, February 18, 2004).26 Keister (2005) provides evidence from the 1979-2000 National Longitude Survey of Youth that conservative Protestants accumulate less overall wealth in early adulthood than others, even controlling for demographic and economic factors (including those, such as educational attainment, fertility behavior, job market status and income, that might themselves be a¤ected by religious beliefs).27 2 5 Formally, if observations are ordered by year and then by MSA identi…er (the HinesvilleFort Stewart, GA MSA is dropped to give a balanced panel and simplify the calculations, giving 10 362 = 3620 observations), then the spatial weights matrix W is a 3620 3620 symmetric matrix comprising 100 362 362 submatrices, where the symmetric matrix w gives its diagonal submatrix elements and 0 matrices make up its1other elements. The matrix w 0 ! 1 362 X has elements fwr;c g = @ dr;c1 dr;c1 j r 6= c; 0 j r = cA where dr;c gives the distance c=1 in miles between MSA r and MSA c (i.e. the spatial weights matrix is row-normalized so that the non-zero elements of each row sum to one). In the spatial lag model, the dependent variable is directly related to that of neighboring observations, while in the spatial error model only the error terms are related. In both cases, the spatial autocorrelation coe¢ cient is given by . Both speci…cations also include year dummies and MSA …xed e¤ects. Estimation is undertaken using spatreg and associated Stata commands (Pisati, 2001). 2 6 According to an April, 13, 1998 report in the New York Times, it was also possible to obtain “rapture insurance” up until relatively recently, when pressure from within the insurance industry (rather than a lack of demand) halted the practice. 2 7 Keister argues that the direct e¤ect of denominational membership on wealth accumulation – distinct from indirect e¤ects via the demographic and economic channels discussed in 16 Nevertheless, the positive price e¤ect uncovered in the data is at …rst glance surprising, since the most simple asset pricing model would predict that more aggressive discounting behavior should reduce the net present value of the income stream associated with any asset, lowering its price. I conjecture that the positive e¤ect could re‡ect a response to time inconsistency in believers’ preferences, created by the tension between their end times beliefs and Biblical injunctions to behave reasonably even while anticipating Jesus’s return. It is well established that time inconsistency raises the value of commitment, potentially generating a premium on illiquid assets that help agents to commit (Laibson, 1997; Kocherlakota, 2001). In fact, Kocherlakota (2001) argues that testing for a commitment premium is a means of testing the validity of models incorporating time-inconsistent preferences. My results can therefore be interpreted as o¤ering some support to this class of models. In the appendix I outline a simple 3-period model, based on that of Kocherlakota, that illustrates this conjecture. The model incorporates two types of agents: believers (whose preferences are time inconsistent) and non-believers (whose preferences are not). The model adopts a simple islands formulation, with agents homogeneous within islands. Trade in liquid assets is possible across islands, but trade in illiquid (commitment) assets is not. The latters’illiquidity also means that they are also non-tradable in the intermediate period, allowing the believers to commit to their …rst-best consumption path over all three periods. In equilibrium an endogenous fraction of the believers choose to follow a commitment strategy (holding the illiquid assets), while the remainder hold liquid assets. The commitment strategy delivers the …rst-best consumption pro…le (given asset prices); to equalize utility across the two strategies, commitment assets must then deliver a lower return, or trade at a premium. Islands can be aggregated to generate heterogeneous areas to mimic the MSAs in the data. Then the model predicts a positive interaction e¤ect as in equation (1) with b 0 (Proposition 1). This explanation remains only a conjecture, and further research focusing on individual-level savings data is required to verify if it is a convincing explanation. However, one bene…t of the simple general equilibrium model outlined above is that it makes a number of additional predictions with respect to borrowing behavior that can be tested against mortgage data. Rejecting the null hypothesis of zero e¤ect on mortgage borrowing is of course only a …rst step toward assessing the model’s validity; however, if it were to fall at this …rst hurdle one would doubt its usefulness. 5 Evidence from mortgage data The model’s …rst prediction relates to the total number of loans. A mortgage transaction typically re‡ects two o¤setting asset transactions on the household’s balance sheet: the purchase of a real asset, and the acquisition of a …nancial the text – might arise from Biblical injunctions against hoarding or from generous charitable giving or ‘tithing’to the church, but does not look at the role of ‘end times’beliefs. 