social conformity and suicide
TRANSCRIPT
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The Journal of Socio-Economics 42 (2013) 67–78
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The Journal of Socio-Economics
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ocial conformity and suicide
nna Bussua, Claudio Detottob,∗, Valerio Sterzi c,d
Department of Political Science, Communication Sciences and Information Engineering, University of Sassari, ItalyDepartment of Economics and Business (DISEA) and CRENoS, University of Sassari, Via Torre Tonda 34, Sassari I-07100, ItalyGREThA, CNRS, UMR 5113 Université de Bordeaux, KITES, Bocconi University, ItalyDiSEA, University of Sassari, Italy
r t i c l e i n f o
rticle history:eceived 24 March 2012eceived in revised form 17 August 2012ccepted 6 November 2012
EL classification:2
1
a b s t r a c t
We study the relationship between suicide rates and socioeconomic factors by using a panel data atItalian province level in the time span 1996–2005. Our analysis focuses on the impact of social normson suicidal behaviors. In particular, beyond the usual social correlates of suicide rates, we propose anaggregate measure of social conformity which refers to the religious sphere as an area of conflict betweenindividual and social behaviors. GMM and dynamic spatial panel data approach are implemented tocontrol for serial and spatial autocorrelation.
The results confirm the primary role of family, alcohol consumption and population density in explain-
1
eywords:uicideamily
ing the suicide rates in Italy, while the economic variables, namely income per capita and economicgrowth, do not appear to have any effects.
© 2012 Elsevier Inc. All rights reserved.
onformityocial norms
. Introduction
More than one hundred years after his seminal work, Emileurkheim still provides the starting point of any sociological studyn suicide. According to Durkheim (1893, 1897), the frequency ofelf-killing in society depends on two factors: social integrationnd regulation. As a result, four types of suicide can be identi-eded: egoistic, anomic, altruistic and fatalistic suicide. When social
ntegration is weak, the number of “egoistic” suicides rises: as thentegration in the family or in the peer groups decreases, individ-als feel more isolated and more vulnerable to suicide, which isiewed as the extreme solution to better their condition. Secondly,anomic” suicides are determined by under-regulated communi-ies, which are endemic in modern society, where moral disordernd deregulation lead individuals to lose their role in society byroducing a lack of self-consciousness. Thirdly, to the extent that
ndividuals put the community well-being before their own util-ty, excessive social integration could lead to a rise in “altruistic”uicides. Finally, all types of society impose a social order to theirembers which create a brake to a broad spectrum of impulses,
nd could incentive “fatalist” suicidal behaviors among people whoave low expectations about the future.
∗ Corresponding author.E-mail address: [email protected] (C. Detotto).
053-5357/$ – see front matter © 2012 Elsevier Inc. All rights reserved.ttp://dx.doi.org/10.1016/j.socec.2012.11.013
Hence, according to the aforementioned theory, suicide is asocial rather than a psychic fact, and its causes should be soughtamong the characteristics of the society and its ability to stim-ulate social cohesion. Suicide is a collective phenomenon drivenby social issues not related to individual attitudes and elements.Furthermore, in Durkheim’s Theory of Anomie (1893), the nor-mative conflict between past and present plays the main role inexplaining suicidal behaviors. In other words, changes in regimedetermine the overlapping of old and new systems of social rules.Such anomic societies, poised between the old rules no longerapplicable and the new ones not yet (perceived as) binding, can-not provide a solid guide to the conducts of individuals (Durkheim,1897; Merton, 1938). From this point of view, it is not the rules perse that cause suicidal incidents but their changes over time. On thecontrary, the social disorganization theory (Kubrin and Weitzer,2003) points to the social disintegration caused by rapid urban-ization processes as the main factor in explaining suicide rates.Economic inequality, ethnic and cultural heterogeneity, high resi-dents’ mobility and family breakdown affect the efficacy of socialcontrol by the community. The driving factors of suicide are thusthe structural characteristics of society and not individual attitudesof the victims, which are only precipitating causes.
A similar point of view is found in Halbwachs (1930) who
observes and theorizes, on the one side, the prevalence of anomicsuicides in large urban areas due to the absence of social cohesion,and, on the other side, the high frequency of suicidal incidents inrural regions in response to the excessively binding social norms.
6 Socio
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depends both on the individual religious sentiment (individual reli-giousness) and on the social conformity. We use the frequencyof religious marriages (as a proportion of the total number of
8 A. Bussu et al. / The Journal of
As defined by Cialdini and Trost (1998, p. 152) social norms arerules and standards that are understood by members of a group,nd that guide and/or constrain social behavior without the forcef laws”. In this sense they are a collection of rules accepted by theajority, and changes in rules or deviation from the establishedodel create a conflict that leads to the marginalization of thoseho have exhibited deviating (Sherif, 1935). Informal sanctions are
n fact provided for those who fail to stick to the rules.In this sense, the causes of suicidal behaviors could be traced in
he absence of stable relationships between people, and the rigidnd compact social structure. A lack of individualization ensues,nd “for the individual to occupy so little place in collective lifee must be almost completely absorbed in the group and the
atter, accordingly, very highly integrated” (Durkheim, 1897, pp.20–221).
