Luc Arrondel
email: arrondel@pse.ens.fr.

Hector Calvo Pardo

Xisco Oliver

Carl Eeckhoudt

Michael Emmerson

Andre Haliassos

Muriel Masson

Jean-Marc Roger

Pamela Robin

Christian Spadaro

Jackie Schluter

Wahba

Temperant portfolio choice and background risk: evidence from France

Keywords: C33, C35, D12, D91 portfolio choice, background risk, risk aversion, prudence, temperance

We explore empirically whether earnings uncertainty and borrowing constraints deter households from the stockmarket, consistent with the predictions of theoretical studies of portfolio choice in the presence of uninsurable earnings. Recent extensions highlight the importance of the correlation between earnings and financial risks. We use a selfassessed proxy for the correlation from the DELTA-TNS 2002 crosssectional survey. While income risk does not deter from the stockmarket those households' reporting a negative correlation, it does for those who report a non-negative sign, consistent with economic theory predictions.

Introduction

The main challenge incorporating background risks is to specify a realistic model for the joint distribution of these risks with asset returns... Michael [START_REF] Brandt | Portfolio Choice Problems[END_REF].

There has been growing interest on the implications of incomplete markets for both theoretical and empirical reasons. Perhaphs among the most important ones are the puzzles identified in the economics and finance literatures when confronting theoretical predictions with real data ('equity premium', 'nonparticipation', 'home bias'...). Recent availability of household-level data sets is guiding new theoretical developments and shaping the understanding of older ones, since new puzzles are emerging [START_REF] Guiso | Household Portfolios[END_REF][START_REF] Guiso | Stockholding in Europe[END_REF]).

The classical theory of portfolio choice was developed in a complete markets framework, meaning that all individual risks could be traded. It identified, as determinants of households' demand for stocks, the expected excess return of stocks over riskless assets, the objective risk of stocks as measured by its variance, and households subjective perception of that risk as measured by their risk aversion. The observation that severe informational restrictions precluded most households from insuring their labor earnings, and yet, was their most important source of lifetime income, motivated the reconsideration of the complete markets assumption. This reconsideration led to important departures from the predictions of the classical theory. Drèze andModigliani (1966, 1972) already observed that an important consequence of the non-insurability of earnings risks was that portfolio and labor market decisions become connected. Intertemporal extensions to incorporate nontradable and undiversifiable income [START_REF] Koo | Consumption and Portfolio Selection with Labor Income: A Discrete-Time Approach[END_REF], [START_REF] Davis | Occupation-Level Income Shocks and Asset Returns: their Covariance and Implications for Portfolio Choice[END_REF] or [START_REF] Viceira | Optimal Portfolio Choice for Long-Horizon Investors with Non-Tradable Labor Income[END_REF] among many others), borrowing and liquidity constraints [START_REF] Koo | Consumption and Portfolio Selection with Labor Income: A Discrete-Time Approach[END_REF], [START_REF] Haliassos | Portfolio Choice and Liquidity Constraints[END_REF]), indivisibilities like housing [START_REF] Brueckner | Consumption and Investment Motives and the Portfolio Choices of Homeowners[END_REF], [START_REF] Flavin | Owner-Occupied Housing and the Composition of the Household Portfolio[END_REF]), age [START_REF] Gollier | Time Horizon and Portfolio Risk[END_REF], [START_REF] Viceira | Optimal Portfolio Choice for Long-Horizon Investors with Non-Tradable Labor Income[END_REF] or [START_REF] Campbell | Strategic Asset Allocation: Portfolio Choice for Long-Term Investors[END_REF]), or information and transactions costs [START_REF] King | Asset Accumulation, Information, and the Life Cycle[END_REF], [START_REF] Vissing-Jorgensen | Towards an explanation of Household Portfolio Choice Heterogeneity: Nonfinancial Income and Participation Cost Structures[END_REF] or [START_REF] Haliassos | Portfolio Choice and Liquidity Constraints[END_REF]), have also been pervasively studied empirically thanks to the increased availability of household-level data. In this work we use household-level survey data to examine these theoretical developments on a sample of French households.

One of the most recent theoretical extensions of the classical portfolio choice model has formalized the following common wisdom intuition: when risk averse households are confronted with a risk beyond their control -exogenous or 'background' risk (hereafter)-, they should be willing to decrease their exposure to other avoidable risks -endogenous risks-in order to adjust their desired total risk exposure [START_REF] Pratt | Proper Risk Aversion[END_REF], [START_REF] Kimball | Standard Risk Aversion[END_REF], or [START_REF] Gollier | Weak Proper Risk Aversion and the Tempering Effect of Background Risk[END_REF]). Households observing this behaviour are called 'temperant' 1 . Accordingly, and as labor income is uninsurable, those 'temperant' households who suffer more from labor market uncertainty should choose to be less exposed to financial risk, ceteris paribus. As well, changes in the income risk that increase households exposure to unavoidable risks should compel them to crowd out from the stock market 2 . Although there is empirical evidence supporting this theoretical prediction using household-level data [START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF] for Italy, [START_REF] Massa | Hedging, Familiarity and Portfolio Choice[END_REF] for Sweden or [START_REF] Haliassos | Why Do So Few Hold Stocks?[END_REF] and Vissing-Jorgensen (2002) for the US), other empirical studies have not been able to confirm it [START_REF] Hochguertel | Households' Portfolio Choices[END_REF] or [START_REF] Alessie | Household Portfolios in The Netherlands[END_REF] for The Netherlands, [START_REF] Arrondel | Gestion du risque et comportements patrimoniaux[END_REF] or [START_REF] Arrondel | Temperant Portfolio Choice with a Correlated Background Risk[END_REF] for France).

More recently, surprising empirical results about the correlation between earnings and financial risks have been known. [START_REF] Davis | Occupation-Level Income Shocks and Asset Returns: their Covariance and Implications for Portfolio Choice[END_REF] or [START_REF] Heaton | Portfolio Choice in the Presence of Background Risk[END_REF] show that, contrary to educated intuition received from equilibrium economic models, both risks tend to be independent in the aggregate and differently correlated depending on the income decomposition criterion chosen. Vissing-Jorgensen (2002) for the US or [START_REF] Massa | Hedging, Familiarity and Portfolio Choice[END_REF] for Sweden, provide empirical evidence on the absence of a significant impact of the correlation on households' demand for risky assets using individual longitudinal datasets. Yet, both the standard theory of portfolio choice and empirical works emphasize the importance of the correlation component, e.g. in addressing the home-bias puzzle (Botazzi et al. (1996), [START_REF] Palacios-Huerta | The Human Capital of Stockholders and the International Diversification Puzzle[END_REF] or [START_REF] Julliard | Labor Income Risk and Asset Returns[END_REF]). Confronted with such ambiguity, we follow [START_REF] Dominitz | Earnings Expectations, Revisions and Realizations[END_REF][START_REF] Dominitz | Estimation of Income Expectations Models using Expectations and Realizations Data[END_REF], [START_REF] Dominitz | Using Expectations Data to study Subjective Income Expectations[END_REF] or [START_REF] Manski | Inference on Expectations and Decisions[END_REF] and propose individually self-assessed measures that proxy both the correlation and earnings uncertainty exploiting French household survey data (DELTA -TNS 2002). Earnings risk is found to have a negative impact on households' decision to hold risky assets provided that we control for the correlation, in line both with the results obtained for other countries and theoretical predictions.

The rest of the work proceeds as follows. In section 2 we summarize the theoretical assumptions and empirical implications underlying the adverse impact of correlated undiversifiable earnings on financial risk taking (temperant stockholding behaviour). In section 3, we describe the 'DELTA -TNS 2002' household survey and assess empirically the theoretical predictions on households' decisions to invest in stocks. Section 4 concludes.

