The housing channel of intergenerational wealth persistence

Wold, Ella Getz; Aastveit, Knut Are; Brandsaas, Eirik Eylands; Juelsrud, Ragnar Enger; Natvik, Gisle James Working Paper The housing channel of intergenerational wealth persistence Working Paper, No. 16/2023 Provided in Cooperation with: Norges Bank, Oslo Suggested Citation: Wold, Ella Getz; Aastveit, Knut Are; Brandsaas, Eirik Eylands; Juelsrud, Ragnar Enger; Natvik, Gisle James (2024) : The housing channel of intergenerational wealth persistence, Working Paper, No. 16/2023, ISBN 978-82-8379-306-2, Norges Bank, Oslo, https://hdl.handle.net/11250/3166797 This Version is available at: https://hdl.handle.net/10419/310387 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ Working Paper The housing channel of intergenerational wealth persistence Norges Bank Research Authors: Ella Getz Wold Knut Are Aastveit Eirik Eylands Brandsaas Ragnar Enger Juelsrud Gisle James Natvik Keywords: Housing market, intergenerational wealth, wealth inequality 16 | 2023 Norges Bank Working Paper 1 Working papers fra Norges Bank, fra 1992/1 til 2009/2 kan bestilles på epost: [email protected] Fra 1999 og senere er publikasjonene tilgjengelige på www.norges-bank.no Working papers inneholder forskningsarbeider og utredninger som vanligvis ikke har fått sin endelige form. Hensikten er blant annet at forfatteren kan motta kommentarer fra kolleger og andre interesserte. Synspunkter og konklusjoner i arbeidene står for forfatternes regning. Working papers from Norges Bank, from 1992/1 to 2009/2 can be ordered by e-mail: [email protected] Working papers from 1999 onwards are available on www.norges-bank.no Norges Bank’s working papers present research projects and reports (not usually in their final form) and are intended inter alia to enable the author to benefit from the comments of colleagues and other interested parties. Views and conclusions expressed in working papers are the responsibility of the authors alone. ISSN 1502-8143 (online) ISBN 978-82-8379-306-2 (online) The housing channel of intergenerational wealth persistence∗ Ella Getz Wold†Knut Are Aastveit‡Eirik Eylands Brandsaas§ Ragnar Enger Juelsrud¶Gisle James Natvik‖ December 2023 Abstract We use Norwegian tax data and a life-cycle model with housing to study how wealth transmits across generations through the housing market. After controlling for a rich set of attributes, households with richer parents are nearly 15% more likely to be homeowners at age 30. Moreover, when entering, they have higher leverage and buy homes worth 15% more. Estimates using international stock market returns as a shiftshare instrument support a causal interpretation. We further document that housing outcomes when young are important determinants of midlife wealth. This holds also when using plausibly exogenous variation in homeownership caused by the timing of intra-family deaths. As a result, housing gaps caused purely by parental wealth explain 12% of intergenerational wealth persistence, making housing equally important as the combined impact of a wide range of household characteristics including income and education. We explore new mechanisms for parental support, such as intra-family housing transactions below market value. Through the lens of our model, house price expectations stand out as a key driver of the magnitude of the housing channel of intergenerational wealth persistence. Keywords: Housing market, intergenerational wealth, wealth inequality JEL Codes: D31, E24, G51, R21 ∗This paper should not be reported as representing the views of Norges Bank or the Federal Reserve System. The views expressed are those of the authors and do not necessarily reflect those of Norges Bank or the Federal Reserve System. We gratefully thank Matteo Bennetton, Alessandra Fogli, Lars Lochstoer, Erling Røed Larsen, Nitzan Tzul-Ilan and an anonymous referee for the Norges Bank Working Paper Series for insightful comments, as well as participants at the BI Norwegian Business School, the 2023 CEBRA Annual Meeting at Columbia University, the 14th Nordic Conference on Register Data and Economic Modelling, Norges Bank, the Norwegian School of Economics, the Norwegian University of Science and Technology, Statistics Norway, the UCLA/SF Fed Conference on Housing, Financial Markets and Monetary Policy, the University of St. Gallen workshop on Macroeconomic implications of housing, household finances, and wealth dynamics, the 3D-In-Macro Workshop, the 12th European and 17th North American Meetings of the Urban Economics Association. †BI Norwegian Business School. Email: ella.g.w[email protected] ‡Norges Bank and BI Norwegian Business School. Email: kn[email protected] §Board of Governors of the Federal Reserve System. Email: [email protected] ¶Norges Bank. Email: [email protected] ‖Norges Bank and BI Norwegian Business School. Email: [email protected] 1 Introduction Many parents continue to financially support their children as they enter adulthood – either indirectly or directly. The housing market stands out as especially attractive for parental support as i) barriers to entry make parental support key to early homeownership, and ii) high leverage in housing investments amplifies returns to equity. More than 40% of homeowners in the United States report receiving financial support from parents in order to buy a home. The same holds in Norway, the setting of our study.1In this paper we first study how parental wealth affects child housing outcomes, and second, to what extent these housing outcomes increase later-in-life wealth. Together, these two effects pin down the housing channel of intergenerational wealth persistence. To illustrate how important housing can be for wealth accumulation, consider a numerical example using the actual evolution of asset prices. Imagine investing $100 in stocks or the Norwegian housing market in the early 1990s. Crucially, and in line with the data, the housing investment is initially levered at 0.9, whereas the stock purchase is not. Twenty-five years later, the $100 has grown to $6,000 in the housing market, compared to $4,600 in the stock market (with the equivalent of mortgage payments re-invested each year).2In this simple example, the owner stays in the home throughout and pays down the mortgage uniformly, yielding an average leverage of only 0.26 over the 25 years of our thought experiment. If the household instead re-invests in more expensive housing over time, as young people typically do, the housing return will be substantially higher. The high return on equity in the housing market applies to everyone – irrespective of parent wealth. Still, substantial barriers to entry means that housing can be important for intergenerational wealth persistence. First, housing is generally indivisible. Second, buying or selling a home entails sizable transaction costs. Third, and perhaps most importantly, lenders apply borrowing constraints, such as loan-to-value and debt-to-income caps. Frictions thus prevent many young households from accessing the relatively high returns that the housing market provides. This creates a natural role for affluent parents to support their offspring in the housing market, by accelerating entry and facilitating higher home investments relative to income. As our numerical example illustrates, the consequences for later-in-life wealth can be large. In this paper, we use Norwegian tax data merged with housing transactions data from 1These numbers are based on an online survey we performed on homeowners below the age of 50 using the platform Survey Monkey, see Appendix Figure A.1. The share is similar to that in other surveys. 2Specifically, we assume an additional amount equal to the debt servicing costs of the mortgage is re-invested each year when calculating the return on the stock investment. For detailed calculations, see Appendix B. 1 the Land Registry to study the importance of parental wealth for housing market outcomes and thereby midlife wealth. To complement the administrative data we also perform surveys in Norway and the US on financial support from parents to child. To better understand why parental wealth matters, we document several mechanism and assess their quantitative importance. Thereafter, we build a life-cycle model with housing that fits the empirical patterns and use it to assess the importance of house price growth and mortgage regulation for the magnitude of the housing channel of intergenerational wealth persistence. We first document large gaps in housing outcomes by parental wealth. Our baseline wealth measure is simply an indicator for whether within-cohort parental wealth is in the upper half of the wealth distribution, although we also consider percentile wealth ranks for robustness. We show that households with richer parents are 15 percentage points (≈30%) more likely to be homeowners at age 30. Conditional on entering the housing market, they buy homes that are worth $60 000 (≈30%) more and are eight percentage points (≈10%) more leveraged. We refer to these differences as “housing gaps”. The documented housing gaps serve as our starting point for making four distinct contributions to the existing literature. Our first contribution is to document the impact of parent wealth on housing outcomes, using a structural mediation analysis (a statistical decomposition) and a shift-share instrument for parental wealth. We decompose the housing gaps into three components or mediators: pure parental wealth,other parental attributes and household attributes. This is useful, as it allows us to determine not only the relative importance of different attributes and how it has evolved over time, but also determine why certain attributes are important. Specifically, an attribute can be important if there is a large gap in this attribute or because it has a large impact on housing outcomes. Our mediation analysis attributes nearly half of the observed gaps in homeownership and purchase price to parental wealth, and the other half to household attributes. For leverage however, parental wealth alone explains the entire gap. Other parental attributes have modest importance. This means that even after accounting for a wide set of parental and household characteristics, we still find that households with richer parents are nearly 15% more likely to be homeowners at age 30. Moreover, conditional on entering, they buy homes that are worth 15% more and are nearly 10% more levered. If unobservable variables correlated with parental wealth have direct impacts on housing outcomes, this could bias our results. We therefore exploit plausibly exogenous variation in parent wealth resulting from international stock market returns interacted with lagged stock market exposure in a shift-share analysis. The estimated impact of parental wealth on entry probabilities aligns quantitatively with the pure parental wealth component identified in the mediation analysis, supporting a causal interpretation of our findings. 