Mind the Gap: Inheritance and Inequality in Retirement Wealth

Drawing on detailed panel data, we find that gifts and inheritances substantially increase households’ private pension savings in accounts which are costly or impossible to withdraw prematurely. Back-of-the-envelope calculations suggest that (a) the average difference in bequest-induced private pension savings between heirs and non-heirs accrues to more than 40,000 EUR at retirement and that (b) it would take an average non-heir household roughly 14 years to match this gap. The sizable difference in private pension savings between heirs and non-heirs persists when we take into account other investments of heirs and non-heirs potentially intended to provide for old age. Our evidence supports the impact of gifts and inheritances on inequality in retirement wealth highlighted in recent research on intergenerational justice. We discuss several policy implications of our results.


Introduction
In most developed economies, gifts and inheritances play a major role in sustaining and increasing household wealth. 1 Early work by Kotlikoff and Summers (1981) and Kotlikoff (1988) documents that intergenerational wealth transfers account for a larger proportion of households' overall wealth than prescribed by Modigliani's life-cycle hypothesis. Subsequent studies for the US and Europe confirm that a considerable fraction of households' total wealth stems from gifts and inheritances (Fessler and Schürz 2015;Gale and Scholz 1994;Kessler and Masson 1989;Wolff and Gittleman 2014). With the baby-boomer generation retiring in the near future, this intergenerational stream of capital is likely to become even more important. In Germany, for instance, a recent study by Braun (2015) estimates that as much as 2.1 trillion euro will have been transferred in the ten-year period from 2015 to 2024. This would mark a substantial increase of annual gifts and inheritances by about 20% as compared to 2001. 2 At the same time, sweeping pension reforms in many countries of the world have forced people to fund their own retirement through savings and investments earlier in life. Recent research in the field of intergenerational justice has thus highlighted the moral significance of inequality among retirees and, in particular, how this wealth gap is compounded by the added effect of gifts and inheritances on top of unequal earnings during working age (Halliday 2018;Wolff forthcoming).
Specifically, it is argued that " [t]he economic consequences of inheritance are not a matter of how much people leave, but rather what people (expect to) receive" (Wolff forthcoming,p.9). Hence, intergenerational wealth transfers can have very important effects earlier on in life, especially when it comes to retirement planning, and, as a consequence, have the potential to reinforce the divide the economic wellbeing of retired citizens. 1 While we realize that a small fraction of gifts or inheritances might in fact be transferred within a given generation, we follow Brown and Weisbenner (2004) and Westerheide (2005) and use the terms 'intergenerational wealth transfer ', 'gift', 'bequest', and 'inheritance' interchangeably. This paper takes this conjecture to the data and aims at providing quantitative empirical evidence as to the impact of intergenerational wealth transfers on the financial situation of retirees. At this, we investigate the fraction of gifts and inheritances households use for the specific purpose of old-age provision. While we also include alternative options for households to save for old age, such as investments in mutual funds or housing, the focus of this study is on private pension plans designed to provide secure funds during old age. 3 Why so? Unlike other savings and investments, these products are at least partially illiquid and incur substantial early withdrawal penalties (in addition to any applicable income taxes). Such stipulations may be regarded as self-commitment tools and we can thus be reasonably certain that private funds flowing into these illiquid accounts are indeed available for use in retirement, while this is not a foregone conclusion for savings and investments in non-commitment contracts which households may intend to consume in retirement but-frequently owing to self-control problemsliquidate early (cf., e.g., Beshears, Choi, Harris, et al. 2015;Agarwal, Pan, and Qian 2019). Thus, the quantitative effect of intergenerational transfers which we document in this study may be regarded as a lower bound of the difference in savings accumulated at retirement between heirs and non-heirs.
In order to explore the relationship between gifts or inheritances and commitment savings for old age, we draw on household panel data provided by the German Central Bank including detailed information on intergenerational wealth transfers. The panel structure of the data allows to employ a difference-in-difference approach to examine the effect of bequest flows as well as to circumvent the issue of household heterogeneity by looking at within-household effects only.
