Luc Arrondel

Didier Blanchet

David Blum

Bruno Crépon

Olivier Donni

Pierre-Yves Geoffard

Raúl Sampognaro

Anne Solaz

Keywords: civil union, taxation, marriage, pacs, difference in difference JEL Classification : H31, J12, K36

. This paper tests if the tax system could alter the decision to contract a civil union, which is a less binding marital contract. In France, since 1999, couples can either contract a marriage or a civil union (pacs). I assess the impact of taxation on the decision to contract a pacs using a difference-in-differences evaluation of the 2005 reform of income taxation of newly pacsed couples. As the control group is contaminated by the reform, I propose an original estimation method based on a difference-in-differences-in-differences setting to estimate bounds to the impact of the reform. My results suggest a positive and increasing impact of taxation on pacs rates, but also a change in the timing of pacs indicating that taxation alters the decision to contract a pacs. I find a slightly significant impact of taxation on the decision to break up a pacs.

Introduction

Marriage markets have changed a lot since Becker's seminal theory of marriage (1973; 1981). Both in the US and in Western Europe, the most notable changes are the increasing divorce rate and the decreasing marriage rate. These changes tend to show that marriage is no longer a cohabitation contract that goes without saying. Today, the why and when couples get married is a choice. [START_REF] Stevenson | Marriage and Divorce: Changes and their Driving Forces[END_REF] highlight that "social and economic factors strongly influence the marriage market" and that the marital status give labels that "have substantive economic content". This economic content could influence marital choices of couples, indicating that it is not neutral to political choices.

In a classic cost/benefit framework, couples decide to marry if their utility when married is greater than when cohabiting. Therefore, an attractive taxation for married couples should marginally impact the marriage rate: the more benefic the taxation of married couples, the higher the marriage rate.

In the analysis of the marriage contracts proposed by [START_REF] Matouschek | The Economics of the Marriage Contract: Theories and Evidence[END_REF], an attractive taxation of married couples can be considered as an exogenous benefit given to married couples. They show that it should increase the marriage rate, through an increase of low quality couples' marriage (low quality couples meaning high probability of divorce). But if the cost of marriage is high, the elasticity of marriage to taxation could be low. Therefore, examining the link between marriage and taxation is an empirical question.

The empirical literature tends to support the idea that taxation slightly impacts marriage rates.

Using the heterogeneity in the 'marriage penalty', papers by [START_REF] Alm | The rise and fall and rise... of the marriage tax[END_REF][START_REF] Friedberg | Did Unilateral Divorce Raise Divorce Rates? Evidence from Panel Data[END_REF] show that if significant, the impact of taxation on marriage rate is small in the US. In France, [START_REF] Buffeteau | Fiscalité et Mariage[END_REF] study the impact of the reform of taxation for cohabiting couples with children in 1995. They show that couples are sensitive to taxation: the probability of marriage has increased by about 5 points for young cohabitant couples with children.

Maybe couples do not react much to fiscal incentives because the cost of marriage is high compared to its fiscal benefit1 . In particular, the symbolic cost of marriage is still high and the cost of divorce is still important in France. In that case, what would happen if marriage was less symbolic and divorce less costly? It would change the overall cost of marriage: by changing the balance between costs and benefits, it could change the incentive to react to the benefits of marriage.

In France, different-sex couples can choose between two kind of marital contracts. The pacs2 was created the November 15 th , 1999. It aimed at giving same-sex couples a marital contract as same-sex couples can not marry in France. It was made as a median way between cohabitation and marriage.

It gives more rights and duties to the partners than cohabitation but less than marriage [START_REF] Waaldijk | More or Less Together : Levels of legal consequences of marriage, cohabitation and registered partnerships for different-sex and same-sex partners. A comparative study of nine European countries[END_REF]. Especially, one important difference is that it is easier to break up a pacs than a marriage and that it is less symbolic: pacs are contracted at a court and marriage at the town hall. Since it was created, the pacs had been popular among both different-sex and same-sex couples: the number of pacs contracted increased from 20,000 in 2000 to 172,000 in 20093 (excluding overseas départements).

The pacs has been modified twice since it was created. Income taxation was different for pacsed partners compared to married partners, it has been reformed in 2004 and taxation of pacsed couples had been made similar to income taxation of married couples. In 2006, rights and duties of pacsed partners changed and the pacs became a more binding contract, although it is still not as binding as marriage is because it is easier to break than a marriage. The increasing number of pacs has been largely attributed to the profitable taxation of pacsed couples, although this idea has not been verified.

In France, the tax system takes into account the size of the household (including children) but tax units are defined by the matrimonial status. Cohabiting couples have to fill two separate tax returns, and pacsed and married can declare jointly their income so they fill only one tax return.

This system of joint taxation of married/pacsed couples makes them pay less taxes, especially if the difference between the spouses' incomes is large. The year of the marriage/pacs, couples have to fill three tax returns: each spouse fills its own to declare the income earned before the marriage, and they jointly fill one for the incomes earned after the marriage. This system leads to large gain on taxes for couples, especially if they marry/pacs in the middle of the year. Therefore, it divides the year between an attractive part and an unattractive part to contract a pacs. The goal of the paper is to test the idea that taxation boosted pacs rates. For that purpose I analyze the 2005 reform of taxation of pacsed couples. Before 2005, pacsed partners could not directly jointly fill one tax return right after the pacs but they had to wait for three additional years before pooling their income for taxation issues. Married couples could jointly declare their income right after the marriage. After 2005, pacsed partners jointly declare their income right after the pacs. Therefore, the day of the pacs did not matter before the reform but it does after the reform. The same system is applied for the year the pacs is broken up. I analyze the impact of the reform in a difference-in-differences framework. I assume that the reform has two impacts: first, it increases the pacs rate, second some couples may delay their pacs from the unattractive part of the year to the attractive part. I show that a simple differencein-differences approach, that compares the evolution of pacs rates during the attractive part of the 2 The pacs, the income tax and the 2005 reform

The pacs: history and main changes

Demographic trends show that the use of marital institutions changed in France over the last decades. With 3.97 marriage for 1000 inhabitants in 2007, the marriage rate in France is lower than the average marriage rate in OECD countries (5 in 2007) and much lower than in the United-States (7.31 in 2007).

Couples tend to marry less and if they do, they marry older. In France, the marriage rate was about two times higher in 1970 with 7.75 per 1000 persons (OECD, 2010). Moreover, in 2008, the age at the first marriage in 29.7 for women and 31.6 for men. It was 26.7 and 28.6 in 1990. Then, marriage often occurs after a long period of cohabitation. In 2006, in France, 38% of men and women aged between 25 and 29 lived with their partner and are not married whereas 22% are married (INSEE, 2009). But describing marriage rates give a partial story of the marital strategies in France because marital institutions also changed.

One of the most important change in the institution of marriage in France was the creation of the pacs4 , a new legal form of union. It was inspired by other European countries. In 1989, Denmark paved the way to other countries by creating a new legal form of union, the registered partnership.

Then, a lot of countries (mostly European, but also in South America and some states in Canada and the United States) created registered partnerships or civil unions5 . They targeted same-sex couples and their claim for legal recognition. As same-sex couples had become an important lobby, their legal recognition was highly demanded. But the report directed by [START_REF] Waaldijk | More or Less Together : Levels of legal consequences of marriage, cohabitation and registered partnerships for different-sex and same-sex partners. A comparative study of nine European countries[END_REF] shows that the rights given to partners by civil unions are very different from one country to another. Most countries decided to create a median way between marriage and cohabitation. In Netherlands or in Sweden, civil unions are very close to marriages. In France or in Belgium, at least when it was created, civil unions were very different from marriage. Three main features distinguish most of civil unions from marriages, whatever the country. First, partners are less committed because duties towards the other partner are weaker. Second, civil unions do not give as many benefits to partners as marriage do.

Third, civil unions are easier to break. In most countries, civil unions are exclusively made for samesex couples. The French system is quite different. As in the Netherlands or in Belgium, different-sex couples can also contract a civil union, and not only same-sex couples. Today, different-sex couples can also contract a civil union in Brazil, South Africa, New Zealand, Quebec or Uruguay. Therefore, it provided an alternative to the marriage for different-sex couples in a context of decrease in the use of marriage. During the years following its creation, the pacs turned to be successful, especially among different-sex couples. In France, from its creation in 1999 to the end of 2009, 697,779 pacs have been contracted (excluding overseas départements, DOM). From 22,276 pacs contracted in 2000 to 172,104 in 2009, the pacs turned to be very successful. In 2009, 40% of the unions celebrated were pacs.

Different-sex couples have found a legal form that fits very well their need: the Ministry of Justice declared that in 2007 only 7% of new pacs were contracted by same-sex couples [START_REF] Carrasco | Le pacte civil de solidarité : une forme d'union qui se banalise[END_REF] and this proportion is still decreasing (INSEE, 2009). The increase of pacs compensates the decrease of the marriage rate: 6.71 unions (pacs+marriages) for 1000 persons were contracted in France in 2009France in (5.5 in 2000)).

When the pacs was created, the political area was highly divided on the topic and the success of the pacs was unexpected6 , because the political issue was mostly giving a legal recognition to same-sex couples or not. The effect of such a contract on different-sex couples was not debated. In 1999, the pacs was creating and legal dispositions made it different from the marriage but still attractive enough to satisfy same-sex couples claims for recognition. It was made to give a legal recognition to couples but without the symbolic meaning of marriage. Except the symbolic meaning, there were three main differences between the marriage and the pacs. First, the pacs was not (and is still not) recognized as a matrimonial status. This leads to different access to social benefit such as alimonies or survivor's benefit. Second, married couples benefited more from the tax system than pacsed couples. Third, it was easier to break out a pacs than a marriage. However, the success of the pacs made it difficult to sustain some inequality of treatment between the different types of couples. Therefore, three reforms have made the pacs closer to the marriage. In 2005, the income taxation has been made similar for pacsed couples and married couples. This change results from the claim for equity between couples, as there was no reason why a pacsed couple would be taxed differently from a married couple. Before 2005, pacsed couples were taxed differently from married couples. Especially, couples benefited from an attractive taxation the year they got married but not the year they get pacsed (this system is explained below). The reform was announced in September 2004 and settled on the 1 st of January 2005. A more general reform was voted in June 2006 and was settled on January 2007. Its goal was to strengthen the commitment between pacsed partners. And in 2007, inheritance tax system was changed both for pacsed and married couples. They are now the same for both types of couple.

Then, the 2005 reform coupled with the 2007 reform made the tax system similar for both married and pacsed couples. Taxation makes the pacs attractive, and the anti-pacs politicians pointed out that it was too benefic for a contract easy to break up as they feared tax evasion. The increasing number of pacs contracting raises questions. Which couples get pacsed? Why do they contract a pacs? Is the pacs a substitute to the marriage, a first step toward marriage or a substitute to cohabitation? But, it is difficult to explain the growing number of pacs because a very few data are available on pacsed couples and pacsed couples are mostly unknown. [START_REF] Carrasco | Le pacte civil de solidarité : une forme d'union qui se banalise[END_REF] describes that they are as old as married couples and that despite they are easier to break, pacs are not more broken than marriages.

Both the relationship between marriage, pacs and cohabitation and the reason to contract a pacs are difficult to understand because of the lack of data. The increasing success of the pacs has been read as tax-related (INSEE, 2009;[START_REF] Carrasco | Le pacte civil de solidarité : une forme d'union qui se banalise[END_REF] although no study assess a link between taxation and the decision to contract a pacs.

The income taxation in France

The income taxation in France is collective: members of the same tax unit pool their income and fill only one tax return. The tax unit is defined by the marital status of the partners. Cohabiting partners are considered as two different tax units. Married partners are considered as one tax unit since the wedding day. Before 2005, pacsed partners were considered as different tax units for the first three years of their pacs, and as one tax unit after. Since 2005, as married partners, they are considered as one tax unit since the day of the pacs. Therefore, since 2005, married and pacsed couples are taxed the same way in France. The next paragraph describes how this taxation system changes the amount of taxed paid.

