Risk and returns to residential real estate: Evidence from 28 EU countries

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Risk and returns to residential real estate: Evidence from 28

EU countries

Sahir Rana 11299207

June 2020

Bachelor of Science Thesis

Thesis coordinator: Dr. P.J.P.M. Versijp

Thesis supervisor: Dr. M.I. Dröes

University of Amsterdam Faculty of Economics and Business

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2 Abstract

In current times, the consensus that ‘buying a house, is a good investment’ seems to be dominantly present. Various media report house prices rising and breaking records every month. Low mortgage interest rates, scarcity on housing supply and growing population seem to be the cause. What other variables explain house price risk and it return? Is now a good time to buy a house? In this thesis, the determinants of housing returns in the EU were examined. More specifically, several multi-risk-factor models were used, to explain the housing returns observed from 2009-2018, in 28 European countries. This was done by performing a pooled-OLS, fixed effects, and first differences regression. Also, a Fama Macbeth two-step regression was conducted to see if any idiosyncratic risk was priced into the observed housing returns. Concluding, it can be stated that multi-factor models can be used to explain housing returns in Europe. Especially income, unemployment rate and population showed strong statistical evidence to influence housing return. Idiosyncratic risk premia did not seem to have any explanatory power, at least not when looking at country-wide housing returns. However, current research using lower-level housing data, such as ZIP codes, does seem to verify that idiosyncratic risk is priced in residential real estate. Results from the Fama Macbeth two-step regressions suggest that differences in observed housing returns between Germany, France and the Netherlands, can partially be explained by housing risk-factor models.

Statement of originality

This document is written by, S. Rana, who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business of the University of Amsterdam is responsible solely for the supervision of completion of the work, not for the contents.

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1. Introduction

Institutional investors, such as pension funds, insurance companies, mutual and hedge funds might consider buying residential real estate as an investment. This could be to generate long-term revenue stream through rental income or short-long-term gains by selling the property for a higher price. Individuals and households are also participants in buying and selling residential real estate, though this is typically seen as consumption, rather than an investment (Piazzesi, Schneider & Tuzel, 2007, p. 532). Regardless of the underlying goals, both institutional investors and households are interested in the price they must pay or receive for acquiring or selling residential real estate. For both parties, having a model that explains movements in returns to residential real estate, would be beneficial as a guidance whether now is a good time to invest in the housing market or not. Mortgage lenders, such as commercial banks, are also interested in the price development, as this value often serves as collateral for a mortgage loan. Figure A in the appendix shows the house price development in 28 European countries. A great variation in housing returns can be observed here, and there are also considerable differences in volatility (risk). This raises the question why housing returns in some countries are higher than others. What factors could be underlying these differences? Therefore, the main research question of this thesis is as following:

‘What are the determinants of residential real estate price risk and returns in Europe?’

In the stock market, the capital asset pricing model (CAPM) was developed to explain stock returns, based on a single market risk-factor. Fama and French (1996, p. 56) gradually extended this model to include multiple risk-factors to predict stock price changes. Beracha and Skiba (2013, p. 289) applied this multi-factor model to predict returns to residential real estate. Their model tries to explain quarterly observed housing returns in 380 Metropolitan Statistical Areas in the United States from 1983 to 2009. For this they used four systematic risk factors, namely market risk, income growth, land supply elasticity and momentum. Of course, other factors could also be considered. Research by Cannon, Miller and Pandher, (2006, p. 522) showed that population and unemployment have a direct effect on residential real estate prices. Mortgage market factors as the mortgage interest rate and loan-to-income ratio also seem to matter (van Gool, Jager, Theebe and Weisz, 2013, p. 263). Lastly, inflation rate can be added to estimate the model in real terms. However, these models only capture systematic risk. Dröes and Hassink (2013, p. 92) argue that typical homeowners cannot perfectly diversify their housing investments across locations. As such, idiosyncratic housing risk should be accounted for. According to Eiling, Giambona, Aliouchkin and Tuijp (2019, p. 19), this idiosyncratic housing risk can be accounted for, with use of the Fama Macbeth two-step regression model.

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5 To conduct this research, data is extracting from several databases. The dependent variable is the house price index (HPI), which resembles the development of residential real estate prices in each of the 28 European countries. This data is obtained from Eurostat and it contains yearly data from 2009 up to and including 2018. Therefore, the sample consists of panel data. The base year of this index is set on 2007. From this, the return on residential real estate can be calculated. Furthermore, there are six independent variables, that are commonly used in the literature. These are the mortgage interest rate, disposable income of households, mortgage loan-to-income ratio (LTI), unemployment rate, inflation rate and population. Data on these six variables are also yearly from 2009 to 2018, for all 28 European countries. The data for these independent variables is retrieved from databases of the European Mortgage Federation, Eurostat, the European Central Bank and the World Bank. Except for income and population, all data is already expressed in percentages.

The research question will be answered by an empirical analysis, using four different multiple linear regression models. The first is the pooled-OLS regression. The second regression model adds country and time fixed effects to find out if country characteristics and time periods have an effect on the estimators. The third regression model takes the first differences of the variables, to see if lags in variables add to explaining housing returns. This also more closely resembles the arbitrage pricing theory (APT) type of modelling. Finally, the fourth regression model follows the method set forth by Fama and Macbeth (1973, p. 616). In this method, which is called Fama Macbeth two-step regression, idiosyncratic risk premium is added as an independent variable to explain housing returns. The endogenous variable in all four regressions is the return to residential real estate, whereas the earlier mentioned six independent variables are assumed to be exogenous.

The results show that all four regression model specifications can to some extent explain the return to residential real estate observed in 28 European countries, from a period of 2009-2018. The risk factors disposable income growth of households, unemployment rate and population growth are significant at a 5% level. Therefore, these three risk factors seem to affect housing returns in EU countries. If disposable income of households grows by 1%, this increases housing returns in EU countries, on average, by 0.288%. If unemployment increases by 1%, this affects house prices by -0.031%. A 1% population growth leads to an average increase in housing returns of 0.601%. These numbers represent the predicted effect that each risk factor has on housing returns, across all EU 28 countries. However, these effects will have different values for each individual country. For example, a 1% increase in disposable income, is predicted to increase housing returns in Germany by 0.30%, in France by 0.16% and in the Netherlands by 0.28%. For unemployment rate, the values are respectively -0.16%, -0.29% and -0.16%. Finally, for population growth, the predicted values are resp. 0.04%, 0.13%

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6 and 0.18 for the Netherlands. The difference in magnitude that each risk factor has on housing return, is due to differences in individual country characteristics.

For this reason, it is useful to include idiosyncratic housing risk premia to the model. However, idiosyncratic risk premia do not seem to be priced in housing returns, when the data is taken at a country-wide level within the EU. The results show that the idiosyncratic housing risk is 0.04%, but it is statistically insignificant. The remaining systematic risk is on average 0.37%. This would suggest that European countries have an already diversified housing portfolio, where housing returns are mostly explained through systematic risk factors. More specifically, the Fama Macbeth two-step regression shows that disposable income and unemployment are still significant at resp. 1% and 5% level. In this regression, a 1% growth in income or unemployment, leads to a change in housing returns by resp. 0.39% and -0.02%. Looking at Germany, this would imply that a 1% increase in income or unemployment, leads to a change in housing return by resp. 0.40% and -0.10% For France, these numbers are 0.22% and -0.19%. For the Netherlands, this implies 0.38% and -0.10%. Research by Eiling et al (2019, p. 2) suggest that idiosyncratic housing risk is priced in, when low-level housing data, such as ZIP codes, are used. The average systematic risk premia are 0.77% (2019, p. 16) and the idiosyncratic housing risk accounts for 0.12% on housing returns.

