WORKING PAPER Regional US house price formation: One model fits all? NORGES BANK RESEARCH AUTHOR: ANDRÉ KALLÅK ANUNDSEN CHRISTIAN HEEBØLL Working papers fra Norges Bank, fra 1992/1 til 2009/2 kan

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WORKING PAPER Regional US house price formation: One model fits all? NORGES BANK RESEARCH AUTHOR: ANDRÉ KALLÅK ANUNDSEN CHRISTIAN HEEBØLL Working papers fra Norges Bank, fra 1992/1 til 2009/2 kan bestilles over e-post: Fra 1999 og senere er publikasjonene tilgjengelige på Working papers inneholder forskningsarbeider og utredninger som vanligvis ikke har fått sin endelige form. Hensikten er blant annet at forfatteren kan motta kommentarer fra kolleger og andre interesserte. Synspunkter og konklusjoner i arbeidene står for forfatternes regning. NORGES BANK WORKING PAPER XX 2014 RAPPORTNAVN Working papers from Norges Bank, from 1992/1 to 2009/2 can be ordered by Working papers from 1999 onwards are available on Norges Bank s working papers present research projects and reports (not usually in their final form) and are intended inter alia to enable the author to benefit from the comments of colleagues and other interested parties. Views and conclusions expressed in working papers are the responsibility of the authors alone. ISSN (online) ISBN (online) 2 Regional US house price formation: One model fits all? André K. Anundsen Norges Bank Christian Heebøll University of Copenhagen May 27, 2014 Abstract Does a one model fits all approach apply to the econometric modeling of regional house price determination? To answer this question, we utilize a panel of 100 US Metropolitan Statistical Areas over the period 1980q1 2010q2. For each area we estimate a separate cointegrated VAR model, focusing on differences in the effect of subprime lending and lagged house price appreciation. Our results demonstrate substantial differences in the importance of subprime lending for house price determination across regional housing markets. Specifically, we find a greater impact of subprime lending in areas with a high degree of physical and regulatory restrictions on land supply. Likewise, lagged house price appreciation interpreted as capturing an adaptive expectation channel is found to be more important in areas where the supply of dwellings is more constrained, in areas located in a state with non-recourse lending and in more populous areas. Our results also suggest that disequilibrium constellations are restored more slowly in areas located in a state with non-recourse lending. Keywords: Cointegration; Panel heterogeneity; Regional house price dynamics; Subprime lending. JEL classification: C32; C51; C52; G01; R21; R31. This Working Paper should not be reported as representing the views of Norges Bank. The views expressed are those of the authors and do not necessarily reflect those of Norges Bank. The paper was presented at the 13th OxMetrics User Conference in Aarhus, September 2013, the 36 th meeting of the Norwegian Economic Association, the 7 th RGS Doctoral Conference in Economics in Dortmund, March 2014, the 2014 Annual Conference of the Royal Economic Society in Manchester, April 2014, and at workshops and seminars in Norges Bank and Statistics Norway. We would like to thank the participants at these events for their comments and suggestions. The paper has been improved as a result of discussions with, and comments from, Farooq Akram, Steinar Holden, Håvard Hungnes, Søren Johansen, Andreas Kotsadam, Svein Olav Krakstad, Ragnar Nymoen, Asbjørn Rødseth, Bernt Stigum and Jean-Pierre Urbain. For great proof reading, we would like to thank Veronica Harrington. We would also like to thank the New York Library staff and Frederic Jean-Baptiste at Moody s Analytics for helping us collecting the data. Contact details: André Kallåk Anundsen: Norges Bank Research, Norges Bank, Bankplassen 2, P.O. Box 1179 Sentrum, NO-0107 Oslo, Norway. 1 1 Introduction The evolution of US house prices differed markedly across geographical regions over the recent house price cycle. For example, coastal areas experienced much greater house price volatility relative to inland areas (Huang and Tang, 2012; Cohen et al., 2012; Sinai, 2012; Anundsen and Heebøll, 2013). Higher house price volatility was also related to a more severe worsening of employment conditions and a higher rise in foreclosures during the financial crisis period (Rogers and Winter, 2013). Against this background, the objective of this paper is to understand what the drivers of regional US house prices are. For that purpose, we analyze individual time series models for the 100 largest Metropolitan Statistical Areas (MSAs) in the US, paying particular attention to regional differences in the effect of lagged house prices, the speed of equilibrium adjustment and the role of subprime lending. To analyze the heterogeneity across local US housing markets, we apply a modeling strategy built on three steps. First, we estimate an autoregressive distributed lag (ARDL) model on our sample of 100 MSAs over