Temperant Stockholdings with a Correlated

Background Risk Drèze andModigliani's (1966, 1972) pioneering work has lead researchers to reconsider the classical theory of portfolio choice, originally developed by [START_REF] Arrow | Aspects of the Theory of Risk Bearing, Yrjo Jahnsson Lectures[END_REF] under the assumption that all individual income risks can be traded (complete markets). In this section we only consider the theoretical implications of removing the assumption of complete markets for the standard static portfolio choice problem 3 . Under complete markets, the problem a household faces is how to invest her current wealth w 0 when there are only two assets available: a risky asset promising to deliver tomorrow a random return r and a riskless asset promising the delivery of a sure return r. Her individual objective function is a continuous differentiable representation of his preferences that admit an expected utility form over final wealth w f . Denoting by α the amount of initial wealth that is invested in the risky asset, by z ≡ rr the excess return of the risky asset over the riskless asset, and by w ≡ w 0 (1 + r) the final wealth had she invested all her current wealth w 0 in the riskless asset, we can write the solution α * to her individual optimization problem under the small risk approximation as:

α * E z σ 2 z A u (w) ∈ arg max α Eu(w + α z) (1)
Where A u (w) ≡ -u (w) u (w) is the standard Arrow-Pratt coefficient of absolute risk aversion evaluated at the agents' wealth w when the agent's preferences are represented by utility u(.). Now, assume that the household cannot trade her labor income risk y (incomplete markets). Will she invest more in risky asssets? Under the small risk approximation, optimal stockholdings become:

α E z σ 2 z A v (w) ∈ arg max α Eu(w + α z + y) (2)
Where now A v (w) ≡ -v (w) v (w) and v(t) ≡ E y u(t+ y) is the indirect utility function, as defined by [START_REF] Kihlstrom | Risk Aversion with Random Initial Wealth[END_REF]. Common wisdom would suggest that increasing household's exposure to risks beyond her control should lead her to decrease her optimal exposure to risks under her control, i.e. risks are substitutes rather than complements. Formally, [START_REF] Pratt | Proper Risk Aversion[END_REF], [START_REF] Kimball | Standard Risk Aversion[END_REF] or [START_REF] Gollier | Weak Proper Risk Aversion and the Tempering Effect of Background Risk[END_REF] showed that substitution between risks means conditions under which the change in preferences from u(.) to v(.) leads households to be more risk averse in the presence of the independent background risk on income y :

A v (w) ≥ A u (w) =⇒ α ≤ α * (3)
Using a cross-section of Italian households (SHIW), [START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF] were the first to provide empirical validity for this comparative statics property. Vissing-Jorgensen (2002) and [START_REF] Heaton | Portfolio Choice in the Presence of Background Risk[END_REF] also find evidence that background risk reduces stock market participation in the United States, as do [START_REF] Massa | Hedging, Familiarity and Portfolio Choice[END_REF] for Swedish households. Hochguertel (1998) results for the Netherlands are inconclusive and those of Alessie et al. (2001) for the same country did not find a significant effect of income uncertainty on the demand for risky assets. Arrondel andMasson (1996, 2003) or [START_REF] Arrondel | Temperant Portfolio Choice with a Correlated Background Risk[END_REF] obtain a different result for France: as households are more exposed to earnings risk (proxied by occupation sectors), they tend to own more stocks. Rather than dismissing the theoretical prediction, a natural assumption to relax is the hypothesis that household income y and stock market excess returns z are independent.

Specializing to the assumptions 4 of [START_REF] Kimball | Standard Risk Aversion[END_REF], [START_REF] Arrondel | Temperant Portfolio Choice with a Correlated Background Risk[END_REF] extend the results of this literature to dependent background risks of the form introduced by Elmendorf and [START_REF] Elmendorf | Taxation of Labour Income and the Demand for Risky Assets[END_REF]. Following the latter, define now income risk as y c = h + β z where subindex 'c' accounts for 'correlated', since the parameter β captures a non-zero correlation between y c and z. Then, under the small risk approximation the household's risky asset demand is given by:

α E z σ 2 z A v (w) -β ∈ arg max α Eu[w + α z + y c ] (4)
We can then define total stockholdings θ as the sum of two components: a fixed implicit component given by the correlation β, and a variable explicit component α directly managed by the household so as to adjust total stockholdings to its optimal value θ ≡ α + β E z σ 2 z A v (w) ( 5 ). We can then express the analogue of property (3), that will be the object of empirical scrutiny in section 3, as 6 :

A v (w) ≥ A u (w) =⇒ α + β ≡ θ ≤ α * (5)
CRRA Example: Specifying the utility function to be u(w) = w 1-γ 1-γ : γ ≡ wA u (w), and assuming that rate of return risk and earnings are jointly lognormally distributed, the (approximation) technique presented in Campbell and [START_REF] Campbell | Strategic Asset Allocation: Portfolio Choice for Long-Term Investors[END_REF] yields the following decomposition of the weak inequality in the right hand side of (5):

θ -α * = 1 E z σ 2 z γ -β - E z σ 2 z γ (6) = 1 - 1 c E z σ 2 z γ (-) Risk Substitution Effect + 1 c -1 E z σ 2 z γ (+) Income Effect - 1 β ≤ 0
Hedging Effect:

(+ ) if β>0; (-) if β<0 (7)
precautionary premium as defined by [START_REF] Kimball | Precautionary Saving in the Small and in the Large[END_REF]. In intuitive terms, they are risks that make the agent willing to pay a bigger amount than its expected value in order to keep as optimal the decision prevailing before the risk was introduced. Finally observe that if preferences are DARA, every undesirable risk is loss-aggravating. 5 In a CAPM framework, [START_REF] Davis | Occupation-Level Income Shocks and Asset Returns: their Covariance and Implications for Portfolio Choice[END_REF] termed them, respectively, by 'endowed' (Hedging component), 'desired' (Markowitz component) and 'total' exposures to rate of return risk. Here we follow the terminology of [START_REF] Elmendorf | Taxation of Labour Income and the Demand for Risky Assets[END_REF]. 6 Because the independent component of the background risk h has a negative impact on total stockholdings if and only if it is in the loss-aggravating class of risks and households' preferences are standard (DAP and DARA). Therefore θ ≤ α * .

where

1 = 1 + E y exp{-1 2 σ 2 y } exp{E r+w 0 } > 1 c = 1 + E y exp{E r+w 0 } . 1 1 c
is the inverse elasticity of total wealth with respect to financial wealth when labour income is stochactic and (non-stochastic but) non-tradable. When non-stochastic, it is equal to the expected value of uncertain earnings y c .

The equality from ( 6) to [START_REF] Arrondel | Gestion du risque et comportements patrimoniaux[END_REF] follows from adding and subtracting the optimal portfolio 1 c E z σ 2 z γ of a household with certain but nontradable labour income y = E y c . The first additive term in [START_REF] Arrondel | Gestion du risque et comportements patrimoniaux[END_REF] captures the negative effect on the complete markets optimal portfolio α * of introducing an independent zero-mean background risk yy : E y = E y c (risk-vulnerable reaction, in Gollier and Pratt's (1996) terminology). The second term in [START_REF] Arrondel | Gestion du risque et comportements patrimoniaux[END_REF] captures the positive effect on α * of introducing an independent background risk with positive mean E y = y > 0, i.e. because preferences display decreasing absolute risk aversion, richer households are more willing to invest in stocks. The last term in [START_REF] Arrondel | Gestion du risque et comportements patrimoniaux[END_REF] captures the 'hedging effect' to the extent that we allow for correlated earnings y c . Notice that it is interacted with the inverse elasticity 1 , which is itself a function of earnings variance σ 2 y , because for those households whose income risk is small, the hedging component will be negligible 7 .

