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Consumption, house prices and credit constraints:
an Euler equation approach
Michiel van der Veen
1Master Thesis Economics EBM877A20.2017-2018.2 June 08, 2018
Abstract
Since housing assets can be used as collateral, house price increases have the potential to loosen the binding borrowing constraints of indebted households. This study is conducted to analyze whether this can explain the
observed correlation between aggregate household consumption and house prices in the Netherlands. To investigate this, an aggregate consumption Euler equation is estimated using macro data for the period 1996Q1
to 2017Q4. The results suggest that aggregate household consumption responds to predictable changes in the current house price. Moreover, a non-negligible proportion of Dutch aggregate consumption originates from credit
constrained households. Nevertheless, it is found that the borrowing capacity of credit constrained households is not determined by the value of its housing assets. Hence, credit constraints do not seem to be an explanation for
the consumption - house prices correlation in the Netherlands.
JEL Classification: C26, E21, R2
Keywords: House prices, consumption, credit constraints
1 Michiel van der Veen. MSc student Economics, Faculty of Economics and Business, University of Groningen, Groningen, The Netherlands.
Email address: m.van.der.veen.26@student.rug.nl
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1. Introduction
This study is motivated by the observed co-movement between the housing market and real gross domestic output (GDP) in the Netherlands during the last two decades. Specifically, the house price index of Statistics Netherlands (CBS) and household domestic consumption exhibit a correlation
of roughly 0.572 between 1996 and 2018.2 This correlation observed in the Netherlands is by no
means unique. According to Browning et al (2013), the extant literature finds substantial evidence in favor of a sensitivity of aggregate consumption to house price fluctuations. Nevertheless, they also argue that the literature disagrees about the explanation for this link. As will be illustrated below, the empirical literature finds contradictory evidence when trying to explain the consumption – house price association. To see why, let this study proceed by outlining the most common explanations put forward for the observed correlation between house prices and aggregate consumption.
As Campbell & Cocco (2007) state, it is tempting to attribute this correlation to a direct housing wealth effect. The direct housing wealth effect implies that economic agents allocate part of an increase in housing wealth to all categories of goods they currently consume, such that also non-housing consumption is affected. Campbell & Cocco (2007) find evidence in favor of the non-housing wealth effect in the United Kingdom. Using micro data, they are able to confirm that the consumption of older homeowners responds more strongly to house price changes. This provides evidence in favor of the housing wealth channel since young homeowners are expected to consider the increased costs of future housing services resulting from these house price increases (Campbell & Cocco, 2007). Since younger households tend to trade up in the housing market and thus face these higher future costs, they are not expected to spend the increase in wealth.
Various other studies also find empirical evidence in favor of a housing wealth effect. Bhatia (1987) finds that the market value of real estate assets is able to predict consumer spending in the United States. Carroll et al (2011) confirm this housing wealth effect in a later US study. Specifically, they find that the immediate marginal propensity to consume out of housing wealth is 0.02, but this can increase to 0.09 as time proceeds. International evidence is also found in favor of a housing wealth effect. For example, Case et al (2005) find that household consumption responds strongly to changes in housing market wealth for a panel of 14 countries.
Nevertheless, other plausible explanations cast substantial doubt on the presence of a large direct housing wealth effect. Using a Danish sample, Browning et al (2013) find little evidence for the housing wealth effects after ‘controlling for factors related to competing explanations’ (pp. 401). One such competing explanation is provided by Campbell & Cocco (2007), who argue that the observed correlation between consumption and house prices could be driven by unobserved third factors. This implies that a substantial part of the correlation may be the result of a joint sensitivity to
macroeconomic factors. This is the explanation Attanasio et al (2009) propose. Using the same data as Campbell & Cocco (2007) but a different methodology, they find the exact opposite, that is, younger households tend to respond more strongly to house price changes. Based on reasons
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outlined previously, this can be interpreted as evidence against a housing wealth effect. Instead, Attanasio et al (2009) attribute the observed correlation between house prices and consumption in the United Kingdom to common factors.
King (1990) proposes changes in expected future income as such a common factor. In case agents are able to borrow against expected future income increases, both housing demand and consumption are expected to increase following better future prospects. Given that housing supply is inelastic, house prices increase following higher housing demand (Alessie & Rouwendal, 2002). Attanasio et al (2009) argue that this explains why young households react more strongly to house price changes, since they have a longer remaining life in which these future income changes can occur.
Besides direct wealth effects and common factors, Campbell & Cocco (2007) propose credit constraints as a third explanation for the co-movement between house prices and consumption. Housing usually serves as the most important source of wealth storage for households. Given that lenders generally require protection in case of default, it is not unlikely that some households pledge housing assets as collateral. Moreover, credit suppliers are likely to base their decision on how much to lend on the market value of this collateral. In case a household borrows up to the maximum relative to the value of its assets, he is said to have a binding borrowing constraint. This prevents these households from further increasing their leverage with the intention of transferring future consumption to today. These households are said to be credit constrained. Put differently, although these
households want to transfer consumption to today, they are inhibited by their binding borrowing constraint. As a consequence, house price appreciations may lead to consumption increases, since they loosen binding borrowing constraints. Recent contributions that find empirical evidence in favor of this so-called ‘collateral channel’ are Iacoviello (2004) and Leth-Petersen (2010).
Apart from Case et al (2005) where the Netherlands is included into the panel of countries, none of the above-mentioned contributions considers the Netherlands. To the best of knowledge of the author, there exist relatively few studies that explicitly investigate the impact of house prices on consumption behavior in the Netherlands. One exception is Alessie & Rouwendal (2002) which investigate the impact of house prices on the saving behavior of owner-occupiers. They find evidence in favor of a direct wealth effect of house prices on savings. Specifically, they find that increasing house prices reduced savings for home-owners in the Netherlands for the period 1988 – 1994.
The scarce availability of Dutch evidence on the consumption – house price relationship is one of the motivations for conducting this study. The lack of evidence is surprising in light of the substantial positive correlation that can be observed in recent times. As one of the largest components of GDP, household consumption represents an important measure of the overall economic performance. Moreover, due to its connection to savings, it is related to capital
accumulation and thus future economic growth. Therefore, this study argues that any potential driver of household consumption should be subject to extensive inquiry. This study hopes to increase the availability of empirical evidence for Dutch policymakers regarding the response of consumption to house prices.
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drives this widely documented relationship. Hence, the main objective of this study is to explicitly investigate an explanation for the observed correlation between house prices and consumption in the Netherlands. By doing this, it hopes to contribute to the ongoing discussion in the extant literature. This study chooses to analyze whether the presence of credit constrained households can explain the positive correlation between house prices and aggregate Dutch consumption.
The rationale for investigating credit constraints builds on the fact that Dutch households are the most heavily indebted after the Danish in the entire OECD. Specifically, it can be observed that the Netherlands consistently ranks second in the 1995 – 2016 period (as measured by the annual
household debt to net disposable income ratio).3 Whereas it can also be a sign of well-developed
capital markets, the ratio is compared to other OECD countries which tend to have well-developed capital markets as well. In summary, the main research objective is to investigate whether Dutch aggregate consumption is driven by house prices due to the presence of credit-constrained households. To the best of knowledge of the author, no research has investigated whether credit constraints can explain the observed co-movement in the Netherlands during the two last decades.
Let this study now proceed by outlining the approach to carry out the main research objective. The approach comes from part of the consumption literature that is inspired by the life cycle –
permanent income hypothesis (LC-PIH). Friedman (1957) argues that permanent income is the only relevant income for consumption decisions. This is based on the notion that rational agents efficiently use all available information when making intertemporal consumption decisions. Therefore, rational agents are able to consider all expected lifetime income when making their consumption choice.
