Is there a two-way relationship between household savings and house
prices?
Roxanne Schultz
10248684
Master’s thesis MSc Business EconomicsSpecialisation Finance & Real Estate Finance University of Amsterdam
Supervisor: dr. Martijn I. Dröes Second supervisor: prof. dr. Marc K. Francke
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Statement of Originality
This document is written by Roxanne Schultz 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 is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
This paper examines the dynamic link between household savings and house prices in European countries over the years 2005 to 2015. The analysis is based on a panel vector autoregressive (VAR) model, which is estimated with the use of quarterly panel data on a national level for 18 European countries. The main results of the analysis emphasize the importance to allowing for interdependency between household savings and house prices. Furthermore, household savings and house prices are not only explained by the two-way effect, but also by their lagged components and other macro-economic factors as the short-term interest rate and inflation. Finally, it is found that ignoring the dynamic interaction between household savings and house prices leads to bias in the estimates of other factors, with the coefficients on GDP and interest rates in the house price equation in particular. However, different estimations show some ambiguous results, so these results should be interpreted with caution. Further research might give more insights in the dynamic interaction between savings and house prices.
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Table of Contents
Abstract ... 2
1 Introduction ... 4
2 Literature review ... 7
2.1 Household savings and house prices ... 7
2.2 Interest rates and the saving-house price relationship ... 10
2.3 Hypotheses ... 11 3 Data ... 13 3.1 Data description ... 13 3.2 Household savings ... 15 3.3 House prices ... 16 3.4 Macroeconomic variables ... 17 3.5 Validity checks ... 18 4 Empirical methodology ... 20 5 Empirical results ... 21 5.1 Baseline regressions ... 21 5.1.1 Equation-by-equation estimation ... 21 5.1.2 Joint estimation ... 23 5.1.3 Estimation implications ... 26 5.2 Robustness ... 27
5.3 Implications of ignoring the interaction between savings and house prices ... 27
6 Conclusion ... 30
References ... 32
Appendices ... 34
Appendix 1: List of country codes ... 34
Appendix 2: Tables ... 35
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1
Introduction
History suggests that financial crises are often associated with booms and busts of the real estate housing markets (Reinhart & Rogoff, 2008). The most recent financial crisis that started in 2008 is no exception. The burst of the European housing bubble in 2008 did not only strongly affect the economy, governments and financial institutions, but also hit European households. After the burst, house prices fell dramatically and mortgage lending conditions have tightened, making it harder for households to (re-)finance their mortgage. According to the IMF (2015), Denmark, Ireland, the Netherlands and Spain experienced large house price deviations compared to other European countries, of which Ireland and Spain encountered the most severe house price shocks. In these four countries, house prices heavily increased in the 2000-2007 period, partly because of easy financing conditions. After the start of the global financial crisis in the third quarter of 2008, real house prices declined in each of these countries with 25 percent or more.
Housing represents a large fraction of households’ wealth and therefore plays an important role in the consumption and saving behaviour of households (Bostic, Gabriel & Painter, 2009). Existing literature provides evidence for the existence of this link. Engelhardt (1996) was one of the first to examine the effect of house price shocks on the saving behaviour of US homeowners. He found that only house price declines significantly affect savings. A more recent study of CPB Bureau of Economic Policy Analysis (Bijlsma, Mocking & Van Beers, 2015) examined the effect of house price shocks on saving behaviour in the Netherlands and found that the opposite is true for Dutch households: the response to house price increases is stronger than to house price declines. However, the empirical link between house prices and household saving behaviour remains significant. Several other studies found an empirical link between housing wealth and consumption (Cocco & Campbell, 2011; Disney, Gathergood & Henley, 2010), which also links housing wealth to household savings. On the contrary, there are some studies that have found a positive effect of income and financial wealth on house prices (Kranendonk, Toet, Van Leuvensteijn & Verbruggen, 2005). This suggests that savings positively affect house prices.
This study elaborates on these existing studies by examining whether the link between house prices and household savings consists of an interdependent relationship. More specifically, this paper includes the two-way effect of household savings and house prices in both equations and examines the dynamic interaction between these variables. This has not been investigated yet, while it is reasonable to assume that such a two-way relationship could exist. An increase in savings as the result of an exogenous shock (that is, other than an increase in housing wealth) could reduce borrowing constraints for households, which in turn could affect house prices. As existing literature suggests, house price shocks in turn have an effect on savings (Engelhardt, 1996; Bijlsma et al., 2015). It becomes especially interesting when analysing the interest rate effect. Interest rates are a well-known determinant of house prices (Englund & Ionnides, 1997; Goodhart & Hofmann, 2008), but are also
5 taken into account in studies on saving and consumption behaviour (Balta & Ruscher, 2011; Cocco & Campbell, 2011). They have a dual effect on household savings and house prices as they are a proxy for the cost of borrowing (e.g. to construct new housing), but also for earnings on savings. When the house price equation does not allow for savings, the interest rate coefficient could capture both the saving and borrowing effect. Therefore, this study does not only look into the interdependency between household savings and house prices, but also investigates in which extent ignoring this two-way relationship leads to bias in the estimated coefficients on other macro-economic variables, the interest rate in particular.
This study makes use of quarterly panel data on a national level for 18 European countries. The sample period includes the years 2005-2015 to fully capture the house prices shocks on the European housing market before and after the crisis. Figure 1 shows the average house price index and the average savings rate (gross household savings as a fraction of gross disposable income) for the selected European countries. It is clear that both experienced a significant shock at the start of the crisis in 2008. While average house prices dropped, the average savings rate increased substantially.
Figure 1: Average house price index and savings rate over time
Notes: The figure shows the average house price index (2010=100) and savings rate over the period 2005-2015 for 18 European countries.
A panel vector autoregressive (VAR) model is used to examine the existence of a two-way relationship between household savings and house prices. As most of the variables appear to be non-stationary, the model is estimated in first differences. The model is tested with the use of equation-by-equation IV estimation and joint estimation, both based on generalised moments of methods (GMM). This paper discusses which variables are found to be key determinants of both savings and house prices and how ignoring the dynamic interaction between saving and house prices leads to biased
6 results. It is important to note that this studies focuses on the short-run rather than the long-run effects, as it does not make use of an error correction model.