17 liability. In terms of the model, the liquid long term asset can be thought of as a claim on future income, so the model’s proxy for mortgage borrowers is the share of agents following the commitment strategy (selling the liquid asset to buy the illiquid asset). In the appendix it is demonstrated that this share falls as the subjective probability of the ‘end times’increases (for ! in the region of 0; Proposition 3).28 The mechanism driving the result is simple: an increase in ! leads to a decline in the period 3 consumption of the believers who choose not to commit. However, overall consumption of these agents is essentially …xed. Hence a lower average consumption level requires there to be more of these agents, and hence fewer believers following the commitment strategy. We should therefore expect to see the volume of mortgage lending decline in response to an increase in the Rapture Index in areas with high shares of evangelicals. This is not a trivial prediction, since alternative explanations for the relationship between house prices and the interaction term (for instance, that the interaction term is correlated with some other variable associated with a boom in lending activity that drives up prices) might generate the opposite prediction. The second prediction relates to the average loan-to-income ratio, which is predicted to increase – for believers – as the subjective probability of the ‘end times’ increases (for ! in the region of 0; Proposition 4).29 The logic of this result is the inverse of the previous result: since the share of believers choosing to commit has decreased, then, given that the real stock of commitment assets does not change, the per-borrower value increases. Hence, we should see an increase in the average mortgage size in response to an increase in the Rapture Index in areas with high shares of evangelicals. Given that we have already observed rising house prices in response to this interaction term, an increase in the loan to income ratio would not be a surprising result. However, this nevertheless o¤ers a useful additional test of the model since the mortgage data is independent of the house price data and also because the measured e¤ect on house prices could be due to a correlation between the interaction term and some unobserved component of household income, whereas the model speci…cally predicts an increase in household leverage. To test these additional predictions, I use data on individual loan applications from the Home Mortgage Disclosure Act (HMDA) Loan Application Registry collected and aggregated to the MSA level by Dell’Ariccia, Igan and Laeven (2008). As with the main panel results, identi…cation rests on entering the interaction term ! on the right hand side. In terms of dependent variables, I use the ratio of the number of loan applications to the total population within each MSA as a proxy for testing Proposition 3 and the mean of the loan to income ratio of loans originated within each MSA for testing Proposition 4. For the latter I use two di¤erent measures: the simple unweighted mean (the average of the loan/income ratio for each loan) and the weighted mean (total loans to total income). Both dependent variables are transformed into …rst di¤erences. Data 2 8 See Appendix. In K01 the relationship holds for all values of !; the addition of islands with non-hyperbolic agents ( < 1) leads to changes in the relative consumption levels across islands (h) that can o¤set this e¤ect somewhat. 2 9 Again, for = 1 (so that h = 1) this result will hold for all values of !. See Appendix. 18 are available for 360 MSAs covering 1997-2006. Results are presented in Table 9. Each equation follows the speci…cation of Table 2, column I with respect to the right hand side, and includes MSA …xed e¤ects and year dummies. Column I presents results for the volume of loan applications; columns II and III present results for the loan to income ratio (using the unweighted and weighted mean, respectively). The results are in line with the model’s additional predictions: the coe¢ cient on the interaction term carries the predicted sign and is highly statistically signi…cant in each case. Taken together with the main results, these additional results, testing some auxiliary predictions using a di¤erent dataset, o¤er some preliminary support for my conjecture. [Table 9 about here] 6 Conclusions This paper has attempted to achieve two objectives. First, to test whether ‘end times’ beliefs have a measurable impact on consumer behavior. Second, to shed light on theories of portfolio choice with time inconsistent preferences, based on my conjecture that those with ‘end times’beliefs might face a tension between their belief that the world could end soon and Biblical injunctions to behave reasonably in the meantime that could generate time inconsistency in their preferences. The paper focuses on house prices, and my identi…cation strategy relies on interacting two exogenous variables: a geographically varying proxy for the population share of believers in each area, and a time-varying measure of believers’subjective probability of the world ending, and restricting my attention to within-area and within-time period variation by including area and time …xed e¤ects. I test for an e¤ect using a 10-year panel of 363 U.S. Metropolitan Statistical Areas (MSAs) and …nd a statistically and economically signi…cant positive e¤ect that is robust across subsamples, speci…cations and alternative data sources. In particular, the e¤ect is robust to specifying the estimation equation in levels or …rst di¤erences, assuming one-period lags or contemporaneous e¤ects, dividing the sample by area or time period, focusing