Faculty of Economics and Business
MSc Business Economics: Real Estate Finance & Finance
The Relationship between the Homeownership
Rate and Volatility
July 2014
Master Thesis Pepijn Holst (10672753) Supervisor: Marc Francke Second Reader:
This paper explores the relationship between the homeownership rate and volatility by examining panel data on five OECD countries between 1970 and 2012. To determine the sign and causality of the relationship a VAR analysis is performed. Next, an explanation for this phenomenon is sought by exploring the influence of housing policy factors on volatility in an OLS regression. The VAR results uncover the presence of an inflexion point in the relationship, where the sign of the causal relationship changes from negative to positive, and the strength of the causality is minimised. This occurs at a homeownership rate of approximately 50%. Here, the housing market volatility is minimised. Furthermore, the OLS regression results demonstrate that the effect of housing policies is smallest at the inflexion point, and is an increasing function of the distance from the 50% rate.
Table of Contents
1. Introduction ... 4
1.1 Focus Area ... 4
1.2 First Hypothesis ... 6
1.3 Second Hypothesis ... 6
1.4 Validity of Research ... 7
1.5 Methodological Approach ... 8
1.6 Structure of Paper ... 8
2. Literature Discussion ... 9
2.1 Volatility Literature ... 9
2.2 Tenure Literature ... 12
2.3 Volatility and Tenure Literature ... 17
2.4 Key Articles ... 18
3. Methodology ... 19
3.1 ARMA and GARCH Model ... 19
3.2 VAR Model ... 20 3.3 OLS Model ... 21 4. Data ... 23 4.1 Data Collection ... 23 4.2 Data Transformation ... 24 4.3 Descriptive Statistics ... 25 5. Results ... 28 5.1 Volatility Creation ... 28 5.2 Causality Results ... 29
5.3 Housing Policy Results ... 32
5.4 Model Verification ... 34
5.4.1 VAR Verification ... 34
5.4.2 OLS Verification ... 36
6. Robustness Checks ... 37
6.1 Volatility Series Robustness ... 37
6.2 VAR and OLS Robustness ... 38
7. Conclusion ... 40
7.1 Hypotheses ... 40
7.2 Implications of Findings ... 40
7.3 Limitations and Further Research ... 41
8. List of References ... 43
9. Appendix ... 47
1. Introduction
The majority of developed nations promote homeownership. This is because it permits wealth accumulation, in addition to increasing community engagement and enabling children to perform better at school (Andrews & Sanchez, 2011). In the United States, the government has pushed lenders to extend mortgages to low-‐income households (Wallison, 2010). In the Netherlands, the extensive tax deductibility of mortgage payments has produced the highest wedge between the prevailing interest rate and the after-‐tax cost of financing of any OECD country (Andrews & Sanchez, 2011).
The promotion of homeownership does not come without costs. The prime example of this was the Financial Crisis, which resulted from the inability of American households to service their mortgages. An “unsophisticated population of new homebuyers” (Gelain, Lansing, & Mendicino, 2013) had been issued mortgages based only on the expected appreciation of the value of their house. When house prices stopped rising, the ensuing mortgage defaults sent shockwaves through the financial system. Subsequently, the Case-‐Shiller Home Price Index tumbled 30% between the fall of 2007 and early 2009. Switzerland on the other hand did not follow suit in promoting homeownership; it kept lending standards tight and continued providing substantial rent subsidies (Bourassa, Hoesli, & Scognamiglio, 2009). The crash of the Swiss housing market was inexistent. 1.1 Focus Area
The relationship between the promotion of homeownership and the risk present in the housing market forms the topic of this paper. By comparing the approach to housing adopted by the Swiss government to other OECD economies, the findings of this paper provide food for thought for macroeconomic planning.
The idea is that the relationship between homeownership rates (HOR) and volatility (VLTY) does not follow a linear pattern, but presents an inflexion point. When around 50% of households are homeowners, the causality between the homeownership rate and volatility switches from negative to positive, and the trade-‐off between the benefits of homeownership and volatility is optimised. This relationship is displayed in Graph I.