Both estimations show some inconsistency in the results, which means that the results do not provide clear evidence for the magnitude of a two-way effect. However, the results do emphasize the importance of allowing for interdependency between household savings and house prices. The following results are found, based on the joint estimation. A one percent increase in the (log) house prices decreases savings by 16.6 percent, which is in line with findings of previous studies (Engelhardt, 1996; Cocco & Campbell, 2011; Bijlsma et al., 2015). On the other hand, the results show that a one percent increase in savings increases house prices by 0.004 percent. This effect is very small, but is found to be statistically significant. Additionally, there is found strong evidence for momentum effects in both savings and house prices. The autoregressive coefficient on house prices is 0.5 and the autoregressive coefficient on savings is -0.1. This negative lagged effect of savings is quite odd, as it would have been expected to be positive. On the contrary, the equation-by-equation estimate of the autoregressive coefficient on savings is 0.2, which would be more logical. In addition to the two-way and momentum effects, the short-term interest rate and the HICP are found to be key determinants of household savings, and the HICP is found to be a key factor in explaining house prices. Furthermore, the effects of the short-term interest rate and GDP are not only overestimated by 0.3 percentage points and 0.03 percentage points respectively when the house price equation is not correctly specified (i.e. does not account for household savings), they also lose their statistical significance when household savings are included in the model. This is an important result, because it suggests that most of the effect of GDP and the short-term interest rate found in studies on house price dynamics are mostly explained by household savings (Hofmann, 2004; Goodhart & Hofmann, 2008). Nevertheless, these results are rather ambiguous and therefore one should be careful with the interpretation of these coefficient estimates. Further research in the dynamic interaction between household savings and house prices should give more insights in the actual implications of ignoring this relationship.
The results of this paper are relevant for several reasons. First, it is important for academics to know whether this interdependent relationship should be considered when one is examining household savings and house prices. Especially since it could lead to incorrect results of the interest rate coefficient if savings are not included in the house price equation. Furthermore, it is relevant for policy makers and governments to not only know how interest rates affect both savings and house prices, but also how these two variables interact.
The remainder of the paper is structured as follows. Section 2 provides an extensive literature review. Section 3 describes the data used in this study. In section 4, the empirical methodology is explained. Section 5 covers the empirical results and section 6 concludes.
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2
Literature review
This section will discuss relevant literature with regard to the relation between house prices and household savings. First, the existing research on the effect of house price shocks on household savings is discussed. Secondly, the existing research on interest rates and the effect on both savings and house prices is addressed. Thereafter, the two-way relation between savings and house prices is discussed. Finally, the results of previous literature are translated into several hypotheses in order to answer the research question.
2.1
Household savings and house prices
There exists extensive literature on the effect of house price shocks on household saving and/or consumption behaviour with the use of data on household level. However, these papers show slightly different results, which could be caused by differences in measures of savings and house price changes and focus on homeowners and/or renters.
Engelhardt (1996) was one of the first to examine the empirical link between house price shocks and homeowner saving behaviour. With the use of US household data over the 1984-1989 period, he investigated the effect of house price changes on homeowners’ saving behaviour. As a measure of changes in house prices, he used the difference in self-reported house values by homeowners less the value of additions to and repairs of the home made by the household. He made a clear distinction between two types of saving: active saving and passive saving. Active saving is defined as the fraction of income that is not consumed. Passive saving is defined as the real capital gains on existing non-housing assets that are not consumed. Engelhardt (1996) did not find a significant effect of house price shocks on passive household saving, but did find a significant result for active household saving. Another striking result is the asymmetric effect of house price changes: homeowners experiencing real housing capital gains did not change their saving behaviour, while homeowners experiencing real housing capital losses increased their savings.
Savings are often defined as the amount of disposable income that is not used for consumption, which is in line with the definition of active saving used by Engelhardt (1996). This means that savings heavily depend on spending and consumption, which directly links studies on the relation between house prices and consumption behaviour to the relationship between housing wealth and household savings. Campbell and Cocco (2007) investigated in the effect of house price changes on household consumption using household level data from the UK Family Expenditure Survey (FES) for the 1988-2000 period. In their research, they distinguished between households based on age and whether they are renters or homeowners. Their results show that the consumption of older homeowners is more responsive to house price shocks than younger renters, controlling for interest rates, disposable income and other demographic variables. This could also be referred to as the “life-cycle hypothesis”.
8 Another common hypothesis is the collateral hypothesis, which states that younger households experience stronger effects of house price changes because they are more likely to be credit constrained. For example, younger households need to increase their savings when house prices decline in order to still be able to make the down-payments required by the bank when purchasing a new home due to lower housing wealth. These hypotheses are examined by Lehnert (2004) and he has found evidence for both: the highest marginal propensity to consume (MPC)1 is found for the youngest households (age 25 to 34), and the second highest MPC is found for the oldest households (age 63+).
A similar study as Campbell and Cocco (2007) is done by Disney, Gathergood and Henley (2010), who studied the effect of unanticipated housing capital gains on household consumption behaviour in the United Kingdom. They made use of data on individual consumer spending from the British Household Panel Survey and house price data on county-level. They did find deviations in the response of homeowners and renters, but did not find differences between younger and older households, which contrasts with the results of Campbell and Cocco (2007). In addition, Disney et al. (2010) did not find evidence for the asymmetric effect as found by Engelhardt (1996). However, their results show that an asymmetric effect does exist for households with a negative equity position. Households in negative equity have a higher MPC than households in a positive equity position, which could be explained as the relieve of savings as a response to unexpected gains in housing capital.
Recently, the CPB Bureau of Economic Policy Analysis (Bijlmsa et al., 2015) examined the impact of house price shocks on household savings in the Netherlands. They used household level data on Dutch homeowners over the 2006-2011 period. The CPB (Bijlsma et al., 2015) defined savings as the real amount of money that the household holds in a saving account. This does not allow them to distinguish between active and passive saving. House price shocks were measured as the change in the real house price of a household’s home. The CPB study (Bijlsma et al., 2015) focused on both the life-cycle hypothesis and the collateral hypothesis. In this case, the life-cycle hypothesis states that households tend to save more during their early age and consume these savings during their retirement. The collateral hypothesis states that younger households are more affected by changing house prices since they are more likely to be credit constrained. They also incorporated the negative equity position of a household to examine whether these households respond differently to house price shocks. Additionally, they distinguished between house price increases and house price declines to examine the asymmetric effect as found in previous literature (Engelhardt, 1996; Disney et al., 2010). Their results show a significant but weak negative effect of house price shocks on household savings. They found stronger effects for subgroups: the response to house price changes is stronger for younger households than older households, which is most in line with the collateral hypothesis.
1
This also concerns the marginal propensity to save (MPS), since the sum of MPC and MPS must be equal to 1 when it is assumed that a household can only distribute its income to either consumption or saving.
9 This is contrasting to the results of Engelhardt (1996) and Campbell and Cocco (2007), who found a stronger effect for older households. Their results also indicate a stronger effect for households in a negative equity position, which is in line with previous researches of Engelhardt (1996), Campbell and Cocco (2007) and Disney et al. (2010). Finally, the CPB (Bijlsma et al., 2015) has found that the response to house price increases was stronger than the response to house price decreases. This contradicts with the asymmetric effect found by Engelhardt (1996), who did not find any effect of housing capital gains on savings at all. The reason for these contrasting results could be the fact that the CPB (Bijlsma et al., 2015) did not distinguish between active and passive saving in their study.
