Family Income Splitting and the Number of Children ...€¦ · Family Income Splitting and the Number of Children: Evidence from a Natural Experiment Peter Egger∗and Doina Maria

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Family Income Splitting and the Number of Children: Evidence from a Natural Experiment

Peter Egger and Doina Maria Radulescu

Family Income Splitting and the Number of Children:

Evidence from a Natural Experiment

Peter Egger∗and Doina Maria Radulescu†

University of Munich and CESifo

March 2009

Abstract

This paper analyzes the effects of family income vs. spouse income splittingon the number of children. The former implies ceteris paribus lower marginaland average income taxes than the latter. We set up a stylized model ofhousehold utility maximization to show that households will choose a highernumber of children the lower marginal and average income taxes are. Weprovide support of this hypothesis from a natural experiment: Saarland’s re-accession to Germany in 1957. Prior to this date, Saarland was part of France.While Germany uses spouse income splitting, France relies on family incomesplitting through the so-called ‘Quotient familial’. After 1957, families inSaarland were subject to spouse income splitting instead of the previous familyincome splitting. We identify the causal impact of this change at the level ofmunicipalities. Specifically, we use panel data on newborn children in 45municipalities in Saarland (treated units), and altogether 350 municipalities(control units) in surrounding regions in Germany (the state of Rheinland-Pfalz) and France (the départements of (Bas-Rhin, Moselle, and Meurthe-etMoselle). The results suggest that the more extensive taxation of householdincomes after the change led to a reduction of births in Saarland by aboutone-fifth.Keywords: Family income splitting; Natural experiment; FertilityJEL-classification: J13, H24, C21

∗Ifo Institute, University of Munich, CESifo, GEP University of Nottingham, and Oxford Centerof Business Taxation. Address: Ifo Institute, Poschingerstrasse 5, 81679 Munich, Germany. E-mail:[email protected].

†Center for Economic Studies, University of Munich, and CESifo. Address: Center for EconomicStudies, University of Munich, Schackstrasse 4, 80539 Munich, Germany. E-mail: [email protected].

"The empirical evidence on a causal effect of tax incen-

tives on fertility is [...] rather limited. In particular,

there is no empirical evidence of the impact of the tax

system alone on fertility in France."

(Dell and Wrohlich, 2006, p.53-54).

1 Introduction

Declining birth rates entail a common demographic problem in most of the developed

countries, such as the members of the Organization for Economic Co-operation and De-

velopment (OECD). Figure 1 illustrates that these countries have faced a decline in the

number of children born over the past decade, an issue which approaches the center of

political limelight as social security and pension systems are at danger to collapse under

currently applied rules. While most of the OECD countries reflect upon changing ac-

cess criteria to pension payments, nowadays’ low birth rates will significantly amplify the

pressure on public sector budgets and on politicians in decades ahead.

−− Figure 1−−

Figure 1 summarizes total fertility rates (TFR) for seven OECD countries,1 namely

France, Germany, Italy, Japan, Spain, Sweden, and the United States. All countries

display a downward-trend with the sharpest decline in the 1960s and 1970s which partly

can be ascribed to the introduction of the birth control pill. The TFR of the United States

amounted to 3.5 births per woman between 1950 and 1955 and declined to a current level

of about 2.1 — i.e., about the replacement rate.2 In Germany, the TFR was only 2.16 in

the 1950s and it declined dramatically to a current rate which is as low as 1.4.3 In the

1950s, France had a TFR of around 2.7 and it fell to a current level of about 1.9 which is

slightly lower than the replacement rate but significantly higher than that of Germany.1Total fertility rates represent the average number of children that would be borne to a woman during

her lifetime if she were to pass through her childbearing years conforming to the age-specific fertility ratesof that period.

2The replacement rate is the rate of fertility at which the population of developed countries can remainconstant in the long run.

3It is approximately the same as in Italy and Spain. The current TFR of Japan is even lower.

1

The general decline in developed countries’ TFRs is not only associated with the access

to birth control possibilities (Goldwin and Katz, 2000, 2002), but also with increased

income and, hence, higher opportunity costs of children (Becker, 1981)4, the rise in the

labor-force participation of women (Mira and Ahn, 2002, and Feyrer, Sacerdote, and

Stern, 2008) and abortion legalization (Ananat, Gruber and Levine, 2009).

To the extent that raising children involves both direct costs and opportunity costs, the

parents’ decision with regard to the number of children will depend on fiscal incentives

as well. For instance, the relatively high birth rate in France is often attributed to

the generous rules about maternity leave, tax incentives to families with many children

(including high-income families), and to subsidized child care facilities.

To counteract the demographic problem of reduced birth rates, some countries have

implemented incentives to increase the number of children. A justification for tax in-

centives towards larger numbers of children per household may be seen in the positive

intra- and intergenerational fiscal externality in pay-as-you-go social security systems:5

the present discounted value of net contributions to such systems is positive on aver-

age.6Among the tax-related incentives of that kind, spouse income splitting (as applied

in Germany) and family income splitting (the so-called ‘Quotient familial’ as applied in

France) feature prominently. While gross family income is divided by 2 in order to de-

termine marginal and average income tax rates under spouse income splitting, family

income splitting divides gross family income by a factor greater than 2 for that purpose,

depending on the number of children. Accordingly, the marginal and average income tax

rates ceteris paribus tend to be smaller under family income splitting than under spouse

4For instance, the total cost incurred by raising a child up to 18 years in Germany is estimated ata net present value (as of the year 2000) of €284,400 (see Werding and Hoffmann, 2005). Thereof,parents contribute 52.6% and the public sector covers the rest. Consistent with these figures, Lino (2006)computes an annual total financial cost of raising a child through age 17 of $11,600 (at 2006 U.S. dollars)for families in the middle income bracket in the United States. Of the €149,600 accumulated cost coveredby parents in Germany, €84,200 are estimated to be opportunity costs.

5Another justification of lower income tax rates for larger families may be seen in the principle ofhorizontal equity of taxation, since larger families display a lower per capita income on average.

6For instance, when taking into account the effects on ones’ descendants, Werding and Hoffmann(2005) estimate the net contributions of an individual at around € 77,000 in net present value terms (ofthe year 2000) for Germany.