Indeed, we document that heir households appear to have a head start when it comes to old-age provision. Our first set of results suggests that, all else equal, households who receive a gift or inheritance put on average 15,268 EUR, i.e. more than four times as much money in their private pension accounts as their sociodemographic twins among the group of non-heirs. To capture the magnitude of this effect over the household lifecycle, we perform two back-of-the-envelope calculations. 4 On the one hand, we compute the time it takes to accumulate the gap in commitment savings for households that have subscribed to a monthly savings plan. Assuming that the average household is able to allocate half of their monthly total savings of 250 euro to private pension accounts, it would take them roughly 14 years to accumulate the respective amount of old age provision. On the other hand, we are interested in an average assessment of what difference a gift or inheritance makes by the time the heir-household retires and find that the initial gap in commitment savings accrues to more than 40,000 EUR at retirement for the average household under review. In further analyses, we show that this sizable difference in private pension savings between heirs and non-heirs persists even when we take into account other investments of heirs and non-heirs potentially intended to provide for old age. In particular, our results are not explained by nonheirs focusing on other means of asset accumulation, most prominently private housing, as a way to provide for old-age. We examine the sum of outstanding mortgages on households' main residencies during our period under review to determine whether non-heirs pay down their mortgages rather than investing in private pension products. However, the difference in installment amounts is statistically indistinguishable from zero.
Our second set of results documents that heir households vary considerably in their use of intergenerational wealth transfers. Consistent with the literature (e.g. Wolff 2002;Elinder, Erixson, and Waldenström 2018), we document that households with above-median income and wealth put a significantly higher percentage of any gift or inheritance in their private pension accounts. Notably, this difference is not explained by lower-income heir-households receiving smaller gifts and inheritances. Nor do we observe that heir-households with lower income and wealth levels use the wealth transfers to pay down any unsecured debt prior to increasing private pension savings. Quite contrarily, we find that below-median income (below-median wealth) unsecured debt levels of heir-households slightly increase. In addition, the positive impact of receiving gifts or inheritances on private pension savings is almost exclusively driven by households in which the household member 4 See section 3.2 for details on these calculations. in charge of financial decision-making belongs to an above-median age cohort. This finding cannot be explained by younger households receiving smaller gifts and inheritances, either.
Third, we shed light on whether expecting a larger gift or inheritance in the future alters peoples' saving habits. In the vein of Börsch-Supan et al. (2016), who highlight that wrong expectations about future (public) pensions are a potential reason for under-saving for old age, we run an additional analysis, in which we focus on the potential impact of inheritances which the household under review anticipates, but has not received yet. Corroborating the earlier results, however, we find that the mere anticipation of receiving a gift or inheritance at some point in the future does not decrease the amount presently put in private pension accounts.
Fourth and finally, we find some evidence suggestive of a sustained long-term effect of intergenerational wealth transfers on individuals' private pension savings. Studying a subsample of households that received a large gift or inheritance in the 1990s and comparing these households with matched non-heir households in 2010 and 2011, we document a significantly higher level of funds accrued in commitment savings.

Data and key variables
To investigate the impact of gifts and inheritances on individuals' private pension savings, we draw on the Panel on Household Finances (PHF) survey data provided by the Deutsche Bundesbank, which is representative of the German population and provides us with detailed data on intergenerational transfers. The PHF data is elicited via personal face-to-face interviews and covers a wide range of individual and household finances. Specifically, it includes details on households' consumption patterns, real-and financial assets, liabilities and intergenerational transfers, as well as data on individuals' pensions and insurance contracts. 5 Interviews with the 3,565 households sampled in the first wave of the PHF were conducted between September 2010 and July 2011. The most recent second wave was administered between April and November 2014 and samples 4,461 households. A total of 2,138 households participated in both waves and are the subject of our study. We exclude households in which the FKP has either retired or changed between waves, which leaves us with a final sample of 1,254 households. Except for respondents' demographic characteristics, which are available for the household's FKP only, all variables are recorded at the household level.