The income tax is a progressive tax calculated on the income earned within the year. First of all, a 10% relief is applied, then only 90% of the annual income is submitted to the income taxation. The amount of income up to a certain amount t 1 is taxed at a rate r 1 , then the remaining money, up to a certain amount t 2 is taxed at rate r 2 , etc... The amount t i+1t i is taxed at a rate r i , with r i+1 > r i .

So, the income tax on the income I can be represented by f , a piecewise linear, continuous, increasing and convex function.

A tax relief targets low-income households. If the amount of tax is less than an amount D, so if f (I) < D, the household does not pay exactly f (I) but it benefits from a tax relief which is important if f (I) is very low.

Let g be the amount paid by the household. Therefore,

g(I) =    max f (I) -D-f (I) 2 , 0 if f (I) ≤ D f (I) if f (I) > D
The fiscal administration considers tax units, which size s depends on the matrimonial status and the number of children. For a single, the size is equal to (1 + k), with k a function of the number of kids. For a married couple, the size is equal to (2 + k). For example, a married couple without children has a size s = 2, with one child the size is s = 2.5. The total amount of tax paid for a tax unit of size s is s × g(I/s), where I is the total income of the tax unit. This fiscal system is called quotient familial (family ratio). An unmarried couple is considered as two tax units. If they have children, they have to divide children and put them in different tax units or put them all in the same tax unit. A married couple with children is considered as a single tax unit.

When they cannot pool their income, the two partners have to fill one tax return each. So the total amount of taxes paid by the household is given by:

g (C) (I) = s m g(I m /s m ) + s f g(I f /s f )
where I m (resp. I f ) denotes the male's (resp. female's) income and s m (resp. s f ) the size of the male tax unit. s m and s f depends on how children are split between the two tax returns. When they can pool their income, the two spouses have to fill only one tax return instead of two. They pay two times what someone earning the average income would have paid. Therefore, under the assumption that children do not earn income: the household pays

g (M ) (I) = s × g( I m + I f s ) Let f (C) (resp. f (M )
) be the amount of tax paid by an unmarried (resp. married) couple if the tax burden does not exist. Because of the convexity of f , f (C) ≥ f (M ) (the proof is given by [START_REF] Buffeteau | Fiscalité et Mariage[END_REF]). However, [START_REF] Legendre | Les concubins et l'impôt sur le revenu en France[END_REF] explain that it could be sometimes more interesting to stay in cohabitation because of the tax relief, which introduces non-linearities in the tax system for low income. So, f (C) ≥ f (M ) does not necessarily implies g (C) ≥ g (M ) for low incomes. Therefore, marriage is not tax attractive for all couples. But as a general matter the more different incomes are, the more couples benefit from being married. An interested reader should report to [START_REF] Buffeteau | Fiscalité et Mariage[END_REF], [START_REF] Legendre | Les concubins et l'impôt sur le revenu en France[END_REF] or [START_REF] Amar | Se marier ou non, le droit fiscal peut-il aider à choisir ?[END_REF] for further explanations on that point. A particular fiscal arrangement the year of marriage sharply decreases the amount of taxes. The decrease is so large that it benefits to all couples, even low income households for whom marriage is not tax-benefic. So, low income couples benefit from being married the first year of marriage, but not for the years after. Other households benefit for marriage, even in the long term, but the benefit is larger the first year of marriage.

The year they marry (or the year they contract a pacs since 2005), the partners have to fill three tax returns: each partner fills her own tax return for the amount of income earned from the 1 st of January to the marriage day and they fill a common tax return for the income earned from the marriage day to the 31 st of December. If they get married (or pacsed) after a period of (t * 100)% of the year, they have to pay an amount of tax of:

g (Y M ) (I) = s m × g(t * I m /s m ) + s f × g(t * I f /s f ) =B(t) + s × g (1 -t)(I m + I f ) s =A(t)
with s = (s m + s f ) in most cases. As the rates are not changed when incomes are earned on a few months, the partners can minimize the amount of taxes by choosing the optimal marriage day.

Indeed, B(t) is increasing with t while A(t) is decreasing with t. Then, the amount of income taxes to be paid for the year of the wedding depends on the difference of incomes between the partners and on the wedding day. Most of the time, the optimal date occurs during the second or the third quarter of the year. Figure 1 shows examples of the amount of taxes paid by five couples depending on the day they marry. The greater the difference of income between the spouse, the closer to the beginning of the 2 nd quarter the optimal day is: even if they still pay taxes, the couples for whom one spouse earns 40,000 euros a year and the other one does not work and the couple with incomes 30,000 and 10,000 save more taxes marrying during the second quarter. Lower income households do not pay taxes at all if they marry during the third quarter. Using data from the Labour Force Survey (LFS), it is possible to compute for each unmarried couple which day (or days) is (are) the optimal one(s) for them. Notice that because of the tax relief for low income, lot of couples could have no tax at all to pay for the year of marriage. They could have the choice between a large number of optimal day. The LFS provides information for each couple about their marital status, the number of children and their wages. I compute for each unmarried couple with at least one employed partner the amount of taxes that they would pay if they decided to get married, for each day of the year7 .

I can therefore simulate which day would be the optimal one for each couple, and how much they save compare to a regular year when married and compare to a regular year when unmarried. Figure 2 gives the distribution of the optimal days among the population of unmarried couples, depending on the number of children they have 8 . The figure clearly shows that for most couples, the optimal day occurs during the 2 nd or the 3 rd quarter, including when they have children. Couples for whom the optimal day occurs during the first or the fourth quarter are mostly low income couples that do not pay taxes including for a regular year. Figure 3 simulates the amount of tax that unmarried couples would pay (in % of income) for a regular year if unmarried/unpacsed, for a regular year if married/pacsed and for the year of marriage/pacs. It clearly shows that couples pay less taxes for the year of their marriage/pacs. Only the 10% richest couples are not able to avoid paying any taxes the year they get married/pacsed, but they only pay 3% of their annual income. The remaining 90%

of the population are able to avoid paying any taxes for the year of their marriage/pacs, providing they get married/pacsed the optimal day.

The 2005 reform of the taxation of pacsed partners

Before 2005, the taxation of pacsed partners was different from the taxation of married couples.

Especially, they did not benefit from the fiscal arrangements the year of pacs as married couples did.

The pacsed partners had to wait for the third year after they contracted their pacs in order to pool incomes and to fill one tax return for the incomes earned during the whole year. And then, they were taxed the same way as married couples. As a consequence, the date of pacs did not have any effect on the amount of taxes paid neither the year the pacs was contracted nor three years later, when they pooled their income. Since 2005, pacsed couples have to fill three tax returns for the year of the pacs, exactly as married couples do. The reform reduces significantly the amount of taxes paid for the year of the pacs. If the incomes of partners are significantly different, it leads to reduce the amount paid the two years after the pacs. After, the amount of taxes paid is the same before and after the reform.

Most of the time, couples marry and celebrate their marriage the same day. So, as the partners have many factors to deal with when deciding the date for marriage, it is hard to believe that couples choose the date of the marriage in order to minimize the amount of taxes paid. On the contrary, a pacs is not as celebrated as a marriage. If it is celebrated, the celebration is not organized the day the pacs is contracted because as the pacs is contracted in a court, it is contracted during the week, without any witness [START_REF] Rault | L'invention du PACS[END_REF]. Then it is possible to choose the optimal date to contract the pacs and to celebrate it later. As there are not as many factors that could determine the pacs day as for marriage day, couples are able to choose the date in order to minimize the amount of tax paid.

The reform makes the pacs more attractive than what it was to unmarried couples, because it can lead to pay less taxes the year of the pacs. Moreover, breaking a pacs is easy and costless 9 , then the couples in France but the number of optimal days. 9 It has changed in 2006. It is still easy to break a pacs but the reform of the pacs of 2006 made the commitment commitment induces by a pacs is not very strong. However, if the pacs is broken during the same year or during the following year, the effect on the income tax is canceled. Notice that when a pacs is broken at least two years after it is contracted, the partners have to fill three tax returns for the income earned the year of the dissolution, one for the couple for the period from 1 st of January to the dissolution day and one for each partner from the dissolution day to the end of the year. A letter is sufficient to break a pacs10 , making the dissolution easy and fast. As a consequence, the partners have the opportunity to pay less taxes the year the pacs is broken up by choosing the optimal date.

Thus, under the assumption that couples answering to the incentive induced by the reform have the optimal answer, four effects should be observed. First, as the pacs is made more attractive, more pacs should be contracted after 2005. Second, tax-induced pacs should be observed during the second or the third quarter. Third, couples should not break their pacs during the same year or during the following year they contracted their pacs (i.e. until the next tax return). Fourth, couples who break their pacs may do it during the second or the third quarter.

One should bear in mind that the reform also changed the amount of income taxes paid for the next two years of the pacs year, compared to the amount of income taxes paid by partners that had pacsed before the reform. Three years after the year of the pacs, the income taxation is the same after and before the reform. Therefore, a positive impact of the reform on the number of pacs contracted means that short-term issues are taken into account in the decision to pacs. The last interesting point is that in 2005 nothing changed for the pacs except the income taxation.

However, some changes in the legislation of the pacs occured after 2005. Moreover, the legislation of divorce has also changed in 2005, making the divorce easier11 . It could change the opportunity cost of being pacsed. The competition between pacs and marriage could be more fierce: couples that would have contracted a pacs do not hesitate contracting a marriage because it is less committing.

But the link between pacs and marriage is unclear and it depends on the model of formation and dissolution chosen. The cost of divorce is still higher than the cost of separation of a pacs, so it is very unlikely that couples consider that the two contracts are now closer. Moreover, as explained in the section on the estimation strategy, these two changes are not likely to affect my results.

between partners stronger and it gives the partners the right to court the partner for the damages induced by the dissolution.

3 Data and preliminary evidences

Available Data

A pacs is not contracted at the town hall as marriages but at the closest court from the place where at least one partner lives. Then, data belong to the Ministry of Justice. Micro data have been highly

protected until 2004. The legislator feared for homophobia and violence towards pacsed people.

Therefore, they decided to protect couples by registering pacsed couples on a secret file that was not available, even for statisticians from the Ministry of Justice and by preventing national surveys from asking couples if they were pacsed or not. Therefore, the main surveys in France, such as the Labor Force Survey, do not include any information about pacs. Because of the growing number of pacs, the protection disappeared in 2005 but micro data are still not available, except for statisticians from the Ministry of Justice. That is why some descriptive figures on pacsed couples are available thanks to [START_REF] Carrasco | Le pacte civil de solidarité : une forme d'union qui se banalise[END_REF]. But, only aggregated data on the number of contracted are available, which make it impossible to have access to crucial information, such as the incomes of the partners. Therefore, only the total impact of the reform and not the heterogeneity of the impact in the population as it is not possible to gauge the effects of the reform at different level of income. Similarly, the data give the aggregated number of broken pacs, and not the duration of the broken pacs. So it is not possible to evaluate the hasard rate of dissolution of pacs.

The data only give the number of pacs contracted and broken up in each court, for each quarter.

There are 462 courts in France (20 in Paris, so it makes 443 when Paris is aggregated). Then I consider 10 years, i.e. 40 quarters. Therefore I have 18480 observations (17720 when Paris is aggregated).

Controls are constructed using census data, at the town level. Towns are then gathered into courts. Therefore, the geographical unit is the smallest unit on which the pacs rate can be computed.

Demographic trends

The marriage rate decreased since 1980, except for some short period of time. Since it was created in 1999, the number of pacs contracted by year increased a lot leading to an increasing overall union rate.

The number of pacs contracted has increased a lot since it was created (see table 2). 22,108 pacs were contracted in 2000, the first complete year of the pacs, and 172,104 were contracted in 2009.

In 2000, approximately 284,000 marriages were celebrated, and 254,000 in 2009. Therefore, the total number of unions increased in France over the last decade. However, the proportion of pacs couples in the population remains small, because it is still a recent form of union. The fiscal statistics 12

indicates that in 2009, over 100 persons filling their fiscal form, 1.6 is filled by a pacsed person, 50.8 by a married couple, 29.4 by a single, 10.1 by divorced individual and 8.1 by a widow.