Graph I: the relationship between ownership rates and volatility
To the left of the inflexion point the benefits of increasing the homeownership rate outweigh the cost of volatility due to the strength of the ‘liquidity effect’. The latter occurs when an increase in the amount of people searching for a house dampens volatility. As more people trade in the housing market, so demand will be better satisfied. For a seller, the probability of finding a buyer has increased, which means the asking price is less likely to be altered. This effect is widely reported in stock markets.
To the right of the inflexion point the cost of volatility weighs more heavily than the benefits of homeownership. This is due to the ‘default effect’ increasing in strength. When the homeownership rate is high, the promotion of owning will start affecting risky buyers, those without the normal means to own a house but obtain the means through the lowering of borrowing requirements and favourable housing policies. As the concentration of risky buyers increases, so does the probability of defaults. This induces volatility, as the supply of houses will experience increased fluctuation.
Furthermore, as Belsky, Retsinas and Duda (2005) found, low-‐income households (risky buyers) often receive subprime loans, to compensate investors on the secondary mortgage market for their increased risk. This means the interest rate is higher, and the
30% 40% 50% 60% 70% 80%
Volatility
debt service a bigger burden, certainly when compared to the level of income. This in turn makes defaults even more likely than in the case of non-‐subprime loans.
In addition, the authors found housing expenditures to be positively related to income, meaning that low-‐income households spend less on maintenance. As a result, not only does the supply of housing fluctuate more, but it also becomes more heterogeneous. Together these effects will induce volatility in the housing market.
1.2 First Hypothesis
The first hypothesis of this paper states that countries with a low proportional amount of homeowners should exhibit negative time-‐causality between ownership rates and volatility. Those with a high rate should demonstrate positive time-‐causality. For simplicity’s sake, the inflexion point is hypothesised to lie at a rate of 50%.
!!: ↑ !"#!"#$% !"% → ↓ !"#$, ↑ !"#!"#$% !"% → ↑ !"#$
!!: ↑ !"#!"#$% !"% ↛ ↓ !"#$, ↑ !"#!"#$% !"% ↛ ↑ !"#$
The countries used in this paper were chosen because their homeownership rates differ widely. Switzerland and the Netherlands have experienced relatively low rates (below 50%) for the majority of the chosen time period, whereas the United States, Denmark, and the United Kingdom present higher rates. Due to limitations in the availability of data, the homeownership rate used for each country is the average homeownership rate over the chosen time period. This rate is used for comparative purposes only, as the analysis itself is based on a series of homeownership rates and volatility.
1.3 Second Hypothesis
The idea of an inflexion point can be further refined. Notably, within the OECD countries studied, demographic characteristics drive a ‘natural’ demand for homeownership, which is hypothesised to coincide with the inflexion point in each country. It is the influence of housing policies that shifts the rate, by either promoting or restricting access to funding or housing. The movement away from the inflexion point, through the creation of artificial demand, is what drives volatility.
The second hypothesis of this paper posits that the promotion or restriction of homeownership causes volatility in the housing market. In fact, the further away from the inflexion point the homeownership rate needs to be held, the more volatility is caused. In practical terms, this means that volatility caused by an increase in the debt-‐ to-‐income ratio, or the expenditure of the government, is larger when it drives the homeownership rate from 60 to 61% than when it drives the rate from 50 to 51%. Similarly, more volatility is caused when the rate is reduced from 40 to 39% than from 50 to 49%. The cost (in terms of volatility) of increasing the ownership rate increases with the distance from the inflexion point.
!!: !!"!"#$!%! !"# > !!"!"#$!%# !"# !!: !!"!"#$!%! !"# ≤ !!"!"#$!%# !"#
Here, !"# is the coefficient on the housing policy measure, where volatility is the dependent variable. The housing policy measure in question could be either the debt-‐to-‐ income ratio or government expenditure as a percentage of GDP. The sub-‐notation of ‘extreme’ or ‘average’ refers to the distance to the inflexion point of the average ownership rate, where extreme is distant and average is close to the hypothesised point. 1.4 Validity of Research
Studying the causal relationships between volatility, homeownership, and housing policies is important because housing forms the largest part of an individual’s wealth portfolio (Blanchflower & Oswald, 2013). Furthermore, in the aftermath of the Crisis governments have started rethinking their housing policies. As such, maximum loan-‐to-‐ value ratios have been lowered in most countries, and the tax deductibility of mortgage payments will slowly disappear in the Netherlands (ABN Amro, 2012). These are but a few of the developments currently taking place. This paper adds to the debate about housing policies by shining light on the cost of homeownership. By comparing different countries, it is able to demonstrate what rate minimises risk.
