Emmanuel Duguet
email: emmanuel.duguet@u-pec.fr.

THE EFFECT OF THE INCREMENTAL R&D TAX CREDIT ON THE PRIVATE FUNDING OF R&D: AN ECONOMETRIC EVALUATION ON FRENCH FIRM LEVEL DATA

Keywords: crédit d'impôt, évaluation, recherche et développement Classement JEL : H25, O32, O38 tax credit, evaluation, research and development JEL Classification: H25, O32, O38

Nous étudions, sur données d'entreprises, si le crédit d'impôt recherche (CIR) en accroissement a augmenté le financement privé de la recherche et développement sur la décennie 1993-2003. Afin de répondre à cette question, nous utilisons les enquêtes annuelles du Ministère de la Recherche, ainsi que les données fiscales individuelles relatives au CIR. La question principale est de déterminer si les entreprises auraient quand même augmenté leur financement privé en l'absence d'incitation fiscale. Nous utilisons une méthodologie à la Rubin. Dans un premier temps, nous étudions les déterminants de la probabilité d'obtention du crédit d'impôt recherche, c'est-à-dire le processus de sélection des participants à cette mesure. Nous trouvons que la probabilité d'obtention du crédit d'impôt recherche en accroissement augmente avec le ratio R&D/Ventes et décroît avec l'obtention de subventions à la R&D. Après avoir évalué la probabilité d'obtention du CIR de chaque entreprise nous corrigeons les biais de sélection. Dans un second temps, nous évaluons l'effet du CIR en accroissement sur le financement privé de la recherche (net de subventions attribuées par d'autres sources). Nous trouvons que, globalement, le crédit d'impôt s'ajoute au financement privé de la recherche, de sorte qu'un euro de CIR mène à un accroissement d'un peu plus d'un Euro de recherche totale. Nous trouvons également que le CIR en accroissement augmente le taux de croissance du nombre de chercheurs employés dans les entreprises.

Introduction

The many empirical studies that have been conducted in OECD countries over the past fifteen years show that research and development significantly improves the firms' performances, however measured (Kleinknecht ed, 1996;Kleinknecht and Mohnen eds, 2002).

The economic performance of a country therefore depends on its capacity to provide the right incentives to research and development (R&D) in the private sector. Unfortunately, R&D raises specific investment issues that do not always occur for physical investment. First, R&D creates information, and it cannot always be protected efficiently from competitors. Through imitation, some firms can get a part of the benefits of their competitors' investments. Second, in some specific markets, the competition focuses on innovation itself more than on the organization of production. A firm that launches a new product gets a strategic advantage. Third, the output of research is naturally random. These three elements reduce the private incentives to perform research investments compared to physical investments. If no policy measure was to be taken, firms would show a tendency to under invest in R&D [START_REF] D'aspremont | Cooperative and non cooperative R&D in duopoly with spillovers[END_REF][START_REF] Kamien | Research joint ventures and R&D cartels[END_REF].

In order to achieve higher incentives for R&D, one needs to make this activity more profitable from the firms' viewpoint. Two types of measures have been implemented: On the one hand, enforcing stronger property rights and, on the other hand, promoting financial support to R&D. The first type of measures relies on patents and brands. By forbidding imitators to get, freely, the benefits from the investments of innovators, the property rights aim to increase the gross return on R&D. This first array of policies is often not sufficient, because it is hard to apply property rights in some lines of business. Moreover, in order to protect themselves from imitation, the firms have to incur additional secrecy costs that reduce the return on R&D (Levin et al., 1987, Duguet and[START_REF] Duguet | Appropriation strategy and the motivations to use the patent system in France: an econometric analysis at the firm level[END_REF]. The second type of measure is based on R&D subsidies and R&D tax credit. Their goal is to reduce the sunk cost of R&D. Compared to subsidies, the fiscal regulations present some advantages and one drawback. Among the advantages, fiscal incentives apply equally to all the firms whatever their line of business or their size are; they also let the initiative of the technological choices to the market, that is to the consumers of the new products; moreover, they reduce the administrative burden to fulfilling a simple form. The main drawback, compared to subsidies, is that there is no selection of the R&D projects by an independent institution. Therefore, there is a higher probability that firms that did not need any public support for their R&D projects apply for the R&D tax credit. In this last case, it is difficult to predict the effect of the tax credit on the private funding of R&D.

According to a recent study [START_REF] Warda | Tax treatment of business investments in intellectual assets: an international comparison[END_REF], the practice of R&D tax credit is expanding among the OECD countries, from 12 countries in 1996 to 19 countries in 2005. This expansion of fiscal deductions raises the additional issue of fiscal competition among countries, which could influence the location of the private R&D laboratories. Therefore, in addition to the classic issue of the private incentives for R&D, the expansion of R&D tax credit could also exert an influence over the location of the future knowledge production.

In France, the R&D tax credit (« Crédit d'Impôt Recherche », CIR) was introduced in 1983.

Until 2003, it was computed on the growth of R&D investments so that only firms with a steadily increasing R&D budget could benefit fully from it. This tax credit was equal to the half of R&D growth, and was refundable when the firms paid no taxes. Since 2004, this first tax credit has been completed by a "volume" tax credit, which is a tax credit computed on the amount of R&D regardless of the R&D growth. Up to 2005, the firms located in France have a right to a refundable R&D tax credit equal to the sum of 5% of their R&D total amount and to 45% of their R&D growth. This policy direction has been extended in 2006 with 10% for the amount and 40% for the growth of R&D expenditures. It is noticeable that this "doublededuction" system now exists in several countries, even though the eligible expenditures differ from one country to another, that the tax credit is not always refundable, and sometimes even taxable (in 9 countries out of 19). Out of 19 OECD countries with a R&D tax credit, 18 countries apply a volume tax credit (the exception being the USA) and 8 countries apply a growth tax credit. Seven countries apply a "double-deduction" system but with different eligibility rules (Australia, Austria, France, Ireland, Korea, Portugal and Spain).

This tax measures also involve a revenue loss for the State. It is quite difficult to make an international comparison on this variable. For France, averaged over the decade 1994-2003, the R&D tax credit represents 465 millions Euros a year. The extension to a volume tax credit in 2004 almost doubled this figure, up to 890 millions Euros, and has strongly increased afterwards (1.5 billions Euros in 2006). For 2008, the incremental part of the tax credit has been suppressed and the firms can get 30% of their total expenditures, with an estimated cost of 4 billions Euros. From the viewpoint of the society, these fiscal deductions are interesting only as far as they really increase the private R&D investments. The fact that they are taken on public funds (exactly like subsidies, from a public finance viewpoint) calls for the evaluation of this fiscal measures. This first motivation can be reinforced by noticing that, for France, its budget cost has considerably increased and, more generally, that these measures have been extended to larger number of innovating countries.

The public support to R&D faces the following evaluation problem. Two situations can occur when a tax credit is granted. On the one hand, a firm can integrate the tax credit into its investment decision process and decide to invest more because the deduction exists (i.e. because the price of R&D is lower with the tax deduction). But, on the other hand, it is possible that a firm does not account for this measure at the investment decision stage, realize afterwards that it has the right to a tax deduction, and asks for it in order to increase its profit. In the former case, the tax measure has the expected effect, while in the latter case it has no effect at all on private R&D. At the firm level, it is likely that both situations occur, therefore we wish to evaluate the average effect of the measure, in order to know whether the positive effects dominate or not.

An important point when performing the evaluation is to consider a period with no policy change on the R&D tax credit at all. For this reason, we have restricted our data to 1993-2003, where the R&D tax credit is computed on the same eligible expenditures, on the growth of R&D, with a flat rate of 50%, refundable and not taxable.

Data sources and sample statistics

An interesting quality of our data set is that it includes true fiscal data at the firm level and not a theoretical computation of firms' rights. It is important since all firms that could apply to the R&D tax credit do not apply for it in practice.2 This feature of the data allows to define a control group and to apply the Rubin methods explained below. This would not be possible without such data since a theoretical computation would allocate a tax credit to all firms with a R&D growth. Here, among firms with a positive R&D growth, we can separate firms that get a tax credit from the other firms.

Data Sources

The data comes from three different sources:

the « enquêtes annuelles d'entreprises » (yearly firm census) provide information on the accounting data (sales, line of business) ;

-

The R&D survey is collected by the Ministry of Research and provides information at the firm level on R&D, and especially the amount of subsidies from all the ministries. Matching with this data set is important because it allows to correct the R&D amounts from subsidies and to determine the part of R&D expenditures that is privately funded;

-

The tax credit (CIR) file is collected by the fiscal administration (Direction Générale des Impôts). It is not a survey; it is exhaustive and includes the amount of tax credits granted at the firm level. 3 It allows to perform a study on the real recipients of the tax credit and to remove the bias related to self-selection.

We use the Frascati (OECD, 2002) definition of R&D provided by the R&D survey. Our main performance variable is computed from the private funding of R&D that we define as the difference between the total R&D expenditures on the one hand and the sum of all subsidies and tax credit on the other hand. It represents the amount of R&D actually paid by the firm. We also use data on R&D personnel in order to examine the robustness of our results.

In order to evaluate the effect of the R&D tax credit on the growth rates of the private funding of R&D, we have matched our samples by couple of years over the period 1993-2003. 4 This convention insures that there remain a large number of firms in the sample. 5 After these operations, we have 10 samples covering the two-year periods 1994-1993 to 2003-2002. A description of the samples is provided in Table 1. The samples include between 1133 and 1645 firms each year, in all lines of business (including services). Approximately 20% of the firms benefit from the tax credit alone or from a subsidy only and 7% benefit from both a subsidy and the tax credit. Over the decade, between 50% and 60% of the firms have benefited neither from a subsidy nor from a tax credit. 6 This point is important because the evaluation relies on a comparison between the recipients and the other firms. In the evaluation literature, the nonrecipients represent the reservoir from which we extract the counterfactuals [START_REF] Rubin | Matched sampling for causal effects[END_REF]. The size of this reservoir seems reasonable.

The amounts of public supports to private R&D are reported in Table 2. As expected, the R&D subsidies represent the most important amounts, while the R&D tax credit reach 10% of the support given to firms. This is related to its incremental nature. However, it is important to keep in mind that these are not the same firms that get these two kinds of public support. The R&D tax credit, by its fiscal nature, is open to all the firms. It is often argued that the firms do not have the same size depending on they benefit from subsidies or from the tax credit. Figure 1 shows the median size of the recipients depending on the R&D support that has been granted.

Figure 2 present the corresponding average size. We find that while the median size does not differ between the two R&D mechanisms (a median of about 300 employees), there is a strong difference in the average size. The difference between these two measures comes from the biggest firms that are more present among the subsidy recipients.

