Using panel cointegration analysis, we show that a cointegration relationship exists among fertility choice, infant mortality, real wages and real per capita output. The results suggest that in low mortality economies reductions in infant mortality will decrease fertility.

Evangelia Papapetrou

George Hondroyiannis

English

Research Papers in Economics

DEMOGRAPHIC TRANSITION IN EUROPE 
George Hondroyiannis Evangelia Papapetrou
Bank of Greece, Economic Research Department and
Harokopio University
University of Athens and Bank of Greece, Economic
Research Department
Abstract
Using panel cointegration analysis, we show that a cointegration relationship exists among
fertility choice, infant mortality, real wages and real per capita output. The results suggest
that in low mortality economies reductions in infant mortality will decrease fertility.
The views expressed in this paper are those of the authors and not those of the Bank of Greece. The authors wish to thank
Chiang and Kao who offer the NPT 1.2 as public program and Peter Pedroni for providing his program for the estimation of
FMOLS. All errors and deficiencies are the responsibility of the authors.
Citation: Hondroyiannis, George and Evangelia Papapetrou, (2002) "DEMOGRAPHIC TRANSITION IN EUROPE."
Economics Bulletin, Vol. 10, No. 3 pp. 1−8
Submitted: March 27, 2002.  Accepted: March 29, 2002.
URL: http://www.economicsbulletin.com/2002/volume10/EB−02J10001A.pdf1
1.  Introduction
Most countries, industrialized or not, experience important demographic changes, one of the
most important of which is the transition from a phase of rapid population growth to one in
which population growth is low. Initially, a country experiences a mortality decline and
fertility rises, both contributing to a rise in population growth. With some time lag, the
reduction in mortality triggers a steady and continuous decline in fertility. This pattern is
called the “demographic transition”.
The debate between followers of the Malthusian theory and neoclassical economists shows
the crucial link between fertility, mortality and economic growth. However, the modern
economic theory of population emphasizes the interdependence between infant mortality and
fertility in the context of economic theories of behavior (Sah 1991; Cigno 1998; Becker et al.
1999). In Cingo’s model an exogenous reduction in child mortality may either raise or lower
fertility. When the level of child mortality is high, reductions in it are likely to raise both
fertility and survival-enhancing expenditures on children, because it lowers the price of a
surviving child. When fertility is low, further reductions in it are likely to reduce fertility and
survival-enhancing expenditures on children. Sah (1991) finds that when parents have a target
fertility level and are sufficiently risk averse, then better survival opportunities for their
children tend to reduce fertility. In the analysis by Becker et al. (1999) parents choose their
number of children and investments in the human capital of each child to maximize their
dynastic utility. In their model birth rates are lower in the modern world with growing human
capital than in the agricultural economies partly because adult and child mortality is much
lower.
However, limited empirical research addressed the issue of fertility, infant mortality and
economic growth with rather inconclusive evidence on the relationship among the variables.
Schultz (1985), using Swedish data from 1860 to 1910, has shown that a quarter of the
decline in fertility over this period was due to a 50 percent reduction in child mortality.
Yamada (1985) using a sample of developed and less developed countries showed that infant
mortality and fertility are jointly determined. He found that a decline in infant mortality that is
due to an increase in per capita real income causes a subsequent decline in fertility. Rostow2
(1990) uses cross- section data from seventy-six countries and finds that birth and death rates
are negatively correlated with per capita GNP.
This paper’s contribution to the existing literature is as follows. First, using country by