Furthermore, volatility in the housing market is also known to influence volatility in consumption (Gelain, Lansing, & Mendicino, 2013), which is itself a prime driver of economic success. Ultimately, aiding citizens in accumulating wealth is encouraging
them to consume. As such, a stable housing market prompts stable consumption, and is thus an important consideration for any modern government.
1.5 Methodological Approach
The methodological approach adopted in this paper is based on VAR and OLS regressions. The former is used to uncover the presence of causality between the homeownership rate and volatility, whereas the latter shows which determinants of homeownership are important in explaining volatility.
A contrast is made across five OECD economies, namely the Netherlands, the United States, Switzerland, Denmark, and the United Kingdom. These were chosen not only for their widely different ratios of homeownership to volatility, but also because the necessary data for each country is publicly available. The analysis is purposefully focused on developed economies, as there are a host of other factors influencing homeownership rates in developing economies, beyond demographic and housing policy factors. These make it hard to give a causal interpretation to variables.
The volatility that is analysed in this paper is based on the appreciation of average national house prices. It is constructed by inserting the residuals from an ARMA into a GARCH model. Clarifications are provided in the methodology section.
The time period analysed covers 1970-‐2012 in the VAR model, and 1990-‐2012 in the OLS model. This difference is due to the dearth of demographic variables.
1.6 Structure of Paper
This paper is divided into seven sections. First, the existing literature discussing volatility and tenure decisions is analysed, and the added value of this paper is clarified. The third section explains the methodological approach adopted in this paper. Next, the data used for the analysis is examined. This involves a discussion of sources and descriptive statistics. The fifth section is a discussion of the results, while the sixth section provides an attempt to limit the downfalls of the methodology by testing for the robustness of results. Finally, section seven contains the conclusion.
2. Literature Discussion
In light of the Financial Crisis of 2007-‐2009, the risk of promoting homeownership should be clear. However, though the determinants of volatility and homeownership have been studied in detail, there has never been an attempt to empirically uncover what the relationship between both variables is, and whether it differs across countries. As this paper attempts to link the development of homeownership rates to volatility levels, the relevant literature covers the determinants of volatility and tenure decisions. Until recently, these subjects were covered separately. However, there is a nascent focus on the direct link between volatility and tenure decisions, which constitutes the final section of this literature discussion.
2.1 Volatility Literature
There is an extensive literature on the determinants of volatility in the United States. Usually consisting of equating changes in macroeconomic variables to specific volatility events, current findings agree on the majority of relevant determinants. Nonetheless there remain fundamental questions regarding the volatility of house prices. Notably missing is an explanation for cross-‐sectional differences in long-‐term volatility levels, be it between regions or countries. The United States, for example, has a housing market that consistently displays a higher level of volatility than its European counterparts. Homeownership rates could go some way in explaining this phenomenon.
The literature on housing market volatility has uncovered several macroeconomic determinants that are relevant to isolate the relationship between aggregate homeownership rates and volatility levels. Dolde and Tirtiroglue (2002) find personal income growth to be the most significant determinant, in addition to inflation and interest rates. Furthermore, the literature finds the rate of house price appreciation (Hossain & Latif, 2009) (Miller & Peng, 2006), the population growth rate (Miller & Peng, 2006), and the change in the prevailing mortgage rate (Hossain & Latif, 2009) to explain variations in housing market volatility.
Dolde and Tirtiroglue (2002) use repeat transaction data between 1975 and 1993 for four regions in the United States. They identify 36 volatility events, defined as a squared
deviation significantly different from the sample mean. The average level of volatility observed understates the one used in this paper by 1%, which is consistent with the upward trend of both volatility and homeownership in the United States.