The studies of Engelhardt (1996), Campbell and Cocco (2007), Disney et al. (2010) and the CPB (Bijlsma et al., 2015) all made use of household level data for the US, the UK or the Netherlands. Balta and Ruscher (2011) examined the relation between mortgage decisions, savings and housing wealth in order to identify the “down-payment channel” in the euro zone. They made use of quarterly data for the 1980-2000 period on euro area level. They stated that household savings might not only be affected by the traditional channel (housing capital gains resulting in lower savings), but also by the down-payment channel. The down-payment channel occurs when house prices increase and households need to increase their savings in order to meet the down-payment requirements by banks. They found that the key determinant of household savings is financial wealth, but that savings is also determined by mortgage levels, net housing worth, the long-term interest rate and inflation. Their results also show that house prices affect household savings in two ways: an increase in house prices increases consumption through the traditional channel, but reduces consumption because of credit constraints, which is referred to as the down-payment channel.
Most of the existing literature focusses on the effect of household savings on house prices. The paper of Kranendonk et al. (2005) examined this relationship the other way around. They investigated which factors explained house price dynamics in the Netherlands in the years 1980-2003 with the use of an error correction model. Their results show that besides the interest rate, real disposable income and financial wealth are key factors in explaining house price dynamics. More specifically, the increase in real disposable income and financial wealth of households in the years 1980-2000 was the most important explanation for the increasing house prices. In addition, housing supply and the CPI (inflation) were also found to be important determinants of house prices. They measured financial wealth as the sum of household savings and other liquid assets less the non-mortgage debt. Stocks were not included in the measure of financial wealth.
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2.2
Interest rates and the saving-house price relationship
Previous studies show that interest rates significantly affect savings. Changes in interest rates can have two effects on consumption: the income effect and the substitution effect (Weber, 1970)2. Weber (1970) concludes that the income effect is greater than the substitution effect, which is supported by the results of Balta and Ruscher (2011), who found that the long-term interest rate has a significant negative effect on savings, and Campbell and Cocco (2007), who found a positive effect of the real interest rate on consumption3.
Interest rates are not only taken into account in explaining household savings, but also in explaining house price movements. Englund and Ioannides (1997) studied house price dynamics in 15 OECD countries and found that house prices are not only significantly explained by their lagged values, but also by the lagged value of GDP growth and the change in real interest rates. Multiple papers looked into the two-way relation between house prices and credit and found significant evidence for the existence of this relationship. Hofmann (2004) investigated this relation in 16 industrialised countries by using a multivariate approach to study the dynamics between property prices, real GDP and real interest rates. His results show that credit is positively related to GDP and real estate, and is negatively related to real interest rates. He measured property prices as the weighted average of residential and commercial property prices. Tsatsaronis and Zhu (2004) studied house price dynamics for 17 industrialised countries. Their results report that there is a strong relationship between house prices on one hand, and nominal interest rates and inflation on the other. Goodhart and Hofmann (2008) analysed the empirical link between money, credit, house prices and macroeconomic activity in 17 industrialised countries using a panel VAR approach. They have found evidence for a strong link between these factors and a significant effect of changes in GDP, the CPI and the interest rate on house prices, credit and money. More specifically, an increase in GDP is found to have a positive effect on house prices, a CPI shock is negatively related to house prices and an increase in the nominal interest rate results in a decline of house prices. Another interesting result is that these effects are found to be stronger when house prices are strongly increasing rather than decreasing.
Table 1 shows a comparison of the most important results found by these previous studies. It is clear that house price shocks significantly affect household savings through several channels. More specifically, Balta and Ruscher (2011) have found evidence for the existence of the “traditional channel” and the “down-payment channel. The traditional channel explains that households will decrease their savings as a response to increases in housing equity. The down-payment channel explains that households will increase their savings when house prices increase as the result of higher down-payment requirements by banks for mortgages. Moreover, there are some studies that allow for
2 The income effect occurs when interest rates increase and households need a lower level of savings in order to
maintain the current level of consumption in the future and thus increase their current consumption. The substitution effect states that saving becomes more attractive than spending when interest rates increase.
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11 an effect of savings when examining house price dynamics by including financial wealth in the house price equation (Kranendonk et al., 2005). This implies that house prices are affected by household savings, and vice versa. However, there are no studies yet that investigate the relation between household savings and house prices as a dynamic process. When this relationship is not taken into account, the estimated effect of other macro-economic variables could be biased. This is especially the case for interest rates, as existing literature shows that interest rates both affect household savings and house prices. Therefore, this study will examine whether there exists a two-way relationship between household savings and house prices and how ignoring this interdependence affects the estimated effects of other macro-economic variables, with the interest rate in particular.
2.3
Hypotheses
Previous studies provide clear evidence of a significant effect of house price shocks on household saving behaviour across a variety of countries. However, there are no studies yet examining the interdependence between these two variables. Ignoring this dynamic relation might lead to biased estimates of other macro-economic factors, particularly interest rates. Interest rates do not only give an indication of the cost of borrowing, which directly affects mortgage demand and therefore house prices, but they also reflect the earnings on savings. Therefore, this study looks into different aspects of the link between household saving behaviour and house price dynamics.
This link is tested with the use of several hypotheses. First, it is tested whether there exists a direct two-way relationship between household savings and house prices. This is the case when not only house price shocks have a significant effect on household savings, but also when shocks in household savings significantly affect house prices. This is translated in the following two hypotheses:
Hypothesis (1): House price shocks significantly affect household savings. Hypothesis (2): Shocks in household savings significantly affect house prices.
Hypothesis (1) has already been tested extensively in previous literature. Some studies have found an asymmetric effect (Engelhardt, 1996; Bijlmsa et al., 2015) of housing capital gains and losses. Moreover, Balta and Ruscher (2011) decomposed the house price effect into two components: the traditional channel, which is a negative relation between household saving and house prices, and the down-payment channel, which reflects a positive relation between the two. However, this study does not decompose the house price effect. Therefore, it is expected that house price shocks negatively affect household savings, which is in line with traditional and general findings of previous literature (see Table 1). Hypothesis (2) has been tested not as extensively as hypothesis (1), but there are some studies who link households’ financial wealth to house prices. Kranendonk et al. (2005) found a positive effect of financial wealth on house prices in the long-run. Therefore, the effect of savings on
12 house prices is expected to be positive. In order to prove there exists a two-way relationship between household savings and house prices, both hypotheses (1) and (2) need to true. Testing the interdependence between savings and house prices is the main contribution of this paper.
Table 1: Comparison of previous studies on household savings and house prices
Article 1 2b 3 4 5f 6 7 8 The effect on household savings of.. House prices −a − −c +/−e Interest rates − − GDP +d Inflation − The effect on house prices of..