2 Our second contribution is to document the impact of housing outcomes on intergenerational wealth persistence, again using a structural mediation analysis and an instrumental variable approach based on the timing of intra-family deaths. We decompose the wealth persistence into a pure parental wealth channel, an other parental attributes channel, a household attributes channel, and a housing channel. For the housing channel to be important, two conditions must be satisfied. First, housing outcomes must be highly correlated with parental wealth (our first contribution). Second, housing outcomes must have a substantial impact on wealth accumulation. We find that households with richer parents are 15 percentage points (=35%) more likely to themselves be wealthy at midlife. More than 1/4 of this intergenerational wealth persistence is accounted for by earlier homeownership for households with richer parents. Of the homeownership effect, roughly half is due solely to the impact of parental wealth on housing. This impact is large, equal in size to the combined effect of parental wealth on household income, education, location and number of household members. If unobservable variables correlated with housing outcomes have direct impacts on midlife wealth, this could bias our results. We therefore exploit plausibly exogenous variation in the timing of housing market entry caused by the timing of intra-family deaths. The estimated impact of entry age aligns quantitatively with the mediation analysis, supporting a causal interpretation of our findings. Our third contribution is to uncover through which mechanisms parental wealth affects housing outcomes. We consider a novel channel referred to as intra-family sales. Richer parents are 60% more likely to co-purchase a house with a child, and nearly 10% more likely to sell a house directly to a child. Homes sold by parents to their offspring have an estimated price discount of 25%. Moreover, as previously established for other countries, e.g. Guiso and Jappelli (2002), we find evidence supportive of direct wealth transfers. Finally, following Benetton et al. (2022), we show that parental equity extraction is positively correlated with entry in the housing market. We extend their results and document that the importance of this channel varies with parental wealth – also when conditioning on homeownership. To quantify the importance of the mechanisms considered, we perform back-of-the-envelope calculations based on i) the share of parents who engage in each mechanism, and ii) the impact on children’s entry probabilities. We find that the mechanisms discussed can explain more than half of the impact of parental wealth on offsprings’ housing outcomes. Our fourth contribution is to use a standard life-cycle model with housing and exogenous parental wealth to i) show that our empirical findings can be recovered under a standard calibration and ii) assess counterfactual scenarios. We model parental support as a financial transfer in early adulthood, and pick the transfer size in the model to match 3 the empirical magnitude of the housing channel of intergenerational wealth persistence (contribution 2), which results in plausible transfer magnitudes. Having shown that a standard model augmented to include exogenous parental wealth can replicate the empirical estimates, we move on to a counterfactual analysis in which we change (expected) house prices and mortgage market regulation. This is interesting for at least two reasons. First, policy makers have a number of tools they can use to influence these factors. Second, these factors vary substantially across both time and space, making them important for thinking about external validity and what we can expect of the housing channel of intergenerational wealth persistence moving forward. Our model findings suggest that while realized house price growth has a modest impact on the housing channel, expected house price growth has a substantial impact. Lowering house price expectations and allowing households to adjust their portfolios and leverage in response to these expectations substantially reduces the housing channel of intergenerational wealth persistence. This is driven by a large reduction in the impact of parent support on homeownership, as homeownership – especially at early ages – becomes less attractive. As a second counterfactual scenario, we use the model to evaluate how the housing channel of intergenerational wealth persistence depends on mortgage regulation. Tighter mortgage regulation, especially stricter loan-to-value limits, increases the importance of parental support, thereby strengthening the housing channel of intergenerational wealth persistence. Related literature Our paper lies at the intersection of three distinct literatures, which study i) the persistence of wealth across generations, ii) the importance of parents for child housing market outcomes, and iii) the relevance of housing outcomes for later-in-life wealth. In this paper, we lean on the combined insights of these three literatures, and offer the first decomposition and quantification of the housing channel of intergenerational wealth persistence. First, several studies have documented that wealthy parents tend to have wealthy children. See for instance Chiteji and Stafford (1999), Charles and Hurst (2003), Boserup et al. (2016), Black et al. (2017), Adermon et al. (2018) and Fagereng et al. (2021). We contribute by focusing on the housing market as a key driver of wealth persistence across generations. Because the housing market is heavily regulated, policy makers have ample room to affect intergenerational wealth persistence working though housing. Second, a number of papers have shown that parents matter for children’s housing market outcomes. Most of these studies – including Engelhardt and Mayer (1998), Guiso and Jappelli (2002), Luea (2008), Kolodziejczyk and Leth-Petersen (2013), Blickle and Brown 4 (2019), Brandsaas (2021) and Boileau and Sturrock (2023) – focus on the impact of parental transfers on housing market entry. Relatedly, Benetton et al. (2022) study the importance of parental home equity extraction. Halvorsen and Lindquist (2017), Lee et al. (2020) and Bond and Eriksen (2021) document a positive correlation between parental wealth and entry into the housing market, while Daysal et al. (2023) show that increases to parental housing wealth passes through to child housing wealth. We contribute by taking a broader approach, focusing not only on parental transfers or one single mechanism, but on the causal influence of parental wealth in general. This is crucial, as it allows us to quantify how important housing is for intergenerational wealth persistence. We also document novel mechanisms, and assess the quantitative importance of each mechanism. Finally, there exists a somewhat smaller literature establishing the importance of housing and mortgage decisions for wealth accumulation over the life cycle. Using Norwegian data, Eggum and Larsen (2023) show that capital gains on housing are important for wealth inequality. Di et al. (2007) and Turner and Luea (2009) show that homeownership status is important for wealth accumulation using PSID data, while Bach et al. (2020) use Swedish tax data and find that housing and mortgage choices taken while young are key determinants of households’ position in the wealth distribution at retirement. Relatedly, Bernstein and Koudijs (2020) document the “critical importance” of mortgage decisions for household wealth building. We contribute by using plausibly exogenous variation in age of entry caused by the timing of intra-family deaths to quantify the impact of entry age on midlife wealth, and by isolating the impact which is working through parent wealth. 2 Data In this section we present the register data which is the basis of our empirical analysis and two online surveys we conducted to complement the register data. 2.1 Register data We use Norwegian administrative data from Statistics Norway, merged with housing transaction data from the Land Registry. The former provides household balance sheet information and allows us to link parents and children. The latter gives us accurate information on housing transactions and allows us to follow the ownership of specific houses over time. In this section we discuss sample selection and the measurement of key variables, and provide some summary statistics of special interest. 5 The homeownership gap at age 30 is decomposed according to equation (2). The household attribute component is marked in red in Figure 1a, and accounts for roughly half of the homeownership gap on average. That is, the fact that households with richer parents have other observable characteristics than those with poorer parents can account for half of their extra ownership rates. Among these attributes, household income is by far the most important characteristic, followed by the number of household members and education, as shown in Appendix Figure A.5. The total importance of household attributes has increased over time. Other parental attributes – education, income, location and number of children – are less important in explaining ownership gaps, as captured by the gray area. The share of this component has remained small and stable throughout the sample period. Finally, the pure parental wealth component is captured by the blue area in Figure 1a and accounts for roughly half the ownership gap on average. This implies that, even after controlling for a large set of household and parent characteristics, households with richer parents are nearly 15% more likely to be homeowners at age 30. The size of the pure parental wealth component has remained quite stable over time. .45 .5 .55 .6 .65 .7 Homeownership 30 2005 2007 2009 2011 2013 2015 2017 Low PW (PW20=0) High PW (PW20=1) i) pure parental wealth ii) parent attributes iii) household attributes (a) Homeownership at age 30 100000 150000 200000 250000 300000 House price upon entry (USD) 2005 2007 2009 2011 2013 2015 2017 Low PW (PW20=0) High PW (PW20=1) i) pure parental wealth ii) parent attributes iii) household attributes (b) Purchase price upon entry ($) 75 80 85 90 95 Leverage upon entry (%) 2005 2007 2009 2011 2013 2015 2017 Low PW (PW20=0) High PW (PW20=1) i) pure parental wealth ii) parent attributes iii) household attributes (c) Leverage upon entry (%) Figure 1: Housing outcomes by parental wealth Notes: The housing outcome gaps are decomposed into three observable components, pure parental wealth, parental attributes and households attributes, in accordance with equation (2). hiis (a) homeownership rate at 30, (b) the purchase price upon entry, or (c) the computed leverage upon entry. pw20 i= 1 if average parental financial wealth when the household is aged 19-21 is above the year-specific median, po iis parent income, education, location and number of children, xiis hh income, financial wealth, education, location and number of adult household members. As a robustness exercise, we add two-year future income growth and the risky asset share for parents and offspring as additional control variables in Appendix Figure A.6a. This shortens the sample by two years and increases the importance of other parental attributes 12 slightly. Otherwise the results are largely unchanged. We also report results when parent wealth is captured by contemporaneous parent wealth in Appendix Figure A.7a. Both the total homeownership gap and the pure parental wealth component become slightly larger, but the main impression remains unchanged. Housing outcome II: House purchase price We next consider the association between parental wealth and the house purchase price upon entry, which is observed only for those households who enter the housing market. Figure 1b depicts the purchase price upon entry in real USD by parental wealth.8By the end of our sample period, households with richer parents buy homes worth approximately $60,000 (≈30%) more when entering the housing market. The purchase price gap has roughly doubled in absolute terms over the time period, and has increased also in percentage terms. By the end of our sample, the household attributes component can explain about 40% of the purchase price gap. The most important household characteristic is the number of household members, which is higher for those with parents in the upper half of the wealth distribution. As before, also income and education are important household attributes. Other parental attributes are somewhat more important in explaining differences in purchase prices than differences in homeownership rates. Still, the other parental attributes component is modest in size. This leaves a substantial role for the pure parental wealth component, which accounts for 50% of the observed difference in purchase prices between households with above versus below median wealthy parents. That is, even after controlling for a rich set of observables, households with richer parents buy homes worth an additional 15% when entering the housing market. Note that the pure parental wealth component has increased over the sample period. Appendix Figures A.6b and A.7b confirm that, once again, the results are robust to also controlling for future income growth and risky asset shares, as well as using contemporaneous parental wealth. Housing outcome III: Leverage upon entry Leverage is another margin of adjustment that is likely to vary with parental wealth, and which again conditions on entry. Indeed, Figure 1c shows that households with richer parents are roughly eight percentage points (≈10%) more levered. The leverage gap has increased over time, and households with richer parents have leverage rates above 90% towards the end of the sample. This is high considering the LTV-cap of 85%, and can be explained by i) banks being allowed to deviate from the cap for 10% of new mortgages, ii) measurement error in our LTV-measure and iii) additional 8Prices in NOK are first deflated to obtain constant 2015-prices, and are then converted to USD using a constant exchange rate of USDNOK=8.5. 