Focusing on the United States again, Miller and Peng (2006) use median sales price data from 1978 to 2002 for 316 metropolises. They control for both metropolitan-‐specific and time-‐varying factors in uncovering volatility determinants. The former is done by creating subsamples by metropolitan size and estimating a new VAR system using only the most and least populated metropolises. The latter is achieved by diving the sample period in two. Though the dynamic interrelations between variables are present in both small and large metropolises, their effects vary. Volatility reduces population growth in small metropolitan areas, but not large ones. Furthermore, volatility has a smaller effect on the variables in less populated areas. In terms of time-‐varying factors, the dynamic interrelations between variables are similar in both period subsamples, meaning there are no regime shifts between 1978 and 2002. As a result, no attempt is made to control for time-‐varying factors in this paper.
Others authors have looked beyond macroeconomic factors for determinants of volatility. Their results are not relevant to isolate the effect of homeownership on volatility, but hint at the relevance of this relationship.
Stein (1995) and Gelain, Lansing and Mendicino (2013) have looked at the link between financing policies and the volatility of house prices. Stein analyses a theoretical price-‐ demand equilibrium model, and finds there are multiple equilibriums present when down payment constraints are introduced. This is due to the fact that when prices rise beyond a certain point they relax liquidity constraints for homeowners saddled with a mortgage, while still having the ‘normal’ effect of decreasing demand on prospective buyers. A situation of multiple equilibriums causes prices to react more violently to changes in macroeconomic determinants. The violence of this movement depends on the amount of active constrained movers relative to active unconstrained ones, which increases as prices rise. His finding suggests that countries with an active role for the government in promoting or restricting housing, experience more volatility. He hereby provides ammunition for a comparison of policies and volatility levels across countries.
Gelain, Lansing and Mendicino (2013) analyse the policy actions that are most effective in diminishing excess house price volatility, which is defined as “volatility that cannot be explained by a rational response to fundamentals.” They find that a debt-‐to-‐income constraint is most effective in this regard, as it does not increase the volatility of other macroeconomic series. Next, a lower loan-‐to-‐value ratio is also effective in dampening house price volatility, but at the cost of a small increase in inflation volatility. Furthermore, the authors find that a debt-‐to-‐income ratio is subject to less speculative distortions than a loan-‐to-‐value ratio, because the latter enables the issuance of debt to follow movements in house prices. As a result, this paper makes use of the debt-‐to-‐ income ratio as a proxy for housing policies, as it gives the best approximation of the effect of policies on the mean household.
Reichart (1990), in his study of the US housing market, finds that similar factors affect volatility differently in different regions; mortgage rates are most important in New England, whereas permanent income has the largest effect in the western regions of the United States. This means that homeownership rates could also affect volatility differently depending on the region being studied, not to mention the country. The author thus clears the way for a comparison of the effect of changes in the homeownership rate on volatility in different countries.
The relevance of the articles by Hossain and Latif (2009) and Miller and Peng (2006) also lies in their use of rational expectations models for analysing the appreciation of home values. The residuals from such a model constitute the unpredictable component that is used to model volatility. In addition, because the volatility series created with this model is used for comparative purposes, the potential underestimation of real volatility is not problematic (Gelain, Lansing, & Mendicino, 2013).
In Hossain and Latif (2009), the rational expectations model is constructed using an ARMA and GARCH technique. Recreating this series for the relevant countries enables the development of volatility to be analysed alongside the homeownership rate and other macroeconomic variables in a VAR model. Hereby the authors provide a base from which to commence the methodological study of this paper.
Flood and Hodrick (1986) look at the ability of variance bound tests to model volatility during rational speculative bubbles. They argue against the common view that these rational models are unable to process a bubble-‐like movement in a time series, due to the latter appearing as irrational. The authors find that the design of a rational model, like the one used in this paper, “precludes bubbles as a reason for failure.” In other words, a rational model can handle the presence of a bubble movement in a time series of house prices, which is what this paper attempts to do. However, they caution that a variance bound model cannot be used to identify the presence of a bubble, as the expectations of agents would require remodelling (rationality evaporates during a speculative bubble).
Furthermore, Brailsford and Faff (1996) analyse the applicability of ARCH models to make volatility forecasts. By employing forecasting techniques ranging from simple (random walk model) to complex (ARCH family models) on daily Australian stock market data, they are able to rank their accuracy. Their findings suggest that the GARCH (1;1) model ranks second to the Glosten, Jagannathan, and Runkle modified GARCH in terms of forecasting performance, which is what this paper attempts to use the GARCH model for. Both models predict around 60% of the actual observed volatility (all models under-‐predict observed volatility).