Financial wealth + Interest rates − − − − GDP + + +𝑔 Inflation − + Credit/lending + + + Sample period 1984-1989 1988- 2000 2006-2011 1980-2008 1980-2001 1990-2003 1973-2006 1980-2003 Data level US House-hold UK House-hold Dutch House- hold Euro area level Country level, 16 countries Country level, 17 countries Country level, 17 countries Country level, 1 country Methodology OLS OLS OLS/
RE/FE VAR VAR VAR
Panel
VAR ECM Notes: + indicates a positive effect, - indicates a negative effect
Articles:
1. Engelhardt (1996) 2. Campbell & Cocco (2007) 3. Bijlsma et al. (2015) 4. Balta & Ruscher (2011) 5. Hofmann (2004) 6. Tsatsaronis & Zhu (2004) 7. Goodhart & Hofmann (2008) 8. Kranendonk et al. (2005)
Comments:
a. Assymmetric response: only households experiencing housing capital losses increase their savings.
b. Cambell & Cocco examined the effect on consumption.
c. Asymmetric response: stronger response to house price increases compared to house price declines.
d. Bijlsma et al. (2015) included real disposable income on household level. e. Balta & Ruscher (2011) found both a positive and negative effect of house
price changes on household savings.
f. Hofmann (2001) examined the relation between credit and property prices, including commercial real estate prices.
g. Kranendonk et al. (2005) include the average real disposable income of households.
13 Furthermore, it is interesting to see what the effect is on the estimates of other macro-economic variables in both the saving and house price equation when one does not account for this two-way effect. This results in the following hypotheses:
Hypothesis (3): Excluding house prices in the saving equation gives incorrect
estimates of the coefficients on other macro-economic variables,
interest rates in particular.
Hypothesis (4): Excluding household savings in the house price equation gives
incorrect estimates of the coefficients on other macro-economic
variables, interest rates in particular.
By testing hypothesis (3), it will become clear what the implications are for other coefficients in the model when house prices are not incorporated in the saving equation. This is in particular interesting for the interest rate coefficient. As mentioned earlier, the interest rate plays an important role in determining household savings and house prices. If one does not account for house prices in the saving equation, it is expected the interest rate coefficient is overestimated as interest rates typically have a negative effect on both savings and house prices (see Table 1). This is also expected when savings are excluded as a determinant in explaining house prices, which is testing with the use of hypothesis (4).
By testing these four hypotheses, the research question whether there exists a two-way relationship between household savings and house prices can be answered.
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Data
This study investigates whether there exists a two-way relationship between household savings and house prices. The panel data includes information on household savings, house prices, GDP, interest rates and inflation. The sample includes quarterly data on the 2005-2015 period to fully capture the house price fluctuations on the European housing market before and after the burst of the housing bubble in 2008. This section discusses the data sources and data preparation, and provides descriptive statistics of the dataset.
3.1
Data description
The most relevant variables in this study are the measures of household savings and house prices, which are both provided by Eurostat. These variables are also the most limiting variables as they are not available for all European countries. This is especially the case for eastern European countries like Hungary, Estonia and Slovakia, and relatively small countries like Malta and Cyprus. Therefore, the final dataset includes the following 18 countries: Austria, Belgium, Czech Republic,
14 Germany, Denmark, Spain, Finland, France, United Kingdom, Greece, Croatia, Ireland, Italy, Netherlands, Norway, Portugal, Slovenia and Sweden. Data on interest rates in Eurostat is quite limited. Therefore, interest rates are complemented with data provided by the OECD as both databases use the same definition of interest rates. This resulted in a fully balanced dataset. Data on other macro-economic variables as GDP and inflation are also available in Eurostat.
As household savings and house prices are the main variables of interest, all observations with missing values of gross household savings or house price index (HPI) are dropped from the sample. Furthermore, all countries with less than 3 years (12 quarters) of data are excluded from the sample. It is important to note that for Austria, Croatia and Italy only data after the start of the 2008 financial crisis is available. The descriptive statistics of the levels of household savings, house prices, GDP, the long- and short-term interest rate and inflation are provided in Table 2. Table 3 provides the summary statistics of the differenced (log) variables.
Table 2: Household savings, house prices and other macro-economic variables (levels)
Variable Mean Std. Dev. Min Max
Savings (in millions) 15,123 21,562 35 97,538
House prices (index) 100.0 12.7 66.8 151.7
GDP (in millions) 189,525 206,262 7,944 772,920 Long-term interest rate (%) 3.52 1.78 0.31 15.50 Short-term interest rate (%) 1.69 1.63 -0.47 6.60
HICP (index) 94.2 5.4 77.2 103.1
Inflation (%, quarterly) 0.05 2.55 -22.77 3.72
Sample period 2005Q1-2015Q4
Number of countries 18
Number of observations 641 (quarterly data)
Table 3: Household savings, house prices and other macro-economic variables (differences)
Variable Mean Std. Dev. Min Max
∆ log savings 0.0012 0.9062 -4.1169 4.0461
∆ log house prices (index) 0.0040 0.0230 -0.0842 0.1325
∆ log GDP 0.0069 0.0517 -0.1928 0.1212
∆ long-term interest rate (%) -0.0567 0.5192 -2.0267 4.4633 ∆ short-term interest rate (%) -0.0707 0.4391 -2.5346 0.6800 ∆ log HICP (index) 0.0043 0.0080 -0.0195 0.0365 ∆ inflation (%, quarterly) 0.3865 2.8596 -3.8659 23.7645 Sample period 2005Q1-2015Q4
Number of countries 18
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3.2
Household savings
Household savings are measured as gross saving. Eurostat provides this measure of savings on a national and quarterly level for a selection of European countries. Balta and Ruscher (2011) also used this measure of household savings on EU-level in their study and is also a form of active saving, in line with the study of Engelhardt (1996). Gross household saving is defined as the difference between gross national disposable income and final individual consumption expenditures and is the sum of all gross savings of individuals and institutions in the household sector. The household sector consists of all households, household firms and non-profit institutions serving households. The advantage of using gross household saving is that is does not incorporate changes in housing wealth as a part of savings. Moreover, households’ savings in pension funds reserves are also not included in the measure of saving, since these kind of savings might be less sensitive to (short-term) economic conditions. This could mean that savings in countries with large pension funds have lower savings than one would initially expect. The countries with the largest pension funds in terms of assets in Europe are the Netherlands and the UK (OECD, 2015). Figure 2 shows the average savings rate (savings as a fraction of gross disposable income) over the 2005-2015 period. It shows that Greek households relatively saved the smallest fraction of their income (7 percent), and German households relatively saved the highest fraction of their income (17 percent). Figure 1 in Appendix 3 shows the saving behaviour of households in the 18 selected countries over time.
As can be seen in Table 3, average quarterly savings growth over the entire sample period is 0.12 percent. Table 4 presents the average quarterly growth of household savings per country. Portugal has the highest average quarterly growth rate of 7.6 percent. Greece has the lowest average growth in household savings with an average growth rate of -6.4 percent. Table 4 does not give a clear view on whether household saving behaviour has changed due to the 2008 financial crisis. Figure 1 shows a large increase in the savings rate in 2008, but the overall growth rate of savings after the start of the crisis is -1.5 percent versus an average growth rate of 5.6 percent before the start of the financial crisis4.