13 unobserved collateral or mortgage guarantees. Interestingly, and in contrast to the other housing outcomes, household attributes are not important in explaining the leverage gap. In fact, the leverage gap is entirely attributed to the pure parental wealth channel for most of the sample. We interpret this to reflect that most first time buyers are constrained by the regulatory LTV-cap at 85%, and that especially households with richer parents are likely to receive additional collateral or guarantees from their parents that enable them to exceed this limit.9Appendix Figures A.6c and A.7c confirm that, also for leverage, the results are robust to controlling for future income growth and risky asset shares, as well as using contemporaneous parental wealth. 3.2 The causal impact of parental wealth The previous section showed that, even after controlling for a rich set of parental and household characteristics, parental wealth is an important mediator for housing outcomes. However, there could be omitted variables which influence this relationship, challenging a causal interpretation. For instance, preferences are likely to influence housing outcomes directly, but are unobserved to us as econometricians.10 If these preferences are correlated with wealth and transmitted from one generation to the next, they will impact our β-estimates in equation (1). In this section we use plausibly exogenous variation in parental wealth caused by a shift-share (Bartik) type instrument, in order to gauge the extent to which our above estimates imply a causal impact of parental wealth on housing outcomes. Our instrument is based on international stock market returns and initial stock market exposure. We measure international stock market returns by the return on the S&P 500 index, rt.11 The annual return varies from -24% to 18% during our sample period, creating non-trivial variation in financial wealth. Parents have different exposure to stock market returns based on their balance sheets, and we use this to obtain cross-sectional variation. Our instrument is the interaction between stock shares and international stock market returns. The first-stage equation is pw i,t =α+β1stock-sharei,t−1×rt+β2po i,t +β3xi,t +ϵi,t (3) 9This is also consistent with findings in Aastveit et al. (2022) who study the household balance sheet effects of introducing LTV-caps in Norway. 10As discussed in the previous section however, including the risky asset shares of parents and offspring as a proxy for risk aversion has very limited impact on our results. 11In principle, we could also use Norwegian stock market returns. However, the exogeneity threats might be larger in this case. Also, the financial asset holdings of Norwegian households contain a substantial share of international stock market exposure, ensuring a strong first stage. According to Statistics Norway, 55% of stock ownership is through mutual funds, in which 80% of investments are international – implying an international exposure of at least 40%. 14 We measure parental wealth contemporaneously in order to obtain a strong instrument. The exclusion restriction is that stock-market wealth changes for parents only affect households’ entry probabilities through their effect on parental wealth. To address the concern that there might be direct effects on the households own stock market wealth, we can control for the (child) household’s stock market wealth changes. The second-stage is hi,t =αIV +βIV 1ˆpi,tw+βIV 2po i,t +βIV 3xi,t +ϵIV i,t (4) (1) (2) (3) (4) (5) P(entry) P(entry) pw i,t P(entry) P(entry) pw i,t 0.0131*** 0.0189*** 0.0204*** (0.00156) (0.00180) (0.00167) stock-sharei,t−1×rt0.0166*** 0.875*** (0.00187) (0.0838) Model OLS OLS OLS IV IV N 3,955,433 3,955,433 3,955,433 3,955,433 3,955,433 Clusters 1,043,389 1,043,389 1,043,389 1,043,389 1,043,389 Mean 0.0438 0.0438 0.457 0.0438 0.0438 Standard controls Yes Yes Yes Yes Yes HH stock share interaction No No No No Yes Table 2: IV-analysis: stock market return. Notes: entryi,t = 1 if household ipurchases a house in year tand did not own housing in year t−1, entryi,t = 0 if household idid not purchase a house in year tand did not own housing in year t−1.pw i,t = 1 if average parental financial wealth is above the year-specific threshold, and zero otherwise. Stock-share is the share of non-deposit financial wealth, rtis the annual return on the S&P 500. The regression results are reported in Table 2. Column 1 reports the OLS results. The point estimate indicates that having parents in the upper half of the wealth distribution increases the entry probability by 1.3 percentage points in a given period. The reduced form results are reported in the second column, while the first-stage results are reported in the third column. The F-statistic on the first stage is well above 100, suggesting a strong instrument. Scaling the reduced form results by the first stage results gives the same estimate as the IV-estimate reported in Column 4. It says that having parents in the upper half of the wealth distribution increases entry probabilities by 1.9 percentage points. The IV-estimate exceeds the OLS-estimate, but the 95% confidence intervals overlap – consistent with a causal interpretation of the OLS-estimates. 15 In Column 5 we explicitly control for the interaction of (child) household stock market shares and international stock market returns. This increases the estimated impact of parental wealth slightly, but the take-away remains unchanged. In sum, our evidence indicates a causal effect of parental wealth on offspring’s entry rates into the housing market.12 4 The housing channel of intergenerational wealth persistence So far we have documented large housing gaps caused by parental wealth. This is important in itself, as homeownership is generally thought to provide both private and social benefits (Coulson and Li (2013), Sodini et al. (2023)). In this section we quantify the role of the housing market in driving intergenerational wealth persistence. As in Section 3, we proceed in two steps. First, we use a mediation analysis to statistically decompose intergenerational wealth persistence into different components and isolate the housing market channel. Second, we use plausibly exogenous variation in housing outcomes caused by the timing of intrafamily deaths to estimate the causal impact of housing outcomes on midlife wealth. 4.1 Mediation analysis In this section we consider the correlation between household wealth and parental wealth and decompose this correlation into four observable channels: pure parental wealth,other parental attributes,household attributes, and housing. Framework Let midlife wealth ¯widepend on parental wealth when the household is aged 19-21 (denoted pw20 i), other parental attributes at midlife (¯po i), household attributes at midlife (¯xi) and housing outcomes (hi) – as in equation (5). Any other variables which affect household wealth are grouped together in the error term ϵi. We first lay out the structural framework, and thereafter we describe the measurement of variables. ¯wi=α0+α1pw20 i+α2¯po i+α3¯xi+α4hi+ϵi(5) 12With some assumptions, the impact on entry rates can be translated into an estimated impact on homeownership rates at age 30. Assume that adults enter the economy at age 18, and that the baseline entry rate equals the sample mean of 4.4%. If the entry rate increases by 1.9 percentage points each year (column 4), the homeownership rate at 30 increases by 13 percentage points. If the entry rate increases by 1.3 percentage points each year (column 1), the homeownership rate at 30 increases by 9 percentage points. The latter is roughly equal to the size of the pure parental wealth channel in Figure 1a. 16 Using equation (5) to express the covariance between ¯wiand pw20 i, and dividing by the variance of pw20 i, we arrive at cov( ¯wi, pw20 i) var(pw20 i)= i)parental wealth z}|{ α1+ ii)parental attributes z }| { α2 cov(¯po i, pw20 i) var(pw20 i)+ iii)hh attributes z }| { α3 cov(¯xi, pw20 i) var(pw20 i)+ +α4 cov(hi, pw20 i) var(pw20 i) | {z } iv)gross housing +cov(ϵi, pw20 i) var(pw20 i) | {z } v)unobservables (6) The left-hand side in equation (6) is the correlation between parental wealth and household wealth, and captures our measure of intergenerational wealth persistence. As before, this term is simply the regression coefficient from regressing household wealth on parental wealth without controls. The decomposition in (6) features four distinct observable channels. First, there is a pure parental wealth channel, captured by the α1coefficient from equation (5). The remaining channels are the products of two terms. The other parental attributes channel is the impact of other parental attributes on household wealth, α2, times the correlation between these other parental attributes and parental wealth. The household attributes channel is the impact of household attributes on household wealth, α3, times the correlation between these household attributes and parental wealth. Finally, the gross housing channel is the impact of housing outcomes on midlife wealth, α4, times the correlation between housing outcomes and parental wealth, cov(hi, pw20 i)/var(pw20 i). Note that the latter ratio is the left-hand side of equation (2) in the previous section, i.e. it is the regression coefficient from regressing housing outcomes on parental wealth. Substituting this term from equation (2), we can rewrite equation (6) as cov( ¯wi, pw20 i) var(pw20 i)= i)parental wealth z}|{ α1+ ii) (net) housing z}|{ α4β1+ iii)parental attributes’ z }| { (α2+α4β2)cov(¯po i, pw20 i) var(pw20 i) + (α3+α4β3)cov(¯xi, pw20 i) var(pw20 i) | {z } iv)hh attributes’ +cov(ϵi, pw20 i) var(pw20 i)+α4 cov(ηi, pw20 i) var(pw20 i) | {z } v)unobservables’ (7) Here, the gross housing channel has been replaced by the (net) housing channel, which is what we refer to as the housing channel of intergenerational wealth persistence. This channel is given by α4×β1, and captures the impact of parent wealth on child midlife wealth through 17 housing. Specifically, β1is the impact of parent wealth on housing outcomes from equation (1), and α4is the impact of housing outcomes on child midlife wealth from equation (5). The difference between the gross and the net housing channel is attributed to other parental attributes or household attributes. In the upcoming analysis we first estimate the α-coefficients from equation (5) and the covariance-variance terms. We use these coefficients to compute the components of intergenerational wealth persistence as specified in equation (6). Using ˆα4and ˆ β1we also separately report the (net) housing channel from equation (7). Measurement Net household wealth at midlife is measured when the household is in its early 40s. Parental wealth is, as before, measured based on average financial wealth when the household is aged 19-21. However, again, we also consider contemporaneous measures. In our baseline analysis, both household wealth and parental wealth are dummy variables which capture whether wealth holdings are above or below the year-specific median. Findings from the recent literature on intergenerational wealth persistence suggest that the correlation between parent and child wealth ranks (from 1 to 100) is quite well approximated by a linear relationship, see for instance Adermon et al. (2018) and Fagereng et al. (2021). This is also the case in our sample, as shown in Appendix Figure A.8. This suggests that the simple division of above/below the median captures the main features of the data. Still, we also report results using wealth ranks for robustness. Crucially, we include housing outcomes hias mediators. As our baseline, we focus on the extensive margin, i.e. homeownership. To