Given that all expected future income is considered, an implication of LC-PIH is that rational agents only revise their initial intertemporal consumption choice following unexpected revisions to permanent income. This proposition is outlined in the random walk hypothesis of Hall (1978). Flavin (1981) is the first to retest the random walk hypothesis and finds instead that aggregate consumption is sensitive to anticipated changes in current income. This is called ‘excess sensitivity’ of consumption to current income. The presence of credit constraints is often proposed as the explanation for this excess sensitivity (see e.g. Campbell & Mankiw, 1989 and Jappelli & Pagano, 1989).
Although research on the excess sensitivity of consumption initially focused on current
income, it is by no means limited to current income and can also be applied to house prices4.This is
what Campbell & Cocco (2007) do. They recognize that the housing wealth effect occurs once it can be anticipated and not when the house price change actually occurs. On the other hand, while not causing a wealth effect, an anticipated change in the current house price does relax the borrowing constraint of liquidity constrained consumers (Campbell & Cocco, 2007). Therefore, this study is able to separate the wealth effect from other explanations by investigating predictable changes in the current house price. However, as Campbell & Cocco (2007) note based on the findings of Carroll (1997), precautionary savings or myopic behavior can also trigger a response of consumption to predictable house price changes. Nevertheless, they lack the theoretical model necessary to separate the effects from myopic behavior, precautionary savings and liquidity constraints.
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In order to overcome this problem, this study uses the theoretical model developed by Iacoviello (2004). This theoretical model yields an aggregate log-linearized consumption Euler
equation featuring house prices. This aggregate consumption Euler equation is estimated using Dutch
data and self-constructed estimates of predictable changes in the right-hand side variables. Given that the Euler equation is log-linearized, this study is also able to obtain estimates for the structural parameters of the underlying theoretical model. One of these structural parameters represents the share of aggregate consumption that originates from credit constrained households. Hence, the main advantage of the Iacoviello (2004) theoretical model is that it enables one to explicitly estimate whether liquidity constraints play a role in aggregate Dutch consumption dynamics. Another structural parameter can be estimated to investigate whether housing assets play a role in the borrowing / lending decisions in the Netherlands. This is important since the ability of credit constraints to explain the house price – consumption correlation relies on the fact that housing assets are put up as
collateral.
To summarize, this study finds evidence for credit constraints as the explanation for the correlation between house prices and consumption if (1) aggregate consumption exhibits excess sensitivity to house prices, (2) a significant proportion of Dutch aggregate consumption originates from credit constrained households and (3) housing assets determine the borrowing capacity of credit constrained households. Regarding (1), this study finds that aggregate household consumption responds to predictable changes in the current house price. Moreover, the results found in this study suggest that macroeconomically significant part of Dutch households is credit constrained.
Nevertheless, it is found that the borrowing capacity of households is not determined by the value of its housing assets. Therefore, it is argued that the effects from credit constraints do not explain the association between aggregate household consumption and house prices in the Netherlands.
This study is organized as follows. Section 2 presents more related literature, whereas section 3 introduces the theoretical model underlying the empirical analysis. In Section 4, this study turns to the data and empirical methods. Section 5 presents the results which are discussed in Section 6. Finally, section 7 concludes.
2. Related literature
This section presents a review of the consumption literature relevant to this study. The roots of consumption theory lie in the Keynesian consumption function, also known as the absolute income hypothesis (Keynes, 1936). It outlines that aggregate consumption can be expressed as a function of autonomous consumption and current disposable income. The Keynesian consumption function can be denoted as:
𝐶𝐶 = 𝐶𝐶̅ + 𝑐𝑐𝑐𝑐 (1)
where 𝐶𝐶̅ is autonomous consumption, 𝑐𝑐 is the constant marginal propensity to consume out of current
disposable income (𝑐𝑐). However, in the presence of developed financial markets, it is unlikely that
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incorporated in the theory of intertemporal choice (Fisher, 1930). Fisher (1930) argued that households are rational, forward-looking such that they choose current and future consumption to maximize lifetime utility subject to an intertemporal budget constraint. The intertemporal budget constraint outlines that the present value of lifetime consumption must equal the present value of lifetime income. The optimal intertemporal consumption choice is outlined in the consumption Euler
equation:5
𝑈𝑈′(𝐶𝐶
𝑡𝑡) = 𝑅𝑅𝑅𝑅𝐸𝐸𝑡𝑡𝑈𝑈′(𝐶𝐶𝑡𝑡+1) (2)
which is an optimality condition that equates current marginal utility to next period’s expected marginal
utility adjusting for the gross real interest rate (𝑅𝑅) and the rate of time preference (𝑅𝑅). Intuitively, at the
optimal solution, households should not be able to increase lifetime utility through intertemporal shifting of consumption in case they are able to freely borrow and lend.
The theory of intertemporal choice is the basis for further thinking from which the permanent income hypothesis (PIH) emerged (Friedman, 1957). Consistent with the forward-looking agent described by Fisher (1930), the main prediction of the PIH is that ‘consumers form estimates of their ability to consume in the long run and then set current consumption to the appropriate fraction of that estimate’ (Hall, 1978, p.971). This quote reflects Friedman (1957) in the sense that the consumption decision is solely determined by one’s permanent income. Permanent income is a measure of one’s lifetime resources (Flavin, 1981). As such, it consists of current income and future expected income. It should be noted that income can be generated from human capital (i.e. labor income) and non-human capital (financial or physical assets). The rationale for considering lifetime resources rather than current resources builds on the fact that consumers should be able to substitute consumption intertemporally using borrowing and lending (Fisher, 1930).
The PIH is frequently merged with the life-cycle theory by Modigliani & Brumberg (1954) due to their similarity. Attanasio & Weber (2010) summarize one of the most important virtues of the life cycle – permanent income hypothesis (LC-PIH). It is able to explain a range of stylized facts through inclusion of ‘intertemporal consumption and saving decisions within a coherent optimization problem’ (p.694). Although Friedman (1957) initially based its arguments on intuition, the theory was later formalized in a mathematical optimization problem (Carroll, 2001).
Attansio & Weber (2010) argue that Hall (1978) was the first to recognize that the first-order condition from this optimization problem can be used to test the prediction that consumption is solely determined by permanent income. They call this the ‘Euler equation approach’ and propose the three main advantages of using this approach. First, it prevents the need to derive a closed form solution to the optimization problem. Once one abandons the quadratic utility assumption, one is unable to derive a closed form solution to the optimization problem (Attanasio & Weber, 2010). However, they argue that the Euler equation is a desirable alternative given it captures the ‘main economic essence’ underlying the intertemporal consumption decision. Second, as argued above and as will be elaborated on shortly, it allows one to test the predictions of the most celebrated theory of
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consumption. Third, it makes possible the estimation of structural parameters underlying the theoretical model, which proves to be very useful for this study.
Let this study now proceed by outlining how Hall (1978) empirically investigates the prediction
of LC-PIH. Assuming constant real interest rates, 𝑅𝑅𝑅𝑅 = 1 and using a linear quadratic utility function,
Hall (1978) derives the following Euler equation:
𝐸𝐸𝑡𝑡(𝐶𝐶𝑡𝑡+1) = 𝐶𝐶𝑡𝑡 (3)
which outlines that 𝐸𝐸𝑡𝑡∆𝐶𝐶𝑡𝑡+1= 0. Subsequently, Hall (1978) combines (3) with rational expectations
such that the actual change in consumption is expressed as a function of 𝐸𝐸𝑡𝑡∆𝐶𝐶𝑡𝑡+1 and a random
forecast error where 𝐸𝐸𝑡𝑡𝜀𝜀𝑡𝑡+1 = 0. This leads to the renowned random walk hypothesis of Hall (1978):
∆𝐶𝐶𝑡𝑡+1 = 𝜀𝜀𝑡𝑡+1 (4)
The Euler equation in (4) implies that no information known at time 𝑡𝑡 should be helpful in predicting
consumption growth between 𝑡𝑡 and 𝑡𝑡 + 1 (Attanasio & Weber, 2010). Hence, under the assumption
made by Hall (1978), LC-PIH proposes that forward-looking agents have already considered all
predictable future income changes in their consumption decision at time 𝑡𝑡. It then follows from (4) that
no information about macroeconomic variables dated 𝑡𝑡 or earlier should affect 𝐶𝐶𝑡𝑡+1 since 𝐶𝐶𝑡𝑡 is
controlled for. Intuitively, (4) proposes that only unexpected revisions in permanent income induce
households to revise their consumption choice made at time 𝑡𝑡.