country and panel cointegration modeling for nine European countries for the period 1960-
1998, we show that a long-run cointegration relationship exists between demographic
variables, such as fertility and mortality, real wages and real per capita output. Second,
consistent with the theoretical findings of Cigno (1998), Sah (1991) and Becker et al. (1999)
we demonstrate that in modern economies, where the level of infant mortality is already low,
further reductions in it are likely to reduce fertility.
For this purpose the Pedroni technique (1997, 2000) for heterogeneous panel data is applied
to search for the existence of cointegration in the panel setting to explicitly accommodate and
estimate the dynamic long-run interrelations in levels. Finally, the fully modified OLS for
heterogeneous panel (FMOLS) technique is applied to estimate the long-run estimates in
country -by -country basis and in panel modeling.
The remainder of the paper is organized as follows. Section 2 presents the data and describes
briefly the panel cointegration methodology. Section 3 presents the empirical results. Section
3 concludes.
2.  Empirical Analysis
2.1 Data description
The empirical analysis has been carried out using annual data for the period 1960 to 1998 for
nine European countries. The nine European countries are: Germany, France, Italy, United
Kingdom, Spain, Ireland, Netherlands, Finland and Sweden. The wage variable (RWAGE) is
the real wage; the fertility choice variable (FERT) is the total fertility rate (i.e. the number of
children which a woman would bear if she followed throughout her life the current age specific
birthrates); the infant mortality rate (MORT) is defined as the number of children aged under
one year old who die per 1000;  the output variable (RCGDP) is the real per capita GDP at
market prices. The data on real wage and real per capita output are obtained from the
International Financial Statistics data set. The data of fertility and infant mortality are3
obtained from the Eurostat Demographic Statistics published by the Eurostat. All variables are
expressed in logarithmic form (LFERT, LMORT, LRWAGE, LRCGDP).
2.2 Panel Cointegration
Following Sah (1991) and Cigno (1998), it is possible to derive an equation for fertility 
LFERT = f(LMORT, LRWAGE, LRCGDP)                          (1)
In the empirical analysis we estimate equation (1) to test for the validity of “demographic
transition” theory and for the contribution of economic forces to the demographic transition
process. In particular, we employ the panel cointegration approach and the fully modified
OLS estimation technique to test whether a cointegration relationship exists among fertility
mortality, real wages and real per capita output. 
Table 1 summarizes the results of cointegration analysis among the four variables using the
Johansen maximum likelihood approach employing the trace statistic
1,2. The tests provide
evidence to reject the null of zero cointegrating vectors in favor of one cointegrating vector at
5% level for all the countries. On the basis of the results, the long-run relationship between
demographic variables, real wages and real per capita output finds statistical support in each
individual country.
Next, panel unit roots are used to examine if the panel data series are I (1). The Hadri (2000)
unit root tests for each variable for the panel data are estimated. Table 2 presents the results. 
The null hypothesis of stationarity is rejected at 1% level of significance in both cases
(constant, constant and trend). Therefore, the results from the tests suggest that all the series
appear to be non-stationary in the panel data set.
Next, since all the variables in the panel data are integrated of the same order, it is appropriate
to look for a relationship among the variables. Kao (1999), and Pedroni (1997, 1999, 2000)
developed several tests to examine the existence of cointegration in a multivariate framework.
The proposed statistics test the null hypothesis of no cointegration versus the alternative of
                    
