Theory

face a higher risk of becoming unemployed. Our preferred specification includes both year and labor market region fixed effects, see columns (4) and (8). German nationals have a job loss hazard rate that is 20% lower than the respective hazard rate for workers without German citizenship, who are thus on average more likely to lose their jobs. For transitions into employment, the hazard rate of Germans is 5% lower than the hazard rate for foreigners. Thus, workers without German citizenship find new jobs out of unem-ployment quicker than Germans, their unemunem-ployment duration is on average shorter. An explanation for this finding are lower reservation wages, for example due to lower unem-ployment benefit entitlements or because for some nationalities continued emunem-ployment is a necessary requirement for residence status.¹²⁵

Note that the estimated hazard rates reflect differences between Germans and a di-verse group of individuals without German citizenship. One would expect that labor market transition probabilities vary greatly across individuals of different foreign nation-alities. For example, citizens of other EU15 countries face no legal barriers to employment in Germany and unemployment benefit entitlements can be transferred across countries.

Thus, they might be more comparable to German workers in terms of labor market at-tachment than workers from non-EU countries are. The hazard rate differences we find can therefore be interpreted as a lower bound for the differential exposure to labor market risk for workers without German or EU15 citizenship.

Finally, women are 12% less likely to become unemployed and about 14% less likely to move into employment according to our preferred specification. That is, women are on average employed longer, but it takes them longer to find a new job out of unemployment.

Thus, the need for additional insurance after the reform might be higher for women.

using a static matching model with transferable utility between spouses in the spirit of Becker (1973, 1974). Choo and Siow (2006) generate the market demand for marriages using the extreme-value logit random utility model of McFadden (1974), which yields characteristic functional forms.

4.4.1 Marriage Surplus

The marriage surplus reflects the gains from marriage for both partners, and those gains may change systematically in response to changes in the institutional environment. The marriage surplus is calculated using market clearing conditions and, thus, depends on the relative numbers of married and single individuals of a particular type.

The independent utility of a typeimangmarried to a typej women is given by equa-tion 4.1.¹²⁶ It consists of a systematic gross return ( ˜αij) that depends on the particular type combination, a systematic utility transfer from the man to the women (τ_ij) and an independently and identically distributed random variable with a type I extreme-value distribution (_ijg). Thus, the systematic gain from marrying a type j for a type iman is given by ˜αij −τij.

Vijg = ˜αij −τij +ijg (4.1)

Symmetrically, for a female of typej the systematic gain from marrying a typeiman is denoted ˜γ_ij. Following the notation of Choo and Siow (2006) the sign of the utility transfer (τ_ij) is positive for women. A male (female) individual g will choose the type of the marriage partner type j (i) according to

V_ig = max

j {V_i0g, ..., V_ijg, ..., V_{iJ g}}. (4.2) Following McFadden (1974) and assuming a large number of men and women, this translates into a quasi-demand function for typei, j marriages demanded by typei men:

126In our empirical implementation, type i and j are a combination of nationality and age. See Section 4.5 for more details.

lnµ^d_ij = lnµ^d_i0+ ˜α_ij−α˜_i0−τ_ij

= lnµ^d_i0+α_ij−τ_ij, (4.3)

whereα_ij = ˜α_ij−α˜_i0is the systematic gross return to a typeiman for a typei, j marriage relative to being unmarried. Symmetrically, the supply of type i, j marriages by women j is given by:

lnµ^s_ij = lnµ^s_0j +γ_ij +τ_ij. (4.4) In equilibrium—when all I×J submarkets of the marriage market clear—the joint surplus generated by a marriage between a typeiman and typejwoman can be calculated by adding equations (4.3) and (4.4). The utility transfers between both spouses cancel out and only the two systematic components,α_ij and γ_ij, remain:

lnµ_ij − lnµ^d_i0+ lnµ^s_0j

2 = α_ij+γ_ij

2 , (4.5)

so the joint surplus for both partners consists solely of the systematic gains from marriage.