Flavin (1981) retests the random walk hypothesis and finds contradictory evidence to the random walk hypothesis. Specifically, she finds that consumption responds to predictable changes in income. She argues that rational agents consider that income ‘is a stochastic process which exhibits a high degree of serial correlation’ (p.986). Hence, consumption responds to fluctuations in current income because these income fluctuations signal new information about future income. This new information causes permanent income revisions such that contemporaneous consumption should be affected. She obtains an estimate of this new information by regressing contemporaneous income on its lagged values such that the error term represents the new information. However, after explicitly controlling for this unexpected revision in income, she finds that consumption still responds to changes in current income.
This finding is attributed to the fact that consumption responds to predictable changes in current income (Bacchetta & Gerlach, 1997; Campbell & Cocco, 2007; Attanasio & Weber, 2010). This is called ‘excess sensitivity’ of consumption to current income. It is excessive in the sense that consumption reacts more to current income than would be predicted by the LC-PIH. LC-PIH proposes that consumption only reacts to unexpected revisions in permanent income because the initial
consumption choice already reflects all anticipated future income changes. Hence, the finding of Flavin (1981) clearly indicates that consumption does not solely respond to permanent income changes.
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types of agents: permanent income consumers and rule-of-thumb (Keynesian) consumers. Whereas the former group consumes according to the LC-PIH, the latter group consumes its current income.
Hence, the change in consumption at time 𝑡𝑡 can be denoted as follows6:
∆𝐶𝐶𝑡𝑡= 𝜆𝜆∆𝑐𝑐𝑡𝑡+ (1 − 𝜆𝜆)∆𝑐𝑐𝑌𝑌𝑡𝑡= 𝜆𝜆∆𝑐𝑐𝑡𝑡+ (1 − 𝜆𝜆)𝜀𝜀𝑡𝑡 (5)
where 𝜆𝜆 is the percentage of aggregate income (𝑐𝑐) that accrues to rule of thumb consumers.
Permanent income consumers receive (1 − 𝜆𝜆) of 𝑐𝑐, but consume out of their permanent income (𝑐𝑐𝑌𝑌).
𝜀𝜀𝑡𝑡 captures the fact that the change in permanent income cannot be forecasted as is implied by the
random walk hypothesis. It should be noted that (5) reduces to the random walk hypothesis if 𝜆𝜆 = 0.
Campbell & Mankiw (1989) argue that 𝑐𝑐𝑡𝑡 is likely to be endogenous.7 Therefore, they take an
instrumental variable (IV) approach to obtain an estimate for 𝜆𝜆. They instrument ∆𝑐𝑐𝑡𝑡 using various
combinations of lagged values of ∆𝐶𝐶, ∆𝑐𝑐 and the change in the real interest rate as instruments. Given
that they use past information to instrument ∆𝑐𝑐𝑡𝑡., they essentially obtain an estimate of the predictable
∆𝑐𝑐𝑡𝑡. Campbell & Mankiw (1989) find a highly significant estimate of approximately 𝜆𝜆 = 0.5 using
various sets of instruments. Hence, they find evidence that aggregate consumption growth is driven by anticipated changes in current income. Again, this is not in line with rational, forward-looking agents that consider only permanent income. Permanent income would have been revised at the moment of anticipation such that consumption should have responded at that moment and not when the predictable change in income actually occurred.
Campbell & Mankiw (1989) propose credit constraints as the explanation for the presence of rule of thumb consumers. As Jappelli & Pagano (1989) argue, excess sensitivity can be attributed to the failure of the perfect capital market assumption underlying the theory of intertemporal choice and the LC-PIH. Credit constraints may prevent the agent from borrowing against anticipated future income increases. Hence, he consumes the anticipated income change when it occurs.
The presence of credit constraints limits the ability of the economic agent to stay on the optimal consumption path in case the agent can freely borrow and lend stipulated in (2) (Jappelli & Pagano, 1989). As such, Zeldes (1989) derives a consumption Euler in the presence of borrowing constraints which, when ignoring other determinants of utility, can be denoted as:
𝑈𝑈′(𝐶𝐶
𝑡𝑡) = 𝑅𝑅𝑅𝑅𝐸𝐸𝑡𝑡𝑈𝑈′(𝐶𝐶𝑡𝑡+1) + 𝜙𝜙𝑡𝑡 (6)
where 𝜙𝜙𝑡𝑡 is the Lagrange multiplier connected to the borrowing constraint 𝐴𝐴𝑡𝑡+𝑘𝑘≥ 0 for 𝑘𝑘 = 0, 1, … , 𝑇𝑇 −
𝑡𝑡 − 1 (Zeldes, 1989). This borrowing constraint reflects the fact that the current value of net assets
must be at least zero in the entire time horizon.8 Zeldes (1989) argues that the Lagrange multiplier is
positive in case the borrowing constraint is binding. The Lagrange multiplier reflects the lifetime utility that can be obtained from slightly relaxing the borrowing constraint at the optimal solution.
By comparing (6) to (2) one can observe that the difference between marginal utility of
6 The notation is borrowed from a later version: Campbell & Mankiw (1991).
7 As was mentioned in Section I, consumption is one of the main components of gross domestic output.Hence, straightforward explanation for this argument is reverse causation.
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consumption today and tomorrow is higher in case the agent is credit constrained (Zeldes, 1989). In
the absence of a positive 𝜙𝜙𝑡𝑡, 𝑈𝑈′(𝐶𝐶𝑡𝑡) would have been lower. Hence, under the usual assumption of
diminishing marginal utility, constrained agents desire to increase current consumption by shifting resources from the future to today. However, they are prevented from doing so, since they are credit
constrained. From (6), it can also be seen that the larger is 𝜙𝜙𝑡𝑡, the farther the agent is away from its
desired intertemporal consumption allocation. Hence, it follows that a higher 𝜙𝜙𝑡𝑡 implies a more severe
borrowing constraint.
Zeldes (1989) puts (6) to the test and finds a positive average Lagrange multiplier for a group of consumers with low liquid assets to income in the United States. This suggests that credit
constraints play a role in the violation of the Euler equation in (2). Credit constrained agents are unable to transfer future income to the present, such that the optimal level of consumption smoothing is not achieved. Hence, a relaxation of the borrowing constraint should induce current consumption increases.
Jappelli & Pagano (1989) propose another test for the liquidity constraints hypothesis by arguing that liquidity constraints should be more severe in countries with less developed credit markets. However, they also note that these differences in consumer debt levels between countries can also be explained by differences in the appetite for credit. Therefore, they also investigate the
characteristics of local credit markets. They proceed by estimating the Campbell & Mankiw (1989) 𝜆𝜆
for six developed countries. Their findings are threefold. First, they find that countries with a higher 𝜆𝜆
tend to have low levels of consumer debt.9 Second, credit demand side features are not able to
explain these international differences in 𝜆𝜆. Thus, the appetite for credit does not seem to play a role.
Supply side credit rationing is better able to explain these international differences. This leads them to conclude that the excess sensitivity of consumption to income is driven by credit constraints.