The PHF asks households about the three largest gifts or inheritances they have received at the time the interview is conducted, along with asset type and amount as well as the year in which these transfers were received. 6 Using this data, we generate our first key explanatory variable Gift/inheritance received which assumes a value of one for the 111 sampled households that received a gift or inheritance of at least 10,000 EUR during wave 1 and wave 2 (henceforth referred to as 'heirs') and zero for non-heirs. 7 Moreover, the PHF asks households to indicate if they anticipate a gift or inheritance in the future. Based on this item, we construct the second key explanatory variable Gift/inheritance anticipated which takes a value of one for the 185 households that stated in wave 2 that they expect to receive a gift or inheritance. 8 Our key dependent variable, Private pension (EUR), is the total amount of private pension savings in a given household. At this, private pension savings include state-subsidized pension plans as well as endowment life insurances and 6 The respective questions in the PHF are worded as follows: "Have you or another member of your household received a larger gift or inheritance, e.g. money or other valuables, from someone who does not belong to the household"; "How many larger gifts or inheritances were there?"; "In what year did you receive the gift/inheritance that was the most important for your current financial situation?"; "What type was the gift/inheritance?"; "What value did the gift/inheritance have when you received it?". Table A1 provides descriptions of all variables used in the analysis. 7 We exclude observations of Gift/inheritance received whose distance from the sample mean exceeds three times the standard deviation. 8 The respective question in the PHF is worded as follows: "Does your household expect a larger gift or inheritance from someone who is not a household member in the future?". Note: in order to make sure we capture the actual impact of expected gifts or inheritances, we further exclude households that already stated that they expect a gift or inheritance in wave 1 for the regression analyses. This reduces our initial sample from 185 households that expect a gift or an inheritance in wave 2 to 91 households that for the first time expect a gift or an inheritance in wave 2. all other private pension plans. Unlike other savings and investments, these products are at least partially illiquid and incur substantial early withdrawal penalties (in addition to any applicable income taxes). Such stipulations may be regarded as self-commitment tools and we can thus be reasonably certain that private funds flowing into these illiquid accounts are indeed available for use in retirement, while this is not a foregone conclusion for savings and investments in non-commitment contracts which households may intend to consume in retirement but-typically owing to self-control problems-frequently liquidate early (cf., e.g., Beshears, Choi, Harris, et al. 2015;Agarwal, Pan, and Qian 2019).
Heirs in our sample differ from non-heirs along several dimensions. 9 To circumvent a potential selection bias confounding our analyses, we follow Andersen and Nielsen (2011) and apply a propensity score matching to identify the appropriate benchmark group of non-heir households. Specifically, we use the nearest neighbor matching procedure with one-to-one matching and assign heir-households to nonheir households with similar propensity scores (cf., e.g., Abadie and Imbens 2006). 10 We choose the covariates proposed by Smith and Todd (2005) and take into consideration that they should simultaneously impact the outcome variable (here Private pension (EUR)) and the treatment status (here, e.g., Gift/inheritance received). In doing so, we account for the fact that households with a higher education and income are, e.g., more likely to come from a wealthier family background which in turn increases the probability of receiving significant intergenerational transfers. To provide an unbiased starting point for our matched sample, we remove households that have received a large gift or inheritance at some point before our first observation in 2010/2011. We end up with a sample of 118 households featuring data in both waves.
[Please insert Table 1about here.] 9 Table A2 and A3 report summary statistics of the sampled households. 10 Given the large number of non-heirs in the sample, we require the difference in propensity scores of matched twins be no larger than 0.01 (cf. Andreou, Louca, and Petrou 2017). Moreover, in the vein of Grilli and Rampichini (2011), we use wave 1 as our matching base to ensure that our covariates used for matching are either fixed (e.g. gender) or measured before the treatment. Additionally, Table 2 provides summary statistics on the intergenerational transfers under review. The average transfer amounts to 100,244 EUR, 42% (58%) of transfers are gifts (inheritances), and that the majority of assets (71%) are passed on by parents to their children.

Univariate evidence
As an initial assessment of the impact of receiving a gift or inheritance on private pension saving, we calculate the average treatment effect (ATE). At this, we follow Abadie and Imbens (2011) and apply a nearest neighbor matching approach with bias-corrected matching estimators and cluster-robust standard errors.
[Please insert Table 3 about here.] Table 3 reports the corresponding results. We calculate ATEs at two points in time: at wave 1, i.e. before any gift or inheritance is received by households in the treatment group, and at wave 2 after these households have received a gift or inheritance of at least 10,000 EUR. Initially, the group of heirs holds 2,511 EUR more in their private pension savings account as compared to non-heirs and this difference turns out indistinguishable from zero (z=0.65). By contrast, we observe a statistically and economically significant difference in the amount of money households hold in their private pension accounts at wave 2: pension savings of heirs are 10,765 EUR larger than those of the average non-heir household (z=2.14). ownership of private pension products (in the latter case estimated by means of an linear probability model).