4
16 Figure 2: Average household savings as a fraction of disposable income per country
Notes: The figure shows the average savings rate (savings as a fraction of gross disposable income) per country over the period 2005-2015.
3.3
House prices
House prices are measured with the use of the nominal house price index (HPI). The year 2010 is the base year (index = 100). The HPI provided by Eurostat measures the price changes of all residential properties per country which are purchased by households. It includes both new built and existing houses and does not depend on the final use or the previous owner of the property. The HPI is available from 2005Q1 onwards and is a good measure of house prices as it allows us to properly compare house prices of different European countries. Table 4 reports the average quarterly return on housing per country. Sweden has experienced the highest average quarterly returns on housing of 1.7 percent. Croatia and Italy have the lowest average return of -0.7 and -0.6 percent respectively. However, this is only based on the 2012-2015 period. Spain has the lowest average return (-0.6 percent) over the entire sample period. Figure 2 in Appendix 3 presents the house price index per country over the 2005-2015 period. The figure clearly shows the increase in house prices from 2005Q1 until 2008Q3 and a significant drop in the house price index after the start of the financial crisis.
17 Table 4: Average quarterly return on housing and growth of savings
Average growth of savings Average return on housing
Country Total period Before crisis After crisis Total period Before crisis After crisis
Austria 0.029 0.029 0.014 0.014 Belgium -0.010 0.048 -0.036 0.009 0.019 0.004 Czech Republic 0.006 -0.230 0.014 0.001 0.040 0.000 Germany 0.001 -0.003 0.003 0.004 -0.001 0.007 Denmark -0.064 -0.047 -0.071 0.006 0.029 -0.004 Spain 0.012 0.038 0.005 -0.006 0.026 -0.014 Finland 0.013 0.094 -0.023 0.007 0.014 0.004 France -0.016 0.015 -0.024 0.002 0.011 -0.001 United Kingdom -0.004 0.031 -0.019 0.009 0.015 0.006 Greece -0.011 -0.001 -0.016 0.003 0.015 -0.004 Croatia 0.002 0.002 -0.007 -0.007 Ireland -0.039 0.087 -0.088 -0.004 0.019 -0.013 Italy 0.023 0.023 -0.006 -0.006 Netherlands 0.019 0.130 -0.029 -0.001 0.010 -0.005 Norway 0.005 -0.056 0.031 0.015 0.023 0.011 Portugal 0.076 2.558 -0.007 -0.002 0.003 -0.002 Slovenia -0.016 0.007 -0.020 -0.005 0.022 -0.009 Sweden 0.017 0.118 -0.028 0.017 0.025 0.014
Notes: The total period comprises the years 2005-2015. The period before the crisis contains the 2005Q1-2008Q2 period and the period after the crisis is based on the 2008Q3-2015Q4 period. Austria, Croatia and Italy only have data available after the start of the 2008 financial crisis (that is, after 2008Q3).
3.4
Macroeconomic variables
Gross domestic product (GDP), interest rates and inflation serve as control variables in this study and are considered to be exogenous. Both the long-term and short-term interest rate are included in the analysis. The long-term interest rate is the yield on government bonds with a maturity of ten years. The short-term interest rate is the three-month money market interest rate. The interest rate is the most important exogenous variable since it serves both as a proxy for earnings on savings and the cost of borrowing. Greece and Portugal have the highest average long-term interest rate of 6.3 and 5.9 percent respectively. The long-term interest rate is the lowest in Austria and Germany with 2.2 and 2.6 percent respectively. Austria and Italy have the lowest average short-term interest rate of 0.53 percent. The average short-term interest rate was the highest in Norway and Greece with 2.9 and 2.7 percent respectively.
The average quarterly GDP growth for all the countries is 0.7 percent. The countries with the highest quarterly growth in GDP are Austria and Sweden, which both have an average quarterly GDP growth of 1.1 percent. Spain and Greece have the lowest average growth rate of 0.3 and -0.1 percent respectively. Inflation is measured with the use of the harmonized index of consumer prices (HICP),
18 which measures the changes in prices of consumer goods and services acquired by households. The advantage of the HICP is that it provides a comparable measure of inflation in European countries. The countries with the highest (quarterly) average inflation are Greece (0.9 percent) and the UK (0.5 percent). Inflation is the lowest in Austria (-0.01 percent) and Ireland (0.2 percent).
3.5
Validity checks
All variables in the model need to be integrated I(1), or stationary. Variables like house prices and GDP often tend to be non-stationary. Therefore, all series are tested for a unit root with the use of a Fisher-type unit root test based on the Augmented Dickey Fuller test. The Fisher-type unit root test conducts unit root tests for each panel individually and combines the p-values in one test afterwards. The null hypothesis states that all panels contain unit roots, which is rejected when at least one panel is stationary. All tests include one lag. Both the level and differenced variables are tested with and without a trend. The results of the unit root test are reported in Table 5 and report the inverse squared and the corresponding p-values. The inverse normal, inverse logit t and modified inverse chi-squared provide approximately the same results.
Table 5 shows that whether a trend is included in the unit root test significantly influences the test results of the level variables. Most of the level variables without a trend have at least one panel that is stationary at a significance level of 1 percent, except for log house prices, the long-term interest rate and the log HICP. However, when a trend is included, only the log of savings has at least one panel that is stationary at this significance level. The differenced variables all contain at least one panel that is stationary at the 1 percent significance level, both with and without a trend. The results of the unit root tests provide evidence that some level variables are non-stationary, but are stationary in the first difference. Therefore, the first difference of the variables will be used in the analysis.
19 Table 5: Fisher-type Dickey Fuller panel unit root test
Variable Specification Inverse chi-squared P-value Log savings Levels (without trend) 361.31 0.0000 ***
Levels (with trend) 394.31 0.0000 *** Differences (without trend) 692.30 0.0000 *** Differences (with trend) 590.50 0.0000 *** Log house prices Levels (without trend) 15.99 0.9984
Levels (with trend) 24.62 0.9243 Differences (without trend) 220.47 0.0000 *** Differences (with trend) 193.51 0.0000 *** Log GDP Levels (without trend) 51.60 0.0445 **
Levels (with trend) 55.33 0.0207 ** Differences (without trend) 432.55 0.0000 *** Differences (with trend) 354.71 0.0000 *** Long-term interest rate Levels (without trend) 31.65 0.6755
Levels (with trend) 21.18 0.9765 Differences (without trend) 300.15 0.0000 *** Differences (with trend) 253.95 0.0000 *** Short-term interest rate Levels (without trend) 102.18 0.0000 *** Levels (with trend) 63.37 0.0032 *** Differences (without trend) 127.99 0.0000 *** Differences (with trend) 86.71 0.0000 *** Log HICP Levels (without trend) 33.71 0.5778
Levels (with trend) 31.93 0.6625 Differences (without trend) 227.80 0.0000 *** Differences (with trend) 195.27 0.0000 *** Inflation Levels (without trend) 553.04 0.0000 *** Levels (with trend) 509.15 0.0000 *** Differences (without trend) 973.64 0.0000 *** Differences (with trend) 890.10 0.0000 *** Notes: cross-sectional mean removed from the level variables by using demeaned level variables. The null hypotheses states that all panels contain unit roots with the alternative that at least one panel is stationary. All unit roots test include one lag. ***, ** and * represent 1%, 5% and 10% significance respectively.
