François-Charles Wolff

Lemna

Decomposition of non-linear models using simulated residuals #

Keywords: Blinder-Oaxaca decomposition, non-linear models, simulated residuals JEL Classification: C20

This paper proposes to decompose non-linear models deduced from a latent regression framework using the latent dependent outcome as dependent variable and the Oaxaca-Blinder decomposition technique. Values of the unobserved latent outcome are obtained using simulated residuals.

Introduction

A common approach used to identify the cause of gender or racial differences in labor market outcomes is the well-known Blinder-Oaxaca decomposition [START_REF] Blinder | Wage discrimination: Reduced form and structural estimates[END_REF][START_REF] Oaxaca | Male-female wage differentials in urban labor markets[END_REF]. The mean difference in wages between two groups, for instance men and women, is divided into one component that is explained by differences in characteristics like education or experience and one component attributable to differences in the return to these observable characteristics. This unexplained part of the gap is most often seen as a measure for discrimination.

One reason of the success of this decomposition technique lies in its large application potential. As emphasized in [START_REF] Jann | The Blinder-Oaxaca decomposition for linear regression models[END_REF], this technique may be used to study group differences in any outcome variable. When the dependent variable is continuous, the decomposition is very easy to implement as it only requires estimates from linear regressions for the outcome of interest and sample means of the covariates used in the regressions. However, the problem becomes a little bit more complex when the outcome variable is non-linear since OLS estimates cannot be used directly in the Blinder-Oaxaca decomposition equation.

Recently, a few papers have attempted to generalize the Blinder-Oaxaca decomposition to non-linear models. [START_REF] Fairlie | The absence of the African-American owned business: An analysis of the dynamics of self-employment[END_REF] provides a decomposition method for binary dependent variables explained by either Logit or Probit models. [START_REF] Yun | Decomposing differences in the first moment[END_REF] proposes a general methodology for decomposing differences in the first moment when the dependent variable may be expressed as a once differentiable function of a linear combination of covariates. Finally, [START_REF] Bauer | An extension of the Blinder-Oaxaca decomposition to nonlinear models[END_REF] rewrite the usual decomposition equation in terms of conditional expectation to obtain a general version of the Oaxaca-Blinder decomposition that can be applied to models with either discrete or limited dependent variables (see also [START_REF] Sinning | The Blinder-Oaxaca decomposition for nonlinear regression models[END_REF].

In this paper, I propose an alternative procedure to decompose non-linear models deduced from a latent regression framework by a non-linear mapping, which includes as special cases Probit, ordered Probit or Tobit models among others. Instead of working on the conditional expectation of the observed dependent variable, I decompose the corresponding latent outcome following the Oaxaca-Blinder decomposition technique. Values of the unobserved latent dependent variable are obtained using simulated residuals [START_REF] Gouriéroux | Simulated residuals[END_REF] 1 .

The remainder of my presentation is organized as follows. In the next Section, after a brief description of the Oaxaca-Blinder decomposition, I explain how to simulate the latent outcome corresponding to a discrete or limited dependent variable. In Section 3, I perform a Monte-Carlo analysis using a binary dependent variable. Section 4 concludes.

Decomposition methodology

For the presentation, I consider the Oaxaca-Blinder decomposition in the context of a linear model. In a setting with two groups = ( , ), I denote by * a continuous dependent variable and assume that * is explained by a vector of explanatory variables following a linear regression model:

* = + (1)
with the corresponding estimates and a random perturbation. The gap between the mean outcomes * and * may be expressed as [START_REF] Blinder | Wage discrimination: Reduced form and structural estimates[END_REF][START_REF] Oaxaca | Male-female wage differentials in urban labor markets[END_REF]:

where is the identity matrix and Ω is a matrix of weight. (2) is the case when Ω = , but other possibilities for the Oaxaca-Blinder decomposition are for instance Ω = 0 or diag(Ω) = 0.5. In the case of a non-linear model, the problem with (2) or (3) is that the conditional expectation ( * | ) is likely to differ from .

In what follows, I consider models deduced from a latent regression framework by a nonlinear mapping, which includes a large set of discrete and limited dependent models (like univariate Probit, ordered Probit or Tobit regressions). In that case, the dependent variable is defined by = * where * is a continuous, latent outcome such that * = + . If the latent variable * were observed, then a simple strategy to decompose the gap * - * would consist in an application of (2) or (3).

A solution to this problem of unobservability was suggested more than twenty years ago by [START_REF] Gouriéroux | Simulated residuals[END_REF]. Drawing on simulated residuals, the idea consists in simulating the values of the unobserved latent variables * and * . The methodology involves two steps. First, maximum likelihood estimates of are obtained from the appropriate specification given and . Then, one simulates values * for the latent dependent outcome * given , and .

For the sake of illustration, consider the case of a Probit model. The dependent variable is such that = 1 if * > 0 and = 0 when * ≤ 0, is the normal distribution function and residuals are such that ~%(0; 1). Application of simulated residuals is implemented as follows. First, estimation of two Probit models gives for both groups and . Then, residuals are drawn from %(0; 1) and * is the first value satisfying * = + > 0 when = 1 and * = + ≤ 0 when = 0. As a final step, I estimate * = + ' and * = + ' using OLS and apply a linear decomposition to the difference * - * = ( -) + following (2)2 .

A Monte Carlo experiment

I evaluate the decomposition procedure by undertaking a Monte Carlo experiment, which consists of 200 replications on a sample of 10,000 observations. The explanatory variables are drawn from normal distribution with ~%(4; 1) and ~%(5; 1). Then, I calculate the values of the latent dependent variables such that * = 2 + 0.5 * + and * = 2 + 0.6 * + , with ~%(0; 1) and ~%(0; 1). I set to 0.5 the proportion of individuals belonging to each group.

Since * and * are continuous, implementation of the Oaxaca-Blinder decomposition is straightforward. By construction, when the reference group is Ω = , then * - * = ( -) + ( -)

and the contributions of ( -) and ( -) amounts to 60% and 40% respectively. Conversely, when Ω = 0, then * - * = ( -) + ( -) and the gap is explained equally by differences in characteristics (50%) and differences in coefficients (50%).

I define my binary dependent variable as follows. Denoting by + * the average value of the dependent variable on the whole sample (it is equal to 4.5 by construction), I define two dummy variables ( = , ) such that = 1 when * > + * and = 0 otherwise. Then, I proceed in the following way. First, I calculate the Oaxaca-Blinder decomposition using the latent observed outcomes * -+ *3 . As shown in Table 1, I obtain the expected values for the characteristics and coefficients effects: respectively 60% and 40% when Ω = , and 50% and 50% when Ω = 0. Then, I focus on the binary outcomes and implement a non-linear Probit decomposition following [START_REF] Sinning | The Blinder-Oaxaca decomposition for nonlinear regression models[END_REF]. Very similar results are obtained since 59.3% of the gap is explained by differences in characteristics when Ω = . The corresponding percentage is 51.0% when Ω = 0.

Next, I suppose that the latent variables * are unobserved, but information on the binary outcomes is available. I turn to simulated residuals to get simulated values of the unobserved latent variables * . As shown in Table 1, the estimates and obtained from OLS regressions are very similar to the original parameters since I get = 0.501 and = 0.604. When decomposing * - * following the Oaxaca-Blinder procedure, the values found for the characteristics and coefficients effects are very close to expectations: 60.4% for the characteristics effect when Ω = and 50.0% when Ω = 0.

I perform additional simulations on the binary dependent variables defined as = 1 when the latent outcomes * exceed the 25th percentile of * and the 75th percentile of * respectively. I find that decomposing the observed binary variables and the latent outcomes leads to substantial differences. For instance, when Ω = , the weight of the characteristics effect obtained from a nonlinear decomposition is 54.2% at the 25th percentile instead of 60% with the Oaxaca-Blinder technique. Of course, this is due to the different definition of the dependent variables 4 . When decomposing the simulated values of the latent outcomes, I again find estimated weights that are very close to expectations. The contribution of the characteristics effect is 60.4% at the 25th percentile and 60.1% at the 75th percentile when Ω = . Furthermore, and are almost equal to 0.5 and 0.6. A difficulty with the Probit model is that the error variance is not identified (and thus normalized to one). This normalization imposes equality of error variances between the two groups in the decomposition, but the true error variances may very well be different. Unfortunately, the linear decomposition of the simulated latent variable will perform poorly in such situations. The problem is that knowing the binary outcomes and provides no information on the variances of the residuals of the latent variables. An assumption on error variances is needed to draw simulated residuals, and results from the decomposition of the simulated latent variable will clearly be conditional on the assumption made about the error terms 5 .

For some non-linear models, data provides information on the variances of and . Consider for instance the case of a Tobit model. With the same latent outcome * -+ * as before, the dependent variable is now = * -+ * if * > + * and = 0 if * ≤ + * . Estimation of Tobit models respectively for and gives not only the coefficients and , but also the error variances 4 5 1 and 4 5 1 . Application of simulated residuals thus requires to draw residuals such that ~%(0; 4 5 1 ) and ~%(0; 4 5 1 ). In additional simulations (not reported), I show that in that case the decomposition based on the latent simulated outcome performs very accurately with unequal error variances. When Ω = , I find a weight of 59.9% for the characteristics effect with 4 5 1 = 0.5 and 4 5 1 = 1 and of 60.1% with 4 5 1 = 1.5 and 4 5 1 = 1. These results are similar to those obtained from the 4 If the purpose is for instance to explain the labor force participation of men and women, then * is a measure of the propensity to work while is equal to one when an individual is working. 5 In an appendix available upon request, I present results from Monte Carlo simulations with residuals and drawn from normal distribution with different variances. With unequal error variances, the contribution of the characteristics component when Ω = increases with the variance of and (the reverse pattern is found when Ω = 0). At the same time, it is interesting to think about the meaning of different error variances for and . If I consider for instance labor force participation by gender, an assumption is needed on the error variance of the unobserved propensity to work for men and women respectively. It seems very difficult to claim on a priori grounds that the error variance is higher either for men or women, so that the assumption of equal error variances is certainly not unreasonable.