allow for some dynamic effects, we include homeownership indicators at different ages, specifically ages 27, 30, 33 and 36. We do not include ages below 27, as the number of households we observe both in their early 20s and in their early 40s is limited. These housing outcomes capture only the extensive margin, that is, the decision to become a homeowner or not at different points over the life cycle. As an extension, we also use outcomes conditional on entry to capture the intensive margin. These estimates are necessarily based solely on the roughly 70% of households who become homeowners by middle age. Estimation We estimate all the components of intergenerational wealth dependence separately, reporting detailed regression results in the appendix, and summarizing the main results here. We first estimate equation (5) to obtain ˆα1,ˆα2,ˆα3and ˆα4. The results are reported in the first column of Appendix Table A.1. After obtaining the α-estimates, we regress po i,xiand hion pw20 i, one-by-one, to get the covariance-terms in equation (6). The results are reported in Columns 2-11 of Appendix Table A.1. Given the β1-estimate from 18 the previous section, we then have what we need to calculate the distinct components of intergenerational wealth persistence as specified in equations (6)-(7). The components are summarized in Table 3. First, total intergenerational wealth persistence is 15 percentage points. This means that households with parents in the upper half of the wealth distribution are 15 percentage points (=35%) more likely to themselves be in the upper half of the wealth distribution at midlife. This number is simply the estimated coefficient from regressing midlife household wealth on parental wealth, i.e. the left-hand side of equations (6) and (7). Intergenerational wealth persistence 0.15 (100%) Parental wealth channel 0.08 (55%) Parental attributes channel 0.01 (5%) Household attributes channel 0.02 (13%) Gross housing channel 0.04 (27%) Net housing channel 0.02 (12%) Table 3: Decomposing intergenerational wealth persistence Notes: The table shows results from decomposing intergenerational wealth persistence in accordance with equation (6). The gross housing channel is further decomposed into a net housing channel as in equation (7). Parental wealth is pw20. Parental attributes are education, income, location and number of children. Household attributes are education, income, location and number of adult household members. Housing market measures are homeownership indicators at ages 27, 30, 33 and 36. As seen from the second row of Table 3, the pure parental wealth component accounts for 55% of intergenerational wealth persistence. Other parental attributes – such as parental income, education, location and number of children – do not account for a large share of the observed intergenerational persistence. Household attributes, on the other hand, are more important, explaining 13% of the correlation between parental wealth and child wealth. Strikingly, housing outcomes are substantially more important than both parental attributes and other household attributes in explaining intergenerational wealth persistence – see the fourth row of Table 3. In fact, more than 1/4 of the correlation between parental wealth and household wealth is explained by households with richer parents having better housing outcomes, i.e. the gross housing channel. Finally, the net housing channel accounts for 12% of intergenerational wealth persistence and implies that households with richer parents are two percentage points more likely to be in the upper half of the wealth distribution at midlife due to the impact of parental wealth on housing. This key number will serve as an important moment to match in the 19 theoretical model in Section 6. Note that the net housing channel is about the same size as the household attributes channel. A useful interpretation of the magnitude is thus that the direct impact of parental wealth on homeownership is equally important for intergenerational wealth persistence as the direct impact of parental wealth on household income, education, location and number of household members. The results so far have been based on whether wealth is above or below the median. In Appendix Table A.2 we instead use the rank from 1 to 100 to capture household wealth and parental wealth. In total, increasing the parental wealth rank by one increases the household wealth rank at midlife by 0.3, which is similar in magnitude to previous findings.13 Compared to the results in Table 3, the net housing channel becomes slightly smaller, and drops from just above 10% to just below 10%. Qualitatively, the results are unchanged. The intensive margin of homeownership A benefit of using homeownership indicators at different ages is that no household is excluded from the sample, as long as it is in the data for that particular age. However, we do not capture the impact working though variables such as purchase price and leverage, which are defined only for households who enter the housing market. To evaluate the importance of the intensive margin, we redo our analysis on a sample of (eventual) homeowners. The results are reported in Appendix Table A.3. Measuring housing outcomes by only purchase price and leverage upon entry yields a net housing channel of 11%. If we also include age of entry, the net housing channel increases to 16%. These results suggest that the extensive margin result discussed above should be viewed as a lower bound for the total effect. 4.2 The causal impact of housing on wealth accumulation Precisely estimating the housing channel of intergenerational wealth persistence requires an unbiased estimate of the impact of housing on midlife wealth, i.e. coefficient α4from equation (5). In this section we use plausibly exogenous variation in housing resulting from variation in the timing of grandparent death to estimate the causal impact of age of entry in the housing market on midlife wealth. We restrict our sample to households for whom we observe exactly one grandparent death in our sample period.14 This means that we rely on variation in timing only for identification. 13For instance Fagereng et al. (2021) find a rank-rank coefficient of 0.24 (for non-adoptees) using Norwegian data, Adermon et al. (2018) find a rank-rank coefficient of 0.3-0.4 using Swedish data and Pfeffer and Killewald (2015) find a rank-rank coefficient of 0.39 (for ages 35-44) using US PSID data 14Note that a grandparent is defined as an individual, not a household. In the analysis, we consider the death of any one grandparent. The results are similar if we only consider the death of a ”final” grandparent on one side, i.e if we condition on the deceased grandparent not having a surviving spouse. 20 The strength of the instrument relies on grandparent death having a non-trivial impact on housing outcomes. To document that this is the case, we estimate en event study around grandparent death, based on the following equation yi,t =α+δt+ k=3 X k=−2 βkIk i,t +ϵi,t (8) The outcome variable yi,t is the probability of entering the housing market, defined for households who are not in the housing market (yi,t = 0) or are entering the housing market in year t(yi,t = 1). We define a vector of time dummies for the years prior to and following the death of a grandparent, Ik i,t, with kdenoting the number of years since the grandparent death took place. All βk-coefficients are relative to k=−3, which we set as our baseline. δt captures time fixed effects. .044 .046 .048 .05 .052 -3 -2 -1 0 1 2 3 Time relative to grandparent death Entry probability Figure 2: Event study around grandparent death Notes: Regression results from estimating equation (8) with yi,t =entry probabilityi,t. Sample: households who experience exactly one grandparent death in the sample period. Figure 2reveals a substantial spike in the probability of entering the housing market exactly in the year of grandparent death. The entry probability increases by more than ten percent, from around 4.6% to 5.1%. This response confirms that the timing of grandparent death causes variation in age of entry in the housing market. Note that there is a small decline in entry probabilities in the year prior to grandparent death. This could mean that some households anticipate the upcoming death of a grandparent, and choose to delay entry. This anticipation effect might be especially relevant for households who expect to inherit their grandparents’ house. If we exclude such households from the sample, there are no significant anticipation effects - see Appendix Figure A.9.15 All our results are robust to 15Specifically, we exclude households who enter the housing market in the same municipality in which 21 To evaluate whether parents sell homes to their children at discounted prices, we predict house purchase prices based on square meters, number of rooms, number of bathrooms, municipality and year of purchase – as in equation (11). Data for these variables are often missing, leaving a sample of nearly 99,000 entries to the housing market for which we have all the housing characteristics. Of these transactions, 3,300 are sales from parent to child and are excluded in the estimation. Regression results are reported in Table A.8 in the appendix. hpricei,t =α+β1sqmi,t +β2rooms +β3bathrooms +δkmunicipalityk+δtyeart+ϵi,t.(11) 0 .00002 .00004 .00006 .00008 Density -80000 -60000 -40000 -20000 0 20000 Residual house price (USD) Figure 4: Estimated house sale discounts (USD). Notes: The residual house price is the difference between the listed purchase price and the estimated market value (11). The dashed line represents the average residual house price when parents sell to their children. The distribution represents the average residual house price from 1,000 randomly drawn samples. Using the estimated coefficients from equation (11), we calculate the difference between actual purchase prices and predicted purchase prices for all transactions in our sample. For the intra-family sales, the average purchase price is $87,000 less than predicted, which implies a discount in excess of 25%. To make sure that the large estimated discount for parental sales is not a statistical fluke, we do a simple exercise in which we redo the calculations for randomly drawn samples of actual transactions, unconditional on whether they are within family or not. Specifically, from our transactions data we draw 1,000 random samples of 3,300 transactions, which is the size of our intra-family sales sample. Leaving out each sample oneby-one, we re-estimate equation (11) and use the results to predict purchase prices for all transactions. We then calculate the average residual house price for each sample, resulting in the smooth distribution in Figure 4. On average, residual house prices are close to zero, 28 and virtually all mass lies between -$20,000 and $20,000. This is in stark contrast to the average residual for intra-family sales, which is captured by the dashed, red line to the left in Figure 4. We thus conclude that parents are indeed selling houses to their children at sizable discounts. 