Previous research primarily investigated either major European cities or metropolitan statistical areas (MSAs) in the United States. This research adds value by investigating returns to residential real estate across the whole European Union. In doing so, individual country characteristics can help explain the differences found in housing returns across the 28 EU countries. Furthermore, in this research the methods performed by Eiling et al (2019, p.35) in the United States on residential real estate, are tested to see if these could be applied to the European continent.

The rest of the thesis is organized in the following way. Section 2 is a literature review which explains how earlier research was conducted and what risk factors where used. This leads to the formal research hypothesis that ‘the risk and return on housing in European countries can be explained by market risk factors’. Section 3 explains why certain variables are chosen and where these were retrieved. Next, in section 4, the regression model specifications will be explained extensively, and the null hypothesis will be tested. Thereafter, the outcome of these models is discussed in section 5. Lastly, in section 6, the research question will be answered, together with the implications of this research and its limitation. This is concluded with a proposal for further research.

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2. Literature review

In this section, the characteristics of residential real estate are first put forth. Secondly, the development of the multi-factor model from asset pricing theory is explained. The third part elaborates on the risk-factors chosen by earlier literature for determining returns to residential real estate. Finally, the hypotheses for this research are stated in the fourth part.

2.1 Characteristics of residential real estate

Real estate can have both the properties of consumption good (Piazzesi, Schneider & Tuzel, 2007, p. 532) and investment good (Han, 2013, p. 883). According to Eiling, Giambona, Aliouchkin and Tuijp (2019, p. 2) households typically buy real estate, such as residential real estate, for own consumption. Financial institutions, pension funds and investors typically buy real estate as an investment (Piazzesi & Tuzel, 2007, p. 536). Construction, development and exploitation is a costly investment both in time and cost. Contrary to stock investments, real estate investments are less liquid and tie investors’ money for time period longer than equity investment usually do (Berk & DeMarzo, 2017, p. 521).

According to van Gool, Jager, Theebe and Weisz (2013, p. 49), price effects on the value of residential real estate are delayed, due to long time periods associated with development of land and construction of buildings. This implies that real estate would not instantly price in external market shocks, as is the case with stocks, but would lag 3 quarters to a year. Also, house returns usually follow underlying fundamentals as income growth, loan-to-income ratio, construction costs, mortgage rates and supply and demand on housing (van Gool et al, 2013, p.115).

However, Beracha and Skiba (2013, p. 290) claim that other systematic market factors could affect the return on housing, and this should be accounted for. For example, the amount of land available for development, expressed as land supply elasticity (Glaeser, Gyourko & Saiz (2008, p.201). The findings of Case and Shiller (1989, p. 128) and Beracha and Skiba (2011, p. 302) suggest momentum factor plays a crucial role in housing returns. Jegadeesh and Titman (1993, p. 68) found that the momentum factor also holds in stock returns. In the first three to twelve months, returns on stock that were rising, continued to do so, and vice versa for returns on stock that were falling. These abnormal returns dissipated in the following two years. Intuitively, pricing of stocks could be translated to prices in the residential real estate market.

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8 2.2 Asset pricing models

Historically, over long time periods, investments in stocks have had higher returns than investments in bonds (Berk & DeMarzo, 2017, p. 352). However, returns in stock investment also showed a higher volatility than bonds. For a risk-neutral investor, this implies that stock investments are riskier (Fama & Macbeth, 1973, p. 614). This typical investor would prefer stocks with lower volatility. Rather than picking a single stock, a portfolio of stocks could achieve this goal. Markowitz (1952, p. 78) explains this as the diversification benefits that are achieved through mean-variance portfolio optimization.

However, stock investments consist of both volatility and returns. A rational risk-neutral investor would therefore prefer the highest expected portfolio return, for the lowest possible volatility. Sharpe (1964, p. 436) built upon the Markowitz portfolio theory by considering both the expected excess return and the volatility of a given portfolio. This risk-reward relationship is called the Sharpe ratio and rational risk-neutral investors would prefer choosing a portfolio that maximizes this ratio, over a minimum-variance portfolio. The outcome is called the efficient or market portfolio (Berk & DeMarzo, 2017, p. 419) and is often approximated by a broad stock market index. According to Lintner (1965, p.16), any given stock return is considered to co-move with its market index, with a sensitivity ‘beta’. These insights to risk-return relationship led to the derivation of the Capital Asset Pricing Model (CAPM) and is frequently used in the finance literature to price securities. Cannon, Miller and Pandher (2006, p. 532) found the same risk-return relationship in a cross-section study of real estate. However, the traditional CAPM contains a single systematic risk factor, which critics (Roll, 1977, p. 132) found too simplistic. Fama and French (1996, p. 56) extended the simple CAPM to include additional risk factors, into a multi-factor model.

Using the multi-factor model to price securities, has also shown its application to real estate. According to Case, Cotter and Gabriel (2011, p.90), the multi-factor CAPM could be used to explain returns in the residential real estate market. It is important to emphasis that the single-factor (CAPM) and multi-factor models explained just earlier, try to capture the systematic risk alone. According to modern portfolio theory (Sharpe, 1964, p. 439), investors do not expect any compensation for idiosyncratic risk, as this could be diversified away. However, completely diversifying away idiosyncratic risk in the housing market, could prove hard to achieve, as every housing market segment has its unique characteristics (Eiling et al, 2019, p. 27). As such, great caution is required when adopting these models, which only capture systematic risk, in residential real estate.

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9 2.3 Risk factors in housing returns

Beracha and Skiba (2013, p. 289) opt using a multi-factor asset pricing model to help explain systematic risk in cross-sectional housing returns in the United States. More concretely, their multi-factor model tries to explain the quarterly observed housing returns in 380 Metropolitan Statistical Areas (MSAs) from 1983 to 2009. Their research makes use of four systematic risk factors, which are roughly categorized into respectively a market, an economical, a geographical and a psychological risk-factor. How much each individual factor explains this four-factor model, is tested by running regressions, using times series of each of the MSAs in their sample. This results in a coefficient for each risk factor, for every time period. By dividing this over the number of time periods, the average value of each risk factor coefficient is retrieved. However, these coefficients are only meaningful if the intercept term of the model is not significantly different from zero (Keller, 2012, p. 634). Otherwise, the model would have misspecifications and not meet its purpose to capture all systematic risk of residential real estate returns (Stock & Watson, 2015, p.524). Therefore, the average coefficient values of the intercepts (Jensen’s alphas) have been tested on significance.