The preceding sections have focused on the excess sensitivity of consumption to income. Nevertheless, the excess sensitivity of consumption is by no means limited to current income. For example, Bacchetta & Gerlach (1997) investigate the excess sensitivity of consumption to financial variables in a cross-country study. In doing so, they adopt a similar approach to Campbell & Mankiw (1989) and obtain predictions of the right-hand side variables by using lagged instruments. The main difference is that they also include financial variables such as the borrowing/lending spread and growth of mortgage credit and consumer credit. They find that consumption is excessively sensitive to all three financial variables. Moreover, once these financial variables are controlled for, the excessive sensitivity to income reduces and often disappears. Given that all three variables should act as a proxy for the tightness of credit conditions, Bacchetta & Gerlach (1997) find international evidence in favor of an influence of credit constraints on aggregate consumption.
Campbell & Cocco (2007) investigate the excess sensitivity of consumption growth to house prices in the United Kingdom. First, they capture the essence of the random walk hypothesis
eloquently: ‘if households are forward looking, then the wealth effect of a house price change occurs when the change can be anticipated, not when it actually occurs’ (p. 612). On the other hand, while
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not causing a wealth effect at the moment of occurrence, an anticipated change in the current house price does relax the borrowing constraint of credit constrained households (Campbell & Cocco, 2007). The main takeaway is that unexpected house price changes cause both wealth effects and loosen the borrowing constraint. On the contrary, an anticipated house price change should not induce a wealth effect but does loosen the borrowing constraint of a credit constrained consumer. Therefore, by investigating predictable house price changes, one is able to separate wealth effects from the effects of credit constraints (Campbell & Cocco, 2007).
Campbell & Cocco (2007) estimate an equation similar to Campbell & Mankiw (1989) which, in their eyes, is ‘the usually estimated equation in the excess sensitivity literature’ (p. 613). They instrument the house price and income change by lagged macroeconomic variables and obtain an estimate for their predictable values. Subsequently, the change in consumption is regressed on these predictable changes in current income and the current house price. They find that consumption growth responds positively to predictable changes in current house prices. However, as Campbell & Cocco (2007) note based on the findings of Carroll (1997), precautionary savings or myopic behavior can also trigger a response of consumption following predictable house price changes. Nevertheless, the absence of a theoretical model prevents separation of the effects from myopic behavior,
precautionary savings and liquidity constraints (Campbell & Cocco, 2007).
The theoretical model developed in Iacoviello (2004) does offer the opportunity to link potential excess sensitivity to house prices to the presence of credit constrained households. Iacoviello (2004) takes a different approach than the ad-hoc addition of house prices to the usual
excess sensitivity equation.10 Specifically, by including housing services into the utility function, he
derives an aggregate consumption Euler equation that features house prices such that the relationship between house prices and consumption is micro founded. The relationship between house prices and consumption explicitly arises from the fact that housing assets are used as collateral and thus determine the tightness of the borrowing constraint. In other words, a lower value of the housing stock implies that a household is less able to transfer future consumption to today.
Iacoviello (2004) fits the aggregate consumption Euler equation to United States data for the period 1986Q1 to 2002Q4. Similar to much of the literature discussed above, he also instruments the right-hand side variables by using lags of these regressors. He finds that US aggregate consumption is sensitive to predictable changes in the current house price.
As was mentioned earlier, one of the main advantages of using Euler equations is that the structural parameters can be estimated. This is also what Iacoviello (2004) does. He finds that 20 to 25% of United States consumption originates from credit constrained households. Moreover, he finds significant loan-to-value estimates ranging between 0.58 and 0.67. Hence, the value of housing assets plays a role in the US borrowing/lending decisions, as well as in the borrowing capacity of credit constrained households. Considering these three findings, Iacoviello (2004) confirms ‘the presence of collateral effects in the aggregate consumption Euler equation’ (p.306). In other words,
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house prices seem to affect consumption in the United States because they loosen the borrowing constraints of credit constrained households.
3. Theoretical model
In order to pursue its research objective, this study borrows the theoretical model derived in Iacoviello (2004). This theoretical model is chosen based on the following three reasons. First, the aggregate consumption Euler equation features house prices. This consumption Euler equation can then be estimated in order to test whether Dutch aggregate consumption responds to predictable changes in the current house price. Second, the channel through which aggregate consumption responds to house prices coincides with the channel this study wants to investigate for the
Netherlands. Hence, it should be the proper theory underlying the empirical analysis. Third, the main virtue of the model is that the aggregate consumption Euler equation can be used to retrieve
estimates of the structural parameters. These structural parameter estimates enable one to link potential excess sensitivity to credit constraints.
This study proceeds by elaborating on the workings of the model.11 It starts by outlining the
working assumptions. First, the model economy is populated by two types of infinitely lived households that maximize their lifetime utility by making optimal consumption, housing and borrowing/lending decisions. As will be addressed shortly, one of household types is always credit constrained. Second, stochastic shocks are absent in the model such that there is no uncertainty. Hence, under rational expectations, households make no forecast errors and thus have perfect foresight. Third, the aggregate housing stock is assumed to be constant and finite. Housing can change ownership and house prices respond to these demand pressures. Nevertheless, in the presence of a fixed housing stock, housing wealth is merely redistributed between households. In
other words, a housing wealth increase between period 𝑡𝑡 − 1 and 𝑡𝑡 is entirely offset by a housing
wealth loss for the other household12. Fourth, each period households receive an equal and
exogenous amount of income that can be spent on consumption and housing.
Households are endogenously credit constrained and unconstrained due to a difference in discount rates. As can be glimpsed from their utility function, credit constrained households have a discount factor of zero, such that they do not value future housing and non-housing consumption. On the contrary, unconstrained households do value the future, such that they are willing to lend resources to constrained households. However, in order to obtain the loan, constrained households need to put up their housing stock as collateral.
Given that constrained households do not value the future, they have incentive to accumulate an infinite amount of debt. This is limited by a borrowing constraint (imposed by credit constrained
11 The formal derivation of the Iacoviello (2004) model can be found in the Appendix. This section is only meant to clarify the workings of the model.
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households) that links the borrowing capacity to the expected (and discounted) next period market value of the constrained households’ housing stock:
𝐵𝐵𝑡𝑡𝑐𝑐 ≤ 𝑚𝑚𝐸𝐸𝑡𝑡(𝑄𝑄𝑡𝑡+1)𝐻𝐻𝑡𝑡 𝑐𝑐
𝑅𝑅𝑡𝑡
� (7)
where 𝐵𝐵𝑐𝑐 is the amount borrowed by constrained households through a riskless one-period bond, 𝑚𝑚 is
the loan-to-value (LTV) ratio, 𝑄𝑄 is the house price, 𝐻𝐻 is the housing stock and 𝑅𝑅 is still the gross real
interest rate. 𝑚𝑚 is assumed to be smaller or equal to 1, such that constrained households cannot
borrow more than the value of the housing stock. This ensures that unconstrained households can cover liquidation costs in case of default (Iacoviello, 2004). Given that the housing stock is put up as collateral, unconstrained households receive the market value of the housing stock upon default. This should then cover the amount lend as well as the liquidation costs.
This study recognizes that 𝑚𝑚 ≤ 1 is not in line with the historical regulatory LTV ratios on
mortgages in the Netherlands (which were above 1). Nevertheless, it argues that 𝑚𝑚 does not
correspond one-for-one with the regulatory LTV ratio on mortgages. In case (7) binds, 𝑚𝑚 also
determines the borrowing capacity of a household that was credit rationed prior to a house price increase. This study argues that it is unlikely that credit suppliers are willing to lend more than the increase in the value of the housing stock to an already heavily indebted household. In the eyes of
this study, this justifies the assumption regarding 𝑚𝑚.
Another relevant observation with respect to borrowing and lending is that unconstrained
households are the only lenders in this model economy. Hence, each period they lend −𝐵𝐵𝑡𝑡𝑢𝑢 to credit
constrained households such that −𝐵𝐵𝑡𝑡𝑢𝑢= 𝐵𝐵𝑡𝑡𝑐𝑐 . This implies that there is no aggregate saving in this
model economy.