The average size is around 500 employees for the tax credit recipient and around 2500 employees for the subsidy recipient. A part of this difference can be attributed to the fact that, over this period, the tax credit is computed on the growth of R&D, and that the higher the level of R&D the harder it is to make it grow. The comparison of these two figures also confirms that the tax credit is more favorable to the small and medium sized firms. 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Subsidy CIR Both None

Sample Statistics

In a first step, we will simply perform a comparison of the average growth rate of private R&D, in order to assess the descriptive effect of the tax credit. Two types of comparisons can be made. A first comparison, "static", compares the growth rates of the private funding of R&D depending on the mechanism of the recipients benefit from. A second comparison, "dynamic", examines the same growth rates, depending on the position of the firm inside the tax credit mechanism. Four cases are possible: no tax credit for two years, tax credit during two years, entry into the tax credit and exit from the tax credit mechanism.

The static comparison is presented in Table 3. We find, as expected, that the firms that benefit from the tax credit have the strongest growth rate, partly because it is attributed on that basis (and not fully, because subsidies are deducted from the eligible R&D). Then come the firms that got both the tax credit and the subsidies. The lowest growth rates have been achieved

by the firms that received subsidies alone and the firms that benefited no support.

Our definition of private R&D excludes both subsidies and the tax credit; therefore a zero growth rate for the private R&D variable means that the R&D tax credit would be efficient since it involves that the firms have not reduced their private R&D when they have benefited from the tax credit. In this case, the total R&D expenditures increases by the amount of tax credit granted. When the effect is positive, there is a multiplier effect, the total R&D increases by more than the amount of tax credit granted.

However, this first comparison suffers from a serious limitation. It does not allow seeing the effect of the tax deduction since what really matters is how the firms change their behavior when they get the public support. It is why we insist on the dynamic comparison.

The dynamic comparison is performed in Table 4. Here we examine how the growth rate of private R&D is affected when the firms enter or exit the tax credit mechanism. The variation of the growth rates should be a better proxy for the R&D tax credit than their levels, even though we are conscious that there remains a selection bias issue. An incentive effect of the measure would involve that the private R&D does not decrease when a firms enters the mechanism.

The dynamic comparison shows that the firms that enter the tax credit mechanism maintain a significant growth rate of their private R&D expenditures, which is often above 10%. The firms that enter in or exit from the mechanism do not behave significantly differently from the non recipients. Overall, we find that the firms add exactly the tax credit to their private funding when they enter the mechanism, and add more than the tax credit to their private funding when they stay inside the mechanism.

The "naïve" estimator and a critic of sample statistics

The "naïve" estimator is defined as the difference of means. Its definition comes from the fact that this estimator is the one we should use on experimental data. The result is clear-cut: over all the decade the firms that have benefited from the R&D tax credit had a stronger growth rate of their R&D tax credit, except in 2000-2001 which corresponds to the burst of the dot-com bubble.

In practice, R&D data are not experimental and are affected by selection biases. The firms that get the R&D tax credit do not have the same characteristics that the firms that get it, and if these unbalanced characteristics are correlated to our performance variable, we should expect a bias when comparing the mean performances of the recipients to the mean performance of the non-recipients. This difference is given in Table 5.

Another critic is related to the type of tax credit that is given: when the tax credit is computed on the growth of R&D, the firms that do not experience a growth of their R&D are not eligible to the tax credit. Therefore comparing the recipients with all the non-recipients is less relevant. Indeed what we would like to measure is the difference the R&D investment the firms have made and the R&D investment they would have made without the policy measure.

For this, we need a counterfactual computed on the firms that did not benefit from the policy measure but the right counterfactual set seems to be the set of firms that have experienced a growth of their R&D expenditures and did not ask for the tax credit. 7 In this paper, we will account for that critic by reporting the results restricted to the firms with a positive growth of R&D.8

Methodology

In order to measure the effect of CIR, one should evaluate the difference between the performance that a firm achieved with the CIR and the performance the same firms would have achieved without this mechanism. The latter quantity is called the counterfactual. There are many ways to estimate a counterfactual. In this paper, we consider two families of methods:

standard regression analysis and matching methods. Among the latter we distinguish kernel matching and the weighted estimator.

Let i , 1

y the performance (i.e., the growth rate of private R&D) of firm i when it benefits from CIR and i , 0 y its performance when it does not. The evaluation problem comes from the fact that we cannot observe both quantities at the same time. Either we observe i 1 y when the firm benefits from CIR or we observe i 0 y when it does not. The observable data is therefore:

( ) i 1 i i 0 i i y T y T 1 y + - = with    = otherwise 0 CIR from benefits i firm if 1 T i

Regression methods

The simplest method is the naïve estimator that takes the difference of the average performance of recipients and non-recipients. Technically this reduces to perform an OLS regression of the performance on the intercept and a CIR dummy variable (equal to 1 for 7 The lack of information and the fear of a fiscal control are often used to explain such behavior.

recipients, 0 for the other firms). The OLS coefficient of the CIR dummy variables gives the difference of the mean performances in both groups:

∑ ∑ ∈ ∈ - = 0 1 I i i 0 I i i 1 y N 1 y N 1 c ˆ
where 1 I is the index set of recipients (number: 1 N ), and 0 I the index set of non-recipients (number 0 N ).This is the « naive » estimator.

A second method extends the previous model by adding explanative variables i X into the previous regression. The model becomes:

i i i i u T c b X a y + + + = .
where i u is the usual disturbance. From this model, we get the two cases: 0 T i = , with an expected average performance ( )

, b X a 0 T y E i i i + = =
and 1 T i = , with an expected average performance ( )

c b X a 1 T y E i i i + + = =
This implies that the effect of CIR for the individual i is equal to:

( ) ( ) c 0 T y E 1 T y E i i i i = = - = .
Compared with the naïve estimator, this regression allows dropping from the evaluation the part that is attributable to the explanative variables i X .

But, strictly speaking, the previous estimators are not fully consistent with the evaluation problematic. A third regression method is more rigorous. We assume that there are two equations corresponding to each of the potential outcome, so that:

i 0 0 i 0 i 0 u b X a y + + = and i 1 1 i 1 i 1 u b X a y + + = ,
And the observable performance is:

( ) ( )( ) ( ) i 1 1 i 1 i i 0 0 i 0 i i 1 i i 0 i i u b X a T u b X a T 1 y T y T 1 y + + + + + - = + - = ,
After some simplification, we get:

i 3 i i 2 i 1 i 0 i u X T T X y + β + β + β + β = ,
which implies that one should estimate a model with the cross product of the explanative variables and the CIR dummy. Moreover, if the variables i X are centered, we can show that the coefficient of the CIR dummy, 2 β , measures the average effect of the tax credit on the performance. 9

The results produced with the standard regression methods are presented in Table 6. The simple OLS regression method, depending on the year, give results that vary between no effect of the CIR on private R&D (in 2000-2001) and an important effect of +11,4%. The effects are globally lower than the ones obtained with the naïve estimator (up to +12.2%), which shows that the explanative variables explain a part of the growth difference between the recipients and the non-recipients. When we include the cross products of the explanative variables with the CIR dummy we get an effect that varies, depending on the year, between 0 and +10.4%, which

shows that the cross product themselves explain a part of the performance differences between the recipients and the other firms.

Overall, the growth rate gap of private R&D remains in favor of the CIR recipients. The standard OLS regression fails to control for all the differences between these two groups of firms.

Qualitatively, these first results indicate that the effect of CIR would vary between a simple addition effect of CIR and private R&D (so that the measure is just efficient), and a multiplier effect of CIR on private R&D (so that firms would increase their R&D expenditures by more than the amount of the CIR). But it is well known the regression estimators can suffer from selection biases, therefore we turn to the matching methods.

Methods that account for the selection bias

The "evaluation methods" are the most important in this paper since the naive regression methods do not account for the fact that the individuals are not comparable in the recipient and the non recipient groups. We follow the propensity score approach initiated by Rosenbaum andRubin (1983, 1985) and surveyed in Lee (2005) and [START_REF] Rubin | Matched sampling for causal effects[END_REF]. We aim to estimate the three following parameters:

( )

0 1 y - y E c =
, the average effect of the treatment, 9 The structure of this model also implies that the disturbance of the model is heteroskedastic since the disturbance is different depending on 0 T i = or 1 T i = . We account for this property in our estimations.

( )

1 T | y - y E c 0 1 1 = =
, the average effect of the treatment on the treated;

( )

0 T | y - y E c 0 1 0 = =
, the average effect of the treatment on the not treated.

These three quantities are related by the following relationship:

0] Pr[T c 1] Pr[T c c 0 1 = + = = .
Following [START_REF] Rubin | Estimating causal effects of treatments in randomized and non-randomized studies[END_REF] and Rosenbaum andRubin (1983, 1985), we make the conditional independence assumption:

( ) ( ) ( ) X 1 T P T y , y X T y , y 1 0 1 0 = ⊥ ⇒ ⊥
The intuition of this result is the following: if two firms have the same probability to get the CIR, and the first firm does have it while the other has not, then the allocation of CIR can be considered as random between these two firms, and we can use the second firm as a counterfactual for the first firm.

Estimation of the average effect on the treated c 1 . We consider the CIR recipients and, for each of them, we estimate the performance they would have had without the CIR. In practice, we compare the performance of the CIR recipient with the average performance of the non recipients that have the same probability to get the CIR. In this paper, we use the method of Heckman, Ichimura and Todd (1998). The average performance that the CIR recipients (

1 I i ∈ )
would have had without the CIR is estimated by:

[ ] [ ] 1 I j I j i j j i j i , 0 I i , h / ) p p ( K y h / ) p p ( K y ˆ0 0 ∈ - × - = ∑ ∑ ∈ ∈
Where K(.) is a Gaussian kernel, h the rule-of-thumb window and i p ˆ the estimated probability to get the CIR for the firm i. Symmetrically, the performance that the non recipients

( 0 I i ∈ ) would have had if they had benefited from CIR is estimated by: [ ] [ ] 0 I j I j i j j i j i , 1 I i , h / ) p p ( K y h / ) p p ( K y ˆ1 1 ∈ - × - = ∑ ∑ ∈ ∈
, Therefore, the average effect of CIR on the treated is defined as:

{ } ∑ ∈ - = 1 I i i , 0 i , 1 1 1 y ŷ N 1 c ˆ,
the average effect on the not treated by:

{ } ∑ ∈ - = 0 I i i , 0 i , 1 0 0 y y N 1 c ˆ,
and the average effect on the whole population by:

{ } { }         - + - + = ∑ ∑ ∈ ∈ 1 0 I i i , 0 i , 1 I i i , 0 i , 1 1 0 y ŷ y y N N 1 c ˆ.
The standard errors of these statistics are complicated to write, so that we use the bootstrap method with 1500 repetitions (including the Probit step for i p ˆ).