20
4
Empirical methodology
The following panel vector autoregressive (VAR) model will be estimated with the change in household savings (𝑆𝑖,𝑡) and house prices, (𝐻𝑖,𝑡) as dependent variables:
(1) [∆ log 𝐻∆ log 𝑆𝑖,𝑡 𝑖,𝑡]=[ 𝛼1,𝑡 𝛼2,𝑡] + [ 𝛽1 𝛾1 𝛽2 𝛾2] [ ∆ log 𝑆𝑖,𝑡−1 ∆ log 𝐻𝑖,𝑡−1] + [ 𝛿1 𝛿2] ∆𝑋𝑖,𝑡+ [ 𝜀1𝑖,𝑡 𝜀2𝑖,𝑡]
where αt are year fixed effects and εi,t are the errors. Vector Xi,t comprises the log gross domestic
product (gdpi,t), the long-term interest rate (lri,t), the short-term interest rate (sri,t), and the log
harmonized index of consumer prices (hicpi,t). These variables are considered to be exogenous.
There are several advantages of using a panel VAR model (Canova and Ciccarelli, 2013). They can include lags of all endogenous variables for all units 𝑖, which is referred to as “dynamic interdependences”. Additionally, the panel VAR model can capture static interdependences, which is the correlation of 𝜀𝑖,𝑡 across variables.
As described in Section 3.5, differenced values are used because of non-stationarity in some of the variables. Differenced values are used for the long-term interest rate, the short-term interest rate and differenced log values are used for the variables savings, house prices, GDP and the HICP. One lag of the dependent variables is included in the analysis based on several panel VAR lag-order selection criteria (see Appendix 2, Table 2). Anderson and Hsiao (1981) found that in dynamic models with panel data an instrumental variable approach produces more consistent estimators as the lagged dependent variable is not strictly exogenous. Arellano (1989) has shown that using lagged differences as instruments produces an estimator with a large variance, and Arellano and Bond (1991) have shown that using instruments in levels results in a more efficient estimator with smaller variances. This is referred to as the “Arellano-Bond” estimator. Therefore, these lagged components of household savings and house prices are instrumented with their second, third and fourth lagged levels.
The coefficients 𝛽1 and 𝛾2 are the dynamic interdependences of gross household savings and house prices and are expected to be positive. The coefficients 𝛽2 and 𝛾1 capture the two-way effect of
(lagged) household savings and house prices. Previous research has shown that savings are negatively affected by house prices. Therefore, the 𝛾1 coefficient is expected to be negative. The 𝛽2 coefficient
indicates how savings affect house prices. This coefficient is expected to be positive as higher savings could reduce borrowing constraints for households, which in turn positively affects house prices. If this is true, it is expected that the coefficients on the interest rates are overestimated when savings are not included in the house price equation.
First, the model (1) is estimated by instrumental variable estimation, based on two-stage least squares (IV/2SLS) estimation and generalised moments of methods (GMM) estimation. The difference between these two estimations is that the GMM estimator brings the advantage of efficient
21 estimates when there is arbitrary heteroskedasticity, while IV/2SLS estimation does not. Additionally, equation (1) is jointly estimated based on GMM. The difference between joint and equation-by-equation estimation is that joint estimation allows for cross-correlation between (the errors terms of) the equations while equation-by-equation estimation does not. The check the robustness of these results, the dependent variable of saving is replaced by the household savings rate. Finally, single equations are estimated with the use of IV/2SLS and GMM to examine the bias in the coefficients as a result of ignoring the two-way effect of household savings and house prices.
5
Empirical results
In this section, the existence of the two-way relationship between household savings and house prices is tested with the use of various estimations. First, the baseline regressions results are discussed. Second, the robustness of these results is checked. Finally, the implications of ignoring the two-way relationship in both the saving and house prices equation is discussed.
5.1
Baseline regressions
5.1.1 Equation-by-equation estimation
The main regressions results based on equation (1) are provided in Table 6. Column 1 shows the regressions results of the 2SLS estimation of equation (1) and column 2 shows the GMM estimation results. Both estimations include the full set of macro-economic variables, which are GDP, the long- and short-term interest rate and the HICP (inflation), and both lagged dependent variables of household savings and house prices in order to identify the existence of a two-way relationship. It is important to note that the results in Table 1 show the short-term rather than the long-term effects on household savings and house prices.
The results show that changes in GDP have a significant negative effect on house prices across European countries. However, GDP does not seem to be of great influence in explaining household savings as it has a positive, significant effect in column 1 but loses its statistical significance in column 2. This is also true for the long-term interest rate. Moreover, the long- and short term interest rates do not seem to be key determinants of average house prices in both estimations. Based on previous literature, it would have been expected that the interest rate has a significant negative effect on house prices. However, only the sign of the long-term interest rate coefficient is negative and both effects do not turn out to be statistically significant. The statistical insignificance of the long-term interest rate coefficient could have been expected, as this study focusses on the short-term rather than the long-term effect on savings and house prices. However, the coefficient on the short-term interest rate would have been expected to be significant. A possible explanation could be that quarterly changes on national level are relatively small such that they do not
22 influence house prices. As expected, the HICP turns out to have a positive and statistically significant effect on both household savings and house prices.
Based on different IV heteroskedasticity tests, arbitrary heteroskedasticity seems to be present in both the 2SLS and GMM estimation (see Appendix 2, Table 2). This would mean that the GMM estimation results in column 2 are more efficient, although the two estimates do not show striking differences in the effects of the macro-economic variables. The results show that the short-term interest rate and the HICP are key determinants of household savings. However, their estimated coefficients are rather odd as they are unusually large. A one percentage point increase in the short-term interest rate, decreases households savings by 30.3 percent. Furthermore, a one percent increase in the HICP, increases household savings 44.5 percent. GDP and the HICP are key factors in explaining house prices, even though their effects are relatively small. A one percent increase in GDP, decreases house prices by 0.04 percent. This is unexpected, as Table 1 shows that previous studies mostly found a positive effect of GDP (and disposable income) on house prices. Additionally, a one percent increase in the HICP increases house prices by 0.5 percent.