2

income splitting with a progressive income tax schedule.7

Theoretical and empirical work on the effects of family income splitting on the number

of children is rather scarce. We aim at filling this gap in the following way. We set up

a stylized model in which household utility is maximized depending on the number of

children. In that model, a switch from spouse income splitting to family income splitting

leads to lower marginal and average income tax rates and, in turn, a larger number of

children. For the empirical exercise, we use data from a natural experiment, namely the

re-accession of the state Saarland to Germany in 1957.8

Across the past centuries, Saarland experienced a fickle history. It has been sought-

after by French as well as German emperors and — depending on the state of the power-

play between the two giants at the time — has been part of the one or the other at time

spans of various length. It was Saarland’s destiny to switch banner for the last time —

for now — in 1957, when it became one of the German states after having been part of

France since 1945. As a part of France, households in Saarland were taxed according to

the ‘Quotient familial’, i.e., family income splitting, while they were taxed according to

Germany’s spouse income splitting in the aftermath of 1957. We collected data on births

at the level of municipalities for Saarland (treated units) as well as municipalities of all

regions surrounding Saarland:9 the German state of Rheinland-Pfalz as well as three

French départements, namely Bas-Rhin, Moselle and Meurthe-et-Moselle. Altogether,

our data-set contains birth rates for 45 municipalities in Saarland, for 77 municipalities

in Rheinland-Pfalz, for 119 municipalities in Bas-Rhin, 73 municipalities in Moselle, and

77 municipalities in Meurthe-et-Moselle. Altogether, the data-set contains annual obser-

vations for 18 years between 1952 and 1970.

7The notion that family income splitting is more favorable towards larger families than spouse incomesplitting has ignited a hot public debate in Germany in 2007. For instance, Kurt Biedenkopf, the formerPrime Minister (Ministerpäsident) of the Free State of Saxony, and Ursula von der Leyen, the FederalMinister of Family Affairs, publicly supported the implementation of family income splitting in Germanyto raise the country’s total fertility rate.

8In a descriptive way, already Sinn (2003) mentions possible consequences of the change in familytaxation due to Saarland’s re-accession to Germany. However, we aim at estimating causal effects byusing the experimental nature of the reform.

9We focus on municipalities in a German state and French départements which are adjacent to Saarlandto ensure the largest possible degree of homogeneity among the units of observation.

3

The re-accession of Saarland to Germany forms a natural policy experiment since the

associated change in income tax systems was clearly exogenous from an individual house-

hold’s or municipality’s perspective. The data are suitable to provide causal inference of

the effects of the personal income tax policy change on the number of children.

The choice of municipality rather than state data entails the possibility to control for

differences across municipalities and to avoid aggregation bias in higher aggregates. We

will make use of difference-in-difference analysis with fixed time effects to ensure that

common effects (such as the introduction of the birth control pill) are eliminated and may

not invalidate the estimate of the re-accession effect associated with the change in income

tax policy.

In our empirical analysis, we consider two inflection points in Saarland’s re-accession

history: while political integration took place in 1957, full economic integration was de-

layed until 1959. Our findings suggest that the income tax reform associated with Saar-

land’s re-accession into Germany led to a reduction in births by about one-fifth. This

result is generally robust in qualitative terms and quantitatively robust across the pre-

ferred econometric models.

The remainder of the paper is structured as follows. In Section 2 we provide an

overview of the literature and the next Section introduces a stylized model to show the

effect of spouse versus family income splitting on the number of children. In Section 4 we

present the empirical strategy and our results, and Section 5 concludes with a summary

of the most important findings.

2 Review of the Literature

The literature on household decisions about the number of children has been started off by

Becker (1960,1981). In that work, the demand for children is a function of the associated

cost as well as individual preferences. Both direct costs and opportunity costs of having

children depend on fiscal incentives. Thus, in models of household decisions about the

number of children both tax credits and cash benefits which reduce these costs have a

4

positive effect on fertility if the associated income effect exceeds the substitution effect

(see, for instance, Cigno, 1986; Cigno, 1991; and Ridao-Cano and McNown, 2005).10

Empirical work suggests that fertility is higher in countries with lower direct costs of

children, a better provision of child care, and longer spells of possible maternity leave

(see d’Addio and d’Ercole, 2005, for a survey). Yet, the degree of cash benefits or the

availability of tax credits varies to a great extent between countries.

Work for single countries typically assesses the tax burden for families of different size.

An influential study assessing the effects of personal exemption for dependents in the

United States is the one by Whittington, Alm, and Peters (1990). For the time period

1913-1984 the authors estimate an aggregate fertility equation and find that personal

exemption exerts a significant and positive effect on fertility.

A number of studies specifically addresses financial incentives supporting families in

France. For instance, Laroque and Salanié (2004) simulate a joint structural model of

labor force participation and fertility to assess the impact of the ‘Allocation Parentale

d’Éducation’ (APE) on outcome. This financial incentive has been granted to families

with two or more children since 1994 and stipulates that during the first three years, one

of the parents receives a monthly benefit of €500 if he/she has held a job during two

years in the past five years and stopped working after the birth of the child. The authors

find positive responses of fertility to fiscal incentives, with the magnitude of results being

higher for first-born children and almost zero for the third child or further ones.

Landais (2003) investigates the effect of financial incentives on fertility in France by

means of a natural experiment. The author uses two concomitent measures which were

enacted at the beginning of the 1980s, namely the extension of the ‘Quotient familial’

towards the third child and the introduction of a ceiling of its effects. Using data for the

time period 1915-1998, Landais shows among others that the effect of this policy measure

on the fertility of families in top revenue tax brackets was of very low magnitude.

We are interested in the effects of spouse versus family income splitting on fertility.

10In this kind of models, when assuming children can be interpreted as a normal good, higher incomewill increase the demand for children. However, there may be a so-called quantity-quality trade-off. Then,higher income may render parents inclined towards raising less children at better conditions.

5

This has received very little attention in previous research. One possible reason for the

latter is that data have not been abundant to enable a systematic comparison of the

consequences of spouse versus family income splitting. To the extent that family income

splitting is a decisive element of the French system of fiscal incentives to stimulate fertility

(see also Dell and Wrohlich, 2006)), and the interest in other countries such as Germany

in creating similar incentives, it is interesting to aim at quantifying its effects on fertility.

Thus, the joint taxation of family members accompanied by a so-called income splitting

constitutes a different kind of granting tax relief to families. Different forms of this type

of income taxation are in place in countries like Germany, France or Portugal. According

to this method, the income of spouses is added together and then divided by two. This

split income is then taxed according to the regular tax schedule. The household’s overall

tax liability amounts then to twice this tax liability on split income. If the difference in

the income of spouses is large and given a progressive tax system, income splitting will

generate a lower tax burden compared to individual taxation. A slightly different tax

system is in place in France. Here, the income is split by more than two, since dependent

family members are also taken into account (Dell and Wrohlich, 2006).