the period 1980q1 2010q2. The econometric analysis takes as a starting point a standard inverted demand equation, allowing for shifts in credit constraints as approximated by developments in subprime lending. The model is estimated both the conventional dynamic fixed effects (DFE) approach, and the mean group (MG) and the pooled mean group (PMG) estimators suggested by Pesaran and Smith (1995) and Pesaran et al. (1999), respectively. Considering all approaches allows us to study similarities and differences in the results obtained, and of particular relevance to the focus of this paper to test the homogeneity assumption imposed in standard panel studies of house prices (Abraham and Hendershott, 1996; Gallin, 2006, 2008; Mikhed and Zemcik, 2009a,b). Our results firmly reject the assumption of equal slope coefficients. This suggests that econometric models for regional house prices should allow for possible heterogeneity in the effect of changes in the drivers of house prices. Models based on the homogeneity assumption can obscure important differences in the effect on house prices of changes key economic variables across regional markets, cf. Muellbauer (2012). After rejecting the homogeneity assumption in the first step of our estimation strategy, we estimate separate cointegrated VAR models using the Johansen (1988) method. While our approach is comparable to Ashworth and Parker (1997) who study heterogeneity for 11 regions in the UK, the scope and focus of this paper are different in several respects. Our attention is paid to the US housing market, where we investigate the role of subprime lending and lagged house price appreciation during the recent housing boom, by allowing them to affect house prices differently in each area. The results from our second step indicate several substantial differences in house price formation across Metropolitan Statistical Areas. These heterogeneities relate to both the long-run elasticities, the speeds of adjustment towards equilibrium, the effect of lagged house price appreciation, and the role of subprime lending. Finally, we investigate what factors may explain these heterogeneities. In particular, we analyze the characteristics of the areas in which subprime lending is found to have a greater influence on house price developments. Further, we explore possible explanations of regional differences in the coefficients for lagged house price appreciation and the speed of equilibrium adjustments, which using the terminology of Abraham and Hendershott 2 (1996) may be interpreted as capturing a bubble builder and a bubble burster effect, respectively. For these purposes, we utilize both cross-sectional models and a logit model. We find that subprime lending had a greater influence on house price developments in areas with more restrictions on land supply. This finding is consistent with recent crosssectional studies by Glaeser et al. (2008), Huang and Tang (2012) and Anundsen and Heebøll (2013), who demonstrate that disparities in restrictions on land supply between areas are important in explaining inter-msa differences in house price volatility over the course of a boom-bust cycle. While it is reassuring that this finding is retained when using a different methodological approach, the main advantage with the approach taken in this paper is that it also allow us to study heterogeneities in house price dynamics. In this regard, we find that the coefficients on lagged house price appreciation are significantly greater in areas with more restrictions on land supply. To the extent that these coefficients reflect differences in the importance of expectations, our results suggest a stronger priceto-price feedback loop in more supply restricted areas. We also find that lagged house price appreciation is significantly more important in areas with a higher population and in areas situated in a state with non-recourse lending. This might be related to a greater prevalence of herd behavior in large urban areas and the lower (perceived) risk associated with a housing purchase faced by home buyers in states where lending is non-recourse. Finally, the bubble burster (the adjustment parameter) is found to be stronger in areas where lending is recourse. Mian and Sufi (2010) have shown that the areas which experienced the greatest runups in household leverage are the same areas that saw the greatest fall in consumption and the greatest hike in unemployment rates during the financial crisis period. At the same time, Mian and Sufi (2009) and Pavlov and Wachter (2011) have shown that areas with more subprime lending also witnessed a greater build-up of house prices, while Goetzmann et al. (2012) have shown a positive impact of house price appreciation on approval rates. Our study suggests that areas that have many restrictions on land supply were more influenced by subprime lending and an adaptive expectation channel. Thus, supply restrictions are found to amplify the effects of price-to-price feedback loops. Combined with slow adjustments in states