Housing demand shocks and households’ balance sheets

We examine the dynamic effects of housing demand shocks on a large set of macroeconomic series and detailed household balance sheet components for different wealth groups. The results show that a positive housing demand shock translates into a large boom in economic activity and reveal notable heterogeneity among wealth groups. While households of all wealth groups make heavy use of home equity-based borrowing, we find a larger consumer spending sensitivity for poorer households. A historical decomposition suggests that housing demand shocks have largely contributed to the pronounced drop in poorer households’ consumption during and after the Great Recession.


Introduction
The financial crisis of 2007-2008 was closely related to the collapse of the US housing market. Accordingly, the growing literature suggests that housing demand shocks are significant drivers of business cycle fluctuations (Iacoviello and Neri 2010;Liu et al. 2013).
The tight connection between economic activity and housing is often ascribed to three main channels. The first one stems from Tobin's q effect, which indicates that rising house prices lead to an increase in real estate values over construction costs, thereby stimulating residential investment which can be a key component of GDP growth (Leamer 2007). A second transmission channel works via the credit market. A positive housing demand shock increases homeowners' assets and thus the value of collateral, mitigating households' and firms' credit constraints (Iacoviello 2005;Mian and Sufi 2011;Liu et al. 2013). The same balance sheet mechanism applies to the lending side, as financial intermediaries expand credit supply along with the increase in assets held (Adrian et al. 2010). The third channel is an implication of consumption smoothing in life cycle models. An unexpected and permanent increase in wealth leads households to borrow more and increase consumption. The dynamic interdependence between household balance sheets, the credit market, and the housing market is thus able to amplify each channel, possibly making it a powerful driver of real economic activity.
The experience of the Great Recession indicated that the strength of such feedback loops also depends on the heterogeneity of households' balance sheets. While traditional macroeconomic models assume a representative agent framework in which households are insured against individual wealth shocks, recent empirical evidence points to the importance of modeling housing, credit, and consumption using heterogeneous agent models (Bostic et al. 2009;Mian and Sufi 2011;Aladangady 2017). Of particular, interest has been the relationship between a shock to housing wealth and the cross-sectional response of consumption, as housing market spillovers are suggested to be largely concentrated on consumption (Iacoviello and Neri 2010, see also channel 2 and 3 above). A prominent example is Mian et al. (2013), who show that an increase in housing wealth implies markedly different consumption responses depending on households' initial net wealth. Berger et al. (2017) develop a quantitative model that stresses the importance of individual households' borrowing constraints in explaining the large reaction of aggregate consumption.
A proper understanding of the joint dynamics of the real economy, the financial sector, and households' balance sheets is thus crucial in forming more preemptive policy measures, be it fiscal or monetary. Given the many variables involved, a comprehensive empirical analysis requires an econometric framework that is able to sufficiently model such rich joint dynamics.
This article reexamines the empirical evidence concerning housing demand shocks and its propagation mechanisms in a dynamic environment consisting of a broad range of macroeconomic and financial series. To show the robustness of the results, we use a smaller dataset consisting of 73 variables and a larger one with 160 series. Both datasets comprise various balance sheet components for households belonging to four different wealth percentile groups. We estimate dynamic factor models (DFMs), which allow us to extract a few latent common factors from a large panel of economic series, thus capturing the underlying information without running into degrees of freedom problems. This is especially important in the case considered here, as the impact of a housing shock on household balance sheet components is less likely to be homogeneous across wealth groups. The dynamic effects of a housing demand shock are then obtained by imposing a set of theoretically motivated sign restrictions on the contemporaneous response of a few selected economic indicators and a large number of housing variables. The paper's main contributions to the literature are the following. First, the identification of the housing demand shock is arguably sharper than in the existing literature. The vast majority of studies impose potentially strong identifying assumptions by employing a temporal ordering to the impact matrix while using quarterly data (Jarocinski and Smets 2008;Cardarelli et al. 2009;Bagliano and Morana 2012;Cesa-Bianchi 2013;Buch et al. 2014). Based on the transmission channels described above, however, it seems likely that all economic indicators react within one quarter when the housing market is disrupted. While Furlanetto et al. (2019) identify a housing shock using only sign restrictions, it is not possible to analyze the effects on the housing market due to the use of a six-variable vector autoregression (VAR). Our identification scheme relaxes the possibly contaminated zero restrictions, while the model environment allows us to restrict and analyze the response of a broad set of housing series. Second, for four different wealth percentile groups, we assess the reactions of balance sheet components when faced with a housing demand shock. This allows us to analyze not only if the dynamic consumption and credit response differ with respect to the initial level of net wealth, but also whether the distribution of net wealth gains is uniformly distributed across wealth segments. A historical decomposition enables us to crosscheck the popular narrative that negative housing demand shocks have caused poorer households to cut consumption sharply during the Great Recession, while households at the top of the wealth distribution were unaffected. Finally, we compute the elasticity of consumption with respect to house prices for each wealth group and compare it to the literature on wealth effects. To the best of our knowledge, this is the first study to analyze these effects in a widely data-driven and dynamic environment. It is thus highly complementary to the empirical literature on the heterogeneous effects of housing shocks using microdata (Bostic et al. 2009;Mian and Sufi 2011;Mian et al. 2013;Aladangady 2017), which often relies on cross-regional regressions to obtain partial equilibrium estimates of the consumption or credit response. While we are concerned with the general equilibrium effects of a housing demand shock, our DFM imposes little structure a priori in contrast to studies on the wealth effect of housing using DSGE models (for example, Berger et al. 2017;Guren et al. 2020b).
Our results show that an unexpected positive housing demand shock causes a large and persistent boom of real economic activity and a brightening of labor market conditions, despite an immediate increase in interest rates. The expansion of credit and consumption aggregates along with house prices suggests that both the credit mechanism and the wealth effect are important transmission channels of housing shocks. The strong positive response of all unrestricted housing start series and residential investment provides some comfort to the identifying assumptions. The second part of our analysis provides evidence that housing demand shocks are key to understanding household balance sheet dynamics across the wealth distribution. In particular, impulse responses suggest that the reaction of durable consumption is a decreasing function of net wealth. Variance decompositions assign a bulk of the variation found in consumption to the housing shock, especially for the bottom 50% of households. The historical decomposition shows that the cumulative effects of housing demand shocks have significantly affected the consumption of the poorest during the Great Recession. However, we also find evidence that part of the cutback in the top 1% consumption is explained by housing demand shocks in that period. Elasticities of consumption with respect to house prices, which are a by-product of our structural model, suggest a larger spending sensitivity for weaker balance sheet households. Our results are highly robust across both datasets.
The rest of the paper is organized as follows. Section 2 discusses the econometric framework and structural identification of the housing demand shock. The data are outlined in Sect. 3. Impulse response functions and variance decompositions are analyzed in Sect. 4. Section 5 concludes. The Appendix provides additional results with alternative model specifications and gives a detailed overview of the data.