1 The Augment Dickey Fuller (ADF), Phillips-Perron and KPSS tests for the four variables in levels and first
differences on individual country bases have been performed. The combined results from all the tests suggest
that all the series under consideration are I(1) processes.
2 To determine the lag length of the VAR, three versions of the system were initially estimated: a four, a three and a
two-lag version. Then, an Akaike Information criterion (AIC), a Schwarz Bayesian Criterion (SBC) and a likelihood
ratio test (Sims’ test) were used to test whether all three specifications are statistically equivalent. All tests reject the
null hypothesis that all the specifications are equivalent. In particular, the tests suggest different lag structure for
each country. In most cases the appropriate lag structure was equal to two.4
cointegration. However, pooling time series has resulted in a substantial sacrifice in terms of
the permissible heterogeneity of the individual time series. It is important in the process of
polling time series to permit as much heterogeneity as possible among individual time series.
Therefore, testing for cointegration among the variables should permit for as much
heterogeneity as possible among the individual countries of the panel. Pedroni (1997, 1999,
2000) developed several tests to test for no cointegration in dynamic panel allowing for
heterogeneity among the individual countries. Seven tests are estimated to examine whether
the error process of the estimated equation is stationary.
Table 3 summarizes the results of cointegration analysis among the four variables using the
Pedroni statistics. All the statistics provide evidence of cointegration to support the long-run
relationship among the variables.  In particular, all the country-by-country and panel
cointegration test results suggest that there is a cointegrating relationship among real per capita
output, fertility, infant mortality and real wage in the sample of European countries. In addition
the estimated results suggest that all the variables used in the analysis can be treated as “long-
run forcing” variables for the explanation of the others. 
Having established that the variables are structurally related the long-run equations are
estimated using the fully modified OLS (FMOLS) for heterogeneous cointegrated panels
(Pedroni 1997, 2000) (Table 4). From the estimated equations three main points can be
concluded. First, real per capita income for the panel has a positive sign and is statistically
significant which implies that an upward shock in real GDP per capita, due for example to an
improvement in the terms of trade, leads to higher fertility. This implies a positive income
effect on the demand for children. The estimated coefficient is positive and statistically
significant for Italy (0.73), Spain (2.40). For the other countries, except for Ireland,
Netherlands and Finland, is positive but not statistically significant. Second, the empirical
results for the panel and for each country, except for Finland, imply that an upward shock in
real wages, due for example to technological change, leads to lower fertility. This implies that
the opportunity cost of time devoted to childcare has increased and consequently fertility has
declined. Finally, the empirical results for the panel data indicate a downward shock to infant
mortality, due for example to medical advances, leads to lower fertility. This result is
consistent with the theoretical explanations provided by Sah (1991), Cigno (1998), Becker et
al. (1999).5
3.  Conclusions
This paper provides an empirical model that supports a long-run relationship between fertility
choice, infant mortality, real wages and real per capita output using panel cointegration
techniques for a sample of European countries. In agreement with the theoretical findings of
Sah (1991),  Cigno (1998) and Becker  et al. (1999) the results suggest that in industrial
economies with low mortality reductions in infant mortality will further reduce fertility.
4. Acknowledgment
The views expressed in this paper are those of the authors and not those of the Bank of Greece.
The authors wish to thank Chiang and Kao who offer the NPT 1.2 as public program and Peter
Pedroni for providing his program for the estimation of FMOLS. All errors and deficiencies are
the responsibility of the authors.6
References
Becker, G.S., E. L. Glaeser and K. M. Murphy (1999) “Population and Economic Growth”
American Economic Review, Papers and Proceedings, 89,2, 145-149.
Chiang, M. H. and C. Kao (2001) Nonstationary Panel Time Series Using NPT 1.2-User
Guide. Center for Policy Research, Syracuse University.
http//www.maxwell.syr.edu/maxpages/faculty/cdkao/working/npt.pdf.
Cigno, A. (1998) “Fertility Decisions when Infant survival is Endogenous”  Journal of
Population Economics 11, 21-28.
Hadri, K. (2000) “Testing for Stationarity in Heterogeneous Panel Data”  Econometric
Journal 3, 148-161.
Kao, C. (1999) “Spurious Regression and Residual Based Tests for Cointegration in Panel
Data” Journal of Econometrics 90, 1-44.
Pedroni, P. (1997) “Panel Cointegration: Asympotic and Finite Sample Properties of Pooled
Time Series Tests with an Application to the PPP Hypothesis. New Results” Indiana
University mimeo.  
Pedroni, P. (1999) “Critical Values for Cointegration Tests in Heterogeneous Panels with
Multiple Regressors” Oxford Bulletin of Economics and Statistics, 61, 653-70.
Pedroni, P. (2000) “Fully Modified OLS for Heterogeneous Cointegrated Panels”  in
Nonstationary Panels, Panel Cointegration and Dynamic Panels, Elsevier Science
Inc., 15, 93-130.
Rostow, W.W (1990) “Theorists of Economic Growth from David Hume to the Present”
Oxford University Press, New York, NY.
Sah, R (1991) “The Effect of Child Mortality Changes on Fertility Choice and Parental
Welfare” Journal of Political Economy 99, 582-606.
Schultz, T.P (1985) “Changing World Prices, Women’s Wages and the Fertility Transition:
Sweden, 1860-1910” Journal of Political Economy 93, 1126-1154.
Yamada, T. (1985) “Causal Relationships between Infant Mortality and Fertility in Developed
and Less Developed Countries” Southern Economic Journal 52, 364-370.7
Table 1
  Johansen and Juselius Cointegration Test based on Trace of the Stochastic Matrix
Fertility Choice, Mortality Rate, Real Wages and Real Per Capita Output: Sample: nine
European countries during  1960-1998
Country 0 = r 1 £ r 2 £ r 3 £ r
Germany 63.97** 35.57 19.57 6.30
France 58.84** 35.55 15.53 3.03
Italy 67.28** 36.14 17.52 3.90
U.K. 70.04** 31.08 12.96 4.09
Spain 69.60** 39.32* 14.75 2.82
Ireland 69.57** 31.20 16.55 5.82
Netherlands 64.05** 35.85 14.52 4.18
Finland 59.01** 30.87 12.92 3.37
Sweden 66.91** 29.35 13.39 2.61
Notes: r indicates the number of cointegrating relationships. **, * indicate rejection of the
null hypothesis at 95 and 90 percent critical value, respectively.
 