only on within-State variation in the interaction term, including macroeconomic variables interacted with the share of believers proxy, using alternative data proxies, running speci…cations with temporal or spatial lagged dependent variables, and correcting for spatial or temporal correlation in the error term’s variance-covariance matrix. I also identify a positive interaction e¤ect using an event study centered on 9/11. To account for this positive e¤ect, I conjecture that believers in Biblical prophecy face a tension between their eschatological beliefs and other aspects of their religious values that stress the need to behave reasonably even while anticipating the end times. This could generate time inconsistency in their preferences. In the appendix I outline a model with time inconsistent preferences, adapted from Kocherlakota (2001) to enable it to be taken to the data, that can replicate the positive interaction term identi…ed in the empirical work. The bene…t of outlining a formal model in this way is that it can generate auxil- 19 iary predictions that can then be taken to data on mortgage lending as a …rst attempt at falsifying the hypothesized channel. In fact, the evidence from the mortgage data supports the model’s additional predictions. This paper re‡ects only a …rst attempt to gauge the economic relevance of ‘end times’ beliefs. The e¤ect I identify could turn out to be particular to the data and sample employed, and the hypothesized channel is simply a conjecture. 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(2005), “A …nite sample correction for the variance of linear e¢ cient two-step GMM estimators,”Journal of Econometrics, Vol. 126, pp. 25-51. 23 7 Appendix: Model, Comparative Statics, Propositions 1-4 with Proofs. This appendix outlines a general equilibrium model which is su¢ ciently simple to o¤er an analytic solution but can also be taken to the data. Its starting point is the three-period model with both commitment and liquid assets and consumers with either hyperbolic (time-inconsistent) or exponential (timeconsistent) preferences outlined in Kocherlakota (2001).30 The three periods represent the current period and the two relevant decision horizons: the short term and the long term. The key modi…cation from Kocherlakota (2001; appendix, henceforth K01) is the coexistence of the two types of agents in a single economy, modeled by assuming a collection of island economies with immobile consumers but with inter-island trade in consumption and the liquid asset.31 The illiquid, or commitment, asset is assumed to be nontraded across islands to allow its price to vary across regions. Subsets of islands can be aggregated into regions, corresponding to the MSAs in our dataset, that include both types of consumer. The average price of the commitment asset in each region –proxied for by housing assets in our dataset –will then vary depending on the degree of time-inconsistency in the preferences of the hyperbolic consumers (as in K01) and also the share of each type of consumer in the population of the region. The economy consists of a number of geographically distinct island economies whose total mass of population is unity. The set of agents within each island i is denoted mi (where mi also denotes its mass). All the agents within each mi are identical and are of one of two types, either ‘believers’(denoted superscript B) or non-believers (denoted superscript N ). These islands can be aggregated X into larger regions M r : mi 2 M r with mass M r = mi , containing both mi 2M r types of consumers, corresponding to the MSAs in our dataset. The proportion r of agents , while a proportion X in region r that are of type B is denoted r r M of all the agents in the economy as a whole are of type B. Agents r live for three periods and in period 1 receive an endowment of income of value 1 as well as endowments of assets yielding 1 in each of periods 2 and 3. Period 3 assets consist of two types: a liquid asset b13 and a commitment asset acom which is illiquid in two senses: it cannot be traded in period 2 and also cannot be traded across islands. The period 2 asset b12 and the liquid period 3 asset b13 can be traded across islands. In addition, the liquid period 3 asset can be retraded in period 2. The commitment asset makes up a proportion k of the 3 0 This paper also assumes log utility to arrive at an analytic solution, as in the model presented in the Appendix to Kocherlakota (2001). 3 1 Laibson, Repetto and Tobacman (1998) simulate a more complex model with both types of agent in a single economy. This paper adopts the islands formulation (where each island has homogeneous consumers) since in our model (which is kept extremely simple in order to yield analytical results), if the two types of agents existed in a single economy with no barriers to trading the commitment asset, then the price of the commitment asset would be identical regardless of the share of the hyperbolic consumer in the economy (assuming an interior solution). 