Econometric framework
Structural macroeconomic shocks are often identified using small-scale VAR models in order to conserve degrees of freedom. The inclusion of only a couple of series, however, is likely to cause omitted variable problems that may affect impulse responses and variance decompositions alike (see Bernanke et al. 2005 for a thorough discussion). Moreover, economic concepts such as "real activity" are hard to capture using only a specific data series. This issue is especially pronounced in the case considered here. Using only one or two housing series to identify a housing shock introduces an arguably large degree of arbitrariness. Finally, VARs allow the construction of impulse responses only for the included variables, which is often a subset of what the researcher or policymaker is interested in.
To take advantage of the information contained in large panel datasets, we employ a dynamic factor model (see Stock and Watson 2016 for an overview). Intuitively, the DFM approach boils down to extracting a small number of latent common factors that summarize the information from a much richer dataset. Consider the following dynamic factor model where y t is a (k × 1) vector of observed variables and f t is a (m × 1) vector of latent factors. The number of factors is typically much smaller than the length of the cross section, m << k. The idiosyncratic disturbances e t are uncorrelated at all leads and lags with f t and t and are assumed to have a diagonal covariance matrix R. The (k × m) loading matrices λ l relate the factors to all economic and financial indicators. Note that if s > 0 then the factor lags are allowed to directly affect the series in y t . Finally, φ p are coefficient matrices, each of dimension (m × m), governing the dynamics in the state Eq. (1b). Clearly, the state equation follows the common VAR structure. The factor model can also be expressed in static form (see Stock and Watson 2016) if we let h ≥ s + 1, F t = ( f t , . . . , f t−h+1 ) and * = (λ 0 , . . . , λ s ): Note that in contrast to studies using factor-augmented VAR (FAVAR) models, we do not impose that any factor be observed (for example, Bernanke et al. (2005) impose a short-term interest rate as an observed factor and use this assumption for identification of the structural shock). For our purposes, it is also not necessary to provide an economic interpretation of the latent factors as in Belviso and Milani (2006).

Estimation
We rely on now standard Bayesian methods to estimate the model in (2a-2b). The likelihood-based approach is able to explicitly exploit the structure of the state equation in the estimation of the factors (see Bernanke et al. 2005). As a by-product, it also delivers full posterior distributions naturally quantifying the extent of uncertainty. The estimation procedure consists of a multimove Gibbs sampler (Carter and Kohn 1994; see Kim and Nelson 1999 for an overview) in which the parameters are sampled conditional on the most recent draws of the factors, and the factors are drawn conditional on the most recent parameter estimates. Following Bai and Wang (2015), we employ the Jeffreys prior to account for the lack of a priori information about the model parameters. The Bayesian framework considered here is thus able to perform estimation and inference of large dynamic factor models with a dynamic structure in both the observation and the state equation.
It is well known that due to indeterminacy the factor model is not identified without further restrictions (see Stock and Watson 2016). The unobserved factors can always be rotated into an observationally equivalent representation. To achieve identification, we rely on the minimal restriction conditions derived in Bai and Wang (2015). More exactly, we assume that the upper (m × m) block of λ 0 is an identity matrix. Since the identifying restrictions concern only the contemporary loadings, the VAR(h) dynamics of the factors are left completely unrestricted. In other words, it is not necessary to impose the conventional practice that the covariance matrix of the dynamic factors f t is an identity matrix. A disturbance arising from the state equation is thus able to affect all macroeconomic and financial indicators in y t with no lags. The use of this minimal restriction strategy allows us to impose contemporaneous sign restrictions on any series to identify our structural housing demand shock.