The weighting approach, surveyed in Lee ( 2005), uses the same assumptions than kernel matching, but merely expresses the non observable sample moments by their observable counterparts, and replaces them by the corresponding empirical moments. We get the following results:

Effect of the treatment on the not treated:

∑ = -         -       = N 1 i i i i 1 0 0 1 p T y N N N 1 c ˆ
Effect of the treatment on the treated:

∑ = -         - -       = c N 1 i i i i i 1 1 1 p 1 p T y N N N 1 c
Effect of the treatment on the whole population:

( ) ∑ =         - - = N 1 i i i i i i p 1 p ˆp T y N 1 c ˆ
Where i p ˆ is the estimated value of the propensity score for the individual i, N the number of firms in the common support, 0 N the number of not treated firms in the common support and 1 N the corresponding number of treated firms. The variances of theses estimators must be corrected to account for the estimation of the Probit model in the first step, but it can be determined by the delta method. The details are given in appendix.

It is possible that the regression methods give inconsistent estimators because the CIR is not distributed at random to the firms. As for all policy measures, there are attribution procedures that determine who is eligible. This creates differences between the sample of recipients and the other firms and, provided that these differences are correlated with the performance measure, the OLS regression estimates can be inconsistent. It is therefore desirable to "balance" the covariates so that the firms are comparable. In practice, this creates an incentive to match each recipient firm to the non-recipient firms that share the same value of the observable covariates.

There are many matching methods in the literature. In this paper, we follow the approach by Rosenbaum andRubin (1983, 1985), and match our firms on the propensity score, which is simply the probability to get the CIR.

The intuition of this theoretical result is the following: if two firms have the same probability to get the CIR, that the first one got it and the second one did not, everything happens as if the CIR was allocated at random among these two firms. Therefore, for each recipient, we look for all the non-recipients that have the same probability to get the CIR and then we compute the difference between the performance of the recipient and the average performance of the other firms (the counterfactual). These operations are performed for all the recipients, and the effect of CIR is given by the average of all these differences (i.e., the "effect on the treated").

The same method can be used to determine the potential effect of CIR on the firms that did not get it. One just needs to match each non-recipient firm with the recipients that have the same probability to get the CIR.

The only problem that remains is therefore to estimate the probability to get the CIR. We estimate a Probit model and use the predicted probabilities. 10 Notice that the replacement of the true probabilities by the estimated probabilities implies to modify the way to compute the Student statistics. We have used the bootstrapped Student statistics to account for it. The last point is to make sure that the probabilities between the recipients and the non-recipients have a sufficient overlap so that we compare firms with similar probabilities. We have used the common support of the predicted probabilities to fix this problem.11

Last, notice that this method is related to the instrumental variable method in the following way. The estimation relies on the estimated probabilities to get the CIR, and these estimated probabilities depend on instrumental variables only (mostly lagged variables in our application).

In our application, we have applied three different estimation methods on the common support of the CIR probabilities:

-the OLS regression methods, so as to see what is the influence of changing the data set by dropping the extreme probabilities;

-The kernel matching method (Rubin approach). It allows for distinguishing the effect on the treated from the effect of the non-treated;

-The weighted estimator (or "moment estimator"), which is equivalent to kernel matching but much faster to compute since it replaces the bootstrap method by the delta method (see the appendix).

The Rubin methodology implies to drop some observations from the sample when the probabilities take extreme values (close to 0 or to 1). The estimations are performed on the common support of the estimated CIR probabilities. Therefore, if we wish to compare this method with the OLS regression methods, we should do it on the same sample, on the common support, so as to make sure that the differences comes from the method itself and not from a sample difference only.

Table 7 presents the OLS regression methods on the common support. We do not find important differences with the regressions over the whole sample, so that the difference of samples cannot be advocated to explain difference of results among the standard and Rubin methods.

Empirical strategy

A problem specific to the tax credit systems computed on the growth of R&D comes from the fact that our performance variable is correlated to the attribution conditions. Therefore we cannot use the standard method without caution. There are two ways to tackle that problem:

-First, one can restrict the analysis to the firms that have a positive growth rate of their R&D. This is because only these firms are eligible and it should improve on the quality of the matching. This is only possible however because some firms that have the right to the tax credit do not ask for it.

-Second, one can use another variable than the growth rate of R&D. We need a variable that is both related to the R&D effort and not to a "short-run" effect caused by the CIR. We use the growth rate of the (full-time) number of researchers. Indeed, the researchers are the ones that hold the knowledge of the firm, so that the firms should be reluctant to hire or lay-off researchers just to benefit from a short-run tax deduction. The number of researchers is an essential input of the innovation process so that is should be a good indicator of the "real" innovation policy of the firm. Keeping the researchers inside the firm avoids the dissemination of knowledge to competitors and many studies show that the firms care about this issue (Levin et al., 1987, Duguet and[START_REF] Duguet | Appropriation strategy and the motivations to use the patent system in France: an econometric analysis at the firm level[END_REF].

We have also tried instrumental variables methods (not reported) but their results were similar to those of the standard regression methods, and often gave a stronger effect of CIR on the growth of private R&D.

In order to measure the effect of CIR on private R&D, we use the following empirical strategy:

-Estimators over the whole sample;

-Estimators restricted to the firms with a positive growth rate of private R&D;

-Estimators on the growth rate of the number of researchers.

Multipliers computation

There are two ways to compute the tax credit multipliers in the literature: first, one divides the tax credit amount by the amount of R&D the firms would have made without it (impact of the tax credit on R&D); second, one divides the incremental amount of R&D performed under the tax credit by the amount of tax credit distributed (additional number of Euros of R&D for one Euro of tax credit distributed). This section writes the explicit relationships between our estimates and these two kinds of multipliers. We need the following notations:

-1 c denotes the effect on the treated; -0 R is the amount of R&D that would have been invested without the CIR and 1 R is the amount of R&D that would have been invested under the tax credit.

-We have the following relationship between these quantities:

( ) 0 1 1 0 0 1 1 R c 1 R R R R c + = ⇔ - = .
-"R" denotes the private R&D expenditures.

-The R&D subsidies have been subtracted from all our measures of R&D (private and total) so that we really measure the net effect of the tax credit on R&D.

R&D expenditures multipliers

All our multipliers are computed on the subset of CIR recipient firms, since there is no direct effect on the others by definition. This is a significant difference with aggregated data where total R&D usually refers to country R&D and therefore includes the non recipients.

Private R&D expenditures multiplier

Consider first the private R&D multiplier. With the tax credit, a firm invests 1 R while without it, the same firm would have invested (

)

1 1 0 c 1 / R R + =
, therefore the private R&D multiplier is equal to:

1 1 1 1 P c 1 c 1 R R m + =         + = ,

Total R&D expenditures multiplier

Consider now the total R&D multiplier. The total R&D of a recipient firm is equal to CIR R 1 + under the tax credit, while it is ( )

1 1 0 c 1 / R R + =
without it. The total R&D multiplier is therefore equal to:

( )( ) 1 1 1 1 1 T R / CIR 1 c 1 c 1 R CIR R m + + =         + + = ,
In this paper, we present the mean value of this multiplier over the sample, which gives:

( )(
)

1 1 T R / CIR 1 c 1 m + + =

Tax credit multipliers

Private R&D tax credit multiplier

The variation of private R&D induces by CIR is equal to:

, R c 1 c c 1 R R R R 1 1 1 1 1 1 0 1 + = + - = - so that the multiplier equals: CIR R c 1 c CIR R R M 1 1 1 0 1 P + = - = .
We estimate it at the mean point of the sample by:

      + = CIR R c 1 c M 1 1 1 P ,

Total R&D tax credit multiplier

The variation of total R&D induced by the CIR is equal to:

CIR R c 1 c R CIR R 1 1 1 0 1 + + = - +
So that the multiplier equals:

P 0 1 T M 1 CIR R R CIR M + = - + = .

Results

In a first subsection, we report the determinants of the probability to get the CIR and, in a second subsection, we comment on the evaluation.

The probability to get CIR

The main determinant of CIR is its lagged value (Table 8). This result illustrates the importance of the dynamic comparison reported in Table 4. But other variables also influence the probability to get the CIR: the R&D/sales ratio increases the probability to get the tax credit and the benefit from R&D subsidies reduces it. In the latter case, there could be a mechanical effect coming from the fact that the R&D subsidies are not eligible to the tax credit. Finally, we also find that some lines of business use more the tax credit on some years, but we do not find time persistence on this point. This could come from the fact that the tax credit is more open to firms than R&D subsidies.

A second interesting result is the small number of significant explanative variables in the Probit regressions. This also suggests that entry into the tax credit mechanism is more open than for R&D subsidies [START_REF] Duguet | Are R&D subsidies a substitute or a complement to privately funded R&D? An econometric analysis at the firm level[END_REF]. In order to test the robustness of this result, we have also run the Probit regressions without the lagged tax credit variable (not reported). We find that the most important determinant of the probability to get the tax credit is the R&D/sales ratio.

Therefore the R&D tax credit is directed toward the firms that allocate the biggest part of their sales to R&D. This selection of recipients certainly explains for a good part, the results of the evaluations that follow.

The effect of CIR

The kernel matching and weighting methods provide similar results (Table 9). We comment mostly on the weighting estimators because they provide smaller standard errors.

The estimation on the recipients represents the evaluation strictly speaking (the « effect on the treated »): we seek to estimate the effect of the tax credit on the firms that have indeed benefited from it, and not on the whole sample of R&D performers. The basic results show a multiplier effect on 6 years out of 10, and an addition effect for the 4 remaining years.

The estimation on the sample of firms that have not benefited from the tax credit represents the effect the CIR would have had if it has been extended to more R&D firms. We find that the potential effect of the tax credit on this subsample of firms is weaker than on the recipients since we find a multiplier effect for 1 year and an addition effect on 9 years. However, we do not find a (firm-level) « crowding-out » effect.

However, these first estimates must be taken with caution. Since the tax credit is incremental, we could think that the standard evaluation procedure overestimates the effect of CIR on the growth rate of private R&D. Therefore, we also present the estimation, with the same methodology, on the subsample of firms that had a positive growth rate of their private R&D and, despite of this, did not ask for CIR. The results, reported in Table 10, should represent a lower bound of the effect of the tax credit. This « lower bound » shows an addition effect for all the 10 years. According to it, the firms would add the tax credit to their private funding so that there would be no « crowding out » effect.

It is possible to convert the results reported in Tables 10 and11 into multipliers of the total R&D expenditures. Since the study is performed over ten couple of years, we comment on the average value (Tables 11 and12).

The estimations based on the total sample (Table 10) indicate that the CIR would have increased private R&D by 7.9% (Table 11, multiplier 1.079) and total R&D (with the CIR) by 11.2%. The effect would thus be important on the recipients. When we restrict the analysis to the firms that have increased their private R&D (Table 11), the corresponding effects would be between 0% (unit multiplier), a simple addition effect, and the total R&D would have increased by 3.2% only.