24 total period 3 asset endowment in each island. The model di¤ers from that of K01 in two key regards. First, K01 has a single economy consisting of identical agents who have either hyperbolic or non-hyperbolic preferences. Second, in K01 the commitment asset is tradable across all agents in period 1. The introduction of two types of agent and the island formulation is the simplest way of introducing geographical heterogeneity in agent types. The assumption that acom is non-tradable across islands is required to deliver di¤erent average prices for the commitment asset across regions. Given that we are using housing as a proxy for the commitment asset, then this assumption requires that each agent owns property in only one small area, and does not move between areas. One could conjecture that qualitatively similar results would obtain if there was rather some …nite cost of trading the commitment asset across islands. Utility of the two types in period 1 is given as U1B = U1N = ln c1 + [ln c2 + ln c3 ] (10) while utility in period 2 is given as U2B U2N = ln c2 + = ln c2 + (1 !) ln c3 ln c3 (11a) (11b) where the believers place a probability ! on the world ending.32 The believers’ preferences in period 1 re‡ect their desire to behave responsibly regardless of their belief that the world is likely to end soon: hence, they discount the future similarly to other agents. Their period 2 preferences re‡ect the temptation to allow their discounting behavior to be guided by their ‘end times’ beliefs, implying a discount factor (1 !). Agent j’s decision problems in periods 2 and 1 are given below: Period 2 j Agent j enters period 2 with liquid wealth Wliq = q23 bj13 + bj12 that can be j = q23 ajcom . Then, traded freely with all agents and committed wealth Wcom following K01, DP2 can be written as: max [ln c2 + ln c3 ] cj2 ;cj3 ;bj23 (12) subject to j j cj2 + q23 b23 cj3 bj23 j = Wliq = bj23 0 + (13) q231 Wjcom (14) (15) where = (1 !) for the believers and otherwise. The solution to DP2 can be written as c2 (Wliq ; Wcom ) ; c3 (Wliq ; Wcom ). 3 2 In addition to the substantive chages from K01 detailed in the text, we also normalize the total endowment of each island (and the overall economy) in each period to 1, and have the non-hyperbolic discount factor equal between periods 1-2 and 2-3. 25 Period 1 Agent j’s period 1 decision problem (DP1) can be written as: h i j 2 max ln c + ln (c (W ; W )) + ln (c (W ; W )) (16) liq com liq com 2 3 1 j j j j c1 ;acom ;b12 ;b13 subject to cj1 + pcom ajcom + q12 bj12 + q13 bj13 j Wliq j Wcom bj12 ; bj13 ; ajcom = 1 + pcom k + q13 (1 = q23 bj13 + bj12 q23 ajcom = k) + q12 (17) 0 (18) (19) (20) Equilibrium Equilibrium is de…ned in terms of consumption, asset holdings and prices. Equilibrium satis…es the following three conditions: …rst, cj2 ; cj3 solves DP2 j j given q23 , Wliq = q23 bj13 , and Wcom = q23 ajcom ; second, cj1 ; bj12 ; bj13 ; ajcom solves DP1 given q12 , q13 , q23 , and pcom ; and third, markets clear so that: Z cjt dj = 1; t = f1; 2; 3g (21) Z bj12 dj = 1 (22) Z Z bj23 dj = bj13 dj = 1 k (23) Z ajcom = kmi 8i (24) j2mi The principal di¤erence between this model and K01 is seen in the last set of market clearing conditions for the commitment asset (24), which hold for each island individually (while the market clearing conditions for the liquid bonds hold for the economy as a whole). Solution The solution to DP2 for the type B agents, following K01, is given below: c2 (Wliq ; Wcom ) c3 (Wliq ; Wcom ) Wliq + Wcom ; Wliq 1 + (1 !) Wliq + Wcom = q231 max (1 !) ; Wcom (1 !) = min As in K01, the nonconcavity of c2 generates asymmetrical equilibrium allocations for the type B consumers. As with K01, the equilibrium is …rst guessed and then veri…ed: Guessing: 26 De…ne ( ; h) as the solution to 0 (1 )h 0 = ln @ 1 h 1 (1 !) 1+ 1+ (1 ln 0 k (1 + ln (1 k ) !) 1+ = h 1+ + 2 1 k 1 k + 1 A !) (1 + ) 2 1 k 1 k (1 ) 1+ (1 !) + (1 + (1 !)) (1 + ) ln (1 !) 11+k + ! (25) (26) Equation (25) de…nes the share of hyperbolic consumers that hold the liquid asset in each island, while equation (26) de…nes the period 1 consumption of the representative hyperbolic consumer, h. In K01 an interior solution for is guaranteed (setting = 1 gives this result). For a solution to exist in the augmented model with < 1 requires that33 ! 1+ 1+ k (1 + ) (1 ) ln + ln (1 !) ln > ln 1 + (1 !) 1 k 1 + + 2 11 kk Given and h, de…ne asset prices as q12 = 1+ q13 = pN com = h 1+ 1+ (1 !) 1 (27) 2 pH com = q23 = (1 q13 q12 ) k 1 2 k 1 h 1 (1 !) 1+ 1+ (1 h !) (28) (29) (30) Within each island with hyperbolic agents (of mass mi ), then a mass mi receive the following allocation cj1 = h (31) 1+ = q12 1 + (1 cj2 = bj12 cj3 = bj13 = bj23 = ajcom = 2 0 !) h (1 !) 1+ q13 1 + (1 (32) !) h (33) (34) 3 3 This expression is obtained by setting > 0. When there are a comparatively large number of N types ( is low) then the e¤ective demand for the type B’s liquid asset b13 is high, driving up the price and lowering the return. This crowds out B type agents wishing to hold the liquid asset, requiring a lower as more choose the commitment asset. However, the market incompleteness that prevents direct trade in acom requires that > 0. 