Human Development Paper Due 08/06/2018

Human Development and the Determinants of the Incidence of Civilian Disability Pensions in Italy: A Spatial Panel Perspective

Massimiliano Agovino • Giuliana Parodi

Accepted: 11 July 2014 / Published online: 20 July 2014 � Springer Science+Business Media Dordrecht 2014

Abstract The aim of this paper is to study factors which may affect the incidence of civilian disability pensions in Italy from a macroeconomic point of view, taking into

account all age groups, and introducing spatial effects by taking into account possible

interaction among the policies of individual regions. The analysis is developed on a panel

of the 20 Italian regions over the period 2002–2008. Education, life expectancy, and the

environment appear to reduce the incidence of civilian disability pensions; spillovers in the

policies of neighboring regions are connected with the ageing of the population, and with

the environment. Policy recommendations are developed.

Keywords Disability � Pensions � Models with panel data � Spatial models

1 Introduction

In most Western countries a high variability is observed in the distribution of disability

pensions 1

across areas, and their number is growing. This is a problem at the level of

government finances, as the increase in disability pensions puts long term pressure on

government 2

finances, as disability pensions are not a flexible instrument, as once granted,

they are rarely withdrawn (McVicar and Anyadike-Danes 2008). Also, it is a problem at

the level of social inclusion; people who benefit from disability pensions are generally

inactive with respect to the labour market, and therefore at risk of social exclusion. Overall,

M. Agovino (&) � G. Parodi Department of Economics, University ‘‘G. D’Annunzio’’ of Chieti-Pescara, Viale Pindaro 42, 65127 Pescara, Italy e-mail: [email protected]

1 The term disability pensions covers a variety of forms of income support to people with disability, which

differ according to institutional arrangements within the various countries. We specify in paragraph 4 which data we use to investigate the situation in Italy. 2

Throughout the paper we generically talk about government to indicate intervention of the public sector, without specifying the geographical level of the public intervention, which may vary among countries.

123

Soc Indic Res (2015) 122:553–576 DOI 10.1007/s11205-014-0705-8

the variability in the distribution of disability pensions can be considered as an indicator of

socio economic differences within areas of a same country, which governments may want

to tackle with appropriate policy instruments, so it is important to investigate factors which

affect disability pensions. For the purpose of policy, it is important to remember that the

observed number of disability pensions depends on the interaction between the demand for

disability pensions made by individuals, and the supply of disability pensions made

available by the government.

This work studies factors which may affect the incidence of disability pensions from a

macroeconomic point of view, with reference to Italy, and we bring a new approach not

found in the existing literature with respect to three directions: first, we investigate the

incidence of civilian disability pensions (ICDP) for all ages, not just the working age

group, therefore including the very young, for whom disability is likely to arise at birth,

and the old ones, for whom disability is mainly connected with age. Second, given the

wider age group considered, it seems appropriate to widen the frame of investigation to

include explanatory variables connected with human development 3

and with the envi-

ronment where people operate. 4

In particular, we want to test whether factors connected

with human development. i.e. a decent standard of living, education, and a long and

healthy life affect the incidence of disability pensions; also, we introduce additional

explanatory variables, i.e. public health expenditure per capita, and also environmental

variables, as availability of public urban green and an index of criminality. Third, we

introduce spatial effects which take into account possible interactions and spillovers among

the policies of individual regions with respect to disability pensions.

The analysis is developed on a panel of the 20 Italian regions over the period

2002–2008. In particular, we adopt the spatial Durbin model (SDM) as a point of departure

and conduct a variety of tests to investigate whether the general model can be reduced to a

spatial lag, spatial error, or an OLS model. Then, we proceed further to attempt to tackle

the endogeneity issue in the life expectancy regressor, by applying the Granger causality

test in order to find the true causality relationship between life expectancy and civilian

disability pensions.The rest of the paper is organised as follows: Sect. 2 reviews the

literature, and introduces the argument for spatial analysis; Sect. 3 specifies the spatial

model; Sect. 4 illustrates the data used; Sect. 5 provides empirical results; Sect. 6 provides

concluding remarks.

2 Review of the Literature

2.1 Background Literature

Factors which determine variability in the distribution of, and increase in, disability

pensions seem to be interrelated, and they all pivot around causes of ill health, and

therefore of disability. We list the main ones: concentration of dangerous economic

activities in specific areas; poverty, with particularly strong effects on areas with an ageing

3 The Human Development Report (UNDP 1990) presents the Human Development Index (HDI) as a three-

dimensional indicator of well being. Throughout this paper we use the three components of the HDI separately, as for Italy the component Income is highly correlated and dominates the other two. See ‘‘Appendix’’ 2 for evidence. 4

For the importance of environmental factors in affecting the employment of disabled people see Agovino and Rapposelli (2012, 2013a, b).

554 M. Agovino, G. Parodi

123

population; unemployment, and poverty, as a source of poor health (Smith 1998; Currie

and Madrian 1999). For Italy in particular, an important factor in determining variability in

the distribution of disability pensions could be migration, which characterizes the history

of Italian regions. Migration flows alter the natural demographic tendencies, and could

strongly affect the sustainability of pensions systems of each geographical area. Bonasia

and De Siano (2012) find that in Italian regions an increase of internal migration flows

negatively affects the sustainability of regional pension schemes, and this is particularly

evident for regions in the South of Italy.

So far, quantitative investigations on factors determining the number of disability pensions

have developed mainly along three lines of approach, sometimes interrelated, focusing on

labour market factors, income support factors, and financial/institutional factors.

Disney and Webb (1991) consider the unemployment rate as the determinant factor to

explain the spatial concentration of disability pensions in the UK Eligibility criteria and

generosity of alternative public benefits are stressed by Blundell and Johnson (1998) for the

USA. More recently, for the UK McVicar (2008), and McVicar and Anyadike-Danes

(2010) point to the observed increase in the replacement rate of scarcely qualified workers

as main causes of the increase in the number of disability pensions among the 15–64 age

group, as a possible ‘‘early retirement vehicle’’. Also McVicar (2006) stresses the influence

of the unemployment rate on the number of disability pensions in the USA, but also the

influence of the rules governing eligibility for disability pensions. Interestingly, Mc Vicar

finds a clusters of regions characterized by similar policies towards disability pensions,

both in the North of UK and in the South of USA (McVicar 2006). For Italy, in a

pioneering work, Beltrametti (1996) explains the high variability in the distribution of the

number of disability pensions in Italian regions in terms of local interpretations and

implementations of the National rules for granting disability pensions. Baldacci and De

Santis (2003) find a relationship between the unemployment rate and disability pensions,

but also comment on the use of disability pensions as an improper instrument of income

support, with special reference to the South of Italy. This relationship mirrors earlier results

by Castellino (1976), Beltrametti (1996) and Baldacci and Milan (1998). More recently,

Agovino and Parodi (2012) confirm that, among the 15–64 age group, disability pensions

are used as an antipoverty policy instrument in areas characterized by economic diffi-

culties, and find two clusters, in the North and the South of Italy.