The evidence for momentum in house prices is quite strong, as a one percent increase in house prices at time 𝑡 significantly positively affects house prices at time 𝑡 + 1 by 0.7 percent. The same is true for households savings. Column 2 shows that a one percent increase in household savings at time 𝑡 increases savings at time 𝑡 + 1 with 0.2 percent. The most interesting estimates are the coefficients on the lagged house price variable in the saving equation and the coefficient on the lagged household saving variable in the house price equation. As expected, house prices have a lagged negative effect on household savings, which is statistically significant. A one percent increase in house prices at time 𝑡 decreases household savings at time 𝑡 + 1 by 7.2 percent. Moreover, household savings seem to have an effect on house prices. A one percent increase in household savings at time 𝑡 increases house prices by 0.003 percent in the next quarter. Even though this is a very small effect, it is statistically significant. This is important as it shows that household savings are of some influence in determining house prices, while they are typically not incorporated directly in the house price equation. Finally, the results in column 2 show a quite low or even negative centred R-squared. This is not a rare result in IV estimation and is not a cause for worry, as the R-squared typically has no natural interpretation in IV estimation (Wooldridge, 2015).
23 Table 6: The two-way relationship between household savings and house prices:
Panel VAR (1) (2) (3) 2SLS GMM Joint estimation ∆ log saving [t] ∆ log house price [t] ∆ log saving [t] ∆ log house price [t] ∆ log saving [t] ∆ log house price [t] ∆ log saving [t-1] 0.072 0.003* 0.208** 0.003* -0.111* 0.004*** (0.155) (0.002) (0.102) (0.002) (0.057) (0.001) ∆ log house price
[t-1] -7.144*** 0.611*** -7.150*** 0.705*** -16.573*** 0.526*** (2.320) (0.117) (2.318) (0.083) (4.775) (0.095) ∆ log GDP [t] 3.058** -0.055** 2.236 -0.036* 1.405 -0.023 (1.558) (0.026) (1.521) (0.020) (1.033) (0.022) ∆ long-term interest rate [t] -0.113* -0.001 -0.067 -0.001 0.045 -0.000 (0.069) (0.002) (0.056) (0.002) (0.129) (0.002) ∆ short-term interest rate [t] -0.237* 0.004 -0.303*** 0.003 -0.385** 0.003 (0.130) (0.003) (0.104) (0.003) (0.186) (0.004) ∆ log HICP [t] 46.445*** 0.613*** 44.484*** 0.538*** 0.418*** 0.005*** (11.803) (0.202) (11.661) (0.155) (0.064) (0.001)
Year fixed effects Yes Yes Yes Yes Yes Yes Number of
observations 522 522 522 522 522 522
Centred R2 0.130 0.246 -0.056 0.197 . .
Notes: The dependent variables are the differenced log saving and log house prices. All estimations include the differenced lagged variables of both saving and house prices, which are instrumented by their second, third and fourth lagged levels. The differenced log GDP, long- and short-term interest rate and log HICP are included as exogenous variables. Clustered (country) robust standard errors in parentheses. ***, **, * represent 1%, 5% and 10% significance respectively.
5.1.2 Joint estimation
Equation (1) is also jointly estimated with the use of GMM of which the estimates are summarized in column 3 of Table 6. The main advantage of joint estimation over equation-by-equation GMM is that it allows for cross-equation-by-equation correlation, which should not affect the consistency of the GMM estimator but may result in efficiency gains (Holtz-Eikin, Newey and Rosen, 1988). In other words, severe changes in the sign and magnitude of the estimates are not expected. This is the true for some of the variables, but there appear to be some serious differences. The effect of the long- and short-term interest rate in the house price equation have not changed and remain statistically insignificant. The short-term interest rate coefficient in the saving equation has slightly increased in magnitude from -0.30 to -0.39 and is still statistically significant. This remains an unusually large effect. The coefficient on the long-term interest rate in the saving equation has however changed in sign, from -0.07 to 0.05, but remains statistically insignificant. Furthermore, the effect of a one percent change in GDP on savings decreases by 0.8 percentage points, but remains insignificant. The
24 GDP coefficient in the house price equation has slightly decreased in magnitude to -0.02 but loses its statistical significance. Although the effect of the HICP remains statistically significant, the size of the effect has decreased enormously and has now a more natural interpretation. A one percent increase in the HICP, increases savings by 0.4 percent and house prices by 0.005 percent. Additionally, the effect of house prices on savings is larger than in the equation-by-equation estimation, but is still negative and statistically significant. A one percent increase in house prices at time 𝑡 decreases savings at time 𝑡 + 1 by 16.6 percent (compared to 7.1 percent). The effect of savings on house prices has not changed much (increased by 0.001 percentage points) and also remains statistically significant. While the autoregressive coefficient on house prices has only slightly decreased by 0.2 percentage points, the lagged effect of savings has quite changed. Even though the coefficient on lagged saving remains statistically significant, a one percent increase savings at time 𝑡 has now a negative effect on savings at time 𝑡 + 1 of 0.1 percent. This means that the lagged effect of savings not only decreased 0.1 percentage points in magnitude, but also changed in sign, which is quite an uncommon result.
Even though the jointly estimated results seem to be not entirely consistent, the two-way effect of household savings and house prices remains significant. Furthermore, the joint estimation allows us to create impulse response functions. Table 7 shows the pairwise Granger-causality Wald-test results based on the jointly estimated panel VAR model. The table shows that house prices not only Granger-cause household savings, but that savings also Granger-cause house prices. This emphasizes the importance of including the two-way relationship between household savings and house prices in both equations. Section 5.3 discusses the implications for the estimates of other macro-economic variables when this two-way effect is excluded in the analysis.
Table 7: Panel VAR Granger-causality Wald test
X granger causes Y Chi-squared P-value logS
→
logH 12.045 0.001 logH→
logS 7.332 0.007 Note: the null hypotheses states that Y does not Granger-cause X, with the alternative that Y Granger-causes XWith the use of impulse response functions, the impact of shocks in household savings and house prices in the system of dynamic equations can be examined. In order to create impulse response functions, the model needs to be stable. Figure 3 shows the eigenvalues of the joint estimation of the panel VAR model. For the panel VAR model to meet the stability condition, all eigenvalues need to lie inside the unit circle. As shown in the figure, the panel VAR model meets this stability condition. This is important as stability also implies stationarity of the VAR process and that the model is correctly specified.
25 Figure 3: Stability of the panel VAR model
Notes: The figure displays the eigenvalues of the jointly estimated panel VAR model as reported in Table 6. The panel VAR model meets the stability condition if all eigenvalues lie inside the unit circle.
The cumulative impulse response functions are shown in Figure 4. They show the interaction between household savings and house prices over time, based on the results of the joint estimation of the panel VAR model as presented in Table 6, column 3. Simple impulse response functions show the effect of a one unit increase on other shocks over time, holding all other variables constant. However, in this case the (errors terms of both) equations are correlated. Therefore, Figure 4 presents the orthogonalised impulse response functions. These are based on a Cholesky decomposition with household savings ordered first to allow for an immediate effect on house prices. The robustness check shows that changing the ordering does not have a substantial effect on the results (see Figure 3, Appendix 3).