A common practice expresses the multipliers as a function of CIR itself. Over the whole sample (Table 10) we find that 1 Euro of CIR would generate 2.33 Euros of private R&D that is 3.33 (=1+2.33) Euros of total R&D (Table 12). When we restrict the analysis to the positive growth rates (Table 12) we find a more pessimistic result that 1 Euro of CIR would not generate any Euro of private R&D, so that 1 Euro of CIR would generate 1 Euro of total R&D. However, since our evaluation is a short-run one (one year), this figure is in fact rather high.

Testing the robustness of our estimators: the number of researchers

A basic reason that may reduce the trust that we have in the previous estimates is the incremental nature of the R&D tax credit. We reply to this critic by proposing the following robustness test. The R&D performers may have an interest in asking for tax deductions even when they do not need it, but the same R&D performers have no interest in letting their knowledge leak out for free to their competitors. Therefore, if they do not use the R&D tax credit for research, we should see no R&D personnel variations. We use growth rate of the number of researchers, in equivalent full time, since they are the holders of the firm's knowledge. The results are reported in Table 13. We find that, over the whole population, the R&D tax credit is always associated to positive growth of the number of researchers, varying between 7.5% and 12.6% depending on the couple of years. If we restrict our analysis to the firms that had a positive growth rate of their private R&D, we find a positive effect 5 years out of 10 (from 6.6% to 10%) and no effect on five years. These results suggest that the R&D performers would use the incremental R&D tax credit in order to invest in R&D.

Conclusion

We find that the incremental R&D tax credit benefits to a different population of firms than the ones that benefit from subsidies. The tax credit recipients have a smaller size and a high R&D to Sales ratio. This confirms the view that the tax measures favor equality among the innovative firms.

Applying methods that control for selection biases, we find that the incremental R&D tax incentive is effective, since it is associated both to a growth of the private funding of R&D (or adds to it), and to a growth of the number of researchers on most years.

However, the results in this study apply to the incremental tax credit only, which is based on the growth of the privately funded R&D. It does not seem to be extendable to other form of tax mechanism, since they apply to a different population of firms (larger, especially). New research should be done in order to evaluate the reforms that have been taken place in France since 2004.

Appendix: Estimation of the variance of the weighting estimators

Slightly extending the analysis in [START_REF] Crépon | Innovation, emploi et performances[END_REF], we write the three estimators under the following form:

( )

∑ = = θ N 1 i i i b ĝ y N 1 ˆ
where b ˆ is the estimated parameter from the Probit model. Using the delta method, we can estimate the variance of our estimate by: ( ) ( )

∑ = ϕ - ϕ = θ N 1 i 2 i N 1 V ˆ with ( ) ( ) ( ) ( ) b ŝ N b Ĵ b ' b g y N 1 b ĝ y ˆi 1 N 1 i 1 i i i i i - = ∑       ∂ ∂ + = ϕ where ( ) ( ) ( ) ( ) , b b , X T f ln b s , b , X T ' b b f ln E b J i i i 2 1 ∂ ∂ =       ∂ ∂ ∂ - = and ( ) ( ) ( ) ( ) ( ). b X 1 ln T 1 b X ln T b , X T f ln i i i i i i Φ - - + Φ =
Notice that these formulas are valid for any binary model estimated by the maximum likelihood method, provided that one replaces ( )

b X i Φ Φ by ( ) b X F 1 i - -
where F(.) is the cdf of the disturbance of the new model (or by ( ) 1994-1993 1995-1994 1996-1995 1997-1996 1998-1997 1999-1998 2000-1999 2001-2000 2002-2001 2003-2002 Coeff 1994-1993 1995-1994 1996-1995 1997-1996 1998-1997 1999-1998 2000-1999 2001-2000 2002-2001 2003-2002 Coeff 1994-1993 1994-1993 1995-1994 1995-1994 1996-1995 1996-1995 1997-1996 1997-1996 1998-1997 1998-1997 Coeff 1999-1998 1999-1998 2000-1999 2000-1999 2001-2000 2001-2000 2002-2001 2002-2001 2003-2002 2003 We use the Probit regressions reported in Table 8 for the matching and the weighting. In both cases we consider the firms belonging to the common support of the treatment probability. We report the effect of the CIR on the growth rate of the private funding of R&D. ** significant at 5%. *significant at 10%. 1994-1993 1995-1994 1996-1995 1997-1996 1998-1997 1999-1998 2000-1999 2001-2000 2002-2001 2003 We use the Probit regressions reported in Table 8 for the matching and the weighting. In both cases we consider the firms belonging to the common support of the treatment probability. We report the effect of the CIR on the growth rate of the private funding of R&D.. ** significant at 5%. *significant at 10%. 1994-1993 1995-1994 1996-1995 1997-1996 1998-1997 1999-1998 2000-1999 2001-2000 2002-2001 2003 On the positive growth rates (Table 11) :

b X F i if the distribution is symmetric).
Weighting estimator 0,011 -0,503 0,525 1,011 0,497 1,525

Kernel matching estimator 0,119 -0,436 0,675 1,119 0,564 1,675 *We use the weighted average of the effects over the period 1994-2003, where the (optimal) weight is equal to the inverse of each estimator's variance.

Table 13: Effect of the R&D tax credit on the growth rate of the number of researchers

We use the Probit regressions reported in Table 8 for the weighting estimator. The « performance variable » is the growth rate of the number of researchers (in full-time equivalent). We consider the firms belonging to the common support of the treatment probability. ** significant at 5%. *significant at 10%. -1993 1995-1994 1996-1995 1997-1996 1998-1997 1999-1998 2000-1999 2001-2000 2002-2001 2003

1994

Figure

  Figure 1 -Median number of workers depending on the R&D support mechanism

Figure 2 -

 2 Figure 2 -Average number of workers depending on the R&D support mechanism

Table 1 : Public Support to Private R&D

 1

				Both
	Year	Subsidy Alone	Tax Credit Alone	Subsidy and Tax	No Public Support	Sample size
				Credit
	1994	21,1%	19,5%	8,6%	50,9%	1553 (100%)
	1995	19,1%	18,4%	7,4%	55,1%	1645 (100%)
	1996	19,5%	16,7%	7,0%	56,9%	1639 (100%)
	1997	18,8%	17,3%	6,1%	57,9%	1570 (100%)
	1998	20,1%	17,2%	6,3%	56,3%	1482 (100%)
	1999	20,1%	17,2%	7,1%	55,5%	1491 (100%)
	2000	20,0%	17,6%	8,5%	53,9%	1213 (100%)
	2001	16,8%	19,1%	7,9%	56,2%	1133 (100%)
	2002	17,0%	18,3%	6,5%	58,1%	1299 (100%)
	2003	17,6%	16,7%	5,8%	59,8%	1542 (100%)

Table 2 : Amount of Public Support to R&D

 2

	Year	Subsidies	Tax Credit	Total*
	1994	94,8%	5,2%	2 292 (100%)
	1995	92,5%	7,5%	2 045 (100%)
	1996	92,0%	8,0%	1 542 (100%)
	1997	90,2%	9,8%	1 253 (100%)
	1998	88,4%	11,6%	1 207 (100%)
	1999	91,1%	8,9%	2 083 (100%)
	2000	93,1%	6,9%	1 727 (100%)
	2001	87,7%	12,3%	1 573 (100%)
	2002	90,5%	9,5%	1 901 (100%)
	2003	90,3%	9,7%	1 194 (100%)
	Notes *In millions Euros, computed on the sample

Table 3 : Static comparison of the growth rates of the private funding of R&D

 3

	* Significant at the 5% level
		Subsidy	Tax Credit (CIR)	Both	None
	1993-1994 Average	-11,5%	-6,3%	0,9%	-18,3%
	Student	4,99*	3,07*	0,29	12,71*
	1994-1995 Average	3,2%	11,6%	9,1%	2,9%
	Student	1,72	6,46*	3,31*	2,91*
	1995-1996 Average	0,6%	6,8%	3,3%	1,1%
	Student	0,31	3,54*	1,15	1,05
	1996-1997 Average	-1,6%	9,7%	7,2%	2,3%
	Student	0,89	5,19*	2,31*	2,34*
	1997-1998 Average	1,6%	10,3%	2,4%	1,0%
	Student	0,83	5,53*	0,65	0,93
	1998-1999 Average	-2,1%	10,5%	8,6%	0,2%
	Student	0,84	4,21*	1,83	0,13
	1999-2000 Average	-0,3%	6,9%	3,1%	-1,1%
	Student	0,12	2,84*	0,68	0,74
	2000-2001 Average	6,5%	6,6%	8,1%	3,9%
	Student	2,15*	2,58*	2,18*	2,11*
	2001-2002 Average	0,0%	11,5%	1,0%	-1,4%
	Student	0,00	5,24*	0,22	0,92
	2002-2003 Average	-2,6%	8,1%	-1,2%	-1,8%
	Student	0,88	3,28*	0,32	1,32

Table 4 : Dynamic comparison of the growth rates of private R&D

 4 * Significant at the 5% level. * Significant at the 10% level.

		(Tax credit in t-1, Tax credit in t)	Entry inside the tax credit mechanism	Exit from the tax credit mechanism
			Growth rates		Difference of growth rates	Difference of growth rates
		(Out,				(Out,In)-		(In,In)-
		Out)	(Out, In) (In, Out) (In, In)	(Out,Out)	Student	(In,Out)	Student
	(1993,1994) -0,162	-0,131	-0,168	-0,015	0,032	0,77	0,154	4,27**
	(1994,1995)	0,028	0,079	0,042	0,119	0,051	1,56	0,077	2,43**
	(1995,1996)	0,010	0,054	0,006	0,059	0,044	1,16	0,054	1,60
	(1996,1997)	0,010	0,026	0,040	0,118	0,016	0,52	0,078	2,40**
	(1997,1998)	0,009	0,032	0,032	0,103	0,023	0,64	0,070	1,82*
	(1998,1999) -0,004	-0,004	-0,006	0,164	0,000	0,01	0,170	4,32**
	(1999,2000) -0,015	-0,012	0,040	0,088	0,004	0,10	0,048	1,03
	(2000,2001)	0,047	0,003	0,030	0,098	-0,043	1,12	0,068	1,39
	(2001,2002) -0,012	0,010	-0,001	0,122	0,022	0,55	0,123	3,08**
	(2002,2003) -0,018	-0,006	-0,036	0,085	0,012	0,31	0,120	2,65**

*

Table 5 : Global comparison of the average growth rates of the private funding of R&D

 5

		Tax credit recipient	Non recipient	Difference	Student
	1993-1994	-0,041	-0,163	0,122	5,80*
	1994-1995	0,108	0,030	0,079	4,52*
	1995-1996	0,058	0,010	0,048	2,60*
	1996-1997	0,090	0,013	0,077	4,22*
	1997-1998	0,081	0,012	0,070	3,59*
	1998-1999	0,099	-0,004	0,104	4,10*
	1999-2000	0,056	-0,009	0,065	2,53*
	2000-2001	0,070	0,045	0,025	0,97
	2001-2002	0,087	-0,011	0,098	4,07*
	2002-2003	0,057	-0,020	0,077	3,14*

* Significant at the 5% level.