27 ) mi receive while a mass (1 cj1 = h (35) cj2 bj12 = cj3 = ajcom = bj13 = bj23 = 0 = q12 h (36) 2 pH com h (37) (38) Consumption allocations for the non-hyperbolic consumers are given by (39) - (41): 1 1 h cN 1 = cN 2 = bj12 = cN 3 = bj13 + ajcom = bj23 + ajcom = (39) 1 q12 1 h (40) 2 1 q13 1 h (41) 0 requires that34 Finally, the condition bN 13 cN 3 k 0 (42) Verifying the Solution The veri…cation that this set of allocations and prices constitutes an equilibrium follows K01. The type N agents have time consistent preferences, so that their problem DP2 can be collapsed into DP1 (recall that there is no uncertainty, 3 4 This condition will be met in equilibrium since the N types consume more than their endowment (1) in period 3, and are therefore net purchasers of b13 . To see this note that, rewriting the N types’budget constraint, one obtains: cN 2 1 q12 + cN 3 which implies that, if cN 1, then cN 2 3 resource constraint to yield: cN 2 1 q13 = (h 1) 1 1. To see that cN 2 1= cB 2 1 0 1, one can rewrite the period 2 1 where cB 2 gives the (weighted) average period 2 consumption of the B types. This implies that, if the B types consume above their endowment (on average) in period 2, then the N types must consume below their endowment. In fact, period 2 consumption is given by: cN 2 cB 2 = = q12 q12 1 1 1+ h q12 1+ ! (1 !) q12 which implies that the N type’s consumption in period 2 is below their endowment. Hence cN 1 and bN 0. 3 13 28 so the problems at the two time periods are identical if the time preference parameter is stable). Standard arbitrage conditions require that pN com = q13 . Then DP1(N) is given by: (c1 ; c2 ; c3 ) 2 arg max (c1 ;c2 ;c3 ) ln c1 + ln c2 + 2 ln c3 (43) subject to c1 + q12 c2 + q13 c3 1 + q12 + q13 (44) which yields (39) –(41) given the period 1 aggregate resource constraint and the 35 de…nition of h. Next, I show that pH Substitution among equations com > q13 . (28), (29) and (25) then yields (45). ln pH com ln (q13 ) = ln (1 !) + (1 + ) ln 1+ 1+ (1 !) >0 (45) The commitment premium can therefore be decomposed into three separate terms: a positive e¤ect from the inadequate period 3 (far future) consumption, ln (1 !), a negative term from the excessive period 2 (near future) consumption, ln 1+ 1+ (1 !) , and the relative weight placed on consumption in each period, (1+ ) . Note that equation (45) is identical to that in K01, which indicates that the presence of non-hyperbolic consumers in other island economies and the tradability of the liquid assets do not alter the main result. This is not surprising, since with log utility the ratio of the asset returns (or equivalently prices) is related only to the di¤erent e¤ective discount factors for the two groups of hyperbolic consumers (those that commit, by holding acom and do not commit, by holding b13 , respectively), via the indi¤erence relation that equates utility across the two strategies. However, note that the introduction of non-hyperbolic consumers gives the hyperbolic consumers an additional opportunity to trade current and future consumption, leading to higher consumption in period 1 for these agents compared to K01 (equation (??))36 . It is easy to show that markets clear and that cj2 = c2 ; cj3 = c3 8j. The rest of the proof directly follows that in K01 and is therefore not reproduced here. Solution in ; h space Totally di¤erentiating (25) with respect to ; h yields the following relationship along the line de…ned by the equation in ; h space: dh j eq (25) > 0 d (46) 3 5 This condition is required for the later stages of the veri…cation of the solution, detailed in Kocherlakota (2001). k(pH com q13 ) 1+ 1+q 3 6 Rewriting the expression for h in terms of asset prices, we have h = 12 +q13 . k(pH com q13 ) 1+ 1+q12 +q13 Then it is clear that h > 1 since pH com > q13 . To see the intuition, note that the ‘believers’ that buy the commitment asset sell their liquid assets b13 to other ‘believers’ (since they cannot trade the commitment asset with agents in other islands). This depresses the price of the liquid assets, encouraging the ‘non-believers’ to buy these assets in exchange for current consumption. In e¤ect, the ‘non-believers’lend indirectly to the ‘believers’seeking to commit. 29 while di¤erentiating the same equation with respect to !; h yields: 0 1 1 h 1 (1 !) 1+ 1+ (1 !) dh ! j eq (25) = h @ h (1 + )A d! (1 !) (1 + (1 !)) (47) dh Hence d! j (25) is negative for ! ! 0 and positive for ! ! 1 (conversely, d d! j (25) is positive for ! ! 0 and negative for ! ! 1). Totally di¤erentiating (26) with respect to ; h yields the following relationship along the line de…ned by the equation in ; h space: dh j eq (26) < 0 d (48) while di¤erentiating the same equation with respect to !; h yields: dh j eq (26) > 0 d! (49) Figure A1 illustrates the equilibrium and comparative statics for changes in !. [Figure A1 about here] Proofs of propositions 1–4 @ 2 ln pr com q 13 Proposition 1: 0 @!@ r Proof. Aggregating across islands within geographical regions r (corresponding to the MSAs in the data) yields: prcom ln @ 2 ln prcom q13 prcom q13 @!@ pH com = = r r (1 r 1 (q13 ) ln (1 ! !) (1 + r !) + (1 dpN (50) (1 + ) !)) ln 0 1+ 1+ (1 !) (51) (52) com = dqd!13 0 in the region of ! = 0 Proposition 2: d! @q13 Proof. To show that @! 0, note that the primary e¤ect of an increase in ! will be to reduce the average consumption of the B types in period 3, and to increase the consumption of N types. To persuade the N types to shift consumption from earlier periods requires a higher return on their period 3 assets, and hence a lower price. To see this algebraically, one can rewrite the period 3 aggregate resource constraint to give: " !# 1 q13 1 + (1 !) 2 q13 = (1 h) + h + (1 ) (53) pcom 1+ 30 (1 !) 13 The main e¤ect of an increase in ! will be to decrease pqcom and 1+ 1+ . Since these e¤ects will tend to dominate e¤ects via and h, then the e¤ect on 13 q13 will be negative. Substituting pqcom using (45) yields: " 1 !# 1+ (1 !) (1 + ) 2 q13 = (1 h) + h + (1 ) 1 + (1 !) 