Flood and Hodrick (1986) and Brailsford and Faff (1996) thus confirm the use of an ARMA and GARCH combination to process the bubble in house prices that was present in this paper’s chosen time period, and subsequently forecast volatility series.
2.2 Tenure Literature
The literature on tenure decisions also has its roots in the United States. However, the range of countries studied in these articles is far wider than is the case with the determinants of volatility. Furthermore, the determinants of homeownership have been studied for different demographic tranches.
The problem with the existing literature is that is uses almost solely cross-‐sectional data sets, based on survey results. As such, even though mortgage policies have been studied extensively, there is no coverage of the effect of gradual loosening of financing standards, for example, in the run-‐up to the Crisis on tenure decisions. In addition, there is no possibility to test for non-‐linear relationships, as the use of two surveys forms the
maximum number of time snapshots (see (Andrews & Sanchez, 2011) (Chambers, Garriga, & Schlagenhauf, 2009) (Linneman & Wachter, 1989) (Gabriel & Rosenthal, 2005)).
Starting off at the cross-‐country level, Fisher and Jaffe (2003) attempt to explain what factors determine the homeownership rate across a sample of 106 countries. They find that the rate of urbanisation and government consumption have significant negative effects on the homeownership rate, while the proportion of people between the ages of 15 and 64 and the presence of a mandatory financing system have a significant positive impact. The problem with the cross-‐panel dataset that the authors use is that it cannot explain how the impact of their determinants varies across countries, only what the average effect is. In particular it cannot explain differences in the effect of varying mandatory finance schemes.
Next, Andrews and Sanchez (2011) focus on a range of OECD countries, excluding ‘transitory’ economies that might induce bias in the significance of variables. They posit that the evolution of homeownership rates is due to a mix of demographic and public policy influences. The former contains factors such as age of household head, household size, and real disposable income, amongst others. In terms of public policy influences, they analyse the relaxation of down-‐payment constraints, mortgage interest deductibility, and rent regulations. They find that changes in household characteristic account for 75% of the increase of the homeownership rate in the UK, but only 33% in Switzerland and the US. This result agrees with the second hypothesis of this paper, as Switzerland and the US are both expected to depend more on housing policies than countries closer to the inflexion point. Furthermore, population ageing has had a large effect in both Switzerland and Denmark. In the latter, changes in income are also found to be significant, unlike other European countries. In addition, demographic changes cannot explain changes in their entirety, leaving a substantial role for public policy measures in numerous OECD economies. However, the authors are unable to demonstrate where the impact of housing policies has had the biggest impact on the homeownership rate.
At the single country level, Chambers, Garriga and Schlagenhauf (2009) employ a similar hypothesis. They relate the boom in the US homeownership rate between 1994 and
2005 to development in demographics and mortgage innovations. They do this by estimating the contribution of each factor in 1994, and projecting this contribution forward to 2005 while holding other factors constant. This enables them to calculate a hypothetical homeownership rate, and subsequently compare this to the actual rate to determine the influence of each variable. They find that the change in demographics is responsible for 16 to 31% of the increase in the aggregate homeownership rate, while mortgage market innovations account for between 56 and 70%, depending on the factors held constant. The former is especially important in explaining the development of the homeownership rate for older cohorts, whereas new mortgage products mainly help younger households acquire a home. Thus it would seem that the United States has relied largely on financing innovations to drive up its ownership rate; a result agrees with Andrews and Sanchez (2011) and again confirms this paper’s second hypothesis.
Bourassa and Hoesli (2006) attempt to explain the low ownership rate in Switzerland. They analyse 3588 households in 1998, and model the tenure decision as a function of the cost of owning and renting, the borrowing constraint gap, household after-‐tax income, and a host of demographic characteristics. The first variable takes into account the extensive rent subsidies provided by the government, the high level of rent security, the taxation of imputed rent, high house prices, and the stringent underwriting criteria. The outcome points to the importance of high house prices relative to incomes, which is only indirectly a result of national mortgage policies. The most important explanatory variable however is the set of demographic variables, such as the age of the household head, his marital status, and the presence of children. As such, their study disagrees with later findings (Andrews & Sanchez, 2011) about the importance of non-‐demographic factors in Switzerland. It is important however to consider the different timeframes used by both studies. Whereas Bourassa and Hoesli (2006) look at households in 1998, Andrews and Sanchez (2011) analyse a development between 1994 and 2004. It thus appears the importance of mortgage market innovations has increased over the years in Switzerland; an observation going against the second hypothesis posited in this paper.