Oaxaca-Blinder decomposition, while the characteristics effect is very different when implementing the non-linear Tobit decomposition (respectively 76% and 46.9%).

Conclusion

In this paper, I propose to decompose non-linear models deduced from a latent regression framework using the latent dependent outcome as dependent variable. Since the latent outcome is unobserved, I turn to simulated residuals and apply the standard Oaxaca-Blinder to the simulated latent variable. Results from a Monte Carlo experiment indicate that this procedure provides accurate estimates of the characteristics and coefficients effects. This combination of simulated residuals and linear decomposition is straightforward to implement and may be of interest to researchers interested in decomposing models with discrete or limited dependent variables.

Decomposition of non-linear models using simulated residuals François-Charles Wolff

Highlights

• A method is proposed to decompose non-linear models deduced from a latent regression.

• Values of the unobserved latent outcome are obtained using simulated residuals.

• The latent outcome is decomposed following the Oaxaca-Blinder technique.

February 23 th , 2012

François-Charles Wolff Professor of Economics LEMNA, Université de Nantes BP 52231 Chemin de la Censive du Tertre, 44322 Nantes Cedex 3, France Tel:+33 2 40 14 17 79 E-mail: francois.wolff@univ-nantes.fr http://www.sc-eco.univ-nantes.fr/~fcwolff Ref:

"Decomposition of non-linear models using simulated residuals" Economics Letters, first revision, EL31257

To the Editor, Professor Badi Baltagi Dear Professor Baltagi, I have now carefully gone through the comments provided by the anonymous reviewer on my manuscript entitled "Decomposition of non-linear models using simulated residuals", under revision at Economics Letters.

The main issue raised by the anonymous reviewer was about the assumption of equal error variances: "However, this is generally not going to be the same as group differences in the parameters of the latent variable model because the true error variances may very well be different". I would like to thank the anonymous reviewer for this very relevant remark, and I have decided to further elaborate on this issue (see page 4).

First, I mention that the error variance is not identified in the Probit model, which explains the normalization to one. As a consequence, this normalization imposes equality of error variances between the two groups in the decomposition. If I assume that the error variances are different, then the linear decomposition of the simulated latent variable will perform poorly. The problem is that knowing the binary dependent variables and provides no information on the variances of the residuals of the latent variables. An assumption on error variances is hence needed to draw simulated residuals, and it is clear that results from the decomposition of the simulated latent variable will be conditional on this assumption made about the error terms.

To highlight that point, I have performed additional simulations with residuals and drawn from normal distribution with different variances. These additional results are enclosed (Table A), but please note that I have decided to place these results in an appendix available upon request given space constraints in Economics Letters. With unequal error variances, the contribution of the characteristics component when Ω = increases with the variance of and , while the reverse pattern is found when Ω = 0. At the same time, it is interesting to think about the meaning of different error variances for the residuals and . If I consider for instance the case of the labor force participation by gender, this means that an assumption is needed on the error variance of the unobserved propensity to work respectively for men and women. It seems very difficult to claim on a priori grounds that the error variance of the residual associated to the latent outcome is higher either for men or for women, so that the assumption of equal error variances is certainly not unreasonable. In fact, the assumption of equal (unitary) error variances is also made when estimating gender-specific Probit regressions to decompose non-linearly the probability to work.

I have also decided to consider the case of non-linear models when data provides information on the variances of and . This is for instance the case of a Tobit model, the dependent variable being now = * -+ * if * > + * and = 0 if * ≤ + * . The estimation of Tobit models respectively for and gives not only the coefficients and , but also the error variances 4 5 1 and 4 5 1 . Application of simulated residuals thus requires to draw residuals from ~%(0; 4 5 1 ) and ~%(0; 4 5 1 ). In additional simulations described in Table B (these results are again in an appendix not for publication) and keeping the same setting, I show that the decomposition based on the latent simulated outcome performs very accurately with unequal error variances. When Ω = , I find a weight of 59.9% for the characteristics effect with 4 5 1 = 0.5 and 4 5 1 = 1 and of 60.1% with 4 5 1 = 1.5 and 4 5 1 = 1. These results are similar to those obtained from the Oaxaca-Blinder decomposition, while the characteristics effect is very different when implementing the non-linear Tobit decomposition (respectively 76% and 46.9%).

Finally, please note that I have changed the style of the references following the Economics Letters guide for authors. I hope that you will find this revised version of my manuscript satisfactory and I look forward to hearing from you.

Sincerely,

François-Charles Wolff

Part B. Decomposition of a Tobit model, with different error variances

Setting:

~%(4; 1), ~%(5; 1), * = 2 + 0.5 * + , * = 2 + 0.6 * + Dependent variable: = * -+ * if * > + * and = 0 if * ≤ + *

Table 1 . Decomposition from Monte Carlo simulations

 1

	Decomposition			= 1 -. * /-+ *			= 1 -. * /012(- * )			= 1 -. * /032(- * )
			Oaxaca	Probit	Simulated	Oaxaca	Probit	Simulated	Oaxaca	Probit	Simulated
	Ω =
	Dif. in characteristics proportion	0.600	0.593	0.604	0.600	0.542	0.604	0.600	0.649	0.601
		mse	0.018	0.023	0.029	0.018	0.033	0.029	0.018	0.020	0.034
	Dif. in coefficients	proportion	0.400	0.407	0.396	0.400	0.458	0.396	0.400	0.351	0.399
		mse	0.018	0.023	0.029	0.018	0.033	0.029	0.018	0.020	0.034
	Ω = 0
	Dif. in characteristics proportion	0.500	0.510	0.500	0.500	0.605	0.500	0.501	0.411	0.500
		mse	0.018	0.023	0.026	0.017	0.021	0.028	0.017	0.029	0.028
	Dif. in coefficients	proportion	0.500	0.490	0.500	0.500	0.395	0.500	0.499	0.589	0.500
		mse	0.018	0.023	0.026	0.017	0.021	0.028	0.017	0.029	0.028
	Estimated parameters
		coef	0.501	0.501	0.501	0.500	0.500	0.501	0.500	0.500	0.500
		mse	0.015	0.020	0.023	0.013	0.019	0.022	0.013	0.027	0.029
		coef	0.601	0.604	0.604	0.600	0.604	0.605	0.599	0.599	0.600
		mse	0.013	0.021	0.024	0.014	0.027	0.029	0.015	0.023	0.025
	Source: calculations from author.
	Note: results from Monte Carlo simulations with 200 replications (N=10,000).

Table A . Decomposition from Monte Carlo simulations -Probit model

 A Note: results from Monte Carlo simulations with 200 replications (N=10,000).

	Decomposition		~%(0; 0.5), ~%(0; 1)	~%(0; 1.5), ~%(0; 1)		~%(0; 0.5), ~%(0; 1.5)
			Oaxaca	Probit	Simulated	Oaxaca	Probit	Simulated	Oaxaca	Probit	Simulated
	Ω =
	Dif. in characteristics proportion	0.598	0.468	0.400	0.601	0.691	0.724	0.599	0.383	0.301
		mse	0.019	0.017	0.018	0.022	0.032	0.039	0.028	0.021	0.020
	Dif. in coefficients	proportion	0.402	0.532	0.600	0.399	0.309	0.276	0.401	0.617	0.699
		mse	0.019	0.017	0.018	0.022	0.032	0.039	0.028	0.021	0.020
	Ω = 0
	Dif. in characteristics proportion	0.498	0.609	0.665	0.499	0.426	0.398	0.498	0.680	0.749
		mse	0.012	0.019	0.023	0.026	0.027	0.030	0.014	0.024	0.029
	Dif. in coefficients	proportion	0.502	0.391	0.335	0.501	0.574	0.602	0.502	0.320	0.251
		mse	0.012	0.019	0.023	0.026	0.027	0.030	0.014	0.024	0.029
	Estimated parameters
		coef	0.499	1.000	0.999	0.499	0.332	0.332	0.499	0.999	1.000
		mse	0.007	0.031	0.033	0.022	0.019	0.022	0.007	0.031	0.035
		coef	0.599	0.600	0.601	0.602	0.603	0.603	0.600	0.401	0.401
		mse	0.015	0.020	0.022	0.014	0.022	0.025	0.023	0.020	0.022
	Source: calculations from author

Table B . Decomposition from Monte Carlo simulations -Tobit model

 B Note: results from Monte Carlo simulations with 200 replications (N=10,000).