5.3 How important are the mechanisms considered? We end this section by performing back-of-the-envelope calculations to assess how important the different mechanisms are in explaining the entry gap between households with richer and poorer parents. Note that the mechanisms considered seek to explain only the part of the entry gap which is accounted for by parental wealth. To assess each mechanism’s magnitude, we first multiply the share of parents who engage in mechanism i={equity withdrawal, transfer, co-purchase, direct sale}by the impact of mechanism ion the entry probability. Both terms are allowed to differ by parental wealth. This gives us the implied entry rate explained by each mechanism for households with richer and poorer parents. Then, we take the difference in implied entry rates between households with richer and poorer parents, and divide by the total entry gap accounted for by parental wealth. This gives us the share of the entry gap which is attributed to each mechanism. (1) (2) (3) (4) (5) (6) (7) Share of parents Impact on entry Entry accounted for Share of gap pw20=1 pw20=0 pw20=1 pw20=0 pw20=1 pw20=0 accounted for Equity extraction 24% 19% 1.40 pp 0.94 pp 0.34 pp 0.18 pp 29% Transfer 8.5% 3.9% 1.55 pp 1.55 pp 0.13 pp 0.06 pp 13% Co-purchase 0.012×0.052 0.007×0.037 100 pp 100 pp 0.062 pp 0.026 pp 7% =0.062% =0.026% Direct sale 0.022×0.052 0.020×0.037 100 pp 100 pp 0.114 pp 0.074 pp 7% =0.114% =0.074% Sum 33% 23% 0.65 pp 0.34 pp 56% Table 7: Mechanisms: assessing the magnitudes Notes: The numbers in columns 5-6 are found by multiplying the numbers in columns 1-2 and columns 3-4 based on parental wealth. The numbers in column 7 are found by taking the difference between the numbers in columns 5 and 6, and dividing by the total entry gap explained by parental wealth of 0.55 pp. Parental equity extraction The results of the back-of-the-envelope calculation for parental equity extraction are reported in the first row of Table 7. Considering only (potential) first time buyers, 24% of high-wealth parents and 19% of low-wealth parents extract equity in a given period. For households with richer parents, parental equity extraction increases the 29 entry probability by 1.40 percentage points (see Column 6 of Table 5, row 1 + row 3). For households with poorer parents, parental equity extraction increases the entry probability by 0.94 percentage points (see Column 6 of Table 5, row 1). Combining these two sets of numbers, we have that – for households with richer parents – parental equity extraction increases their entry probability by 0.24×1.40 = 0.34 percentage points. For households with poorer parents, parental equity extraction increases their entry probability by 0.19×0.94 = 0.18 percentage points. The entry probability gap between households with richer and poorer parents accounted for by parental equity extraction is thus (0.34-0.18)/0.55=29%.23 Parental transfers The results of the back of the envelope calculation for parental transfers are reported in the second row of Table 7. Considering only (potential) first time buyers as before, 8.5% of richer parents and 3.9% of poorer parents provide transfers in a given period. Receiving a transfer increases the entry probability by 1.55 percentage points, with no significant difference across parental wealth groups (see Column 6 of Table 6). Combining these two sets of numbers, we have that – for households with richer parents – transfers increase their entry probability by 0.085×1.55 = 0.13 percentage points. For households with poorer parents, transfers increase their entry probability by 0.039×1.55 = 0.06 percentage points. The entry probability gap between households with richer and poorer parents accounted for by parental transfers is thus (0.13-0.06)/0.55 =13%. Co-purchasing The results of the back of the envelope calculation for parental co-purchasing are reported in the third row of Table 7. 1.2% of households with richer parents entering the housing market co-purchase together with their parent, see Figure 3a. Given an entry rate of 5.2%, this implies that 0.062% of high-wealth parents of (potential) entrants co-purchase a home together with a child in a given period. For households with poorer parents, 0.7% of entrants co-purchase together with a parent. Given an entry rate of 3.7%, it follows that 0.026% of low-wealth parents of (potential) entrants co-purchase a home together with a child in a given period. Because co-purchasing only takes place conditional on the child household entering the housing market, the impact on entry is set to one. This implies that co-purchasing increases entry rates by 0.062 percentage points for households with richer parents, and 0.025 percentage points for households with poorer parents. As a result, co-purchasing can explain 7% of the total entry gap accounted for by parental wealth. Direct sales The results of the back of the envelope calculation for direct housing sales from parent to child are reported in the fourth row of Table 7. 2.2% of households with 23On average over the sample period, the gap in entry rates is 1.5 pp, see Appendix Figure A.3. Roughly 1/3 or 0.55 pp is due to parental wealth. 30 richer parents entering the housing market buy directly from a parent, see Figure 3b. Given an entry rate of 5.2%, this implies that 0.114% of high-wealth parents of (potential) entrants sell a house to a child in a given period. For households with poorer parents, 2.0% of entrants buy directly from a parent. Given an entry rate of 3.7%, this implies that 0.074% of lowwealth parents of (potential) entrants sell a house to a child in a given period. Because a direct sale from parent to child only takes place conditional on the (child) household entering the housing market, the impact on entry is again set to one. This implies that direct sales increases entry rates by 0.114 percentage points for households with richer parents, and 0.074 percentage points for households with poorer parents. As a result, direct sales can also explain 7% of the total entry gap accounted for by parental wealth. Total Adding up the mechanisms considered, we have explained 56% of the difference in entry probabilities caused by parental wealth.24 Which mechanisms are we missing? One mechanism generally considered to be important based on surveys and anecdotal evidence – and consistent with the importance of parental wealth for LTVs in Figure 1c – is mortgage guarantees. That is, a parent agrees to be liable for the mortgage in case the child should fail to meet the payment obligations. In general, there are likely a number of different ways parents can assist their children financially in the housing market. Our back-of-envelope calculations suggest that parental equity extraction, other transfers and intra-family transactions can account for more than half of the impact of parental wealth on housing market entry rates. Before moving on to the model, we briefly summarize our results. First, we have documented substantial housing gaps between those with richer vs. poorer parents, and decomposed these gaps into a pure parental wealth component, an other parental attributes component and a household attributes component. Instrumenting parental wealth with a shift-share IV based on international stock market returns support a causal impact of parental wealth on housing market outcomes. Second, we have seen that the gross housing channel can account for roughly one quarter of total intergenerational wealth persistence, and that half of this is driven purely by parental wealth. An instrumental variable approach based on the timing of intra-family deaths supports a causal interpretation of the impact of housing on midlife wealth. Finally, in terms of how parental wealth is transmitted, we find evidence of parental housing equity withdrawal, financial transfers, co-purchasing, and 24An implicit assumption when adding up the importance of each mechanism is that there is limited overlap. This might not be the case. For instance, parents who extract equity might also give financial transfers. However, only four percent of parents extracting equity or giving transfers engage in both support forms simultaneously. We thus consider the assumption of no overlap to be acceptable for our back-of-theenvelope calculation. 31 direct sales from parent to child at substantially discounted prices. 6 Model and counterfactual exercises In this section, we build a life-cycle model with housing and exogenous parental support to i) explore if a calibrated staple model, augmented with financial support from parents, can reproduce our empirical estimates of the housing channel of intergenerational wealth persistence and ii) conduct counterfactual analyses to understand the roles of house price growth and mortgage market regulation. These counterfactuals are chosen to address external validity and the most immediate policy question stemming from our empirical analysis. 6.1 Model set-up Parental support is fixed in accordance with a “warm glow” bequest motive and takes the form of an initial cash transfer or an annual cash transfer. Modeling parental support as a transfer is in line with the survey evidence presented in Appendix Figure A.11, as well as the results from Section 5. We first describe the baseline model without parental support in Sections 6.1.1-6.1.2. In Section 6.1.3, we add parental support to the model. We discuss the implications of endogenizing parental support given alternative bequest motives in Appendix D.1. Computational details are reported in Appendix D.5. 6.1.1 Environment We extend a workhorse life-cycle model with housing, modified to match our Norwegian setting, to isolate the effect of parental support. For a thorough discussion of these models we refer to Yang (2009); Attanasio et al. (2012); Davis and Van Nieuwerburgh (2015). Demographics A household is born at age Ts, retires at age Tr, and dies at age Td. Each period is one year, and we do not consider mortality risk or bequest motives for the (child) household. Preferences The expected lifetime utility of a household is given by E  Td X a=Ts Bau(ca, ha, sa) (12) 32 where B>0is the discount factor, c > 0is non-housing consumption, h∈ H(s)⊂R2 is housing consumption, and s∈ {0,1}is the ownership status which equals 0 for renters and 1 for owners. The feasible set of housing depends on whether the house is renteror owner-occupied. The expectation Eis taken over sequences of idiosyncratic shocks that we specify below. In what follows, we omit the dependence of variables on age a, except where it is misleading. Households have CRRA preferences with a Cobb-Douglas aggregator over housing and consumption u(c, h, s) = (c1−ηhηχ(s))1−γ 1−γ,(13) where 0< η < 1is the weight on housing, γmeasures risk aversion, and χ(s)is the homeownership premium. The ownership premium is 1 for renters and 1 + χfor owners. Endowments Households are endowed with an uncertain labor income stream during working age log yi,a =f(a) + νi,a +εi,a, a =Ts, . . . , Tr.(14) We let f(a)denote the deterministic component, νis a persistent income shock, and ε∼ N(0, σ2 ε)is a transitory shock. The persistent shock follows an AR(1) process νi,a =ρνi,a−1+ui,a,(15) where ρis the persistence parameter and u∼ N (0, σ2 ν). In retirement, income is constant and equal to a fixed proportion (ϕret)of the household’s income in the last period of working life (a=Tr) log(yi,a) = log(ϕret) + f(a=Tr) + νi,T r, a =Tr+ 1, . . . , Td(16) Social welfare systems provide a consumption floor cafter rent of the cheapest unit. Households are endowed with an initial level of net worth xTs. Housing market The market value of a house is linear in house size h. The house price follows a stochastic process with drift µhand volatility σh log(pa+1) = log(pa) + ϵh a+1, ϵ ∼ N (µh, σ2 h).(17) The rental price is assumed to be a constant fraction κof the market value ph. Households have the option to rent, denoted s= 0, or own, s= 1, in order to consume housing services. Houses are characterized by their sizes, which belong to discrete finite sets H(s)that depend 33 on ownership status. Buying and selling owner-occupied housing entails adjustment and transaction costs that are proportional to the market value of the house and we denote these proportional costs by mband ms, respectively. We let tc(p, s, h, s′, h′)denote the total transaction cost for a household who switches housing tenure from sto s′and house size from hto h′. For example, a current renter (s= 0) living in a rental unit of size hwho buys (s′= 1) a house of size h′when the price is p, pays a transaction cost of tc(p, 0, h, 1, h′) = (1+mb)ph′. Moreover, homeowners experience depreciation δ, which includes maintenance and taxes. Financial market Households can save in a one-period risk-free bond with return rf. Borrowing against collateral (owner-occupied housing) is allowed, but households must satisfy a loan-to-value (LTV) and a loan-to-income (LTI) constraint. We model borrowing as a one-period mortgage that is rolled over each period. The mortgage has an interest rate of rf+rm, where rm≥0is the mortgage premium. Households will never simultaneously hold both a mortgage and save in the risk-free bond since the mortgage premium is positive. We let bdenote the net position in bonds. The effective interest rate is rffor net savers and rf+rmfor borrowers 6.1.2 Household optimization We now outline the decision problem for households with non-wealthy parents. For readability, we denote all one-period-ahead variables with primes (′). Budget equation All households choose consumption cand a net bond position b. Renters pay rent while homeowners have the value of their house on their balance sheet. Changing housing status involves transaction costs. For a household with wealth xand income y, the budget equation is x+y=c+b+tc(p, s, h, s′, h′) + (1 −s′)κph′+s′ph′(18) Evolution of wealth Next-period wealth is given by the net position in bonds and the stochastic market value of owner-occupied housing net of depreciation x′=b(1 + r(b)) + s′p′h′(1 −δ)(19) Decision problems There are five discrete choices. Current renters choose to rent or own and current owners choose to sell and rent, sell and buy, or remain in the current house. 