Table 6 :

 6 Regression methodsAll the explanative variables are lagged one year. The left-hand variable is the growth rate of the private funding of R&D. The explanative variables are: log of the private funding of R&D, log of sales, log of total R&D to sales ratio, export dummy, export rate, 2-digit activity dummy. The standard errors are robust to heteroskedasticity. The coefficient presented is the one of the CIR dummy. ** Significant at the 5% level. * Significant at the 10% level.

Table 7 : Regression methods on the common support of the probabilities to get the CIR All

 7 the explanative variables are lagged one year. The left-hand variable is the growth rate of the private funding of R&D. The explanative variables are: log of the private funding of R&D, log of sales, log of total R&D to sales ratio, export dummy, export rate, 2-digit activity dummy. The standard errors are robust to heteroskedasticity. The coefficient presented is the one of the CIR dummy. ** Significant at the 5% level. * Significant at the 10% level.

Table 8 : Probit estimates of the probability to benefit from CIR Left

 8 -hand variable: CIR benefit dummy (yes/no). All the right-hand variables are lagged one year. Maximum likelihood estimates of the Probit model.

Table 9 : Evaluation estimators à la Rubin on the whole sample

 9

Table 10 : Evaluation estimators à la Rubin on the positive growth rates

 10

  The asymptotic Student t are computed by the bootstrap with 1500 repetitions, including the Probit step)

																					-2002
		Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student
										Weighting estimators
	Average effect on the population	-0,032	1,40	0,075 2,25** 0,014	0,64	0,048	1,71*	0,033	0,92	0,089 2,11** -0,043	1,60	-0,034	1,32	0,004	0,14	-0,028	1,17
	Average effect on the not treated	-0,043	1,47	0,103 2,38** 0,025	0,93	0,052	1,54	0,057	1,29	0,104 1,98** -0,047	1,56	-0,050 1,68*	0,010	0,30	-0,039	1,48
	Average effect on the treated	-0,014	0,62	0,016	0,56	-0,012	0,59	0,036	1,46	-0,026	0,90	0,055	1,64	-0,033	1,06	0,001	0,05	-0,011	0,36	0,004	0,14
										Kernel matching estimators
	(Average effect on the population -0,043 1,90* 0,042 1,46	0,020	0,85	0,032	1,28	0,026	0,85	0,065	1,87* -0,011	0,35	-0,040	1,47	0,015	0,52	-0,013	0,44
	Average effect on the not treated	-0,054 2,02** 0,053	1,51	0,033	1,20	0,032	1,09	0,047	1,34	0,067	1,67* -0,011	0,30	-0,052 1,76*	0,010	0,30	-0,013	0,42
	Average effect on the treated	-0,026	1,02	0,020	0,67	-0,012	0,52	0,033	1,27	-0,028	0,88	0,060	1,79* -0,011	0,33	-0,013	0,37	0,025	0,92	-0,011	0,29

Table 11 : Multipliers according to the private R&D expenditures Average estimation over the period 1994-2003*

 11 We use the weighted average of the effects over the period1994-2003, where the (optimal) weight is equal to the inverse of each estimator's variance.

		Private R&D	Lower bound 95%	Upper bound 95%	Total R&D expenditures	Lower bound 95%	Upper bound 95%
	Over the whole sample (Table 10):
	Weighting estimator	1,079	1,060	1,097	1,112	1,093	1,131
	Kernel matching estimator	1,078	1,059	1,098	1,112	1,092	1,131
	On the positive growth rates (Table 11) :
	Weighting estimator	1,000	0,983	1,017	1,032	1,015	1,050
	Kernel matching estimator	1,003	0,985	1,022	1,035	1,017	1,054

*

Table 12 : Multipliers according to the amount of tax credit distributed Average estimation over the period 1994-2003*

 12

	Private R&D	Lower bound 95%	Upper bound 95%	Total R&D expenditures	Lower bound 95%	Upper bound 95%

Over the whole sample (Table 10):

	Weighting estimator	2,327	1,774	2,881	3,327	2,774	3,881
	Kernel matching estimator	2,315	1,743	2,887	3,315	2,743	3,887

On the positive growth rates of private R&D

																					-2002
		Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student	Coeff	Student
										Over the whole sample
	Average effect on the population	0,105**	3,36	0,116**	4,13	0,088**	2,81	0,118**	3,54	0,061	1,87	0,112**	3,13	0,119**	2,63	0,082**	2,71	0,099**	2,90	0,102**	3,00
	Average effect on the not treated	0,099**	2,75	0,115**	3,61	0,078**	2,19	0,117**	3,08	0,045	1,24	0,107**	2,71	0,134**	2,52	0,082**	2,45	0,096**	2,56	0,100**	2,68
	Average effect on the treated	0,120**	3,78	0,121**	3,84	0,122**	3,79	0,123**	3,81	0,109**	3,08	0,126**	3,83	0,075**	2,00	0,084**	2,20	0,108**	2,89	0,109**	2,97
	Average effect on the population	0,008	0,19	0,098**	2,3	0,069*	1,73	0,075*	1,72	0,042	0,99	0,020	0,44	0,082	1,62	0,070*	1,80	0,081*	1,74	0,069*	1,70
	Average effect on the not treated	0,022	0,43	0,113**	2,18	0,071	1,46	0,073	1,41	0,032	0,61	0,008	0,14	0,103*	1,71	0,056	1,25	0,074	1,42	0,076*	1,72
	Average effect on the treated	-0,015	0,39	0,069	1,49	0,066**	2,08	0,080**	2,32	0,068*	1,84	0,049	1,19	0,031	0,72	0,100**	2,07	0,100*	1,91	0,048	0,93

This fact is well known at the Ministry of Research and seems do derive from either a bad knowledge of tax deductions or from the erratic nature evolution of growth tax credit. The latter point is consistent with the fact that when the system was extended to the level of R&D in 2004, some firms entered the system for the first time, while they were performing R&D for a long time.

Another property of this data set is that it cannot be accessed by the standard procedure in France. The data were made available because there is a law that compels to provide an evaluation of the R&D tax credit to the Parliament. Access to the data set was decided after a call for offer on the tax credit evaluation among economic research laboratories.

The French firms have a compulsory identification number (the SIREN number) that is available in all our files. This precludes losses due to matching.

A balanced sample over the period would reduce to about 200 firms only, instead of 1500.

The effect of subsidies has been studied separately in[START_REF] Duguet | Are R&D subsidies a substitute or a complement to privately funded R&D? An econometric analysis at the firm level[END_REF] with comparable evaluation methods.

This critic also raises an issue when the data comes from the "innovation surveys". The fiscal deduction dummy variable should be merged with R&D growth data in order to get the right counterfactual when the tax credit is defined on the growth of R&D.

We have performed Vuong test of the Probit model against the Logit model. We find that the models are equivalent for all the couples of years, except for 2000-2001 were the Probit model outperforms the Logit model. Therefore, we kept the Probit model for all our regressions.

In practice, we define the probability support by the first and 99th percentiles in order to suppress the influence of outliers.

The author thanks B. Guédou for his suggestions and comments on a previous version of this paper, as well as the participants to the EPEE Seminar (University of Evry), to the


Emmanuel Duguet
email: emmanuel.duguet@u-pec.fr.y

Christine Le Clainche
email: christine.leclainche@cee-recherche.fr.

The impact of health events on individual labor market histories : the message from di¤erence in di¤erences with exact matching

Keywords: C14, I10, J20, J60

We studied the e¤ect of health events (accidents and chronic diseases) on the occupation probabilities at the individual level, while accounting for both correlated individual and time e¤ects. Using di¤erencein-di¤erences with exact matching estimators, we found that health events have a strong impact on individual labor market histories. The workers a¤ected by a healt event have a stronger probability of entering inactivity and a lower probability of keeping their jobs. We also found that the less quali…ed workers, women, and workers with short term jobs are the most negatively a¤ected by health events.

1 Introduction1

This article presents a study of the impact of health events (an accident or a chronic disease) on participation in the labor market. This topic usually raises causality issues, since health a¤ects labor, and labor a¤ects health. In order to adress this problem, we use a data set that provides annual information about labor and the occurrence of health events. This allows us to distinguish clearly the period before and after the health events, and to perform a di¤erence in di¤erences analysis. The time dimension is especially important in disentangling the joint causality between health and labor.

This topic had already been studied with reference to seniors in France, where there is now a signi…cant literature about the "health shocks" that provides evidence on early exits out of the labor market through early retirement [START_REF] Barnay | Santé déclarée et cessation d'activité[END_REF], [START_REF] Blanchet | Souhaiter prendre sa retraite le plus tôt possible : Santé, satisfaction au travail et facteurs monétaires[END_REF], Barnay, Debrand, (2007), [START_REF] Blanchet | Souhaiter prendre sa retraite le plus tôt possible : Santé, satisfaction au travail et facteurs monétaires[END_REF], [START_REF] Behaghel | Disability and Social Security Reforms: The French Case[END_REF] for France, for example). However, there is no comparable evidence for younger populations. In this paper, we exclude the retired workers and focus on the impact of health events on the labor market history of young and middle-aged workers.

One possible outcome of this analysis is the possibility of reducing the economic and social costs implied by accidents and chronic diseases. There has been no economic evaluation in France of the costs implied by poor health, mainly because there are no aggregated accounts associated with prevention policies as a whole (Heijink, Noethen, Renaud, Koopmanshap, Polder (2008), Cour des Comptes (2011)). So, a better knowledge of the e¤ects of health events on employment history could allow us to better target health measures in relation to work, by including health issues within the employment histories of workers.

We use the survey " Health and Professional Histories" (Santé et Itinéaires Professionnels, SIP), collected between 2006 and 2007. It is a representative sample of individuals from 19 to 74 years old, which describes both health events and employment history, on a yearly basis. This is the …rst time that such information is available in France, and it allows us to perform a dynamic analysis of health and occupation. In order to estimate the impact of accidents and the chronic diseases on occupation, we implement a method of di¤erence-in-di¤erences with exact matching. This method is non parametric and allows us to identify the causality running from health events to occupation. We …nd that health events have signi…cant and important e¤ects on participation in the labor market.

The paper is organized as follows : in the second section, we summarize the evidence from the economic literature. The third section presents the data used in this application and is followed by a presentation of the econometric method in the fourth section. The results are presented in the …fth section, after which we reach the conclusion.