The increase in the number of pacs and the decrease in the number of marriages is wide spread in France. As table 2 shows, the pacs rate per 1000 persons aged 15-59 years old 13 has increased in all courts: the mean pacs rate has increased from 0.5 in 2000 (with a standard deviation of 0.22) to 4.05 in 2009 (with a standard deviation of 1.11). it was equal to 10.0 in 1981, it is equal to 10.3 in 2009 but it was equal to 7.5 when the pacs was created in 1999.

As expected, the seasonality of the pacs changed after the reform. Figure 4 shows that the pacs rate increased for each quarter, but the seasonality was completely reversed after the reform. The number of pacs contracted during the first quarter decreased right after the reform. This could be explained by a schedule impact: some couples decided to contract a pacs but instead of contracting it immediately after they took their decision, they have waited for a few months in order to benefit from the newly attractive tax system.

The evolution of the number of broken pacs should follow the same pattern. However, the duration of the broken pacs is not observed. As a consequence, the hazard rate can not be computed. Using the number of ever contracted pacs in the court as a denominator would be an inaccurate estimate of the hazard rate because the increasing number of contracted pacs change the composition of pacs couples. Indeed, the proportion of newly pacsed couples tends to increase, making difficult the interpretation of the stability of the pacs rate. As a consequence, I study the evolution of the crude rate of dissolution. It is computed as the number of broken pacs for 1000 persons aged 15-59. Table 12 Déclarations Nationales d'Impôt sur le Revenu, http://www2.impots.gouv.fr/documentation/statistiques/2042_nat/Impot_sur_le_revenu.htm 13 Although the age of pacsed spouses is unknown, I assume that most pacs are contracted by partners less than 60 years old. This assumption seems reasonable since (a) [START_REF] Carrasco | Le pacte civil de solidarité : une forme d'union qui se banalise[END_REF] showed that pacsed couples are similar to couples getting married for the first time and (b) only 2.3% in 2000 and 4.7% in 2009 of marriages were contracted by partners aged more than 60. This rate seems more intuitive than the classic raw rate for 1000 persons.

13 3 shows that the number of dissolution increased a lot. But the level of the rate of dissolution heavily relies on the number of ever contracted pacs. However, if couples change their separation behavior for fiscal reasons, the seasonality of the dissolution of pacs should change after the reform. Therefore, I will not comment much on the level of the dissolution rate but on the seasonality. The seasonality of the dissolution of pacs is presented in figure 5. The number of dissolutions was already higher during the attractive part of the year before the reform. The seasonality does not change after the reform, and it tends to be reinforced after.

I also present the results for the dissolution rate computed as the number of dissolution per 1000 pacsed couples. Table 4 shows that after a large increase during the first years the dissolution rate tended to become stable. But this evolution is difficult to interpret. Indeed, the large increase in the pacs rate changes the population of pacsed couples over the time. Figure 6 presents the seasonality of this dissolution rate: it is not changed after the reform of taxation.

4 The estimation strategy

Limits of a difference-in-differences estimator

The identification strategy relies on the characteristics of the taxation system. Indeed, the way the quotient familial is implemented introduces a distinction between two parts of the year: the attractive part and the unattractive part for taxation matters. The attractive part is composed of the 2nd and the 3rd quarters (spring and summer) and the unattractive part is composed of the 1st and the 4th quarter (autumn and winter).

The identification strategy relies on the idea that couples getting pacsed because of the reform are going to contract their pacs during the attractive part of the year. The estimation of the total impact of the reform is easily obtained by a difference-in-differences estimation strategy using the quarters of the unattractive part of the year as a control group and the quarters of the attractive part of the year as a treated group. This estimation gives the impact of the reform under two main assumptions:

(a) The number of pacs contracted during the unattractive part of the year is unaffected by the reform.

(b) Without the reform, the number of pacs contracted during the attractive part of the year would have evolved the same way as the number of pacs contracted during the unattractive part of the year (common trend assumption).

If the two assumptions are verified, comparing the evolution of the number of pacs contracted during the attractive part of the year to the evolution of the number of pacs contracted during the unattractive part of the year gives the total impact of the reform.

These two main assumptions could be unverified for two main reasons. First, remember that the reform modified the income taxation for the three years following the pacs, even if the first year is the most affected. So, the unattractive part of the year could also be affected because couples contracting a pacs during this part of the year see the taxes they pay modified during the first three years following the pacs. So the number of pacs contracted could increase during both part of the year.

As a consequence, if the unattractive part of the year is also affected by an increase in pacsed couples because of the reform, this increase is going to be interpreted as the year effect, so the difference-indifferences estimation is biased and it underestimates the true impact of the reform, because it takes as a baseline the number of pacs contracted during the unattractive part of the year, which is boosted by the reform. However, as it is much more profitable to contract a pacs during the attractive part of the year, it is likely that couples getting pacsed for fiscal reasons are going to contract their pacs during the attractive part of the year, so it is highly believable that the number of pacs contracted during the unattractive part of the year is unaffected by the reform even if couples contracting their pacs during this part of the year are also affected by the reform.

Moreover, the difference-in-differences method only gives the total impact of the reform, which is composed of two effects. First, the reform could have a direct and positive impact on the number of pacs contracted. Second, the reform could have an indirect impact: couples that would have contracted a pacs anyway are now more likely to do so during the attractive part of the year. Let's call this impact the "schedule impact". In that case, the number of pacs contracted during the unattractive part of the year is lower than what it would have been if the schedule impact was null.

In other words, the stable unit treatment value assumption defined by Joshua D. [START_REF] Angrist | Identification of Causal Effects Using Instrumental Variables[END_REF] does not hold. Therefore, the difference-in-differences estimator estimates the total impact of the reform, including the schedule impact. It is not possible to disentangle the direct impact of the reform from the schedule impact of the reform unless one assumption is added. This problem is similar to a problem of contamination between the two groups: let y iqT be the rate of pacs contracted in the court i, during the quarter q of the year T . Years are recoded in order to begin with the 4th quarter and to end with the 3rd quarter. The recoding makes sense because: (a) the pacs was created in the 4th quarter 1999 (b) the reform was announced just before the beginning of the fourth quarter 2004. As, it was an unexpected reform, couples were not able to delay their pacs in order to benefit from the reform before the 4 th quarter of 2004. y iqT is written as:

y iqT = α 0 + α T + α iq + δ qT + u iqT
where α T is the year fixed-effect, α iq is a combined fixed effect for courts and quarters and δ qT are a combined fixed effect of year and quarters. The impact of the reform on the pacs rate is given by the evolution of the δ qT s. The δs are composed of the direct and the schedule impact. On the one hand, let β T give the direct impact of the reform: the pacs rate increases with β T during the attractive part of the year in year T . On the other hand, let γ T represent the schedule impact: it increases the pacs rate during the attractive part and decreases the pacs rate during the unattractive part of the year. The attractive part of the year is divided into two quarters: let p 1T (resp. p 2T ) be the part of the direct impact β T (resp. schedule impact γ T ) of the reform contracted during the 2 nd quarter. The unattractive part is also divided into two quarters: let p 0T be the proportion of couples delaying their pacs that would have contracted their pacs during the 1 st quarter. Therefore, the δ qT are:

δ qT =                -(1 -p 0T )γ T , if q=4 -p 0T γ T , if q=1 p 1T β T + p 2T γ T , if q=2 (1 -p 1T )β T + (1 -p 2T )γ T , if q=3
The δ qT represents 5 parameters and there are only 4 equations. There are clearly too much parameters and the estimation of such a model is infeasible.

As we are interested in the β T s, the γ T s and the α T s, the pacs rate can be written as y isT where s indicates the semester. s = 1 for the unattractive part of the year and s = 2 for the attractive part of the year. y iT,s=1 = y iT,q=1 + y iT,q=4 is the pacs rate for the unattractive part of the year and y iT,s=2 = y iT,q=2 + y iT,q=3 is the pacs rate for the attractive part of the year.

y isT = 2α 0 + 2α T + α is + δ sT + u isT (1)
where

δ sT =    -γ T , if s=1; β T + γ T , if s=2;
A difference-in-difference estimation would give an estimation of α Tγ T as the year effect and β T + 2γ T as the impact of the reform. Therefore, if γ T > 0, it tends to underestimate the year fixed effect and to overestimate the incentive impact of the reform. Nevertheless, the DID estimator provides an estimation of the total impact of the reform on couples's behavior.

Identifying bounds: extended difference-in-differences-in-differences

The usual way to get rid off externalities consists in using two control groups and to compute a difference-in-differences-in-differences (DDD) estimator. One control group (C1) is affected by the reform and loose γ T pacs, but the other (C2) is not affected. The treated group (T) receive the direct impact of the reform and the delaying pacs (β T + γ T pacs). Comparing T and C2 identifies β T + γ T , comparing C2 and C1 identifies γ T and the comparison of the differences identifies β T .

Unfortunately, I cannot distinguish two control groups in the pacs case, but the DDD estimator could be extended in the case in which there are two controls group that are not affected with the same intensity by the reform. Taking advantage of the variation between the control groups does not permit a point identification of the incentive impact of the reform, but it gives bounds for the incentive impact of the reform. The estimation method is called thereafter "extended difference-indifferences-in-differences" or E3D for clarity reasons.

I consider two control groups: the fourth and the first quarter of the year. Both quarters are untreated, because they are part of the unattractive part of the year. Yet, both of them can suffer from negative externalities: some couples are likely to delay their pacs to wait for a more attractive part of the year to contract their pacs. But both quarters are not likely to be affected the same way:

if couples have a large enough preference for the present, it might be more difficult to delay a pacs from the fourth quarter to the next spring/summer than from the first quarter to the next spring.

In order to disentangle the direct impact of the reform from the schedule impact, I recode the time windows q in a variable t such as, t = 0 for the fourth quarter, t = 1 for the first one and t = 2

for the sum of the second and the third quarters. Then:

y itT = α 0 + α T + α it + δ tT + u itT (2)
with

δ tT =          -(1 -p T )γ T , if t=0; -p T γ T , if t=1; α 0 + α T + β T + γ T , if t=2;
p T is the proportion of delayed pacs that would have been contracted during the first quarter, have they not delay their pacs. The closer p T from 1/2, the more similar the two controls group are.

The extreme case, p T = 1/2 prevents from identifying γ T , because the difference between the two controls group is 0. On the contrary, p T = 1 and p T = 0 corresponds to the DDD estimator.

The difference-in-differences-in-differences method gives an estimation of the β T s, the γ T s and the α T s that depends on the value of p T . Indeed, the estimated equation is:

y itT = α 0 + α it + a 0T + a 1T + a 2T + u itT (3)
with the α iT s are court crossed with period of the year fixed effect, the a 0T s are year fixed effects, the a 1T s (resp. the a 2T s) are year fixed effects crossed with a dummy for t = 1 (resp. t = 2) and

         a 0T = α T -(1 -p T )γ T a 1T = (1 -2p T )γ T a 2T = α T + β T + (2 -p T )γ T
The a kT are statistical parameters, used to estimate the interpretable parameters α T , β T and γ T .