Structural identification
We assume that the reduced-form vector of state-equation shocks t is a linear combination of structural shocks w t , such that t = A 0 w t . Under the assumption One popular approach to fully identify the system is to choose A 0 to be the Cholesky factor of the VAR covariance matrix as in Sims (1980). It is well known that the triangular nature of the Cholesky factor implicitly imposes a temporal ordering (see, for example, the discussion in Canova and De Nicolo 2002). In the context of housing shocks, this identification scheme has been followed by Cesa-Bianchi (2013) and Bagliano and Morana (2012). In contrast, Buch et al. (2014), Cardarelli et al. (2009) and Jarocinski and Smets (2008) impose a mixture of sign and zero restrictions, assuming that output or prices react to housing shocks only with a lag. Given the many channels through which the housing market may affect the economy, such zero restrictions are arguably imposing strong identifying assumptions. For that reason, we adopt the agnostic identification strategy by Uhlig (2005) and, for the factor model framework, Ahmadi and Uhlig (2015), and only restrict the sign of selected variables.
All sign restrictions are theoretically motivated and are keeping with the large literature summarized in Justiniano et al. (2015), Christiano et al. (2014), andFurlanetto et al. (2019). More specifically, we identify the housing demand shock by imposing that real GDP, core prices of personal consumption expenditures (PCE) and the 3month treasury bill rate react positively upon impact. This rules out that the identified shock is contaminated with supply or monetary shocks. It is, however, more challenging to disentangle the housing demand shock from investment shocks (see Justiniano et al. 2010) and other demand shocks (for example discount factor or fiscal shocks). Our strategy follows Furlanetto et al. (2019), who suggest that traditional demand shocks can be excluded by imposing a positive sign restriction on the response of the ratio of (real gross private domestic) investment over output. 1 Investment and housing shocks are thus assumed to create investment booms. To further separate housing from investment shocks, we restrict stock prices as measured by the S&P 500 to react positively. 2 Note that up to now, it is still not possible to distinguish a positive housing shock from a shock originating in the credit markets. Keeping with Furlanetto et al. (2019) and the literature in Justiniano et al. (2015), we restrict the loan-to-value (LTV) ratio to react negatively. This allows total credit to increase under the restriction that the value of the real estate does so by more. 3 Finally, a positive housing demand shock increases real estate loans as well as the quantity and prices of housing (Iacoviello and Neri 2010). We therefore use our detailed dataset to impose positive sign restrictions on aggregate real estate loans as well as on building permits and house prices in all four Census regions. 4 Since a shock is unexpected by nature, it is arguably more appropriate to constrain permits instead of housing starts, which are left unrestricted. 1 Restricting the ratio allows investment to increase when faced with a demand shock but less so than the remaining part of aggregate demand. 2 A positive investment shock increases the supply of capital and lowers its price. Since the price of capital is taken as a proxy of the stock market value for firms, an investment shock negatively impacts the value of equity (see the discussion in Furlanetto et al. 2019;Christiano et al. 2014). 3 More exactly, total credit amounts to total loans to the non-financial private sector, while housing value is given by real estate at the market value of households and nonprofit organizations. 4 The US Census Bureau splits the USA into four regions: the Northeast, the Midwest, the South, and the West.
In contrast to small-scale VAR studies also using sign restrictions (André et al. 2012;Furlanetto et al. 2019), our factor model allows testing whether the identified housing shock actually leads to new housing units being built.
To incorporate the sign restrictions we employ the procedure described in Rubio-Ramirez et al. (2010). For each draw from the reduced-form posterior, the algorithm works as follows. First, we produce A chol 0 using the Cholesky decomposition of the covariance matrix Q to obtain uncorrelated shocks as in a recursively identified model. Then we compute the QR decomposition of W = Q R, where W is a (m × m) matrix filled with independent standard normally distributed variables. Post-multiplying A chol 0 by Q forms a candidate structural impact matrix A cand 0 = A chol 0 Q. Contemporaneous impulse responses are then generated according to y irf 0 = * A cand 0 , which allows checking the sign restrictions. If this is not the case, we draw a new W and repeat the procedure until the sign restrictions are satisfied. Note that we follow the recommendations of Canova and Paustian (2011) in two ways. First, we restrict only impact responses to avoid the often questionable dynamic constraints. Second, the factor model framework allows us to impose a large number of sign restrictions to identify the structural shock. Moreover, all sign restrictions are motivated by the dynamic stochastic general equilibrium (DSGE) literature as advised by Musso et al. (2011).