Let this study now outline the optimal decisions for both types of household that follow from a
lifetime utility maximization problem. For the unconstrained households (denoted by superscript 𝑢𝑢) the
optimal decisions can be represented as:
(𝐶𝐶𝑡𝑡𝑢𝑢)−1 𝜎𝜎� = 𝑅𝑅𝑅𝑅𝑡𝑡𝐸𝐸𝑡𝑡((𝐶𝐶𝑡𝑡+1𝑢𝑢 )−1 𝜎𝜎� ) (8)
𝑄𝑄𝑡𝑡(𝐶𝐶𝑡𝑡𝑢𝑢)−1 𝜎𝜎� = 𝑗𝑗𝑢𝑢𝑈𝑈′(𝐻𝐻𝑡𝑡𝑢𝑢) + 𝑅𝑅𝐸𝐸𝑡𝑡(𝑄𝑄𝑡𝑡+1(𝐶𝐶𝑡𝑡+1𝑢𝑢 )−1 𝜎𝜎� ) (9)
𝐶𝐶𝑡𝑡𝑢𝑢+ 𝑄𝑄𝑡𝑡(𝐻𝐻𝑡𝑡𝑢𝑢− 𝐻𝐻𝑡𝑡−1𝑢𝑢 ) + 𝑅𝑅𝑡𝑡−1𝐵𝐵𝑡𝑡−1𝑢𝑢 = 𝐵𝐵𝑡𝑡𝑢𝑢+ 𝑐𝑐𝑡𝑡𝑢𝑢 (10)
where 𝐶𝐶 stands for consumption, 𝑅𝑅 is the discount factor, 𝜎𝜎 is the elasticity of intertemporal
substitution, 𝑐𝑐 is exogenous income and 𝑗𝑗 is the share of housing in the utility function. (8) reflects the
regular consumption Euler equation outlined in (2) under iso-elastic utility. (9) outlines the housing demand equation for unconstrained households. (10) represents the lending decision that results from the budget constraint.
The optimal decisions for the credit constrained household (denoted by superscript 𝑐𝑐) can be
presented as follows: 1
𝐶𝐶𝑡𝑡𝑐𝑐
13
𝑄𝑄𝑡𝑡 𝐶𝐶𝑡𝑡𝑐𝑐 � = 𝑗𝑗𝑐𝑐𝑈𝑈′(𝐻𝐻 𝑡𝑡𝑢𝑢) + 𝜙𝜙𝑡𝑡𝑚𝑚𝐸𝐸𝑡𝑡(𝑄𝑄𝑡𝑡+1) (12) 𝐶𝐶𝑡𝑡𝑐𝑐+ 𝑄𝑄𝑡𝑡(𝐻𝐻𝑡𝑡𝑐𝑐− 𝐻𝐻𝑡𝑡−1𝑐𝑐 ) + 𝑅𝑅𝑡𝑡−1𝐵𝐵𝑡𝑡−1𝑐𝑐 = 𝐵𝐵𝑡𝑡𝑐𝑐+ 𝑐𝑐𝑡𝑡𝑐𝑐 (13) 𝐵𝐵𝑡𝑡𝑐𝑐 = 𝑚𝑚𝐸𝐸𝑡𝑡(𝑄𝑄𝑡𝑡+1)𝐻𝐻𝑡𝑡 𝑐𝑐 𝑅𝑅𝑡𝑡 � (14)where 𝜙𝜙 is the shadow value related to the borrowing constraint. (11) is the consumption Euler
equation of these credit constrained households, (12) describes their optimal housing decision while (13) and (14) are concerned with the borrowing decisions of credit constrained households. (14) outlines that it is optimal for constrained households to borrow up to the limit. Given that credit constrained households do not value the future, next period’s expected consumption does not feature in (11). Moreover, it can be observed that the marginal utility of consumption depends on the
tightness of the borrowing constraint as measured by 𝜙𝜙𝑡𝑡. A tighter borrowing constraint implies that
households are less able to transfer future consumption to today. Hence, under diminishing marginal utility, a tighter borrowing constraint implies a higher marginal utility of consumption.
It is shown in the Appendix that 𝜙𝜙 is strictly positive in the deterministic steady state and in its
neighborhood. A strictly positive shadow value implies that households are willing to transfer resources from the next period to now, but are constrained from doing so at the optimum (Zeldes, 1989). Hence, households would like to increase their debt burdena such that they can transfer future consumption to today. Nevertheless, they are prevented from doing this because their borrowing constraint binds at the optimum.
In the absence of stochastic shocks, the deterministic steady state is not left after it is reached. Given that house prices are fixed in the deterministic steady state, the convergence to the steady state is analyzed in order to formalize how households react to house price changes in this model. This can be done by log-linearizing the Euler equations outlined in (8) and (11). Technically, log-linearization serves the purpose of describing the dynamic behavior of the model in the
neighborhood of the steady state. Log-linearization of the Euler equations is carried out by applying a first-order Taylor approximation around the steady state. As a result, one obtains an approximation of the aggregate consumption Euler equation that is linear in terms of the variables’ log deviations from their steady state value.
Based on the log-deviations of the right-hand side variables, the log-linear aggregate Euler equation describes the optimal consumption decision that can be taken such that the economy moves to the steady state in which lifetime utility is maximized. The main advantage of log-linearizing the Euler equations is that it enables one to link parameter estimates resulting from the empirical
investigation to the structural parameters of the theoretical model. Moreover, it enables one to obtain an aggregate Euler equation that explicitly links house prices to aggregate consumption.
Log-linearization of the constrained households’ housing demand equation enables one to relate the
tightness of the borrowing constraint, as measured by 𝜙𝜙𝑡𝑡, to the house price. As was highlighted by
Zeldes (1989), the tightness of the borrowing constraint affects intertemporal consumption decisions.
Hence, by relating house prices to 𝜙𝜙𝑡𝑡, one is able to derive a relationship between housing and
14
Let this study proceed by presenting the results from log-linearization of the Euler equations. 𝑋𝑋𝑡𝑡
� is defined as the logarithmic deviation of 𝑋𝑋𝑡𝑡 from its steady state value 𝑋𝑋, that is, 𝑋𝑋� ≡ ln 𝑋𝑋𝑡𝑡 𝑡𝑡− ln 𝑋𝑋.
The log-linearized versions of (8) and (11) are:13
𝐶𝐶� = 𝐸𝐸𝑡𝑡𝑢𝑢 𝑡𝑡𝐶𝐶� − 𝜎𝜎𝑅𝑅𝑡𝑡+1𝑢𝑢 � 𝑡𝑡 (15)
𝐶𝐶� = 𝑡𝑡𝑐𝑐 (1−𝑚𝑚𝑚𝑚)1 𝑄𝑄� − 𝑡𝑡 (1−𝑚𝑚𝑚𝑚)𝑚𝑚𝑚𝑚 𝐸𝐸𝑡𝑡𝑄𝑄� + 𝜃𝜃𝐻𝐻𝑡𝑡+1 � + 𝑡𝑡𝑐𝑐 (1−𝑚𝑚𝑚𝑚)𝑚𝑚𝑚𝑚 𝑅𝑅� 𝑡𝑡 (16)
where 𝜃𝜃 is defined as the long-run inverse elasticity of housing demand by constrained households to
the house price. From (15) it can be seen that the consumption of unconstrained households does not directly respond to house price changes. From (16) it can be glimpsed that the log deviation in
consumption of the credit constrained households is positively related to the house price change at
time 𝑡𝑡.14 Hence, ceteris paribus, aggregate consumption should respond to house price changes near
the steady state.
An expression for the aggregate consumption Euler equation can be derived by combining (15) and (16) and using the following aggregator:
𝐶𝐶� = 𝜉𝜉𝐶𝐶𝑡𝑡 � + (1 − 𝜉𝜉)𝐶𝐶𝑡𝑡𝑐𝑐 � 𝑡𝑡𝑢𝑢 (17)
where 𝜉𝜉 is defined as the consumption share of constrained households in aggregate consumption.