When the ‘Quotient familial’ was introduced in 1945 for the first time, there was

no such progression of the divisor with the number of children. But rather, the divisor

was two for married couples without children and was increased by one-half for each

child. These personal income tax rules did not change until the late 1970s, when the

generosity of the rules was even increased. In the current French system, the splitting

divisor is increased by one-half for the first and second child each and by one for the

third and every subsequent child. The higher divisor for families with many children, is

often justified by the more than proportional increase in costs for raising three or more

children as compared to one or two children (see Dell and Wrohlich, 2006).11 However,

Meister and Ochel (2003) argue that such a system can also be seen as an instrument to

increase fertility especially among high-income earners, since the advantage from family

income splitting increases with the joint income of spouses.12 Using micro data, Baclet,11In France, it is also argued that the decision to have the first child on the part of parents is not so

much influenced by fiscal incentives (see Meister and Ochel, 2003).12For instance, families with two children multiply their household income by 1/(2 + 2 · 0.5) while

6

Dell, and Wrohlich (2005) assess the tax benefits of the French system and compare it to

the German system of child benefits and tax allowances. Their findings suggest that for

families with one or two children, the French system applied currently (including the cap

on the tax gains from family income splitting) is not more generous to families with up

to three children than the German system. However, the tax gains rise more steeply in

France and are higher for families with four or more children.13

However, while the personal income tax implications of the French and German sys-

tems are now well understood, their consequences on fertility are under-researched as

pointed out by Dell and Wrohlich (2006; see the introductory quote). Our contribution

aims at filling this gap. In particular, we will use data from a natural experiment to shed

light on the causal effect of switching between the systems of spouse income splitting and

family income splitting on fertility.

3 The Model

We apply a simplified version of the model by Apps and Rees (2004) and look into the

effects of family income vs. spouse income splitting on the number of children. Household

utility u depends on consumption c and the number of children n in the following way

u = γ lnn+ (1− γ) ln c. (3.1)

The female earner divides her time between household work (in the present case child

care) z ∈ [0, 1] and the rest, 1− z, which she provides to the labor market in exchange for

a gross wage of wf . For convenience, we assume that the male earner in the household

just supplies time to the labor market, earning a gross wage of wm. Both earners pay

income taxes of tmwm and tfwf , respectively. We assume a continuous progressive income

families with four children multiply it by 1/(2+2 ·1) to determine the marginal and the average personalincome tax rate.13They also point out that low-income earners are better off in Germany while high-income earners

tend to be better off in France.

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tax schedule such that tm > tf .14 Accordingly, the production function of child care is

n = αz; α > 0, (3.2)

and the household budget constraint can be defined as

c = wm(1− tm) + wf(1− tf)(1− z). (3.3)

Under spouse income splitting, both spouses’ income is summed up, divided by two,

and taxed at the respective tax rate tSS such that the household budget constraint becomes

c = wm + wf(1− z)− 2tSS(wm + wf(1− z)

2), (3.4)

where continuity and progressivity of the income tax system ensure tm > tSS > tf .

Moreover, we can derive the unit cost per child by solving

minC = wf(1− tSSf )z

s.t. n = f(z). (3.5)

Accordingly, the cost function per child, C(·), depends on the female net wage, wSSf =

wf(1− tSSf ), where p(·) denotes the price of a child:

C = p(wSSf )n. (3.6)

From this, we can derive the optimal division of time between child care and labor

supply

z∗ = z(wf , tSSf )n with z =

δp(wf , tSSf )

wSSf

.

14See Apps and Rees (2009a,b) for a an analysis of income taxation under discontinuous tax schedules.

8

Thus, the household’s maximization problem can then be written as

max γ lnn+ (1− γ) ln c = u

s.t. p(wSSf )n+ c = wm + wf(1− z)− 2tSS(wm + wf(1− z)

2). (3.7)

By maximizing household utility subject to the budget constraint, we can derive the

demand for (optimal number) children per household as

nSS =γ(wm + wf(1− z)− 2tSS(wm+wf (1−z)

2))

p(wSSf )

. (3.8)

By introducing family income splitting, the tax burden of the household now changes

to

T (wm, wf) = (2 + βn)tFSµwm + wf(1− z)

2 + βn

¶, (3.9)

where β denotes the splitting factor per child. For simplicity, we assume the income

divisor, which determines marginal and average tax rates of the household, (2 + βn), to

be linear in the number of children.15 Therefore, given that total household income can

be divided by a number greater than two, the marginal and average tax burden of this

household are ceteris paribus lower than under spouse income splitting with a progressive

tax schedule so that tm > tSS > tFS > tf . The household budget constraint now reads

c = wm + wf(1− z)− (2 + n)tFSµwm + wf(1− z)

2 + n

¶, (3.10)

and the household tax burden declines with the number of children in the family.

From the household’s utility optimization problem, the demand for children under

family splitting can now be derived as

nFS =γ(wm + wf(1− z)− (2 + n)tFS

³wm+wf (1−z)

2+n

´)

p(wFSf )

. (3.11)

15As mentioned before, this was the case in France after 1945, where the income divisor was (2+0.5 ·n).

9

where wFSf = wf(1 − tFSf ) is the female net wage under family income splitting. With

a progressive tax system, (2 + n)tFS³wm+wf (1−z)

2+n

´< 2tSS(

wm+wf (1−z)2

) holds. Thus, the

demand for children will be higher under family income splitting compared to spouse

income splitting, nFS > nSS.

4 Historical background and data

A key problem with the identification of causal effects of personal income tax systems

on fertility is that the consideration of children in the tax formulas changes quite rarely

so that inference commonly has to rely on cross-sectional data. However, it is likely

that countries which select into personal income tax systems that are favorable towards

larger numbers of children and bigger families have other characteristics which may affect

fertility, too. Then, it is difficult if not impossible — unless suitable instruments to isolate

the exogenous variation of personal income tax systems across countries are available —

to estimate the causal effects of differences in personal income tax systems on fertility.

In this paper, we pursue an analysis of a natural experiment taking place in the

German state of Saarland. What is now known as the 2.569 square kilometers large state

looks back on a turbulent history. Saarland is located at Germany’s border to France and

was part of both France and Germany (or, its predecessors), several times. For instance,

it was part of Germany between 1871 and 1920. It formed part of France after the Treaty

of Versailles in 1920, which required a referendum about the nationality of Saarland at

a later stage. By virtue of that referendum, Saarland became part of Nazi-Germany in

1935. In the aftermath of World War II — more precisely, from 1947 onwards — Saarland

formed an economic part of France with some autonomy. Finally, on January 1 of 1957

Saarland changed nationality for the last time in its past, becoming the tenth state of the

Federal Republic of Germany. Economic integration lagged somewhat behind, but from

July 6 of 1959 onwards, Saarland functioned by the same economic rules as the other

states of Western Germany at the time.