with non-recourse lending, these results contributes to explain why areas located in non-recourse states with many restrictions on land supply, such as California, witnessed the greatest volatility over the boom bust cycle, and also why the housing bust has been relatively long-lasting in these areas. There exists a voluminous time series literature on the determinants of national US house prices (see e.g. Meen (2002); Duca et al. (2011a,b); Anundsen (2013), as well as the references therein). These studies are important both in order to assess the vulnerability of the housing market to different types of national economic shocks, and to get an understanding of potential spill-over effects from the housing market to the real economy, see e.g. Aron et al. (2012). Aggregate models, however, remain limited to the extent that they do not shed light on the variations that exist at a disaggregate level. In addition, aggregate models make it difficult to distinguish between alternative mechanisms, because a number of different economic forces are at work at the same time in different regional markets. The results established in this paper are interesting in this respect, as they suggest that there exists large heterogeneities at the disaggregate level that may be relevant for the monitoring of local housing markets, and for both policy analysis and 3 forecasting purposes. The rest of the paper proceeds as follows. As a theoretical background, the life-cycle model of housing is discussed in the next section. In Section 3, we present the data and the three steps that constitute our modeling approach. In Section 4, we test the validity of the assumption of coefficient homogeneity, while the results from estimating the separate cointegrated VAR models are summarized in Section 5. The results from the individual models demonstrate very wide geographical variations in house price determination, and possible explanations of the observed regional heterogeneity are analyzed in Section 6. The final section concludes the paper. 2 Theoretical background Our theoretical starting point is the life-cycle model of housing, as described in e.g. Buckley and Ermisch (1983), Meen (2001) and Muellbauer and Murphy (1997). The theory is based on a utility maximizing framework, resulting in a long-run equilibrium relationship between real house prices, real income, the real user cost of housing and the housing stock. Extensions of the model include an explicit role for credit constraints, see e.g. Dougherty and Van Order (1982), Meen (1990) and Meen and Andrew (1998). If we consider a particular regional housing market j, the life-cycle model with credit constraints postulates the following equilibrium relationship: [ U H,j = P H j (1 τ y j U )(i j + τ p j ) π j + δ j ] P H j + λ j (1) C,j P H j where P H j measures real house prices in area j, τ y j is the tax rate at which interest expenses are deducted, while i j and τ p j are the nominal interest rate and the property tax rate, respectively. The term π j is the general CPI inflation rate, δ j is the depreciation rate on housing capital, and λ j is the shadow price of a mortgage credit constraint. The optimality condition given by (1) states that the representative consumer s marginal willingness to pay for housing goods in terms of other consumption goods should on the margin be equal to the cost of owning one more unit of the property (in terms of forgone consumption of other goods), where the user cost also takes into account credit constraints. Imposing a no-arbitrage condition between the rental market and the owner-occupied market, we further have: P H j Q j = U C,j 1 UC j + CC j (2) where Q j is the real imputed rent in housing market j, UC j = (1 τ y j )(i j + τ p j ) π j + P H j P H j δ j denotes the real user cost of housing, whereas CC j = λ j U C,j is a measure of credit constraints. The real imputed rent is unobservable, but two approximations are common in the literature: either to substitute Q j with an observed rent, or to assume that it is a function of income and the stock of dwellings. In this paper, we confine our analysis to the second approximation, which gives: P H j = f j (Y j, H j ) UC j + CC j (3) 4 A log approximation yields: ph j = β h,j h j + β y,j y j + β UC,j UC j + β CC,j CC j (4) where lower case letters indicate that the variables are measured on a log scale. In both Poterba (1984) and Meen (2002), (4) is interpreted as an inverted housing stock demand equation. In the empirical analysis, we shall make two assumptions: first, we shall assume that expected house price appreciation is captured by the short-run dynamics of the econometric models, i.e. modeled by the lagged house price appreciation terms. A similar assumption has been made in Abraham and Hendershott (1996), Gallin (2008), Anundsen and Jansen (2013) and Anundsen (2013). This assumption is also consistent with the view that lagged house price appreciation does not have permanent effects, but rather that it picks up a momentum, or a bubble builder