(17) shows that the log deviation in aggregate consumption from the steady state is driven by the
considerations of both constrained and unconstrained households. On the other hand, 𝜉𝜉 cannot be
interpreted as the percentage of the household that is credit constrained. It should be interpreted as the share of aggregate consumption that originates from constrained households. Hence, by
estimating 𝜉𝜉, this study can investigate whether the consumption behavior of credit constrained
households is an important driver of aggregate Dutch consumption dynamics.
Ultimately, one can arrive at the following aggregate consumption Euler equation:
𝐶𝐶� = 𝜉𝜉(1 + 𝜔𝜔)𝑄𝑄𝑡𝑡 � − 𝜉𝜉𝜔𝜔𝐸𝐸𝑡𝑡 𝑡𝑡𝑄𝑄� − 𝜉𝜉𝜃𝜃𝐻𝐻𝑡𝑡+1 � − 𝜎𝜎(1 − 𝜉𝜉)𝐿𝐿𝑡𝑡𝑐𝑐 � − [(1 − 𝜉𝜉)𝜎𝜎 − 𝜉𝜉𝜔𝜔]𝑅𝑅𝑡𝑡 � 𝑡𝑡 (18)
where (1 + 𝜔𝜔) = 1
(1−𝑚𝑚𝑚𝑚) and 𝐿𝐿� is the log deviation in the total gross real rate of return on a long-term 𝑡𝑡
bond at time 𝑡𝑡. (18) relates aggregate consumption to the house price. Moreover, it can be seen that
the response of aggregate consumption to house prices depends on 𝜉𝜉. This implies that aggregate
consumption responds more strongly in case a larger of part of consumption originates from credit constrained households. This indicates that credit constraints lie at the heart of the consumption response to house prices in this model economy.
As is shown by Iacoviello (2004), (18) can be rewritten such that four of the structural parameters can be estimated:
13 (16) does not directly follow from log-linearizing (11) but involves some other procedures as well. Again, this study refers the reader to the Appendix for the formal derivation of (15) and (16).
15
𝐶𝐶� = −𝜎𝜎(1 − 𝜉𝜉)�𝑅𝑅𝑡𝑡 � + 𝐿𝐿𝑡𝑡 � � + 𝜔𝜔𝜉𝜉�𝑄𝑄𝑡𝑡 � + 𝑅𝑅𝑡𝑡 � − 𝐸𝐸𝑡𝑡 𝑡𝑡𝑄𝑄�� + 𝜉𝜉𝑄𝑄𝑡𝑡+1 � + 𝜃𝜃𝜉𝜉𝐻𝐻𝑡𝑡 � 𝑡𝑡𝑐𝑐 (19)
The reader should note that (18) and (19) play a central role in the empirical analysis conducted here.
Regarding the structural parameter estimates, this study is particularly interested in 𝜉𝜉 and 𝜔𝜔. From
(18), it can be glimpsed that the response of aggregate consumption to house prices depends on
these two parameters. 𝜉𝜉 represents the portion of aggregate consumption that originates from these
households. By estimating 𝜉𝜉, this study could confirm whether a macroeconomically significant part of
Dutch households is credit constrained. The term macroeconomically significant is used here because household consumption is an important macroeconomic aggregate, since it represents a substantial
share of gross domestic product. A positive 𝜔𝜔 implies that housing assets determine the borrowing
capacity of credit constrained households. Hence, house price increases loosen the borrowing constraint of credit constrained households. This is a necessary prerequisite for the ability of credit constraints to explain the house price – consumption association.
Before turning to the empirical analysis, this study needs to elaborate on one characteristic of this model. It should be remembered that there are no aggregate wealth effects from house prices in this model economy while there are also no aggregate savings. Combining (10) and (18), this implies that aggregate consumption is always equal to aggregate income. Given that income was assumed to be exogenous, aggregate consumption is also exogenous. This implies that house price increases cannot cause aggregate consumption increases in this model economy. An increase in house prices triggers changes in the other variables of the model economy, such that ultimately aggregate consumption is unaffected.
Nevertheless, this does not imply that aggregate consumption does not respond to house price changes. However, it does imply that aggregate consumption responds to house prices ceteris paribus. This is confirmed by (15) and (16), where it can be seen that only the consumption of credit constrained households reacts to house prices. Ultimately, unconstrained households reduce their consumption following changes in the short-term interest rate, such that aggregate consumption is unaffected. Given that this study is only interested in investigating the correlation between house prices and consumption, a ceteris paribus impact suffices. Therefore, the assumption of exogenous income seems reasonable.
4. Data and methodology
This section outlines the data collection procedure, adjustments made to the raw data, the hypotheses and the empirical methods. The bottom line is that the aggregate consumption Euler equations described in the previous section (see (18) and (19)) are estimated using Dutch data. The decision to estimate (18) is based on the following three considerations. First, given that house prices feature as a right-hand side variable, (18) offers the opportunity to investigate whether Dutch
16
equation to empirically test the theory which attributes the house price – consumption association to credit constraints.
Before this study proceeds to discussing the data, it needs to make one remark regarding the relationship between the empirical analysis and the theoretical model. The theoretical model is derived under the assumption of perfect foresight. Hence, the agents are able to anticipate all the changes in the right-hand variables. Obviously, this is not the case in reality. Therefore, in the empirical analysis, this study needs to obtain an estimate for the predictable change in the current house price. The method for obtaining these estimates is discussed later in this section.
4.1 Data
This study has collected multiple time series with a quarterly interval for the period 1996Q1 to
2017Q4.15 The sample period is chosen based on data availability. This was the largest possible
sample period for which none of the included time series had any missing values. A house price index (base year = 2010) excluding newly built houses is obtained from CBS Statline. The house price index is calculated based on the sale price appraisal ratio. In short, this implies that the selling prices of
houses are related to the appraisal value in the base period (de Haan et al, 2008).16 Given that selling
prices are used to construct the index, this study suspects that the house price index is in nominal terms.
Total household domestic consumption expenditures, total gross fixed capital formation (GFCF) of dwellings, short-term interest rate, long-term interest rate and the consumer price index (CPI) are collected from the OECD database. Household domestic consumption expenditures and GFCF are seasonally adjusted and are measured in chain linked volumes (reference year = 2010) to adjust for inflation. GFCF of dwellings reflects residential investment net of disposals and should proxy for the demand for housing of credit constrained households. This idea is borrowed from Iacoviello (2004). It builds on the assumption that first time home buyers tend to be credit constrained. Of course, part of the new dwellings is owned by unconstrained households and part of the dwelling improvements are carried out by these households. However, given that disposals are adjusted for, GFCF reflects the net increase in the housing stock. In case demand for housing stock stays fixed, it can be argued that residential investment is roughly canceled out by disposals. Therefore, GFCF is aimed at accommodating increases in the total demand for housing. It can be argued that variation in total demand is driven by variation in the amount of first time home buyers.
The short-term interest rate in the OECD database is measured by the 3-month EURIBOR whereas the long-term interest rate represents the 10-year Dutch government bond yield. The 3-month EURIBOR and 10-year yield on government bonds are obtained as percentages per annum and in nominal terms. Since this study uses data with a quarterly interval, it uses the 3-month
EURIBOR as a proxy for the one-period rate on riskless bonds. This seems reasonable, given that the 3-month EURIBOR is the interest rate charged for interbank lending in the European Monetary Union.