2.2 Spatial Interaction and Expenditure Externality Hypothesis

The literature reviewed so far brings in economic variables as explanatory variables of

disability pensions, and also discusses the implications of applying different rules, whether

officially or unofficially, to the granting of disability pensions. However, the literature so

far ignores the formal analysis of possible spatial interaction among the policies of dif-

ferent regions in terms of concession of disability pensions. The introduction of this aspect

into the analysis appears to be essential; the results previously quoted in terms of identi-

fication of clusters (Beltrametti 1996; McVicar 2006, 2008; Agovino and Parodi 2012)

suggest spatial interaction among neighboring areas, as clustering is an indicator of similar

socioeconomic and cultural characteristics. To consider spatial interaction is relevant, as it

allows to identify possible processes of spatial spillovers among neighboring regions; it

also allows to eliminate problems of distortion in case of an existing but overlooked spatial

correlation (Anselin 1988).

In what follows we briefly discuss the main literature on spatial interaction in gov-

ernment spending, and also stress how likely spatial interaction among Italian regions is in

A Spatial Panel Perspective 555

123

terms of policies for granting disability pensions. This hypothesis is enhanced by the

dualism found in the distribution of the incidence of disability pensions in Italy (Beltra-

metti 1996; Agovino and Parodi 2012). Were data available over a long period of time,

probably pre-unit historical factors, going back to the nineteenth century, would appear to

be very important in explaining similarities in policies of Italian regions.

The literature on possible spatial interaction of local government choices on public social

expenditure is wide [for a review see for instance Brueckner (2003) and Revelli (2005)]. 5

Several mechanisms have been proposed to explain fiscal interaction among governments,

and among local governments (Manski 1993). We refer to the expenditure externality

hypothesis, according to which public expenditures of a local government can produce both

positive and negative effects in neighboring areas as well. With reference to disability pen-

sions, this would show up in an imitation process in the criteria to allocate disability pensions,

according to cultural, social and economic characteristics of the imitating areas. The closer

regions are in terms of geographical distance, the more likely it is that the assumption of

interaction and imitation among the policy of the various regions is valid. Geographical

clusters in the incidence of disability pension, and therefore the similarity in behavior among

regions, could be justified by what Manski (1993) calls a ‘‘common intellectual trend’’, which

for Italian regions could be interpreted as a ‘‘common cultural trend’’.

Spatial interaction among regional choices about the allocation of civilian disability

pensions is not in contrast with the National regulation on the criteria about how to allocate

them. The fundamental Law 104, 1992, which rules the rights of disabled people, attributes

major discretionary powers and responsibilities to local and regional authorities about

organizing and financing local services, hospices, and centers for disabled people, and

these service, locally managed, could contribute to enhance a widening between the quality

and quantity of services provided at regional level (Baldacci and De Santis (2003). Should

more disaggregated data become available, further discrepancies may emerge in terms of

incidence of disability pensions.

At this point it is necessary to specify how do we model the interrelationships among

Italian regions. The expenditure externality hypothesis suggests a spatial proximity matrix

whose weights are represented by the inverse distance expressed in Km. between a location

and another: with increasing distance, links tend to be weakening; as a consequence, the

possibility of spatial interaction decreases as regions are further from each other. 6

In our

case this leads to a matrix of distances where each element is the inverse of the distance

between the two regions, expressed in Km, and subsequently normalized in order to obtain

a condition according to which the sum of each row equals one; a square matrix is obtained

(20920) where each element is:

wij ¼ 1 � dij

P

j

1 � dij

for i 6¼ j and wij ¼ 0 for i ¼ j

where dij is the geographical distance between two generic regions i and j measured in Km.

In particular, we calculate dij as the distance in Km between the main administrative town

of one region, and that of another region. 7

5 We are interested in the regional distribution of the incidence of civilian disability pensions, not in the

expenses for it. But the spatial link among regions about public expenditures is likely to exist among regions about the incidence of civilian disability pensions. 6

‘‘Everything is correlated, but nearer things are more correlated than things further apart’’ (Tobler 1970). 7

In ‘‘Appendix’’ 1 we show the contiguity matrix used in the econometric estimates.

556 M. Agovino, G. Parodi

123

3 Spatial Model Specification

In this section we refer to the SDM (for details see LeSage 2008; Elhorst 2010a, b, c).

These models fit well our goal, that is to verify if human development and experimental

variables explain civilian disability pensions, considering not only the effects of the local

explanatory variables on civilian disability pensions, but also the effects of the explanatory

variables in contiguous locations: in fact we want to investigate possible spatial spillovers

among regions (Elhorst 2010c; Manski 1993).

We proceed, in the empirical analysis, considering first panel models without spatial

effects:

yjt ¼ a þ xjtb þ lj þ kt þ ejt ð1Þ

where yjt is the dependent variable for the cross-sectional unit i at time t (j = 1,…,20; t = 2002–2008). xjt is a vector of exogenous variables and b is an unknown vector of fixed parameters. li

8 represents a specific regional effect, kt

9 represents a specific temporal

effect and eit is the stochastic error term. This equation is estimated by OLS. In the panel analysis we distinguish between fixed effects (FE) and random effects (RE). In

particular, in a panel analysis the error can be decomposed as: ejt = li ? kt ? tjt, where li and kt represents a specific temporal effect and tjt is the stochastic error term. In the panel with RE, these three variables are independent and identically distributed random noise, assumed

to be uncorrelated with the explanatory variables included in the model. In the panel with FE,

on the contrary, is not a random variable but a parameter to be estimated and it is specific to

the Region; it captures a structural aspect of the Region that differentiates it from other

Regions. Also is a parameter that captures annual changes that are common to all Regions.

The choice between the FE or RE models is not simple, and can be solved with the

Hausman test that allows a comparison between the results of alternative estimators. In

particular, under the null hypothesis, the estimates are statistically similar and, therefore,

we choose the RE model; vice versa under the alternative, we will choose the FE model

because it is efficient.