34 A household solves V(x, h, s, ν, p, a) = max c,h′,b′,s′{u(c, h′) + BE[V(x′, h′, s′, ν;, p′, a + 1)]}(20) subject to c > 0(21) h′∈ H(s′)(22) s′∈ {0,1}(23) b′≥ −LTV ph′s′(24) b′ y≥ −LTIs′(25) and the budget constraint and the law of motion (equations (18) and (19)). If the household chooses to rent (s′= 0), the last two constraints collapse to a single no-borrowing constraint. 6.1.3 Modelling parental support To be consistent with the empirical strategy, exactly half of the households in our model are assumed to have wealthy parents. Parental support is exogenous and takes the form of a financial transfer, in line with our empirical findings. We model two different forms of transfers, an initial transfer or an annual transfer, to allow for different transfer timing. Initial transfer We first consider an initial one-time transfer, modelled as an additional cash endowment that households hold at the beginning of adulthood, τP W Ts. For households with non-wealthy parents, τP W Ts= 0. Modelling intergenerational transfers as a once-anddone transfer occurring when households enter working life is a standard way to model intergenerational persistence, see e.g., Lee and Seshadri (2019). Annual transfer The second form of parental support we consider is instead an annual transfer, τP W , every year from t=Tsfor twenty years. For households with non-wealthy parents, τP W = 0. Frequent transfers is normally a prediction of models with altruistic parents and children (e.g., Altonji et al. (1997); Barczyk et al. (2022)), and is consistent with empirical transfer patterns (McGarry,2016). 35 6.2 Parameterization Our parameterization strategy consists of three steps. First, we fix the external parameters, i.e., parameters we can set without relying on model dynamics and that are common across all types of households. Second, we internally calibrate two preference parameters, the discount factor Band the ownership utility premium χ, to match homeownership and financial wealth at different ages. Here we match moments for households with below-median wealthy parents. Third, we pick the parental support parameters to match the net housing channel of intergenerational wealth persistence as specified in equation (7) in Section 4.1. Model parameters are reported in Appendix Table D.1, and we relegate the discussion of the standard first step to Appendix D.2. 6.2.1 Internal calibration In the second step we choose the remaining preference parameters to match life-cycle moments of wealth and homeownership for households with non-wealthy parents. Specifically, we set the discount factor Band the utility shifter for homeownership χby targeting the homeownership rate and financial wealth at each age between 25 and 45. The moments are calculated as the average across our sample of households with non-wealthy parents. Appendix Figure D.1 shows the empirical moments along with the corresponding model-implied moments for wealth and homeownership. The calibrated model matches the empirical moments quite well, but it somewhat over-predicts both financial wealth and homeownership rates as households become middle-aged. 6.2.2 Calibrating parental parameters We choose our parental transfer parameters, τP W Tsand τP W to match the estimated housing channel of intergenerational wealth persistence as defined in equation (7) in Section 4. Specifically we target a net housing channel of β1α4= 0.02, which means that households with richer parents are two percentage points more likely to be rich themselves at midlife, due to better housing outcomes as a result of higher parental wealth. We here perform the same regressions on model data as we did on the actual data, details in Appendix D.3. The transfer parameters are well identified since higher transfers increase the effect of parental wealth on housing β1, while leaving the positive relationship between housing outcomes and midlife wealth α4almost unchanged. The results are reported in Table 8. 36 Model Data Initial Transfer Annual Transfer Net housing channel 0.02 0.02 0.02 sum(α) 0.45 0.75 0.74 sum(β) 0.20 0.12 0.11 Table 8: Mediation analysis in the data and in the model Notes: The net housing channel is Pj=27,30,33,36 α4,j β1,j , where α4,j is the effect of homeownership on wealth and β1,j is the impact of parental wealth on homeownership, at age j. We set the initial transfer τP W Ts= 39.3and the annual transfers τP W = 1.14 to replicate a net housing channel of intergenerational wealth persistence of two percentage points, as seen from the first row of Table 8. These transfer parameters imply life-time values of roughly $40,000 and $17,000 respectively, using the discount factor Bover 20 years for the annual transfers. The life-time value of the initial transfer is larger because young households to a greater extent are constrained from smoothing consumption intertemporally. Hence, when households receive their entire transfer at a very young age, they spend less on housing and more on consumption than if part of the transfer is paid out later. Also note that housing is more important for wealth accumulation in the model than in the data (larger α’s), while parental wealth is somewhat less important for housing. The latter reflects that in these models, all households become owners when they are sufficiently wealthy, which diminishes the link between parental wealth and housing outcomes. Are the implied transfer sizes reasonable? Brandsaas (2021) finds the mean transfer size for housing purposes in PSID data to be roughly $4,000. However, there are two reasons why our calibrated transfers should be larger. First, house prices are considerably higher in Norway than in the US – about three times higher per square foot.25 Second, we target the total impact of parental support, while direct transfers in practice are only one of many support forms. 6.3 Counterfactual exercises In this section we run two experiments to better understand how the housing channel of intergenerational wealth persistence depends on features of the housing market. First, we 25For example, in 2017 the median listing price per square feet in the US was $132 while the average sale price per square feet in Norway was about $400. Sources: National Association of Realtors (FRED mnemonic medlispripersqufeeus) and Statistics Norway (Table 06035) 37 Halvorsen, E. and Lindquist, K.-G. (2017). Getting a foot on the housing ladder: The role of parents in giving a leg-up. Norges Bank Working Paper 19/2017. Kaplan, G., Mitman, K., and Violante, G. L. (2020). The housing boom and bust: Model meets evidence. Journal of Political Economy, 128(9):3285–3345. Kolodziejczyk, C. and Leth-Petersen, S. (2013). Do first-time house buyers receive financial transfers from their parents? The Scandinavian Journal of Economics, 115(4):1020–1045. Lee, H., Myers, D., Painter, G., Thunell, J., and Zissimopoulos, J. (2020). The role of parental financial assistance in the transition to homeownership by young adults. Journal of Housing Economics, 47:101597. Lee, S. Y. and Seshadri, A. (2019). On the intergenerational transmission of economic status. Journal of Political Economy, 127(2):855–921. Luea, H. M. (2008). The impact of financial help and gifts on housing demand and cost burdens. Contemporary Economic Policy, 26(3):420–432. McGarry, K. (2016). Dynamic aspects of family transfers. Journal of Public Economics, 137:1–13. Pfeffer, F. T. and Killewald, A. (2015). How rigid is the wealth structure? intergenerational correlations of family wealth. Population Studies Center, University of Michigan. Rouwenhorst, K. G. (1995). Asset pricing implications of equilibrium business cycle models. In Cooley, T. F., editor, Frontiers of business cycle research, pages 294–330. Princeton University Press. Sodini, P., Van Nieuwerburgh, S., Vestman, R., and von Lilienfeld-Toal, U. (2023). Identifying the benefits from homeownership: A swedish experiment. American Economic Review. forthcoming. Turner, T. M. and Luea, H. (2009). Homeownership, wealth accumulation and income status. Journal of Housing Economics, 18(2):104–114. Yang, F. (2009). Consumption over the life cycle: How different is housing? Review of Economic Dynamics, 12(3):423–443. Yao, J., Fagereng, A., and Natvik, G. (2015). Housing, debt and the marginal propensity to consume. Working Paper. 44 A Additional figures and tables 42% 44% 0 10 20 30 40 50 Norway USA Online survey, Norwegian and US homeowners below age 50, n=677. Share who received financial support in order to buy a home (%) Figure A.1: Share of homeowners who report receiving financial support from parents or grandparents when buying a home (%). Online survey. Notes: The figure shows results from an online survey conducted on the survey platform Survey Monkey. The sample consists of 300 respondents in Norway and 377 respondents in the US. All respondents are homeowners below age 50. The figure shows the share (%) of respondents receiving financial support from parents or grandparents when buying a home. 0 20 40 60 80 Share responses (%) Low wealth Medium low Medium high High wealth Online survey, Norwegian parents, n=240. For what purpose would you prefer supporting your child financially? Housing Consumption Stocks Other assets (a) Preferred financial support form 0 20 40 60 80 Share responses (%) Low wealth Medium low Medium high High wealth Online survey, Norwegian parents, n=240. Have you financially supported a child in the housing market, or is this something you would consider in the future? Yes No Don't know (b) Attitudes towards housing support Figure A.2: Survey responses by (self-reported) wealth Notes: The figure shows results from an online survey conducted on the survey platform Survey Monkey. The sample consists of 240 individuals residing in Norway, aged 40+, with children. Panel (a) shows results for the preferred way of providing financial support to a child. Panel (b) shows results for whether the parents have or plan to support their child in the housing market. 45 .03 .04 .05 .06 .07 Entry probability 2005 2007 2009 2011 2013 2015 2017 Low PW (PW20=0) High PW (PW20=1) i) pure parental wealth ii) parent attributes iii) household attributes Figure A.3: Entry probability by parental wealth: decomposed into channels i)-iii) as in equation (2). Notes: The figure shows the entry probability for households with parental wealth below and above the median. The entry probability gap is then decomposed into three observable components, pure parental wealth, parental attributes and households attributes, in accordance with equation (2). hiis the probability of entering the housing market. pw20 i= 1 if average parental financial wealth when household is aged 19-21 is above the year-specific threshold, po iis parent income, education, location and number of children, xiis hh income, financial wealth, education, location and number of hh members. Sample consists of households not in the housing market or entering the housing market. .3 .4 .5 .6 .7 Homeownership at 30 0 20 40 60 80 100 Parental financial wealth rank at 20 (a) Homeownership at age 30 150000 200000 250000 300000 350000 House price upon entry (USD) 0 20 40 60 80 100 Parental financial wealth rank at 20 (b) Purchase price upon entry (USD) Figure A.4: Housing outcomes by parental wealth rank (1-100) Notes: Parental wealth rank from 1 to 100 is calculated based on the year-specific distribution of parental financial wealth when the child is aged 19-21. 