Remark 1: (Empirical Implication) Recalling that we observe explicit asset holdings α and not total asset holdings θ, expression [START_REF] Arrondel | Temperant Portfolio Choice with a Correlated Background Risk[END_REF] shows that any empirical attempt to validate it requires a measure for the correlation β. For example, establishing empirically that α * ≥ α does not imply that households invest less in risky assets because they cannot trade their earnings risk (risk substitution effect). Households may explicitely hold less risky assets just because they are already implicitely investing in the stock market through their earnings, i.e. β > 0 (Hedging effect). Conversely, suppose that we empirically detect that α * ≤ α, concluding that the average (e.g. French) household invests more in risky assets the more exposed she is to earnings risk. This is only true provided that β = 0. If on average β < 0, it may actually be the case that θ = α + β ≤ α * in line with what risk substitution prescribes when income risk is correlated, i.e. [START_REF] Arrondel | Temperant Portfolio Choice with a Correlated Background Risk[END_REF]. ( 8) 7 We thank an anonymous referee for pointing out this observation. 8 Notice that assuming CARA preferences precludes any impact of introducing a correlated background risk beyond the hedging component, because then risk aversion is independent of wealth, i.e. A v (w) = A u (w). This is also the case when mean-variance preferences are used as long as the income risk is non-tradable, for general joint statistical distributions of financial and labour returns.

Remark 2: (Effect on Participation) [START_REF] Arrow | Aspects of the Theory of Risk Bearing, Yrjo Jahnsson Lectures[END_REF] established that under complete markets, if the expected excess return of investing in risky assets is positive, every risk averse household whose preferences can be represented by a differentiable felicity function should invest a fraction of her wealth in risky assets. [START_REF] Haliassos | Why Do So Few Hold Stocks?[END_REF] noticed that this theoretical prediction lacked empirical support using the 1983 US Survey of Consumer Finances, and called it the stockholding puzzle. Under incomplete markets however, if income risk is negatively correlated and non-diversifiable, rational risk averse households may optimally invest in the risky asset even if the expected excess return E z is negative, since it provides partial insurance against the exogenous earnings risk. And conversely: even if the stock market delivers a considerable positive risk premium, households whose incomes covariate positively with the stock market will optimally choose not to hold stocks if participation increases their global risk exposure beyond wish 9 . To the extent that at the individual level this correlation changes with the educational level and sector of activity [START_REF] Davis | Occupation-Level Income Shocks and Asset Returns: their Covariance and Implications for Portfolio Choice[END_REF], professional status and asset ownership [START_REF] Heaton | Portfolio Choice in the Presence of Background Risk[END_REF], or stockownership status (Palacios-Huerta, 2001), this is likely to generate cross sectional variation in participation.

Remark 3: (Risk aversion as a determinant of the participation equation) If transaction costs are present (ex. sign-up or brokerage fixed fees), differences in risk aversion will also determine the decision to participate if households become less risk averse as their wealth or income increases [START_REF] Haliassos | Why Do So Few Hold Stocks?[END_REF], [START_REF] Haliassos | Stockholding: Lessons from Theory and Computations[END_REF], [START_REF] Haliassos | Portfolio Choice and Liquidity Constraints[END_REF]). Further, conditioning on income and wealth, households with riskier incomes are also less prone to pay the fee for investing in risky assets.

sign W (α)| α=0 = sign{E z + cov[ z, u ] Eu } > 0 Since u (.) < 0, the term cov[ z, u ] > 0 is equivalent to cov[ z, y c ] < 0 by Gollier's (2001)
proposition 15. And conversely.

3 Empirical evidence [START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF] provided empirical support to the adverse impact of unavoidable income risk and anticipated liquidity constraints on household stockholding decisions using Italian data 10 . Using their same specification and similarly constructed relevant variables, we confirm their findings on French household data if we control for the correlation between earnings and financial returns. When we exclude the correlation variable, income risk has no effect on the decision to invest in risky assets, at odds with theoretical predictions.

Data description and risk variables

We rely on the 'Mode de vie et épargne' household survey conducted by DELTA and Taylor Nelson-Sofres in 2002 (DELTA -TNS 2002) on a sample of 4000 French households with individuals between 35 and 55 years old, representative of the French population in the age bracket. Only 2518 households answered, of which 2460 could be exploited. This survey contains information on earnings, income, wealth, socio-economic status and demographic characteristics of the household. Questions that capture the degree of individual exposure and aversion to risk include those proposed by [START_REF] Barsky | Preference Parameters and Behavioral Heterogeneity : an Experimental Approach in the Health and Retirement Study[END_REF], based on relative risk-aversion to lotteries on lifetime labour income, and by Guiso andPaiella (2001, 2004), based on the degree of absolute risk-aversion to financial lotteries 11 . Finally, a question to proxy for the correlation between earnings and financial risk as subjectively perceived by individuals is for the first time available.

The DELTA-TNS 2002 survey contains qualitative information on the distribution of household financial assets in ten categories: cash, transactions and savings accounts, homeownership savings accounts, bonds (Treasury bills, certificates, fixed-rate long term bonds and other government paper), stocks from privatized public companies, private companies listed stocks, stocks of foreign firms, mutual funds and managed investment accounts, annuities, life insurance contracts and contributions to complementary pension plans. Table 1 reports the proportion of households holding each asset.

(Table 1 here)

We define direct stockholdings as the sum of stocks of privatised public companies, private companies listed stocks and stocks of foreign firms held, and as indirect stockholdings, those held through mutual funds and managed investment accounts. Although in some countries bonds have a considerable risk of default justifying their inclusion in the risky asset holdings (i.e. [START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF], this is not the case of France and we therefore exclude them. As well, we exclude homeownership from the risky asset category despite of being highly illiquid and indivisible (and therefore risky), because French households mostly buy houses for the flow of services it provides rather than as a financial investment [START_REF] Arrondel | Gestion du risque et comportements patrimoniaux[END_REF]. Still, in the estimation we control for the level of total net worth (real plus financial) and include a dummy variable that takes value one when houseownership status is observed. The proportion of households who hold stocks directly is 21%, and 33% either directly or indirectly. Although low, the participation rates are similar to those obtained from previous INSEE surveys 12 and to the figures from other European countries studied in Guiso et al. (2003) (13 ). The extent to which such low participation rates in financial risk are explained by both earnings risk and the expectation of being liquidity constrained is subject to empirical scrutiny.

Available data to capture earnings uncertainty is scarce, as we show below. Therefore we construct a proxy for the subjective income variance as follows: we estimate it conditional on a vector of characteristics from the wealth INSEE survey 'Patrimoine 98', and predict earnings uncertainty for DELTA-TNS 2002 households. Since each labor income recipient in 1998 was asked to attribute probability weights to given intervals of real income increases five years ahead, we can match 1998 and 2002 data 14 . In the Appen-dix it can be seen that the structual parameters can be reasonably thought as stable 15 , given that most of the determinants evolve slowly over the relevant time span (e.g., risk preferences, occupational and personal status, region of residence or having had health problems in the past). This procedure facilitates the comparison with previous results [START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF] as well as to partially overcome the potential endogeneity problem of this measure, i.e. that more risk averse households hold both safer occupations and tend to participate less in the stock market [START_REF] Lusardi | Precautionary Saving and Subjective Earnings Variance[END_REF]. Criticisms to the use of this self-assessed measure of income risk are well-known: it is a sufficient indicator of risk for a very restrictive class of preferences, potentially underestimates the probability of very low income events and it is too low when compared to panel data estimates 16 .

(Table 2 here) Table 2 reports descriptive statistics for the sample (columns 1 and 2), by the sign of self-assessed correlations (columns 3 and 4, for non-negative and negative correlations respectively) and for varying levels of earnings uncertainty (columns 5 and 6, for low and high levels respectively). The sample average of the predicted income risk is 6.3%, strikingly low when compared with the values from the precautionary savings literature, i.e. between 10% and 20% of the earnings' level (e.g. [START_REF] Deaton | Understanding Consumption[END_REF] reports a standard error of 15% for next year expected earnings in the US), but of the same order of magnitude as in [START_REF] Guiso | Earnings Uncertainty and Precautionary Saving[END_REF][START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF]. A decomposition of the sample by varying levels of income uncertainty below and above the median of the predicted distribution (table 2, columns 5 and 6) confirms that households with higher uncertainty hold marginally less risky assets [START_REF] Arrondel | Temperant Portfolio Choice with a Correlated Background Risk[END_REF], [START_REF] Arrondel | Stockholding in France[END_REF]), are younger, financially poorer, earn less at work, have more irregular incomes (discrete income risk variable), are more often unemployed, are more risk averse (see below) and more often women, hold lower educational degrees but are better informed (as proxied by parents holding risky assets, and having access to internet), and are more often liquidity constrained than households in the low income risk group.