	Decomposition		~%(0; 0.5), ~%(0; 1)	~%(0; 1.5), ~%(0; 1)		~%(0; 0.5), ~%(0; 1.5)
			Oaxaca	Tobit	Simulated	Oaxaca	Tobit	Simulated	Oaxaca	Tobit	Simulated
	Ω =
	Dif. in characteristics proportion	0.600	0.750	0.599	0.602	0.469	0.601	0.599	0.800	0.601
		mse	0.018	0.011	0.026	0.022	0.036	0.030	0.027	0.011	0.037
	Dif. in coefficients	proportion	0.400	0.250	0.401	0.398	0.531	0.399	0.401	0.200	0.399
		mse	0.018	0.011	0.026	0.022	0.036	0.030	0.027	0.011	0.037
	Ω = 0
	Dif. in characteristics proportion	0.500	0.527	0.500	0.498	0.097	0.499	0.498	0.642	0.497
		mse	0.012	0.014	0.017	0.027	0.055	0.035	0.013	0.015	0.019
	Dif. in coefficients	proportion	0.500	0.473	0.500	0.502	0.903	0.501	0.502	0.358	0.503
		mse	0.012	0.014	0.017	0.027	0.055	0.035	0.013	0.015	0.019
	Estimated parameters
		coef	0.499	0.499	0.499	0.498	0.500	0.500	0.499	0.498	0.498
		mse	0.008	0.016	0.017	0.022	0.026	0.031	0.007	0.015	0.015
		coef	0.599	0.599	0.598	0.602	0.602	0.602	0.600	0.600	0.602
		mse	0.016	0.017	0.021	0.014	0.016	0.020	0.022	0.025	0.030
	Source: calculations from author

In the context of linear models,[START_REF] Yun | An extension of the Oaxaca decomposition using generalized residuals[END_REF] proposes an extension of the Oaxaca-Blinder decomposition using generalized residuals, which refer to conditional expectations of residuals.

The second-stage estimator is a strongly consistent estimator of (seeGouriéroux et al., 1987, Theorem 1).

By definition, * - * = ( * -+ * ) -( * -+ * ).

Appendix, not for publication

Part A. Decomposition of a Probit model, with different error variances

Setting:

~%(4; 1), ~%(5; 1), * = 2 + 0.5 * + , * = 2 + 0.6 * + Dependent variable: = 1 -. * /-+ *


Seymour Spilerman

Florencia Torche

Peter Bearman

Vered Kraus

The role played by parental wealth in facilitating the life chances and living standards of offspring is a topic of growing interest in stratification research. For working and middle class households much of their intervivos transfers to children is provided in the form of assistance with a home purchase. This paper examines the impact of parental wealth and transfers of wealth on several aspects of the homeownership decision--the timing of the purchase, the cost of the home, and the downpayment proportion, as well as living standards subsequent to the purchase. We utilize a unique data set from France which contains information on parental wealth and wealth transfers from both sets of parents of a couple. We correct for possible endogeneity of parental transfers and model the joint determination of the downpayment proportion and home value. The results make clear the complex pathways by which parental wealth influences the tenancy arrangements and living standards of offspring.

I. INTRODUCTION

The impact of parental resources on the life chances of offspring is a theme that has received much attention in the stratification literature. In early studies based on the socioeconomic attainment paradigm (e.g., [START_REF] Blau | The American Occupational Structure[END_REF][START_REF] Jencks | Inequality: A Reassessment of the Effect of Family and Schooling in America[END_REF] the outcome variables of primary interest were the occupational achievements and earnings of children, and the parental resources that were stressed were father's education and father's occupational status. In more recent investigations the array of resource items has been broadened to include both maternal characteristics and the assets of parents, and the range of outcome measures has similarly been extended to encompass a variety of aspects of the well-being of children (e.g., [START_REF] Conley | Being Black, Living in the Red: Race, Wealth, and Social Policy in America[END_REF][START_REF] Attias-Donfut | Les Solidarites Entre Generations: Vieillesse, Familles[END_REF][START_REF] Mayer | What Money Can't Buy: Family Income and Children's Life Chances[END_REF][START_REF] Spilerman | The Impact of Parental Wealth on Early Living Standards in Israel[END_REF]).

Household wealth is probably the most significant addition to the parental resource portfolio. Inclusion of this asset has altered our imagery of the transfer process in two ways. First, it has heightened the emphasis on financial and material resources, in comparison with socialization effects.

In the earlier formulations, in which parental education and occupational status were stressed, it was presumed that the main pathway by which parental resources exerted its influence on children's attainment was through the promotion of attitudes, values, and aspirations conducive to labor market success [START_REF] Hauser | Socioeconomic Background and Educational Performance[END_REF][START_REF] Sewell | Social Class, Parental Encouragement and Educational Aspirations[END_REF][START_REF] Duncan | Socioeconomic Background and Achievement[END_REF], though the benefits of parental income and wealth were certainly appreciated (Henretta and Cambell 1978;[START_REF] Rumberger | The Influence of Family Background on Education, Earnings and Wealth[END_REF]). However, it was only with the formal expansion of the parental resource array that the role played by financial and material assets in the transmission of advantage could be explicitly modeled [START_REF] Spilerman | Wealth and Stratification Processes[END_REF].

Second, before the inclusion of parental wealth, when the intergenerational effects were sought in value transmissions, it was appropriate to associate parental resources with a respondent's teenage years, the period when socialization processes have their peak impact on children's decisions in regard to schooling and occupational choice. Indeed, this is the age point at which parental background characteristics were measured in the early studies of socioeconomic achievement 1 . However, a consideration of parental financial and material assets, and transfers of the assets, requires a recognition that the transmissions can take place at multiple points along the life course and in varying amounts. This opens issues of parental motives, the timing of allocations, the sums transferred, and the intended purpose of the assistance--issues that do not arise when the parental resource array is limited to measures of educational attainment and occupational status.

2 Transfers of parental wealth can influence the life chances and wellbeing of offspring in several ways: the transmissions can be targeted to enhance permanent income (e.g., investments in schooling; assistance with opening a business), support living standards (e.g., aid with the purchase of a home or an auto), insulate offspring from the financial trauma of job loss or illness, or the transfers can be used to build up the net worth of children. Parental wealth effects have been examined with regard to all these outcomes (e.g., [START_REF] Boehm | Housing and Wealth Accumulation: Intergenerational Impacts[END_REF][START_REF] Torche | Parental Wealth Effects on Living Standards and Asset Holdings: Results from Chile[END_REF][START_REF] Mcgarry | Transfer Behavior in the Health and Retirement Study[END_REF]Lindh and Ohlsonn 1998), though it is probably the case that the greatest attention has been given to the investigation of parental transfer effects on the home acquisition decision.

Home ownership is recognized as a significant factor in the economic well being of households. For working and middle class families housing equity is often the item of greatest value in their asset portfolio (e.g., [START_REF] Orzechowski | Net Worth and Asset Ownership of Households: 1998 and 2000[END_REF] on the US; Hamnett, et. al. [1991, chap 3] on England ;[START_REF] Brandolini | Household Wealth in Italy in the 1990s[END_REF] on Italy; [START_REF] Arrondel | Consumption and Investment Motives in Housing Wealth Accumulation: A French Study[END_REF] on France). Moreover, homeownership has served as a crucial vehicle in the buildup of household wealth [START_REF] Belsky | Housing Wealth Effects: Housing's Impact on Wealth Accumulation, Wealth Distribution, and Consumer Spending[END_REF][START_REF] Boehm | Wealth Accumulation and Homeownership: Evidence for Low-Income Households[END_REF], a consequence of the secular rise in home values in western countries since World War II, accentuated by the leveraged nature of a home purchase.

Additionally, homeownership is treated favorably in the tax laws of many 1 OCG I, the survey used by [START_REF] Blau | The American Occupational Structure[END_REF] asked about parental characteristics when the respondent was age 16. This same age was also the reference point about parental status in the study by [START_REF] Featherman | Opportunity and Change[END_REF].

2

A consideration of financial transfers also opens up matters of "backward flows" of resources from children to parents, and the possible interaction between public transfer programs and private family transfers. See [START_REF] Attias-Donfut | Family Transfers and Cultural Transmissions Between Three Generations in France[END_REF] and [START_REF] Kohli | Private and Public Transfers Between Generations: Linking the Family and the State[END_REF] for discussions of these topics. countries; see, for example, [START_REF] Bernardi | Home Ownership and Social Inequality in Italy[END_REF] on Italy; Diamond and Lea (1992, chap. 3) on France. In the U.S., real estate taxes can be deducted from federal taxable income and there is an exclusion from taxes of $500,000 from the profit of a home sale. Thus, while tenancy choice may reflect a life style preference rather than an investment calculation, families that selected homeownership have typically seen their net worth grow over the years.

3 There are also externalities from home ownership that can enhance the life chances of children. Where parents own their residence, then, net of other background characteristics, the offspring have fewer behavioral problems [START_REF] Haurin | Impact of Homeownership on Child Outcomes[END_REF], are more likely to complete secondary education and undertake college study [START_REF] Aronson | A Note on the Benefits of Home Ownership[END_REF][START_REF] Boehm | Does Home Ownership by Parents Have an Economics Impact on Their Children?[END_REF], avoid public welfare in their adult years (Harkness and Newman 2003), abstain from having children while teenagers [START_REF] Green | Measuring the Benefits of Homeownership: Effects on Children[END_REF], and become homeowners themselves [START_REF] Boehm | Housing and Wealth Accumulation: Intergenerational Impacts[END_REF][START_REF] Kurz | Labor Market Position, Intergenerational Transfers and Home-ownership: A Longitudinal Analysis for West German Birth Cohorts[END_REF][START_REF] Pla | Home Ownership and Social Inequality in Spain[END_REF].

While there are methodological problems with several of these studies, especially the failure to distinguish homeownership effects from pure wealth effects, the findings are consistent with other documented consequences of homeownership: greater residential stability and an interest in protecting property values, such as by surpressing neighborhood crime and ensuring quality schools [START_REF] Lee | Neighborhood Context and Residential Mobility[END_REF][START_REF] Harkness | Homeownership for the Poor in Distressed Neighborhoods: Does this make Sense?[END_REF][START_REF] Rossi | The Social Benefits of Homeownership: Empirical Evidence from National Surveys[END_REF].