The regression models are divided into seven specifications, of which the first four only use a single risk-factor to explain housing returns (Beracha & Skiba, 2013, p. 299). All four single-factor specification models show a statistically significant coefficient value, which indicates that each of risk factor has some explanatory power by itself. However, in all four of these factor models, the alpha intercept is also significant, suggesting that a single-factor model fails to explain the cross-sectional housing return variations. Therefore, the remaining three specifications include more than one risk-factor. To understand the outcome of these housing-risk-factor models, the categorized risk factors are now elaborated.

The first factor in Beracha & Skiba’s study (2013, p. 300) is the market risk factor. When valuing stock, a broad stock market index such as the S&P500, is often used as a proxy (Berk & DeMarzo, 2017, p. 375; Bodie & Marcus, 2014, p. 292). In valuing the housing market, the residential real estate return of a whole country or continent could be used as a proxy for systematic market risk (Beracha and Skiba, 2013, p. 294; Eiling et al, 2019, p.3). Beracha and Skiba (2013, p. 296) use the Housing prices Indices (HPI), retrieved from the Federal Housing Finance Agency, for a time period of Q1-1984 to Q2-2009 as source for the market risk. Results show that market risk as a single factor, has no statistical significance (2013, p. 299). But, in conjunction with an economical, geographical and psychological risk factor, the market risk factor does display statistically significant explanatory properties. However, using HPI as risk factor has a potential drawback. Dröes and Hassink (2013, p. 98) suggest that using aggregate house price indices, could average away idiosyncratic risk.

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10 The second factor is of economical nature. The rationale behind this has its origin in supply and demand analysis. As income rises, households have more money available for expenditure, which increases the demand for housing. As construction of residential real estate takes time, the supply of housing lags. Consequently, house price appreciation could occur. Case and Shiller (2003, p.300) found that income growth alone explained virtually all house price increases observed in forty U.S states from 71 quarters between 1985 and 2002. Other chosen fundamentals, such as population, unemployment rate, and average mortgage rate, seemed to have less pronounced explanatory power (Case and Shiller, 2003, p. 318). Capozza, Hendershott and Mack (2004, p.26) also found the income growth factor a significant determinant of commercial real estate returns. Findings by Fama and French (1992, p.428) revealed that stock returns could be explained with the stock return differential between high and low market-to-book ratio stocks, which they called ‘High-Minus-Low (HML)’. Carhart (1997, p.63) found comparable evidence for mutual fund returns. Similarly, Beracha and Skiba (2013, p. 294) put forth that housing returns could be explained by taking the house return differential between the top and bottom third area in terms of income growth, which they denoted as HML. However, their findings (2013, p. 299) suggest that income growth is not a statistically significant factor in any of their multi-factor models.

The third potential factor is a geographical risk factor. It is based on land available in each city for real estate development. This is expressed as the land supply elasticity (LSE). Similar as with the income growth factor, Beracha & Skiba (2013, p. 305) use the house return differentials of top third and bottom third cities in terms of LSE values, which they call Inelastic-Minus-Elastic (IME). A low LSE implies less land available for real estate development. If demand for housing increases, these low LSE-areas provide less building opportunities. As a result, the supply in these areas lag. Through the supply and demand logic, it is expected that these low-LSE areas would appreciate relatively more than high-LSE areas. Glaeser, Gyourko and Saiz (2008, p.47) found that coastal areas, which by its nature have a low LSE, show more deviation in housing returns than the underlying macro risk-factors would predict. Their results indicate that LSE has a higher explanatory power during a high economic conjecture (2008, p. 44), than during a low economic conjecture (2008, p. 45). Results by Beracha & Skiba (2013, p. 299) show that LSE is not a statistically significant factor in any of their multi-factor models. The fourth and last factor, is a psychological risk factor, expressed as return momentum. Jegadeesh and Titman (1993, p. 65) had already found evidence that this ‘previous-period momentum-effect’ was persistently present in the stock market. Their results revealed stocks that displayed abnormal returns last year (1993, p. 69), continued to display abnormal returns the following 3-12 months. Daniel, Hirschleifer and Subrahmanyam (1998, p. 1840) and Goetzmann and Ibbotson (1994, p. 12) found the same momentum effect

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11 persistent with observed abnormal returns of mutual funds. Research conducted for Real Estate Investment Trusts in the U.S. exhibited a similar momentum effect (Chui, Titman & Wei, 2003, p. 385; Hung & Glascock, 2008, p. 61). Therefore, it is reasonable to assume a similar momentum effect might be present with residential real estate returns. Case and Shiller (1989, p. 131) were the first to document the momentum factor as predictor for future housing returns. They examined housing returns in Atlanta, Chicago, Dallas and San Francisco and found statistically significant evidence that returns for previous periods, could predict returns in the future (1989, p. 132). However, Case and Shiller noted that their lack of control variables, could result in biases that were picked up in the error term (1989, p. 134). Also, the scope of their research was limited to four cities, which makes it hard to translate to other housing markets. Beracha & Skiba (2011, p. 305) built upon Case and Shiller’s study and extended the scope to 370 MSAs in the United States. They took the quarterly house return differentials between the top third and bottom third cities, in terms of their previous quarterly returns, for a time period from 1983 to 2009 (2011, p, 310). Whether there is momentum, is tested with the help of basic autoregression. Stock and Watson (2015, p. 569) explain autoregressions as a regression of a dependent variable against itself. In other words, regressing the quarterly excess housing returns of a period t, on the same excess housing returns of previous periods (t-1, t-2,…., t-n), to find out if a forecast on housing returns can be made purely on with past values of the same variable. Beracha and Skiba (2011, p. 308) use up to seven quarterly lags. Their results show that quarterly lags between t-2 and t-5 are positive and statistically significant. This would confirm that momentum plays a role in predicting future housing returns. It is interesting to note that t-1 is negative and statistically significant in all seven autoregression specifications. This implies that a reverting effect takes place during quarter t-1. Since the other periods show values that are positive and larger in magnitude, this reverting effect does not alter the effect that momentum has on housing returns.

But how would momentum be linked as a psychological factor? The underlying explanation for momentum, is found in overconfidence. A behavioral study conducted by Daniel, Hirschleifer and Subrahmanyam (1998, p. 1840) revealed that investors’ overconfidence is positive correlated to momentum in stock returns. Similarly, Chui, Titman and Wei (2008, p. 1844) found that this positive correlation between overconfidence and momentum to be present in 41 countries worldwide and applied to the real estate market. By comparing 41 countries, Chui et al found each country had its own country-specific momentum, of which overconfidence was found to be linked with cultural individualism (2008, p. 1863). In other words, countries with a high value on individualism, displayed higher overconfidence and thus a stronger momentum effect. This effect was shown to hold for the United States and EU countries. Japan showed a weak and insignificant evidence of momentum (2008, p. 1868).