In terms of regional determinants, Eilbott and Binkowski (1985) analyse the tenure decision using data on a large number of metropolitan areas covered by the 1970 US Census. Though testing for both supply-‐ and demand-‐side variables, the former are
found irrelevant in explaining differences in homeownership rates, and are thus dropped from the model. The authors hereby provide ammunition for the sole focus on demand-‐side variables in this paper.
House values are found to be most significant, decreasing the ownership rate as they rise. In addition, income and household size are found to have a positive relationship, whereas population growth and the percentage of people under 35 years of age are found to bear a negative relationship. On the other hand, the level of rent is consistently found to be insignificant in explaining high homeownership rates in the US. This finding agrees with the results of this paper about the decreasing importance of government expenditure (proxy for sponsoring of the rental market) when the ownership rate rises.
Though touched on previously, there are also a host of articles that specifically study the influence of public policy measures on tenancy choices. Malpezzi (1996) looks at the effect of housing regulation on house prices and homeownership rates. He constructs a variable measuring the amount of regulation in 56 US cities by adding together seven measures reported by the Wharton regulatory practices data. These contain measures for zoning practices, approval times and the quality of infrastructure. Though the coefficient on the regulation variable is not statistically significant, it raises house values and rents, but the former by more than the latter. Combined these effects will thus have a negative impact on the homeownership rate, namely a reduction of 10 percentage points when switching from a lightly regulated environment to a heavily regulated one. This result helps explain the low homeownership rate in Switzerland.
Next, Linneman and Wachter (1989) study the effect of mortgage underwriting criteria on homeownership rates. Using income, the relative cost of ownership versus renting, and borrowing constraints on household data covering 1975-‐77 and 1981-‐83, the authors test whether income and wealth constraints reduce the probability of homeownership. In the first period, income-‐constrained families were 32% less likely to be homeowners, whereas for wealth-‐constrained families this was 61%.
These figures are smaller for the second period, due in part to lower interest rates. Thus, income-‐constrained and wealth-‐constrained families were 19 and 21% less likely to be homeowners, respectively. The reduced importance of the income constraint in the
second period is likely to be a result of the widespread use of adjustable-‐rate mortgages, which had a lower rate compared to fixed-‐rate instruments.
Their results, namely a decrease in the probability for risky buyers to be less likely to be homeownership, points not only to a slump in interest rates, but also the relaxation of borrowing constraints in the United States.
There is also a range of articles that studies the determinants of homeownership for specific demographics. Chiuri and Jappelli (2003) look at the distribution of homeownership rates across age groups within 14 OECD countries. They hypothesise that countries with tight lending standards have lower occupancy rates amongst young individuals, because they lack collateral. The authors use the down payment ratio as a measure of finance standards. They find that an increase in the down payment ratio by 20% lowers the owner-‐occupancy rate by the same amount for people aged 26-‐35, while it lowers it by 15% for those aged 36-‐45. This result is maintained even when controlling for income. Though they confirm their hypothesis, their results are based on a pair of surveys from different time periods for each country. Furthermore they do not control for other factors that affect the homeownership decision, such as tax incentives, that might change over time.
Gabriel and Rosenthal (2005) analyse whether the Clinton and Bush administrations have been able to narrow the racial gap in owner-‐occupancy rates. Drawing on data from the Consumer Finance Survey between 1983 and 2001, the authors decompose racial homeownership rate gaps into a portion that can be explained by household demographics (other than race) and one capturing the impact of credit barriers. They find that the increase in homeownership is primarily a result of changing household demographics, which was responsible for 14 out of the 26-‐percentage point white-‐black gap and 20 out of the 30-‐percentage point white-‐Hispanic gap. Furthermore credit barriers consistently account for 5 percentage points of the gap for all years, meaning mortgage market policies designed to enhance homeownership amongst minorities have had limited success.