1 + (1 !) (54) @q13 dq13 13 For ! = 0, @q = = 0, and is therefore given by: @h @ d! dq13 j [! = 0] = d! 0 1+ Proposition 3: Proportion of believers following the commitment strategy declines with increases in ! in the region of ! = 0 Proof. The proportion of believers following the commitment strategy is given d by (1 ). The proposition is therefore that d! 0 for ! ! 0. Note that: dh j [eq (25) ; ! = 0] = d! (1 k) (1 + ) < 0 (55) dh d! j (26) 0, then reference to Figure A1 immediately establishes that 0 in equilibrium (in the region of ! = 0).37 Proposition 4: The loan to income ratio for believers following the commitment strategy increases in the region of ! = 0 Proof. The loan to income ratio is given by: Since d d! pcom (acom loan = income 1 k) = 2 h (56) 0 for ! ! 0. Consider a series of ‘isoThe proposition is therefore that dd!h h’ lines plotted in ; h space (a series of downward sloping lines where those located above and to the right correspond to a higher value of the product h). We know that the movement to a new equilibrium involves a downward shift in the line plotting equation (25) and an upward shift in the line plotting equation (26). Then a su¢ cient condition for dd!h 0 is that the iso- h lines have a steeper (negative) slope than the lines plotting (26). These slopes are given by: dh d dh d 2 j [eq (26) ; ! = 0] = (1 + ) (1 1 1 k j [ h = c; ! = 0] = (1 ) k )+ 2 (1 k) (57) (58) 3 7 For the model in K01 ( = 1), the proofs for Propositions 2 and 3 hold for all values of !. Since h = 1, then Proposition 2 implies Proposition 3. Proposition 2 clearly holds: equation (25) simpli…es to: 1 ln and d d! = (1 ) 1+ (1 !) = ln k 1 k + 0. 31 1 ln 1+ (1 1+ !) Then the su¢ cient condition for d h d! 2 1 1 k (1 + ) (1 0 is given by: (1 ) k )+ 2 (1 k) 0 (59) and hence: (1 + ) (1 k )+ which clearly holds. 32 2 (1 k) 0 (60) Tables and Figures Table 1. Table 1. Descriptive Statistics Variable Mean Std. Dev. Min Δln(house price index) 0.06 0.04 -0.07 Δln(population)-1 0.01 0.01 -0.07 Δln(p.c. income)-1 0.04 0.02 -0.42 Max 0.29 0.10 unemployment-1 0.21 1.2 30.1 sB 5.0 2.1 (2000 Data) 0.10 0.11 0.00 0.48 sH 0.09 0.14 0.00 0.94 0.76 0.17 0.17 0.13 (Annual Data) 3.3 10.3 0.05 0.01 0.97 0.57 -15.0 21.0 sW evang Δri-1 growth-1 3.2 1.2 0.8 4.5 inflation-1 2.5 0.8 1.6 3.4 unemployment-1 5.0 0.6 4.0 6.0 Δoil price-1 15.2 26.2 -32.1 57.0 fed funds-1 3.9 3,625 Observations (363 MSAs) 1.8 1.1 6.2 33 Table 2. evang*Δri-1 Δln(population)-1 Δln(p.c. income)-1 unemployment-1 evang*Δri Δln(population) Δln(p.c. income) unemployment evang*ri ln(population) ln(p.c. income) unemployment evang I .00446*** (.000307) 1.44*** (.145) .196*** (.0590) -.0104*** (.000832) Table 2. Panel Regression Results II III IV .00494*** (.000320) 1.30*** (.100) .269*** (.0655) -.00397*** (.000414) .00371*** (.000277) 1.15*** (.156) .0839*** (.0317) -.0118*** (.000932) .00618*** (.000391) .537*** (.0425) .631*** (.0694) .00555*** (.00120) -.0883*** (.00693) Δri-1 V .00510*** (.000345) 1.26*** (.102) .278*** (.0577) -.00182*** (.000412) VI .00503*** (.000335) 1.35*** (.0988) .323*** (.0549) -.00258*** (.000386) VII .00139*** (.000526) 1.47*** (.140) .182*** (.0548) -.00699*** (.000789) -0.0860*** (.00663) -0.00258*** (.000105) -.0862*** (.00667) -.00148*** (.000114) .00577*** (.000300) .41 3,625 363 RE No No No .62 3,625 363 FE Yes No Yes year 2 R (within) Obs. MSAs Estimation Technique Year Dummies State Dummies*year State Dummies*Δri-1 .50 .50 .93 .47 .31 3,625 3,624 3,987 3,625 3,625 363 363 363 363 363 FE FE FE RE RE Yes Yes Yes Yes No No No Yes No No No No No No No Dependent variable is Δln(house price index) except column III: ln(house price index). Robust Standard Errors in parentheses. Sig. level: 1 percent: ***; 5 percent: **; 10 percent: *. All regressions also contain a constant term. 2 For comparison, estimating column I without the interaction term yields (within) R =.47. 34 Table 3. evang*Δri-1 evang*growth-1 Table 3. Robustness to addition of Macroeconomic Variables I II III IV V VI VII .00461*** .00477*** .00407*** .00489*** .00293*** .00277*** .00410*** (.000329) (.000316) (.000310) (.000344) (.000345) (.000542) (.000486) -0.00403* -0.0157*** (.00241) evang*inflation-1 (.00298) .0187*** .0290*** (.00434) evang*unemployment-1 (.00821) -.0174*** .0167* (.00469) (.00997) evang*Δoil price-1 .000416*** (.000128) evang*fed funds-1 .0130*** (.00199) -.000388** (.000263) .0233*** (.004729) evang*year-1 Δln(population)-1 1.45*** 1.43*** 1.45*** 1.43*** 1.44*** (.146) (.144) (.144) (.144) (.144) Δln(p.c. income)-1 .194*** .196*** .200*** .195*** .205*** (.0589) (.0593) (.0596) (.0592) (.0599) unemployment-1 -.0104*** -.0104*** -.0104*** -.0104*** -.0103*** (.000832) (.000833) (.000832) (.000832) (.0656) 2 R (within) .50 .50 .50 .50 .50 Obs. 3,625 3,625 3,625 3,625 3,625 MSAs 363 363 363 363 363 Dependent variable is Δln(house price index) for all specifications. Robust SEs in parentheses. Sig. level: 1 percent: ***; 5 percent: **; 10 percent: *. All regressions contain a constant term, year dummies and MSA Fixed Effects. 