As suggested by the theory, a test of the proposition that undiversifiable earnings crowds households out of the stockmarket requires controlling for its potential covariation with financial returns, as well as for all variables that determine the decision to invest in the stock market. To control for the correlation, a question in the survey asks households about the reasons that may lead big firms to downsize the labour force: a binding bankruptcy constraint (a positive correlation is assumed, ρ > 0) or the expectation of a positive price impact on the firm's listed stocks (a negative correlation is attributed, ρ < 0). From table 2, 62% report a negative correlation, while 34% reports a positive one. The remaining 4% are non-respondents. The descriptive statistics in table 2 by the reported sign of the correlation, columns 3 and 4, show that households who assessed a negative correlation participate more often in the stock market (as predicted by the theory), are more risk averse (see below), work more often in a big firm and are considerably more educated 17 . This last point seems to be at odds with the current consensus that earnings of college educated household heads covariate positively with financial returns [START_REF] Haliassos | Stockholding: Lessons from Theory and Computations[END_REF], [START_REF] Haliassos | Portfolio Choice and Liquidity Constraints[END_REF]), and if accepted, would relegate our variable to an informational proxy status. But Palacios-Huerta (2001,2003) notices that standard panel data computations of the correlation have neglected the skill premium component of earnings. Since this skill premium is negatively correlated with the returns to domestic capital 18 , taking it into account reverses the positive correlations obtained by [START_REF] Campbell | Understanding Risk and Return[END_REF] for stockholders (see table 1 in Palacios-Huerta, 2001). Lustig and Van Nieuwerburgh (2006) also provide evidence of a robust negative correlation between human capital and financial returns in the US 19 . 17 Unreported probit estimations confirm that those who have graduate studies (+14%) and college education (+11.9%) and work in a big firm (+6.2%) tend to report a negative correlation assessment. 18 Rubinstein and Tsiddon (2001) use the 1968-1992 PSID data on white males to show that higher educational attainments correspond to less cyclical unemployment, employment and wages. Furthermore, controlling for parents' educational levels, college graduates with educated parents face acyclical unemployment and wage increases in absolute terms during recessions, while the less educated with less educated parents face highly pro-cyclical wages and employment. See also [START_REF] Keane | Real Wages over the Business Cycle: Estimating the Impact of Heterogeneity with Micro Data[END_REF] for additional evidence along these lines. 19 Botazzi et al. (1996) use OECD data for 16 countries from 1970 to 1992, and find significant negative covariation between innovations to human wealth and innovations to financial wealth, for all but 4 countries (Austria, Germany, Norway and US) including France (see tables 3 Contrary to most of the existing studies, two different questions that proxy households' degree of risk aversion are available. The first mimics the methodology of [START_REF] Barsky | Preference Parameters and Behavioral Heterogeneity : an Experimental Approach in the Health and Retirement Study[END_REF] (see Appendix) and assumes that housholds risk preferences are in the constant relative risk aversion (CRRA) class: 8% of the sample has a CRRA coefficient lower than 1, 20% has a CRRA between 1 and 2, 28% has a CRRA between 2 and 3.76 and 37% has a risk aversion coefficient greater than 3.76 ( 20). The second is based on work by Guiso andPaiella (2001, 2004), who construct a measure of the coefficient of absolute risk aversion 21 . It asks individuals their maximum willingness to pay to enter a lottery representing a relatively large financial risk (around 16% of average annual income) 22 . We use the first to obtain estimates of the subjective income variance (because it was the only variable available in the 'Patrimoine 98' survey) and the second to estimate the probability of participation, since this variable has more explanatory power and it is continuous. More importantly, accounting for risk aversion significantly contributes to avoid endogeneity issues between occupational choice and financial risk taking attitudes 23 .

Finally, to capture households' ability to gain access to credit markets, two questions in the survey identify both 'discouraging borrowers' and 'turned down applicants'. The variable that proxies for liquidity constraints takes value one if households qualified themselves in either category, and is similar to the one used by [START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF]. 481 of the 2460 surveyed households data, to find statistically non significant negative correlation for both college educated and high school dropouts, while zero for high school attendants (see table 3 in their paper). 20 The proportion of households in each CRRA coefficient bracket for the 35-55 year old subsample in the INSEE survey 'Patrimoine 98' (column 3, table A1 in appendix) are similar to those for the DELTA-TNS 2002 survey (column 2, table A1 in appendix). 21 For sampled households, both measures are positively correlated though less than expected. The reason seems to stem in the different type of lotteries they propose to survey respondents: the first relates to lifetime labour income prospects, while the second proposes a financial investment opportunity. Arrondel et al. (2002) consider 'domain dependent' risk averse preferences. 22 A potential drawback of this measure is that the magnitude of the risk is too large for a second order Taylor approximation to be accurate (it is claimed to be valid for small risks, i.e. between 1% and 5% of average income). This is to be traded-off against the inaccuracy of responses if the lottery is small, since expected utility maximizers are risk-neutral in the small [START_REF] Rabin | Risk Aversion and Expected Utility Theory: A Calibration Theorem[END_REF]. Still, it is likely to be a poor measure for poorer individuals. are liquidity constrained (20%) (24 ). Households exposed to higher earnings risk (by both the discrete and predicted income risk proxies) are also more likely to be liquidity constrained, in line with theoretical predictions25 .

Empirical results

For estimation purposes, we assume that households' indirect utility function can be written as a linear function of household i observable characteristics x i , plus an error term e i normally distributed. The error term includes household-specific factors affecting her utility. Let U s i = β s x i + e s i be the indirect utility function of stockholders, and U 0 i = β 0 x i + e 0 i that of nonstockholders (s = 0). Since the indirect utility function cannot be observed, only participation status, we accordingly define the dichotomous variable y i that takes value 1 if the household participates, and 0 otherwise:

Pr(y i = 1| x i ) = Pr(U s i -U 0 i > 0) = Pr(β x i + e i > 0| x i ) = Φ(β x i ) (8)
where Φ(.) denotes the standard normal cumulative distribution function.

The vector x i contains a proxy for anticipated liquidity constraints (cl i ), the expected variance of earnings (σ 2 i,y ), the coefficient of absolute risk aversion (γ i ), the proxy of the subjectively assessed correlation (ρ i ) and its interaction with income risk (see above), and a vector w i of other variables previously demonstrated to be significant in explaining positive stockholdings such as age, gender, labour income, financial wealth, homeownership status, inter vivos or mortis causa transfers, and a set of variables that proxies for the stock of financial information (living in Paris, parents stockownership status and having acces to internet) (26 ). Since demographic factors give also an approximation of potential future sources of income risk the exclusion of which can lead to misspecification problems [START_REF] Burgess | Measuring Income Risk[END_REF], we include a dummy that takes value 1 if the household has children. Finally, to control for inertial factors (mainly incentive remuneration schemes) that may explain involuntary stockmarket paricipation, we also introduce the variable 'working in a big firm'. In specification [START_REF] Arrondel | Stockholding in France[END_REF], income risk is assumed to be exogenous.