Data
We estimate the dynamic factor model on two quarterly datasets, one containing 73 and the other 160 indicators. As suggested by  and Boivin and Ng (2006), a larger cross section may not necessarily improve estimation accuracy in factor models. It thus seems appropriate to use both a relatively small dataset consisting of only key series and a large one to check the robustness of the results. The sample starts in 1989Q3 and ends in 2019Q3. All indicators are transformed to induce stationarity, see the Appendix for a detailed description. The large dataset is an augmented version of the FRED-QD database (see McCracken and Ng 2020) with the main difference that household balance sheet data has been added. The smaller dataset builds on the same database but focuses on key economic indicators, the housing and credit market, and household balance sheet data.
To evaluate whether a housing demand shock has heterogeneous effects on households' balance sheets, we draw on the Distributional Financial Accounts (DFAs) provided by the Board of Governors (see Batty et al. 2019). The relatively new DFAs contain detailed time series on the assets and liabilities held by four different wealth percentile groups (bottom 50%, 50th to 90th percentiles, 90th to 99th percentiles, and the top 1%). Figure 1 shows the evolution of real net wealth for all wealth percentile groups. The greatest wealth losses are found between 2007Q3 and 2009Q1 and are especially concentrated in households belonging to the top decile. The subsequent recovery is associated with an unprecedented wealth level, however unequally distributed among the population. While the net worth of the bottom 50% is close to zero for the entire sample, the top 1% accounts for a substantial fraction of US wealth. In 2019Q3, around 70% of wealth is held by the top decile. The heterogeneous evolution among wealth groups is clearly related to individual composition effects. Wealthier households have traditionally been exposed more to cyclical assets like equity, as the largest fraction of wealth is of financial nature (see Fig. 2 for 2019Q3). Real estate is the principal asset component for households belonging to the bottom 50%. In contrast to other percentile groups, financial assets account for only a minor share of total assets. The liability side shows the poorest households' dependence on consumer credit, as they hold over half of the total consumer credit.
In order to ensure that results are not driven by population differences from the different-sized wealth groups, we scale the series of each group by the respective number of percentiles. 5 Moreover, all series enter the estimation procedure in standardized form.

Results
In this section, we present empirical results from our dynamic factor model with both datasets. To determine the number of unobserved factors, m, we compute the information criteria IC p2 and BIC 3 by Bai and Ng (2002) (see also the discussion in Bai and Ng 2008b), the ER and GR criteria by Ahn and Horenstein (2013) and the IC T * 1,c,n and IC T * 2,c,n criteria by Alessi et al. (2010). For the smaller dataset, all criteria suggest five factors except for ER = 2 and IC p2 = 8. The same two criteria are estimated to be ER = 2 and IC p2 = 6 with the rich dataset, while all others suggest four factors. We follow the majority and set m = 5 for the narrow and m = 4 for the more extensive database, but report results for a range of alternative specifications in the Appendix. We set s = 1 in the observation Eq. (1a), thus allowing a dynamic relationship between the latent states and the variables. According to the Bayesian information criterion (BIC), the factor dynamics in (1b) are characterized by a VAR(1) for the smaller and a VAR(2) for the larger dataset. We follow Uhlig (2005) and report the pointwise median together with 68% posterior bands. The y t vector has been ordered such that the first m series are given by leading indicators of different data groups. 6 All results are based on 90,000 draws from the Gibbs sampler, from which the first 87,000 are discarded as burn-in.
The presentation of our empirical results is organized around our two research questions. We begin with the question of how the housing demand shock is transmitted to the aggregate US economy before analyzing the responses of households' balance sheets. Figure 3 plots the impulse responses, estimated on the smaller sample, of the level of key indicators to a one standard deviation housing demand shock. The black line reports the median response. Results from the large dataset are vastly similar and therefore relegated to the Appendix (see Fig. 8).