2.3 Volatility and Tenure Literature
The focus on homeownership decisions and volatility is interesting because there are a host of similar factors that influence both variables, as the previous two sub-‐sections have demonstrated. Most notably, both are the result of a mix of demographic and housing policy factors. This would suggest that movements in homeownership rates and volatility levels are not independent. As a result, recent literature has focused on uncovering whether a relationship exists, and whether it is causal.
First, Ortalo-‐Magné and Rady (2002) analyse the relationship between homeownership and housing market volatility, and find evidence of a positive relationship. Enabling homeownership in a first period increases the variance of house prices in the second period, due to the decrease in household mobility. However their analysis is constrained to two periods within the same city. As such they ignore cross-‐country differences and factors that influence volatility in the long run. Furthermore their analysis holds only theoretical value as it fails to account for absolute changes in the ownership rate and the subsequent impact on mobility and volatility. Nonetheless they uncover causality between both variables, flowing from homeownership to volatility, which supports the first hypothesis made in this paper.
On the other hand, Banks et al. (2004) attempt to make a comparison across the United States and the United Kingdom. They discuss the role volatility in the housing market has on the decision to own. They find that the higher the level of housing uncertainty, the higher the demand for housing, as risk-‐averse individuals seek to insure themselves from the risk of house price rises. However, volatility is analysed as a given, and they make no attempt to model the reversed causal relationship.
As a result, the literature confirms the existence of a relationship between tenure decisions and volatility. The causality is predicted to flow in both directions, but only the effect of changes in the homeownership rate on volatility will be analysed in this paper, leaving the reverse causality to be developed in future research.
2.4 Key Articles
The three key papers discussed in this literature review are Hossain and Latif (2009), Andrews and Sanchez (2011), and Ortalo-‐Magné and Rady (2002). The former provides the control variables and models that are used to analyse the causal relationship between homeownership rates and volatility, and judge the first hypothesis. The second OECD article introduces the idea of equating homeownership rates to demographic and policy factors, and hereby provides a base from which to test the second hypothesis. Finally, the third article’s relevance lies in testing precisely the relationship between ownership rates and volatility, and hereby providing a source of comparison for the findings of this paper.
3. Methodology
The methodological approach of this paper employs four different models in three separate processes. The first of these creates a volatility series for each country based on the appreciation of house prices between 1970 and 2012. The second uncovers whether there is a positive causal relationship between homeownership rates and the level of volatility. Finally, the third process uses a set of determinants from both the literature and the hypotheses presented in this paper to analyse the significance of policy measures in explaining homeownership rates and volatility levels.
3.1 ARMA and GARCH Model
To construct a volatility series, use is made of an autoregressive moving average (ARMA) and generalised autoregressive conditional heteroskedasticity (GARCH) model. The data necessary for this operation is quarterly house prices between 1970 and 2012, from which appreciation rates are constructed. As the variable of interest is an appreciation series of house prices, it is stationary. This means the ARMA model is appropriate, as opposed to an autoregressive integrated moving average (ARIMA) model, which models a nonstationary series.
The ARMA model assumes the development of house price appreciation rates (HPA) is due to a series of unobserved shocks as well as its own past values. This means it is based on a rational development of rates, based on the information available. This is made clear in the equation below. The irrational component is the residual from the model, and simultaneously the variable of interest in constructing a volatility series.
!"#!= ! !"#! !"!#$!%$& !"#$%&'(!$"!!! + !!
The Bayesian information criterion (BIC) was used to determine the number of lags to be inserted in each ARMA model.
To create a variance series from house price appreciation rates, the residuals from the ARMA model were inserted into a GARCH (1;1) model. The latter is applicable when modelling series containing non-‐uniform volatility clustering (Stock & Watson, 2011).
3.2 VAR Model
The VAR model is used to uncover whether a causal relation exists between homeownership rates and volatility. It models every variable as being dependent on its own lags in addition to those of the other variables. As such, it permits a dynamic structure that is stipulated by the data itself. Furthermore it requires specification of the common lag of variables. These should affect each other inter-‐temporally.