15 Descriptive statistics and plots of the raw time series can be found in the Appendix
17
As a proxy for the total return on a riskless long-term bond, this study uses the 10-year Dutch
government bond yield. This is based on the argument that the 10-year government yield does reflect the time-varying willingness of agents to lend their funds long-term. Moreover, Dutch government bonds are generally seen as riskless. Hence, the long-term interest rates capture two features of the riskless long-term bond. Moreover, this choice is consistent with Iacoviello (2004). Finally, the CPI (base year = 2010) is collected to express the nominal variables in real terms. The CPI index is chosen rather than the GDP deflator, since it is argued that the CPI better reflects the price changes that households face. The GDP deflator reflects only domestic goods whereas households also import goods from abroad. In addition, the CPI measures the price changes of the goods bought by
consumers only. Time series plots and descriptive statistics of all the raw data can be found in the Appendix.
The reader may have noted that the conditional expectation of house prices at time 𝑡𝑡 appears
as a right-hand variable in (18). The intention was to use an expected house price index. However, the desired index was not found. Hence, an expectation for the house price is estimated using the regular house price index. This is discussed in more detail in Section 4.3.
This study now proceeds by describing the adjustments made to the raw data. Given that the aggregate consumption Euler equation is log-linearized, the variables appear in the form of log deviations from the steady state. Therefore, this study proceeds by deriving the logarithmic growth rates of consumption, house prices, CPI and the GFCF of dwellings.
A closer look at the plots of the raw data shows that most time series exhibit a trend. A major advantage of using logarithmic growth rates is that it filters the trend in the macroeconomic time series and thus deals with potential non-stationarity. This is beneficial given that regressing two trending time series may lead to spurious results, i.e. finding a significant relationship while there is
none (Granger & Newbold, 1974). The quarterly logarithmic growth rate for a variable 𝑋𝑋𝑡𝑡 is computed
as follows:
𝑥𝑥𝑡𝑡= ln �𝑋𝑋𝑋𝑋𝑡𝑡−1𝑡𝑡 � (20)
This study proceeds by adjusting the short-term- and long-term interest rates. It converts the
percentages per annum (𝑟𝑟𝑎𝑎) to quarterly rates (𝑟𝑟𝑞𝑞) by using the following procedure:
𝑟𝑟𝑞𝑞= �(1 + 𝑟𝑟𝑎𝑎)1�4� − 1 (21)
18
An important issue that needs to be addressed in time series analysis is potential non-stationarity. Non-stationarity of time series describes the situation in which it has a time-varying mean and possibly a time-varying variance. Using non-stationary time series may lead to spurious results in the sense that one may find a significant relationship between two variables when, in fact, they are independent (Granger & Newbold, 1974). Hence, this study may find incorrect evidence for excess sensitivity of consumption to house prices.
To investigate the issue of non-stationarity, an Augmented Dickey-Fuller (ADF) test is conducted. The null hypothesis of the ADF test is that a particular time series is non-stationary. The
test equation of the ADF test for a variable 𝑤𝑤 is expressed as follows:
∆𝑤𝑤𝑡𝑡= 𝛼𝛼0+ 𝑅𝑅𝑤𝑤𝑡𝑡−1+ 𝛼𝛼1∆𝑤𝑤𝑡𝑡−1+ 𝛼𝛼2∆𝑤𝑤𝑡𝑡−2+ ⋯ + 𝛼𝛼𝑞𝑞∆𝑤𝑤𝑡𝑡−𝑞𝑞+ 𝜀𝜀𝑡𝑡 (22)
where 𝛼𝛼0 is the intercept, 𝑞𝑞 is the number of lags included and 𝜀𝜀𝑡𝑡 is the error term.
It is important to select a sufficient amount of lagged values, given that serial correlation biases the ADF test. Therefore, this study uses a procedure that follows from Ng & Perron (1995) to select the appropriate lag length. This study estimates (22) with the maximum lag length which is
determined according to the rule outlined in (23). It obtains the t-statistic corresponding to 𝛼𝛼𝑞𝑞. If the
absolute value of the t-statistic exceeds 1.6, the maximum lag length is selected. If not, the lag length is reduced by one and the procedure is repeated until the absolute value does exceed 1.6. The maximum lag length is chosen based on Schwert (1989) where the it is determined as follows: 𝑞𝑞𝑚𝑚𝑎𝑎𝑚𝑚= �12 ∗ �100𝑇𝑇 �
1�4
� (23)
Based on the sample size, this leads to the selection of 𝑞𝑞𝑚𝑚𝑎𝑎𝑚𝑚 = 12. The results of the ADF test
are reported in Table 1. It should be noted that the ADF test is carried out on the adjusted data. The null hypothesis of non-stationarity can be rejected for the interest rates at a 1% level. Moreover, for consumption and GFCF, it can be rejected at a 5% significance level.
Table 1
Augmented Dickey-Fuller results*
Time series Z-statistic Lag length
Consumption -2.543 8
House price -1.398 7
Long-term interest rate -6.098 6
Short-term interest rate -4.908 6
GFCF -2.445 7
* This table shows the Z-statistics of the Augmented Dickey-Fuller test alongside with the number of lags included in the test equation. The intercept is excluded from the test equation given that all five adjusted time series have a mean of roughly 0. The critical values are: -2.608 (1% critical value), -1.950 (5% critical value) and -1.610 (10% critical value).
19
hypothesis for the following reasons. The p-values associated with the test statistic is below 0.20. This implies that the null hypothesis can be rejected at a 20% significance level. It is recognized that it is unconventional to consider the 20% significance level. However, the following argument carries more weight in the eyes of this study. Given that house prices already appear in first difference, it would need to construct the second difference of house prices in order to address the non-stationarity. This would make the results hard to interpret, since it involves regressing the quarterly log change in consumption on the semiannual log change in house prices.
4.2 Regression models
This study now proceeds by presenting the first linear regression model that is to be estimated using Dutch data:
𝑐𝑐𝑡𝑡= 𝜓𝜓0+ 𝜓𝜓1𝑞𝑞𝑡𝑡− 𝜓𝜓2𝐸𝐸𝑡𝑡𝑞𝑞𝑡𝑡+1+ 𝜓𝜓3ℎ𝑡𝑡𝑐𝑐− 𝜓𝜓4𝑙𝑙𝑡𝑡+ 𝜓𝜓5𝑟𝑟𝑡𝑡+ 𝜀𝜀𝑡𝑡 𝑓𝑓𝑓𝑓𝑟𝑟 𝑡𝑡 = 1, … , 𝑇𝑇 (24)
where 𝜀𝜀𝑡𝑡 is the error term at time 𝑡𝑡. 𝑐𝑐 is the logarithmic growth rate of domestic household
consumption, 𝑞𝑞 refers to the logarithmic growth rate of house prices, ℎ𝑐𝑐 is the logarithmic growth rate
of GFCF of dwellings that proxies for constrained household housing demand, 𝑙𝑙 reflects the log
change in long-term interest rate and 𝑟𝑟 reflects the log change short-term interest rate. For further
information about the variables, this study refers to the Appendix, where the time series plots and the descriptive statistics of the transformed data can be found. This study uses (24) to investigate whether Dutch aggregate consumption exhibits excess sensitivity to house prices.
This study now proceeds by outlining some considerations surrounding 𝐸𝐸𝑡𝑡𝑞𝑞𝑡𝑡+1. This study
considers adaptive expectations. However, the adaptive expectations approach implicitly assumes that households lack the capability of using current information to predict the future, that is,
expectations are formed solely based on past information and past expectational errors. Hence, the assumption of adaptive expectation seems hard to reconcile with the forward-looking behavior outlined in the intertemporal optimization of lifetime utility in the previous section.
The alternative to adaptive expectations are rational expectations. As is argued in the literature review, rational expectations theory proposes that economic agents have the ability to
optimally use all available information at time 𝑡𝑡 to form a rational expectation about some variable in
period 𝑡𝑡 + 1. Under rational expectations, it is assumed that economic agents understand the
structure of the model economy. In turn, they use this understanding to form expectations along the lines of the economic model.