Impulse responses
In line with the transmission channels discussed above, a housing demand shock generates a significant and persistent economic boom. Real GDP, industrial production, and capacity utilization increase between 0.5 and 0.6% within 1 year. Residential investment, a subcomponent of GDP measuring the purchase of newly built residential structures, rises disproportionally by 2% after four quarters. The economic expansion is reflected in the labor market indicators, as the unemployment rate decreases while the total number of nonfarm employees grows. On the credit side, real estate loans and consumer credit increase persistently over the impulse horizon, which conforms to the collateral channel of a housing demand shock. The fact that business loans grow only slightly and return to their initial level stands in contrast to studies identifying credit shocks (for example, Boivin et al. 2018), thus pointing toward a successful disentanglement of credit and housing shocks. The LTV ratio is restricted to be negative on impact but stays so for at least 4 years. Conforming to consumption smoothing arguments from life cycle models, both durable and nondurable consumption rise. Importantly, the response of durable consumption is more pronounced in magnitude than for nondurable consumption. Financial variables mirror the boom of real economic indicators. The 3-month treasury bill rate is hump-shaped, suggesting that the Fed increases its benchmark rate as a reaction to the initial rise of GDP growth and the capacity utilization index. The median response of the S&P 500 stock market index increases by around 4% over the horizon. Interestingly, the reaction of the consumption price index is relatively muted despite the economic expansion, confirming the empirical results in Furlanetto et al. (2019). More exactly, the core PCE price index is slightly positive for only a few quarters, after which the posterior distribution centers around the zero line. In contrast, house price indices of all four Census regions react strongly positively to the housing demand shock over the entire horizon. The S&P/Case-Shiller 10-City home price index, which was left unrestricted also on impact, confirms the price hike. In line with Tobin's q effect, rising prices for housing are associated with a general increase in building permits for at least 3 years. The fact that unrestricted housing starts rise in all four geographic areas provides further comfort to our identifying assumptions. All impulse responses discussed are robust to the choice of the dataset, even though the model specification differs and the extensive dataset contains more than twice as many variables as the smaller one. 7 Among these additional series are sectoral employment indicators, which provide further evidence that a housing shock has in fact been identified. Figure 9 in the Appendix plots the respective impulse responses and shows that the construction sector features the most pronounced reaction among all sectors. Table 1 shows the importance of housing demand shocks in explaining economic fluctuations during our 1989-2019 sample. While variance decompositions are calculated for each draw that satisfies the sign restrictions, the table presents median values at a 32-quarter horizon. The second column reports the fraction of the common component of the series explained by the housing demand shock. The third column shows the contribution of the common component to the overall variance of the indicators. The fourth column is simply the product of the previous two and represents the fraction of the total variability explained by the housing demand shock. The next three columns show the results for the large dataset.

Variance decompositions
In line with the literature, our variance decompositions show that housing demand shocks are significant drivers of business cycle fluctuations. The housing shock explains between 24 and 44% of the variance of the common component of real economic indicators such as GDP, the industrial production index, and the capacity utilization measure. Labor market indicators, credit series, and the 3-month TB rate are also well explained. Importantly, the housing demand shock has high explanatory power for housing starts, housing permits, and house price variation for all four Census regions. Columns 4 and 7 indicate that our structural model explains around 20% of the total variation in the house price series. Columns 3 and 6 of Table 1 show that five and four unobserved factors are able to capture a large fraction of fluctuations in key economic indicators. The second column reports the fraction of the common component of the series explained by the housing demand shock at a 32-quarter horizon. The third column shows the contribution of the common component to the overall variance of the indicators. The fourth column is simply the product of the previous two and represents the fraction of the total variability explained by the housing demand shock. The next three columns show the results for the large dataset

Do households respond differently to the housing demand shock depending on net wealth?
The substantial aggregate effects of a housing demand shock demonstrate the importance of understanding the underlying transmission channels. Of particular interest after the financial crisis has been the relationship between fluctuations in housing wealth and the response of consumption. In fact, housing market spillovers are suggested to be largely concentrated on consumption (Iacoviello and Neri 2010). As outlined above, an increase in housing wealth may (a) raise collateral and therefore mitigate credit constraints and (b) increase consumption due to the wealth effect. Both channels are arguably sensitive to the cross-sectional distribution of wealth and the composition of households' balance sheets. For example, richer households are less likely to face credit constraints and may give the precautionary savings motive a small role. This translates into a smaller elasticity to consume out of wealth compared to the poor. As a consequence, the aggregate consequences of a housing shock might largely be driven by the consumption response of poorer households, although housing is a substantial balance sheet component for all wealth percentile groups. Given the economic importance, an extensive number of studies have analyzed whether and to what extent (housing) wealth shocks cause heterogeneous responses among households. The hypothesis of a representative agent is typically rejected and economically significant wealth effects are reported (see, for example, Mian and Sufi 2011;Mian et al. 2013;Guren et al. 2020b;Aladangady 2017;Berger et al. 2017). To isolate the housing wealth effect, empirical studies frequently rely on cross-regional regressions using exogenous sources of housing variation as instruments. This strategy delivers partial equilibrium estimates, as aggregate general equilibrium effects are absorbed by the constant or the time fixed effect in a panel regression. 8 In contrast and highly complementary to this strand of literature, we are interested in the general equilibrium effects of housing shocks. Looking again at the consumption response of different wealth percentile groups, it is interesting to see whether the implications of partial equilibrium estimates still hold. For example, it is well possible that the financial wealth effect associated with booming stock markets ignites consumption of the rich, thus leveling the cross-sectional consumption response. To understand the aggregate general equilibrium dynamics in the last section, we thus analyze the general equilibrium behavior of households' balance sheets. In contrast to studies using DSGE models (Berger et al. 2017;Guren et al. 2020b, among others), our DFM imposes little structure a priori, thus mitigating the possibility that results are driven by a potentially misspecified model structure. Clearly, this comes at the cost of not being able to obtain "deep" structural parameters, for example the wealth effect of housing values conditional on household characteristics. It is also important to note a drawback concerning the disaggregated consumption measures used in this study. The use of household balance sheet data implies that nondurable consumption is not available, so that only the reaction of durable consumption can be estimated. However, comparing both aggregate consumption responses in the last section shows a relatively muted reaction for nondurable consumption in terms of magnitude. Durable consumption and (residential) investment are the primary forces driving the pronounced GDP response. The literature also suggests that increased spending due to housing wealth is largely concentrated on durable goods (Mian et al. 2013; Andersen and Leth-Petersen 2019).