2 Review of the literature 2.1 E¤ects of health events in the labor market Poor health has negative and signi…cant economic and social impacts in the labor market, especially due to the exits out of the labor market it induces. For example, Chaupain-Guillot and Guillot (2010) evaluate, from Eurostat data, the direct and indirect costs induced by inactivity periods due to ill health at 90 billion euros in Europe, that is about 1% of the GDP of European countries. Since the 1990s, there has been a growing literature dealing with the impact of health on labor market participation, earnings and wages, following the seminal theoretical model of health capital by [START_REF] Grossman | On the Concept of Health Capital and the Demand for Health[END_REF] and its Mincerian extensions. In such models, a higher stock of health capital is expected to increase earnings and wages because it allows workers to increase the number of hours worked and also because a higher health capital involves higher productivity. Most of the empirical studies based on these theoretical grounds use cross-section data which do not take into account unobservable heterogeneity. An overview of the empirical literature by [START_REF] Currie | Health, Health Insurance and the Labor Market[END_REF] shows that poor health reduces the ability to work and has signi…cant e¤ects on wages, labor force participation and job choice but the results are sensitive to the measurement of health chosen, and within the surveyed literature relatively few studies are based on longitudinal surveys.

The dynamic analysis of the impact of health on labor market histories is just beginning. Using six waves of the British Household Panel Survey (BHSP, 1991(BHSP, -1996)), [START_REF] Contoyannis | The Impact of Health on Wages : Evidence from the British Household Panel Survey[END_REF], produced one of the …rst studies shedding light on the e¤ects of overall and on psychological health on wages, by taking into account unobservable heterogeneity. They used a single …xed e¤ects wage equation with self-reported health indicators among the regressors. They found that reduced psychological health has an e¤ect on hourly wage for men, while excellent self-reported health for women has a signi…cant impact on their hourly wage. Another study by [START_REF] Cai | Health Status and Labour Force Participation: Evidence from Australia[END_REF] includes some dynamic characteristics concerning the labor market, using Australian data from the Hilda data base (2001). They use a selfreported health measure, based on the limitations of everyday activities, and a measure based on the SF 36, which is a measure of general health and well-being, producing scores on eight dimensions of health. The endogenous nature of the health status in the labor force participation equation is addressed by estimating the health equation and the labor participation equation simultaneously. The results show that better health increases the probability of labor force participation for all age groups and both genders, but the biggest e¤ect is obtained for the older groups and for women. For the French case, most of the studies concentrate on seniors except those carried out by [START_REF] Tessier | O¤re de travail et santé en France[END_REF]. The latter is conducted from the "Timetable"survey ", collected by the National Institute for Statistics and Economic Studies ( INSEE) between February 1998 and February 1999, on a selected sample of 7023 individuals from 25 to 55 years old. [START_REF] Tessier | O¤re de travail et santé en France[END_REF] estimate the impact of health on participation in the labor market. They use two measures of health: self-reported health and a measure indicating the existence of chronic disease which the authors consider as "more objective". The simultaneous estimation of a participation equation and of a health equation takes into account the simultaneity between the two variables. The estimations bring to light two main results: the simultaneous estimation of the equations shows that good health has a positive impact on labor market participation and that participation in the labor market has no signi…cant e¤ect on health. The second result is that health signi…cantly a¤ects participation in the labor market from the …rst years of potential activity.

However, the study by Tessier and Wol¤ does not focus on the impact of health events on employment trajectories, due to the lack of adequate data. The SIP survey that we use in this study …lls this gap.2 Moreover, with the SIP survey, we also are able to account for individual variables that have been proved to have an important in ‡uence on health, such as the childhood living conditions.3

The impact of injuries on work and employment

While the impact of accidents on employment is rather well studied, especially in relation to working conditions 4 , the impact of domestic, sport or road accidents on employment has been studied much less. Thesealso deserve to be studied, since the economic and human costs of such accidents are high and the e¤ects on the trajectories of employment are potentially signi…cant. For example, in 2000, road accidents entailed injuries for 1.3 million individuals in Europe [START_REF] Moller-Dano | Road Injuries and Long Run E¤ects on Income and Employment[END_REF]. In France, the direct and indirect total costs estimated by the French O¢ ce for Road Security (ONISR) are estimated as being equal to 1.3 % of the GDP for 2008.

One of the rare studies dedicated to the microeconomic e¤ects of road accidents on employment shows that, for Denmark, the e¤ects of road accidents are serious for both employment and earnings: the rates of employment are respectively 10 and 8 points lower for injured men and women. Besides, earnings are signi…cantly reduced for men whatever their age, but this applies only to the oldest women [START_REF] Moller-Dano | Road Injuries and Long Run E¤ects on Income and Employment[END_REF]). In order to obtain these results, the author had to correct the e¤ects of selection associated with the risk of accidents, so as to identify the causal impact of car accidents on earnings and rates of employment. It is indeed necessary to correct the selection bias insofar as young men are reputed to have more more risky behavior regarding cars. Moreover, their earnings are lower than those of older men. Another rare study was conducted by [START_REF] Crichton | Returning to Work from Injury: Longitudinal Evidence on Employment and Earnings[END_REF] for New Zealand. With a similar methodology, the authors show that there are strong and negative impacts of accidents (including workplace accidents) on employment and earnings. The authors also found that accidents giving the right to long-term earning compensations due to inability to work have a stronger negative impact on women, older workers and people with low incomes.

The SIP survey that we use includes information on accidents and allows us to deal with the impact of accidents on labor market histories.

The Data

The survey "Health and Professional Histories"( SIP) was carried out from November, 2006 until January, 2007, on people from 19 to 74 years old. This survey allows us to identify all the stages of a professional history and to observe the health events occurring over the same period. The survey includes questions about childhood and activity periods. In this paper, we focus on the people between 19 and 59 years old. Since we focus on the relatively young people, we have also discarded all the people with a retirement or pre-retirement period. 5In order to avoid simultaneity issues, we account for the following points : …rst, we include correlated individual and time e¤ects in the model, in order prevent unobserved heterogeneity in ‡uencing both health events and labor market participation. Secondly, we focus on the health events that are not related to work. Thirdly, we account for the date at which the health events occur, and examine their e¤ect on the subsequent labor market history.

Our accident variable will be a yearly dummy variable that indicates whether the individual has had an accident. We exclude two types of accidents : accidents in the workplace and accidents during transport to the workplace. Therefore we keep mostly domestic accidents, sport accidents and those car accidents not related to work.

Our data on chronic disease is based on the health care administration classi…cation ("Sécurité Sociale", in France). Chronic diseases initially selfdeclared, but the declarations must pass through the de…nition of long-term diseases provided by the "Sécurité Sociale". It is so because, in France, such diseases bene…t from a full reimbursement, so the Sécurité Sociale monitors them carefully. In order to identify the chronic diseases we report on epidemiologists'views of diseases causing limitations (see WHO, IDC) and on the French administrative classi…cation of severe diseases (the so-called "A¤ections de Longue Durée" or ALD classi…cation). In the SIP survey, the data set is very detailed about the type of disease from which people su¤er, in a declarative sense. We have retained : chronic cardio-vascular diseases, cancers, incurable deafness, chronic hearing impairment (tinnitus), severe or chronic lung diseases, severe or chronic liver diseases, severe or chronic rheumatism, diabetes, severe or chronic eye disorders (impossible to correct) ; severe or chronic psychiatric disorders, epilepsy, addictions, AIDS or other severe disease. For these data, we keep a yearly dummy variable that indicates whether the individual has a chronic disease.

This allows us to construct four data sets : …rst, the accident data set, that includes the individuals that had an accident and no chronic disease (N = 336); secondly, the chronic disease data set, that includes the individuals that had a chronic disease and no accident (N = 800) : Then come two data sets, that we call the reference data sets, that represent the reservoirs from which we select the individuals that will be used for comparisons with the two previous groups. The third data set includes the individuals that had neither an accident nor a chronic disease and that have the same individual variables as the people in the accident data set (N = 3228): The fourth data set includes the individuals that had neither an accident nor a chronic disease and that have the same individual variables as in the chronic disease data set (N = 3618) : We present the matching method before comparing these groups further.

Methodology

We wish to explore the impact of health events on the employment history of workers. We account for three problems. First, it is likely that health events can cause a break in individual employment histories. In this case, only a dynamic approach can identify the break with a before-after analysis, where the break date is the date of the health event, which is speci…c to each individual. A static approach can only compare individuals with a di¤erent health status at the date of the survey, and cannot analyse directly the impact of health events for each individual. Secondly, the individuals in the data set have di¤erent ages so that the observation window di¤ers from one individual to another. Therefore we need to match individuals by age, so that we compare workers that had a health event (or not) at the same age and during the same year. Thirdly, we account for correlated individual and time e¤ects since we have panel data. Fourthly, we perform a non parametric estimation, so that no speci…c functional assumption is made for the healthactivity relationship.

Observable heterogeneity, unobservable heterogeneity and exact matching on observables

The SIP survey provides a detailled dynamic account of two main variables : health events and occupational status. In this section we analyze how it is possible to evaluate the impact of health events (accident or a …rst chronic disease) on the remaining labor market history. In order to identify successfully the impact of health events we need to account for two types of quantity : on the one hand, the di¤erence in histories between the individuals that experienced a health event and the other individuals; on the other hand, the history variation of one individual before and after the health event.

In this section, we show that the di¤erence-in-di¤erences method allows us to estimate the e¤ect of health events by controlling both for the observable individual variables and the non-observable individual heterogeneity, including when it is correlated to the observable individual variables.

The left-hand variables of interest are the annual activity dummies corresponding to the four following occupations : inactivity, unemployment (more than 1 year), short-term employment (less than 5 years) and longterm employment (more than 5 years). The means of these dummy variables for one individual give the proportions of time spent in these occupations. One can interpret our analysis as an assessment of the impact of health events on these four occupation probabilities.

Formally, we estimate a model in wich our occupational dummies d it can be broken dowm into four parts :

-Observable individual heterogeneity that represents the right-hand variables available in the survey, denoted X i . Typically, in the literature, this type of heterogeneity is often represented by a linear econometric model. In this paper, we perform an exact matching on the observable variables so that we do not need to impose any speci…c functional form relating the lefthand variables to the right-hand variables. Our approach is non parametric. The purpose of the matching is to get rid of the e¤ects of the observable variables on the occupation probabilities. This part of the model is denoted f (X i ) ;where f is unknown.

-Unobservable individual heterogeneity that …nds its source either in time-constant missing individual variables or corrrelated individual e¤ects. This part of the model is similar to the individual correlated e¤ects in the panel data literature. We cannot exclude the possibility that this heterogeneity is correlated both with the observable individual variables and the occurrence of health events. Di¤erence-in-di¤erences will allow us to get rid of this type of heterogeneity. This component is denoted i -We also add an individual-constant time heterogeneity, possibly correlated to the explanative variables, for the following two reasons. First, we are dealing with periods of several decades, so that the job opportunities clearly di¤er over the period under study. Secondly, it is also clear that the probability of getting a given disease or of having a speci…c type of accident can vary over long time periods because of medical or behavioral preventive action. Thirdly, the progress of medicine over long periods also a¤ects the ability to get back to work. Our method allows us to discard these e¤ects, since matching individuals over the same time period allows us to di¤erence it out. This component is denoted t -Lastly, we add a standard white noise error term which correspond to the idiosyncratic error in the panel data models, denoted " it . These errors are uncorrelated with the rest of the model and with each other, and have a mean that can be allowed to vary over time E (" it ) = t . We could …nd the standard panel data model by seting E (" it ) = 0; but this is not required by our method.