46 0 .02 .04 .06 .08 Homeownership 30 2005 2007 2009 2011 2013 2015 2017 Income Financial wealth Location Education Adult members Decomposing the houshold attributes channel Figure A.5: Homeownership at 30 by parental wealth at 20: the household attributes component in equation (2) Notes: The figure decomposes the household attribute component in equation (2). Household attributes are decomposed into household income, location, member of adults in the household, the household education level and household financial wealth. hiis a homeownership indicator at age 30. Sample consists of 30-year old’s. .5 .55 .6 .65 .7 Homeownership 30 2005 2007 2009 2011 2013 2015 Low PW (PW20=0) High PW (PW20=1) i) pure parental wealth ii) parent attributes iii) household attributes (a) Homeownership at age 30 100000 150000 200000 250000 300000 House price upon entry (USD) 2005 2007 2009 2011 2013 2015 Low PW (PW20=0) High PW (PW20=1) i) pure parental wealth ii) parent attributes iii) household attributes (b) Purchase price upon entry ($) 75 80 85 90 Leverage upon entry (%) 2005 2007 2009 2011 2013 2015 Low PW (PW20=0) High PW (PW20=1) i) pure parental wealth ii) parent attributes iii) household attributes (c) Leverage upon entry (%) Figure A.6: Housing outcomes by parental wealth at age 20: decomposed into channels i)-iii) as in equation (2). Future household income growth and risky asset shares for parents and offspring as additional control variables. Notes: The figure shows housing outcome gaps, decomposed into three observable components, pure parental wealth, parental attributes and households attributes, in accordance with equation (2). pw20 i= 1 if average parental financial wealth when the household is aged 19-21 is above the year-specific median, po iis parent income, education, location, number of children and risky asset share, xiis hh income, financial wealth, education, location, number of adult household members, risky asset share and two-year future income growth. The sample behind (a) consists of 30-year old households. The sample behind (b) and (c) consists of only households entering the housing market. 47 .5 .55 .6 .65 .7 Homeownership 30 2005 2007 2009 2011 2013 2015 2017 Low PW (PW_t=0) High PW (PW_t=1) i) pure parental wealth ii) parent attributes iii) household attributes (a) Homeownership at age 30 100000 150000 200000 250000 300000 House price upon entry (USD) 2005 2007 2009 2011 2013 2015 2017 Low PW (PW_t=0) High PW (PW_t=1) i) pure parental wealth ii) parent attributes iii) household attributes (b) Purchase price upon entry ($) 75 80 85 90 95 Leverage upon entry (%) 2005 2007 2009 2011 2013 2015 2017 Low PW (PW_t=0) High PW (PW_t=1) i) pure parental wealth ii) parent attributes iii) household attributes (c) Leverage upon entry (%) Figure A.7: Housing outcomes by parental wealth at t−1: decomposed into channels i)-iii) as in equation (2) Notes: The figure shows housing gaps decomposed into three observable components, pure parental wealth, parental attributes and households attributes, in accordance with equation (2). pw i,t−1= 1 if average parental financial wealth in year t−1is above the year-specific median, po iis parent income, education, location and number of children, xiis hh income, financial wealth, education, location and number of adult household members. The sample behind (a) consists of 30-year old households. The sample behind (b) and (c) consists of only households entering the housing market. 20 40 60 80 Household net wealth rank at midlife 0 20 40 60 80 100 Parental financial wealth rank at 20 (a) Household net wealth 0 20 40 60 80 Household financial wealth rank at midlife 0 20 40 60 80 100 Parental financial wealth rank at 20 (b) Household financial wealth Figure A.8: Household wealth ranking (1-100) in early 40s by parental financial wealth ranking (1-100) when child is 19-21. Notes: The figure shows household net wealth ranking (panel (a)) and household financial wealth ranking (panel (b)) by parental financial wealth ranking when child is 19-21. Household wealth in early 40s is ranked from 1-100 based on the year-specific distribution after removing age effects. Parental financial wealth when the (child) household is 20 years is ranked from 1-100 based on the year-specific distribution. 48 .048 .05 .052 .054 .056 .058 -3 -2 -1 0 1 2 3 Time relative to grandparent death Entry probability Figure A.9: Event study around grandparent death - only households not inheriting their grandparents house Notes: Regression results from estimating equation (8) with yi,t =entry probabilityi,t. Sample: households who experience exactly one grandparent death in the sample period - households entering the housing market in the same municipality as their deceased grandparent resided are excluded from the sample. 150000 160000 170000 180000 190000 200000 -3 -2 -1 0 1 2 3 Time relative to grandparent death Gross parent financial wealth (USD) Figure A.10: Event study around grandparent death Notes: Regression results from estimating equation (8) with yi,t equal to gross parent financial wealth. Sample: households who experience exactly one grandparent death in the sample period. 49 0 10 20 30 Norway USA Online survey, Norwegian and US homeowners below age 50, n=677. Form of parental support by country (%) Transfer Mortgage guarantee Co-owner/co-signer Housing gift Housing purchase Figure A.11: The share of respondents receiving different forms of parental or grandparental housing support (%). Notes: The figure shows results from an online survey conducted on the survey platform Survey Monkey. The sample consists of 300 respondents in Norway and 377 respondents in the US. All respondents are homeowners below age 50. The figure shows the share (%) of respondents receiving various form of parental or grandparental housing support. -5000 0 5000 10000 15000 -3 -2 -1 0 1 2 3 Time relative to (child) entry in housing market Low FW High FW Bank deposits (USD) Figure A.12: Bank deposits (USD). Event study around housing market entry (t=0) Notes: This figure shows the evolution of bank deposits around time of entry into the housing market. entryi,t = 1 if household ipurchases a house in year tand did not own housing in year t−1, while entryi,t = 0 if household idid not purchase a house in year tand did not own housing in year t−1. ”Low FW” (”High FW”) means average parent financial wealth when the household is aged 19-21 is below (above) the year-specific median. 50 -10000 -5000 0 5000 -3 -2 -1 0 1 2 3 Time relative to (child) entry in housing market Low FW High FW Parents secondary housing wealth (USD) Figure A.13: Event study: parental secondary housing wealth (USD). Notes: The figure shows an event study on parental secondary housing wealth around (child) housing market entry. Entry: entryi,t = 1 if household ipurchases a house in year tand did not own housing in year t−1, entryi,t = 0 if household ihousehold idid not purchase a house in year tand did not own housing in year t−1. ”Low FW” (”High FW”) means average parent financial wealth when the household is aged 19-21 is below (above) the year-specific median. 51 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) ¯w citypincomepeducpchildrenpentry-age hprice income educ city hh members pw20 0.0846∗∗∗ 0.0280∗∗∗ 43627.9∗∗∗ 0.115∗∗∗ -0.0433∗∗∗ -0.268∗∗∗ 93206.2∗∗∗ 20926.9∗∗∗ 0.150∗∗∗ 0.0714∗∗∗ 0.145∗∗∗ (0.0103) (0.0044) (1645.9) (0.00696) (0.0135) (0.0590) (3664.8) (918.4) (0.00724) (0.00618) (0.00490) owner-27 0.0269∗∗ (0.0115) owner-30 0.0400∗∗∗ (0.0127) owner-33 0.1081∗∗∗ (0.0157) owner-36 0.2780∗∗∗ (0.0157) cityp0.0680∗∗∗ (0.0240) incomep8.90e-08∗ (4.91e-08) educp0.0125 (0.0113) income 1.80e-08 (8.49e-08) educ 0.0644∗∗∗ (0.0105) city 0.123∗∗∗ (0.0127) hh members 0.0362∗∗ (0.0158) childrenp-0.0203∗∗∗ (0.0053) N 8,909 8,909 8,909 8,909 8,909 8,909 8,909 8,909 8,909 8,909 8,909 Table A.1: Regression results from estimating equation (5) (Col.1) and the covariance-terms in equation (6) (Col.2-11). 52 Intergenerational wealth persistence 0.33 (100%) Parental wealth channel 0.20 (61%) Parental attributes channel 0.02 (6%) Household attributes channel 0.05 (15%) Gross housing channel 0.06 (18%) Net housing channel 0.03 (9%) Table A.2: The importance of various channels of intergenerational wealth persistence. Rankrank analysis. Notes: The table shows results for decomposing intergenerational wealth persistence into a parental wealth channel, parental attribute channel, household attribute channel and gross housing channel as defined in equation (6). The gross housing channel can further be decomposed into a net housing channel as in equation (7). Parental wealth is the rank from 1-100 based on average financial wage when the household is 19-21. Household wealth is the rank from 1-100 based on midlife net wealth. Parental attributes are education, income, location and number of children. Household attributes are education, income, location and number of adult household members. Housing market measures are homeownership indicators at ages 27, 30, 33 and 36. h = Price & LTV h = Price, LTV & Age Intergenerational wealth persistence 0.19 (100%) 0.19 (100%) Parental wealth channel 0.10 (53%) 0.10 (53%) Parental attributes channel 0.01 (5%) 0.01 (5%) Household attributes channel 0.06 (32%) 0.04 (21%) Gross housing channel 0.02 (11%) 0.04 (21%) Net housing channel 0.02 (11%) 0.03 (16%) Table A.3: The importance of various channels of intergenerational wealth persistence. Intensive margin of homeownerhsip. Notes: The table shows results for decomposing intergenerational wealth persistence into a parental wealth channel, parental attribute channel, household attribute channel and gross housing channel as defined in equation (6). The gross housing channel can further be decomposed into a net housing channel as in equation (7). Parental wealth is pw20. Parental attributes are education, income, location and number of children. Household attributes are education, income, location and number of adult household members. Housing market outcomes are purchase price and leverage upon entry (Column 2) or purchase price upon entry, leverage upon entry and age of entry (Column 3). 53 D Model Appendix Parameter Value Source Externally Calibrated σ2 νVar. pers. inc. shock 0.012 Fagereng et al. (2017) σ2 νVar. trans. inc. shock 0.023 Fagereng et al. (2017) ρShock persistence 0.95 Standard ϕret Replacement Ratio 0.842 Fagereng et al. (2017) f(a)Life-cycle income Fig. D.2d Fagereng et al. (2017) cConsumption Floor NOK100,000 Welfare system n/a Initial Wealth Fig. D.2c Fagereng et al. (2017) pini Initial house price 89.78 Own calculation TsStarting age 22 TrRetirement age 67 Fagereng et al. (2017) TdFinal age 100 mbPurchase cost 0.025 Yao et al. (2015) msSales cost 0.025 Yao et al. (2015) κRent-to-price ratio 0.044 Own calculation rfRisk-free rate 0.016 Yao et al. (2015) rmMortgage premium 0.039 Own calculation LTV Maximum loan-to-value 0.9 Regulation LTI Maximum loan-to-income 5.0 Regulation δDepreciation 0.02 Yao et al. (2015) µhPrice growth 0.0288 Own calculation σhPrice std dev 0.0468 Own calculation H(0) Rental sizes [1.0,1.75] Own calculation H(1) Owner-occupied sizes [1.75,2.27,3.25] Own calculation ηWeight on housing 0.35 Standard γRisk Aversion 2.0 Standard Internally Calibrated BDiscount factor 0.9689 Internal estimation (6.2.1) χOwnership utility shift 0.0103 Internal estimation (6.2.1) Parental Parameters τP W TsInitial transfer 39.3 Internal estimation (6.2.2) τP W Annual transfer 1.14 Internal estimation (6.2.2) Table D.1: Calibrated Parameter Values 60 Figure D.1: Model Fit Notes: The data plots homeownership rate and average financial wealth of households with non-wealthy parents in our sample. The model line is the equivalent for the model sample, where financial wealth is 0 for borrowers (b < 0) and the amount saved in bonds for savers (b > 0). D.1 The implications of endogenizing parental support In the model, parental support was treated as fixed. In this appendix we briefly discuss the implications of relaxing this assumption. We assume that parents support their adult offspring in the housing market due to a bequest motive.27 We consider a stylized example in which parents can choose to give ”housing bequests” bhand ”other bequests” bo, in which we can think of other bequests as stocks. Due to barriers of entry in the housing market, we assume that dh dbh>do dbo, i.e. that parental support is more important for becoming a homeowner than becoming a stock owner. Further, we assume that the return on housing exceeds that on stocks – in line with Appendix B– so that d¯w dh >d¯w do . We consider three alternative bequest motives: 1. ”Warm glow” motive: parents receive utility from giving bequests, i.e. u(bh+bo) 2. ”Altruism” motive: parents receive utility from child’s midlife wealth, i.e. u( ¯w) 3. ”Homeownership” motive: parents receive utility from child’s homeownership, i.e. u(h) 27An alternative explanation is that parents support children to minimize dynasty tax payments. Specifically, due to tax valuation rules, parental ownership of secondary housing entails substantially larger wealth and property taxes than if a child owns the same house as a primary house. We find it unlikely that this is an important motivation for two reasons. First, this incentive only applies to parents who own secondary housing and chooses to transfer the home to a child which is not yet in the housing market. This group accounts for only 2% of entrants into the housing market. Second, from 2010 to 2017 (i.e. the years for which we separately observe secondary housing), the share of parents which own secondary housing while their adult child is not in the housing market has increased from less than seven percent to nearly eleven percent. This is the opposite of what the tax motive would predict, as the tax value of secondary housing in this period has increased from 40% to 90% (while the tax value of primary housing has remained unchanged). 