In addition, we verify via Lagrange Multiplier (LM) tests whether a Spatial Lag

Model 10

is more appropriate:

yjt ¼ d XN

i¼1 wijyit þ xjtb þ lj þ kt þ ejt ð2Þ

The variable P

i=1 N

wijyit is a measure of the interaction effect of the dependent variable

yjt with the spatially lagged dependent variables yit of neighbouring areas, where wij is an

element of contiguity matrix W (20 9 20); in this work we use a matrix of inverse

8 The region-specific variable, time-invariant and activated by regional dummy, captures how each region

deviates from the average structural relationship common to all regions (the regional fixed effects). 9

The time-specific variable, activated by time dummies, is useful to clear the structural relationship, which is common to all regions, from cyclical variations that are also common to all regions. 10

The Lagrange Multiplier (LM) tests check for a spatially lagged dependent variable and for spatial error autocorrelation; the robust LM tests check for the existence of one type of spatial dependence conditional on the other. A mathematical derivation of these tests for a spatial panel data model with spatial fixed effects can be found in Debarsy and Ertur (2010). These tests are based on the residuals of the non-spatial model with spatial fixed effects and follow a Chi squared distribution with one degree of freedom. If a non-spatial model is estimated without any fixed effects or a non-spatial model with both spatial and time-period fixed effects, the residuals of these models can be used instead (Elhorst 2010c).

A Spatial Panel Perspective 557

123

distances, expressed in kilometers, between one region and another. This choice of weights

allows us to formalize the hypothesis that the relationship among individual areas tend to

decrease in strength as distances between these areas increase. The spatial weights matrix

is row standardized so that neighboring variables are weighted averages of the values in

neighboring regions (Anselin 1988).

Alternatively, the Spatial Error Model is:

yjt ¼ xjtb þ li þ kt þ /jt

/jt ¼ q XN

i¼1 wij/it þ eit

ð3Þ

where q is the spatial autocorrelation coefficient. Finally, we consider the SDM. The SDM extends the spatial lag model with spatially

lagged independent variables (Elhorst 2010a, b).

yjt ¼ d XN

i¼1 wijyit þ xjtb þ

XN

i¼1 wijxjthþlj þ kt þ ejt ð4Þ

where h is a vector of parameters. For this model we test the following two assumptions: H0 :h = 0 and H0 :h ? db = 0 (respectively, Wald test spatial lag and Wald test spatial error).

11

If both hypotheses are rejected, then the SDM best describes the data. Conversely, if the

first hypothesis cannot be rejected, then the spatial lag model best describes the data;

similarly, if the second hypothesis cannot be rejected, the spatial error model best describes

the data (Elhorst 2010c).

LeSage and Pace (2009) advocate to use the SDM model as the model to test for spatial

interaction effects for two main reasons: (1) if unobserved or unknown but relevant variables

following a first-order spatial autoregressive process are omitted in the model, and these

variables happen to be correlated with independent variables not omitted from the model, the

SDM will produce unbiased coefficient estimates, but a spatial lag model will not; (2) even if

the true data-generating process is the spatial error model, the SDM will still produce

unbiased coefficient estimates. In particular, spatial dependence in the error term modeled in

the spatial error model is usually referred to as nuisance dependence (Anselin 2003). The

spatial error model usually loses its popularity given its lack of interpretation of spatial

dependence and, more importantly, its susceptibility to omitted variables (Brown et al. 2009).

Equation (4) can be estimated with the maximum likelihood estimation techniques,

controlling for the endogeneity problem due to the spatial lag of the dependent variable.

Detailed derivations of the log-likelihood function of Eq. (4) can be found at Elhorst and

Fréret (2009).

4 Data Used

In Italy, there are three ways in which the government financially supports people with

disability, generically referred to as disability pensions. Invalidity pensions are paid to

people with a reduced ability to work, provided that they have reached a certain age and

11 Both tests follow a Chi-squared distribution with K degrees of freedom. For further clarifications on the

building of Wald tests see Elhorst (2010c).

558 M. Agovino, G. Parodi

123

that they have made a certain number of national insurance contributions over the years.

Indemnity pensions are paid for accidents at work or for professionally related diseases.

Civilian disability pensions are not connected with national insurance contributions; they

are paid to disabled people on the basis of their physical characteristics (e.g., people

affected by blindness, deafness, or other types of impairments). These pensions are also

paid to people with no income or insufficient income after the age of 65 (Ministero del

Lavoro e delle Politiche Sociali 2006, 2008).

In this paper, we focus on civilian disability pensions, and therefore we consider all the

age groups, not only people in working age. In order to eliminate the demographic effect,

we analyze as dependent variable the Incidence of Civilian Disability Pensions (ICDP), i.e.

the ratio between the number of those receiving a civilian disability pension and the total of

the resident population (Agovino and Parodi 2012). Data on civilian disability pensions

come from INPS (Istituto Nazionale della Previdenza Sociale); data on the total population

resident in regions come from ISTAT (Istituto Nazionale di Statistica).

The analysis focuses on the Italian regions, which correspond to the EU NUTS-2, and it

covers the period 2002–2008.

For the purpose of conveying an impression on the temporal and spatial persistence of

ICDP we show the maps of the quartiles of the ICDP in Italian regions in the two extreme

years considered (Fig. 1)

The quartile maps indicate spatial and temporal persistence of the ICDP; in particular,

we observe that the ICDP is persistently high especially in the South and Center of Italy,

while it is persistently low in the North of Italy.

The spatial–temporal persistence emerging in the analysis of quartiles is taken care of in

the empirical analysis by including the spatial lag of the dependent variable.

Let us now illustrate in detail the variable used, and their source.

All regressors come from ISTAT. We consider among the regressors the three

dimensions of the HDI, and also some environmental and some demographic variables, as

described hereafter.

The three dimensions of HDI (McGillivray 1991; McGillivray and White 1993; Srin-

ivasan 1994) are:

• A long and healthy life, measured by expected life at birth (variable LIFE). The literature agrees on explaining an increase into expected life at birth in terms of an

improved standard of living, of more and improved medical care, and of preventive

actions. We expect therefore an inverse relationship between ICDP, and the variable

LIFE;

• Education, measured by the rate of adult literacy, and by the educational rate at the level of primary, secondary and tertiary education

12 (variable EDUCATION). We

expect a negative relationship between ICDP, and the variable EDUCATION both as

education is likely to reduce social discrimination against disability, and to generate

self confidence in disabled people (Harmoon et al. 2003; Hanushek and Wößmann

2007);

• A reasonable standard of living, measured by available income per capita (variable INCOME), taking into account Stiglitz et al. (2009) recommendations to consider

available GNP per capita in order to measure people’s welfare. We expect a negative

12 Following the literature, we only concentrate on secondary and tertiary education, as literacy and primary

education do not seem variable applicable to developed economies. Also following the literature we attribute a higher weight, equal to 2/3, to tertiary education, and a lower weight, i.e. 1/3, to secondary education (Marchante et al. 2006).