35 1.44*** (.145) .198*** (.0592) -.0103*** (.0654) .50 3,625 363 -.00188 (.00191) 1.44*** (.145) .198*** (.0592) -.0103*** (.000832) .50 3,625 363 Table 4. evang*Δri-1 Δln(population)-1 Δln(p.c. income)-1 unemployment-1 2 R (within) Obs. MSAs Subsample evang*Δri-1 Δln(population)-1 Δln(p.c. income)-1 unemployment-1 2 Table 4. Subsample Robustness Checks I II III IV .00208*** .00666*** .00450*** .00575*** (.000316) (.000523) (.000365) (.000343) .934*** 1.39*** 1.35*** 1.55*** (.136) (.260) (.148) (.160) .115*** .139* .206*** .221*** (.0370) (.0826) (.0633) (.0711) -.00610*** -.0131*** -.0102*** -.00723*** (.00108) (.00325) (.000865) (.000827) .43 .43 .48 .57 1,810 1,815 3,175 2,725 362 363 318 273 1997-2001 2002-2006 Not NE Not Midwest VI VII VIII IX .00300*** .00311*** .00435*** .00330*** (.000282) (.000630) (.000459) (.000300) 1.44*** 1.72*** 1.63*** 1.40*** (.150) (.311) (.189) (.155) .123* .131*** .277*** .113* (.0640) (.0747) (.0436) (.0659) -.00916*** -.0132*** -.00982*** -.0125*** (.00105) (.00187) (.000919) (.00117) .43 .49 .52 .46 2,825 730 2,320 2,775 283 73 232 278 sW≥.90 sB≤.10 sH≤.10 Not West V .00771*** (.000872) 1.52*** (.223) .241*** (.0467) -.0133*** (.00112) .52 2,150 215 Not South X .00513*** (.000485) 1.56*** (.158) .210*** (.0648) -.0105*** (.000881) .51 3,255 326 evang<90pctile R (within) Obs. MSAs Subsample Dependent variable is Δln(house price index) for all specifications. Robust SEs in parentheses. Significance level: 1 percent: ***; 5 percent: **; 10 percent: *. All regressions contain a constant term, year dummies and MSA Fixed Effects. sJ denotes 2000 population shares of group J (B: Black; H: Hispanic; W: White). 36 Table 5. Table 5. Different Evangelicals Measures Preferred Measure ARDA Measure Strict Premillenialists Summary Statistics Mean .172 .173 .0398 Standard Deviation .129 .129 .0226 Correlations Preferred Measure 1.00 ARDA Measure 1.00*** 1.00 Strict Premillenialists .421*** .422*** 1.00 Estimated Effects Interaction Coefficient .00446*** .00502*** .00662*** (.000307) (.000307) (.00189) Interaction Coefficient estimated using specification as in Table 2, Column I. Table 6. Table 6. Different House Price Indices I II III IV V VI Case-Shiller OFHEO Real Nominal Real Nominal (20 MSAs) (20 MSAs) (27 MSAs) (27 MSAs) (363 MSAs) (363 MSAs) Summary Statistics Mean 0.08 0.08 0.05 0.07 0.03 0.06 Standard Deviation 0.06 0.05 0.05 0.05 0.04 0.05 .96*** .98*** .98*** Correlations Estimated Effects Interaction Coefficient .00575* .00700** .00907*** .00820*** .00445*** .00424*** (.00343) (.00306) (.00244) (.00241) (.000312) (.000303) 2 R (within) .50 .61 .56 .63 .45 .49 Observations 196 263 3,540 Interaction Coefficient estimated using specification as in Table 2, Column I. All variables in log first differences. 37 Table 7. evang*Δri-1 Δln(population)-1 Δln(p.c. income)-1 unemployment-1 evang*Δri Δln(population) Δln(p.c. income) unemployment Δln(house price index)-1 Table 7. Controlling for Serial Correlation I II III IV .00326*** .00446*** (.000387) (.000430) .781*** 1.44*** (.0887) (.170) .136*** .196*** (.0197) (.0603) -.00513*** -.0104*** (.000752) (.00141) .00192*** .00195*** (.000337) (.000382) .488*** .587*** (.119) (.113) .0933*** .154*** (.0380) (.0364) -.00322*** -.00373*** (.000801) (.00109) .585*** .434*** (.0847) (.0982) 2 evang*Δ ri 2 Δ ln(population) 2 Δ ln(p.c. income) Δunemployment 2 Δ ln(house price index)-1 2 R (within) Obs. MSAs Clusters Arellano Bond AR(1) Arellano Bond AR(2) Hansen over-id test .33 3,262 363 n.a. n.a. n.a. n.a. V VI .00110*** (.000334) .315*** (.0923) .0511** (.0242) -.000635 (.000731) -.136** (.0540) n.a. 2,535 363 n.a. -6.66*** .39 6.80 .000958*** (.000316) .307*** (.0932) .0442** (.0206) -.000711 (.000706) -.173*** (.0489) n.a. 2,535 363 n.a. -6.68*** -.43 6.80 .50 n.a. n.a. 3,625 2,898 2,898 363 363 363 363 n.a. n.a. n.a. -6.48*** -4.66*** n.a. 2.66*** 2.66*** n.a. 51.0*** 51.0*** FE Cluster GMM GMM GMM GMM FE (MSA) (1 step) (2 step) (1 step) (2 step) AR(1) Estimation Technique 2 Dependent variable is Δln(house price index) except columns V and VI: Δ ln(house price index). Robust Standard Errors in parentheses. Sig. level: 1 percent: ***; 5 percent: **; 10 percent: *. All regressions contain year dummies and a constant term. Column I: ρ = .56. GMM estimation uses collapsed instrument list to reduce bias due to overfitting with small samples. GMM results are for first-differenced variables (in addition to any differencing already applied). Standard errors from 2 step GMM results incorporate Windmeijer’s (2005) finite-sample correction. 38 Table 8. evang*Δri-1 Δln(population)-1 Δln(p.c. income)-1 unemployment-1 evang D.evang*Δri-1 D.Δln(population)-1 D.Δln(p.c. income)-1 D.unemployment-1 2 R Obs. MSAs/ MSA pairs Clusters ρ 2 LM χ (1) Table 8. Controlling for Spatial Correlation I II III IV .00519*** (.000646) .783*** (.0908) .263*** (.0839) -.00328*** (.000543) -.0414*** (.0103) .00256*** .00163*** .00139** (.000616) (.000514) (.000644) .723*** .557*** .518*** (.0940) (.0866) (.0990) .0980*** .0682** .0853*** (.0297) (.0312) (.0277) -.00519*** -.00425*** -.00323*** (.000703) (.000806) (.000942) .55 .12 .08 .08 3,625 2,520 1,890 1,260 363 253 190 127 500 n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. OLS Cluster (St/Yr) FE Matched Difference V .00312*** (.000245) 1.35*** (.120) .158*** (.0413) -.00893*** (.000695) VI .00384*** (.000305) 1.38*** (.131) .173*** (.0485) -.00927*** (.000824) n.a. n.a. 3,620 3,620 362 362 n.a. n.a. .685 .668 1571.4 1313.4 (p=0.000) (p=0.000) MLE FE MLE Spatial Matched Spatial Lag Error (FE) Difference (FE) FE Matched Difference Estimation Technique ≤75th ≤median percentile None (62 miles) (42 miles) Distance criterion n.a. n.a. n.a. Dependent variable is Δln(house price index) except columns II-IV: D.