Econometric model

Our panel is not balanced so that we observe one individual i over a individual speci…c time period denoted t i ; t + i : Therefore, a health event can occur at any date t i 2 t i ; t + i : In order to evaluate the e¤ect of this health event, we will compare the occupation probabilities over the period t i ; t i 1 and t i ; t + i : Notice that the dates are integer numbers since we only have annual data. Considering …rst an individual j with no health event over the period h t j ; t + j i , we have :

d jt = f (X j ) + j + t + " jt ; 8t 2 h t j ; t + j i ;
where d jt is an occupation dummy. The di¤erent occupation dummies can therefore have di¤erent (f; ; ; ") : If we consider one individual i that experienced a health event at date t i ; we must distinguish two periods, before and after the health event :

d it = f (X i ) + i (t t i ) + i + t + " it ;
with

(t t i ) = 1 if t t i 0 if t t i 1
where i is the individual e¤ect of the health event on individual i: It is our parameter of interest. Overal, we can write that :

d it = f (X i ) + i + t + " it if t i t t i 1 f (X i ) + i + i + t + " it if t i t t + i
In order to estimate an average value for i we must proceed in several steps.

Step 1 : we compute the occupation di¤erences between the individuals that experienced a health event and the others. The average performance of an individual with a health event before the event occurs is equal to :

p 0 i = 1 t i t i t i 1 P t=t i d it = f (X i ) + i + 1 t i t i t i 1 P t=t i ( t + " it )
and the average performance of the individuals j that never experienced a health event over the same period is equal to :

p 0 j = 1 t i t i t i 1 P t=t i d jt = f (X j ) + j + 1 t i t i t i 1 P t=t i ( t + " jt )
where t i ; t + i h t j ; t + j i guarantees that we can match the individuals on the same years, so that we can restrict the comparison to t j = t i and t j = t i : This condition is equivalent to matching the individuals on the time period before the accident. Further, in order to eliminate the e¤ect of the observable variables, we match our individuals on the right-hand variables so that we de…ne :

j 2 J (i) = fj : X j = X i g therefore j 2 J (i) ) f (X i ) = f (X j )
and we can write the occupation di¤erence over the matched individuals :

D 0i = p 0 i p 0 j = i j + 1 t i t i t i 1 P t=t i (" it " jt )
unobservable individual heterogeneity clearly drives this di¤erence, so that we need to go further. Notice however that time heterogeneity has been di¤erenced out.

Step 2 : we compute the same type of di¤erence on the period after the health event. The average performance for an individual with a health event is :

p 1 i = 1 t + i t i + 1 t + i P t=t i d it = f (X i ) + i + i + 1 t + i t i + 1 t + i P t=t i ( t + " it )
and the average performance for a matched individual without a health event over the same period is :

p 1 j = 1 t + i t i + 1 t + i P t=t i d jt = f (X i ) | {z } f (X j ) + j + 1 t + i t i + 1 t + i P t=t i ( t + " jt ) ; j 2 J (i)
so that we get the di¤erence :

D 1i = p 1 i p 1 j = i j + i + 1 t i t i t i 1 P t=t i (" it " jt ) ;
where time heterogeneity has been di¤erenced out.

Step 3 : we compute the di¤erence of the di¤erences This gives :

D i = D 1i D 0i = i + 1 t + i t i + 1 t + i P t=t i (" it " jt ) 1 t i t i t i 1 P t=t i (" it " jt )
Now, using the assumption E (" it ) = t ; we get :

E (D i ) = i + 1 t + i t i + 1 t + i P t=t i ( t t ) 1 t i t i t i 1 P t=t i ( t t ) = i ;
where both time and individual heterogeneity have been di¤erenced out.

The quantity i is the e¤ect of the health event for the individual i on the occupational dummy d it . Our purpose is to estimate its average value over all individuals (or over subsets of individuals) :

= 1 N h N h X i=1 i ;
where N h is the number of individuals that experienced a health event.

So far, our expressions involve theoretic expressions so that we need to …nd empirical counterparts to proceed to estimation. This is the topic of the next section.

Estimation

We estimate D i by using its empirical counterpart. Since the relationships are linear, it is an unbiased estimator. However, in order to improve on the e¢ ciency of the estimator, we will not take only one individual j to be matched with i but all the individuals j in the data set that can be matched with i. Therefore the probabilities p k j ; k 2 f0; 1g will be estimated by :

b p k J(i) = 1 N i X j2J(i) b p k j with b p 0 j = 1 t i t i t i 1 P t=t i d jt and b p 1 j = 1 t + i t i + 1 t + i P t=t i d jt
where

N i = #J (i) is the number of individuals in J (i) : b p k
j is the empirical occupational probability of one individual j, matched with individual i since j 2 J (i) b p k J(i) represents the average empirical occupational probability of all the individuals that can be matched with individual i: Its variance is lower than the variance of b p k j ; and this is why we prefer this estimator to b p k j .

For one individual i; the di¤erences are estimated by :

b D 0i = b p 0 i b p 0 J(i) and b D 1i = b p 1 i b p 1 J(i) ;
therefore we take the mean of these di¤erences over all the individuals that experienced a health event (number N h ):

b D 0 = 1 N h N h X i=1 b D 0i and b D 1 = 1 N h N h X i=1 b D 1i
and we …nally estimate the average e¤ect of a health event by :

b = b D 1 b D 0 ;
this is an unbiased estimator for :

E (b ) = ;
which is the average theoretical e¤ect of health over all the individuals that had a health event.

It remains to compute the variance of b : One di¢ culty appears. We can match the same individual j (without a health event) with di¤erent i individuals (with a health event). Indeed, the only important point is that the observations periods verify t i ; t + i h t j ; t + j i and that the observable variables are the same (X i = X j ), since the time period of any individual without any health event can be split at will. We use as many individuals in the reference sample as possible. This implies that the empirical quantities within the means are correlated.

One can easily solve this problem by using the bootstrap, since the empirical means are asymptotically pivotal functions (see Horowitz, 1999). We take a large number of draws in order to get as close as possible to the ideal bootstrap estimate : 10000 draws. More precisely we performed the non parametric bootstrap method on the data base that includes both individuals with and without a health event. This implies that our bootstrap estimates also account for the variation of the number of individuals that can be matched. The whole estimation process is therefore replicated after each draw in the original data base. We performed the estimation under SAS.

Results

The matching variables

We matched the individuals on 8 variables : gender (2 classes), age (4 classes), highest degree (3 classes), nationality of the mother (2 classes), nationality of the father (2 classes), country of birth (2 classes), health problems of the parents (2 classes) and separation from the parents during childhood (2 classes). This makes 384 possible combinations. To these combination, we must add matching over the time periods. Therefore, the exact matching method cannot be applied to all the workers. Table 1 presents both the matching percentages and the average individual characteristics of the workers that could be matched or not. We …nd that 73% of the accident sample can be matched, and 68% for the chronic disease sample. Therefore, we should look at the characteristics of the people that could not be matched. We …nd that, overall, the individuals that could be matched have almost the same characteristics as the other people, so that the matching impossibilities comes from the di¤erences in the time periods. This is good news, since the individuals that are not in the estimates share comparable individuals variables with the individuals that are in the estimates, so that the applicability of our conclusion should extend beyond the matched sample. A comparison between the accident and the chronic disease samples is also meaningful since it reveals di¤erences between the two heath events. We …nd that accidents involve younger people (27% under 36 years old, versus 19%) and more men (60% versus 38%) than chronic diseases.

The di¤erence in di¤erences estimations are presented in Table 2 for the accidents and in Table 3 for chronic diseases. It is important to notice two points. First, the sum of the di¤erences always equals zero since the occupation dummies sum to 1. What we measure is therefore similar to a deformation of the occupation probabilities after a health event. Secondly, it is possible to compute these di¤erences for sub-samples of the original data set, provided that there are enough observations. We …nd that this is the case for gender and education level. Therefore we will examine whether men and women face comparable consequences on the labor market after a health event, and whether a higher education level allows individuals to compensate for the anticipated negative e¤ect of health events on activity.

E¤ect of an accident on occupation

Overall, an accident increases the inactivity probability by 5.3%. Compared to the benchmark probability at 10.7%, it means that the workers that had an accident have, on average, an inactivity probability of 10.7%+5.3%=16% instead of 10.7%. This e¤ect is balanced by a comparable negative e¤ect on employment (-6%). If we look in more detail, we …nd that the whole e¤ect on employment comes from short-term jobs. Therefore, the workers that had long-term jobs are not signi…cantly a¤ected by an accident, while the workers with a short-time job move to inactivity. However, this global result conceals signi…cant di¤erences among genders and education levels.

Considering gender e¤ects, we …nd that women are more strongly affected than men by an accident. Their inactivity probability increases by 7.2%, instead of 3.8% for men. We also …nd that the e¤ect of an accident decreases with the education level. The increase in the inactivity probability is 9.2% for primary education, 5.1% for secondary education and 3.6% for tertiary education. This is balanced by a negative e¤ect for employment.

Therefore the e¤ect of an accident is to move workers out of the labor market, mostly women and those in the less quali…ed jobs.

E¤ect of a chronic disease on occupation

Overall, a chronic disease has a strong impact on occupation : we …nd that the probability of becoming inactive increases by 7.7%. Compared to the benchmark probability of 14.1%, the workers that face a chronic disease see their inactivity probability rising to 21.8%, and their probability of being employed is reduced by 6.7 points. This e¤ect on employment is equally split between short-term jobs (-3.4%) and long-term jobs (-3.2%). However, this overall e¤ect conceals important composition e¤ects concerning gender and education levels.

The lowest education level clearly concentrates the most negative effects on occupation : the inactivity probability increases by 17.2% and the employment probability decreases by a comparable …gure. The types of job that are the most a¤ected by a chronic disease are the long-term jobs (-14%) and, in a much lower extent, the short term jobs (-4%). We notice that the number of transition to unemployment is not a¤ected by the appearance of a chronic disease; therefore it is likely that the less educated individuals make a direct transition from long-term jobs to inactivity. In addition to this, their inactivity probability was already high (benchmark : 24.8%) so that the inactivity probability rises to 42% in the case of a chronic disease. Notice that, with our de…nition, inactivity does not include retirement, so that the previous result is not driven by the older workers that would retire after a chronic disease. The medium education level is associated with a smaller e¤ect of a chronic disease. The inactivity probability increases by 6.8%, almost the half of the lowest education level. This increase corresponds to a reduction of both the probabilities of unemployment and employment. Within employment, only short-term jobs are a¤ected. Therefore, the incidence of a chronic disease does not modify the probability of keeping a long term job, but makes workers move from unemployment and short-term jobs to inactivity. The highest education level is associated with the lowest impact of chronic diseases : the probability of inactivity increases by 3.1% and the other di¤erences are not signi…cant. Overall, the negative impact of chronic diseases on employment is strongly decreasing with the education level.