The LHS of equation (4.5) can be rewritten as Φ_ij = ln µij

√µ_i0 µ_0j

!

. (4.6)

Choo and Siow (2006) refer to this expression as themarriage market matching function:

the number of marriages between type i men and type j women is given by µ_ij in the numerator. It is scaled by the the number of single men and single women of the same type, µ_i0 and µ_0j, in the denominator, so the expression is scaled by the observed pop-ulation vectors. Intuitively, the total systematic gain (surplus) to marriage per partner for any i, j pair can be expected to be high if we observe many i, j marriages relative to the respective single populations.

For a constant marriage surplus Φ_ij, a percentage increase in the stock of available singles of a particular type (µ_i0andµ_0j) should result in a percentage increase of marriages that include this particular type (µ_ij). Consequently, changes in the marriage surplus are

deviations from this constant relationship between marriages and single stocks.¹²⁷ Thus, any inflow of singles of a certain type should—in case the systematic factors underlying the marriage surplus did not change—result in a proportional increase of marriages that include this particular type.

4.4.2 Reform Effects on Marital Surplus

The labor market reform we consider in this paper lowered the generosity of social insur-ance in case of prolonged unemployment. The need to self-insure within the household increased. Thus, the systematic component of the marriage surplus changed, assuming that married individuals take into account that they may have to support their partner.

From the male perspective, the reform affected both ˜α_ij and ˜α_i0 in the model. On the one hand, the lower generosity of social insurance reduced ˜α_i0 and thus increased incentives to get married due to the need for additional insurance through a partner.

On the other hand, stricter means testing decreased ˜α_ij, the gains from being married, because of the larger need to support the partner in case of unemployment. From the female perspective, the reform affected ˜γ_ij and ˜γ_i0 in the same way.

The net effect of the changes to both model objects is a priori unclear. We evaluate it empirically in Section 4.5 by exploiting the reform-induced variation in observed marriage rates and the estimated surplus for different types of individuals.

Note that, according to the model, utility transfers, τ_ij, do not matter for marital surplus and, thus, do not have to be observed to study the reform’s effect on marital surplus. In theory, however, they are part of an important adjustment mechanism. Utility transfers change relative gains to marriage for both partners by transferring resources to one partner at the expense of the other. For example, the loss of systematic gains from marriage for a certain type of women may have to be compensated by men through a larger transfer to keep the marriage preferable to singlehood for both partners. If increasing the transfer sufficiently is infeasible, a lower number of marriages of that particular type i, j, and, potentially, more divorces (which are not modeled here) would be the consequence.

127Implicitly, the marriage surplus is always defined relative to the value of being single. Thus all changes that affect both the value of being single as well as the value of being married to the same extend will not alter the marriage surplus.

4.4.3 Expected Gains to Entering the Marriage Market

In addition to the marriage surplus, the Choo and Siow (2006) model also provides functional forms for the expected gains to marriage that can be computed directly from the data. The labor market reform arguably also affected gains to entering the marriage market for both genders, due to the aforementioned insurance considerations. Thus, we will also study how these gains evolved over time in conjunction with the institutional changes in the labor market.

Starting from the demand for marriages, equation (4.3) above, the expected value of entering the marriage market for a typei man g before all individual realizations ofijg

is

EVig =c+ ˜αi0+ ln mi

µ^d_i0

!

, (4.7)

where c is a constant and ˜α_i0 the gains from being single of this particular type. The value of entering the marriage market is proportional to the log of the number of type i men who enter the marriage market, m_i, divided by the number of type i men who remain single. The last term can thus be interpreted as the expected gains to entering the marriage market for type i men, denoted

Q_i = ln m_i µ^d_i0

!

. (4.8)

By symmetry, the expected gains to enter the marriage market for women are Q_j = ln f_j

µ^s_0j

!

, (4.9)

where f_j is the number of type j women who enter the marriage market.