In light of these extensive effects of home ownership, the role played by parental resources in facilitating a home purchase has hardly been ignored by researchers. In particular, parental assistance has been found to reduce the waiting time from marriage to ownership--a finding that has been replicated in many western countries (e.g., Mulder and Wagner 1998 [West Germany and the Netherlands]; Kurz 2004 [West Germany]; Guiso and Jappelli 1999 [Italy]; Lewin-Epstein, et. al. 2004 [Israel};Mayer and Engelhardt 1996 3 As of this writing in mid-2011 the real estate crisis is in full bloom and housing prices are much depressed. Our discussion refers to the long time period from the end of World War II through early 2008. In the US, this period was characterized by a secular increase in home prices with only brief reversals in the trend. Whether or not home ownership will retain its status as a dependable vehicle for equity buildup in the population remains to be seen.

[United States], thought not in some Latin American states 4 [START_REF] Torche | Parental Wealth Effects on Living Standards and Asset Holdings: Results from Chile[END_REF]. Because the financial sums transferred to assist with a home purchase can be considerable, and because early entrance into homeownership provides a longer duration in which to accrue the economic returns from this tenancy status, several authors (e.g. [START_REF] Kurz | Labor Market Position, Intergenerational Transfers and Home-ownership: A Longitudinal Analysis for West German Birth Cohorts[END_REF][START_REF] Boehm | Housing and Wealth Accumulation: Intergenerational Impacts[END_REF] have come to view parental assistance with a home purchase as a critical vehicle in the transmission of parental wealth across the generational divide.

A limitation of this literature stems from the paucity of attention given to the alternative pathways by which parents can assist their children with the acquisition of a home. The availability of parental funds can affect a young couple's calculations in several ways: the transfers can be used to shorten the waiting time to homeownership, permit a larger downpayment, or enable a residence of greater value to be acquired. Only the first of these options has been the focus of sustained research--the literature noted in the prior paragraph--though some work has been done on the other pathways (e.g., [START_REF] Englehard | Intergenerational Transfers, Borrowing Constraints, and Saving Behavior: Evidence from the Housing Market[END_REF]Gusio and Jappelli 1999).

Yet all three must be considered as they represent different routes by which parents contribute to the acquisition of a home and thereby to living standards; indeed, a focus solely on the waiting time will underestimate the magnitude of the full parental effect. In Chile, for example, parental resources have but a modest impact on the waiting time to ownership but strongly influence the value of an acquired residence [START_REF] Torche | Parental Wealth Effects on Living Standards and Asset Holdings: Results from Chile[END_REF]. Similarly, by facilitating a larger downpayment a parental transfer can reduce monthly mortgage costs, thereby permitting a higher level of nonhousing consumption to be maintained (Engelhardt and Mayer 1998). In short, to understand the details of how parental assistance influences the home acquisition process, it is necessary to consider the full panoply of uses of the parental funds, rather than restricting attention to a single component.

In the present study we use a unique data set from France, the Actifs Financiers Survey (Survey of Financial Assets) conducted by INSEE in 1991-92, 4 In Chile, and elsewhere in Latin America, there is much squatter tenancy, often on government owned land. In population surveys, respondents with such housing usually respond that they are homeowners though they lack legal title. See de [START_REF] Soto | The Mystery of Capital New York: Basic Books[END_REF] on untitled assets in developing countries.

which permits us to investigate parental effects on each component of the home acquisition process. Moreover, we can examine both parental resource effects and transfer effects. While parental resources capture the "potential" for making transfers, the realized transfers do not necessarily encapsulate the full impact of parental resources. In particular, if parents have resources, children who receive little assistance may nonetheless believe that they can overspend from their savings when purchasing a home in the knowledge that, if required, parental aid will be forthcoming. Finally, with these data we can correct for the possible endogeneity of the parental transfers and model the joint determination of the downpayment proportion and the value of the home.

II. INSTITUTIONAL ARRANGEMENTS AND HOME OWNERSHIP IN FRANCE

The tenancy pattern and home ownership rate in a country are deeply influenced by governmental policies and by the generosity of financial supports available to builders, homeowners, and renters. Attempts to make sense of the diversity of housing policies in Europe have given rise to a number of typologies of housing systems, some based on Esping-Andersen's (1990) seminal classification of welfare states (e.g. [START_REF] Barlow | Success and Failure in Housing Provision[END_REF]) while others derive from the structure of the housing market or from the housing statistics categories used by the individual countries. [START_REF] Kemeny | Comparative Housing and Welfare: Theorising the Relationship[END_REF] emphasizes the state's role in the organization of the rental market as a factor underlying the prevalence of the different tenancy types--co-residence with parents, market rental, public housing, and home ownership. Central to his scheme is the distinction between dual and unitary rental markets. In countries with a dual market system the state assumes responsibility for the provision of rental housing for poor families, separating this segment of the rental market from the private, profit-seeking sector. The result is a system with two distinct rental markets, one subsidized, the other demanding market prices. In contrast, in countries with a unitary rental market, access to public housing is not limited to poor families; rather, the profit-seeking sector must compete for tenants with the public sector. As a result, rents in the profit-seeking market are kept low, and the distinction between the two sectors is minimized.

Kemeny argues that the type of rental market system prevalent in a country bears strong implications for the home ownership rate. In the dualist system (e.g., England, U.S.), where all but the very poor confront high rents, the possibility of home ownership is an attractive alternative to renting.

But in a unitary system (e.g., Germany, Denmark), where private sector rents are kept low by competition from public housing, rental tenancy is able to compete with home ownership. Data presented by Kemeny (2001, p. 67) A different sort of literature seeks to explain tenancy patterns and the home ownership rate by focusing on aspects of the credit market, often in a regression analysis framework (e.g., [START_REF] Chiuri | Financial Market Imperfections and Home Ownership: A Comparative Study[END_REF]; [START_REF] Scanlon | International Trends in Housing Tenure and Mortgage Finance[END_REF]). Here, the main attention is given to issues in the judicial enforcement of contracts, the socialization of business risk, and the structure of mortgage instruments. [START_REF] Chiuri | Financial Market Imperfections and Home Ownership: A Comparative Study[END_REF] rate 14 OECD countries on several of these measures; from their Table 2 it is evident that

France is in the bottom third of countries in regard to efficiency of the judicial system and protections afforded to the mortgage lender ("rule of law"), and in the top third in terms of legal expenses of the lender in foreclosure proceedings. [START_REF] Scanlon | International Trends in Housing Tenure and Mortgage Finance[END_REF] examine the features of mortgage finance markets. In a comparison of 14 European countries (year 2000 data or thereabouts) France ranks second lowest in average loan-to-home value ratio (Scanlon and Whitehead 2004, Table 10). Also, the mortgage repayment period tends to be shorter in France than in most European countries, and the percentage of home owners holding a mortgage is the second lowest of the ten countries for which data were available [START_REF] Scanlon | International Trends in Housing Tenure and Mortgage Finance[END_REF], Table 15). Thus, in France, home purchasers typically must make larger down payments and repay the loan in a short period; as a result, fewer mortgages are held.

The summary picture from these comments is one of little state support for home ownership in France, either in the form of direct financial assistance to home buyers or in terms of risk mitigation for mortgage lenders.

There is a robust program for the provision of social housing, but these efforts have focused on rental units (e.g. the programs of Habitat à Loyers Modérés). Even the limited funds for supporting home ownership have largely been allotted for the purchase of newly built structures, rather than more broadly available for the acquisition of existing homes (Miron 2001, p. 62). 5

Not unexpectedly, given these considerations, the home ownership rate in France (56%) is much below the average of the European countries (67%)-- Scanlon and Whitehead (2004, Table 2). More relevant for our purposes, the ownership rate by "young entrant households" is 17% in France, in comparison with an average of 48% for the other European countries (Scanlon and Whitehead [2004, Table 5]). While the definition of young entrant household is a bit 5 There is a savings plan in France, intended to encourage home ownership, which permits the savings accumulations to be converted into low rate mortgages (Epargne-Logement). However, the mortgage loans in this program are not large and the minimum accumulation period is five years (18 months in a second type of account), precluding rapid entry into home ownership status.

Complicating matters for a potential buyer, mortgages in France tend to be closely tied to the credit-worthiness of the borrower, with the loan amount capped so that annual payments do not exceed a third of household income (Miron [2001, p. 64]; Diamond and Lea [1992, pp. 55, 73;Table 3.3]).

complex, 6 Chiuri and Jappelli (2000, Table 6) report analogous figures for household heads aged 25-29: an ownership rate of 20.4% in France which is the second lowest among the 12 countries they surveyed.

7

In light of these matters we expect parental resources to play a considerable role in France in the home acquisition process. Young couples have little in the way of savings and, in the context of an inefficient mortgage market and few governmental supports for home ownership, the availability of parental aid can be a crucial factor. As noted, parental transfers can be used in several ways to assist with a home purchase; they can permit a reduction in the waiting time, facilitate the acquisition of a more costly home, or enable a higher downpayment and thereby reduce the carrying costs of the mortgage. To obtain a comprehensive picture of the impact of parental assistance on the home ownership decision and on living standards, we consider parental effects on all three outcomes.