If capital markets are imperfect (transaction or informational costs) households' income and wealth influences portfolio choice 27 . The empirical analysis reveals that their effect is best captured by a second order polynomial. Although this facilitates the comparison with existing results in the literature [START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF][START_REF] Guiso | Household Portfolios[END_REF][START_REF] Guiso | Stockholding in Europe[END_REF], [START_REF] Haliassos | Why Do So Few Hold Stocks?[END_REF] or King and Leape (1998)), it has the disadvantage of introducing heteroscedasticity in the error term e i :

V ar( e i | x i , z i ) = [exp (υ z i )]
2 : z i ≡ Financial wealth Table 3 reports the regression results of the heteroscedastic probit estimation 28 by measures of income risk 29 . The variables have the expected signs with minor differences across columns. Financial wealth has a positive effect on participation and is significant at the 1% level. An increase in financial wealth from the first decile (6,500 euros) to the ninth decile (410,000 euros) increases the probability of participation by 25%. Income also increases the probability of participation in the stock market, moving from the first to the ninth decile increases the probability of stockownership by 7%. The effects are consistent with fixed transaction and information costs of accessing the stock market, as well as of decreasing aversion to financial risk taking, since both capture households' initial endowments other than housing. Homeownership status has a positive and significant effect, increasing the probability of participation by 7%. [START_REF] Heaton | Portfolio Choice in the Presence of Background Risk[END_REF] rationalize this finding by means of the negative correlation detected between housing and financial risks, i.e. owning a house serves as a hedge against financial fluctuations 30(see also [START_REF] Brueckner | Consumption and Investment Motives and the Portfolio Choices of Homeowners[END_REF] or [START_REF] Flavin | Owner-Occupied Housing and the Composition of the Household Portfolio[END_REF]). But it can also be interpreted as a proxy for total wealth if trasaction costs are present, so that homeowners are less risk averse because they are wealthier.

(Table 3 here) Previous empirical studies find that education increases the probability of participation. We excluded it because of its strong correlation with income and the set of information variables. More information significantly increases the probability of participation: Having Internet at home 31 raises the probability of participation by 11% and if parents hold risky assets, the probability increases to 16% ( 32 ). Households living in Paris are 13% more likely to hold risky assets. The age variables indicate that the probability of owning risky assets is lower for younger households, although it has a hump-shaped effect reaching its maximum at the age of 46. Younger individuals are less informed [START_REF] King | Asset Accumulation, Information, and the Life Cycle[END_REF] tend to be more often liquidity constrained [START_REF] Cocco | Cosumption and Portfolio Choice Over the Life-Cycle[END_REF], [START_REF] Haliassos | Portfolio Choice and Liquidity Constraints[END_REF], [START_REF] Viceira | Optimal Portfolio Choice for Long-Horizon Investors with Non-Tradable Labor Income[END_REF]) and have a stronger preference for homeownership [START_REF] Flavin | Owner-Occupied Housing and the Composition of the Household Portfolio[END_REF]) but enjoy greater labour supply flexibility [START_REF] Bodie | Labor Supply Flexibility and Portfolio Choice in a Life-cycle[END_REF], [START_REF] Chan | Asset Allocation with Endogenous Labor Income: The Case of Incomplete Markets[END_REF]). But the reduction in the probability of stockownership after 46 is difficult to explain by life cycle motives alone 33 .

In accordance with theoretical predictions, more risk averse individuals have a lower probability of participation 34 . Surprisingly, once we control for risk aversion, being a woman significantly reduces the probability of being a stockholder (by a 8%), confirming the results obtained by [START_REF] Schubert | Financial Decision making: Are Women more Risk Averse?[END_REF]. Households with children are 3% less likely to invest in the stock market. Having received an inheritance or inter vivos transfers increases the probability of participation (6% and 3% respectively), but the latter is only choice of the house. However, this is rather unlikely given the illiquid nature of the asset in France, and that most households do not buy it for investment purposes. 31 The positive effect of information on the probability of holding stocks, as proxied by having internet access has recently been documented by [START_REF] Bogan | Stock Market Participation and the Internet[END_REF] for the US. 32 [START_REF] Chiteji | Asset Ownership Across Generations[END_REF] or Vissing-Jorgensen (2003) obtain similar results: when parents are stockholders, children have a higher probability of becoming stockholders because informational barriers are smaller. 33 The age coefficients are difficult to interpret also because only individuals between 35 and 55 were interviewed. 34 We have tested the two available variables that capture risk aversion. We have chosen the continuous variable based on Guiso andPaiella (2001, 2004) because it has more explanatory power, its wording is closely related to financial risk taking and the CRRA variable is used as a predictor in the income risk estimation. significant at 10%.

Households who have been liquidity constrained or who think that they will be so in the future are less likely to participate (around 13%). The effect of liquidity constraints reinforces the risk substitution effect, in line with the empirical results obtained by [START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF] and with theoretical predictions. [START_REF] Gollier | The Economics of Risk and Time[END_REF] proves that the willigness to take risk is reduced in the presence of a liquidity constraint if absolute risk tolerance is increasing and convex in wealth. Koo's (1999) theorem 2 (iii) states that liquidity constrained households invest strictly less in risky assets than households who are not constrained, because their risk tolerance is smaller. [START_REF] Deaton | Understanding Consumption[END_REF] explains how the expectation of being liquidity constrained in the future leads prudent households to save more ('buffer stock'), while [START_REF] Elmendorf | Taxation of Labour Income and the Demand for Risky Assets[END_REF] prove that the positive wealth effect of increased precautionary savings that leads decreasing risk averse (DARA) households to invest more in stocks is dominated by the negative increase in risk if households are also decreasingly prudent (DAP), resulting in an overall reduction in stockownership.

To avoid a possible endogeneity bias of the liquidity dummy, we conducted [START_REF] Davidson | Estimation and Inference in Econometrics[END_REF] test. The instruments used in the auxiliary IV regression are: squared log of income, education, marital status, health status, a dummy variable for those individuals who have asked for a credit and labour status. We also tested the validity of the instruments, and the null hypothesis of exogeneity of the regressors cannot be rejected 35 .

The available correlation proxy is an imperfect assessment of individual earnings' degree of covariation with rate of return risk. Still it has the advantage of being self-assessed, and behaves empirically in accordance with the theoretical predictions: households who assess a negative sign, ρ < 0, are 9 percentage points more likely to participate (at 1% level of significance, in both columns 1 and 2, table 3). A possible interpretation comes from Botazzi et al. (1996) or [START_REF] Danthine | Labour Relations and Asset Returns[END_REF]: a negative average correlation indicates that redistributive shocks dominate over the cycle. In accordance with this observation, individuals reporting a negative correlation answered that 'big firms fire employees because they want to increase the price of their stockmarket shares'. A probit regression of the probability to assess a negative sign confirms 'working in a big firm' and having received college education or above as the two main determinants. Another possible interpretation in terms of the skill premium content of wages rationalizes the second main determinant: educated individuals tend to have counter-cyclical labour earnings [START_REF] Rubinstein | Born to be Unemployed: Unemployment and Wages over the Business Cycle[END_REF], and therefore have a higher propensity to become stockowners because the returns to human capital are negatively correlated with the stock market (Palacios-Huerta, 2001) ( 36 ). The skill premium interpretation is consistent with the descriptive evidence in the bottom row of table 2: college educated households (last two rows) tend to report a negative sign (columns 3 and 4) and have lower income risk (columns 5 and 6), while less than college educated ones (rows three to five from the bottom) tend to report a non-negative sign (columns 3 and 4) and have higher income risk (columns 5 and 6). While other recent studies have not been able to find evidence of a correlation effect using longitudinal individual data (e.g. Vissing-Jorgensen (2002) or [START_REF] Massa | Hedging, Familiarity and Portfolio Choice[END_REF]), none of them has considered the potential skill premium content of wages that is consistent with our self-assessed correlation proxy.