A Spatial Panel Perspective 559

123

relationship between ICDP, and the variable INCOME, on the assumption that a more

comfortable standard of living reduces ill health, and therefore disability pensions.

• We also consider other regressors which we believe could be relevant in determining ICDP, i.e. PUBLIC HEALTH EXPENDITURE PER CAPITA (PHE) which measures

whatever is spent by the government for health services, including direct health

services, administrative costs, interest, taxes, insurance premium and various contri-

butions. We expect a negative relationship between ICDP and the variable PHE.

We also consider some environmental variables:

• An index of landscape amenity, i.e. square meters of public green (variable GREEN), and an index of criminality. The literature agrees on the fact that the environment can

play an autonomous role on health (with specific reference to various forms of pollution

see for instance (Crombie et al. 1989; Guest et al. 1998; Lynch et al. 1998; Macintyre

et al. 1993). Because available public green is expected to be positively associated with

health, we expect a negative relationship between ICDP and the variable GREEN.

Also, the literature agrees on the negative effects of criminality on health (Macintyre

et al. 1993; Sooman and Macyntre 1995). 13

Here we use the index of widespread

criminality (variable CRIME), and we expect a positive relationship between ICDP and

the variable CRIME.

Finally, we consider some demographic variables:

• The percentage of population over 55 (AGE 55 ?), as disability appears to be correlated with old age (Disney and Webb 1991; McVicar 2006; Agovino and Parodi 2012).

• The internal rate of migration (MIGRATION), defined as the ratio between the internal migration balance in a given year and the level of average resident population in the

same year, multiplied by 1000. We expect a positive relationship between ICDP and

MIGRATION, as an increase in internal migration flows could jeopardize the

sustainability of regional pension schemes (Bonasia and De Siano 2012).

The descriptive statistics of all variables included in this analysis are presented in

Table 1.

Fig. 1 Incidence of civilian disability pensions (ICDP) 2002 and 2008

13 In some disadvantaged areas of the USA the impact of crime on health is very strong, and considered one

of the main causes of ill health (Minkler 1992).

560 M. Agovino, G. Parodi

123

The values of the standard deviation, and the range of the values of the variables, seem

to guarantee sufficient variability for reliable estimations.

5 Empirical Results

In this section, we report the empirical regression results using a panel of 20 regions over

2002–2008. Since the model is estimated using log–log form, the coefficients can be

interpreted as elasticities. First we estimate the model without spatial effects and we

statistically test for the relevance of spatial interaction in determining ICDP. Subsequently,

we estimate a SDM which takes into account spatial effects not only in the dependent

variable, but also in the covariates. Finally, in paragraph 5.2, we further proceed to perform

two additional analysis. First, we check whether our estimates suffer from potential end-

ogeneity bias. Second, we estimate a dynamic panel model.

5.1 Spatial Regression Results

Before implementing the regression analysis we verify that there are no problems of

multicollinearity between the regressors. The collinearity diagnostics, not shown here for

brevity, indicate that, for VIF and tolerance, all variables do not present problems of

multicollinearity; in particular, no variable shows a VIF higher than 10 and a value for

tolerance close to zero. The eingenvalue show values distant from zero, indicating the

absence of multicollinearity for all variables. Finally, the conditional index, with values

less than 30, reveals the absence of multicollinearity for all regressors.

In the first column in Table 2, which excludes spatial effects, the Hausman test by

rejecting the null hypothesis makes us choose a model with FE. In addition, the Likeli-

hood-Ratio (LR) tests, by rejecting the null hypothesis emphasize the importance both of

regional and temporal fixed effect. The LM tests, in both the robust and the not robust

version, reject the null hypothesis; this allows us to conclude that it is appropriate to

estimate a spatial lag or spatial error model rather than a non-spatial model.

We now comment on the regressors (Table 2, column 1):

• The variable INCOME is not significant. This suggests that the number of indigent people over 65 receiving civilian disability pensions solely as income support is small,

therefore the dependent variable ICDP well mirrors the phenomenon of disability;

Table 1 Summary statistics of 20 Italian region over 2002–2008

Variables Obs. Mean SD Min Max

ICDP 140 3.330 1.463 0.703 6.425

INCOME 140 16,581.76 3,268.953 11,045 22,115

EDUCATION 140 36.992 2.659 28.113 42.239

LIFE 140 80.887 0.783 78.56 82.465

CRIME 140 52.042 8.872 25.1 71

GREEN 140 144.819 174.620 18.3 707.7

PHE 140 1,625.307 195.556 1,247.6 2,134

AGE 55? 140 32.266 3.500 24.450 40.395

MIGRATION 140 0.706 2.606 -4.8 6.6

A Spatial Panel Perspective 561

123

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562 M. Agovino, G. Parodi

123

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A Spatial Panel Perspective 563

123

• The variable EDUCATION has the expected negative sign, and is significant; • The variable LIFE has the expected negative sign, and is significant14; • The variable GREEN has the expected negative sign, and is significant; • The variable CRIME is not significant. • The variable PHE is not significant. • The variable AGE 55 ? has the expected positive sign, and is significant. • The variable MIGRATION has the expected positive sign, but it is weakly significant

(only at 10 %).

• The variable SOUTH DUMMY15 which controls for regions in Southern Italy, is not significant. Actually, we control for FE, therefore regional heterogeneity is captured by

regional dummies.

• Time dummies are all positive and significant. It is interesting to remark that their weight grows with time, reaching the climax in 2008, the year of the world economic

crisis. This result shows that ICDP has grown with time, and in particular with the

economic crisis. This suggests a possibly biased use of civilian invalidity pensions as

social shock absorbers in periods of increasing poverty and unemployment.

Given the results of the LM test, we proceed to estimate the SDM; because of the

limited dimension of our database (140 = N9T) we omit the regressors INCOME,

CRIME, PHE, which have turned out to be insignificant in the previous estimate. Table 2

(columns II and III) shows the results of SDM regional and temporal fixed effect. The

Hausman test rejects the null hypothesis and leads us to prefer the model with FE to the

one with RE; consequently, we focus on the results of the model with regional and

temporal FE (column II). Both the Wald test spatial lag and the Wald test spatial error

reject the null hypothesis, confirming that the model that best fits the data is the SDM, so

the estimated elasticities with non-spatial models are biased (Elhorst 2010c).

The Likelihood-Ratio (LR) tests reject the null hypothesis, and emphasize the relevance

both of regional and temporal FE. In addition, the Hausman test rejects the null hypothesis,

so we choose the SDM with FE.

The coefficient of the spatially lagged dependent variable is -0.992 and significant at

1 %. This reveals some interdependence in the ICDP policies of regions, characterized by

negative externalities, as an increase in ICDP in neighboring regions corresponds to a

reduction of ICDP in a given region.