Impulse responses
Estimated on the small sample, Fig. 4 plots impulse responses of the level of real household balance sheet components to the housing demand shock. The first five columns show assets and liabilities, while the last column plots the response of total net wealth. The rows list the four wealth percentile groups. Results from the large dataset are almost identical, 9 see Appendix Fig. 10. Note that responses are highly data-driven, as all balance sheet series are left completely unrestricted. A quick glance is enough to observe that a housing demand shock is associated with a general expansion of balance sheets across all wealth segments. The increase in assets generally dominates the higher debt burden, although net wealth for households belonging to the bottom 50% slowly reverts to the initial state. All groups participate in the newly built structures, as the real estate value held by each segment rises somewhat more than the house price indices in the last section. However, the median response is most pronounced for households in the bottom 50% with a final growth of around 3.5%. In line with the stock market boom, financial assets held by all wealth segments increase. For both groups in the top decile, the response of financial assets clearly drives total net wealth dynamics (in 2019Q3, 85% and 77% of total assets are of financial nature for the top 1% and the 90-99th percentile group, respectively). On the credit side, we would expect a stronger tendency to borrow among poorer households, as net wealth is likely to proxy for credit constraints. In fact, Mian and Sufi (2011) provide evidence that only households at the top of the credit score distribution do not increase total debt leverage when faced with a housing wealth shock. Our impulse responses imply a significant and persistent expansion of mortgages across the wealth spectrum. Heterogeneity is not especially accentuated, although median mortgage expansion is largest for the bottom 50%. Comparing the evolution of mortgages and credit, we find equity extracted from housing to be more pronounced than non-housing-related consumer credit for all groups (note that home equity lines of credit are also included in the mortgage category). Our findings support the evidence that home equity-based borrowing is not used to pay down expensive consumer credit balances (Mian and Sufi 2011), as only the top 1% chooses to deleverage.
The real consequences of even a broad credit growth, however, ultimately depend on how households use their new liquidity. If most households just keep new money in the bank account, we would arguably observe little change in real outcomes. Apart from residential construction, the reaction of consumption is key to understanding the strong linkage of housing shocks and business cycle fluctuations. The obtained impulse responses for durable consumption suggest that household balance sheet strength plays an important role in determining aggregate demand. The estimated long-term increase for the bottom 50% of households centers around 1.75%, while the effect on the next 40% is in the range of 1%. Households in the 90th to 99th percentiles increase durable consumer spending by about 0.75%, although the posterior mass concentrates above the zero line only 3 years after the shock. For the richest percentile of households, the housing demand shock first raises durable consumption before reverting back to the initial value. Conditional on the stock market boom and the remarkable holdings of financial assets of the top 1%, the muted reaction of consumption suggests a small role for financial wealth in determining consumption fluctuations. This conforms to the literature estimating financial wealth effects, which are reported to be substantially smaller than housing wealth effects (Carroll et al. 2011;Bostic et al. 2009;Slacalek 2009;Muellbauer 2008). In summary, the response of aggregate durable consumption to a housing demand shock is estimated to be a decreasing function of net wealth. The evidence provided by the literature that the spending of the rich does not react much to a housing wealth shock thus carries over to the factor general equilibrium case. However, given the notable net wealth of 50th to 90th wealth percentile households, one may wonder why the respective response of durable consumption is pronounced in the first place. Following Kaplan et al. (2014), a possible explanation is that a fraction of households belonging to this wealth segment are "wealthy hand-to-mouth." Despite owning sizable amounts of assets, these households hold balance sheets that carry little liquid wealth. As a result, they are more susceptible to wealth shocks than non hand-to-mouth households. 10 Table 2 shows the importance of the housing demand shock in explaining the variance of balance sheet components for each wealth group.

Variance decompositions
Irrespective of the dataset, the housing shock is a significant driver of the common component of all balance sheet indicators. The variance explained of total net wealth is sizeable, depending on wealth group and dataset between 21 and 42%. The housing demand shock not only has high explanatory power for fluctuations of real estate and mortgage components, i.e., two indicators intimately related to a housing shock, but also for the variation in financial assets. The variance decompositions for consumer durables confirm the heterogeneous pattern found in our graphical analysis. For the bottom 50% of households, the housing shock explains 44% (56%) of the common component of durable consumption using the small (large) dataset. Also for the poorest group, columns 4 and 7 show that the structural model explains between 20 and 25% of the total variation in durable consumption. Although still considerable, the shock only explains about 20% (29%) of the common component and about 5% of total consumption variation for the wealthiest percentile. Our variance decomposition thus confirms that housing shocks are a vital component to modeling balance sheet dynamics in general and consumption dynamics of poorer households in particular. Table 2 also shows that common disturbances are overall able to capture a large fraction of fluctuations in the balance sheet series.