Column 1 reports the estimation results using the discrete income risk dummy. A one is assigned to those who report either irregular or a mix of regular and irregular household earnings, while a zero is attributed otherwise. Contrary to available empirical evidence for the US (Vissig-Jorgensen (2002), [START_REF] Campbell | Strategic Asset Allocation: Portfolio Choice for Long-Term Investors[END_REF]), Italy [START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF] or Sweden [START_REF] Massa | Hedging, Familiarity and Portfolio Choice[END_REF]) and economic theory predictions, it has no significant effect 37 . The absence of a negative effect is confirmed by the results in column 2, where the predicted measure of the subjective earnings variance substitutes the discrete income risk variable, to take into account heterogeneity in earnings risk exposure 38 . 36 Yet a third interpretation in terms of the informational content of unemployment news on equity returns is possible: bad unemployment news are interpreted as "good news" during expansions, but as bad news during recessions [START_REF] Boyd | The Stock Market's Reaction to Unemployment News: Why Bad News Is Usually Good For Stocks[END_REF], [START_REF] Andersen | Real-time Price Discovery in Stock, Bond and Foreign Exchange Markets[END_REF]). But the underlying idea is the one of redistributive shocks, just that they are state-contingent. 37 But in line with previous empirical results for France [START_REF] Arrondel | Temperant Portfolio Choice with a Correlated Background Risk[END_REF] or [START_REF] Arrondel | Stockholding in France[END_REF]) and Alessie and Hochguertel (2003) for The Netherlands. 38 Although the variance is a partial representation of risk, we considered alternative measures like the probability of being unemployed five years ahead, a dummy for households that assign point estimates to reductions in real earnings, and different dispersion measures of the subjectively assessed individual distributions. For none of them a coefficient significantly different from zero was obtained.

Finally, in column 3 we decompose the effect of expected income risk using the self-assessed correlation proxy to separate those who assess a negative sign (ρ < 0) from the rest (ρ ≥ 0). Since the correlation is likely to be more important for those households who face higher earnings uncertainty, we introduce the interaction of both. In line with the theoretical results of section 2, for those households whose earnings are negatively correlated the effect on participation is ambiguous: they tend to participate less to the extent that their labour income is risky, but tend to participate more to the extent that it is negatively correlated and can use the stock market as a hedge against fluctuations in their earnings. Consistently, a positive but insignificant coefficient (at 10%) is obtained empirically. As well, for those who assess a non-negative correlation, from section 2 we know that both the income risk and the correlation effect go in the same direction. Overall a negative impact on participation is obtained (significant at 5%): The point estimate implies that households reporting a non-negative correlation are 4.45 percentage points less likely to hold risky assets than households reporting a negative sign. For those households who assess a non-negative sign, moving a household from the 10th percentile of relative income risk to the 90th percentile, decreases the probability of holding assets by 4.3 percentage points, all other things being equal. Therefore when controlling for the correlation, we do find evidence of a negative impact of uninsurable earnings risk on stockownership.

Conclusion

There has been a resurgent interest on the implications of incomplete markets for portfolio choice theory motivated by the number of portfolio puzzles identified in the literature. One of the most active research areas has concentrated on the study of the determinants of stock market participation and stockholdings. Considerable progress has been made in understanding the interactions between income risk, rate of return risk, borrowing constraints and transactions costs. Using measures proxying for income risk and liquidity constraints available in the literature, we test whether they affect the stockownership decision controlling for the correlation between earnings and rate of return risk as self-assessed by households. Exploiting the 'DELTA-TNS 2002' household survey, the empirical results confirm the theoretical prediction that non-negatively correlated background risks reduce the willingness to bear financial risk, crowding households out from the stock market. As well, we do find evidence that borrowing and liquidity constraints reduce households' propensity to invest in risky assets.

Quantitatively, the effects identified confirm the relative importance of the different factors as obtained in the literature: transactions costs and informational barriers, liquidity constraints, taste for risk parameters and income risk. Each of them is, by decreasing order of magnitude, important to explain households' decisions to enter the stock market. pational dummies to capture heterogeneity in professional tastes.

Table A1 also reports sample means of the variables used to impute income risk. The 'Patrimoine 98 (ages 35-55)' and 'DELTA-TNS 2002' variables can be directly compared, showing similar characteristics. The main differences are: a lower proportion of surveyed households with children and graduate studies, and a higher fraction of risk averters and a positive taste for financial risk taking, relative to the 'Patrimoine 98 (ages 35-55)' mean variables. This increased preference for stockholding might be explained by the dotcom driven stock market boom that took place between 1998 and 2002, in most OECD economies.

Measuring Relative Risk Aversion

To obtain a measure of risk aversion, we asked individuals about their willingness to gamble on lifetime income (see the Appendix) according to the methodology of [START_REF] Barsky | Preference Parameters and Behavioral Heterogeneity : an Experimental Approach in the Health and Retirement Study[END_REF]. The "game" resides in determining sequentially whether the interviewee would accept to give up his present income and to accept other contracts, in the form of lotteries: he has one chance in two to double his income, and one chance in two for it to be reduced by one third (contract A), by one half (contract B), and by one fifth (contract C). More precisely, the question in the survey was: 'Suppose that you have a job which guarantees for life your household's current income R. Other companies offer you various contracts which have one chance out of two (50%) to provide you with a higher income and one chance out of two (50%) to provide you with a lower income.

Are you prepared to accept Contract A which has 50% chances to double your income R and 50% chances that your income will be reduced by one third?

For those who answer YES : the Contract A is no longer available. You are offered Contract B instead which has 50% chances to double your income R and 50% chances that it will be reduced by one half. Are you prepared to accept?

For those who answer NO : you have refused Contract A. You are offered Contract C. which has 50% chances to double your income R and 50% chances that it will be reduced by 20%. Are you prepared to accept?' This allows us to obtain a range measure of relative risk aversion under the assumption that preferences are strictly risk averse and utility is of the CRRA type. The degree of relative risk aversion is less than 1 if the individual successively accepts contracts A and B; between 1 and 2 if he accepts A but refuses B; between 2 and 3.76 if he refuses A but accepts C; and finally more than 3.76 if he refuses both A and C. Among the 2460 households, 172 did not answer, 886 displayed a relative risk aversion lower than 1, 689 between 1 and 2, 517 between 2 and 3.76, and for 195 households relative risk aversion was larger than 3.76.

Absolute risk aversion: the survey asks the following: 'if someone proposes you to invest in a place where you have one chance out of two to win 5000 euros and one chance out of two of losing the capital invested. How much (as a maximum) will you invest?'. Guiso andPaiella (2001, 2004) show that absolute risk aversion can be computed as:

A i (w i ) = 2 5000 -Z i 5000 2 + Z 2 i
, where A i is the absolute risk aversion and Z i is the amount that the individual declares to be willing to invest. Risk-averse are those who declare Z i < 5000, riskneutral if Z i = 5000, and risk-lovers when Z i > 5000. For details concerning the validity of the approximation, we address the reader to their work.

(Table A2 here) To estimate how risk aversion varies with consumers attributes, we have regressed the measure of absolute risk aversion on observable characteristics that can proxy for differences in tastes 40 . In line with their results, table 2 shows that risk aversion decreases with households' financial wealth. This provides further support to temperant risk behaviour, that requires decreasing absolute risk averse houshold preferences. Contrary to the results of [START_REF] Guiso | Risk Aversion, Wealth and Background Risk[END_REF] for Italy, no significant differences between living in different regions 41 or having different ages are obtained. Instead, we find that absolute risk aversion depends on gender, having children and level of education. Being a woman 42 and having children increases risk aversion as well as being poorly educated. Surprisingly, the fact that the individual has been unemployed in the past or is likely to be so in the future 43 has no effect on risk aversion. Since residuals are far from being normally distributed, bootstrapped standard errors are provided in table A2.