With respect to other regressors, we note that:

EDUCATION and LIFE expectancy at birth have an effect on ICDP only at local level,

as (W*EDUCATION) and life expectancy (W*LIFE) are not significant.

The demographic variable (W*AGE 55 ?), and the environmental variable

(W*GREEN) are the only ones which produce significant spillovers. In particular, we

observe that an increase in the elderly population in neighboring regions has the effect of

determining an increase of ICDP on a given region. A catching up behavior appears to

emerge among policies of different regions in this respect, as if each region wanted to be as

generous as neighboring regions in terms of civilian disability pensions granted to the

elderly.

14 In paragraph 5.2 we test for possible endogeneity between this variable and the dependent variable.

15 We list Southern Italy regions: Abruzzo, Basilicata, Calabria, Campania, Molise, Puglia, Sicilia and

Sardegna. Other regions belong to the North of Italy (Emilia-Romagna, Friuli-Venezia Giulia, Liguria, Lombardia, Piemonte, Trentino-Alto Adige, Valle d’Aosta e Veneto) and to the Centre of Italy (Lazio, Marche, Toscana e Umbria).

564 M. Agovino, G. Parodi

123

In addition, we find that the improvement in the environment of neighboring regions

reduces ICDP not only in that region, but in neighboring regions as well.

The variable MIGRATION has no effect on ICDP, either at local or at spatial spillover

level. This result is probably explained in terms of the short length of the analysed spell,

too recent to catch the effects of migration processes, still present but much reduced with

respect to the ones observed in previous periods. 16

Probably the analysis over a longer

period would provide different results (see Bonasia and De Siano (2012) who analyze

panel data over the period 1979–2008).

5.2 Endogeneity Problems: Verifying Causality Relationship

As we mentioned in the introduction it is possible that life expectancy causes civilian

disability pensions. In particular, the estimate of the relationship between ICDP and life

expectancy (LIFE) may be affected by endogeneity problems. It is not clear whether LIFE

drives ICDP or vice versa. In fact, both hypotheses could be plausible:

• life expectancy as a proxy for the improvement of lifestyle due to advances in the medical field, to the development of health services, and to preventive actions, may be

a fundamental cause to explain disability; consequently, a higher (lower) lifestyle leads

to a reduction (increase) of disability and as a consequence of ICDP (LIFE ? ICDP); • life expectancy, however, can depend on disability: the more widespread is the problem

of disability the smaller life expectancy becomes (ICDP ? LIFE).17

In order to check the true causality of this relationship we implement the Granger

causality approach (Granger 1969). In particular, the Granger test verifies the power of a

variable to predict another one (Hamilton 1995), i.e. to check whether y is Granger caused

by x. In other words, we regress y on its own lagged values and on those of x and test

whether the set of coefficients associated with x are statistically different from zero (cf.

‘‘Appendix’’ 3).

In summary, we find an absence of simultaneity due to a single causal relationship; this

confirm the propriety of the SDM model above applied; in fact, if there were simultaneity

problems we should have used the instrumental variables estimator (see the results of the

Granger test in ‘‘Appendix’’ 3). as a consequence, we can exclude an endogeneity problem.

To address the second issue- to verify inertial effect of ICDP (i.e. persistence over

time)—we specify a dynamic spatial panel model to test whether a (one period) lagged

dependent variable ought to be included. We delay the variable ICDP for one period only

because of the small size of our data set.

The estimate of this model has several problems. First, using panel data, ordinary least

square (OLS) coefficients are biased when: unobservable region-specific effects (li) are

16 The choice to use a contemporary MIGRATION variable was determined by the difficulty of identifying

the correct temporal lags which may have provided significant estimates in the econometric analysis. We could have proceeded by trial and error, but this procedure would have been methodologically rough. More properly, we could have used a P-VAR (Vector Autoregressive model for Panel data), which, through the impulse response analysis, would have allowed us to identify the years in which the impact of the MIGRATION variable on ICDP, the dependent variable, would have been statistically significant. After that we would have run a regression analysis with the appropriate lags for MIGRATION. This exercise would have complicated too much the analysis in this paper, but we may consider it in future work. 17

The problem with this hypothesis is to link disability only to the concept of ‘‘disability at birth’’, omitting the presence and the action of environmental factors; consequently, it would exclude the causes of disability arising during the lifetime.

A Spatial Panel Perspective 565

123

statistically significant; the regressors and these effects are correlated. In addition, as regards the

lagged dependent variable, yj(t-1), OLS return inconsistent estimates as yj(t-1) and li are nec- essarily correlated, even if the idiosyncratic component of the error term is serially uncorre-

lated. A solution to these problems is to eliminate the term li by taking first differences in the equation that we estimate. OLS still does not consistently estimate the parameters of interest

because first differencing introduces correlation between the lagged dependent variable and

differenced error terms: yj(t-1)and eit are correlated through the terms yj(t-1) and eit-1. One way to overcome these problems is the use of an instrumental variables procedure

applied to a dynamic model of panel data. In particular, we refer to a GMM estimator that

uses the dynamic properties of the data to generate proper instrumental variables (Arellano

and Bond 1991; Arellano and Bover 1995). 18

The GMM estimator allows to control for

weak endogeneity by using the instrumental variables, which consist of appropriate lagged

values of the explanatory variables. To deal with the fact that measurement errors are likely

to be determined not only by random errors but by specific and persistent characteristics of

each region, we use the GMM-system (Arellano and Bover 1995; Blundell and Bond 1998)

that combines into a single system the regression equation in both differences and level.

The GMM-system estimator allows to control for unobserved region-specific effects that

are potentially correlated with the explanatory variables (Wooldridge 2001).

Since the consistency of the parameters obtained from the GMM estimator depends

crucially on the validity of the instruments, we consider two specification tests: the Sargan test

of overidentifying restrictions, which tests the null hypothesis of overall validity of the

instruments used; and the test for serial correlation of the error term, which tests the null

hypothesis that the differenced error term is first and second order serially correlated. Failure

to reject the null hypothesis of no second-order serial correlation implies that the original

error term is serially uncorrelated and the moment conditions are correctly specified.

Table 3 shows the results of the analysis. We exclude from the analysis the variables

previously excluded as not significant, and also the variable MIGRATION because not

significant in the SDM analysis.

We find that the signs and significance of the parameters are identical to the ones found

in the previous analysis. The impact of EDUCATION and of W*GREEN is stable;

GREEN, W*AGE 55 ? , W*DEPENDENT VARIABLE have a smaller impact in

determining ICDP; on the contrary, LIFE has a greater impact.