III. THE HOUSEHOLD SURVEY AND ANALYTIC APPROACH

The 1991-92 INSEE Survey of Financial Assets consists of a random sample of 9530 French households. The survey covers asset holdings of the respondent and transfer receipts from parents, as well as the usual biographical information about the respondent, spouse, and parents. The strengths of the survey, for our purposes, are that the background questions refer to both sets of parents of the couple and are sufficiently detailed to permit a crude wealth measure to be constructed for each parental household; moreover, the wealth questions pertain to when respondent and spouse were teenagers or young adults, permitting the parental resources to be associated with the startup expenses of a young couple. The precise questions ask about parental economic circumstance--father's occupation, parental asset holdings, financial difficulties--"when the respondent (spouse) was young." A disadvantage of the survey is that it is some 18 years old and does not capture the experiences of 6 Young entrant household is defined in Scanlon and Whitehead (2004, p. 9) as a two-adult household without children, with the household head "around 25 years of age" and of average income for the age group.

7 [START_REF] Meron | Home Ownership and Social Inequality in France[END_REF] provide a comprehensive account of the issues facing young couples in France with respect to the transition to home ownership status, along with annual data on the rate of entry into home ownership.

very recent entrants into the housing market. But this is offset by the unique coverage of the data--detailed information on the downpayment proportion, value of the home, and living standard of the couple, as well as details on parental wealth and the timing of transfers in relation to the purchase decision.

The survey has some limitations. It did not inquire about parental education, though information was gathered about father's occupation and this is a more proximate determinant of parental income. More consequential, the survey asks about the current residence of the respondent, not the first owned home. This is a serious matter since the literature relating home ownership to parental resources generally focuses on the first owned residence.

However, in countries where entrance into home ownership is much delayed and, consequently, where fewer years remain in the life course for residence changes (e.g., Italy), there is a tradition of identifying a currently owned residence with the first acquired home (e.g., [START_REF] Guiso | Private transfers, borrowing constraints and the timing of homeownership[END_REF][START_REF] Bernardi | Home Ownership and Social Inequality in Italy[END_REF]). While such an identification is plausible for

France in light of the aforementioned low ownership rate by "young entrants," our analysis does not rely on this assumption. Rather, in the main, we examine parental resource and transfer effects on features of the currently owned residence. Our imagery of the transfer effects is one of the accumulation of advantage, with the expectation that the financial benefits of parental assistance with a prior residence, in the form of increased home equity, would likely be reflected in the value of the current residence.

Several selection decisions were made. First, the sample was restricted to married or cohabitating couples without a prior marriage or children from an earlier union, and in which the respondent was less than 65 years old at the time of the survey. The limitation of no prior marriage is intended to reduce the complexity of having some couples who have had more than two sets of parents from whom transfers might have been received. The exclusion of respondents with children from a prior union removes problems of financial obligations due to an earlier cohabitation, and the age restriction limits the sample to respondents who reached maturity post World War II. Second, since our intent is to examine features of the purchase decision, respondents who received their home as a gift or bequest are omitted. As a consequence of these decisions, the sample was reduced to 4,471 observations.

Our analysis is reported in two sections. In the first we investigate parental resource effects on the waiting time to home ownership as well as on the ownership rate and the value of the home. The intent of this section is to assess the total effects of parental resources on the ownership decision, which includes the impact of anticipated transfers as well as realized transfers. The modeling strategy involves a consideration of the effects of the resources of husband's and wife's parents, followed by the introduction of terms for the human capital, income, and savings of the respondent's family.

The logic of the strategy is that we first assess the total effects of parental resources on the dependent variables, then tease out the pathways by which the parental assets make their contribution--via direct monetary transfers versus investments in the education and earnings capacity of offspring.

In the second analytic section we restrict attention to homeowners and examine the effects of realized parental transfers on the several outcome variables: downpayment proportion, home value, and non-housing expenditures following a home purchase. In short, we seek here to understand the impact of transfers on the details of the home purchase decision as well as on subsequent living standards. Several methodological issues are taken into account. First, there is the potential endogeneity of transfers. Respondents who could not afford the downpayment might have requested help from parents.

In this case, receipt of a transfer would be correlated with the error term, violating the regression assumptions. A second issue concerns the joint determination of downpayment proportion and home value: if parents have available a fixed sum to transfer, from which the respondent must decide how much to allocate for the downpayment and how much for acquiring a more costly home, then the error terms in the two outcome variables will be correlated.

Both modelling issues are addressed in the formulations.

IV. PARENTAL RESOURCE EFFECTS

In this section we examine parental resource effects on the waiting time to home ownership and home value. The parental resources that are considered are father's occupational status (ISEI scores coded from two-digit occupational categories [START_REF] Ganzeboom | A Standard International Socio-Economic Index of Occupational Status[END_REF]) which is a proxy for permanent income, and parental wealth when the respondent "was young." The latter is an index created from the sum of three items: ownership of a home, other real estate, and a farm. Since working farms typically include a residence, respondents who reported that father was a farmer and owned both a farm and a home do not have farm ownership added to their sum.

8

Admittedly, the resulting measure is a crude index of parental wealth; as a result, the true wealth effect will probably be underestimated. The parental resource variables also contain a measure of the financial well-being of the parental family when the respondent (spouse) was young--a dichotomous term, coded one if there were serious financial problems. Additionally, to tap demands on the parental resources, we added a term for the number of siblings of the respondent (spouse).

Measures of the couple's own resources include several human capital variables--household income, husband's and wife's education--and terms for accumulated savings as indexed by husband's age at marriage and duration of the union. Age at marriage is a proxy for savings prior to the union; individuals who are older at marriage have had more years to accumulate wealth. Similarly, duration of the marriage taps accumulations over the course of the union. Separate terms are introduced because the savings rate may differ before and after marriage; also, the latter captures the joint accumulations of husband and wife. Finally, we include dummy terms for city size and year of marriage; the first adjusts for location differences in the availability of rental housing that are correlated with city size, the second for temporal changes in government housing policy and mortgage availability.

Descriptive statistics for these variables are reported in Table A-1.

Homeownership. Because of the limited resources of young couples and an inefficient mortgage market in France, the financial savings of parents are likely to play a considerable role in facilitating the acquisition of a home.

As motivation for this investigation we present in Figure 1 survival curves of the waiting time from marriage to ownership of the current residence, with non-owners at the survey date treated as censored observations. The curves refer to different parental wealth levels; the top one shows the trajectory when neither set of parents had high wealth, the middle curve indicates the time path when one parental set, but not both, had high wealth, and the low curve pertains to couples in which both parental sets had high wealth.

9

The effects of the extreme categories are consistent: at all time points the couples with low parental wealth are less likely to have made the transition to ownership status.

The path for respondents with one set of high wealth parents is intermediate for much of the time course though it overlaps with the high wealth curve at 18 years. These data, however, refer to the waiting time to a currently owned residence, and the likelihood that this residence is not the first owned home increases with marriage duration. Consequently, as a measure of the parental wealth effect on the waiting time to first owned home, the curves are most reliable for the early decades of marriage. For this period there is an evident tendency for the waiting time to be lessened when parental wealth is available, more so when there is wealth in the hands of both parental sets.

________________________ While these findings are consistent with other studies of the impact of parental resources on the waiting time to ownership of a first home (e.g., [START_REF] Kurz | Labor Market Position, Intergenerational Transfers and Home-ownership: A Longitudinal Analysis for West German Birth Cohorts[END_REF][START_REF] Mulder | First-Time Home-Ownership of Couples: The Effect of Intergenerational Transmission[END_REF], we hesitate to follow [START_REF] Guiso | Private transfers, borrowing constraints and the timing of homeownership[END_REF] or [START_REF] Bernardi | Home Ownership and Social Inequality in Italy[END_REF] in associating a currently owned home with the first owned residence. Therefore, instead of further examination of the waiting time, we turn to a Probit model with the dichotomous variable, ownership of the current residence versus rental tenancy; this formulation does not require an identification of a currently owned residence with the first owned home. However, our argument about parental effects does assume that if the respondent owned a prior residence then the equity in that home, including the contribution from parental assistance, has been transferred to the current residence and not withdrawn from the housing market. In short, we presume that a respondent who owned previously has not moved into rental housing or traded down to a less expensive home; the latter process is important to our subsequent analysis of home value.

How reasonable are these assumptions? Trading down by homeowners does occur, but it mainly takes place among the elderly who are retired or contemplating retirement [START_REF] Megbolugbe | Oh, Yes, the Elderliy will Reduce Housing Equity under the Right Circumstances[END_REF][START_REF] Myers | Cohort Estimation of Homeownership Attainment among Native-Born and Immigrant Populations[END_REF]. In regard to moves from ownership to rental housing, an examination of cohort data suggests that the ownership rate increases with age until the early or mid-60's [START_REF] Banks | Pensions and Live-Cycle Savings Profiles in the UK[END_REF] for the UK; [START_REF] Alessie | Savings and Pensions in the Netherlands[END_REF] for the Netherlands; [START_REF] Borsch-Supan | Household Saving in Germany[END_REF] for Germany; the last referencing real estate wealth). Thus, transitions out of home ownership, along with trading down, appear to be concentrated in the later stages of the life cycle.

We lack comparable data for France; however, there is no reason to expect a different pattern in that country. Further, we do have comparative country statistics on equity withdrawals from the housing market, a category that includes the renegotiation of existing mortgages and the contracting of second mortgages, as well as the preceding strategies for extracting housing market equity. These figures show that equity withdrawals in France (and Germany) are the lowest of the 10 European and North American countries that were surveyed [START_REF] Catte | Housing Markets, Wealth and the Business Cycle[END_REF], Figure 5b). Consequently, we consider the assumptions of a low rate of transition out of ownership status and a tendency by homeowners to transfer equity from a prior residence to the current one to be reasonable. It is these assumptions that provide the rationale for examining ownership status and home value of the current residence in terms of differences in parental resources.