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12 Next to the above-mentioned factors, demographic risk factors are also a plausible candidate that could add explanatory power to predict residential real estate returns. Two of these social factors are population- and unemployment growth rates. Cannon, Miller and Pandher (2006, p. 522) did a cross-sectional asset-pricing approach to predict housing returns in 155 MSA’s in the United States. They found statistically significant evidence that population growth has a positive effect on land prices and housing returns (2006, p. 536). However, they did not find significant evidence that unemployment rates had any negative effect on housing returns (2006, p. 537). Since their model also includes an employment factor (profession), expressed as % of people employed in managerial functions, this has a potential interaction effect with unemployment and housing returns. Households with managerial functions typically enjoy a higher salary. Therefore, these households might want to live in more expensive neighborhoods. This leads to clustering of high-income households in exclusive sub-markets where buyers are willing to pay an ex-ante premium. As a result, housing return growth rates in these sub-markets would decrease. Though this might not seem intuitive, but the factor ‘profession’ could in fact have a negative overall effect on housing returns.

Sinai and Souleles (2013, p. 289) put forth the notion that house ownership, could reduce risk. For their research, they used house-hold level data in the United States across multiple MSAs. A homeowner who sells his house, still needs to live somewhere after the current house is sold. The sale price of the current house is uncertain. But so is the purchase price of the subsequent house. Sinai and Souleles (2013, p. 283) argue that if current and future houses have positive covarying prices, then the gain or decline in value are offset by the increase or decrease in house prices. This positive covariance even seems to hold when a household moves to a different city (2013, p. 308). Therefore, owning a house provides a hedge, so reduces risk, against uncertain future purchase prices of a next house (2013, p. 309). However, Dröes and Hassink (2013, p. 98) found that these hedging benefits are small in comparison to idiosyncratic risk in the Dutch housing market. Eiling et al (2019, p. 1) put forth that especially idiosyncratic housing risk, helps explain residential real estate returns. Their research consists of more than 9000 ZIP codes, within 150 metropolitan statistical areas (MSAs) in the United States (2019, p. 2). The multi-factor model includes four risk factors, namely, the stock market returns, aggregate U.S. housing returns, MSA-level housing risk factor and ZIP-code-level idiosyncratic risk factor (2019, p. 6). The Fama Macbeth two-step regression method is used, to find the idiosyncratic risk factor premium (IVOL). The first step is to take a time-series regression, followed by a cross-sectional regression.

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13 2.4 Hypothesis

As seen from previous mentioned literature, the returns to real estate are affected by market, demographic, geographical and macroeconomically risk factors. Population and unemployment growth rates are demographic risk factors that have been shown to affect housing returns (Cannon, Miller and Pandher, 2006, p. 522). Even though some research showed that income growth was not a significant factor (Beracha & Skiba, 2013, p. 299), other macroeconomic factors did seem to matter. According to Plazzi, Torous and Valkanov (2008, p. 415), GDP growth rate affects returns to commercial real estate. Gross domestic product also seems to affect housing returns in the United States (Case & Shiller, 1989, p. 132). Also, mortgage interest rates and loan-to-income ratios (LTI) are to be considered (van Gool et al., 2013, p. 263). Lastly, inflation should be included to estimate the model in real terms. Besides these systematic risk factors, an idiosyncratic risk factor could be included to improve the housing risk-factor model, as previous research by Dröes and Hassink (2013, p. 93) and Eiling et al (2019, p. 16) has shown.

Earlier work investigated the relationship between housing returns and risk factors in different cities or regions, but within the same country. This implies that different cities and regions have more systematic risk factors in common, i.e. country GDP growth, inflation etc. In this thesis, the focus will be on the relationship between housing returns and multiple risk factors, across 28 European countries. This paper contributes to the existing literature by looking at country specific characteristics to explain differences in observed house price returns between European countries.

As such, the hypothesis states: ‘the risk and return on housing in European countries can be explained by market risk factors’.

3. Data

This section will first explain the dependent variable. Thereafter, the independent variables will be elaborated. Also, the type of data, together with its sources will be explained. Lastly, the reason for choosing certain variables will be elaborated and first findings about descriptive statistics will be checked in conjunction with economic theory.

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14 3.1 Dependent variable

The dependent variable in this research is the House Price Index (HPI). This HPI is derived from the database of Eurostat (Eurostat, 2020). The data contains yearly house prices indices, not seasonally adjusted, for the 28 European Union (EU 28) countries, from 2009 to 2018. From this, the return on housing can be derived. Notice that the United Kingdom is included for the whole sample period, because the official date they left the EU was on 31st_January

2020 (Rijksoverheid, 2020). The base year of this HPI was set on 2007, at an index price of 100. Table 1 shows that the mean of this index is 98.2 and the standard deviation is 22.2 index points. It also shows a large spread between the minimum 46.7 and maximum 175.4 of HPI values. This could be due to the large differences in country characteristics from the sample size. Figure A from the appendix shows that the HPI trend varies a lot between countries. As seen from the graph in Figure 1, the residential real estate prices in Europe showed a considerable drop from 2008-2009, amidst the financial crises’ spillover-effects to Europe. Thereafter, the aggregate house prices remained at a stable, yet lower level. From 2015 onwards, the average residential real estate prices in Europe showed an increasing price trend.

0,0 20,0 40,0 60,0 80,0 100,0 120,0 140,0 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 In d ex 2007 =100 Years

Figure 1: Residential Real Estate Prices

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15 Table 1

Descriptive statistics

Variables Mean Std. dev. Min. Max.

Nominal HPI (2007 = 100) 98.4 22.2 46.7 175.4

Mortgage interest rates on new loans (%) 3.46 1.74 0.81 11.55 Gross disposable income households (euros

in millions)*

326,642 505,905 8,493 2,111,965

Loan-to-disposable income (%)* 69.7 51.01 5.4 219.5

Unemployment (age 20-64yr, %) 6.98 3.57 1.8 20.2

Inflation (annual rate in %, HICP) 1.49 1.47 -1.7 6.10 Population (age> 18yr) 14,682,500 18,703,198 330,123 69,254,205 Sample period 2009 - 2018 (10 years)

Number of countries 28

Number of observations 280

*10 observations from Malta are missing. The dataset is strongly balanced with the number of observations per variable ranging from 270-280.

3.2 Independent variables

The first independent variable is the mortgage interest rate (MIR). Data on this variable is retrieved from the database of the European Mortgage Federation (EMF) and its source is the European Central Bank. It contains monthly data, which is annualized, including the weighted average of 1-30-year mortgage rates, in 28 European countries (ECB, 2020). For non-euro countries, the data is retrieved from their respective National Central Banks. The mortgage interest rate has constantly declined from an average of 4.69% in 2009 to 2.53% in 2018. This is consistent with the overall interest rate trend worldwide, due to quantitative easing programs applied by central banks (The Economist, 2019). The exception to this trend is notable between 2011-2013 in south-European countries. The mortgage interest rate reverses, to increase for 2 years, before continuing its declining trend. The explanation lies with the European sovereign debt crisis (ECB, 2020), which emerged in this period, causing a drop in the respective country bond ratings. Mortgage interest rate is included, because this relates more to the real estate market than the real interest rate. If mortgage rates rise, households would have to pay more interest for their mortgage. This decreases the amount of people who can afford to finance a house via a mortgage loan. As a result, the demand for housing could decrease. Thus, mortgage interest rates (MIR) could have a negative effect on residential real estate prices. According to table 2, the effect of MIR on residential real estate prices is indeed negative. The coefficient is -0,2597, which means the correlation is weakly present.