The temporal delay of the dependent variable (ICDP(t-1)) is significant and positive; this

suggests temporal persistence in the granting of civilian invalidity pensions.

The Sargan test, which allows us to verify the validity of the instruments, does not reject

the null hypothesis and this confirms the validity of instruments used. In addition, there is

evidence of serial correlation of the first order (we reject the null hypothesis); whereas,

there is no evidence of the presence of second-order serial correlation (the null hypothesis

is not rejected). 19

Finally, the goodness of the results is confirmed by the outcome of the spatial tests on

the residuals (GLOBAL Moran MI, Global Geary GC, Global Getis-Ords GO). These tests

18 We use a set of instrument variable L(X, WX, W

2 X,), that is, regressing WICDP on L(X, WX, W

2 X,) and

ICDP(t-1) on L(X, WX, W 2 X,); where, X are the regressors (except LIFE) with W

2 we indicate the second-

order contiguity matrix (Anselin 1988). In the case of temporally lagged dependent variable, ICDP(t-1), we use as additional instrument the temporal lag of second order of dependent variable (ICDP(t-2)). Even though the Granger test has verified the non endogeneity of the variable LIFE, we instrument this variable with the same instruments used for WICDP and ICDP(t-1) (see Hsiao 2003). 19

The consistency of the GMM estimator requires that there is no serial correlation of the second order in the differenced error term.

566 M. Agovino, G. Parodi

123

do not reject the null hypothesis and confirm therefore the absence of spatial autocorre-

lation in the error term.

6 Concluding Remarks

Our analysis provides some new insight into factors affecting the distribution of the incidence

of disability pensions in Italy over the period considered. First of all, human development and

environmental factors rather than income appear to be relevant in explaining ICDP in Italy.

Second, ICDP seems to be a rather local affair, as only few of the explanatory variables

generate spillovers in neighboring regions. As a consequence, policies geared at reducing

ICDP ought to aim at the general improvement of health, education and the environment,

which affect the demand side of civilian disability pensions,

Table 3 Results

Variables GMM-sys

Coeff. t value Sign.

EDUCATION -0.117 -4.400 ***

LIFE -0.748 -3.920 ***

GREEN -0.025 2.740 **

AGE 55? 0.026 1.090

W*EDUCATION 0.042 1.230

W*LIFE -0.016 -1.380

W*GREEN -0.037 -3.890 **

W*AGE 55? 0.886 2.071 **

W*DEPENDENT VARIABLE -0.868 -3.000 **

ICDP (t-1) 0.275 4.020 ***

2003 0.1671977 0.98

2004 2.162647 5.5 ***

2005 2.857231 6.03 ***

2006 2.997727 5.98 ***

2007 3.189959 5.3 ***

2008 3.056513 7.4 ***

constant 25.07045 3.38 **

REGIONAL FIXED EFFECTS Yes

Sargan overidentification test 32.01

AR(1): serial correlation of first order 2.43**

AR(2): serial correlation of second order 1.21

H0: Error has NO spatial autocorrelation

GLOBAL Moran MI -0.052

Global Geary GC 1.0205

Global Getis-Ords GO 0.0024

# observations 100

Standard errors are corrected for heteroskedasticity

***, ** and * indicate coefficients that are significant at 1, 5 and 10 %, respectively

A Spatial Panel Perspective 567

123

We first summarize our findings at the level of individual regions. Of the factors strictly

connected with human development, according to the definition of the HDI, two, i.e. LIFE and

EDUCATION, appear to be significant and with the expected sign, i.e. a higher life expectancy

and increased education decrease the incidence of civilian disability pensions. These results

point in the direction of demand factors, rather than supply factors, affecting the incidence of

civilian disability pensions. The policy implications of these findings are obvious: general

policies on education and health appear to affect the incidence of civilian disability pensions.

Increasing the attendance of tertiary education, and the general improvement of a country

health, as measured by life expectancy, are both important to reduce the demand for civilian

disability pensions, and therefore the incidence of them. This result is not in contrast with the

non significance of the parameter associated with public health expenditure per capita. (PHE);

the non significance of this variable suggests considerations of a different nature: an increase in

public spending on health may be associated with waste, and not necessarily with an increased

quality and quantity of the health services available for the individual.

The third factor associated with the HDI, i.e. available income per capita, does not

appear to be associated with the incidence of civilian disability pensions. This result allows

us to state that the dependent variable approximates well the disability phenomenon. In

particular, since disability is concentrated mainly among the elderly (65 and over), the

absence of links with income indicates that most elderly recipients of civilian disability

pensions receive them as proper disability pensions, and not as income supports. Having

considered all disabled people reduces the distortion introduced by people of working age.

In particular, Agovino and Parodi (2012) observe that in Italy for people aged 15–64,

civilian disability pensions are used as an antipoverty instrument.

We now turn to the spatial effects: two explanatory factors generate spillover effects

among neighboring regions, i.e. environmental and demographic variables. The strictly

environmental variable, i.e. availability of public green, appears to be significant, and with

the predicted sign. Furthermore, the spillover effect of this variable on ICDP is larger

among neighboring regions than at local level. The effect of the environmental variable on

reducing ICDP suggests strong policy recommendations: investing in the environment

generates a reduction in CDP, and therefore in ICDP, both at local level, and at the level of

spillovers among neighboring regions. Recommendations on the coordination of envi-

ronmental policies among regions follow this finding. However, further research should

assess whether the strictly environmental variable is itself a proxy for a particularly open

attitude towards the general quality of life.

The demographic variable is significant both at local level, and at the level of spillover

effects: the increase in elderly people in one region (AGE 55 ?) creates a positive

externality on the ICDP in neighboring regions; this would suggest that regions want to

catch up with each other’s generosity in granting ICDP to elderly people, and therefore

probably reinterpret National rules in a lax way, with possible medium-long run problems

in regional budgets. Policy recommendations emerge, to develop more varied and targeted

instruments to deal with the needs of an increasingly ageing population.

Acknowledgments This paper is part of the 2009 PRIN project ‘‘Measuring human development and capabilities in Italy: methodological and empirical issues’’ financed by the Italian Ministry of Education, University and Research.

Appendix 1

See Table 4.