The impulse response functions show some interesting results about the long-run effect of a one unit shock in both household savings and house prices. Note that the long-run effect here is based on a horizon of 8 quarters (2 years). A one unit shock in household savings, which is a shock of one percent, has a long-run effect on household savings of (approximately) 0.6 percent and a long-run effect on house prices of 0.1 percent. A one percent change in house prices has a long-run effect of 0.03 percent and -0.5 percent on house prices and household savings, respectively. This shows that the momentum effect in house prices is very close to zero. What is interesting, is that the effect of a one unit shock in both household savings and house prices on savings seems to weaken over time, while the effect on house prices slightly amplifies. Moreover, a one unit exogenous shock in (log) saving is
26 equivalent to a 0.03 percentage point change in the short-term interest rate and a 2.4 percent change in the HICP5. For house prices, a one unit shock is equivalent to a 200 percent increase in the HICP.
Figure 4: Cumulative orthogonalised impulse response functions of household savings and house prices
Notes: The figure displays the cumulative orthogonalised impulse response functions based on the jointly estimated model as reported in Table 3, column 3. The horizon is 8 periods (quarters). The Cholesky ordering is: log saving, log house price.
5.1.3 Estimation implications
It would have been expected that the equation-by-equation and joint estimation give consistent estimates of the coefficients. However, there seem to be some significant differences between both estimates. The jointly estimated coefficients in Table 6, column 3 show some unusual results. The autoregressive coefficient on savings in the saving equation has a negative value of -0.1, while the equation-by-equation estimation shows a positive autoregressive coefficient on saving of 0.2, which seems a more reasonable result. However, the equation-by-equation estimate of the coefficient on the HICP in the saving equation is unusually large. A one percent increase in the HICP increases household savings by 44.5 percent. The jointly estimated coefficient has a more logical interpretation, as it shows that a one percent increase in the HICP increases savings by 0.4 percent. Moreover, both estimations show a very large effect of changes in the short-term interest rate on saving. A one percentage point increase in the short-term interest rate decreases savings by 30.3
5
A one unit shock in log saving is equivalent to 1 / 0.418 = 2.4 percent change in the HICP (see Table 6, column 3).
27 percent according to the equation-by-equation estimates, and by 38.5 percent according to the joint estimation results. This suggests that both estimations might not be completely accurate and one should be careful with the interpretation of the coefficient estimates shown in Table 6.
5.2
Robustness
To check the robustness of the estimation results in section 5.1, equation (1) is estimated with the use of the same IV and joint estimation approach. However, the savings rate is now the dependent variable in the saving equation. The savings rate is defined as gross household saving normalized by gross national disposable income. This type of measure is also often used in literature on household savings and might influence the estimation results as it could have a more normalized pattern (Balta & Ruscher, 2011). The regression results are shown in Table 8.
The results in column 1 and 2 are not very different from column 1 and 2 in Table 6. All the coefficients remain the approximately the same in sign and statistical significance. The main differences are the coefficients on GDP in the saving equations. The coefficients are much smaller and GDP is no longer statistically significant in the saving equation in column 1. This is expected, since the savings rate variable depends on gross national disposable income, which in turn is closely related to GDP. Most of the results in column 3 are comparable to the results in column 3 of Table 6, except for the short-term interest rate. The short-term interest rate has now a positive but insignificant effect on the savings rate. On the contrary, the coefficient on the short-term interest rate on house prices has only increased by 0.005, but is now statistically significant. This implies that the interest rate effect is rather sensitive to how household savings are defined.
5.3
Implications of ignoring the interaction between savings and house prices
The results in section 5.1 and 5.2 provide reasonable evidence in favour of the two-way relationship between household savings and house price. In line with previous literature, house prices have a negative effect on household savings. On the other hand, household savings turn out to have a positive effect on house prices which is in line with expectations. Since there is found to be statistical evidence for the possible existence of this relationship, it is interesting to see how this leads to biased results when the two-way effect is ignored in the specification.Table 9 shows the IV/2SLS and GMM estimates without accounting for the two-way relationship between household savings and house prices. That is, the table shows the estimates when house prices are excluded from the saving equation and the estimates when household savings are excluded from the house price equation. It is assumed that the full model including the two-way effect is the correctly specified model.
28 Table 8: Replacing the dependent variable in the saving equation by the
household savings rate
(1) (2) (3) 2SLS GMM Joint estimation ∆ log savings rate [t] ∆ log house price [t] ∆ log savings rate [t] ∆ log house price [t] ∆ log savings rate [t] ∆ log house price [t]
∆ log savings rate
[t-1] 0.044 0.003 0.196* 0.003* -0.152*** 0.004*** (0.148) (0.002) (0.109) (0.002) (0.059) (0.001) ∆ log house price
[t-1] -6.775*** 0.614*** -6.294*** 0.710*** -20.108*** 0.429*** (2.138) (0.118) (2.129) (0.084) (4.020) (0.092) ∆ log GDP [t] 1.987 -0.057** 0.975 -0.039* 2.871*** 0.007 (1.407) (0.026) (1.356) (0.020) (0.778) (0.021) ∆ long-term interest rate [t] -0.109* -0.001 -0.061 -0.001 0.087 0.001 (0.063) (0.002) (0.054) (0.002) (0.120) (0.002) ∆ short-term interest rate [t] -0.199 0.004 -0.303*** 0.004 0.149 0.008* (0.122) (0.003) (0.114) (0.003) (0.137) (0.004) ∆ log HICP [t] 41.437*** 0.606*** 34.779*** 0.531*** 0.326*** 0.004*** (10.772) (0.202) (10.363) (0.155) (0.051) (0.001)
Year fixed effects Yes Yes Yes Yes Yes Yes Number of
observations 522 522 522 522 522 522
centred R2 0.135 0.245 -0.087 0.195 . .
Notes: The dependent variables are the differenced log savings rate and log house prices. All estimations include different lagged dependent variables, which are instrumented by their second, third and fourth lagged levels. The differenced log GDP, long- and short-term interest rate and log HICP are included as exogenous variables. Clustered (country) robust standard errors in parentheses. ***, **, * represent 1%, 5% and 10% significance respectively.
First of all, coefficient on some of the variables already change substantially due to the joint estimation of the model compared to the equation-by-equation GMM estimation including the two-way effect. Therefore it is not appropriate to compare the results in Table 9, column 2 to the jointly estimated results in Table 6, column 3. This concerns the autoregressive effect of savings and the long-term interest rate effect in the saving equation and the HICP coefficients in both the saving and house price equation. The estimated coefficients on these variables in Table 8, column 2 are therefore compared to the GMM estimates in Table 6, column 2. The lagged effect in the saving equation is overestimated by 0.1 percentage points when the model is not correctly specified. The coefficient on the long-term interest rate in the saving equation remains approximately the same and statistically insignificant. The effect of the HICP on savings and house prices is overestimated by 1.4 and 0.1 percentage points respectively in the misspecified model.