The second independent variable is disposable income of households. This data is derived from the AMECO data base and its source is the European Commission. It contains

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16 yearly data on the disposable income of households in 27 European countries. For Greece, the disposable income data is retrieved from ALSTAT’s database. Disposable income of households is defined as the amount of money households have available after-tax deductions and pension contributions (European Commission, 2020). The unit is in millions of euros. Again, countries with non-euro currencies have been converted according to the currency exchange rate prevailing at each year (World Bank, 2020). This variable is included because as income rises, more people could afford buying a house, which could increase the demand for housing. As such, a higher income could have a positive effect on housing returns. Table 2 confirms this positive effect. The coefficient is 0.1433, which implies this positive correlation is weakly present.

Next is the independent variable called ‘mortgage Loan-To-disposable-Income of households ratio’ (LTI). For the first part of the fraction, data on mortgage loans is retrieved from the European Mortgage Federation’s database and its source is the European Central Bank. For the second part of the fraction, data on disposable income is, as described earlier, collected from AMECO and ALSTAT’s database and its source is the European Commission. The definition is therefore the fraction of both earlier mentioned independent variables (European Commission, 2020). It contains yearly data on 28 European countries and the units are fractions multiplies by 100, to be expressed as percentages. The LTI variable is included, because if people receive more loan for the same income, so LTI rises, the maximum mortgage that household can finance, increases. This potentially results in a higher demand for housing, since more household can compete in the buyer’s housing market. Therefore, it is expected that a rise in LTI, has a positive effect on residential real estate prices. Table 2 seems to confirm this. It shows a coefficient of 0.1288, which implies a weak positive correlation.

The fourth independent variable is unemployment rate. Data on this variable is retrieved from Eurostat. It contains yearly data of the unemployment rate in 28 European countries. The unemployment rate is the number of unemployed persons, as a percentage of the labor force. The definition of unemployed is that amount of people actively seeking for a job (International Labor Office, 2020). Only persons between the age of 20-64 years are included in the data (Eurostat, 2020). The rationale for including this variable has to do with the demand on housing. The higher the unemployment rate, the less income people will have to buy a house or ask for a mortgage loan. This will reduce the demand for housing. Intuitively, unemployment rate would have a negative effect on residential real estate returns. According to table 2, the effect of unemployment rate on residential real estate is indeed negative. The coefficient is -0.5728, which implies a moderate negative correlation.

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17 The fifth independent variable is inflation. This data is collected from the Eurostat database. This data comprises of the annual rate of change in consumer prices, expressed in percentages, for 28 European countries. Inflation in this sample is defined as the Harmonized Indices of Consumer Prices (HICP). By using these harmonized definitions, it provides the best statistical basis for international comparisons of consumer price inflation within the European Union (Eurostat, 2020). The trend of inflation growth per year seems stable from 2009 to 2018 at an average around 1.49%. An exception to this is Greece, Spain and Portugal, which show a negative inflation trend between 2012-2015, to recover to slightly above zero thereafter. A possible explanation for this is the intervention of the ECB during the European Sovereign debt crisis (ECB, 2020). The reason for including this variable is as follows. If inflation rate is growing, money loses value over time (Berk and DeMarzo, 2017, p. 136), which implies that households would see their buying power decrease over time. As a result, people will not postpone their purchases and rather buy a house now. This could result, ceteris paribus, in an increase in housing demand. Therefore, inflation could have a positive effect on the return to residential real estate. This intuition seems to correspond to table 2, which shows a positive effect of inflation. The coefficient is 0.1180, which implies a weak, but positive correlation.

Finally, the sixth independent variable is population. Population is derived from the database of Eurostat. It contains yearly data on the population, with age over 18 years, in 28 European countries. All values are in units. The minimum value of 330.123 is observed in Malta in 2009 and the maximum value of 69.254.205 is observed in Germany in 2018. As the countries in this sample considerably vary in size, so does the population. This explains the large standard deviation in table 1. This independent variable is included in the model, because if more people live in a country, it is plausible to assume that more housing is needed to accommodate the extra amount of people. This could result in an increase in housing demand. From supply and demand analysis, this would intuitively imply that population has a positive effect on residential real estate prices and thus also on its return rate. Table 2 shows a positive correlation of 0.0537, which means there is indeed a positive correlation, though very weakly

present. Table 2

Correlation matrix

HPI MIR Disp_inc Loan-to-inc Unemp_rate Inflation Population

HPI 1 MIR -0.2597 1 Disp_inc 0.1433 -0.1991 1 Loan-to-inc 0.1288 -0.3597 0.0773 1 Unemp_rate -0.5728 0.0695 -0.1169 -0.1206 1 Inflation 0.1180 0.7950 -0.0175 -0.01140 -0.1658 1 Population 0.0537 -0.0815 0.9565 -0.0318 -0.0560 0.0098 1

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18

4. Methodology

This section will explain three multiple linear regression models that were used to perform empirical analyses and why these are applied in this thesis. Furthermore, the Fama Macbeth two step regression model is introduced, to allow for pricing in idiosyncratic risk.

4.1 Multivariate regression models

The research question from the introduction stated: ‘What are the determinants of residential real estate price risk and returns in Europe?’. This question will be answered with by an empirical analysis using three multiple linear regression models. These consist of a pooled OLS regression, fixed effects regression, and finally a first-differences regression. These three regression models are defined respectively below as equation (1), (2) and (3). The fixed effects are specified as country fixed effects and time fixed effects. The dataset is a panel data of 28 countries over a 10-year time period. The endogenous variable in all three regressions is the return on residential real estate, whereas the earlier mentioned six independent variables are assumed to be exogenous. Table 3

List of variables

R(HPI)i,t Returns on residential real estate of country i, at time t

MIRi,t Mortgage interest rate of country i, at time t

INCi,t Disposable income of households of country i, at time t

LTIi,t Mortgage loan to income ratio of country i, at time t

Ui,t Unemployment rate of country i, at time t

INFLi,t Inflation rate of country i, at time t

POPi,t Population of country i, at time t

To test the explanatory power of the multi-factor model on residential real estate returns, the beta coefficients, β1 up to and including β6, will be examined in this research. This gives the following three regression equations:

(1) log(R(HPI)i,t) = β0 + β1MIRi,t + β2log(INCi,t) +β3LTIi,t +β4Ui,t +β5INFLi,t +β6log(POPi,t) + εi,t

(2) log(R(HPI)i,t) = β0 + β1MIRi,t + β2log(INCi,t) + β3LTIi,t + β4Ui,t + β5INFLi,t + β6log(POPi,t) +

αi + τt+ εi,t

(3) Δlog(R(HPI)i,t) = β0 + β1 ΔMIRi,t + β2 Δlog(INCi,t) + β3 ΔLTIi,t + β4 ΔUi,t + β5 ΔINFLi,t +

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19 As can be seen from table 3, R(HPI)i,t represents the returns on residential real estate of

country i, at time t. Table 3 also explains the six independent variables. MIR represents the mortgage interest rates of country i, at time t. Disposable income of households is denoted by INCi,t. The factor LTIi,t stands for the mortgage loan-to-income ratio. The unemployment and

inflation rate are denoted respectively by Ui,t and INFLi,t. Finally, POPi,t represents the

population of country i, at time t. Additionally, the country fixed effects are denoted by αi, the

time fixed effect by

τ

t, and the first differences by the Δ-symbol.