Our natural experiment makes use of the last step of political and economic change

10

in Saarland in 1957 and 1959, respectively. In particular, we are interested in its impact

on fertility through the associated fundamental reform of the state’s personal income tax

system. In fact, we assess the compulsory causal effect of the reform on fertility, accounting

for all differences in the income taxation of families in France versus Germany.16

For identification of the causal effect of the change in tax and family policy systems

on fertility, we collected data on newly-born children at the level of municipalities in

three French départements (Bas-Rhin; Moselle; and Meurthe-et-Moselle) and two German

states (Saarland; Rheinland-Pfalz).17 The choice of these units was dictated by their

geographical location: the three considered French départements are adjacent to Saarland

and Rheinland-Pfalz is the only German state bordering it. Our focus on geographically

proximate regions also provides homogeneity in the historical and institutional dimensions

to the largest possible extent. The choice of municipality rather than départements and

state data entails a further significant advantage, namely the possibility to control for

differences across municipalities to avoid aggregation bias in higher aggregates.

From the perspective of households in municipalities of the five mentioned French

and German regions, the change in the tax systems was clearly exogenous so that an

analysis of the impact of this natural experiment on births seems natural. However,

collecting data on births at the level of municipalities proved unexpectedly difficult and

a full coverage of all municipalities in Saarland and Rheinland-Pfalz as impossible. First

of all, birth accounts had not been published in either electronic or printed form for all

16It would be too crude to associate the change with a reduction in the divisor through the incomesplitting factor per child only. The average family in France (cum Saarland) had about 2.73 children inthe mid fifties. Families with an average gross income in France (and Saarland before its re-accession toGermany) received an annual net income which was about 1,011 DM higher in 1958 than it would havebeen in Germany with the same gross income. This was mostly due to child allowance (including extraallowances for mothers) from the first child onwards (Germany offered child allowance only from the thirdchild onwards). A household with a gross income of three times the average saved about 1,023 DM netincome in France as compared to Germany. One with a gross income of five times the average savedabout 1,276 DM. Admittedly savings due to differences in marginal tax rates only accounted for part ofthat. For instance, about 257 DM were due to the difference in the income splitting divisors betweenFrance and Germany with a gross income of five times the average in Saarland. See the Appendix forfurther details.17 The size of these French départements taken together is comparable to that of a German state. In

1970, the population of Rheinland Pfalz was 2,675,026 inhabitants. In 1968, the population of Meurtheet Moselle amounted to 705,554 people, in Moselle to 971,314 inhabitants and in Bas-Rhin to 827,367people.

11

municipalities in a country from a unique source.18 Second, birth accounts in the archives

of the statistical office of Saarland had been destroyed by floods. Accordingly, we had to

collect data from individual municipalities involving a correspondence-intensive process

over the time from October 2007 until December 2008.

Ultimately, we cover 45 of Saarland’s 52 municipalities, 77 of the 110 contacted ones

out of 2,306 municipalities in Rheinland-Pfalz, 119 of 300 contacted ones out of 526

municipalities in Bas-Rhin, 77 of 155 contacted municipalities out of 730 ones in Moselle,

and 73 of 300 contacted ones out of 594 municipalities in Meurthe-et-Moselle.19 Table

1 summarizes the coverage of municipalities in the two German states and the three

French départements we consider. Also, this table provides descriptive statistics about the

average number of births in the municipalities and their average annual change between

1952 and 1970.

−− Table 1 −−

With regard to possible control data, we had to rely on ones about population, per-

capita GDP, and unemployment rates collected by the statistical offices of the state of

Saarland and Rheinland-Pfalz, respectively. However, these data are not available for the

French municipalities (only population would be) and even for the German ones they are

not available for all years covered. So the corresponding results rely on a smaller number

of observations than other regressions and are relegated to a sensitivity analysis.

5 Estimation strategy

Table 2 provides information about the average number of births per municipality in each

of the five regions and years covered. What we are ultimately interested in is whether

Saarland’s integration in 1957/1959 entailed a change in fertility of households in an

18For instance, for municipalities in Moselle or Meurthe-et-Moselle we received data in hand-writtenformat from the 1950s (e.g., for Ville de Moyeuvre-Grande or Ville de Herserange).19We did not contact all municipalities in Rheinland-Pfalz and the French départements but ones that

were geographically close to Saarland and larger ones that operated hospitals.

12

average municipality relative to comparable municipalities in surrounding regions. The

numbers in Table 2 are actually suggestive of such a change. This becomes even more

obvious when considering a graphical illustration for the two German regions in Figure 2

and the German and French regions together in Figure 3.

−− Table 2 and Figures 2 and 3 −−

In the figures, we mark four years: the one where Saarland became a part of Germany

in political terms (1957); when it became economically integrated (1959); and when the

pill was introduced in Germany (1961) and France (1967). The timing and nature of the

four events illustrated in the figures guide the choices of both sample and specification

used for inference below.

For instance, a focus on municipalities only in the two German states together with

an inclusion of time-specific constants eliminates any possible effect of the pill on the

estimated effect of Saarland’s integration into Germany. Moreover, note that the munici-

palities in Saarland are of different size from both each other and ones in Rheinland-Pfalz

or the three départements (see the third column in Table 1) and suggests controlling for

municipality-specific constants. Consequently, focusing on a comparison of the absolute

number of newborn children in an arbitrary year after Saarland’s integration into Western

Germany with municipalities outside Saarland may be misleading. Hence, the difference

in means of births between municipalities in Saarland and outside Saarland — as, e.g.,

in Table 1 — is a statistic of potentially limited value. However, a comparison of the

changes in post-integration births relative to pre-integration births in Saarland relative

to other municipalities is informative. The average statistic of that kind for a sample of

municipalities in Saarland (the treated units) and outside Saarland (the control units) is

referred to as an estimate of the average treatment effect through difference-in-difference

estimation.

This section focuses on an estimation strategy which is suitable to estimate the causal

effect of such a change on fertility. Let us denote the log number of births in municipality i,

i = 1, ..., N and year t, t = 1952, ..., 1970 by ln yit. Furthermore, let us introduce an N×1

13

vector dN which has zero entries except for the ith column. Similarly, let us define a T ×1

vector dT which has zero entries except for the tth column. Finally, we use an indicator

variable dit which is unity for all municipalities in Saarland in the year of political (or

economic) integration or thereafter and zero for all other years or municipalities. Formally,

the log-linear version of the model we estimate may be represented as

ln yit = αdit + μNdN + λTdT + ζFRAdFRA,pill,it + ζDEUdDEU,pill,it + it. (5.12)

α is referred to as the difference-in-difference estimate of the average treatment effect —

in our case, of the integration of Saarland into Western Germany. Notice that the 1×N

and 1 × T vectors of unknown parameters μN and λT , respectively, represent constants

applying to the specific dimension. They ensure that α does not depend on any possible

correlated with time-invariant, municipality-specific effects (such as being a municipality

of Saarland) or time-variant common effects. The latter entail interesting examples in our

application. For instance, common business cycle shocks which affect all municipalities

commonly are fully absorbed in λT .