The results from the Probit model, reported in column (2), are consistent with our contentions. The regressors in this equation are the same ones that appeared in the Cox model and the qualitative findings are quite similar: strong effects for the parental wealth terms but little evidence that other parental resources, aside from sibship size, are consequential as determinants of home ownership. We take the similarity in findings between the two models as evidence that for the great majority of respondents either the currently owned home is the first owned residence or that ownership tenure, once achieved, tends to be maintained, with the equity in an earlier residence transferred to the current one.

What, then, can be said about the pathways by which parental wealth contributes to ownership status? There are two routes of interest. First, parental resources can impact the savings accumulations of offspring through parental investments in schooling and earnings, with the cumulated household savings then applied to a home purchase. Second, direct transfers of parental wealth could be made available to children, to assist with the acquisition of a home.

These possibilities are explored in model (3), in which variables have been added for education of the respondent and spouse, household income, age of husband at marriage, marriage duration, and number in the household. The age and duration terms are proxies for household savings--older respondents would have had a greater opportunity to accumulate resources before marriage;

in the same way, the duration variable indexes savings since marriage.

Similarly, number in the household taps a possible desire by growing families to settle into home ownership and stabilize their housing arrangements. The empirical results provide strong evidence for the respondent's resource effects. The income variable and the proxies for household savings are all significant and have the expected signs. The term for marriage duration squared is negative, suggesting diminishing returns with savings growth;

presumably, after a certain level of wealth accumulation the decision to become a homeowner is a lifestyle choice, not constrained by insufficient savings. The turning point, however, occurs at some 41 years of marriage, so the savings effect is positive over pretty much the full marital course.

Of particular relevance to understanding the transmission pathways concern the effects of the parental wealth terms. Even in the presence of the several measures of the respondent's savings and income, the wealth terms remain highly significant, reduced only modestly in size--husband's parental wealth remains at 87% of its prior value; wife's parental wealth is 76% of its previous magnitude. Thus, while the resources of the respondent are hardly irrelevant to ownership prospects, the residual wealth effects suggest that direct financial assistance to children, rather than parental investments in human capital, is the dominant route by which parental wealth conditions housing tenure status.

Home value. If parental wealth influences the likelihood of ownership, what impact does it have on home value? This issue is addressed in Table 2 where the dependent variable refers to the value of the current home, as estimated by the respondent at the time of the survey. Because home value is a limited dependent variable--continuous for homeowners but zero for renters--we use a Tobit regression model. Also, to reduce skewness from a few large home values, we log this variable. Column (1) reports the total contributions of the parental resource terms, with controls present only for city size and marriage year. The results show that both father's occupational status and parental wealth have sizable impacts and that sibship size is negative, though significant only for wife's parental family. Not surprisingly, these effects indicate that home value is greater when the respondent and spouse come from families that have more wealth and income, the latter proxied by occupational status.

________________________ Table 2 about here

________________________

In column (2) we have added terms for respondent's economic status.

These variables have effects similar to their contributions in the determination of homeownership: home value is greater when respondent and wife have higher household income and savings, the latter proxied by marriage duration and by age of husband at marriage. In the presence of these terms only the parental wealth variables remain significant. Again, the wealth terms are not much reduced--husband's father's wealth is 72% of its prior value, wife's father's wealth is 73% of its former magnitude. These findings suggest that while parental occupational status (and earnings, by implication) affect home value through their impact on the incomes of offspring, parental wealth conditions home ownership through a different path, by facilitating direct financial transfers across the generations.

V. PARENTAL TRANSFER EFFECTS

Having established that parental wealth has strong effects on the ownership rate of offspring and on home value, and that direct transfers are the principal route by which parental wealth exerts its impact, we turn to the ways by which the receipt of transfers, per se, influences the details of the home purchase decision. Specifically, we examine the consequences of parental transfers for the downpayment proportion, home value, and non-housing consumption, the latter viewed as a measure of living standards.

Whereas the previous analysis relied on the residual effects of parental wealth net of investments in the earning capacity of offspring to infer the role of parental transfers in the home acquisition process, we now examine the transfer effects directly. The transfers we assess include intervivos gifts and bequests, whether or not designated by parents as assistance intended for the purchase of a home.

The 1992 Actifs Financiers Survey contains information on both formal gifts signed before a notary and informal ones which are usually of smaller amounts. The gifts could have been money, land, or other valuables. We have detailed information for up to two gifts received by a respondent, with similar information for the spouse. For each gift we know the date and amount; also, when the transfer consisted of real property we have its value as estimated by the respondent. Two variables were created from this information--a dummy term for gift receipt, which takes the value one if assistance was received by respondent or spouse, and a term for gift value which is the sum of the individual gift amounts. Analogous information was collected for bequests, with comparable variables constructed. Since some transfers were received several years before a home purchase, all transfer amounts are capitalized at a 2% per year rate of return from the receipt date to the time of the purchase. Descriptive statistics for the variables used in this section of the paper are reported in Table A-2.

A) Downpayment Proportion

One use of the transfer monies would be to increase the downpayment. A large downpayment means a lower monthly carrying cost; moreover, the mortgage interest rate itself might be reduced since the lender would be assuming less risk. In the INSEE survey, homeowners were asked about the downpayment proportion of the "most important home" they have purchased. In most cases, for reasons we have noted, the current dwelling is the only home that has been owned. However, in cases where a prior home was owned, the most significant residence might refer to that home.

We restrict attention in this analysis to the subsample of respondents who have ever purchased a home. An alternate approach would have been to

retain renters in the sample and use a Heckman-type selection model (Kennedy 2003, p. 284), but we did not have a variable in the INSEE data set that could convincingly be used to identify the selection equation, namely a variable that affects the decision to acquire a home but does not have an impact on the downpayment proportion.

Figure 2 shows the distribution of the downpayment for several categories of gift/bequest amounts received before the home purchase. The entries make clear the close association between the downpayment proportion and the monetary value of a gift or bequest. At the low end of the distribution--downpayment below 10%--households that did not receive a transfer predominate, and there is a clear downward progression in the representation rate of households as the transfer amount is increased. At the upper end--downpayment of more than 50%--the findings are reversed: here there is a concentration of households that have received the largest transfers and an almost uniform increase in the representation rate with transfer amount.

_____________________________ Figure 2 about here _____________________________

We next use a multivariate formulation to explore the impact of parental transfers on the downpayment proportion. Since the dependent variable is ordinal with six categories (downpayment= 0%, less than 10%, 10-30%, 31-50%, 51-99%, 100%), we estimate an ordered Probit model,

Y i * = β'X i + ε i (1) Y i = k if µ k-1 < Y i * • µ k for k = 1...6, (2)
where Y i * is a latent variable, ε i follows a normal distribution, X i is a vector of covariates, and the cut points, µ 1 through µ k-1 , are estimated from the data.

The observations in this analysis are the 3,271 respondents who purchased a home since marriage.

In Column [START_REF]Transition to Home Ownership[END_REF] of Table 3 we report the effects of a gift or bequest receipt. Since the decision to acquire a residence might have been made in anticipation of a transfer, we have added dummy terms for gifts or bequests received subsequent to the purchase, as well as receipts prior to the purchase. We also include proxies for the savings and income of the

_____________________________ Table 3 about here _____________________________

The terms for respondent's resources are all significant in the regression. Husband's occupational status, education, and the proxies for household savings predict to a higher downpayment, while household size is inversely related to the downpayment proportion. Clearly, the ongoing costs of raising a large family mean fewer resources available for reducing the downpayment. In regard to the parental transfer terms, the receipt of gifts or bequests before a purchase increases the downpayment proportion, while transfers after the purchase date have no apparent effect. Thus, we fail to find evidence that, in making a decision about the downpayment, couples take into account the likelihood of a transfer receipt in the years subsequent to the home purchase.

A similar analysis was carried out with measures of the value of a gift or bequest, and the results, reported in column (2) reinforce the preceding account. The larger the gift or bequest received before a home purchase, the greater the downpayment. Thus, from these analyses of incidence and amount, we conclude that one mechanism by which parental transfers advantage offspring in the home acquisition process is to permit a higher downpayment, offsetting the monthly carrying costs of a mortgage. There is no evidence, however, that households take into account in their purchase planning the receipt of future transfers.

Endogeneity issues. There is a potential bias in the preceding account in that the parental transfers may be endogenous. This would occur, for example, if couples that cannot afford the downpayment turn to their parents for assistance. Conversely, it could be the case that parents are more likely to transfer funds to children who have chosen to make a large downpayment. In either case, receipt of a transfer would be correlated with the error term, violating the regression assumptions.

To address this issue we instrument the transfer variables on parental wealth. To secure identification we presume--not unreasonably--that transfers are the principal, if not the sole, channel by which parental wealth affects the downpayment proportion. A Probit model is used in the first stage regression when transfer incidence is addressed; a Tobit model is employed when transfer value is considered.

The second stage results are reported in Table 4. The models here are slightly different from those in Table 3 as it was necessary to combine gift and bequest receipts before a home purchase and delete the (non-significant) terms for transfer receipt after a purchase in order to have only one endogenous regressor in an equation. Otherwise, it would not have been possible to identify the multiple transfer terms. To permit a comparison we present estimates from both the modified exogenous formulation of the transfer terms in columns ( 1) and ( 3) and the instrumented formulation in columns ( 2) and ( 4). In each case the instrumented values are higher, suggesting that the estimates from the exogenous model are downwardly biased and that the "true" contributions of parental transfers are somewhat greater.