Then, for a given p T :

         α T (p T ) = a 0T + 1-p T 1-2p T a 1T γ T (p T ) = 1 1-2p T a 1T β T (p T ) = a 2T -a 0T -(1 + 2 1-2p T )a 1T (4)
Therefore, the identification of the bounds requires some conditions on the parameters: if a 1T < 0

and a 2T -a 0T + a 1T ≥ 0 ∀T ≥ 0 or if a 1T > 0 and a 2T -a 0T -3a 1T ≥ 0 ∀T ≥ 0 then it is possible
to identify an upper and a lower bounds to the β T and the γ T (see the proof in section A.1 in the appendix). These conditions are easily verified in the data. But the estimation of informative bounds requires two assumptions. The first assumption simply states that β T ≥ 0 and γ T ≥ 0, ∀T ≥ T 0 . This assumption is not very strong as it stipulates that if the reform has an impact on couples behavior, it has been indeed incentive and it did not discourage couples to contract a pacs during the attractive part of the year. Moreover, it indicates that delaying pacs are going from the unattractive part of the year to the attractive part of the year. This assumption is likely to be unverified if some couples prefer to wait for the unattractive part of the year to signal that their pacs is not a tax induced pacs. It is also unverified if the reform implied an important increase in the number of pacs, leading to overburden courts and a crowing out effect. Although this story can not be rejected, it is very unlikely to affect the courts the first year after the reform. Indeed, the impact of the reform, albeit strong, is not likely to be strong enough to induce a large crowding out effect: registering a pacs is a simple administrative procedure and some employees were already affected to registering pacs. After some years, the court may adjust their labor force to the increasing number of pacs.

It is always possible to find a p T such as β T (p T ) = 0, and the bound is not informative. So, the second required assumption is that p T , the proportion of delaying couples that would have contracted a pacs during the first semester is constant over time. A change in this proportion could be justified by a relative change of the composition of couples willing to get pacsed during the fourth quarter compared to couples willing to get pacsed during the first quarter. This is unlikely, as the reform of taxation is the only reform of the pacs that might change the seasonal composition of pacsed population.

In order to define the bounds, I fix a p * , which is the only p such as γ T (p) ≥ 0 and β T (p) ≥ 0, for all T and p ≥ p * . If p ∈]1/2, +∞[, the bounds are given by:

         α T (p) ∈ [α T (1); α T (p * )] γ T (p) ∈ [γ T (1); γ T (p * )] β T (p) ∈ [β T (p * ); β T (1)]
Notice that both the DID and the E3D estimation strategy relies on the change in the seasonality of the pacs. As a consequence, the results are likely to be biased if the seasonality is affected at the same time. In 2005, the divorce law has been modified, making the divorce easier. It could alter my results if the couples likely to contract a pacs during the attractive part of the year react to the change in the divorce law differently from those couples likely to contract a pacs during the unattractive part of the year. Although this assumption can not be tested, it seems rather unlikely.

Indeed, as explained if [START_REF] Rault | L'invention du PACS[END_REF], the decision to contract a pacs is led by very different reasons

Results

Effect on the pacs rate

All estimations presented above are based on a difference-in-differences estimation. Therefore, the standard errors might be biased downward in case of autocorrelation of the error terms, as explained in [START_REF] Bertrand | How Much Should We Trust Differences-in-Differences Estimates?[END_REF]. As a consequence, all standard errors are clustered at the court level.

The explained variable is the pacs rate for 1000 persons aged 15-59. First I estimate the differencein-differences model, given by the equation 1. Results are given by the table 5. Columns (1) and ( 2 Then, I estimate the model described by equation 3 using the E3D method, in order to define bounds for the impact of the reform. As a robustness check, I construct another explained variable:

the pacs rate for 1000 couples. However, this variable is likely to have high measurement errors because couples are not well measured in France. Indeed, until the last census, people were not asked if they were single or not. Therefore, the number of couples was approximated by the number of married couples before 2006. For each explained variables, I also test the robustness of the results using different specifications: including crossed court-period of the year fixed effects compared to period of the year fixed effects or including time varying variables as controls regarding the socioeconomic environment, although these controls have not been found having a good explanatory power for the difference in difference estimation.

Results of the regression for the number of pacs contracted are given by the tables 6 and 7. The parameters are not interesting per se but they are used to check if the necessary conditions are verified or not. My results are robust across specifications using both pacs rates. So I construct the results of the estimation of the structural parameters only for the full specification, i.e. the pacs rate per 15-59 years old persons, including controls and court crossed with period of the year fixed effects.

For each specification, the last column indicates if the required conditions a 1T < 0 and a 2T -a 0T + a 1T > 0, ∀T ≥ T 0 are verified (as I suspect p > 1/2, i.e. more delayed pacs for the first quarter than for the fourth). They are clearly verified for all years after the reform. Therefore, it is possible to find a p such as 1 ≥ p > 1/2, in order to construct the upper and lower bounds to the direct and the schedule impacts of the reform. p * = 0.853 is the lowest p such as γ T (p) ≥ 0 and β T (p) ≥ 0 for all years after the reform. The structural parameters α T (p), γ T (p) and β T (p) are estimated using the system 4.

The estimated upper and lower bounds of the reform are given in table 12 and plotted in figures Table 13 presents the proportion of the pacs rate that can be attributed to the reform. The direct impact of the reform increased the average pacs rate by 13%-20% in 2006 until 16%-21% in 2009.

The schedule impacts represents around 7%-10% of the pacs rate in 2006 and 6%-8% in 2009.

The counterfactual of the average pacs rate without the reform is given by figures 11. The figures clearly show that the pacs rate would have been lower without the reform, but it would have increased anyway. Therefore, fiscal incentives only explain part of the total increase of pacs rates in France.

The overall increase of the pacs rate would have been more equally distributed over quarters without fiscal incentives.

Effects on dissolutions

As the pacs is easily broken, couples could adjust their decision to break up their pacs to the tax system in order to benefit from its effects the year they break up.

There are four different ways to break up a pacs. First, if partners agree on the dissolution, they can send a letter to the court to break up the pacs. This is a mutual consent breaking. Second, if partners do not agree, a pacs can be unilaterally broken up: the leaving partner has to write a letter to the court and to the other partner through a lawyer to announce its decision. Third, a pacs is automatically broken when the couple get married in which case partners do not have to send any letter to the court. Fourth, the pacs is automatically broken if one of the partners dies and the surviving partner does not need to write a letter to the court. In all cases but marriage, partners benefit from the three tax returns system. As death is not a choice, only the number of mutual consent and unilateral dissolutions are likely to be affected by the reform. Thereafter, the dissolution rates consider only those two types of dissolution.

A simple letter is sufficient to break up a pacs: the schedule could be manipulated by couples.

I study the impact of the reform on dissolution rates using the same framework as the contracted pacs rate. Indeed, the expected impacts of the reform, if any, should be similar. As for the year the pacs is contracted, couples face the same tax system (but inverted) the year the pacs is broken up. The couple has to fill three tax returns: they pool their incomes for the first part of the year until the day the pacs is broken and they have to fill two tax return for the part of the year after the pacs is broken. Therefore, they could benefit from the same attractive taxation. If couples are sensitive to that incentive, two impacts are expected: (1) an increase in the number of broken pacs, (2) more pacs should be broken during the attractive part of the year, resulting from an incentive effect and a schedule effect. The estimation strategy is the same as before. The difference-in-differences strategy identifies the impact of the reform on the number of dissolutions under the common trend assumption, considering the unattractive part of the year as a control group. As for the contracted pacs, bounds of the direct and the schedule effect could be identified using the E3D method if the number of broken pacs is significantly different between the two control groups, i.e. if the conditions a 1T < 0 and a 2Ta 0T + a 1T > 0, ∀T ≥ T 0 or a 1T > 0 and a 2Ta 0T -3a 1T > 0, ∀T ≥ T 0 are verified.

An increase in the number of dissolutions could be observed right after the reform, because the tax system gives an incentive to break up the pacs to all pacsed couples. But the increase should be more accurate after 2007. The increase in the number of pacs because of the direct impact of the reform on contracted pacs could change the composition of pacsed couples. Especially, couples sensitive to taxation are now pacsed and they could also be sensitive to incentives to break up their pacs. But they have to remain pacsed the year following their pacs to benefit from the attractive tax system. So if they decide to break up their pacs for tax benefit, they should do it two years later.

Therefore, an increase of the dissolution rate could be observe after 2005, another after 2007.

I consider two definitions of dissolution rates: (1) the number of dissolution for 1000 pacs (contracted at least 6 months before), (2) the number of dissolution for 1000 persons aged 15-59 years old.

However, none of them is easily interpretable. The number of dissolutions for 1000 pacs takes into account the at-risk population, i.e. the pacsed couples. However, the large increase in the pacs rate, especially after 2005, change the composition of the pacsed population. It makes the ratio difficult to interpret as it considers all pacs as similarly affected by the risk of separation. Moreover, the seasonality increase the number of pacs differently over the year, adding couples unlikely to break up.

The ratio is computed for 1000 pacs contracted at least 6 months before in order to take into account population more likely to break up. The number of dissolution for 1000 persons aged 15-59 years old does not take into account the at-risk population. It just rescales the number of dissolution to take into account differences in the size of the courts.

The difference in differences estimation is given in tables 8 and 9. Considering the rate of broken pacs for 1000 persons, the affected semester tends to be always different from the unaffected semester (columns (1) to ( 4)). This is no longer the case when considering the rate of broken pacs for 1000 pacs in table 9, especially when court×sem. fixed effects are added (columns ( 7) and ( 8)). It shows that the rate of broken pacs for 1000 pacs is unaffected by the reform. The rate of dissolution for 1000 pacs is affected by the reform when court×sem. fixed effects are not added. Excluding court×sem.

increases the point estimate which could explain that it becomes significant. On the contrary, the DID estimation on the rate of broken pacs for 1000 persons aged 15-59 shows that the variable year×sem.

tend to be significant, indicating that the second semester has followed a different path from the first semester even before the reform. However, this is no longer the case when the court×sem. are added.

So the difference between the first and the second semester was stable across time before the reform.

The point estimate increases suddenly from 0 in 2004 to 0.0166 in 2005: the reform had an impact on the the rate of dissolution for 1000 persons aged 15-59. Surprisingly, it decreases in 2007 from 0.0156 to 0.00862, but it increases after. This change could be attributed to a change in the composition of the population of pacsed partners after 2005. As this impact could be attributed to couples delaying the day they break up the pacs or to the incentive impact of the reform, I estimate the model using the extended DDD method given in 3 for the rate of dissolution for 1000 persons aged 15-59 years old, in order to identify bounds to both effects. It is not necessary to estimate the model using the E3D method for the dissolution rate for 1000 as the difference-in-differences estimation does not exhibit any impact of the reform.

The results of the estimation of the extended DDD are given by the table 11. The results are more difficult to interpret than results on the contracted pacs because the sign of a 1T is not constant after the reform: couples were less likely to break up their pacs during the first quarter than during the fourth quarter from 2005 to 2007, and this is reversed in 2008 and 2009. The coefficients a 1T are not (or slightly) significant in 2007 and 2008. It denotes that the dissolution rates during first quarter is not statistically different from the dissolution rate during the fourth quarter. The identification of bounds requires that the sign of the a 1T is constant across T , in order to determine p * . As a consequence, it is not possible to identify bounds on the two potential effects of the reform in the case of broken pacs.

The difference-in-differences estimation tends to show that the reform did impact the behavior of couples toward the dissolution of their pacs as it increases the relative number of dissolution during the attractive part of the year compare to the attractive part of the year. However, it is not possible to disentangle the incentive impact from the schedule impact of the reform on broken pacs. The difference-in-differences estimation of the impact of the reform on the number of dissolution on the number of ever contracted pacs does not exhibit any impact of taxation on dissolution behavior, but this rate is an inappropriate measure of the hazard rate of dissolution.

Interpretation

The different evolutions of the distinct effects of the reform can be explained by information issues.

During its first years, the pacs was still a new contract and it was thought same-sex couples targeting, because the public debate mostly focused on this point of the contract. The pacs rate did not increase much because couples were not aware that it was an interesting form of registered partnership. But as couples acquired information about the contract, the pacs rate started to grow naturally. When the reform was settled in 2005, most couples did not know that the pacs became more attractive in terms of taxation. Therefore, they did not answer the incentive right after the reform. But information relative to taxation of pacsed couples spread out after the reform, explaining why more couples want to benefit from it as time goes by. In the same time, couples that decide to contract a pacs for reasons distinct from taxation acquired information about the pacs. Then they could react directly to the incentive. This kind of couples could be a stable part of the population, explaining why the schedule impact of the reform did not increase over time.