The model employs the determinants of volatility as put forward by the literature, in addition to the homeownership rate. The seven variables inserted into the model are volatility (VLTY), GDP growth (GDPG), inflation growth (CPIG), population growth (POG), mortgage rate change (MRTC), house price appreciation (HPA), and the homeownership rate (HOR). All variables have been collected over the longest time period available to increase the robustness of the results, meaning 1970 until 2012 for the majority of variables. Only one lag of variables is inserted at a time, to avoid multicollinearity problems. Furthermore, the variables all need to be of the same order of integration, meaning either all stationary, or non-‐stationary but cointegrated. The first option is applied in this model, as some of the variables for each country are differenced to achieve stationarity. In most cases, this means the change in homeownership rate (HORC) is inserted into the model instead of the homeownership rate itself. The resulting estimation of the VAR model is the following:
!!" = !!" × !!"!!+ !!"
Here Yit is a vector of HORC, GDPG, CPIG, POG, MRTC, HPA and VLTY for each country. Ait
is a vector of coefficients, and !!" is a vector of the error term for each country. This model is performed on individual lags, up to a maximum of six.
The two variables of interest are the homeownership rate and volatility. The remainder serve as control variables. Hossain and Latif (2009) have employed a similar model. Based on their findings, GDP growth is expected to have a negative effect on volatility, similarly to the growth in inflation, population, and the appreciation of house prices. These variables all dampen the level of volatility. On the contrary, the changes in mortgage rate and volatility itself both show a positive correlation with volatility.
The causality of the relationship between homeownership rates and volatility will be analysed with a Granger causality test. It poses a statistical hypothesis concerning the causal power of lagged values of homeownership rates on volatility. The null hypothesis can be rejected only when each lagged value is significant according to a t-‐test, and the lagged variables together add explanatory power according to a F-‐test. When this happens, the homeownership rate is said to Granger-‐cause volatility. The first hypothesis predicts this to be the case between homeownership rates and volatility. 3.3 OLS Model
The ordinary least squares (OLS) model is used to determine the effect of housing policies on volatility. It is a linear regression model where the minimisation of the sum of squared errors between observations and predictions will determine the coefficients.
The two variables of interest are the amount of government expenditure as a percentage of GDP (GOVEXP) and the debt-‐to-‐income ratio (D2INC). To analyse their unbiased effect, they are regressed together with demographic variables and control variables in the volatility equation displayed below:
!"#$! = !!+ !!"!"#$%& + !!"!2!"# + !!" !"#$%&!"ℎ!"# & !"#$%"&' !
!!! + !!
According to the second hypothesis, it is expected that the absolute size of the coefficients increase as the homeownership rate distances itself from the inflexion point. This means that the five values for !! will be compared at first, followed by the five values for !!. Thus the hypothesis will be tested for the effect of both rental policies and borrowing constraints.
In the relevant literature the GOVEXP variable has a negative correlation with homeownership, and should thus also affect volatility in the housing market (see (Fisher & Jaffe, 2003) (Matznetter, 1994)). As it promotes renting, the decrease in the homeownership rate should have a positive effect on volatility to the left of the inflexion point, whereas this effect will be negative to the right.
The opposite is expected of the D2INC variable, as a higher value should prompt more homeownership, as more mortgage debt is present in the economy. Consequently, an
increase it is expected to increase volatility on the right side of the inflexion point, but decrease it on the left. This is partly confirmed in the literature, where an increase in the down-‐payment constraint drives US volatility (Stein, 1995).
The demographic variables that are used in the model are a combination of the number of households, the proportion of one-‐person households, the average household size, the rate of employment, of education, and of migration. In terms of control variables, the wealth of the population is measured through either GDP per capita or income. Finally, the rate of inflation and the rate of house price appreciation complete the set.
In the relevant literature, income is negatively correlated with volatility, and inflation tends to be high and increasing when volatility increases (Dolde & Tirtiroglue, 2002). Furthermore, both increases in population and employment are found to positively affect volatility in the US (Reichert, 1990). The appreciation of house prices is positively correlated with volatility (Miller & Peng, 2006), certainly considering volatility that is constructed using past rates of appreciation. The remainder of the demographic variables that are not covered in the literature shall add another novel dimension to the findings reported in section 5.