_____________________________ Table 4 about here _____________________________ B) Home Value

In addition to permitting a larger downpayment, parental transfers could be used to acquire a more expensive home. This possibility is explored in Table 5 using log(home value) as the dependent variable. We restrict the sample to homeowners because our key explanatory variables (transfer receipt before a home purchase; transfer receipt after a home purchase) are not defined for renters, and we use OLS regression. Further, because some of the models in this section require downpayment and home value information for the same residence, we take as observations only respondents who were home owners at the time of the survey and for whom we have matching downpayment data.

With these restrictions the resulting sample contains 2,452 observations.

_____________________________ Table 5 about here _____________________________

The explanatory variables are the ones described in reference to Table 3, except that household income is included as a regressor since both it and home value refer to the survey year.

11

For the same reason, the marriage duration and age variables are computed at the survey year, not the home purchase year. Thus, we seek to examine the impact of parental transfers on current home value, net of the measures of respondent's household resources.

Several of the measures of respondent's resources are significant in column (1) which examines the impact of transfer incidence, and in column (2) which probes the contribution of transfer amount. Clearly, families that have higher incomes and greater savings (as indexed by marriage duration) tend to purchase more costly dwellings. Marriage, in contrast with cohabitation, is also associated with greater home value. Household size, however, has no effect. Whereas large families make a smaller downpayment (Table 3), suggesting financial constraints, there is no evidence of a similar impact on home value. Since the size of a residence is correlated with its value, large families might prefer to not reduce this home feature in their search for an appropriate dwelling.

The transfer terms reported in Table 5 indicate that, net of a respondent's own resources, households that have received gifts (though not bequests) before the purchase tend to own more costly homes. This is the case 11 Home value reflects improvements to the residence made through the survey year and the improvements, at least partially, would derive from household income. For this reason we present results with household income as reported in the survey year. The findings from using our alternative income proxy-husband's occupational status--are very similar to the reported figures. with respect to both transfer incidence and transfer amount. Again, consistent with the findings in Table 3 for downpayment proportion, the receipt of a transfer after the home purchase has no impact on home value.

Clearly, the evidence for anticipation of a transfer affecting the expenditure decision is lacking.

Joint estimation model. Our findings to this point provide strong evidence that parental transfers influence both the downpayment proportion and the value of the acquired residence. But one issue of model specification remains to be explored. It may be the case that, reflecting their resources, parents make available a fixed sum for transfer and that the respondent then decides how much to apply to the downpayment and how much to the acquisition of a larger or an upscale residence. This imagery suggests that the two outcomes are jointly determined, in which case they should be modeled with a formulation that takes this fact into account.

The specific problem posed by jointly determined dependent variables is one of correlated errors. Separate estimation of each equation ignores the correlation and is inefficient. We address this issue with a joint model in which the downpayment proportion is estimated with an ordered Probit and home value with an OLS regression.

12 Joint estimation of the equations was carried out using a maximum likelihood algorithm with numerical integration of the residuals from the statistical package aML [START_REF] Lillard | aML Multilevel Multiprocess Statistical Software: User's Guide and Reference Manual[END_REF]. In order to achieve convergence the transfer variable combines gift and bequest amounts received before the home purchase in place of a separate consideration of the two transfer components.

Our findings are reported in Table 6. In the first two columns we present results for the downpayment proportion and for home value in which the equations were estimated separately. These are our baseline calculations from the condensed specification, intended for comparison with the new formulation.

Column (3) reports the corresponding estimates from the joint model. While the results are not strikingly different, the estimates of the transfer terms tend to be higher; in both the downpayment equation and in the home value equation the increase is some 14%. Moreover, the correlation between the residuals (0.616) is significant, suggesting that unobserved factors have a similar influence on both outcomes. For example, parents who are greatly concerned about the financial welfare of their children might provide greater assistance for both a larger downpayment and a more expensive home.

_____________________________ Table 6 about here _____________________________

Finally, what can be said about the quantitative effects of the parental transfers? By how much is the downpayment increased and by how much is the value of the home raised? Our data do not permit these issues to be addressed in terms of purchase price, only with respect to the value of the home at the survey date. Also, since the downpayment proportion is reported in six categories (see Figure 2), it must be transformed into a continuous distribution in order to estimate the change in proportion. We did so using an approach that is similar to the method of simulated residuals described in Gourieroux et. al. (1987).

The downpayment category midpoints provide a first approximation to a continuous distribution. The resulting measure, however, has its mass concentrated at six points and is not suitable as a dependent variable in a regression. Therefore, for each respondent we drew a random value from the uniform distribution,

f(x) = 1/(b -a), for a<x<b, (3)
where [a,b] corresponds to the respondent's downpayment interval. This distribution has a mean equal to (a+b)/2, which is, in fact, the midpoint of the category. The downpayment value assigned to a respondent is then the random draw that lies within his or her interval.

With this assignment, model (3) of Table 6 was reestimated, leading to the following assessment: For each 10,000 francs received from parents before the purchase, 13 home value (in 1992) was greater by 4,327 francs and the 13 To put this sum into perspective, the average gift before purchase was some 81,000 francs and the average bequest was 86,000 francs (see Table A-2). To translate these amounts into dollars, during the period 1970-1990 the franc downpayment was increased by 0.72 percentage points. In terms of average home value in 1992, the latter amounts to an extra 1,293 francs in home equity.

Admittedly, these are very rough estimates but they provide some sense of the contribution of a parental transfer to home equity.

C) Non-housing consumption

The parental transmissions that are intended to assist with the purchase of a home can have externalities that spill over to other aspects of living standards.

Whether a transfer is used to increase the downpayment proportion or to offset the withdrawal from household savings in order to finance the purchase, there will be a lessening of the draw from a respondent's own resources to meet the ongoing mortgage costs and other expenses associated with home maintenance. The INSEE survey does not permit us to go into detail on these consequences of the parental transfers, but there is one item that provides a summary measure of the impact of the transfers on living standards.

The survey asks whether a respondent's household has reduced its nonhousing consumption expenditures as a result of the home purchase, and we have tabulated the responses in terms of the gift/bequest amount received before the home purchase. The results, reported in Figure 3, provide evidence for the spillover of the parental transfers into other living standard domains.

In particular, the response, "yes, we have reduced non-housing consumption"

shows a consistent (though modest) decline with generosity of the transfer, and the response "no, we did not reduce consumption" shows an evident increase with transfer amount. Indeed, some 49% of respondents who received a large gift or bequest before the purchase reported no reduction in consumption, in contrast with 35% who received no transfer. In short, there is clear evidence of a diffuse effect of the transfers on living standards, extending beyond their direct contribution to the home purchase decision.

_____________________________

Figure 3 about here _____________________________ varied from 4/dollar to 10/dollar. Thus, at a value of 6 francs/dollar, a 10,000 franc transfer amounted to $1,667.

VI. CONCLUSIONS

While a number of studies have documented the impact of parental resources on home ownership, along with the effects of parental transfers on aspects of the ownership decision, the contribution of the present undertaking has been to investigate the linkages among these several factors. Specifically, using a unique data set from France, we have examined how parental resources, especially the wealth component, and parental transfers influence the details of the home acquisition process--the likelihood of ownership, the downpayment proportion, and home value--as well as the contribution of the parental assistance to a broad measure of living standards.

The results provide a consistent picture of the importance of parental wealth for the several outcome variables. Our index of parental wealth makes a significant contribution to the homeownership rate and to home value, effects that remain large even in the presence of controls for respondent's earnings and accumulated savings. This suggests that the mechanism through which parental wealth operates is one of direct transfers, rather than investments in the human capital of children. An examination of the details of the transfer process reveals that the parental assistance is used to both increase the downpayment proportion and raise the value of the acquired residence. Moreover, these effects are robust to modifications in the specification of the transfer process. Yet, while this paper is nominally about the operation of the housing market, the deeper issues that motivated the study concern the role of parental wealth and financial transfers in the transmission of advantage across generations and in the replication of inequality. We have focused on the housing market because for the majority of families in the US, as well as in France, home ownership is the asset of greatest value in their wealth portfolio. Further, the assistance provided by parents for a home purchase tends to involve sums that are considerable and thereby constitutes a major avenue in the transmission of material resources across generations. This is true for the US [START_REF] Engelhardt | Gifts for Home Purchase and Housing Market Behavior[END_REF]1998;[START_REF] Boehm | Housing and Wealth Accumulation: Intergenerational Impacts[END_REF] as well as for France.

Parental wealth and intervivos transfers are understudied topics in stratification research, though see the recent important contributions by [START_REF] Conley | Being Black, Living in the Red: Race, Wealth, and Social Policy in America[END_REF]; [START_REF] Keister | Wealth in America: Trends in Wealth Inequality[END_REF][START_REF] Keister | Getting Rich[END_REF], [START_REF] Wolff | International Perspectives on Household Wealth[END_REF][START_REF] Davies | Personal Wealth from a Global Perspective[END_REF]. This oversight requires remedy because household wealth is a major item in the parental resource base, and because it is used by parents expediently to advantage the attainments and living standards of their offspring. Also, since parental wealth is positively correlated with parental education and occupational status--the parental resources commonly studied--omission of the wealth variable (when it has a positive impact on an outcome variable) means that the effects of the remaining parental terms will be biased upwards.

With respect to the imagery of the transmission process, the absence of a measure of parental wealth effectively removes "agency" from the parental domain--the use of transfers by parents to achieve particular goals, either for themselves or for the child. Without a consideration of parental wealth and financial transfers, we cannot address parental decision making concerning when to transmit, how much to transfer, for what purposes and to which child, a motif that is critical to understanding the ways that parents contribute to the life chances and well-being of their offspring.