The incentive impact of the reform on the decision to contract a pacs indicates that unmarried couples are likely to consider the amount of tax paid at the household level, inducing some income pooling between the partners. However, the lack of micro data forbids a better analysis of intrahouseholds behavior.

Moreover, the results indicate that couples do react to fiscal incentives, meaning that the public policies could impact the marital status of partners. So the marital status of partners could be led by political choices on the family.

The attractive tax system for broken couples after the reform impacts the dissolution behavior of couples. However, it is not possible to distinguish if the reinforcement of the seasonality is explained by an increase in the dissolution rates or an adaptation of couples to the new system. However, the adaptation results in a jump from 0.0167 to 0.0333 of the dissolution rate for 1000 persons aged 15-59 years old (approximatively 40 millions): so it represents roughly 700 broken pacs by court i.e. 1% of all dissolutions. So even if the impact of a dissolution on taxes is large, it did not infer a large increase in the dissolution behavior of couples. Was this result unexpected? Not really, given that the benefit from the tax system is evaluated at the couple level. But at the spouse level the reform is not necessarily attractive, unless spouses transfer income to each other. Contracting/breaking up a pacs is attractive when spouses pool their income or at least if they can easily transfer income from the richer to the poorer one. Getting pacs is part of the construction of the couple: so they can easily pool their income. But breaking a pacs in order to benefit from the tax system require some ex post transfers that are less easily done by a breaking couple. Couples do not take advantage of the tax incentive the year they break up: it tends to show that couples do not do ex post transfers. So, even if this would be benefic at the couple level, they do not pool their income once they decide to break up their pacs. Of course, this system could be used as tax evasion means14 . In that case, fake couples could contract a pacs and break up the pacs every other year in order to optimize the tax they have to pay. We provide suggestive evidence that if this kind of behavior exists, it is very marginal.

Conclusion

A costs/benefits analysis of marital behavior predicts that an attractive taxation of married couples should increase marriage rates. Although taxation is not marriage-neutral in many countries, taxation has not been found to have a clear and significant impact on marriage rates. In some Western Europe countries, couples can either get married or contract an other form of marital contract. In France, this contract is called pacs. I show that taxation does impact the decision to contract a pacs in France and that 16-20% of pacs contracted in 2009 can be attributed to an attractive tax system.

The identification strategy relies on a difference in difference method. The tax system changed for pacsed partners in 2005. Before 2005, the date the pacs was contracted did not change the amount of income taxation paid for that year. After 2005, the date of the pacs impacts the amount of tax paid.

It is now more attractive to contract a pacs, especially if it is contracted during the attractive part of the year. I distinguish two types of reaction to the reform: the incentive impact (couples getting pacsed because of the tax incentive) and the schedule impact (couples that would have contracted a pacs without the reform but change the day they contract it in order to benefit from the tax system).

I show that the schedule impact stays stable and represents 0.15-0.30 points of the average pacs rate in the courts. The incentive impacts was very small right after the reform, but it increased over time and it represents 0.65-0.85 points of the average pacs rates (i.e. 16-20% of the total mean pacs rate) in 2009. I do not find any impact of income taxation on the decision to break up the pacs.

The paper shows that although marriage behaviors are not closely related to tax incentive, pacs behaviors are sensitive to attractive taxation. However, the relationship between pacs and tax is not as close to what politics feared. Indeed, deputies feared that pacs could favor tax evasion. I show that there is no evidence that the dissolution of pacs has been favored by the tax system. The tax system the year of the pacs/marriage has been changed in 2010 (starting in 2011): since 2011, couples do not benefit from the tax system presented in the paper. There were several reasons invoked to justify the reform, among which the idea that pacs favored tax evasion.

A Annexes But the type of contracts can be changed.

• Before 2006: Depends on the contract when the pacs is contracted.

By default, the contract separate assets bought before the marriage, but assets bought after the marriage are common (communauté de biens réduite aux acquêts). But the type of contracts can be changed (for separate or community of all assets.

Debts

No solidarity Solidarity of debts linked to everyday life and housing Solidarity of debts (but protection of the housing)

Adoption

No legal adoption by the partners (but one can adopt on its own)

No legal adoption by the partners (but one can adopt on its own)

Legal adoption authorized

Social protection

No

         a 0T = α T -(1 -p T )γ T a 1T = (1 -2p T )γ T a 2T = α T + β T + (2 -p T )γ T
As a consequence, given the a kT 's the structural parameters α T , γ T and β T are functions of p T :

         α T (p T ) = a 0T + 1-p T 1-2p T a 1T γ T (p T ) = 1 1-2p T a 1T β T (p T ) = a 2T -a 0T -(1 + 2 1-2p T )a 1T
α T , γ T and β T are monotonous functions of p T . In particular, the derivative of γ T is of the same sign as a 1T and the derivative of β T is of the opposite sign as a 1T .

Moreover:

               γ T (0) = a 1T γ T (1) = -a 1T lim p T →1/2 -γ T (p T ) = sgn(a 1T )∞ lim p T →1/2 + γ T (p T ) = -sgn(a 1T )∞
Therefore, γ T has the same sign on ] -∞; 1/2[ and the opposite sign on ]1/2; +∞[. As a consequence, γ T is always positive either on ] -∞; 1/2[ or on ]1/2; +∞[, depending on the sign of a 1T .

Similarly:

               β T (0) = a 2T -a 0T -3a 1T β T (1) = a 2T -a 0T + a 1T lim p→1/2 -β T (p T ) = -sgn(a 1T )∞ lim p→1/2 + γ T (p T ) = sgn(a 1T )∞ If a 1T > 0, β T (p T ) ≥ 0: • ∀p T ∈ [0, p]∪]1/2, +∞[ if a 2T -a 0T -3a 1T ≥ 0, with p such as β T p = 0 • ∀p T ∈]1/2, p[ if a 2T -a 0T + a 1T ≥ 0, with p such as β T p = 0 If a 1T < 0, β T (p T ) ≥ 0: • ∀p T ∈] -∞, 1/2[∪[p, 1] if a 2T -a 0T + a 1T ≥ 0, with p such as β T p = 0 • ∀p T ∈]p, 1/2[ if a 2T -a 0T -3a 1T ≥ 0, with p such as β T p = 0
As a consequence, the conditions β T (p T ) ≥ 0 and γ T (p T ) ≥ 0 are jointly verified if:

1. a 1T > 0 and a 2T -a 0T -3a 1T ≥ 0: β T (p T ) ≥ 0 and γ T (p T ) ≥ 0 ∀p T ∈ [0, p T ], with β T (p) = 0. 2. a 1T < 0 and a 2T -a 0T + a 1T ≥ 0: β T (p T ) ≥ 0 and γ T (p T ) ≥ 0 ∀p T ∈ [p T , 1], with β T (p) = 0.
Depending on the sign of a 1T , the sets [0, p] and [p, 1] define lower and upper bounds to α T , β T and γ T .

However, by construction, the lower bound for β T is always zero and is not informative. But if the sign of a 1T remains constant and the conditions are verified for all T then it is possible to define a unique p * such as

β T (p * ) ≥ 0 and γ T (p * ) ≥ 0. If a 1T > 0, p * = min{p T ; T ≥ T 0 } and if a 1T < 0, p * = max{p T ; T ≥ T 0 }.
To sum up, the important conditions for the identification of bounds to β T and to γ T are:

• either a 1T > 0 and a 2T -a 0T -3a 1T ≥ 0 ∀T ≥ 0 ⇒ p * = min{p T ; T ≥ T 0 } • or a 1T < 0 and a 2T -a 0T + a 1T ≥ 0 ∀T ≥ 0 ⇒ p * = max{p T ; T ≥ T 0 }
As a consequence, it is not possible to identify bounds such as β T ≥ 0 and to γ T ≥ 0 if a 1T > 0 and a 2Ta 0T -3a 1T < 0 or if a 1T < 0 and a 2Ta 0T + a 1T < 0. It means that it is not possible to find a p that ensure that β T ≥ 0 and to γ T ≥ 0 at the same time, meaning that the reform has unexpected impacts on the outcome.

A.2 The tax system in France -T When a 1T < 0, condition is equal to "T" (true) if the condition a 2T -a 0T + a 1T ≥ 0 is verified and to "F" (false) otherwise. When a 1T > 0, condition is equal to "T" (true) if the condition a 2T -a 0T -3a 1T ≥ 0 is verified and to "F" (false) otherwise. Controls include: the rate of households for 1000 inhabitants (as a proxy for household size), the rate of owners, the rate of unemployment, the rate of active adults. Standard errors are clustered at the court level -T When a 1T < 0, condition is equal to "T" (true) if the condition a 2T -a 0T + a 1T ≥ 0 is verified and to "F" (false) otherwise. When a 1T > 0, condition is equal to "T" (true) if the condition a 2T -a 0T -3a 1T ≥ 0 is verified and to "F" (false) otherwise. Controls include: the rate of households for 1000 inhabitants (as a proxy for household size), the rate of owners, the rate of unemployment, the rate of active adults. T When a 1T < 0, condition is equal to "T" (true) if the condition a 2T -a 0T + a 1T ≥ 0 is verified and to "F" (false) otherwise. When a 1T > 0, condition is equal to "T" (true) if the condition a 2T -a 0T -3a 1T ≥ 0 is verified and to "F" (false) otherwise. Controls include: the rate of households for 1000 inhabitants (as a proxy for household size), the rate of owners, the rate of unemployment, the rate of active adults. < 0, condition is equal to "T" (true) if the condition a 2T -a 0T + a 1T ≥ 0 is verified and to "F" (false) otherwise. When a 1T > 0, condition is equal to "T" (true) if the condition a 2T -a 0T -3a 1T ≥ 0 is verified and to "F" (false) otherwise. Controls include: the rate of households for 1000 inhabitants (as a proxy for household size), the rate of owners, the rate of unemployment, the rate of active adults.

Standard errors are clustered at the court level

Figure 7

 7 Figure 7 illustrates the decrease of the marriage rate and the increase of the overall number of unions. The marriage rate for 1000 persons aged 15-59 decreased in all courts: it was 10.0 (sd of 2.70) in 1980 and it is 6.2 (sd 0.81) in 2009. The marriage rate is still higher than the pacs rate, although they tend to be closer. Defining unions as the sum of pacs and marriages contracted in each court, the union rate per 1000 persons aged 15 to 59 years old in 2009 is greater to what it was in 1981:

  and it is impossible to assume a systematic link between the seasonality of pacs and the marriage elasticity of couples to the cost of divorce. The same argument apply for any changes in the pacs law after 2005: it only alters the results if the three parts of the year are not affected similarly. The 2006 reform of the pacs reinforces the duties of pacsed partners toward the other partner and the 2007 reform modifies the taxation of inheritance: both of them should not affect the seasonality of the pacs.

  )give results without introducing fixed effects. The introduction of control variables does not change the point estimate of year effects and year× sem.2 fixed effects, but the point estimate of the constant.It means that adding controls does not necessarily improve the estimation because these controls do not add any relevant information. My favorite estimation is given in column (3). It introduces some court × sem.2 fixed effects. The impact of the reform is given by the evolution of the year×sem.2 fixed effects, which is plotted in figure8. Before 2005, the point estimates for the coefficients for year×sem.2 variables are very low, although they are significant for early years. It means that the second semesters in 2001 and 2002 could have been slightly different from the second semester in 2000.But the main evolution occurs after 2005: after 2005, the coefficients start increasing a lot. It reveals a systematic change in the seasonality right after the reform of the pacs. However, as explained in the previous section, this estimation can result from both the incentive effect of the pacs and from the delaying effect of the pacs.

  10. The direct impact of the reform increased over time: it is very close to zero in 2005, but it raised with 0.23-0.33 points the average pacs rate per 15-59 persons in a court in 2006. In 2009, fiscal incentives resulted in an increase with 0.65-0.85 points in the pacs rate. The schedule impact of the reform stayed constant after the reform. The pacs rate during the unattractive part of the year decreased with 0.16-0.23 point each year, leading to an increase with 0.16-0.23 point each year during the attractive part of the year. This two effects comes in addition to the natural increase in the pacs rate. The average pacs rate remained stable during the first two years compared to the average pacs rate in 2000. It increased with 0.04 points in 2003, until 0.69-0.73 in 2009.