Moreover, our key explanatory variable indicates whether or not a gift or inheritance has been received between wave 1 and wave 2 (Gift/inheritance received) in the first regression specification (cf., e.g., Weil 1994;Arrondel et al. 2014). In the second specification, we follow Andersen and Nielsen (2011) and add 11 Johnson (2005) and Vaisey and Miles (2014) Table 4 reports the results obtained from these regressions. In specification (1) and (2), we examine if the receipt of a transfer between wave 1 and wave 2 has an impact on the euro amount heirs invest in private pension accounts. Specification (1) shows that having received a gift or inheritance significantly increases a given heir household's private pension account balance by as much as 18,457 EUR (t=2.54). This shows that heir households use a substantial part of their received intergenerational transfer to save it for old age in commitment contracts.
While the propensity score matching ensures comparability of heirs and non-heirs with respect to stationary features, we additionally control for time-variant covariates to capture the impact of potential changes in household characteristics between the survey waves. 12 Bucher-Koenen and Lusardi (2011) and Börsch-Supan et al. (2012) find that disposable income is positively related to private pension saving. Similarly, household size has been shown to be positively related to saving for old age (e.g., Börsch-Supan, Reil-Held, and Schunk 2008). Further, we control for a switch of FKPs to self-employment between the two waves. Because selfemployed individuals typically exit the state-granted pension system, the respective FKPs should be more likely to privately save for old age. Lastly, we include information on whether the household has received any professional financial advice in the last three years, since prior literature has shown that the use of financial advice has a positive effect on retirement saving (e.g. Shum and Faig 2006;Von Gaudecker 2015). 13 Yet, even when we include the time-variant controls, our key explanatory variable Gift/inheritance received remains statistically significant (t=2.23) and decreases only slightly in explanatory power. Specifically, specification (2) shows that households that receive a gift or inheritance during the three-year period between wave 1 and wave 2 put on average 15,268 EUR more in their private pension accounts as compared to their sociodemographic twins among the nonheirs. Given that the average non-heir household puts 3,548 EUR in their private pension accounts between wave 1 (private pension balance: 24,397 EUR) and wave 2 (private pension balance: 27,945 EUR), funds from a gift or inheritance, all else equal, increase private pension savings in commitment contracts by as much as 330%.
Regarding the time-variant controls, our results confirm prior evidence, i.e.
show that an increase in income and household size is positively associated with an increase in the euro amount accumulated in the private pension accounts. Likewise, we find a positive relation between a switch to self-employment as well as the use of financial advice and the euro amount invested in private pensions.
In specifications (3) and (4) we follow Andersen and Nielsen (2011) and provide results using the key explanatory variable gift/inheritance (EUR) to analyze how much of every euro in transferred funds is invested in private pension accounts.
Specification (3) reports a univariate contribution of 10 cents per euro of transfers (t=3.46). Even when we control for changes in household demographics during our period under review, we find that roughly 8 cents out of every euro received in the three-year period flow into the private pension saving accounts of households and confirm that this effect remains highly statistically significant (t=2.68).
Next, we regress the binary variable indicating a change in private pension ownership on both our key explanatory variables to see if the documented increase in private pension savings stems from more households starting to save for old age privately after having received funds ('volume effect') or, alternatively, if the households that already save privately simply scale up their investments ('value 13 Only recently, Dolls et al. (2018) show that being provided with personalized information about expected public pension payments stimulates individuals' private retirement savings. effect'). We find that neither of the key explanatory variables impact the ownership probability of private pension products in any significant way. This suggests that the receipt of an intergenerational transfer does not alter the initial decision of households to start investing in private pension products. Rather, our results point to a value effect, i.e. households that are already invested in private pension products use gifts and inheritances to increase their private pension savings.

Asset allocation of non-heir households
Of course, non-heir households might prefer to allocate their wealth to assets other than commitment savings, i.e. private property or investments outside of private pension plans. In this section, we therefore examine the possibility that the observed difference in private pension savings of heirs versus non-heirs predominantly owes to the fact that non-heirs simply prefer alternative ways of investment. To this end, we compare the changes in securities investments (bonds, stocks, and mutual fund shares) as well as home ownership of heirs and non-heirs, respectively, between wave 1 and 2.