Historical decompositions
It is widely believed that the housing market has played a significant role in explaining the outbreak and strength of the Great Recession (Mian and Sufi 2011;Mian and Sufi 2014). According to this narrative, negative house price shocks had a large effect on the economy via consumption spending. The aggregate collapse of consumption, so the argument, was mainly driven by poorer households, who cut spending disproportionally sharp as a result of declining housing wealth. In this section, we show historical decompositions to quantify how much the identified housing demand shock explains of the historically observed consumption patterns. Figure 5 attributes the historical variation in demeaned consumption of each wealth group to housing demand shocks. The shaded area marks the period of the Great Recession. Results from the large dataset are slightly more pronounced and relegated to the Appendix (see Fig. 15). The bottom 50% of households cut durable consumption sharply during the crisis and stayed below the mean growth rate until 2017. The historical decomposition provides evidence that a large fraction of this contraction can be explained by housing demand shocks, both during and in the aftermath of the Great Recession. Although less pronounced, the cumulative effects of housing The second column reports the fraction of the common component of the series explained by the housing demand shock at a 32-quarter horizon. The third column shows the contribution of the common component to the overall variance of the indicators. The fourth column is simply the product of the previous two and represents the fraction of the total variability explained by the housing demand shock. The next three columns show the results for the large dataset shocks also explain part of the cutback in durable consumption by the next 40%. In line with the variance decompositions, our structural model in general does not deliver much explanatory power for the evolution of consumption growth of the richest decile. During the Great Recession, however, the housing demand shock does explain about one percent of the contraction in consumption of the richest percentile. These results may seem contrasting to the findings of Mian and Sufi (2014), which suggest a muted reaction of the richest households' consumption when faced with negative housing wealth shocks. The apparent discrepancy is no contradiction but just highlights the methodological difference: A housing demand shock is a housing wealth shock, but not exclusively. The consumption of each wealth group is arguably determined by distinct channels, and a housing demand shock impacts on all. A result that carries over from the partial to the general equilibrium setting, however, is that households belonging to the bottom 50% have strongly reduced consumption due to negative housing shocks. Importantly, these adverse effects have pushed growth below mean rates until only recently.

Long-term elasticity of consumption
The literature on wealth and collateral effects of housing frequently calculates the elasticity of consumption with respect to house price shocks. For example, Carroll et al. Regarding heterogeneity across the wealth distribution, they provide evidence that elasticities of consumption are smaller for richer households. We compare these results to the longterm elasticities implied by our impulse responses for durable consumption and house prices. To obtain one aggregate price index, we take the population-weighted average over the responses of the four (Census region) house price indices for each draw. Figure 6 shows the implied elasticities for all wealth groups based on the small dataset after 32 quarters. For each boxplot, the bold horizontal line indicates the posterior median. The first and third quartile is given by the upper and lower end of the box, respectively. The lower whisker shows the 16th percentile, while the upper whisker shows the 84th percentile of the posterior distribution. Figure 7 shows the results for the large dataset. The reported long-term median elasticities cover a wide range between 0.1 and 1.1. In line with the literature, we find estimates to be decreasing with household balance sheet strength. A one percent persistent increase in aggregate house prices is associated with a moderate 0.1% increase in durable consumption for the richest percentile. In contrast, consumption of the poorest 50% is estimated to match the rise in house 11 Since they calculate marginal propensities to consume (MPCs) in 2007 dollars, estimates have to be multiplied by the ratio of housing assets to personal consumption expenditures for 2007. 12 Their estimates need to be scaled by the mean ratio of housing to total wealth in order to be comparable. The mean ratio in their data is between 0.25 and 0.33. prices one-to-one in the long term. Median elasticities for households in the 50th to 90th wealth percentiles are between 0.6 and 0.7, which is close to the 0.5 estimates of the next 9%. The fact that median elasticities decline relatively slowly with wealth confirms the empirical results in Berger et al. (2017) and is at the center of recent work by Kaplan et al. (2014) on wealthy-hand-to-mouth households. Except for the richest percentile, the obtained elasticities are on the upper range when compared to the literature on wealth effects. Clearly, our median estimates need to be interpreted with caution, as posterior masses are wide for each boxplot. However, the location of the posterior distributions indicate the presence of heterogeneous elasticities across the wealth distribution.