With the accelerating privatization of essential social services in recent decades, household wealth has become a critical resource, as families increasingly must self-insure against the risk of misfortune. This trend has amplified the importance of intergenerational financial linkages, as well.

Young couples have a great many material needs associated with the start of a new family, while their incomes, relative to median household income, have been declining over the past 30 years (Mishel, et. al. 2009, pp. 55-56); this makes for a precarious financial situation and a heightened dependence on parental resources and parental assistance.

As a final matter, writing in mid-2011, one can hardly ignore the recent collapse in home prices. How might this economic downturn impact the role of homeownership as a vehicle in the buildup of household wealth through the accumulation of home equity? In the US the downturn in home prices was abrupt and substantial--between 2006 and 2009 the Case-Schiller 20 city composite index of home prices fell by 30% [START_REF] Marketwatch | Peak Recoil[END_REF]). However, this decline has brought prices back only to 2003 levels, and families that purchased as recently as the year 2000 are still ahead, on average, by some 28%, as well as having enjoyed the tax benefits associated with homeownership.

While buyers of homes in very recent years have been severely harmed by the price decline--and this has disproportionately impacted young couples--the acquisition of a residence is a long term investment and, going forward, it is not clear that this will fail to be a sound investment. Indeed, in the immediate future, following the steep price decline, a home purchase might be a wise move by a young couple. Yet, what is fairly certain to ensue in the wake of the steep price decline is that mortgage lenders will be more circumspect about the credit worthiness of new home buyers and will require a larger downpayment from them to reduce the risk of default. This, in turn, will mean an even greater reliance on parental assistance in order to purchase a residence. 1 Absolute values of t-statistics are in parentheses. The sample is restricted to respondents who were less than age 65 at the time of the survey. Parental terms refer to period when respondent (spouse) "was young".

2 Also included in the analysis are terms for city size and year of marriage. Parental terms refer to period when respondent (spouse) "was young".

2 Also included in the analysis are terms for city size and year of marriage.

3 Occupational status coded by ISEI scores, divided by 100 [START_REF] Ganzeboom | A Standard International Socio-Economic Index of Occupational Status[END_REF]). Also included in the analysis are terms for city size and year of home purchase. Occupational status coded by ISEI scores [START_REF] Ganzeboom | A Standard International Socio-Economic Index of Occupational Status[END_REF].

Variables Equation ( 1) is an Ordered Probit model for the down payment proportion with 6 categories. Equation ( 2) is an OLS regression for the housing value (in log), and (3) is a joint estimation by maximum likelihood of the Ordered Probit and OLS equations. The equations for downpayment proportion also include dummies for city size and year of home purchase; the equations for home value include dummies for city size and year of marriage. Absolute values of t-statistics are in parentheses.

Figure 1

 1 Figure 1 about here ________________________ Parental wealth is correlated with other parental characteristics, especially income and family size, which can also affect the availability of resources for transfer and thereby influence the waiting time. For this reason we report in column (1) ofTable 1 a Cox model of the hazard to

  household; thus, the parental transfer terms represent direct effects, net of a respondent's own resources. 10 Husband's age, marriage duration in the purchase year, and number of persons in the dwelling serve as indicators of household savings; the last is a measure of demands upon the respondent's resources. Household income, in this analysis, is proxied by education and occupational status. Although income data are available in the INSEE survey they pertain to the survey year, while the purchase might have taken place decades earlier. For this reason, education and occupational status-relatively stable measures of permanent income--are utilized as indicators of household income at the time of the purchase.

1 .

 1 Curves depict survival in the state of non-ownership. N(no parents) = 2,801; N(one parental set) = 1,595; N(two parental sets) = 576. "High wealth" =2,3 on the wealth index.

Figure

  Figure 2. The Effect of Transfer Amount Received Before Home Purchase on Down Payment Proportion

Figure 1 .

 1 Figure 3. Reduction in Non-Housing Consumption Following the Home Purchase, by Transfer Amount 1

  3

1

 1

Table 1 a

 1 Cox model of the hazard to ownership, with regressors present for several measures of parental resources-

	-father's occupational status, financial problems when respondent (spouse) was
	young, and number of siblings, as well as the wealth index. To allow for the
	possibility that assistance comes differentially from one side of the family,
	the resources are tabulated separately for each parental set. Also included,

9

High wealth was defined as scores 2 or 3 on the wealth index. The resulting distribution contains 576 cases in which both parental sets had high wealth, 1,595 observations in which one but not both had high wealth, and 2,801 instances in which neither had high wealth.

parents; a larger sibship means that less assistance is available to each child. None of the other resource measures achieves significance.

Table 1 . Parental Resource Effects on Hazard of Homeownership and Home Ownership Rate 1

 1

	Variables 2	(1) Cox Model	(2) Probit Model	(3) Probit Model
		coef	t-value	coef	t-value	coef	t-value

Table 2 . Parental Resource Effects on Home Value, Tobit estimates

 2

	1

1

Dependent variable is log(home value). Absolute values of t-statistics are in parentheses. The sample is restricted to respondents who were less than age 65 at the time of the survey.

Table 3 . The Impact of Parental Transfers on Downpayment Proportion, Ordered Probit model 1

 3

* p<.05, **p<.01 Source: Survey Actifs Financiers 1992. 1 Ordered Probit model for down payment proportion with six categories. Absolute values of tstatistics are in parentheses. Cut point parameters not shown. Sample is restricted to respondents who were living together at the time of the purchase and were less than 65 years old in the year of the survey.

2

Table 4 . Estimates of the Parental Transfer Effect on Downpayment Proportion with Correction for Endogeneity Bias, Ordered Probit model 1

 4

	2

Table 5 . The Impact of Parental Transfers on Home Value, OLS Estimates 1

 5 Home value (log) at time of the survey. Absolute values of t-statistics are in parentheses. The sample is restricted to respondents who were living together at the time of home purchase and were less than age 65 at the time of the survey.

	Variables 2

1 2

Terms for city size and year of marriage are included in the regressions.

Table 6 . Impact of Parental Transfers on Down Payment Proportion and Home Value, Joint Estimation Model 1

 6

	Variables 2	(1)	(2)				(3)
		Downpayment	Home Value	Downpayment & home value
		coef	t-value	coef	t-value	Coef	t-value	coef	t-value
	Constant			9.611**	(38.01)			9.787**	(27.38)
	Age of husband at marriage/cohab.	0.055**	(8.92)	-0.001	(0.29)	0.060**	(8.28)	0.001	(0.22)
	Duration of union at home purchase	0.019**	(2.07)			0.017*	(1.69)
	Duration squared (/100)	0.106**	(3.50)			0.123**	(3.75)
	Duration of union at current time			0.030**	(3.19)			0.029**	(2.37)
	Duration squared (/100)			-0.067**	(3.69)			-0.070**	(3.01)
	Married vs. cohabitating	-0.088	(0.61)	0.175**	(2.69)	-0.105	(0.60)	0.146	(1.53)
	Number in household	-0.140**	(7.81)	0.004	(0.57)	-0.155**	(7.55)	-0.001	(0.06)
	Husband's education	0.023**	(3.86)	0.015**	(5.99)	0.028**	(4.19)	0.016**	(4.33)
	Wife's education	0.023**	(3.93)	0.007**	(3.07)	0.026**	(3.92)	0.009**	(2.37)
	Husband's occupational status 2 (/100)	0.493**	(2.94)			0.382**	(2.10)
	Household income (log)			0.294**	(16.97)			0.277**	(11.28)
	Gift or bequest amount received	2.045**	(4.67)	0.683**	(3.73)	2.339**	(4.69)	0.780**	(2.93)
	before home purchase (log/100)
	Correlation between residuals (t-value)						0.616** (17.17)
	Log likelihood -R²	-3542.37	-1383.71		-5102.51
	N	2452	2452			2452

* p<.05, **p<.01 Source: Survey Actifs Financiers 1992.

The distribution of this index is nearly identical for husband's and wife's parents. For husband's parents, wealth(0)= 39%, wealth(1)= 31%, wealth(2)= 19%, and wealth(3)= 11%.

Also included in the regressions are controls for city size and year of the home purchase. The latter serves as a control for temporal variations in government policy that have affected access to credit.

The joint model is similar to a SUR (Seemingly Unrelated Regression) formulation in the case of linear equations(Greene 1990, pp. 509-12). In our specification one of the equations is nonlinear, an ordered Probit.

Occupational status coded by ISEI scores, divided by 100[START_REF] Ganzeboom | A Standard International Socio-Economic Index of Occupational Status[END_REF]).

Four category scale. See text for details.

Four category scale. See text for details.

Ordered Probit model for down payment proportion with six categories. Absolute values of t-statistics are in parentheses. Also included in model are terms for city size and year of home purchase. Cut point parameters not shown. The sample is restricted to respondents who were living together at the time of home purchase and were less than age 65 at the time of the survey.

The parental transfer variable is treated as exogenous in models (1) and (3). Instrumentation is from a Probit equation for incidence of transfer receipt in model (2), and from a Tobit model for the log value of transfer amount in model(4). Covariates in the instrumentation equations are father's occupational status, financial hardship in youth, parental wealth (these three variables respectively for husband's and wife's parents), and the variables in the second stage model.

Occupational status coded by ISEI scores[START_REF] Ganzeboom | A Standard International Socio-Economic Index of Occupational Status[END_REF]).

Occupational status coded by ISEI scores[START_REF] Ganzeboom | A Standard International Socio-Economic Index of Occupational Status[END_REF]).