On the other hand, there are country-specific shocks which are not. For instance, the

contraceptive pill was introduced in Germany in 1961 while it was introduced in France

as late as 1967 (although it was only after 1974 that the social security system covered

it). Hence, the introduction of the pill requires including effects of the birth control

pill — beyond fixed municipality and time effects — for identification of α. This can be

achieved by controlling for a dummy variable with elements dc,pill,it which are unity after

the introduction of the pill in country c = {DEU,FRA} and zero otherwise. In the

model presented in equation (5) and estimated below, we have allowed the impact of the

birth control pill to differ between Germany and France (by allowing for ζFRA 6= ζDEU).

However, it turns out that the effect of the pill is hardly discernible from the one of other

common time-specific effects.20

20One reason for this may be that it was hard to avoid illegal use of birth control pills in one countryafter its inception in a neighboring country. This should be particularly relevant for us, since we focuson municipalities which are located close to the border between Germany and France.

14

Notice that the parameters of dN and dT reflect fixed municipality and time effects,

respectively. Their inclusion along with the birth control pill dummies eliminates any

possibility of the error term it to be correlated with either municipality-specific time-

invariant or common time-variant factors — observable or unobservable ones — or with the

inception of the birth control pill.

In the subsequent section, we present results which are based on variants of the model

in (). In some of the models, we disregard the possibility of zero births in a municipality

and estimate the model in log-linear form as outlined in (). Since some of the munici-

palities are rather small, this assumption is not generally justified. Moreover, there is a

non-trivial mass of municipalities with positive but small numbers of births per annum.

Therefore, we consider count data models to consider the discrete nature of the data.

In particular, we consider negative binomial models, since they allow the variance of the

dependent variable to differ from its mean (unlike in Poisson models; see Cameron and

Trivedi, 1998; or Winkelmann, 2003).21 One of the negative binomial models employed

subsequently is a two-part model, where the process of zero versus positive births per

municipality is modeled differently from the process of positive births. However, the

difference between the one-part and the two-part (or hurdle) negative binomial models

should not be large with the data at hand, since the number of municipalities with zero

births in a years is not large.

6 Empirical results

In this section, we discuss findings which are summarized in Tables 3-6. The tables re-

port the parameter estimates of interest for the baseline models for different samples of

the data: excluding French regions (Table 3); including French and Saarland’s regions

while excluding municipalities in Rheinland-Pfalz (Table 4); and covering all municipali-

ties available to us (Table 5). In these tables, we focus on the estimates of the effect of

21A comparison of the average number of births with their standard deviation across municipalities inTable 1 already suggests that negative binomial models may be better suited than Poisson models forthe data at hand.

15

Saarland’s integration into Germany. In all models and tables, we include fixed munici-

pality effects, fixed time effects, and effects capturing the impact of the birth control pill

(one for Germany and one for France).22 However, there are no further controls included

in Tables 3-5. The main reason for that is that potentially relevant determinants of births

and fertility — such as population, per-capita income, or unemployment rates — are not

easily available for municipalities in the time period of interest. However, we will turn to

that issue in Table 6 in a smaller sample of German municipalities only.

Tables 3-5 report parameter estimates for the impact of Saarland’s integration into

Germany on the number of births per municipality. Each of the tables distinguishes

between two blocs of results in the vertical dimension and up to three econometric models

in the horizontal dimension. In the upper bloc of the tables, we include an indicator

variable for Saarland’s political integration (which is unity from 1957 onwards). In the

lower bloc we include two indicator variables, one for Saarland’s political integration (as

before) and one for Saarland’s economic integration (which is unity from 1959 onwards).

Notice that the parameter estimates of the integration effects bear a similar interpretation

across the considered econometric models.

−− Tables 3 - 5 −−

The results may be summarized as follows. First, Saarland’s integration into Germany

led to a significant reduction in the number of births per municipality there as compared

to municipalities in surrounding regions. The point estimates for political integration

amount to in between −0.2 and −0.5, approximately. This suggests that Saarland’s

political integration led to a reduction of births by about 18 to 39 percent.

As expected, the difference between the negative binomial one-part and two-part mod-

els is tiny, since the number of municipalities with zero births in a year is small.23 There is

significant over-dispersion in the data — i.e., the variance is significantly different from the

22Notice that the impact of the birth control pill is not discernible from fixed time effects in Table 4.It is hard to discern from time effects in general in our data-set.23In Table 4, we do not report a two-part (zero-inflated) model since there are no municipalities with

zero births in any of the years in the corresponding sub-sample.

16

mean of the dependent variable — so that estimating negative binomial models is strictly

preferable over estimation of Poisson models. The parameter estimates of the log-linear

models are higher than those of the negative binomial models. The reason for the latter

is the strong linearity assumption of the log-linear model and its poor performance in

accounting for the impact on small versus large municipalities in a non-linear fashion as

compared to the negative binomial models. So, we would conclude that the causal effect

of Saarland’s integration into Germany is a reduction of births by about one-fifth.

We should be careful with drawing strong conclusions about the impact of political

versus economic integration of Saarland into Germany on fertility. The partial correla-

tion coefficient between the two indicator variables amounts to about 0.91. Notice that all

municipalities which get a unitary entry in the political integration indicator from 1957

onwards get a unitary entry in the economic integration indicator from 1959 onwards.

Hence, the impact of economic integration is not properly distinguishable from a perma-

nent effect of political integration on fertility. We will shed some more light on this issue

in the sensitivity analysis in Table 7.

As indicated beforehand, controlling for possible determinants of fertility other than

municipality and time indicator variables is difficult for reasons of data availability. In

Table 6, we approach the problem to the largest possible extent. Specifically, we include

log-transformed population, per-capita income, and unemployment rate on the right-hand

side of the models. These variables are only available for municipalities in Saarland and

Rheinland-Pfalz and even not for all of those. As in Table 4, we summarize the parameters

only for two econometric models, since there are no municipalities left which had zero

births in any of covered years.24 Like the previous tables, Table 6 distinguishes between

two blocs of results in the horizontal dimension.24Note that the number of municipalities is reduced from 122 in Table 3 to 73 in Table 6. The reason

for the limited availability of population and other data were floods and the associated destruction of dataat the Statistical Office of the State of Saarland ("Statistisches Landesamt"). Unemployment rates donot constitute a bottle neck. The registering of unemployment was is by the offices associated with labormarket districts where municipalities are nested in. In the data, unemployment rates are recorded andreported only at the level of 8 labor market districts ("Arbeitsmarktbezirke") in Saarland and another 8such districts in Rheinland-Pfalz. Hence, they are not available at all at the level of municipalities butimputed.

17

−− Table 6 −−

Even though the number of observations is much smaller than in Table 3, there is no

qualitative impact on the estimate of the consequences of Saarland’s political integration

into Germany. The parameter estimates of interest in Table 6 are relatively close to

their counterparts in Table 3. An omission of population, per-capita income, and the

unemployment rate does not seem to be harmful for estimation of the treatment effect we

are concerned about. Altogether, reasonable confidence intervals around the integration

effects are overlapping between Tables 3 and 6. The parameter estimate of log population

is generally negative while those of per-capita income and unemployment are positive.