[Please insert Table 8 about here.] Table 8 reports the corresponding results. As a benchmark, we set our initial dependent variable private pension (EUR) and report a statistically and economically significant difference in changes of 14,909 EUR in commitment savings between our treatment and control group. Once we turn our attention to households' total investment funds (EUR), however, the difference between heirs and non-heirs is small and insignificant: while heirs increase their saving in investment funds by 1,250 EUR, non-heirs do so by only a slightly larger 2,366 EUR. Similarly, our analysis does not suggest that non-heirs save more in stocks or bonds as compared to heir households. This evidence leads us to rule out that the strongly positive effect of gifts and inheritances on investing in private pension commitment savings is not attenuated by non-heirs simply choosing other financial products to save for old age.
Further, we are interested in whether heir households that do not own any private pension products in wave 2 (22% of heirs), possibly use investments in capital markets to save for old age. To this end, we dissect heirs into the two subgroups of private pension holders and non-holders and compare their changes in other investment products over time. Due to the small size of this subgroup of households, we are careful not to overstate the explanatory power of this additional analysis. We do, however, observe that heirs who have not owned any designated private pension products ex ante increase their investments in funds and stocks by a larger magnitude than heirs who have already allocated some money to commitment saving products. In the case of allocations to investment funds, e.g., an average increase of 2,433 EUR among heir-households that previously were not invested in private pension products compares to an increase of merely 920 EUR among heir-households with existing private pension accounts. Generally, this ties in with Brunnermeier and Nagel (2008) and Andersen and Nielsen (2011)  Taken together, the analyses reported in this section corroborate our main result that gifts and inheritances have a sizeable positive impact on households' commitment savings in private pension accounts.

Long-term effects of intergenerational transfers
The PHF data currently features two survey waves covering a period of only three years. While the short panel presents a limitation, it still allows us to make inferences about a potential long-term effect of gifts and inheritances on private pension savings: we are able to identify households that received an intergenerational transfer in the past and examine how this relates to their pension savings today.
Looking at wave 1 households (surveyed in 2010/2011), we identify 228 non-retired households that received a gift or inheritance worth more than 10,000 EUR between 1990 and 2000 such that the intergenerational transfer was received at least ten years prior to the interview date. We denote the respective subsample of households as old heirs. Next, we apply a propensity score matching using nearest neighbors (caliper of 0.01, no replacements) to construct a matched control group of non-heirs obtained from the remainder of wave 1 households.
[Please insert Table 9 about here.] As can be inferred from

Anticipation of future gifts or inheritances
Prior research suggests that children who expect to inherit from their parents tend to build their lives in part around that expectation. Weil (1994), e.g., finds that households that expect an inheritance increase their consumption even prior to actually receiving it by 5%. By the same token, households expecting future transfers might be less disciplined in putting aside money for their retirement. In what follows, we therefore investigate the potential impact of inheritances which the household under review anticipates, but, unlike in the previous case, has not received yet.
We address this question by leveraging the panel structure of our data and look at the subsample of households that switch from 'not anticipating a gift or inheritance' in wave 1 to 'anticipating a gift or inheritance' in wave 2. 15 [Please insert In a second step, to further improve the prediction of Gift/inheritance anticipated in the first-stage regression, we add a second instrumental variable so as to jointly instrument our key explanatory variable. As depicted in the instrumentation framework in Figure A1, we incorporate the additional dummy variable Household never received any gift or inheritance before wave 1 of PHF, which assumes a value of one if the household is a non-heir in wave 1. Our rationale behind this second instrument is that households with no prior receipt of a gift or inheritance are more likely to receive (and thus anticipate) a transfer in the future. 18 The results in specification (3) and (4) closely match those of specification (1) and (2). In specification (4) saving behavior. Pairing decedents and heirs, they examine if an increase in decedents wealth leads to dissaving for heirs, but find no evidence of an impact. In a related study addressing the impact of inheritance receipts on individuals' probability of early retirement, Brown, Coile, and Weisbenner (2010), e.g., find that the likelihood of retiring early after an unexpected inheritance is twice as high as compared to an inheritance which has been anticipated. By contrast, Doorley and Pestel (2016) find no difference between expected and unexpected inheritances with respect to the households' decision to retire earlier. We include the binary variable Gift/inheritance anticipated, indicating if the FKP stated in wave 1 that the household expects to receive a gift or inheritance, and our results show no significant difference between the two groups of inheritances, either.