Liquidity constraints: Households are asked two questions aimed at 40 The results included in table A2 replicate the one developed by Guiso and Paiella (2001) with the exception of father's characteristics, information which is not available in our survey. 41 In table 3 we use a dummy for living in Paris which is not statistically significant. But we also included a dummy variable for each 'département' and they were not jointly significant (results reported upon request). 42 Schubert et al. (1999) find empirical evidence of women being more risk averse. 43 We do not include in the results of table 2 both unemployment variables because the two are highly correlated and multicollinearity problems emerge.

measuring their ability to get access to the credit market. These questions are similar to those of the SHIW Italian survey [START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF]. We classify consumers as being liquidity constrained if they respond positively to at least one of the two following questions. The first indicates whether a consumer is a "discouraging borrower", the second whether he is a "turned down applicant":

-Did you renounce to finance expenditures on durable goods (main residence, cars ...) or did you renounce to restore your home because you expected that bank or other financial intermediaries will refuse the loan or the mortgage?

-Did you renounce to finance expenditures on durable goods (main residence, cars ...) or did you renounce to restore your home because bank or other financial intermediaries refused the loan or the mortgage?

In our 'DELTA-TNS 2002' survey, 481 households are liquidity constrained (20% of the sample), slightly above the average proportion reported by similar studies. The reason is that we only sample households whose head is between 35 and 55 years old [START_REF] Arrondel | Epargne, Assurance-Vie et Retraite[END_REF].

Correlation between stock prices and income risk: there is a question in the survey that asks directly to individuals: 'In your opinion, big firms fire employees when' and the options are: 'when the firm is in financial trouble' or 'when the firm wants to increase its stock market price'. If the individual responds, 'when the firm is in financial trouble', a positive correlation is assumed between the exogenous income risk and the endogenous stock market risk (ρ > 0); the correlation is negative (ρ < 0) if the individual answers 'when the firm wants to increase its stock market price' and we assume that there is no correlation (ρ = 0) when there is no answer. (1) The 54 households who are risk lovers (with negative absolute risk aversion) are dropped off the sample.

(2) See the appendix for further details about the construction of the variables.

(3) Financial wealth: household's total financial wealth in French francs.

  , 4 and 5). This finding has been subsequently corroborated by Palacios-Huerta (2001), Julliard (2004, tables 1, 2 and 4) and more recently, by Santos and Veronesi (2005, tables 1, 2A, 2B, 3 and 4). Cocco et al. (2005) perform a Carroll and Samwick's (1997) labour income variance decomposition by educational levels on PSID

  Source: 'DELTA -TNS 2002'.[START_REF] Alessie | Household Portfolios in The Netherlands[END_REF] The sample only includes households whose head is between 35 and 55 years old.(2) Direct: the household holds stocks of privatised, foreign or other firms publicly listed.(3) Direct and Indirect: the household holds equities directly (includes national and foreign stocks) and indirectly (through mutual funds).

( 4 )

 4 Income: household's annual income in French francs.(5) Income risk: standard deviation of expected income per unit of income estimated from "Patrimoine 98" using household characteristics of 'DELTA -TNS 2002'. Income is in French francs.[START_REF] Arrondel | Hypothèse du cycle de vie, diversification et composition du patrimoine[END_REF] Age: age of the head of the household.[START_REF] Arrondel | Gestion du risque et comportements patrimoniaux[END_REF] Risky asset holdings: the household holds equities either directly (includes national and foreign stocks) or indirectly (through mutual funds). (8) Low-income risk and High-income risk households are those, respectively, below and above the median of the distribution of relative income risk (σ²/y).

Table 1 : 'DELTA-TNS 2002' Households' Financial Assets (1) Financial assets

 1

	Percentage Holding the Asset
	(TNS 2002)
	(1)

Table 2 :

 2 Sample characteristics 'DELTA -TNS 2002'(1) 'DELTA -TNS 2002'. Absolute risk aversion takes value 0 for risk neutrals and 40 for the most risk averse.

				Non-Neg.		Low-	High-
		Whole sample	corr.	Neg. corr.	income	income
				(ρ≥0)	(ρ<0)	risk (8)	risk (8)
		Mean	Std. Dev.
	Continuous variables	(1)	(2)	(3)	(4)	(5)	(6)
	Financial wealth (2) (3)	169,409	1,111,641 220,190	137,804	198,642 140,177
	Income (2) (4)	202,067	256,637 204,419	200,605	234,016 170,120
	Income risk (2) (5)	11,920	12,127	11,949	11,901	11,056	12,783
	Age (6)	45	7	45	45	49	41
	Absolute risk aversion (10 5 ) (2)	29	14	27	31	29	30
	Discrete variables	% of the sample
	Risky Asset Holdings (7)	33%		27%	38%	34%	33%
	Inheritance	19%		19%	20%	22%	17%
	Inter vivos transfers and gifts
	received	52%		52%	52%	50%	54%
	Paris	16%		16%	16%	14%	17%
	Parents own risky assets	24%		22%	25%	22%	26%
	Internet	33%		31%	34%	31%	35%
	Women	15%		15%	15%	17%	14%
	Homeownership	67%		67%	67%	73%	61%
	Child (if n° of children > 0)	44%		47%	43%	23%	65%
	Liquidity constraints (2)	20%		20%	20%	15%	24%
	She has been unemployed	52%		52%	52%	43%	62%
	Working in a big firm	16%		14%	17%	16%	17%
	Relative risk aversion (CRRA):
	Non respondents	7%		8%	7%	12%	2%
	CRRA < 1	8%		22%	20%	11%	4%
	1 ≤ CRRA < 2	20%		24%	30%	21%	19%
	2 ≤ CRRA < 3.76	28%		37%	37%	19%	37%
	CRRA ≥ 3.76	37%		10%	6%	36%	38%
	Correlation between income
	risk and stock market risk: (2)
	ρ > 0 (non-positive correlation)	34%				32%	35%
	ρ < 0 (negative correlation)	62%				61%	62%
	Non-respondents	4%				6%	3%
	Discrete income risk variable
	Non-irregular income	77%		74%	78%	79%	74%
	Irregular income	20%		20%	20%	16%	23%
	Non-respondents	4%		7%	2%	5%	3%
	Education of the head of the
	household:
	No diploma or primary level	6%		7%	5%	3%	9%
	Primary or secondary level	41%		45%	39%	43%	40%
	Baccalaureate	21%		19%	21%	19%	22%
	Graduate studies	25%		22%	27%	27%	23%
	Post-graduate studies	7%		7%	7%	8%	6%
	Number of households	2,406		923	1,483	1,203	1,203
	Source:

Table A2 : Absolute Risk Aversion Estimation (1) Dependent variable Ln Absolute risk aversion

 A2 Source: 'DELTA -TNS 2002' survey and own calculations. Standard errors are in brackets. Absolute risk aversion takes value 0 for risk neutrals and 40 for the most risk averse. (1) Risk lovers are included in the OLS regression. 2088 out of 2460 answered the absolute risk aversion question. Note: The normality test of residuals has been rejected. Therefore bootstrapped standard errors are reported in brackets (based on 200 replications). No diploma is used as the reference group.

	Ln financial wealth	-0.021 (0.010)
	Paris	-0.007 (0.042)
	Women	0.086 (0.042)
	Age	0.002 (0.002)
	Child (if children > 0)	0.076 (0.032)
	She has been unemployed	-0.005 (0.028)
	Parents own risky assets	-0.044 (0.035)
	Education level of head of the household:
	Primary or secondary level	-0.094 (0.044)
	Baccalaureate	-0.122 (0.052)
	Graduate studies	-0.153 (0.054)
	Post-graduate studies	-0.280 (0.088)
	Constant	3.699 (0.156)
	Adj. R-squared = 0.0148	No. of obs. = 2088
	F ( 10, 2077) = 3.84	Prob > F	= 0.0000

Strictly speaking,[START_REF] Eeckhoudt | Putting Risk in its Proper Place[END_REF] show that 'temperance' is a household's preference property characterizing her optimal choices in a class of lotteries (zeromean independent lotteries). We are going to use it in a more general

sense.[START_REF] Andersen | Real-time Price Discovery in Stock, Bond and Foreign Exchange Markets[END_REF] A synthesis of the empirical studies documenting the rise in labor market uncertainty for most OECD countries can be found in[START_REF] Katz | Changes in the Wage Structure and Earnings Inequality[END_REF].