Figure 1 :Figure 3 :

 13 Figure 1: Taxes paid depending on the day of pacs/marriage -simulation

  of Justice Mean pacs rate by quarter for each year

Figure

  Figure 4: Pacs rates

Figure

  Figure 5: Rate of dissolution

Figure 6 :

 6 Figure 6: Rate of dissolution

Table 1 :

 1 Legal features of marital status in France

		Cohabitation	Pacs	Marriage
	Income taxa-	Separate		Common since the day the marriage
	tion		• Before 2005: separate during	is contracted
			3 years, common after
			• After 2005: common since
			the day the pacs is con-
			tracted
	Inheritance
		• Surviving partner has	• Surviving partner has to be	• Surviving partner automati-
		to be declared in the	declared in the testimony	cally inherits from the spouse
		testimony	• Since 2007: No tax	• Since 2007: No tax
		• High tax rates: after a 1564eur allowance, tax rate of 60%	• Before 2007: marginal tax rate of 40% until 15000eur, 50% after	• Before 2007: Taxed, but lower rates than pacsed part-ners
	Assets sharing No asset sharing, unless
		bought together	• Since 2006:	By default,
			the contract separates assets.

Table 2 :

 2 Evolution of the pacs rate for 1000 persons aged 15-59

	year Mean Stan.Dev. Min	Max
	2000	.50	.22	.04	1.65
	2001	.45	.20	0	1.21
	2002	.52	.23	.08	1.34
	2003	.66	.27	.10	1.62
	2004	.83	.36	.15	3.24
	2005 1.36	.47	.19	3.29
	2006 1.70	.56	.33	3.72
	2007 2.20	.67	.36	4.36
	2008 3.42	.90	.61	5.80
	2009 4.05	1.11	.14	6.65
	N=443. Data: Ministry of Justice
	Lecture: In 2000, 0.5 pacs per 1000 persons
	aged 15-59 years old have been contracted by
	court. The minimum rate is 0.04 and the max-
	imum is 1.65.

Table 5 :

 5 Difference in differences estimation: impact of the reform on the pacs rate Standard errors in parentheses. Standard errors are clustered at the court level. include: the rate of households for 1000 inhabitants (as a proxy for household size), the rate of owners, the rate of unemployment, the rate of active adults. * p<0.1, * * p<0.05, * * * p<0.01

	Pacs for 1000 persons aged 15-59

Table 6 :

 6 Regression results -pacs rate for 1000 persons ages 15-59

	Spe	Year	a 0T		a 1T		a 2T		Condition	Sign a 1T	Controls	Fix. Eff.
	1	2001	.0075	( .0087 )	-.0177 * * *	( .0066 )	-.0461 * * *	( .0065 )	-	F
	1	2002	-.0081	( .0156 )	.0192 * * *	( .0064 )	.0432 * * *	( .007 )	+	F
	1	2003	.0426 *	( .0224 )	.0001	( .0067 )	.056 * * *	( .0071 )	NS	F
	1	2004	.0953 * * *	( .03 )	-.0127	( .0103 )	.0775 * * *	( .01 )	NS	F
	1	2005	.1874 * * *	( .0362 )	-.162 * * *	( .0087 )	.4852 * * *	( .0131 )	-	T	N	N
	1	2006	.2252 * * *	( .0434 )	-.1216 * * *	( .0081 )	.6791 * * *	( .0152 )	-	T
	1	2007	.3225 * * *	( .0499 )	-.1632 * * *	( .0086 )	.9349 * * *	( .0201 )	-	T
	1	2008	.5396 * * *	( .0571 )	-.1681 * * *	( .0108 )	1.5167 * * *	( .027 )	-	T
	1	2009	.6885 * * *	( .0638 )	-.2332 * * *	( .0143 )	1.7677 * * *	( .0361 )	-	T
	2	2001	.0058	( .0048 )	-.0177 * * *	( .0066 )	-.0461 * * *	( .0065 )	-	F
	2	2002	-.0116 * *	( .0047 )	.0193 * * *	( .0064 )	.0433 * * *	( .0069 )	+	F
	2	2003	.0374 * * *	( .0053 )	.0001	( .0067 )	.056 * * *	( .0071 )	NS	F
	2	2004	.0884 * * *	( .0079 )	-.0126	( .0103 )	.0776 * * *	( .01 )	NS	F
	2	2005	.1788 * * *	( .0068 )	-.1619 * * *	( .0087 )	.4853 * * *	( .013 )	-	T	N	Y
	2	2006	.2149 * * *	( .0069 )	-.1216 * * *	( .0081 )	.6792 * * *	( .0152 )	-	T
	2	2007	.3106 * * *	( .0076 )	-.1631 * * *	( .0087 )	.935 * * *	( .0201 )	-	T
	2	2008	.526 * * *	( .0096 )	-.168 * * *	( .0108 )	1.5168 * * *	( .027 )	-	T
	2	2009	.6732 * * *	( .0132 )	-.2331 * * *	( .0143 )	1.7678 * * *	( .0361 )	-	T
	3	2001	.0057	( .0049 )	-.0177 * * *	( .0066 )	-.0461 * * *	( .0065 )	-	F
	3	2002	-.0118 * *	( .0052 )	.0193 * * *	( .0064 )	.0433 * * *	( .0069 )	+	F
	3	2003	.037 * * *	( .006 )	.0001	( .0067 )	.056 * * *	( .0071 )	NS	F
	3	2004	.0879 * * *	( .0087 )	-.0126	( .0103 )	.0776 * * *	( .01 )	NS	F
	3	2005	.1782 * * *	( .0083 )	-.1619 * * *	( .0087 )	.4853 * * *	( .013 )	-	T	Y	N
	3	2006	.2142 * * *	( .0091 )	-.1215 * * *	( .0081 )	.6792 * * *	( .0152 )	-	T
	3	2007	.3098 * * *	( .0107 )	-.1631 * * *	( .0087 )	.9351 * * *	( .0201 )	-	T
	3	2008	.5251 * * *	( .0126 )	-.1679 * * *	( .0108 )	1.5168 * * *	( .027 )	-	T
	3	2009	.6722 * * *	( .0165 )	-.233 * * *	( .0143 )	1.7678 * * *	( .0361 )	-	T
	4	2001	.0058	( .0048 )	-.0177 * * *	( .0066 )	-.0461 * * *	( .0065 )	-	F
	4	2002	-.0116 * *	( .0047 )	.0193 * * *	( .0064 )	.0433 * * *	( .0069 )	+	F
	4	2003	.0374 * * *	( .0053 )	.0001	( .0067 )	.056 * * *	( .0071 )	NS	F
	4	2004	.0884 * * *	( .0079 )	-.0126	( .0103 )	.0776 * * *	( .01 )	NS	F
	4	2005	.1788 * * *	( .0068 )	-.1619 * * *	( .0087 )	.4853 * * *	( .0131 )	-	T	Y	Y
	4	2006	.2149 * * *	( .0069 )	-.1216 * * *	( .0081 )	.6792 * * *	( .0152 )	-	T
	4	2007	.3106 * * *	( .0076 )	-.1631 * * *	( .0087 )	.935 * * *	( .0201 )	-	T
	4	2008	.526 * * *	( .0096 )	-.168 * * *	( .0108 )	1.5168 * * *	( .027 )	-	T
	4	2009	.6732 * * *	( .0132 )	-.2331 * * *	( .0143 )	1.7678 * * *	( .0361 )

Table 7 :

 7 Regression results -pacs rate for 1000 couples

	Spe	Year	a 0T		a 1T		a 2T		Sign a 1T	Condition	Controls	Fix. Eff.
	1	2001	.0952 * * *	( .022 )	-.0438 * * *	( .0153 )	-.1114 * * *	( .0151 )	-	F
	1	2002	.1358 * * *	( .0406 )	.0455 * * *	( .0148 )	.1011 * * *	( .0162 )	+	F
	1	2003	.3327 * * *	( .0592 )	.0017	( .0152 )	.1356 * * *	( .0166 )	NS	F
	1	2004	.5357 * * *	( .0792 )	-.0309	( .023 )	.1859 * * *	( .0224 )	NS	F	N	N
	1	2005	.833 * * *	( .0967 )	-.3915 * * *	( .0206 )	1.1753 * * *	( .0347 )	-	F
	1	2006	1.0013 * * *	( .1171 )	-.2982 * * *	( .0197 )	1.6451 * * *	( .0411 )	-	T
	1	2007	1.3059 * * *	( .1339 )	-.3949 * * *	( .0206 )	2.261 * * *	( .0541 )	-	T
	1	2008	1.8997 * * *	( .1546 )	-.418 * * *	( .0261 )	3.6302 * * *	( .0711 )	-	T
	1	2009	2.3269 * * *	( .1715 )	-.5709 * * *	( .0347 )	4.2418 * * *	( .0927 )	-	T
	2	2001	.0127	( .0111 )	-.0429 * * *	( .0153 )	-.1104 * * *	( .0151 )	-	F
	2	2002	-.0282 * *	( .0113 )	.0473 * * *	( .0148 )	.103 * * *	( .0161 )	+	F
	2	2003	.088 * * *	( .0123 )	.0044	( .0152 )	.1383 * * *	( .0166 )	NS	F
	2	2004	.2111 * * *	( .0181 )	-.0275	( .0229 )	.1894 * * *	( .0224 )	NS	F	N	Y
	2	2005	.4294 * * *	( .0165 )	-.3872 * * *	( .0206 )	1.1796 * * *	( .0348 )	-	T
	2	2006	.5196 * * *	( .0171 )	-.2931 * * *	( .0196 )	1.6501 * * *	( .0411 )	-	T
	2	2007	.7467 * * *	( .0187 )	-.3891 * * *	( .0206 )	2.2668 * * *	( .0542 )	-	T
	2	2008	1.2638 * * *	( .0247 )	-.4115 * * *	( .0259 )	3.6367 * * *	( .0712 )	-	T
	2	2009	1.615 * * *	( .0337 )	-.5638 * * *	( .0346 )	4.249 * * *	( .0928 )	-	T
	3	2001	.0201 *	( .0116 )	-.043 * * *	( .0153 )	-.1105 * * *	( .0151 )	-	F
	3	2002	-.0134	( .013 )	.0472 * * *	( .0148 )	.1028 * * *	( .0162 )	+	F
	3	2003	.11 * * *	( .0149 )	.0042	( .0152 )	.1381 * * *	( .0166 )	NS	F
	3	2004	.2404 * * *	( .021 )	-.0277	( .023 )	.1891 * * *	( .0224 )	NS	F
	3	2005	.4659 * * *	( .0211 )	-.3875 * * *	( .0206 )	1.1793 * * *	( .0348 )	-	T	Y	N
	3	2006	.5632 * * *	( .0236 )	-.2935 * * *	( .0196 )	1.6497 * * *	( .0411 )	-	T
	3	2007	.7973 * * *	( .0274 )	-.3895 * * *	( .0207 )	2.2664 * * *	( .0542 )	-	T
	3	2008	1.3214 * * *	( .0328 )	-.412 * * *	( .026 )	3.6362 * * *	( .0712 )	-	T
	3	2009	1.6796 * * *	( .0426 )	-.5643 * * *	( .0346 )	4.2484 * * *	( .0928 )	-	T
	4	2001	.0127	( .0111 )	-.0429 * * *	( .0153 )	-.1104 * * *	( .0151 )	-	F
	4	2002	-.0282 * *	( .0113 )	.0473 * * *	( .0148 )	.103 * * *	( .0161 )	+	F
	4	2003	.088 * * *	( .0123 )	.0044	( .0152 )	.1383 * * *	( .0166 )	NS	F
	4	2004	.2111 * * *	( .0181 )	-.0275	( .0229 )	.1894 * * *	( .0224 )	NS	F
	4	2005	.4294 * * *	( .0165 )	-.3872 * * *	( .0206 )	1.1796 * * *	( .0348 )	-	T	Y	Y
	4	2006	.5196 * * *	( .0171 )	-.2931 * * *	( .0196 )	1.6501 * * *	( .0411 )	-	T
	4	2007	.7467 * * *	( .0187 )	-.3891 * * *	( .0206 )	2.2668 * * *	( .0542 )	-	T
	4	2008	1.2638 * * *	( .0247 )	-.4115 * * *	( .0259 )	3.6367 * * *	( .0712 )	-	T
	4	2009	1.615 * * *	( .0337 )	-.5638 * * *	( .0346 )	4.249 * * *	( .0928 )

Table 8 :

 8 Difference in differences estimation: impact of the reform on the dissolution rate for 1000 persons aged 15-59 Standard errors are clustered at the court level.Controls include: the rate of households for 1000 inhabitants (as a proxy for household size), the rate of owners, the rate of unemployment, the rate of active adults.