61 We ask - what happens to parental support if the option to be a homeowner is completely removed? While this is not a policy relevant counterfactual, it nests more realistic exercises in which homeownership is made less attractive. First, given the warm glow bequest motive, parents only care about giving, and so total bequests are the same. Second, given the altruism motive, total bequest will go down, as they are now less efficient in increasing child midlife wealth. This happens both because dh dbh>do dboand because d¯w dh >d¯w do . Third, given the homeownership motive, parents no longer have any reason for giving bequests, and so parental support falls to zero. What are the implications for total intergenerational wealth persistence? First, keeping parental support fixed, removing homeownership from the table reduces intergenerational wealth persistence, as parental housing bequests had an especially large effect on child midlife wealth (i.e. larger than stocks). Second, if anything, parental support will decline, meaning that there might be an additional reduction in intergenerational wealth persistence. As such, the reductions in intergenerational wealth persistence identified in the model exercises should be viewed as lower bounds. D.2 External Calibration Transaction costs In Norway, home buyers pay a transaction tax (‘document fee’) of 2.5% of the purchase price. We therefore set mb= 0.025. The main direct cost of selling is the real estate agent commission, which averages 2% (Yao et al.,2015). We set the cost to be slightly higher, ms= 0.025, since sellers additionally usually pay for advertisement and other costs associated with home sales. Income Process For the stochastic component we use the parameter values from Fagereng et al. (2017) on Norwegian data. They estimate σ2 ν= 0.012,σ2 ε= 0.023, and ϕret = 0.842. We set ρ= 0.95, a standard value in the literature. We report their estimated income profile f(a)in Figure D.2d. Their estimates do not account for any correlations between parental wealth and income, however. We therefore adjust the income profile f(a)by the income gap between households with poor parents and the average income of all households in our data. Figure D.2d plots the results. For simplicity, we assume that income risk does not depend on parental wealth.28 Finally, we set the consumption floor c=NOK100,000 (≈$12,000), roughly matching what is left after subtracting rental payments from after-tax minimum disability payments. 28Fagereng et al. (2017) find that income risk is almost independent of education. Since education is strongly correlated with parental wealth, this suggests that any difference based on parental wealth is of limited size. 62 Housing Parameters To find the growth rate and volatility of house prices we use existing home price indices. We deflate the nominal index by median household income, after tax, since income is stationary in the model. We then use the observed mean growth and standard deviation to set µh= 0.0288 and σh= 0.0468. Figure D.2b plots the time trends of nominal and realand income-deflated house prices in Norway, as well as the mean growth rates and standard deviations. We calibrate house sizes to match the 5th, 25th, 50th, and 75th percentiles of square meters of residential units, which correspond to 44, 77, 100, and 143 square meters, respectively. We normalize the smallest unit to have a size of 1. We assume that the two smallest units can be rented, so that H(0) = [1.0,1.75]. We then assume that only the 3 largest units can be owned, such that H(1) = [1.75,2.27,3.25]. We estimate rent-to-price ratios κin Norway in two steps. First, we use statistics on yearly rent per square meter, by rooms in the unit and price per square meter, by type (single-family, small multifamily, and multifamily). We then divide the rent per square meter for units with 5 rooms by the single-family square meter price, the 4 room rental price by the small multi-family price, and the 3 and 2 rooms prices by the multifamily price. In the years we have data, 2012-2022, the ratios are relatively stable. We set κequal to 0.044, the average rent-to-price ratios of these four units’ series over all years, see Figure D.2e.29 Preference Parameters We set the preference weight on housing ηto 0.35, roughly equal to the average for households aged 27-45 in Yao et al. (2015). We set the risk aversion parameter γto 2.0, a standard value in life-cycle models. Initial Conditions To find a household’s initial financial wealth, we draw from the empirical distribution of households with non-wealthy parents, estimated non-parametrically (see Figure D.2c). We sort the net worth of households aged 20-23 with non-wealthy parents and divide them into 10 equally sized bins by gross financial wealth. Households are randomly allocated to bins and receive an initial endowment equal to the average of their bin. We draw the households’ initial productivity shock from the stationary distribution implied by equation (15). All households start as renters, but are allowed to choose to become homeowners in the first period. Households draw the initial house price psfrom a uniform distribution. We calibrate the mean of the initial price in the following way. In the early 1990s, the average market value of a ‘starter home’, was about 3.5 times the average household income. Using our calibrated 29For similar models calibrated to the United States, a standard value is 0.05, based on Davis et al. (2008). Our somewhat lower estimate could be driven by difference in tax regulation – rental income in duplexes are tax exempt if the owner lives in one unit – and other institutional differences. 63 income process, the average income for households aged 20-80 is NOK 449,000 (≈$53,000) and so we set the average initial price equal to 89.78 for one unit of housing, so that the price of the smallest owner-occupied unit is 3.5 times the average income. The edges of the distribution are set at ±20%, so that ps∼ U[0.8×89.78,1,2×89.78]. Remaining External Parameters The risk-free rate rfis 0.016, the maximum leverage dis 0.9, the maximum debt-to-income level is 5.0, and housing depreciation δis 0.02. We set the mortgage premium rmto 0.039, the average spread since 1990, similar to what is found in Erard (2014). D.3 Mimicking Empirical Regressions in the Model To re-create the intermediation analysis in the simulated panel from the model, we perform the following analysis. We first simulate households without wealthy parents (the parental wealth dummy pw= 0). We then simulate the same households, giving them the same shocks, but this time with wealthy parents (pw= 1). We define ¯wto be one if households have above median wealth at age 43. We then evaluate whether a given household owned a home at ages 27, 30, 33, and 36 to get the homeownership indicators. To calculate the housing channel, we run two sets of regressions - exactly as in the empirical analysis. First, we regress homeownership indicators hat age jon a parental wealth dummy and household characteristics: hj i=βj 0+βj 1piw+βj 3xi+ηifor j= 27,30,33,36 This mirrors equation (1) in Section 3, but without other parental characteristics powhich are not relevant in our model setting. Household characteristics xiis a vector containing the house price when the household enters the economy (related to the year and regional control variables in the empirical regression) as well as income (y) and dummies for both income shocks (νand ϵ). All of the individual level controls are measured at age j. The β1 parameters capture the effect of parental wealth on the probability of being a homeowner at age j. Next, we regress midlife wealth ¯won parental wealth, household characteristics and homeownership indicators: ¯wi=α0+α1pw i+α3xi+X j=27,30,33,36 αj 4hj i+ϵi 64 This mirrors equation (5) in Section 4, again leaving out the other parental attributes. The α4’s capture the effect of homeownership on the probability of being above median wealthy at age 43. Here, the individual characteristics xiare measured at age 43. We then have what we need to calculate the (net) housing channel of intergenerational wealth persistence, as defined in equation (7), which is Pjαj 4βj 1. The results are reported in Table 8. D.4 Modeling Parental Support To model the initial and the annual transfers without introducing additional state variables we modify the income process. We add an age-dependent transfer to the level of income yi,a = exp(f(a) + νi,a +εi,a) + τ(a).(26) For the initial transfer we define τ(a) =    τP W Tsif a=Ts, 0else. (27) And similarly for the annual transfer τ(a) =    τP W if Ts≤a < Ts+ 20, 0else. (28) D.5 Numerical Details The problem is solved backwards, by first solving the value function of a retiree at age T, when death is certain. For each discrete choice, we solve for optimal consumption choice using Brent’s root-finding algorithm. The optimal policy is then given by the discrete choice, and it’s associated consumption choice, that maximizes utility. This process is repeated backwards, until age a=Ts. The persistent income shock is discretized following Rouwenhorst (1995), while other shocks are discretized on an equal probability basis. That is, for ngrid points, the probably of each outcome is 1/n and the values of the shock at each grid point is equal to the midpoints of the n−1quantiles of the underlying distribution. The persistent income shock νfollows a 4-state Markov chain process, and the transitory income shock is discretized to 2 states, while the house price shock has discretized to 5 states. The net worth xand price pgrids are both unevenly spaced, with higher density 65 for lower values with 63 and 7 grid points, respectively. For values not in the grids we use linear interpolation. The model is solved in Julia 1.8.5, and in addition to standard packages we use Interpolations.jl v0.14.7 and Optim v1.7.4 for interpolation and optimization routines. 66 D.6 Supplementary Model Figures (a) Mortgage Premium rm(b) House Prices (c) Initial Wealth (d) Calibrated Income Process (e) Rent-to-Price Ratios, Select Sizes and Units (f) Rent-to-Price Ratios, All Sizes and Units Figure D.2: Calibration Figures 67 Figure D.3: The Parental Wealth Housing Channel and Price Growth - Coefficients Notes: This figures plots the coefficients from the mediation analysis, see Section 6.3.1 for more. 68 (a) LTV (b) LTI Figure D.4: Coefficients from the Mediation Analysis Notes: This figures plots the coefficients from the mediation analysis, see Section 6.3.2 for more. 69