effect, to use the terminology of Abraham and Hendershott (1996). The assumption that house price expectations are formed adaptively rather than rationally calls for some justification given the strong position that rational expectations have in modern macroeconomics. Perhaps surprisingly, there is strong evidence in the literature that house price expectations are formed in an adaptive manner, see e.g. Jurgilas and Lansing (2013) and the references therein. In particular, survey evidence from the US for the years 2006 and 2007 (Shiller (2008)) suggests that individuals in areas with increasing house prices expected further increases, while the opposite was the case in areas with recent declines in home prices. Conducting a similar survey in the midst of the national housing bust (in the year 2008), Case and Shiller (2012) find that individuals living in previously booming areas now expected a decline in house prices. The second assumption we shall make is that the real direct user cost ( UC j = (1 τ y j )(i j + τ p j ) + δ j π j ) is equal across regional markets, and that it can be approximated by the evolution of the real national interest rate, i.e. UC j = R j, where R denotes the real interest rate. 1 The credit constraint variable is unobservable, but Anundsen (2013) has shown that the expansion of subprime borrowing became an important driver of national US house prices in the previous decade. 2 Consistent with this, we assume that CC j = CC j, where CC is proxied by the share of new loan originations that are given to the subprime segment (CC = SP ). We acknowledge that there are differences in tax policies and credit constraints also at the regional level. Hence, another way to interpret these assumptions is that we analyze regional responses to the developments in national interest rates and credit conditions. 1 We have also experimented with an alternative approach, where we assume equal nominal interest rates, but where we allow for separate MSA inflation effects. The qualitative results are similar to those reported below, but we save valuable degrees of freedom by not pursuing that approach. In addition, we have data for the CPI at the MSA level only from 1980q1, meaning that we lose an additional 4 observations when constructing the annual MSA inflation rate. For that reason, we have decided to retain the assumption that the user cost may be approximated by the real national interest rate. 2 An alternative approach to modeling credit constraints has been advocated in a series of papers by John Muellbauer and co-authors who extract a latent credit conditions index (see e.g. Fernandez- Corugedo and Muellbauer (2006), Aron et al. (2012), and Muellbauer and Williams (2011)). In Duca et al. (2011a,b), a measure of the LTV ratio for first-time home buyers is used to measure credit constraints in the US. 5 Conditional on these assumptions, the inverted demand equation takes the following form: ph j = β h,j h j + β y,j y j + β R,j R + β SP,j SP (5) There is an important difference between the local economic variables and the national variables in that the latter are approximately exogenous with respect to developments in a given regional market especially when each market is small relative to the size of the national economy. From a theoretical point of view, one would expect for all j that β h,j 0, β y,j 0, β SP,j 0. The sign of β R,j is in principle expected to be negative though empirically, the sign has been found to be ambiguous. This may partly be explained by the fact that a large share of the interest rate effect is captured by changes in disposable income. A minimum requirement for the theory model to constitute a relevant representation of the data is that the following set of parameter restrictions is satisfied: β h,j 0, β y,j 0, β SP,j 0. Furthermore, since the theory describes a long-run equilibrium relationship, and since the above variables are usually found to be non-stationary and integrated of the first order, an additional requirement for the theory to be relevant is that there is evidence of cointegration, i.e. that ph j β h,j h j β y,j y j β R,j R β SP,j SP I(0). While it is obvious that the dynamic shocks hitting the regional markets differ across time and space, there might also be differences in the way in which these shocks are absorbed. Specifically, there might be spatial coefficient heterogeneity, where all the coefficients in (5) are regional-specific. 3 Data and econometric approach 3.1 Data Our data set includes the 100 largest Metropolitan Statistical Areas (MSAs) in the United States, covering about 60 percent of the entire US population and all but four of the 50 US states. 3 Following the Census Bureau, the US may be split into four distinct regions: West, South, Midwest and Northeast, confer Figure 1. With reference to those regions, our data set includes 25 areas in the West and the Midwest regions, while we have 20 MSAs situated in the Northeast and 30 in the South. I
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