These estimates may be rationalized as follows. Notice that we control for fixed mu-

nicipality effects. Therefore, an increase in population reflects an increase in population

density, since the size of a municipality’s geographical area is held constant (and captured

by the corresponding fixed effect). We would have expected agglomerations to generate

comparatively less births per household than peripheries. Moreover, a higher per-capita

income renders children more affordable. Yet, we admit that this effect is less clear-cut

than the one of population density: while richer regions are on average populated by

households which can afford larger numbers of children, they are also populated by resi-

dents whose opportunity costs of having children may be higher. However, disentangling

the latter two effects is beyond the scope of this paper due to data limitations. Finally, re-

gions with higher unemployment rates at given per-capita income and population suggest

that opportunity costs are low enough for one household member to have more children

rather than participating at the labor market.

−− Table 7 −−

In Table 6, we summarize the findings from a host of sensitivity checks. For the

sake of brevity, we concentrate on the impact of Saarland’s political integration as in

the upper blocs of Tables 3-6. Moreover, we do not report estimates for the two-part

negative binomial model, since we know that the results will be similar to those of the

one-part negative binomial model. Table 7 is composed of four blocs: we consider effects

18

in the log-linear models in the upper part and ones in the negative binomial models in

the lower part of the table; the results on the left-hand side are based on the sub-sample

of German municipalities in Saarland and Rheinland-Pfalz as in Table 3 while those on

the right-hand side of the table are based on German as well as French municipalities

as in Table 5. Since the inclusion of population and other control variables reduced the

sample size dramatically in Table 6 without changing the qualitative findings, we exclude

these control variables from the models to obtain the estimates in Table 7. The sensitivity

analysis assesses the robustness of the estimates in Tables 3 and 5 along three dimensions.

First, we consider (once, twice, or triple) lagged as opposed to contemporaneous ef-

fects of Saarland’s political integration on the number of births per municipality. Notice

that a twice-lagged impact of political integration is conceptually not distinguishable from

the impact of economic integration in 1959. Overall, the results suggest that the politi-

cal integration of Saarland into Germany reduce fertility with one annual lag somewhat

stronger than contemporaneously. However, the effect seems to stay relatively constant

in the subsequent two years at least. This result seems plausible, especially, since the

consequences of political and predictable economic integration of the state into Germany

should have materialized immediately for family planning but only subsequently for the

number of actual births per (household and) municipality.

Second, in spite of the fairly stable time pattern of political integration effects on

fertility identified before, we may be concerned about spurious effects associated with

heterogeneous dynamics across municipalities. In particular, autocorrelated data on births

could bias the parameter of interest. While part of this bias should be eliminated by the

inclusion of country-specific time effects, autocorrelation may still constitute a problem.

Bertrand, Duflo, and Mullainathan (2004) suggest a number of ways to avoid this bias.

One is collapsing the data to obtain one data point for the pre-treatment and one for the

post-treatment (in our case, the integration) period for each cross-sectional unit, where

the pre- and post-treatment windows should be of identical size.25 Doing so with the data

at hand leads to point estimates that are somewhat smaller than the ones in Tables 3 and

25Alternatively, they suggest a Newey-West-type correction of the variance-covariance matrix withpanel data estimation.

19

5. Hence, the findings suggest that the full effect on Saarland accumulates over several

years.

Third, we use a least-absolute deviations (median) regression approach to estimate the

political integration effect of Saarland on births in the log-linear models. This approach

applies less weight on leverage points — i.e., municipalities with a very large or a very small

number of births — than the least squares models in Tables 3-6 do. Again, the estimates

are smaller than in the log-linear models of Tables 3 and 5 but closer to the negative

binomial regression results, there.

Altogether, we may conclude that the political integration of Saarland into Germany

— which was associated with a change in the tax system, rendering the state less favorable

towards larger family sizes and numbers of children than under French political influence

— led to a reduction of births at the level of municipalities by about one-fifth. This

result is fairly robust in those empirical models that seem preferable from an econometric

perspective. The magnitude of the effect is somewhat larger in other econometric models.

Overall, this outcome is consistent with a stylized household model of taxation and choice

of the number of children.

7 Conclusions

The dramatic decline in birth rates recorded in countries all over the world poses special

problems to governments and constitutes a burden for social security systems in the future.

Given that children generate positive externalities for society by contributing to pension,

health, and unemployment systems, pay-as-you go systems involve a redistribution not

only from the young to the old generation but also from families with (many) children to

families with few or no children. Then, family policies aimed at enhancing fertility seem

to be appropriate measures to deal with the negative effects of this demographic trend.

Such policies are particularly important in both economic and political terms in countries

like Germany, where the total fertility rate with 1.4 children per woman is rather low,

especially compared to France, with 1.9 children per women.

20

The purpose of the present study is to investigate effects of such a fiscal measure,

namely the effects of family income splitting, on births at the level of municipalities. We

apply a stylized household decision model in which household utility depends besides con-

sumption also on the number of children. Using this model we show that lower marginal

and average income taxes as implied by family income splitting as compared to, e.g.,

spouse income splitting have positive effects on the number of children.

One aim of our study is to illustrate that this theoretical argument has empirical bite.

For this, we consider a natural experiment which was entailed by the integration of Saar-

land as Germany’s tenth state, being a region of France in the aftermath of World War

II. As a French region, Saarland applied family splitting but changed to spouse income

splitting — which was uniformly applied in Germany at the time — with its integration into

Germany in 1957. We collected data on births in a relatively large number of municipal-

ities in Saarland and its surrounding regions in Germany (Rheinland-Pfalz) and France

(Bas-Rhin, Meurthe-et-Moselle, and Moselle).

From the perspective of households in municipalities of the five mentioned French and

German regions, the change in the tax systems was clearly exogenous so that an analysis

of the impact of this natural experiment on births seems natural. We collect data for

18 years between 1952 and 1970 of municipalities in all these regions. The choice of

municipality rather than state data entails the possibility to control for differences across

municipalities and to avoid aggregation bias in higher aggregates. The consideration not

only of German but also of French regional data allows for a rich design regarding control

units. Comparing the changes in post-integration births relative to pre-integration births

by means of difference-in-difference estimation suggests that the political integration of

Saarland into Germany reduced births in the average municipality by about one-fifth

relative to the control units. This result is fairly robust in those empirical models that

seem preferable from an econometric perspective.

21

Appendix - Family policy instruments other than taxes

in Germany and France (1952-1968)

The integration of Saarland into Germany brought about a series of changes in the sup-

port to families with children at the time. Besides the switch from family to spouse

income splitting itself, a number of fiscal measures was changed in addition. For instance,

Germany applied so-called child tax credits and child allowances, whereas in France, child

allowances and a so-called ‘woman allowance’ were in place. Moreover, Saarland’s inte-

gration involved a change in the income tax schedules (i.e., the marginal tax rates applied

at different income brackets).