Conclusion
In this article, we have reexamined the evidence on the propagation mechanism of housing demand shocks to aggregate economic activity and provide new evidence on the empirical link between aggregate outcomes and household balance sheet dynamics. Using a dynamic factor model and two different datasets, we identified shocks by imposing theoretically motivated sign restrictions on a few selected economic indicators and a large number of housing series.
The results show that a positive housing demand shock generates a substantial and persistent economic boom. In line with the outlined transmission channels, we find a large increase in residential investment, aggregate mortgage loans and aggregate consumption. Real economic indicators such as GDP, the industry capacity utilization rate, and the industrial production index increase despite an immediate rise of interest rates. Variance decompositions reveal that housing demand shocks explain a large fraction of business cycle fluctuations in general and house price variation in particular. The common factors are shown to adequately capture the movements in observable variables.
The second part of our analysis provides evidence that housing demand shocks are key to understanding household balance sheet dynamics. Based on detailed time series for four different wealth percentile groups, our results support the finding that heterogeneity across the wealth distribution matters. While this is true especially for durable consumption, we also find important cross-sectional similarities: All wealth segments profit from a positive housing demand shock in terms of net wealth. Also, each wealth group extracts a significant amount of equity from housing, although the response is most pronounced for the poorest 50% of households. Given this group's substantial holdings of consumer credit, we might expect that the new liquidity is used to pay down the more expensive consumer credit balances. In line with the literature, we do not find such an effect. Consumer credit increases for all groups but the richest percentile, which holds a negligible amount of consumer credit and is likely not to be drained from the associated costs. Importantly, the response of durable consumption is a decreasing function of net wealth. Variance decompositions attribute a substantial fraction of durable consumption variation to the housing demand shock, especially for the bottom 50% of households. The structural model is in general well suited to explain household balance sheet variation. A historical decomposition of durable consumption confirms the narrative that housing shocks have caused a significant part of the fall in durable consumption for the poor during the Great Recession. However, while the cumulative effects in general are negligible for the wealthiest percentile of households, we find evidence that the shock has negatively affected their consumption in that period. Finally, we translate impulse responses into elasticities of consumption with respect to house prices. Although uncertainty regarding these estimates is high, results suggest a larger spending sensitivity for weaker balance sheet households. This result is important for policymakers, as the strength of housing shocks is to some extent determined by the level of wealth inequality. Negative effects could thus be mitigated by reducing the strong dependency of poorer households on housing assets. Altogether, our findings indicate that household balance sheets play a significant role in determining aggregate outcomes. All results are robust to two different datasets and model specifications.
Further research should be devoted to analyzing the effects of housing demand shocks conditional on other households' characteristics. For example, it would be interesting to see what the implications are depending on tenure choice. The reaction of renters is likely to be different than the one of outright owners and mortgagors, as both the wealth and the credit channel are absent. Campbell and Cocco (2003) show that households in the first 25 percentiles of the wealth distribution do not own any housing, while it accounts for almost 70% of all assets held by households in the 40% wealth percentile. Due to data limitations, it is not possible to disentangle the effects on the two dissimilar groups in this study, which is a promising avenue for further work.

Funding Open access funding provided by Swiss Federal Institute of Technology Zurich
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Technical details
Conditional on the factors, we assume the parameters of the state equation to follow Jeffreys prior. In the observation equation, the covariance matrix R is assumed to be diagonal with the loadings and R following a normal-inverse gamma prior. So given the ((T − s) × m(s + 1)) matrix F and Y containing the factors and the data, each row of * and the associated diagonal entry of R is drawn equation-by-equation. If we denote the ith row of the loadings matrix * by * i , y i the ((T − s) × 1) vector consisting of the ith observation variable, and σ 2 i the ith diagonal entry in R, then the priors are specified as π( . In this case, the posterior is characterized as follows: * Following Bai and Wang (2015), the upper left (m × m) block of * is restricted to be an identity matrix. The state equation can be written in matrix form as where ξ is a ((T − h) × m) matrix containing the factors, X is a ((T − h) × mh) matrix containing the lagged factors, and * is equal to the upper m rows of . Defining φ = vec( * ) and employing a diffuse prior π(Q, φ) ∝ π(Q) ∝ |Q| −(m+1)/2 gives us a posterior in the form of The priors for the observation equation are set to be v 0 = m + 3, s 0 = 0.1, s+1) . The factors are provided by the Kalman filter and subsequent backward sampling. The Gibbs sampler iterates between drawing the factors and drawing the parameters, such that the joint posterior is numerically approximated.

Data
The first column gives the variable names from the FRED-QD database (see McCracken and Ng 2020), except for the series ending with *. For these cases see the description in the second column. The third column gives the code of how each series y i is transformed to stationarity. Here, (1) means no transformation, (2) is y it , (5) is log(y it ), and (6) is 2 log(y it ). The fourth column indicates whether the series is part of the large dataset (0), small and large dataset (1), or only the small dataset (2) (Tables 3,4,5,6,7,8,9,10,11,12,13,14,15).       Producer price index by commodity for fuels and related products and power: natural gas 5 0 WPU0561 Producer price index by commodity for fuels and related products and power: crude petroleum 5 0       To ensure comparability between the household balance sheet series, we eliminate population differences by dividing the series of each group by the respective number of population percentiles. All household balance sheet series are deflated using the core PCE deflator