Discussion and concluding remarks
Using detailed household panel data, we investigate how gifts and inheritances affect the financial decision making of households with respect to private pension savings. At this, we focus on private pension plans designed to be provide secure funds during old age. Our main result is that, on the one hand, intergenerational wealth transfers do seem to provide the average heir household under review with a head start when it comes to old-age provision. All else equal, households who receive a gift or inheritance during the three-year sample period between 2011 and 2014 make on average 15,268 EUR (or as much as 330%) higher payments to their private pension accounts as compared to their sociodemographic twins among the group of non-heirs. This gap accrues to more than 40,000 EUR at retirement and persists even when we control for other investments of heirs and non-heirs which may be intended to provide for old age, such as securities holdings or real estate (including mortgage down payments of existing housing).
On the other hand, we document considerable variation in the effect size of transferred funds with respect to heir-households' commitment savings for old age.
First, heir-households with above-median income and wealth put a significantly higher percentage of a given gift or inheritance in their private pension accounts.
Notably, this difference is not explained by lower-income heir-households receiving smaller gifts and inheritances-in fact, average transferred funds among households with below-median income are roughly 15% larger than those for higher income heirs. In addition, we rule out other alternative explanations, such as the possibility that some heir-households wish to pay off their unsecured debt prior to saving by means of a private pension plan. Third, the positive impact of receiving gifts or inheritances on private pension savings is almost exclusively driven by households with financial decision makers aged 45-65 years. Again, this finding cannot be explained by younger households receiving smaller gifts and inheritances.
Our findings contribute to recent research illuminating the role of intergenerational wealth transfers for intergenerational justice. Halliday (2018) argues that inherited wealth undermines social justice when it helps maintain group-based wealth inequalities over time. Indeed, intergenerational wealth transfers can be a mechanism by which economic segregation is created and transmitted over the generations. Wolff (forthcoming) worries that the retirement divide is one of the most notable examples of economic segregation in the UK. Corroborating this concern, prior empirical research documents that large proportions of gifts and inheritances are not consumed by the recipients. Westerheide (2005) finds that about 80% of an intergenerational wealth transfer is saved by the average heir and that gifts and inheritances considerably affect the wealth creation of households. Joulfaian (2006) confirms those figures using US estate tax records and finds that 79% of inheritances are saved and retained as wealth. Moreover, Braun (2015) documents that those who will inherit are primarily the ones that already own higher-than-average wealth.
Halliday (2018)  Generally, there is a wide consensus among economists and social scientists that the intergenerational replication of inequality is real and that it might have previously been underestimated (e.g. Mazumder 2005). The mechanisms by which status and economic inequality reproduce over the generations, however, are less well understood. For example, it has recently been argued that the bigger cause of massive inequality today is very high earnings rather than inheritance (e.g. Piketty   2014). By providing a quantitative account of how gifts and inheritances affect inequality in retirement wealth, this study hopes to promote discussions on intergenerational justice in society and to provide new perspectives for policymakers. Households that received a gift or inheritance prior to wave 1 and households in which the Financially Knowledgeable Person (FKP) has retired or changed between the two waves are excluded from the sample. 'Heirs' are defined as households that, for the first time, received a gift or inheritance of more than 10,000 EUR between 2011 and 2014. 'Nonheirs' are nearest-neighbor households, based on a propensity score matching, who did not receive a gift or inheritance of more than 10,000 EUR during the period under review. Notes-This table reports summary statistics of gifts and inheritances received by first-time heirs during the period under review (2011)(2012)(2013)(2014). Statistics on the amount and asset type of gift or inheritance in Panel B are not mutually exclusive by category. "Other assets" include (i) land (ii) jewelry/furniture/art and (iii) life insurance. Control 820

Tables and figures
Notes-This table reports average treatment effect (ATE) results of a propensity score matching (PSM) approach with nearest neighbors. The PSM approach excludes households whose FKPs (i) changed, (ii) retired, or (iii) received a gift or inheritance of greater than 10,000 EUR prior to wave 1. The treatment group includes all households (N=60) who, between wave 1 and wave 2, received a gift or inheritance of greater than 10,000 EUR for the first time. ATE shows the difference in private pension (EUR) invested by either group of households. Robust standard errors are calculated following Abadie and Imbens (2011). ***, ** and * indicate statistical significance at the 1%, 5% and 10% level, respectively. ΔPrivate pensioni = β0 + β1Gift/inheritancei + γ'Δci + hi + εi Specifications (1) and (2) show the effect of Gift/inheritance received on the change in private pension (EUR) invested by each household. Specifications (3) and (4) show the effect of the Gift/inheritance (EUR) on the change in private pension (EUR). Applying a Linear Probability Model (LPM), specifications (5) and (6) show the effect of Gift/inheritance received and Gift/inheritance (EUR) on the change in the probability of private pension ownership, respectively. All specifications include a vector of householdlevel control variables, ci, feature household fixed effects hi, and are estimated using robust standard errors reported in parentheses below the coefficients. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively.