In 1952, the tax credit related to children in Germany amounted to 600 DM for every

child. It was gradually raised to 897 DM, to 1,675 DM, and to 1,794 DM for the first,

the second, and the third child, respectively, between 1952 and 1974. Regarding child

allowances, these amounted to 25 DM per month for the third and every subsequent child

between 1955-1957 and were also subsequently raised step by step. Between 1963 and

1974, an allowance of 25 DM per month was also granted to the second child. For the

third and forth child, the allowance amounted to 30 DM per month between 1957 and

1959 and was even doubled to 60 DM per month in 1970. In 1957 (so still under French

ruling), child allowances in Saarland amounted to 2,300 FF (equivalent to 18.80 DM per

month) for the first child and to 3,700 FF (30 DM per month) for every subsequent child.

In 1958, these allowances were raised to 20 DM and 32 DM, respectively.

In addition to child allowances, women in Saarland were eligible for “women allowance”

which applied at the time in France. In Saarland, this was referred to as “Frauengeld”.

It amounted to 16.4 DM per month in 1957 and to 18 DM per month in 1958.

Regarding the income tax rates, the lowest marginal tax rate in Germany was 28.2 per

cent in 1958 and 21.6 percent in 1965 for an annual income of 2,000 DM. The top marginal

income tax rate applied for incomes above 240,000 DM and was 53 percent both in 1958

and 1965. In France, income below 220,000 FF (i.e., about 2,420 DM) was tax exempt

between 1953 and 1959. A similar amount remained tax exempt until 1970. For incomes

22

between 220,000 FF and 350,000 FF (i.e., between around 2,420 DM and 3,850 DM) the

marginal tax rate was 10 percent in the 1950s. This threshold was slightly lowered in

subsequent years. The top marginal tax rate for incomes above 6,000,000 FF (around

66,000 DM) reached 60 percent between 1953 and 1959. Between 1960 and 1963, it was

even applied to incomes of 52,000 DM or higher, and between 1965 and 1968 personal

incomes of about 59,000 DM or higher were taxed marginally at that rate.

Taking stock, we arrive at the following picture. Assume a family with an average

number of children of 2.7 in France at the time and an average gross income of 505,957

FF (i.e., approximately 5,027 DM). Suppose that family resided in Saarland prior and

after its integration into Germany in 1957 and only one of the spouses participated in the

labor force. This household’s annual net income (including all further family allowances)

under family income splitting would have amounted to 633,037 FF (approximately 6,290

DM) but only to 626,441 FF (approximately 6,224 DM) under spouse income splitting

when applying constant French tax rates and other allowances. Hence, net income would

have dropped by about one percent (6,596 FF or 66 DM) due to the reduction in the

income splitting factor with spouse rather than family income splitting.26 The reduction

in net annual income is even larger for households in higher income brackets. For instance,

households with as many children but three times the average annual income would have

lost 69,219 FF (688 DM), and ones with an annual income which was five times the average

would have lost 166,804 FF (1,657 DM) due to the reduction in the splitting factor alone.

Acknowledgements

The authors would like to thank Anna Mickler and Luise Röpke for their assistance in

gathering the data as well as all registers offices in Saarland, Rheinland-Pfalz, Bas-Rhin,

Moselle, and Meurthe-et-Moselle, which have provided us the necessary data. Moreover,

we also appreciate the support form the statistical offices of Saarland and Rheinland-Pfalz

26Note here that net income exceeds gross income for the chosen example, since income up to 220,000FF was not taxed in France and thus the higher net income includes gross income plus child allowanceand so-called ‘women allowance’.

23

as well as from INSEE (Institut National de la Statistique et des Études Économiques)

and INED (Institut National d’Études Demographiques).

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25

Figure 1: Total Fertility Rates in Selected Countries

1

1.5

2

2.5

3

3.5

4

1950-1955

1955-1960

1960-1965

1965-1970

1970-1975

1975-1980

1980-1985

1985-1990

1990-1995

1995-2000

2000-2005

2005-2010

TFR

United States

France

SwedenGermany

JapanItaly

Spain

Source: UNECE Statistical Division

Note: The Total Fertility Rates (TFR) depicted here represent the average number of children that would be borne to a woman during her lifetime if she were to pass through her childbearing years conforming to the age-specific fertility rates of a given year

1.8

2.3

2.8

3.3

3.8

4.3

4.8

5.3

5.8

1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970

Year

Log

bir

ths

Moselle

Bas Rhin

Political integration of

Saarland

Economic integration of

Saarland

The Pill in Germany

Rheinland-Pfalz

Saarland

The Pill in France

Meurthe-et-Moselle

Figure 2: Change in births in Saarland, Rheinland-Pfalz, Bas-Rhin, Moselle and Meurthe-et-Moselle

Figure 3: Change in births in Saarland relative to Rheinland Pfalz

3

3.5

4

4.5

5

5.5

1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970

Year

Log

bir

ths

Political integration of Saarland

Economic integration of Saarland

The Pill

Rheinland-Pfalz

Saarland

Table 1 - Descriptive statistics of births in Saarland, Rheinland-Pfalz, Bas-Rhin, Meurthe-et-Moselle, and Moselle

Region Average Std.dev. Std.dev.

Saarland 45 313.3 628.0 -2.1 65.9

Rheinland-Pfalz 77 266.7 450.4 -0.8 52.0

Bas-Rhin 119 99.2 701.6 1.3 27.0

Meurthe-et-Moselle 73 60.1 187.1 0.2 20.4

Moselle 77 180.1 585.6 3.6 39.0

Levels 1952-1970 Annual change 1952-1970Statistic

Number of municipalities

Year Saarland Rheinland-Pfalz Bas-Rhin Meurthe-et-Moselle Moselle

1952 256.3 171.8 84.0 48.8 134.11953 252.0 174.0 84.1 52.4 138.41954 263.5 180.0 86.3 58.0 147.61955 253.9 182.4 88.0 58.0 151.61956 255.2 177.0 88.9 56.9 160.51957 268.1 160.6 91.9 59.9 163.11958 274.1 158.8 94.7 60.8 173.31959 294.1 161.3 96.4 63.5 182.21960 273.3 161.4 100.0 67.5 188.71961 307.5 170.1 102.7 70.9 205.01962 311.8 166.3 102.4 69.1 198.21963 307.8 176.9 108.3 68.8 205.91964 309.2 167.5 111.6 66.8 207.21965 306.2 157.8 109.7 62.8 198.91966 323.1 170.0 110.1 59.2 198.51967 311.3 155.1 104.5 55.5 193.31968 290.1 148.0 106.6 55.5 186.81969 258.2 138.3 107.8 54.6 190.11970 219.9 120.0 107.5 52.7 198.5