All the above regressions make use of the Ordinary Least Squares (OLS) method. This method assumes a linear relationship exists between an exogenous variable and the endogenous variable (Stock & Watson, 2015, p. 160). More specifically, a linear relationship in the coefficients of the exogenous variables. If the Gauss-Markov assumptions are met, OLS should give the optimal statistical estimators that are unbiased, called Best Linear Unbiased Estimator (Stock & Watson, 2015, p. 115). In order to use the OLS method, four assumptions must hold.

The first is that the error term, on average, must be zero. If this is not true, some of the explanatory power is picked up in the noise term. This would imply omitted variable bias, which invalidates the model as whole. The second assumption is that the variables are drawn from an independent and identically distributed (i.i.d.) set of data. If this assumption fails, the normal distribution characteristics of random variables no longer holds. The third assumption is that large outliers, or ‘fat tails’ are unlikely. If this finite kurtosis assumption does not hold, the random distribution characteristics fails. Lastly, the fourth assumption states that no perfect multicollinearity exists. In other words, no exact linear relation may exist between exogenous variables. If this assumption fails, then one of the regressors fully explains another regression. In a multiple linear regression model, the effect of each X variable on Y, is explained as a partial effect, so keeping all other variables constant (ceteris paribus). But with perfect multicollinearity, this is no longer possible, and the model becomes invalid (Stock & Watson, 2015, p. 247).

To test whether any of the independent variables is individually statistically significant, the t-test will be used. The F-test will be performed to test whether the regression model as a whole is statistically significant. The outcome of both test statistics is done with robust or ‘Eicker/Huber/White’ standard errors for all three models. These so called heteroskedasticity-robust standard errors are selected, to allow for the possibility that error terms do not have a constant variance over the exogenous variables (Stock & Watson, 2015, p.204). All three models make use of panel data, which is notated by the ‘i,t’-subscript in the equations. Stock

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20 for both homoskedasticity and autocorrelation. Therefore, these three models make use of heteroskedasticity- and autocorrelation-consistent (HAC) standard errors, or also called clustered standard errors.

With help of these three regression models, the following hypotheses will be tested to provide an answer to the research question:

H0: β1=β2=β3=β4=β5=β6=0

H1: At least one of these coefficients is non-zero

In Eq. (1) the country and time fixed effects are ignored. In other words, it takes the data on all 28 EU countries as a whole and ignores any country or time characteristics. The independent variables income and population are converted into a logarithmic scale. As is the independent variable, which represents return to residential real estate. The remaining independent variables are already expressed in percentages. As a result, any 1% change in an independent variable, can be interpreted as a β% change in house returns, better known as the elasticity (Stock & Watson, 2015, p. 320).

Equation (2) is like the earlier pooled-OLS regression, with the exception that now fixed effects (αiand τt)are included. More specifically, country and time fixed effects are taking into

consideration to see if the model improves. As noticed earlier from table 1, the sample size consists of countries which vary considerable in their characteristics. This leads to relatively high standard deviations compared to the mean values for each variable. For example, Malta is over 1000 times smaller in country size than Germany or France. Also, the wealth between countries may vary significantly. This could explain why the mean of population is 14.6 million with a standard deviation of 18.7 and the mean of income is 326 million with a volatility of 506 million euros. These individual effects, also known as unobserved heterogeneities (Stock & Watson, 2015, p. 552), are unique to each country in the panel data. By not accounting for these, there may be omitted variable bias in the estimators. According to Stock & Watson (2015, p. 409), this can be resolved by simultaneously including both location (country) and time fixed effect. The panel data in this research is strongly balanced. Since the data set contains 28 countries, there will be 27 dummy variables used for location. One variable is left out intentionally, because otherwise the sum of these dummy regressors adds up to 1, which would give perfect multicollinearity with regressor of the intercept. This so-called dummy-variable trap (Stock & Watson, 2015, p. 250) can be avoid by either dropping the constant or one dummy variable. For time, the panel data includes 10 years, ranging from 2009 up to and including 2018. Thus, nine dummy variables are used for time.

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21 Lastly, Eq. (3) involves taking the first differences of the variables. All first differences are written with a delta (Δ) sign. This approach is used to reduce the problem of omitted variables in panel data (Stock & Watson, 2015, p. 573). However, whether these first ‘lags’ add to the explanatory power of the earlier mentioned models, is questionable. How do you know that the last period values weren’t just caused by pure random chance? Also, why would you assume that the last period results effected the current observed results? For example, second, third, …, nth lags could provide better estimates (Beracha & Skiba, 2011, p. 306). So,

in order to decide if first difference might improve the model, it must be shown that previous period results were not due to randomness, but rather followed a certain pattern. Empirical data on economic time series have been shown that regressors often behave spurious or non-stationary over time (Dickey & Fuller, 1981, p.1057). Specifically, trends and breaks are two of the frequent observed non-stationary types (Stock & Watson, 2015, p. 597). A break is a change in definition for regression coefficient in the model. For example, the earlier mentioned definition for inflation (HICP), could be changed over time. A trend is a persistent long-term movement of a variable over time. (Stock & Watson, 2015, p. 598). The latter is where the unit root test focusses on (Dickey & Fuller, 1981, p. 1060). If a time series has a stochastic trend, the series is said to have unit root. This can be problematic if variables with unit root are regressed on each other, as these leads to spurious regression results. Previous period results would not help predict current period results, as these were assumed to have a random cause. Consequently, the coefficient of estimators and the t-statistic could have non-normal distributions, even for large sample sizes. This diminishes the power of the model. Therefore, Stock and Watson (2015, p. 604) propose to perform unit root tests before proceeding with first, second, …, nth-difference regressions. Because this research uses panel data, a

‘Levin-Lin-Chu panel data unit root’ test is performed (Levin, Lin & Chu, 2002, p. 3). The method builds upon the Augmented Dickey Fuller (ADF) unit root test, by extending the test from data of a single individual to many individuals. First the ADF is run for each cross-section, which comprises 28 in this research. Thereafter, two auxiliary regressions are performed to get the orthogonalized residuals of these cross-sections, which are then run in a pooled OLS regression (Levin, Lin & Chu, 2002, pp. 6-8). The null hypothesis of the Levin-Lin-Chu unit root test states that ‘each time series contains a unit root’ and therefore first differences should be considered. In mathematical terms, the coefficient is 1. The alternative says, ‘each time series is stationary’, which holds if the coefficient is less than 1. Therefore, the unit root test is a one-sided test. According to table 4 column (1), the p-value is insignificant, which implies that there is not enough statistical evidence to infer that each time series is stationary. This does not automatically mean that the series have unit roots (Stock & Watson, 2015, p. 607). Nonetheless, first differences are used in table 4 column (2), which show a significant p-value.

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22 This is a favorable result, as it shows that taking first differences into account, eliminates the random walk in times series and improves the power of the model.