568 M. Agovino, G. Parodi

123

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0 6

1 0

B a si

li c a ta

(P o

te n

z a )

1 ,0

3 0

1 ,1

0 0

9 3

0 9

4 5

7 5

5 8

9 5

8 6

0 7

3 5

6 3

0 5

2 5

C a la

b ri

a (C

a ta

n z a ro

) 1

,2 7 5

1 ,3

4 5

1 ,1

7 5

1 ,1

9 0

1 ,1

3 0

1 ,2

7 0

1 ,1

0 5

9 8

0 8

8 0

7 7

0

S ic

il ia

(P a le

rm o

) 1

,6 0 0

1 ,6

7 5

1 ,5

0 5

1 ,5

2 0

1 ,4

6 0

1 ,6

0 0

1 ,4

3 0

1 ,3

1 0

1 ,2

0 5

1 ,1

0 0

S a rd

e g n a

(C a g li

a ri

) 8 5 5

9 3 0

8 0 5

8 3 0

7 7 0

9 1 0

6 8 5

6 2 0

5 1 5

4 5 0

A Spatial Panel Perspective 569

123

T a

b le

4 c o

n ti

n u e d

d ij

M a rc

h e

(A n

c o

n a )

L a z io

(R o

m a )

A b

ru z z o

(L ’a

q u

il a )

M o

li se

(C a m

p o

b a ss

o )

C a m

p a n

ia (N

a p o

li )

P u

g li

a (B

a ri

) B

a si

li c a ta

(P o

te n

z a )

C a la

b ri

a (C

a ta

n z a ro

) S

ic il

ia (P

a le

rm o

) S

a rd

e g

n a

(C a g

li a ri

)

P ie

m o n

te (T

o ri

n o

) 5

4 5

6 7

5 2

7 5

8 6

0 8

8 5

1 ,0

0 0

1 ,0

3 0

1 ,2

7 5

1 ,6

0 0

8 5

5

V a ll

e D

’a o st

a (A

o st

a )

6 1

0 7

4 5

7 9

5 9

2 5

9 5

5 1

,0 6 5

1 ,1

0 0

1 ,3

4 5

1 ,6

7 5

9 3

0

L o

m b

a rd

ia (M

il a n

o )

4 2

5 5

7 5

6 1

0 7

4 0

7 8

5 8

8 0

9 3

0 1

,1 7 5

1 ,5

0 5

8 0

5

T re

n ti

n o

A lt

o A

d ig

e (T

re n

to )

4 4

0 5

9 0

3 0

5 7

5 5

7 8

5 8

9 5

9 4

5 1

,1 9 0

1 ,5

2 0

8 3

0

V e n

e to

(V e n e z ia

) 3

0 5

5 3

0 3

3 0

6 2

0 7

4 0

7 6

0 7

5 5

1 ,1

3 0

1 ,4

6 0

7 7

0

F ri

u li

V e n

e z ia

G iu

li a

(T ri

e st

e )

4 4

5 6

7 0

4 7

0 7

6 0

8 8

0 9

0 0

8 9

5 1

,2 7 0

1 ,6

0 0

9 1

0

L ig

u ri

a (G

e n o

v a )

5 1

0 5

0 5

6 0

0 7

2 0

7 1

5 9

4 5

8 6

0 1

,1 0 5

1 ,4

3 0

6 8

5

E m

il ia

R o m

a g

n a

(B o

lo g n

a )

2 1

5 3

8 0

4 0

0 5

3 0

5 9

0 6

7 0

7 3

5 9

8 0

1 ,3

1 0

6 2

0

T o sc

a n a

(F ir

e n z e )

3 2 0

2 8 0

3 7 5

4 9 0

4 9 0

7 2 0

6 3 0

8 8 0

1 ,2

0 5

5 1 5

U m

b ri

a (P

e ru

g ia

) 1

6 5

1 7

0 1

7 5

3 8

5 3

8 0

6 1

0 5

2 5

7 7

0 1

,1 0 0

4 5

0

M a rc

h e

(A n

c o

n a )

0 2

8 5

1 9

5 3

2 5

3 9

0 4

6 5

4 6

0 7

8 0

1 ,1

1 0

6 0

5

L a z io

(R o

m a )

2 8

5 0

4 2

5 2

2 5

2 2

0 4

5 0

3 6

0 6

1 0

9 3

5 3

5 0

A b

ru z z o

(L ’a

q u

il a )

1 9

5 1

1 0

0 1

9 0

2 4

5 4

0 0

3 9

0 6

4 0

9 6

5 4

6 5

M o

li se

(C a m

p o

b a ss

o )

3 2

5 2

2 5

1 9

0 0

1 3

5 2

2 0

2 0

0 4

9 5

8 2

5 5

6 5

C a m

p a n ia

(N a p o li

) 3 9 0

2 2 0

2 4 5

1 3 5

0 2 6 0

1 5 5

4 0 5

7 3 5

5 6 0

P u

g li

a (B

a ri

) 4

6 5

4 5

0 4

0 0

2 2

0 2

6 0

0 1

4 5

3 6

5 6

9 0

7 9

0

B a si

li c a ta

(P o

te n

z a )

4 6

0 3

6 0

7 7

5 2

0 0

1 5

5 1

4 5

0 3

5 0

6 8

0 7

0 5

C a la

b ri

a (C

a ta

n z a ro

) 7

8 0

6 1

0 6

4 0

4 9

5 4

0 5

3 6

5 3

5 0

0 3

9 5

9 5

0

S ic

il ia

(P a le

rm o

) 1

,1 1 0

9 3

5 9

6 5

8 2

5 7

3 5

6 9

0 6

8 0

3 9

5 0

1 ,2

8 0

570 M. Agovino, G. Parodi

123

T a

b le

4 c o

n ti

n u e d

d ij

M a rc

h e

(A n

c o

n a )

L a z io

(R o

m a )

A b

ru z z o

(L ’a

q u

il a )

M o

li se

(C a m

p o

b a ss

o )

C a m

p a n

ia (N

a p o

li )

P u

g li

a (B

a ri

) B

a si

li c a ta

(P o

te n

z a )

C a la

b ri

a (C

a ta

n z a ro

) S

ic il

ia (P

a le

rm o

) S

a rd

e g

n a

(C a g

li a ri

)

S a rd

e g n a

(C a g

li a ri

) 6

0 5

3 5

0 4

6 5

5 6

5 5

6 0

7 9

0 7

0 5

9 5

0 1

,2 8 0

0

In th

e ro

u n

d p

a re

n th

e se

s w

e in

d ic

a te

th e

m a in

a d

m in

is tr

a ti

v e

to w

n o

f th

e re

g io

n ,

w it

h re

sp e c t

to w

h ic

h th

e d

is ta

n c e

e x p

re ss

e d

in K

m h

a s

b e e n

c a lc

u la

te d

* T

h e

d is

ta n

c e s

in K

m b

e tw

e e n

th e

m a in

a d

m in

is tr

a ti

v e

to w

n o

f o

n e

re g io

n a n

d th

a t

o f

a n

o th

e r

re g io

n h

a v

e b

e e n

ro u

n d e d

u p

to th

e c lo

se st

in te

g e r

fo r

re a so

n s

o f

sp a c e

A Spatial Panel Perspective 571

123

Appendix 2

HDI: Construction and Some Results

In order to calculate the HDI we proceed in two steps (Saisana and Tarantola 2002;

Freudenberg 2003; Jacobs et al. 2004):

• in the first step, we normalize the variables which make up each indicator; in particolar, for each variable we calculate the ratio between the observed value of each variable and

its minimum with respect to its range of variation, i.e. difference between the maximum

and minimum, of each variable (Boyle and McCarthy 1997; Mazumdar 1999;

Marchante et al. 2006; Marselli and Vannini 2006):

Zij ¼ Xij � minXi

maxXi � minXi where X indicates the original values observed for each variable, Z are the normalized

variables, j and i indicate respectively the regions and years for which we normalize; in this

way the variables are transformed into an indicator ranging between 0 and 1.