Region

Table 2 - Average number of births per municipality in Saarland, Rheinland-Pfalz, Bas-Rhin, Meurthe-et-Moselle, and Moselle per year(1952-1970)

Explanatory variables Log-linear

Political integration (1957 onwards) -0.329 a -0.265 a -0.259 a

0.007 0.058 0.057

Model characteristics Municipalities 122 122 122 Years 19 19 19 Observations 2,254 2,266 2,266 R2 0.830 0.150 0.151 P-value of Wald-test: significance of over-dispersion parameter - 0.000 0.000 P-value of Wald test: joint significance of fixed time effects 0.097 0.000 0.000 P-value of Wald test: joint significance of fixed municipality effects 0.000 0.000 0.000

Political integration (1957 onwards) -0.043 -0.037 -0.0360.102 0.088 0.087

Economic integration (1959 onwards) -0.339 a -0.284 a -0.278 a

0.005 0.082 0.081


Table 3 - Difference-in-difference estimation of the political and economic integration of Saarland into Germany (group of untreated excludes Frenchmunicipalities)

Notes: The standard errors reported below coefficients are robust to heteroskedasticity and clustering at the level of three French arrondissements and twoGerman Länder. - Birth control pill effects for Germany and France are controlled for but not reported for the sake of brevity. - Superscripts a, b, cindicate that coefficients are significantly different from zero at 1, 5, and 10 percent, respectively. - R2 figures for Negative binomial models are Pseudo-R2s.

Economic integration

Econometric model

Negative binomialZero-inflated

Negative binomial

Political integration only


Political integration (1957 onwards) -0.490 a -0.192 a

0.150 0.051

Model characteristics Municipalities 299 299 Years 19 19 Observations 4,215 4,215 R2 0.913 0.269 P-value of Wald-test: significance of over-dispersion parameter - 0.000 P-value of Wald test: joint significance of fixed time effects 0.237 0.000 P-value of Wald test: joint significance of fixed municipality effects 0.000 0.000

Political integration (1957 onwards) -0.033 0.0360.073 0.078

Economic integration (1959 onwards) -0.480 a -0.288 a

0.082 0.073

Model characteristics Municipalities 299 299 Years 19 19 Observations 4,215 4,215 R2 0.913 0.269 P-value of Wald-test: significance of over-dispersion parameter - 0.000 P-value of Wald test: joint significance of fixed time effects 0.078 0.000 P-value of Wald test: joint significance of fixed municipality effects 0.000 0.000

Table 4 - Difference-in-difference estimation of the political and economic integration of Saarland into Germany (group ofuntreated excludes municipalities in Rheinland-Pfalz)

Notes: The standard errors reported below coefficients are robust to heteroskedasticity and clustering at the level of three Frencharrondissements and two German Länder. - Birth control pill effects for Germany and France are controlled for but not reportedfor the sake of brevity. - All municipalities included had positive birth rates in all years recored. Therefore, no zero-inflatedmodel results are reported. - Superscripts a, b, c indicate that coefficients are significantly different from zero at 1, 5, and 10percent, respectively. - R2 figure for Negative binomial model is a Pseudo-R2.



Econometric model

Negative binomial


Political integration (1957 onwards) -0.435 a -0.192 a -0.202 a

0.116 0.051 0.050


Political integration (1957 onwards) -0.033 0.036 0.0300.073 0.078 0.076

Economic integration (1959 onwards) -0.480 a -0.288 a -0.293 a

0.082 0.073 0.071


Econometric model

Table 5 - Difference-in-difference estimation of the political and economic integration of Saarland into Germany (group of untreated includes Frenchmunicipalities)



Notes: The standard errors reported below coefficients are robust to heteroskedasticity and clustering at the level of three French arrondissements and twoGerman Länder. - Birth control pill effects for Germany and France are controlled for but not reported for the sake of brevity. - Superscripts a, b, cindicate that coefficients are significantly different from zero at 1, 5, and 10 percent, respectively. - R2 figures for Negative binomial models are Pseudo-R2s.

Negative binomialZero-inflated

Negative binomial

Table 6 - Sensitivity analysis (controlling for logs of GDP per capita, population, and unemployment)


Political integration (1957 onwards) -0.348 a -0.308 a

0.127 0.107

Log population -0.461 a -0.417 a

0.116 0.110Log GDP per capita 0.284 a 0.213 b

0.090 0.083Log unemployment 0.107 b 0.081 b

0.044 0.036

Model characteristics Municipalities 73 73 Years 19 19 Observations 810 810 R2 0.870 0.169 P-value of Wald-test: significance of over-dispersion parameter - 0.000 P-value of Wald test: joint significance of fixed time effects 0.000 0.000 P-value of Wald test: joint significance of fixed municipality effects 0.000 0.000

Econometric model

Negative binomial

Notes: The standard errors reported below coefficients are robust to heteroskedasticity and clustering at the level of two GermanLänder. - Birth control pill effects for Germany and France are controlled for but not reported for the sake of brevity. - Allcovered municipalities exhibit positive births in all years. - Superscripts a and b indicate that coefficients are significantlydifferent from zero at 1, 5, and 10 percent, respectively. - R2 for Negative binomial model is a Pseudo-R2s.

Table 7 - Sensitivity analysis continued

Experiment German regions

Once-lagged political integration of Saarland in Germany (1957 onwards) -0.332 a -0.470 a

0.065 0.057

Twice-lagged political integration of Saarland in Germany (1957 onwards) -0.338 a -0.475 a

0.066 0.056

Triple-lagged political integration of Saarland in Germany (1957 onwards) -0.354 a -0.511 a

0.066 0.056

Political integration of Saarland in Germany (1957 onwards) in collapsed data-set (pre- and post 1957 are one period each) -0.270 c -0.251 a

0.146 0.072

Median regression -0.251 a -0.363 a

0.072 0.084

Once-lagged political integration of Saarland in Germany (1957 onwards) -0.269 a -0.238 a

0.058 0.050

Twice-lagged political integration of Saarland in Germany (1957 onwards) -0.280 a -0.267 a

0.059 0.050

Triple-lagged political integration of Saarland in Germany (1957 onwards) -0.354 a -0.320 a

0.066 0.049

Political integration of Saarland in Germany (1957 onwards) in collapsed data-set (pre- and post 1957 are one period each) -0.176 b -0.196 a

0.082 0.075Notes: The standard errors reported below coefficients are robust to heteroskedasticity and clustering at the level of three French arrondissements and two German Länder. - Birthcontrol pill effects for Germany and France are controlled for. - Superscripts a, b, c indicate that coefficients are significantly different from zero at 1, 5, and 10 percent,respectively.

Negative binomial models

Regional coverageGerman and

French regionsLog-linear models

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