To consider the effect of liquidity constraints or investor horizons is beyond the scope of this short section, and is relegated to the discussion of empirical results. A good textbook treatment is[START_REF] Gollier | The Economics of Risk and Time[END_REF].

[START_REF] Kimball | Standard Risk Aversion[END_REF] shows that condition[START_REF] Arrondel | Risk Management and Wealth Accumulation Behavior in France[END_REF] holds if and only if utility exhibits standard risk aversion whenever household income risk is loss-aggravating. Utility exhibits standard risk aversion whenever it displays decreasing absolute risk aversion (DARA) and decreasing absolute prudence (DAP). A risk y is loss-aggravating when starting from initial wealth w if and only if Eu (w + y) ≥ u (w). Observe that this is equivalent to E y ≤ Ψ : Ψ is the

If we define the value function of the household evaluated at her optimal choice α as W (α) = Eu(w + α z + y c ), notice that W (α)| α=0 ≥ 0 and thus α ≥ 0 whenever cov[ z, u ] > 0 even if E z < 0 (negative risk premium):

Empirical evidence for other European countries using a homogeneous methodology are collected in[START_REF] Guiso | Stockholding in Europe[END_REF].

See the appendix for details concerning both.

The figures are comparable with those of the 'Patrimoine 1998' household survey conducted by the French National Institute for Statistics and Economic Studies (INSEE). For the 35-55 year-olds corresponding subsample, the proportion of households holding risky assets 'directly' is 21.6 and either directly or through mutual funds, 32.4. Arrondel and Masson (2003) provide a thorough description of household portfolios using the 'Patrimoine 98' INSEE household

survey.[START_REF] Bodie | Labor Supply Flexibility and Portfolio Choice in a Life-cycle[END_REF] The increased participation relative to previous studies using French data is due to the restricted age bracket sampled (i.e. between 35 and 55 year-old individuals are more likely to participate), and not to a real increase in participation as shown in

[START_REF] Arrondel | Epargne, Assurance-Vie et Retraite[END_REF].[START_REF] Bogan | Stock Market Participation and the Internet[END_REF] Assuming that five years ahead expected real income is y t+5 = y t (1 + x), then the formula of the expected variance of household income is var(y t+5 ) ≡ σ 2 y = σ 2 x y 2 t , where y t is current real income, x is the expected growth rate of real income and σ 2x its variance.

We also need that the expectation of earnings uncertainty is positively correlated with current income uncertainty. An ordered probit confirms that both variables are significantly positively correlated.

See Guiso et al. (1992[START_REF] Campbell | Understanding Risk and Return[END_REF] for further details, and[START_REF] Dominitz | Earnings Expectations, Revisions and Realizations[END_REF][START_REF] Dominitz | Estimation of Income Expectations Models using Expectations and Realizations Data[END_REF] for a reassessment of those criticisms.

In table 2, comparing columns 5 and 6 along the rows reporting the two risk aversion measures, those who are more risk averse perceive riskier incomes (see also[START_REF] Guiso | The Role of Risk Aversionin Predicting Individual Behaviours[END_REF]).

Although the percentage seems strikingly high, it is not among the 35-55 year-old households when compared with the INSEE 'Patrimoine 1998' survey (13.25%) or with the figure reported by Guiso et al. (1996) for the 1987 SHIW (15.6%).

Since those who are more likely to be liquidity constrained are also more likely to face higher income uncertainty, we control for potential endogneity problems (see next subsection).

[START_REF] Arrondel | Hypothèse du cycle de vie, diversification et composition du patrimoine[END_REF][START_REF] Campbell | Understanding Risk and Return[END_REF], 2003) show that although fixed transactions and information costs are the main determinants of stockownership, they do not explain the amount of stocks held.

SeeKing and Leape (1987, 1998) and simulated results by Cocco et al. (2005) or Haliassos and Michaelides (2003).

The Likelihhood Ratio test (LR) is distributed as a χ 2 (1) and for each different measure of income risk considered, we cannot reject the null hypothesis of no heteroscedasticity. Under the alternative hypothesis, the estimated coefficients have the same sign and are similar in magnitude.

[START_REF] Davis | Occupation-Level Income Shocks and Asset Returns: their Covariance and Implications for Portfolio Choice[END_REF] Results in Table3only refer to direct and indirect stockownership. But the sign and magnitude of the reported estimates are robust to changes in the definition of stockownership (only direct stockholders) and occupational status (subsample of only active households). They are also robust to a semi-log specification in income and financial

wealth.[START_REF] Deaton | Understanding Consumption[END_REF] A potential endogeneity bias may also explain the positive effect, if we consider the

Instruments appear individually and jointly significant, with a χ 2 (11) statistic of 33.41 and a P-value of 0.005. See also[START_REF] Robin | Modèles structurels et variables explicatives endogènes[END_REF] for further details. The results are available from the authors upon request.

There is just a qualitative question about income risk which, in tables 2 and 3, is labelled 'discrete income risk'. It is a dummy variable constructed from the survey question. The survey asks if the household perceives a regular income, an irregular one, or a mix of both. The dummy variable takes value 1 if the household either answers 'irregular' or 'a mix of both'.

We acknowledge research support from CNRS and SEEUID. The second author acknowledges financial support from the Bank of Spain. Xisco Oliver also acknowledges financial support from the Spanish Government-MYCT (Programa nacional de promocion general de conocimiento SEJ2005-08783-C04-03/econ) and from the EU RTN, under contract HPRN-CT-2002-00235 (AGE).

† CNRS-PSE (Joint Research Unit of CNRS-EHESS-ENPC-ENS)-FEDEA.

Appendix

Financial wealth: in the survey the individual is asked to say in which of the 8 predefined available brackets is her family. Since we are interested in a continuous measure we have used the simulated residual method (Gouriéroux et al., We have regressed an ordered probit of the financial wealth on some household characteristics. Once we have the estimated financial wealth a normally distributed error is added. After that, we check if the value falls inside the bracket chosen by the individual. If not, another normal error is added and so on until we predict the true interval. Doing so allows us to overcome the non-response problem for some households. If there is a missing value, the predicted value plus a normal error is directly used. The financial wealth is given in francs.

Income: for the income of the household the survey has a discrete variable of 13 brackets. The procedure described in the last paragraph to transform it into a continuous variable has been used too. Income refers to the household's annual income in French francs.

Income risk: Since the new survey has no information about different levels of income risk 39 , we use information from the 'Patrimoine 98' survey to discover the determinants of expected income risk. In the 'Patrimoine 98' survey a proxy for the subjective variance of households' income was constructed, following the methodology carried out by the Bank of Italy in 'SHIW 1989'. It asks households to distribute 100 points between different scenarios regarding the evolution of income in the next five years (see [START_REF] Guiso | Earnings Uncertainty and Precautionary Saving[END_REF][START_REF] Guiso | Income Risk, Borrowing Constraints and Portfolio Choice[END_REF] or [START_REF] Arrondel | Temperant Portfolio Choice with a Correlated Background Risk[END_REF]). We then use the estimated coefficients to predict each household's income risk, in our 'DELTA-TNS 2002' sample. Table A1 reports the estimation results.

(Table A1 here)

The estimates indicate that high income risk households earn more at work, are younger, more risk averse, have a preference for risk in financial investments, are more often unemployed, have/had health problems, tend to co-habitate rather than marry, and have children. There are 8 regional dummies to control for labour supply differences across regions, and 8 occu- (4) 0.323 (0.074) 0.324 (0.074) -Income risk (5) -0.649 (1.243) -Income risk effect: Reference values are: for occupational status "Agriculture", for familiar status "Married", CRRA ≥ 3.76, for savings preferences and probability to be unemployed "Very high" and for region "Paris".