Conclusion

We performed a dynamic analysis of health events on occupation, that accounts for correlated individual and time e¤ects. We …nd that health events have a signi…cant and negative e¤ect on activity. Health events always reduce the probability of employment and increase the probability of inactivity. We also …nd that women are more negatively a¤ected than men, and that the negative e¤ects of health events are decreasing with the education level. Comparing accidents and chronic disease, we …nd that accidents have an important but smaller e¤ect than chronic diseases on inactivity.

Overall, we …nd that health events tend to deteriorate the situation of the workers that are already the least favored in the labor market. The less quali…ed workers and women have the strongest increase in inactivity and, for all workers, the most a¤ected are the ones with a short-term job. Since we are studying the …rst health event, and since we have excluded work-related health events, it should be a causal e¤ect. One consequence is that health events would drive a high number of workers toward the minimum assistance revenues. This calls for policies oriented towards adapting the workplace to the most common health events or towards training the workers so that they can …nd another job more compatible with their health problems.

Table 1: Average characteristics of the samples (proportions)

The characteristics of the reference base, regrouping individuals without any health event, are not indicated in the table since we performed exact matching, which implies that the reference data base shares the same characteristics as the matched accident or chronic disease bases. The figures indicate the proportions of individuals for each level of the matching variables. The similarity in proportions between the matched and the not matched individuals indicates that the matching impossibilities came mostly from the differences in time periods between the individuals. -0,084 -0,003 -0,078 -0,009 Incl. less than 5 years 0,260 -0,045** 0,022 2,03 -0,090 -0,001 -0,082 -0,008 5 years and more 0,591 0,001 0,024 0,06 -0,046 0,049 -0,038 0,042 Education: Tertiary Inactivity 0,096 0,031** 0,012 2,65 0,008 0,054 0,012 0,050 Unemployment 0,021 -0,011 0,009 1,13 -0,028 0,008 -0,026 0,005 Employment 0,883 -0,020 0,015 1,37 -0,049 0,008 -0,045 0,004 Incl. less than 5 years 0,232 -0,016 0,018 0,87 -0,052 0,020 -0,046 0,015 5 years and more 0,651 -0,004 0,020 0,22 -0,043 0,035 -0,038 0,029

Accident base

Table 2 : Average effect of an accident on the occupation probabilities

 2 Difference-in-differences with exact matching. The standard errors and the confidence intervals are computed by the bootstrap method with 10000 replications. The confidence intervals need not be symmetric. ** : significant at 5%; * : significant at 10%.

	Sample	Occupation	Benchmark probability ̅	Accident effect ߛ ො	Standard error	Student	Confidence interval 95%	Confidence interval 90%
	Total	Inactivity	0,107	0,053**	0,014	3,73	0,025	0,081	0,029	0,076
		Unemployment	0,023	0,007	0,010	0,67	-0,012	0,026	-0,010	0,023
		Employment	0,870	-0,060**	0,016	3,66	-0,092	-0,027	-0,086	-0,032
		Incl. less than 5 years	0,334	-0,056**	0,019	2,87	-0,094	-0,018	-0,088	-0,024
		5 years and more	0,536	-0,004	0,023	0,16	-0,048	0,040	-0,040	0,033
	Gender: Women	Inactivity	0,202	0,072**	0,027	2,62	0,018	0,126	0,027	0,118
		Unemployment	0,026	-0,007	0,014	0,52	-0,036	0,021	-0,031	0,016
		Employment	0,772	-0,065**	0,029	2,25	-0,121	-0,009	-0,112	-0,018
		Less than 5 years	0,294	-0,045	0,030	1,51	-0,104	0,013	-0,094	0,003
		More than 5 years	0,478	-0,020	0,034	0,58	-0,086	0,046	-0,075	0,036
	Gender: Men	Inactivity	0,038	0,038**	0,014	2,75	0,011	0,065	0,015	0,061
		Unemployment	0,018	0,017	0,013	1,29	-0,009	0,042	-0,005	0,038
		Employment	0,944	-0,055**	0,018	3,04	-0,091	-0,019	-0,085	-0,025
		Incl. less than 5 years	0,227	-0,064**	0,026	2,40	-0,115	-0,011	-0,107	-0,020
		5 years and more	0,718	0,008	0,031	0,26	-0,054	0,069	-0,043	0,059
	Education: Primary	Inactivity	0,269*	0,092*	0,048	1,93	-0,002	0,183	0,014	0,169
		Unemployment	0,002	0,044	0,027	1,61	-0,010	0,092	-0,003	0,086
		Employment	0,729**	-0,136**	0,050	2,70	-0,233	-0,037	-0,217	-0,053
		Incl. less than 5 years	0,296	-0,057	0,047	1,22	-0,148	0,034	-0,134	0,020
		5 years and more	0,433	-0,079	0,064	1,23	-0,203	0,047	-0,183	0,028
	Education: Secondary	Inactivity	0,064	0,051**	0,018	2,80	0,016	0,086	0,021	0,081
		Unemployment	0,040	-0,004	0,018	0,23	-0,040	0,030	-0,033	0,025
		Employment	0,896	-0,047*	0,025	1,88	-0,096	0,002	-0,088	-0,005
		Incl. less than 5 years	0,345	-0,089**	0,029	3,06	-0,146	-0,032	-0,136	-0,041
		5 years and more	0,551	0,042	0,034	1,23	-0,025	0,110	-0,014	0,098
	Education: Tertiary	Inactivity	0,079	0,036*	0,021	1,71	-0,005	0,078	0,001	0,071
		Unemployment	0,014	0,001	0,011	0,07	-0,021	0,021	-0,017	0,018
		Employment	0,907	-0,037*	0,021	1,78	-0,078	0,004	-0,071	-0,003
		Incl. less than 5 years	0,340	-0,020	0,032	0,61	-0,084	0,045	-0,073	0,034
		5 years and more	0,567	-0,017	0,034	0,51	-0,085	0,049	-0,075	0,038

Table 3 : Average effect of a chronic disease on the occupation probabilities

 3 Difference-in-differences with exact matching. The standard errors and the confidence intervals are computed by the bootstrap method with 10000 replications. The confidence intervals need not be symmetric. ** : significant at 5%; * : significant at 10%.

	Sample	Occupation	Benchmark probability ̅	Chronic disease effect ߛ ො	Standard error	Student	Confidence interval 95%	Confidence interval 90%
	Total	Inactivity	0,141	0,077**	0,011	7,00	0,056	0,099	0,059	0,096
		Unemployment	0,024	-0,011	0,007	1,62	-0,024	0,002	-0,022	0,000
		Employment	0,835	-0,067**	0,013	5,21	-0,092	-0,042	-0,087	-0,046
		Incl. less than 5 years	0,236	-0,034**	0,013	2,70	-0,059	-0,009	-0,055	-0,013
		5 years and more	0,599	-0,032**	0,015	2,12	-0,062	-0,002	-0,057	-0,007
	Gender: Women	Inactivity	0,209	0,088**	0,016	5,55	0,057	0,119	0,062	0,115
		Unemployment	0,027	-0,013	0,009	1,50	-0,031	0,004	-0,028	0,001
		Employment	0,764	-0,075**	0,018	4,24	-0,109	-0,040	-0,104	-0,046
		Less than 5 years	0,243	-0,033**	0,017	1,98	-0,066	-0,001	-0,061	-0,006
		More than 5 years	0,521	-0,042**	0,021	2,02	-0,083	-0,002	-0,076	-0,008
	Gender: Men	Inactivity	0,038	0,061**	0,014	4,42	0,034	0,088	0,038	0,083
		Unemployment	0,018	-0,007	0,010	0,69	-0,028	0,013	-0,025	0,010
		Employment	0,944	-0,054**	0,017	3,25	-0,086	-0,021	-0,081	-0,027
		Incl. less than 5 years	0,227	-0,035*	0,019	1,85	-0,072	0,003	-0,066	-0,004
		5 years and more	0,717	-0,019	0,021	0,88	-0,061	0,023	-0,054	0,016
	Education: Primary	Inactivity	0,248	0,172**	0,033	5,22	0,107	0,237	0,118	0,227
		Unemployment	0,023	0,013	0,014	0,94	-0,015	0,038	-0,011	0,035
		Employment	0,729	-0,185**	0,034	5,38	-0,253	-0,118	-0,242	-0,129
		Incl. less than 5 years	0,201	-0,044*	0,025	1,75	-0,093	0,006	-0,085	-0,002
		5 years and more	0,528	-0,141**	0,040	3,56	-0,219	-0,062	-0,207	-0,075
	Education: Secondary	Inactivity	0,123	0,069**	0,017	3,93	0,034	0,102	0,039	0,097
		Unemployment	0,026	-0,025**	0,012	2,02	-0,049	-0,001	-0,045	-0,005
		Employment	0,851	-0,044**	0,021	2,10

This research has bene…ted …nancial support from Drees and Dares (Research Department of the French Ministry of Labour and Social A¤airs). We thank for their comments on earlier versions of this paper: Chantal Cases, Thierry Debrand, François Gardes, Véronique Simonnet , Nicolas Sirven, Christophe Starzec and Claude Mathieu. We also thank the participants to the following seminars and conferences : Health and Safety at Work Conference (Universita Cattolica Milano,

July 2010); Journée de Microéconomie Appliquée (University of Angers, June 2010), Journée des Economistes de la Santé Français (University of Lyon, December 2010), Journées d'Etudes sur l'Hétérogénéité des Comportements Individuels (ANR-06-Blan-0140, University of Paris I, April 2011), Journée Santé-Travail, (Chaire Santé, Risque Assurance, University of Paris-Dauphine, September 2011) and the Third French Econometrics Conference (Aix-Marseille University, Aix en Provence, December 2011).

Concerning the links between health and unemployment see[START_REF] Haan | Dynamics of Poor Health and Non-Employment[END_REF];[START_REF] Böckerman | Unemployment and Selfassessed Health: Evidence from Panel Data[END_REF].

3 For the link with market labor performance, see[START_REF] Lindeboom | Disability and Work[END_REF]. Precarious conditions during childhood have important consequences for health in the future and for labor market participation and

unemployment.4 See[START_REF] Karasek | Healthy Work: Stress, Productivity and the Reconstruction of the Working Life[END_REF] ;[START_REF] Reville | Disabilities from Injuries at Work: the E¤ects on Earnings and Employment[END_REF] ;[START_REF] Wichert | Job Insecurity and Job Intensi…cation: the E¤ects on Health and Well-Being[END_REF]; and for France, see[START_REF] Askenazy | La croissance moderne[END_REF]Askenazy ( , 2009) ) ;[START_REF] Hamon-Cholet | Cost of illness: An international comparison Australia, Canada, France, Germany and The Netherlands[END_REF].

We also let the disable people apart since they will be the topic of a future separate study.