				Dissolution rate for 1000 persons aged 15-59
		(1)		(2)		(3)		(4)
	Year 2001	.0106 * * *	(.000931)	.011 * * *	(.000967)	.0106 * * *	(.000981)	.0121 * * *	(.00168)
	Year 2002	.0236 * * *	(.00137)	.0245 * * *	(.00147)	.0236 * * *	(.00144)	.0266 * * *	(.00304)
	Year 2003	.041 * * *	(.00187)	.0423 * * *	(.00201)	.041 * * *	(.00197)	.0455 * * *	(.00434)
	Year 2004	.0717 * * *	(.00225)	.0736 * * *	(.00252)	.0634 * * *	(.00256)	.0693 * * *	(.00587)
	Year 2005	.0777 * * *	(.00258)	.0799 * * *	(.00294)	.0777 * * *	(.00272)	.0851 * * *	(.00716)
	Year 2006	.0853 * * *	(.0027)	.0879 * * *	(.00308)	.0853 * * *	(.00285)	.0941 * * *	(.00831)
	Year 2007	.111 * * *	(.00316)	.114 * * *	(.00362)	.111 * * *	(.00333)	.121 * * *	(.00945)
	Year 2008	.128 * * *	(.00338)	.132 * * *	(.00378)	.128 * * *	(.00356)	.14 * * *	(.0107)
	Year 2009	.163 * * *	(.00391)	.167 * * *	(.00433)	.163 * * *	(.00412)	.176 * * *	(.0121)
	Year 2000×Sem. 2 .00682 * * *	(.000723)	.00704 * * *	(.00074)	-.00989 * * *	(.00299)	-.00986 * * *	(.00299)
	Year 2001×Sem. 2 .00987 * * *	(.00132)	.0101 * * *	(.00132)	-.00683 * *	(.00333)	-.00681 * *	(.00334)
	Year 2002×Sem. 2	.014 * * *	(.00223)	.0143 * * *	(.00224)	-.00266	(.00368)	-.00265	(.00368)
	Year 2003×Sem. 2	.0151 * * *	(.00233)	.0154 * * *	(.00234)	-.00156	(.00373)	-.00155	(.00373)
	Year 2005×Sem. 2	.0333 * * *	(.00327)	.0336 * * *	(.00327)	.0166 * * *	(.00435)	.0166 * * *	(.00435)
	Year 2006×Sem. 2	.0323 * * *	(.00309)	.0325 * * *	(.00309)	.0156 * * *	(.00423)	.0156 * * *	(.00423)
	Year 2007×Sem. 2	.0253 * * *	(.00352)	.0255 * * *	(.0035)	.00862 *	(.00452)	.0086 *	(.00452)
	Year 2008×Sem. 2	.0324 * * *	(.00401)	.0326 * * *	(.00402)	.0157 * * *	(.00524)	.0156 * * *	(.00524)
	Year 2009×Sem. 2	.042 * * *	(.0044)	.0422 * * *	(.0044)	.0253 * * *	(.00539)	.0253 * * *	(.0054)
	Constant	.00456 * * *	(.00036)	.092	(.0569)	.00456 * * *	(.00163)	-.2	(.191)
	Observations	8860		8860		8860		8860
	R 2	0.487		0.523		0.594		0.600
	Fixed effects	N		N		Y		Y
	Controls	N		Y		N		Y
	Standard errors in parentheses.

* p<0.1, * * p<0.05, * * * p<0.01

Table 9 :

 9 Difference in differences estimation: impact of the reform on the dissolution rate for 1000 pacs Standard errors are clustered at the court level.Controls include: the rate of households for 1000 inhabitants (as a proxy for household size), the rate of owners, the rate of unemployment, the rate of active adults.

				Dissolution rate for 1000 pacs
		(5)		(6)		(7)		(8)
	Year 2001	-.000711	(.00464)	-.000655	(.00464)	.00119	(.00534)	.00162	(.00572)
	Year 2002	.000378	(.00386)	.000577	(.00386)	.00228	(.00446)	.00315	(.00512)
	Year 2003	.00337	(.00353)	.00371	(.00354)	.00527	(.00415)	.00659	(.00522)
	Year 2004	.00677 * *	(.00335)	.00728 * *	(.00336)	.00775 * *	(.00366)	.0095 *	(.00528)
	Year 2005	.00312	(.00338)	.00373	(.0034)	.00502	(.00394)	.00721	(.006)
	Year 2006	-.00429	(.0033)	-.00355	(.00332)	-.0024	(.0039)	.000225	(.00645)
	Year 2007	-.00533	(.00337)	-.00445	(.0034)	-.00344	(.00396)	-.000385	(.00708)
	Year 2008	-.00898 * * *	(.00334)	-.00797 * *	(.00337)	-.00709 *	(.00395)	-.00361	(.00761)
	Year 2009	-.011 * * *	(.00332)	-.00986 * * *	(.00336)	-.0091 * *	(.00393)	-.0052	(.00817)
	Year 2001×Sem. 2
	Year 2002×Sem. 2	.00342	(.0023)	.00349	(.0023)	.00275	(.0044)	.00296	(.0046)
	Year 2003×Sem. 2	.00217	(.0017)	.00224	(.0017)	.00151	(.0044)	.00171	(.0045)
	Year 2004×Sem. 2	.00184	(.0014)	.00191	(.0014)	.00117	(.0045)	.00138	(.0046)
	Year 2005×Sem. 2	.00695 * * *	(.0013)	.00702 * * *	(.0013)	.00629	(.0043)	.00649	(.0044)
	Year 2006×Sem. 2	.00524 * * *	(.00092)	.00531 * * *	(.00092)	.00458	(.0041)	.00478	(.0042)
	Year 2007×Sem. 2	.00178 * *	(.00077)	.00184 * *	(.00077)	.00111	(.0040)	.00131	(.0041)
	Year 2008×Sem. 2	.00171 * * *	(.00059)	.00177 * * *	(.00059)	.00104	(.0040)	.00124	(.0041)
	Year 2009×Sem. 2	.00187 * * *	(.00048)	.00193 * * *	(.0005)	.0012	(.0040)	.0014	(.0041)
	Constant	.0268 * * *	(.00164)	.0505 * * *	(.0108)	.0267 * * *	(.00161)	.129	(.0894)
	Observations	8415		8415		8415		8415
	R 2	0.037		0.044		0.040		0.041
	Fixed effects	N		N		Y		Y
	Controls	N		Y		N		Y
	Standard errors in parentheses.

* p<0.1, * * p<0.05, * * * p<0.01

Table 10 :

 10 Regression results -broken up pacs, rate for 1000 persons 15-59 years old

	Year a 0T		a 1T		a 2T		sign a 1T	condition	Fixed effects	Controls
	2001	0.004 * * *	( 0.001 )	0.002 * *	( 0.001 ) 0.009 * * *	( 0.001 )	+	F
	2002	0.012 * * *	( 0.001 )	-0.001	( 0.001 )	0.018 * * *	( 0.002 )	NS	T
	2003	0.021 * * *	( 0.001 )	-0.001	( 0.002 )	0.029 * * *	( 0.002 )	NS	T
	2004	0.035 * * *	( 0.002 )	-0.007 * * *	( 0.002 ) 0.038 * * *	( 0.003 )	-	F	Y	N
	2005	0.044 * * *	( 0.002 )	-0.011 * * *	( 0.002 ) 0.060 * * *	( 0.003 )	-	T
	2006	0.047 * * *	( 0.002 )	-0.009 * * *	( 0.002 ) 0.063 * * *	( 0.003 )	-	T
	2007	0.058 * * *	( 0.002 )	-0.005 *	( 0.003 ) 0.072 * * *	( 0.004 )	-	T
	2008	0.064 * * *	( 0.002 )	0.000	( 0.003 )	0.090 * * *	( 0.004 )	NS	T
	2009	0.078 * * *	( 0.002 )	0.007 * *	( 0.003 ) 0.120 * * *	( 0.004 )	+	T
	2001	0.002 * * *	( 0.001 )	0.002 * * *	( 0.001 ) 0.017 * * *	( 0.001 )	+	T
	2002	0.010 * * *	( 0.001 )	-0.001	( 0.001 )	0.026 * * *	( 0.002 )	NS	T
	2003	0.018 * * *	( 0.001 )	-0.001	( 0.002 )	0.036 * * *	( 0.002 )	NS	T
	2004	0.032 * * *	( 0.002 )	-0.006 * * *	( 0.002 ) 0.046 * * *	( 0.003 )	-	T
	2005	0.041 * * *	( 0.002 )	-0.010 * * *	( 0.002 ) 0.068 * * *	( 0.003 )	-	T	N	N
	2006	0.045 * * *	( 0.002 )	-0.009 * * *	( 0.002 ) 0.071 * * *	( 0.003 )	-	T
	2007	0.055 * * *	( 0.002 )	-0.004	( 0.003 )	0.079 * * *	( 0.004 )	NS	T
	2008	0.061 * * *	( 0.002 )	0.001	( 0.003 )	0.097 * * *	( 0.004 )	NS	T
	2009	0.075 * * *	( 0.002 )	0.007 * *	( 0.003 ) 0.128 * * *	( 0.004 )	+	T
	2001	0.002 * * *	( 0.001 )	0.003 * * *	( 0.001 ) 0.017 * * *	( 0.001 )	+	T
	2002	0.010 * * *	( 0.001 )	0.000	( 0.001 )	0.026 * * *	( 0.002 )	NS	T
	2003	0.019 * * *	( 0.001 )	0.000	( 0.002 )	0.036 * * *	( 0.002 )	NS	T
	2004	0.033 * * *	( 0.002 )	-0.006 * * *	( 0.002 ) 0.046 * * *	( 0.003 )	-	T
	2005	0.043 * * *	( 0.002 )	-0.010 * * *	( 0.002 ) 0.068 * * *	( 0.003 )	-	T	N	Y
	2006	0.046 * * *	( 0.002 )	-0.009 * * *	( 0.002 ) 0.071 * * *	( 0.003 )	-	T
	2007	0.057 * * *	( 0.002 )	-0.004	( 0.003 )	0.080 * * *	( 0.004 )	NS	T
	2008	0.063 * * *	( 0.002 )	0.001	( 0.003 )	0.098 * * *	( 0.004 )	NS	T
	2009	0.078 * * *	( 0.003 )	0.007 * *	( 0.003 ) 0.128 * * *	( 0.004 )	+	T
	2001	0.005 * * *	( 0.001 )	0.002 * *	( 0.001 ) 0.009 * * *	( 0.001 )	+	T
	2002	0.014 * * *	( 0.002 )	-0.001	( 0.001 )	0.018 * * *	( 0.002 )	NS	T
	2003	0.024 * * *	( 0.003 )	-0.001	( 0.002 )	0.028 * * *	( 0.002 )	NS	T
	2004	0.039 * * *	( 0.004 )	-0.007 * * *	( 0.002 ) 0.038 * * *	( 0.003 )	-	F
	2005	0.049 * * *	( 0.005 )	-0.011 * * *	( 0.002 ) 0.060 * * *	( 0.003 )	-	T	Y	Y
	2006	0.053 * * *	( 0.005 )	-0.009 * * *	( 0.002 ) 0.063 * * *	( 0.003 )	-	T
	2007	0.065 * * *	( 0.006 )	-0.005 *	( 0.003 ) 0.072 * * *	( 0.004 )	-	T
	2008	0.072 * * *	( 0.007 )	0.000	( 0.003 )	0.090 * * *	( 0.004 )	NS	T
	2009	0.087 * * *	( 0.008 )	0.007 * *	( 0.003 ) 0.120 * * *	( 0.004 )	+