Given that the theoretical model used here is derived under the assumption of perfect foresight, it must be that the rational price expectation equals the price observed ex-post. Nevertheless, this seems unreasonable given the sample period which encompasses the Great Recession. In hindsight it seems illogical to assume that the boom and the Great Recession occurred in the presence of rational households with perfect foresight. Taking this all into account, the
assumption of rational expectations also seems unreasonable. This study proposes an alternative way to come up with a house price expectation. Since it is closely related to the estimation method, it is discussed in Section 4.3.
20
𝑐𝑐𝑡𝑡= −𝜗𝜗1(𝑟𝑟𝑡𝑡+ 𝑙𝑙𝑡𝑡 ) + 𝜗𝜗2(𝑞𝑞𝑡𝑡+ 𝑟𝑟𝑡𝑡− 𝐸𝐸𝑡𝑡𝑞𝑞𝑡𝑡+1) + 𝜗𝜗3𝑞𝑞𝑡𝑡+ 𝜗𝜗4ℎ𝑡𝑡𝑐𝑐 + 𝜀𝜀𝑡𝑡 𝑓𝑓𝑓𝑓𝑟𝑟 𝑡𝑡 = 1, … , 𝑇𝑇 (25)
where 𝜉𝜉 = 𝜗𝜗3 , σ = 𝜗𝜗1/(1 − 𝜗𝜗3) , 𝜔𝜔 = 𝜗𝜗2/𝜗𝜗3, 𝜃𝜃 = 𝜗𝜗4/𝜗𝜗3 and 𝜀𝜀𝑡𝑡 is the error term. The reader should note (25) is based on the rewritten aggregate consumption Euler equation outlined in (19).
This study can obtain estimates of four structural parameters by using the estimates of the
coefficients in (25). Most importantly, this study obtains an estimate for 𝜉𝜉 and 𝜔𝜔. The reader should
remember that 𝜉𝜉 represents the share of aggregate consumption that originates from credit
constrained households. Moreover, 𝜔𝜔 is related to the borrowing capacity of credit constrained
households. Specifically, it measures how much these households can borrow against the value of their housing assets. As such, by estimating these two structural parameters, this study can
investigate whether potential excess sensitivity of consumption to house prices can be linked to credit constraints. The reader should remember that excess sensitivity of consumption to house prices is required to separate wealth effects from the other explanations for the house price – consumption correlation.
4.3 Estimation method
This study fits (24) and (25) to the Dutch data by adopting a two-stage least squares (2SLS) approach. This estimation method is chosen for the following two reasons. First, 2SLS estimation helps this study to confront the presence of endogenous regressors. Second, it enables this study to
obtain the change in house prices at time 𝑡𝑡 that can be anticipated prior to time 𝑡𝑡. Hence, it can
investigate the excess sensitivity of Dutch aggregate consumption to house prices. This study proceeds by elaborating on these two arguments for using the 2SLS estimator.
Endogeneity refers to the situation where one (or more) of the explanatory variables are correlated with the error term. Endogenous regressors are a violation of the weak exogeneity
assumption under which the OLS estimator is consistent (or, in other words, asymptotically unbiased). Given that this study aims to draw conclusions based on the parameter estimates, it is desirable to address issues that may introduce bias into these estimates.
𝑞𝑞𝑡𝑡 is likely to be endogenous for various reasons. Campbell & Cocco (2007) suggest that the
correlation between house prices and consumption may be driven by third factors. A macroeconomic factor that drives both consumption and house prices is the business cycle. This study chooses to stick to the aggregate consumption Euler equation such that it does not allow ad-hoc additions of control variables. As such, this study cannot control for common measures of the business cycle such as the national unemployment rate or gross domestic product. Hence, the parameter estimate for house prices may suffer from omitted variable bias.
One could argue that these omitted variable biases are not limited to the parameter estimate
associated with 𝑞𝑞𝑡𝑡. Given that the central bank uses its policy rate for anticyclical policy, it is not
unreasonable to argue that interest rates are correlated with measures of the business cycle.
Similarly, ℎ𝑡𝑡𝑐𝑐 is likely to be higher / lower during an upswing / downturn of the business cycle. In
addition, it is not unlikely that households have more optimistic expectations about house prices during an upswing. Hence, this study suspects that all regressors are to some extent endogenous.
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the theoretical model used here, consumption and housing can be seen as substitutes. If
consumption goods become more expensive, households may choose to substitute consumption for housing. In turn, increased housing demand may put upward pressure on house prices, given the inelastic supply of housing (Alessie & Rouwendal, 2002).
As mentioned before, this study could have controlled for the business cycle by including an appropriate control variable. Instead, it chooses to address the endogeneity by adoption of an instrumental variables (IV) regression approach. As Campbell & Cooco (2007) argue, the correlation between house prices and consumption can also be driven by unobserved macroeconomic factors. Given their unobserved nature, these factors are hard to control for, such that the omitted variable bias is hard to address. Campbell & Cocco (2007) propose financial liberalization as an example. Financial liberalization may lead to more leniency towards debt, such that borrowing constraints are relaxed. Increased borrowing capacity may then increase housing demand and consumption. Future income prospects were also proposed in the introduction as a potential unobserved third factor.
This study proceeds by outlining the 2SLS approach that is used here. As was covered in previous paragraphs, this study has ample reason to suspect that the error term in (24) and (25) is correlated with house prices (and the other regressors). In order to address this endogeneity, a set of instrumental variables is used. Specifically, these are the moment conditions that are being exploited to obtain parameter estimates for the linear regression models outlined in (24) and (25):
𝐸𝐸{𝑧𝑧𝑡𝑡(𝑐𝑐𝑡𝑡− 𝜓𝜓0− 𝜓𝜓1𝑞𝑞𝑡𝑡− 𝜓𝜓2𝐸𝐸𝑡𝑡𝑞𝑞𝑡𝑡+1− 𝜓𝜓3ℎ𝑡𝑡𝑐𝑐+ 𝜓𝜓4𝑙𝑙𝑡𝑡− 𝜓𝜓5𝑟𝑟𝑡𝑡)} = 0 (26)
𝐸𝐸{𝑧𝑧𝑡𝑡(𝑐𝑐𝑡𝑡− 𝜗𝜗0 + 𝜗𝜗1(𝑟𝑟𝑡𝑡+ 𝑙𝑙𝑡𝑡 ) − 𝜗𝜗2(𝑞𝑞𝑡𝑡+ 𝑟𝑟𝑡𝑡− 𝐸𝐸𝑡𝑡𝑞𝑞𝑡𝑡+1) − 𝜗𝜗3𝑞𝑞𝑡𝑡− 𝜗𝜗4ℎ𝑡𝑡)} = 0 (27)
where 𝑧𝑧𝑡𝑡 is a vector that contains the set of instruments to be defined shortly. Specifically, the goal of
the 2SLS procedure is to obtain a set of parameter estimates that makes the left hand side of the moment conditions as close to zero as possible.
In the first stage of the 2SLS procedure, each right-hand side variable in (24) and (25) is regressed on the full set of instruments to obtain predictions. In the second stage of the 2SLS
estimation, 𝑐𝑐𝑡𝑡 is regressed on the set of predicted values. Ideally, the set of instruments is
uncorrelated with 𝑐𝑐𝑡𝑡, such that the predicted values are uncorrelated with the second stage residual.
Let this study now introduce the various tests that accompany the empirical estimation. A Hausman test is conducted to compare the OLS and 2SLS estimator. Under the null hypothesis of the Hausman, both estimators are consistent, whereas under the alternative hypothesis the OLS
estimator is inconsistent. Therefore, assuming that the instruments are valid, rejection of the null hypothesis suggests that the 2SLS approach is more appropriate.
An issue that needs to be addressed is the relevance of the instruments. Instruments need to have explanatory power for the variable that they are instrumenting. This study uses the F-test statistic of the first-stage regression to test for the joint significance of the instruments. Under the null hypothesis, the set of instruments have insufficient explanatory power for the variable they are supposed to instrument.