Metric variables are dichotomized via median splits of the subsample; wave 1 values serve as the base for the split. The suffix _high denotes above-median values of the variable. For the first indicator variable, e.g. , β1 reports the effect of receiving a gift or inheritance on private pension (EUR) given the household is below the median net income. Analogously, β1 + β2 reports the effect for the household above the median net income. β2 shows the difference in the reported effects for low and high net income households, respectively. Panel A is organized by heir-household characteristics; Panel B distinguishes gifts or inheritances including real estate as well as anticipated gifts of inheritances. All specifications include a vector of household-level control variables, ci, feature household fixed effects hi, and are estimated using robust standard errors reported in parentheses below the coefficients. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively.
This model employs a different matched sample of N=182 households whose respective FKPs state to expect a gift or inheritance of greater than 10,000 EUR in the future. The matched sample excludes households whose FKPs (i) changed, (ii) retired, or (iii) stated that they expected a gift/ inheritance already at point in time wave 1. Specification (1) shows the effect of Gift/inheritance anticipated on the change in private pension (EUR) in the matched sample. Specification (2) adds the controls Gift/inheritance received in the period 2011-2014 and changes in household net income or selfemployment status and for financial advice received by a bank agent. All specifications include a vector of householdlevel control variables, ci, feature household fixed effects hi, and are estimated using robust standard errors reported in parentheses below the coefficients. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively. Notes-This table reports descriptive statistics on other investments that are suitable for old age saving, namely (i) other financial investment products (besides private pensions), i.e. investment funds, stocks and bonds, as well as (ii) real estate (i.e. measured by home ownership) for the treatment group "heirs" and the control group "non-heirs". We calculate the absolute increase/decrease for all EUR values (as well as the percentage point increase/decrease for item home ownership) between the two waves. Within the treatment group "heirs", we further divide into heir-households owning private pension products in wave 2 and those heir-households that don't. The second-to-last and last column report the differences of the changes, as well as the t-statistic of a t-test for the equality of the changes. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively. Notes-This table reports descriptive statistics of old heirs (households that received a gift or inheritance of more than 10,000 EUR between 1990 and 2000) and a matched control group of non-heir households. Wave 1 (2010/2011) figures of non-retired households are displayed, hence at least 10 years are in between the intergenerational transfer and the survey. To create our control group of non-heirs we conduct propensity score matching (PSM) with nearest neighbors (caliper of 0.01, no replacements). The second-tolast and last column report the differences between old heirs and the control group, as well as the t-statistic of a t-test for the equality of the means. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively.     Notes: This table reports descriptive statistics of our overall sample of panel households. Households that are retired and households in which the Financially Knowledgeable Person (FKP) has switched during the survey are excluded. Group A includes households that did receive a gift/ inheritance >10,000 EUR during period 2011-2014, Group B includes those who did not receive a gift/ inheritance during this period. Note that households, who received a gift/ inheritance in the years before wave 1 (2010/2011) are not excluded in this summary statistic yet (thus, the larger number of 'heirs'). Panel A displays demographics for wave 1 and wave 2 of both groups. t-tests are calculated for the differences in means between Group A (heirs) and Group B (non-heirs) as displayed in last and second-to-last column. Panel B shows wave 1 (2010/2011) figures and displays conditional means. Taylor-linearized standard errors are used to estimate standard deviations. Data is weighted and representative of the German non-retired population, equal in representation to ~27M households. ***, ** and * indicate statistical significance at the 1%, 5% and 10% level, respectively.  (1) and (2) apply panel weights. Specifications (3) and (4) control for time fixed effects. All specifications feature household fixed effects hi and are estimated using robust standard errors reported in parentheses below the coefficients. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively.

Figure A1-Potential endogeneity and instrumentation framework
Notes-This figure visualizes the instrumentation of Gift/inheritance anticipated.