Δln(house price index). D.x defined as xa-xb, for matched MSA pair {a,b} and any variable x. Robust Standard Errors in parentheses. Sig. level: 1 percent: ***; 5 percent: **; 10 percent: *. All regressions contain year dummies and a constant term (and State dummies, column I). Distance criterion refers to distance between matched MSAs. Row-standardized weights matrix used for columns V and VI. 2 2 All reported R 's are within R , except column I. 39 Table 9. Table 9. Mortgage Data I II III evang*Δri-1 -.000403*** .00666*** .00907*** (.000105) (.00132) (.000847) Δln(population)-1 .124*** 1.77*** 1.74*** (.0375) (.410) (.303) Δln(p.c. income)-1 0.00212 .0297 0.00902 (.00833) (.105) (.0630) unemployment-1 -.000448** -.00778*** -.00741*** (.000186) (.00251) (.00140) 2 R (within) .72 .19 .30 Obs. 3,600 3,600 3,600 MSAs 360 360 360 Dependent Variable Δ(loan apps/ popn.) Δ(loan/inc. ratio, unweighted) Δ(loan/inc. ratio, weighted) Robust SEs in parentheses. Significance level: 1 percent: ***; 5 percent: **; 10 percent: *. All regressions contain a constant term, year dummies and MSA Fixed Effects. 40 Derived from 2000 Religious Congregations and Membership Study, as detailed in text. Subjective "Prophetic Speedometer" giving perceived probability of end times occuring soon. Population shares obtained from 2000 census data at the county level and aggregated to the MSA level Available at the MSA level, Annual Data Available at the MSA level, Annual Data Available at the MSA level, Annual Data Annual average Share of Evangelicals (three definitions) Rapture Index Share of hispanics and non-hispanic blacks and whites (2000) Per capita personal income Population Unemployment Rate Fed Funds Rate GDP Growth CPI Inflation Unemployment Rate Change in WEO Oil Price Number of Mortgage Loan Applications Average Mortgage Loan Size 31 MSA level data from the Home Mortgage Disclosure Act (HMDA) Loan Application Registry MSA level data from the Home Mortgage Disclosure Act (HMDA) Loan Application Registry (National level) Repeat-sales based house price index available for 20 large MSAs Dell'Ariccia, Igan and Laeven (2008) Federal Reserve Board of Governors (Table H15) IMF World Economic Outlook (WEO) database IMF World Economic Outlook (WEO) database IMF World Economic Outlook (WEO) database IMF World Economic Outlook (WEO) database Dell'Ariccia, Igan and Laeven (2008) Bureau of Labor Statistics (http://www.bls.gov/lau/home.htm) Bureau of Economic Analysis (http://www.bea.gov/regional/reis/) Bureau of Economic Analysis (http://www.bea.gov/regional/reis/) Bureau of the Census (http://factfinder.census.gov) http://www.brunching.com/toys/rapture-original.txt (1995-1997). http://web.archive.org/web/*/http://www.raptureready.com (19982004). http://www.raptureready.com/rap2.html (official website, 2005-06). Association of Religion Data Archive (http://www.thearda.com). Available from http://www2.standardandpoors.com. Table A1 Variable Definitions and Sources Definition Source Repeat-sales based house price index derived from data relating to 2007Q2 release, obtained from OFHEO conventional conforming mortgage transactions (Fannie Mae and Freddie Mac). As above, deflated using MSA-specific CPI available for 27 MSAs. CPI from Bureau of Labor Statistics (http://www.bls.gov/cpi/). Case Shiller House Price index OFHEO House Price Index (real) Variable OFHEO House Price Index (nominal) Table A1 Figure 1. Evangelicals: Share of MSA Population Less than 10 percent 15-25 percent 10-15 percent More than 25 percent Source: 2000 Religious Congregations and Membership Study, 2000 Census 31 Figure 2. 1. False Christs 2. Occult 3. Satanism 4. Unemployment 5. Inflation 6. Interest Rates 7. The Economy 8. Oil Supply/Price 9. Debt and Trade 10. Financial unrest 11. Leadership 12. Drug abuse 13. Apostasy 14. Supernatural 15. Moral Standards 16. Anti-Christian 17. Crime Rate 3 2 2 3 3 2 4 4-1 3 5 4 2 4 1 3 3 4 18. Ecumenism 4 35. Date Settings 19. Globalism 3 36. Volcanoes 20. Tribulation Temple 2 37. Earthquakes 21. Anti-Semitism 4 38. Wild Weather 22. Israel 5 39. Civil Rights 23. Gog (Russia) 5 40. Famine 24. Persia (Iran) 5 41. Drought 25. The False Prophet 3 42. Plagues 26. Nuclear Nations 5 43. Climate 27. Global Turmoil 4 44. Food Supply 28. Arms Proliferation 4 45. Floods 29. Liberalism 4 30. The Peace Process 3+1 Rapture Index 159 31. Kings of the East 4 Net Change unch 32. Mark of the Beast 3 33. Beast Government 4 Updated Dec 3, 2007 34. The Antichrist 2 2004 High 157 2005 High 161 2006 High 163 2007 High 163 2004 Low 135 2005 Low 143 2006 Low 151 2007 Low 154 Record High 182 24 Sept 01 Record Low 57 12 Dec 93 Source: http://www.raptureready.com/rap2.html. 32 2 4 5 5 3 3 5 3 3 5 5 Figure 3. 120 130 140 150 160 170 End Times Beliefs: the Rapture Index 1996 1998 2000 Source: see text. 33 2002 2004 2006 Figure 4. 0 .05 .1 .15 Change in log House Price Index (2000 pop. weighted) 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Source: Office of Federal Housing Enterprise Oversight. 34 Residual Change in log House Price Index -.005 0 .005 Figure 5. 9/11 Effect 0 .2 Share of Evangelicals .4 Fitted Relationship 2000q2 2001q2 2000q4 2001q4 Source: OFHEO, 2000 Religious Congregations and Membership Study. 35 .6 Figure A1. 1.03 1.02 Eq (24) 1.01 h Effect of increase in ω 1 Eq (25) 0.99 iso-hθ line 0.98 0.97 0.67 0.69 θ 36 0.71 0.73