Table 4

Unit root tests (Levin-Lin-Chu) (1)

Not adjusted data

(2) First-differenced data Pooled t-statistic 1.821 -7.897 P-value (one-tailed) 1.000 0.0001 Cross-sections 28 28 Observations 10 9

Table 4 shows that first differences regression would provide an improvement to the earlier mentioned regression models. The coefficients of residential real estate returns, income, and population are first converted into logarithmic scale. Thereafter, the first differences between two periods is calculated. The result is expressed as the growth rate of each respective variable between two periods. For clarification, the derivation of the income growth rate is elaborated as following: Δlog(INCi,t) = log(INCi,t) - log(INCi,t-1)

Via the same method, the return on housing and growth rate for population is derived. For return on housing, this is written as ‘Δlog(R(HPIi,t))’ for all three equations. Because first

differences calculate the change between periods, some data points are lost, as can been seen from table 4 column (2) in the observation section. Since the remaining variables are already expressed in percentages, only the first differences are calculated to find the growth rates. The result is that all variables are expressed as percentage changes or elasticity, which makes data interpretation easier.

4.2 Fama Macbeth two step regression model

The previous mentioned models all include error terms, denoted by ‘ε’. One of the OLS assumptions is that, on average, this value is zero. In other words, there is no correlation between the error term and an independent variable. Therefore, these multi-factor models assume that only systematic risk is priced in (Berk & DeMarzo, 2017, p. 504). When using panel data, there is an additional restriction that cross-sectional error terms, denoted by ‘εit’,

are independent of each other (Stock & Watson, 2015, p. 412). But what if a correlation exists in these cross-sectional error terms? For example, if one country experiences a rise in housing return, a neighboring country also observes a rise in housing returns. If these effects are not

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23 captured by the independent variables in a model, the error term in these panel regressions might be correlated. The pooled-OLS estimates might still be consistent, but the standard errors are wrong. This can deteriorate the results of the t-statistics. Petersen (2009, p. 475) found that t-statistics to be off by a factor of 10 if no correction is made for cross-sectional correlations. He also found that 42% of finance papers published in 2008 simply ignored the presence of this correlation (2009, p. 435).

Fama and Macbeth (1973, p. 614) found a method that computes the standard errors, which are needed to correct for cross-sectional correlation in the error terms. This method is better known as the ‘Fama Macbeth two step regression’ model. In residential real estate, this method would allow a house-risk-factor model to price in idiosyncratic risk (Eiling et al, 2019, p. 2).

The first step involves performing a time-series regression of the dependent variable on the independent variables (Fama and Macbeth, 1973, p. 616). This is done to estimate the risk-factor exposures and idiosyncratic volatility for each country i. In this thesis, that would imply running a time-series regression on the housing return for each of the 28 EU countries. This is represented by Eq. (4) below:

(4) log(R(HPI)i,t) = αi,t + 𝜷𝒊𝑴𝑰𝑹MIRt + 𝜷𝒊𝑰𝑵𝑪log(INCt) + 𝜷𝒊𝑳𝑻𝑰LTIt + 𝜷𝒊𝑼Ut + 𝜷𝒊𝑰𝑵𝑭𝑳INFLt +

𝜷𝒊𝑷𝑶𝑷log(POPt) + εi,t

The same dependent variable and six independent variables are used. The alpha represents the intercept. By dividing the sum of these betas through the total number of regressions performed, the average beta estimates, 𝛽̂i, for each risk factor are computed. Similar to Eiling

et al (2019, p. 8), the idiosyncratic volatility is estimated by taking the standard deviation of the residuals from Eq. (2), that is, IVOLi,t = √𝑣𝑎𝑟( 𝜀𝑖,𝑡).

The second step involves running a cross-sectional regression for each time period per EU country. This is done to estimate the price of risk for each factor. The average beta estimates, 𝛽̂i, are used ‘as if they were observed’. This second regression gives the factor risk

premiums for every period per country. Equation (5) shows the second step:

(5) log(R(HPI)i,t) = λ0,t + λ1𝜷̂_𝒊,𝒕𝑴𝑰𝑹 + λ2𝜷̂_𝒊,𝒕𝑰𝑵𝑪+ λ3𝜷̂_𝒊,𝒕𝑳𝑻𝑰 + λ4𝜷̂_𝒊,𝒕𝑼+ λ5𝜷̂_𝒊,𝒕𝑰𝑵𝑭𝑳 + λ6𝜷̂_𝒊,𝒕𝑷𝑶𝑷+ λ7IVOLi,t +ξi,t

Again, the average factor risk premiums are found by dividing by the total number of regressions, which in this case is 10 per country i. In this paper, the results give seven factor risk premiums and the remaining error term ξi,t. To make a distinction with Eq. (4), the

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24 coefficients in Eq. (5) are denoted by λ. Now, the difference in estimates at each time period per country can be used, to find the standard deviation of each average factor risk premiums (Fama and Macbeth, 1973, p. 617). This is found by dividing the period standard deviation, by the square root of the total time period (Stock & Watson, 2015, p. 120). New in this model is the risk-factor ‘IVOL’, which captures the idiosyncratic risk premium in housing returns per EU country. This value is derived from the first step, as noted earlier. The previous Gauss-Markov statements are still assumed to hold. The error term, ξi,t, is on average still zero. An additional

assumption for the Fama Macbeth model is that the estimated beta coefficients derived from time-series, are assumed to remain constant over time (Fama & Macbeth, 1973, p. 616). As such, the regressors only pick up variances from the cross-sectional regressions.

5. Results

In this section, the results of the earlier mentioned regression models are explained. The difference in coefficient values are examined. Thereafter, these results are compared with the Fama Macbeth two step regression output.

5.1 Multivariate regression analyses

Table 5 column (1) shows the results of the pooled-OLS regression earlier specified by Eq. (1), which has log(R(HPI)i,t) as dependent variable. The adjusted R-squared is 0.4643, which

implies that the risk-factors in this model explain 46.43% of the sample variance of return to residential real estate. In other words, how well the fit of the model is. According to Stock and Watson (2015, pp. 242-244), the adjusted R-squared is a better measurement than the standard R-squared. Where the R-squared improves for every risk factor added, the adjusted R-squared only improves if this incremental risk-factor adds explanatory power to the model. This regression model is first tested as a whole with help of the F-statistic, where the earlier mentioned null hypothesis states that all risk-factor coefficients are zero. With a F(6, 263) = 46.57, p<0.01, this implies that with a 1% significance level, there is enough statistical evidence to infer that at least one of the risk-factor in this model influences housing returns. Next, the separate coefficients will be discussed. The first coefficient, mortgage interest rate (MIR), shows a negative coefficient of -0.00268. This means that a one-percentage change in mortgage rates, would lead to a -0.0268% change in residential real estate returns. This negative correlation corresponds to earlier mentioned economic intuition that increases in MIR have a negative impact on house prices. However, the t-statistic of MIR is insignificant. Looking at the correlation matrix in table 2, it seems that MIR is highly correlated with the inflation rate.