 
 
 
  Table 2
  Unit Root Tests for Heterogeneous Panel
  Variable   Hadri (2000)
    No time trend   With time trend
  LFERT   18.79***   630.7***
  LMORT   24.44***   10716.54***
  LRWAGE   21.85***   3286.92***
  LRCGDP   23.51***   4080.26***
  Notes: *** indicates rejection of the null hypothesis of stationarity at 1%
level of significance.8
  Table 3
  Panel Cointegration Tests for Heterogeneous Panel
  Dependent variable   Statistics
  Fertility rate   Infant
mortality rate
  Real per
capita GDP
  Real wage
  Panel ?-Statistic   22.02***   19.12***   26.46***   17.17***
  Panel ?-Statistic   -14.48***   -14.37***   -15.79***   -9.69***
  Panel t-statistic: (non-parametric)   -4.78***   -4.63***   -4.86***   -3.96***
  Panel t-statistic: (parametric)   -215.29***   -147.29***   -329.04***   -249.78***
  Panel ?-Statistic   -16.54***   -15.25***   -18.01***   -10.77***
  Group t-statistic: (non-parametric)   -5.05***   -4.32***   -4.95***   -3.94***
  Group t-statistic: (parametric)   -4.97***   -3.74***   -4.94***   -4.08***
  Notes: All statistics are from Pedroni (1999). NPT 1.2 is used in the estimation as Chiang and
Kao (2001) developed it. *** indicates rejection of  the null hypothesis of no-cointegration at
1%  level of significance.
 
 9
Table 4
Long-run Estimates (Fully Modified OLS)
Dependent Variable: Fertility choice
Country LRCGDP LRWAGE LMORT
Germany 0.19
[0.49]
-1.06***
[-4.71]
-0.06
[-0.52]
France 0.08
[0.32]
-0.56***
[-3.32]
0.01
[0.16]
Italy 0.73***
[2.82]
-0.43***
[2.82]
0.56***
[6.99]
U.K. 0.42
[0.40]
-1.89***
[-2.08]
-0.38
[-1.43]
Spain 2.40***
[2.88]
0.67***
[7.72]
1.12***
[19.85]
 Ireland -0.15
[-0.76]
0.49***
[2.72]
0.66***
[4.38]
Netherlands -0.01
[-0.01]
-1.18***
[-2.69]
0.05
[0.22]
Finland -0.58
[-1.01]
-1.12
[-1.72]
-0.67***
[-2.88]
Sweden 0.55
[1.00]
-0.91*
[-1.92]
0.23***
[1.09]
Panel
0.18**
[2.04]
-0.66***
[-2.94]
0.17***
[9.28]
Notes: Figures in brackets are t-statistics. ***, ** indicate significance at 1%
and 5% level respectively.

Causal Relationships between Infant Mortality and Fertility in Developed and Less Developed Countries”

Changing World Prices, Women’s Wages and the Fertility Transition: Sweden,

Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors”

Fertility Decisions when Infant survival is

Fully Modified OLS for Heterogeneous Cointegrated Panels” in Nonstationary Panels, Panel Cointegration and Dynamic Panels,

Nonstationary Panel Time Series Using NPT 1.2-User Guide.

Panel Cointegration: Asympotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis. New Results”

Spurious Regression and Residual Based Tests for Cointegration in Panel Data”

Testing for Stationarity in Heterogeneous Panel Data”

The Effect of Child Mortality Changes on Fertility Choice and Parental Welfare”

Theorists of Economic Growth from David Hume to the Present”

DEMOGRAPHIC TRANSITION IN EUROPE

http://www.accessecon.com/pubs/EB/2002/Volume10/EB-02J10001A.pdf

DEMOGRAPHIC TRANSITION IN EUROPE

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