• In the second step, we calculate the HDI by combining the three normalized indexes above mentioned, after weighing each of them by 1/3, and aggregating by the

geometric mean. 20

(Klugman et al. 2011):

HDIij ¼ I 1=3 lifeij � I1=3educationij � I

1=3 incomeij

Analysing the correlations among the three variables, INCOME, EDUCATION, LIFE and

the HDI a high correlation emerges (higher than 0.70) with available income per capita

(Table 5). This indicates problems of redundancy (McGillivray 1991; McGillivray and

White 1993), so that HDI will appear to be led mainly by the variable income. In order to

overcome this problem, in the regression analysis we consider separately the three com-

ponents of HDI, so catching the impact of each of them on ICDP.

Table 5 Correlation matrix

* Significatività al 5 %

HDI INCOME EDUCATION LIFE

HDI 1

INCOME 0.8052* 1

EDUCATION 0.4186* 0.1662* 1

LIFE 0.4886* 0.4505* 0.4223* 1

20 Initially, HDI was calculated adopting the arithmetic mean of the three indicators. More recently, the

geometric mean has been adopted; this produces lower index values, with the largest changes occurring in countries with uneven development across dimensions. The geometric mean has only a moderate impact on HDI rankings. The HDI based on the geometric mean takes into account differences in achievement across dimensions. Poor performance in any dimension is now directly reflected in the HDI, which captures how good a country’s performance is across the three dimensions. That is to say, a low achievement in one dimension is not any more linearly compensated for by high achievement in another dimension. The geometric mean reduces the level of substitutability between dimensions and at the same time ensures that a 1 % decline in index of, say, life expectancy at birth has the same impact on the HDI as a 1 % decline in the education or income index. Thus, as a basis for comparisons of achievements, this method is also more respectful of the intrinsic differences across the dimensions than an arithmetic average.

572 M. Agovino, G. Parodi

123

T a

b le

6 G

ra n g

e r

C a u

sa li

ty T

e st

R e g re

ss io

n 1

C o e ff

. t

v a lu

e S

ig n .

R e g re

ss io

n 2

C o e ff

. t

v a lu

e S

ig n .

D e p e n d e n t

v a ri

a b le

: D

.C D

P D

e p e n d e n t

v a ri

a b le

: D

. L

IF E

D 1

.C D

P 0

.5 2

0 6

3 .6

2 *

* *

D 1

.C D

P -

0 .1

6 2

6 -

1 .0

2

D 2

.C D

P 0

.1 7

1 7

3 .9

5 *

* *

D 2

.C D

P 0

.1 0 7

9 1

.5 9

D 1

. L

IF E

- 0

.0 6 2

- 0

.5 4

D 1

. L

IF E

- 0

.5 4

6 5

- 3

.4 *

* *

D 2

. L

IF E

0 .2

8 1

7 3

.0 5

* *

* D

2 .

L IF

E 0

.1 8

2 .7

5 *

*

T e m

p o

ra l

d u

m m

ie s

Y e s

T e m

p o

ra l

d u

m m

ie s

y e s

G R

A N

G E

R T

E S

T 9 .5

5 * * *

G R

A N

G E

R T

E S

T 2 .5

4

H A

N S

E N

J S

T A

T IS

T IC

2 .5

3 2

H A

N S

E N

J S

T A

T IS

T IC

0 .3

0 8

W e

u se

, in

a ll

th e

e st

im a te

s, th

e la

g s

o f

th e

d e p e n d e n t

v a ri

a b le

a s

in st

ru m

e n ts

(H si

a o

2 0

0 3 ).

T h

e H

a n

se n

te st

, te

st o

f o

v e ri

d e n

ti fi

c a ti

o n

, d

o e s

n o

t re

je c t

th e

n u

ll h

y p

o th

e si

s in

a ll

th e

e st

im a te

s a n

d a ss

u re

u s

o n

th e

v a li

d it

y o

f th

e in

st ru

m e n

ts

W it

h D

.X =

X -

X (-

1 );

D 1

.X =

X (-

1 )

- X

(- 2

); D

2 .X

= X

(- 2

) -

X (-

3 );

w h

e re

X =

C D

P ,

L IF

E

* *

* ,

* *

, *

: 1

, 5

, 1

0 %

A Spatial Panel Perspective 573

123

Appendix 3

Granger Causality Test for Panel Data

The procedure used to test the causal relationship in a panel data set was proposed by

Holtz-Eakin et al. (1988). The Granger causality test for panel data is presented as follows:

yit ¼ a0 þ Xm

j¼1 ajyit�j þ

Xm

j¼1 djxit�j þ fi þ eit ðiÞ

where i = 1,…,N are the observation units and t = 1,…,m is the time index. The model in differences allows us to eliminate the FE (fi)

yit � yit�1 ¼ a0 þ Xm

j¼1 aj yit�j � yit�j�1 � �

þ Xm

j¼1 dj xit�j � xit�j�1 � �

þ eit � eit�1ð Þ ðiiÞ

This specification introduces a simultaneity problem because the error term is correlated

with yit - yit-j-1. In this case a consistent estimate can be obtained using the two-stage

instrumental variables method (2SLS).

In order to verify if x causes y it will be necessary to test the joint hypothesis

H0:d1 = d2 = _ = dm = 0. If the null hypothesis is rejected then x Granger causes y. Below we report the Granger test to verify the direction of causality, in the version for

panel data (Holtz-Eakin et al. 1988).

The Granger 21

test performed on ICDP and LIFE shows that LIFE Granger-causes

ICDP (regression 1, Table 6). In particular, we observe that the null hypothesis of the

Granger test which assumes that LIFE does not cause ICDP is rejected at 1 %.

Conversely, when we verify the opposite hypothesis which ICDP Granger-causes LIFE,

the Granger test does not reject the null hypothesis; consequently, it is clear that ICDP does

not cause LIFE (regression 2, Table 6).

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