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25 This value is 0.7950, which could hint at the possibility of multicollinearity. Stock and Watson (2015, p. 251) explain that this can result in at least one of the coefficients being imprecisely estimated or simply inconsistent. The second is the coefficient of disposable income of households, which is 0.16347. This implies that a one-percentage change in disposable income leads to 0.16347% change in residential real estate returns. This effect is significant at a 1% level. An explanation for this could be the lagging of housing supply, when demand increases due to an income rise. For example, van Gool et al (2013, p. 133) mentioned that the whole process from housing development to completion, takes on average two to three years. Therefore, the higher income could cause a bidding war on scare available houses for sale. This puts pressure on house prices and could thus increase housing returns. Next, the coefficient of mortgage loan-to-income ratio (LTI) is -0.00106. This means that a percentage change in LTI, will lead to a -0.00106% change in housing returns. This effect is significant at a 1% level. This result is counterintuitive, as you would expect a higher LTI ratio leading to more demand on housing, which increases house prices. From this logic, a positive effect would be expected. However, the negative effect could be due to omitted variable bias. For example, the number of residential real estate newly added to the housing market is not considered. It is therefore possible that the increase in demand for housing, is more than offset by the increase in housing supply. This could explain the negative effect being measured. Fourth is the coefficient of unemployment rate, which is -0.03292. A one-percentage change in unemployment leads to a -0.03292% change in return to residential real estate. This effect is significant at a 1% level. As was expected in section 3, the higher the unemployment rate, the less households can apply for a mortgage loan, which decreases demand for housing and ultimately has a negative effect on housing returns. The fifth coefficient is that of inflation rate, which is 0.01356. A one-percentage change in inflation rate will affect the residential real estate returns by 0.01356%. This result is significant at a 5% level. The rationale for the positive effect could lie in the concept of ‘time value of money’ (Berk & DeMarzo, 2017, p.136). If inflation is increasing, households lose buying power over time. This could lead to not postponing a house purchase in a few years, but rather buy it now. As a result, the demand on housing and thereby the house prices could increase. Finally, the sixth coefficient is that of population at a value of -0.16342. This implies that a one-percentage change in population will lead to a -0.16342% change in residential real estate returns. This effect is significant at a 1% level. This negative relationship is not as anticipated. It was assumed that, the more population grows, the more housing is needed. This would increase the demand for housing and have a positive effect on the housing returns. This negative effect could be explained by the correlation matrix in table 2. The high correlation of 0.9565 with disposable income could hint on a multicollinearity problem. This could cause for large standard errors and inconclusive and varying results.

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26 The second regression results are shown in table 5 column (2), of which the dependent variable is denoted by log(R(HPI)i,t). The interpretation of the coefficients remains identical to

the first model. The adjusted R-squared is 0.6256, which implies that the model explains 62.56% of the sample variance of residential real estate returns. It appears that adding country and time fixed effects to the model, improves the fit of the model from 46.43% to 62.56%. With a F(6, 26) = 32.28, p<0.01, this implies that with a 1% significance level, there is enough statistical evidence to infer that at least one of the risk-factor in this model has an effect on the returns in residential real estate. The MIR coefficient changed from a negative to a positive value of 0.00176 but is still insignificant. The problem of multicollinearity is not resolved by adding fixed effects to the model. Disposable income has now increased in magnitude from 0.16347 to 0.44069, at a significance level of 5%. The country fixed effect seems explain this difference. An increase of average income by 1% in a more financially developed country, might have a different impact on housing returns, than the same income increase in a less liquid developed country. Next is the mortgage loan-to-income (LTI) ratio coefficient, which has flipped from -0.00106 to 0.00166. This positive effect now corresponds with earlier noted intuition. However, this value is not significant anymore. Omitted variable bias could be the cause. How developed the mortgage market is per country, should be considered when investigating the LTI ratio of that country. Unemployment rate is the next coefficient. The value has a slightly increase in magnitude from -0.03292 to -0.03476 and is still statistically significant at 1% level. The country and time fixed effects did not seem to matter much for this risk-factor. The same can be said for inflation rate, which has decreased slightly in value from 0.01356 to 0.01206 and remains stable at a 5% significance level. However, this is not true for population. As can been seen from table 5 column (2), the coefficient flipped from negative to positive and increased substantially in magnitude from -0.16342 to 1.08167. This value remains significant, though at a slightly lower level of 5%. The positive effect is now in line with earlier reasoning that population growth, would increase housing demand and thereby have a positive effect on housing return. A possible explanation is that the earlier Eq. (1) fails to take individual country effects into account. These unobserved heterogeneities are accounted for with use of country fixed effects in Eq. (2), which leads to less bias in the estimators (Stock & Watson, 2015, p. 552).

The third regression results are shown in table 5 column (3), of which the dependent variable is denoted by log(R(HPI)i,t). The interpretation of this model is, like the other two

models, namely expressed as elasticities. The adjusted R-squared is 0.3431, which implies that the risk factors in this model explain 34.41% of the sample variance of residential real estate returns. It appears that solely using first differences of the variables in model 1, deteriorates the explanatory power from 46.43% to 34.41%. A potential explanation for this is

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27 that with first differences, 27 observations are lost. However, Stock and Watson (2015, p. 244) put forth that the adjusted R-squared value on itself, does not convey if the model is ‘good’ or ‘bad’. Rather, this value should be taking in conjunction with, whether the added variables, indeed have a causal effect on the dependent variable from economic theory. The first differences variables seem to have causal effect supported by economic theory (Jegadeesh & Titman, 1993, p. 65; Fama & French, 1996, p.56 ; Beracha & Skiba, 2011, p. 290). When investigating the model as a whole, this results in F(6, 236) = 24.77, p<0.01. This implies that with a 1% significance level, there is enough statistical evidence to infer that at least one of the risk-factors in this model has an effect on residential real estate returns. Next is the t-test on each coefficient. The mortgage interest rate coefficient is -0.005885, but still insignificant. The problem of multicollinearity does not seem to be solved by adding fixed effects or first differences. Next, is the coefficient of disposable income, which seems to have increased in magnitude from 0.16347 to 0.26089 and with a stable significance level at 1%. This increase is in line with earlier literature which claims that effects on housing returns are lagging on economic development (van Gool et al, 2013, p. 49). Third is the LTI coefficient. This value flips from a negative value of -0.00106 to a positive value of 0.00104. The positive effect of LTI is desirable, as this is now in line with economic reasoning. A higher LTI, leads to more demand for houses, which puts a pressure on house prices to rise. Therefore, a higher LTI increases housing returns. However, the t-statistic has now become insignificant. The fourth coefficient is that of unemployment rate, which decreases somewhat in magnitude from -0.03292 to a value of -0.02641 and remains at a stable 1% significance level in all three models. The fifth is the coefficient of inflation rate. This value decrease in magnitude from 0.01356 to 0.00311 and becomes insignificant. As mentioned earlier, the high correlation of 0.7950 with MIR could cause multicollinearity, which could cause large standard errors and inconclusive and varying results. Lastly, the sixth coefficient is that of population. This shows a substantial increase in magnitude from a negative value of -0.16342 to a positive value of 0.88273. The significance level remains at 1%. This is a favorable outcome, as a growth in population now indeed shows a positive relation with housing returns, as would be expected from economic theory.

Risk and returns to residential real estate: Evidence from 28 EU countries