Table 11 :

 11 Regression results -broken up pacs, rate for 1000 pacs

	Year a 0T		a 1T		a 2T		sign a 1T	condition	Fixed effects	controls
	2002	4.555 * * *	( 1.748 ) -4.422	( 3.138 )	-0.714	( 2.802 )	NS	F
	2003	5.836 * * *	( 1.554 ) -4.292	( 2.942 )	-0.250	( 2.721 )	NS	F
	2004	8.588 * * *	( 1.560 ) -7.100 * *	( 2.965 ) -0.854	( 2.672 )	-	F	Y	N
	2005	7.266 * * *	( 1.428 ) -7.124 * *	( 2.873 ) 2.851	( 2.557 )	-	F
	2006	3.098 * *	( 1.304 ) -5.734 * *	( 2.814 ) -2.105	( 2.282 )	-	F
	2007	1.677	( 1.337 )	-3.872	( 2.754 )	-5.191 * *	( 2.316 )	NS	T
	2008	-0.662	( 1.300 )	-2.820	( 2.766 )	-6.568 * * *	( 2.212 )	NS	T
	2009	-1.948	( 1.316 )	-2.106	( 2.758 )	-7.138 * * *	( 2.265 )	NS	T
	2002	-3.318 * *	( 1.691 ) -2.140	( 1.506 )	16.669 * * *	( 1.870 )	NS	T
	2003	-2.037	( 1.508 )	-2.010 *	( 1.210 ) 17.133 * * *	( 1.480 )	-	T
	2004	0.715	( 1.437 )	-4.818 * * *	( 1.130 ) 16.529 * * *	( 1.292 )	-	T
	2005	-0.608	( 1.355 )	-4.842 * * *	( 0.893 ) 20.234 * * *	( 1.203 )	-	T	N	N
	2006	-4.775 * * *	( 1.240 ) -3.452 * * *	( 0.656 ) 15.278 * * *	( 0.864 )	-	T
	2007	-6.196 * * *	( 1.277 ) -1.590 * * *	( 0.587 ) 12.192 * * *	( 0.746 )	-	T
	2008	-8.536 * * *	( 1.203 ) -0.538	( 0.424 )	10.815 * * *	( 0.504 )	NS	T
	2009	-9.822 * * *	( 1.211 ) 0.176	( 0.323 )	10.245 * * *	( 0.434 )	NS	T
	2002	-3.274 *	( 1.693 ) -2.054	( 1.508 )	16.755 * * *	( 1.871 )	NS	T
	2003	-1.907	( 1.513 )	-1.925	( 1.212 )	17.217 * * *	( 1.479 )	NS	T
	2004	0.929	( 1.443 )	-4.736 * * *	( 1.131 ) 16.612 * * *	( 1.291 )	-	T
	2005	-0.310	( 1.361 )	-4.760 * * *	( 0.896 ) 20.316 * * *	( 1.203 )	-	T	N	Y
	2006	-4.396 * * *	( 1.254 ) -3.372 * * *	( 0.657 ) 15.358 * * *	( 0.865 )	-	T
	2007	-5.737 * * *	( 1.301 ) -1.511 * *	( 0.589 ) 12.272 * * *	( 0.747 )	-	T
	2008	-7.997 * * *	( 1.229 ) -0.460	( 0.429 )	10.893 * * *	( 0.507 )	NS	T
	2009	-9.205 * * *	( 1.247 ) 0.253	( 0.325 )	10.322 * * *	( 0.435 )	NS	T
	2002	4.510 * *	( 1.854 ) -4.436	( 3.079 )	-0.732	( 2.836 )	NS	F
	2003	5.750 * * *	( 1.852 ) -4.304	( 2.878 )	-0.267	( 2.758 )	NS	F
	2004	8.461 * * *	( 2.145 ) -7.111 * *	( 2.900 ) -0.869	( 2.715 )	-	F
	2005	7.099 * * *	( 2.351 ) -7.133 * *	( 2.819 ) 2.838	( 2.598 )	-	F
	2006	2.895	( 2.688 )	-5.741 * *	( 2.755 ) -2.117	( 2.323 )	-	F	Y	Y
	2007	1.439	( 3.124 )	-3.877	( 2.695 )	-5.201 * *	( 2.358 )	NS	F
	2008	-0.934	( 3.513 )	-2.824	( 2.708 )	-6.576 * * *	( 2.253 )	NS	F
	2009	-2.253	( 3.932 )	-2.108	( 2.703 )	-7.145 * * *	( 2.310 )	NS	F
	When a 1T

Table 12 :

 12 Regression results -estimation of the γ T , β T and the α T Explained variable: pacs rate for 1000 persons aged 15-59. Specification included court fixed effect and controls

	year	γ T (p)	σ	γ T (1)	σ	α T (p)	σ	α T (1)	σ	β T (1)	σ	β T (p)	σ
	p = 0.853
	2001	.0251 * * *	( 0.000 )	.0177 * * *	( .0066 )	.0112	( .0081 )	.0075	( .0087 )	-.0861 * * *	( .0144 )	-.0714 * * *	( .0142 )
	2002	-.0273 * * *	( 0.000 )	-.0192 * * *	( .0064 )	-.0121	( .0151 )	-.0081	( .0156 )	.0866 * * *	( .0199 )	.0706 * * *	( .0196 )
	2003	-.0001 * * *	( 0.000 )	-.0001	( .0067 )	.0426 *	( .0221 )	.0426 *	( .0224 )	.0135	( .0258 )	.0134	( .0255 )
	2004	.018 * * *	( 0.000 )	.0127	( .0103 )	.0979 * * *	( .0292 )	.0953 * * *	( .03 )	-.041	( .035 )	-.0304	( .0353 )
	2005	.2294 * * *	( 0.000 )	.162 * * *	( .0087 )	.2211 * * *	( .0357 )	.1874 * * *	( .0362 )	.001	( .0395 )	.1359 * * *	( .0409 )
	2006	.1723 * * *	( 0.000 )	.1216 * * *	( .0081 )	.2505 * * *	( .0427 )	.2252 * * *	( .0434 )	.231 * * *	( .0474 )	.3323 * * *	( .0482 )
	2007	.2311 * * *	( 0.000 )	.1632 * * *	( .0086 )	.3565 * * *	( .0496 )	.3225 * * *	( .0499 )	.3133 * * *	( .0557 )	.4492 * * *	( .0554 )
	2008	.238 * * *	( 0.000 )	.1681 * * *	( .0108 )	.5746 * * *	( .0565 )	.5396 * * *	( .0571 )	.6691 * * *	( .0622 )	.8091 * * *	( .0656 )
	2009	.3303 * * *	( 0.000 )	.2332 * * *	( .0143 )	.737 * * *	( .0629 )	.6885 * * *	( .0638 )	.6518 * * *	( .0739 )	.846 * * *	( .0768 )
			Explained variable: pacs rate for 1000 couples. Specification included court fixed effect and controls
	p = 0.817
	2001	.0691 * * *	( 0.000 )	.0438 * * *	( .0153 )	.1078 * * *	( .0207 )	.0952 * * *	( .022 )	-.301 * * *	( .0344 )	-.2504 * * *	( .0344 )
	2002	-.0718 * * *	( 0.000 )	-.0455 * * *	( .0148 )	.1227 * * *	( .0393 )	.1358 * * *	( .0406 )	.0633	( .0486 )	.0108	( .0494 )
	2003	-.0027 * * *	( 0.000 )	-.0017	( .0152 )	.3322 * * *	( .0585 )	.3327 * * *	( .0592 )	-.1933 * * *	( .0654 )	-.1953 * * *	( .0655 )
	2004	.0488 * * *	( 0.000 )	.0309	( .023 )	.5446 * * *	( .0776 )	.5357 * * *	( .0792 )	-.4165 * * *	( .0875 )	-.3807 * * *	( .0897 )
	2005	.6175 * * *	( 0.000 )	.3915 * * *	( .0206 )	.946 * * *	( .0957 )	.833 * * *	( .0967 )	-.5012 * * *	( .098 )	-.0492	( .1075 )
	2006	.4703 * * *	( 0.000 )	.2982 * * *	( .0197 )	1.0874 * * *	( .115 )	1.0013 * * *	( .1171 )	.0013	( .1207 )	.3456 * * *	( .1303 )
	2007	.6229 * * *	( 0.000 )	.3949 * * *	( .0206 )	1.4199 * * *	( .1331 )	1.3059 * * *	( .1339 )	.1043	( .1368 )	.5602 * * *	( .148 )
	2008	.6593 * * *	( 0.000 )	.418 * * *	( .0261 )	2.0203 * * *	( .1521 )	1.8997 * * *	( .1546 )	.8298 * * *	( .154 )	1.3125 * * *	( .1775 )
	2009	.9005 * * *	( 0.000 )	.5709 * * *	( .0347 )	2.4917 * * *	( .1692 )	2.3269 * * *	( .1715 )	.6848 * * *	( .1819 )	1.344 * * *	( .2035 )

There is no 'unilateral divorce' in France.

Pacs stands for Pacte Civil de Solidarité, Civil Pact of Solidarity.

The pacs is now so popular in France that the terminology has changed. A new verb was created "se pacser" that I translate into "to pacs", meaning "to contract a pacs". The verb "se pacser" appears now in the French dictionary Larousse.

Pacte Civil de Solidarité, Civil pact of solidarity

Let's call civil unions all that new legal forms of unions.

But some authors pointed out that different-sex couples were likely to be interested in contracting a pacs: a report written by the INED (1999) declared that 150,000 to 200,000 pacs a year could be registered.

The computation does not take into account Prime Pour l'Emploi, a tax credit settled in 2001. Only the labor income (wage) is considered. This is obviously an underestimation of the total income of the household as it does not take into account other sources of income.

When a couple has the choice between several optimal days, I keep all of them for the figure. So the couple appears as many times as there are optimal days. Therefore, the area under the line does not give the number of unmarried

A letter is sufficient if both the partners agree on the dissolution. If only one partner wants to dissolve a pacs, he has to send a letter through a lawyer.

However, the change in the divorce law is not a large change: only one hearing with the judge is compulsory instead of two. So it does not change the condition of the divorce, but it can reduce its duration.

This possibility was raised by the deputy Charles de Courson since the pacs was created. In 2010, the tax system has been amended. During the debate, he said "When we were talking about the creation of the pacs, I raised the problem saying that I would write in the classifies in Le Nouvel Obs: 'Single looks for female student without income to contract a six months pacs in order to share fiscal benefit'. Because the mecanism allows to pacs every January 1 st and to unpacs every July 1 st . This risk of embezzlement of this civil goal led to the adoption of an amendment imposing a minimal duration of 3 years before having the fiscal benefit. But alas, our majority [Right parties, majority in France since 2002] got rid off this clause contrary to my opinion. Now we witness the beginning of the embezzlement of the law." -From debates on "Projet de loi de finances pour 2011 : Articles de la deuxième partie"

A.1 Identification strategy

The number of pacs contracted during the quarter q in a court i is given by: y iqT = α 0 + α T + α iq + δ qT + u iqT (5) with:

Let aggregate the quarters of the attractive part of the year, so that: y iT,t=0 = y iT,q=4 , y iT,t=1 = y iT,q=1 and y iT,t=2 = y iT,q=2 + y iT,q=3

Therefore, y iT t can be rewritten as:

with

Then, the parameters of the difference in differences in differences estimation identifies some functions of the structural parameters:

in the fixed effect .362

Marriage and union rates in France