This paper contributes to the empirical literature by evaluat-ng the determinants of suicide rates in Italy at province level inhe time span 1996–2005, looking at both economic and socio-ogical aspects in line with Hamermesh and Soss (1974) approach.ue to its Christians roots, Italy is characterized by lower level of
uicide rates than non-Christian countries, like Japan for example,nd along with other Mediterranean countries, such as Spain andreece, presents the lowest suicide rates in Europe (for an inter-ational comparison see among others Andrès, 2005; Chen et al.,009; Noh, 2009). According to Pescosolido and Georgianna (1989),atholicism offers a high level of integration among individuals
acing personal crises, all other things being equal. Moreover inurope, during mediaeval and modern times, the common beliefhat suicide is a mortal sin was a powerful deterrent to commit-ing extreme gestures (Barbagli, 2010). In this sense, we speculaten the limited role of economic factors in a country with strongocial norms and religious ties. In fact, Italian society, historicallyamily-based and conservative, could generate social tensions and
arginalization that might lead to suicidal behaviors.The aim of the paper is to identify a specific type of social norm
hich refers to the religious behavior of the community and tovaluate its impact on suicide rates. In particular, we propose aew indicator of social conformity which encompasses standardocial conformity indicators referring to the participation in reli-ious rites (O’Dea, 1970) and at the same time explicitly isolateshe component related to the religious sentiment.
The paper is organized as follows. Section 2 discusses the role ofocial conformityin detail. Section 3 describes data and the econo-etric framework. The results of the paper are presented in Section
. Finally, Section 5 concludes the paper.
. Social integration, regulation and conformity
Two core elements characterize Durkheim’s standard work “Leuicide” (1897): the level of social integration and social regula-ion. The former refers to the degree to which people are connectedo each other, the latter indicates the extent to which society hasontrol over the behavior of its members by norms and tradition.
As discussed in the Introduction, Durkheim refers to suicideesulting from low levels of regulation as anomic suicide, which isresumably endemic in modern societies. Conversely, high levels
f social regulations associated with low levels of social integrationharacterize the fatalistic suicide (Durkheim, 1897).1 The subjuga-ion and oppression by an overwhelming force that has control over1 Durkheim argues that fatalistic suicides are very rare in the West and empha-izes the social effect of under-regulation which is typical of the process ofodernization (Watt, 2010). However, Dukheim’s work is based on examination
r records in the late XIX century where registration of non-fatal case of suicidalehaviour was rare; moreover later sociologists (Pearce, 1989; Van Bergen et al.,
-Economics 42 (2013) 67–78
individual action, facilitate suicidal behavior (Acevedo, 2005; VanBergen et al., 2009). According to this view, formal control maybe too strong to the extent that individual beliefs and values arenon-aligned with those of society and this, in turn, may producefeelings of resentment and reactance which may lead to attemptsto evade the social restriction (Brehm and Brehm, 1981; Burgoonet al., 2002).
In the literature the social correlates of suicide rates are mainlyconfined to the analysis of the effect of social integration, while lessattention, to our knowledge, is devoted to the effect of discrepan-cies between individual values and social norms. To represent therelationship between social integration and suicide, many empir-ical works use the marital status and, in particular, divorces askey indicators of low social integration.2 Divorce, by leading tosocial isolation and to dissolution of family ties, constitutes a keyexample of Durkheim’s theory (1893) of social change and sui-cide. However, prior research establishes a link between divorceand suicide risk only at the individual level (Stack, 1982, 2000a,2000b),3 while studies at the aggregate level produce mixed results(Besnard, 2000).
The relationship between social norm and individual behavior isemphasized by Stavrova et al. (2011) who highlight the importancefor the individual well-being of aligning individual values to thosesupported by the community. Analyzing personal life satisfaction in28 OECD countries, they find that the consequences of unemploy-ment areworse in societies characterized by high social pressureand disapproval for the unemployment status. According to thisview, individuals who are placed in contexts with different valuesfind the integration process much more difficult. In this sense, theconformity to the social context is the result of injunctive socialnorms, to the extent that the individual behavior is determined bythe perception of what others in the community believe to be thecorrect conduct (Cialdini et al., 1990; Cialdini, 2007). In this view,conformity may hide conflicts between personal and social aspi-rations, which in turn may lead to irrational and self-destructiveactions (Eckersley, 2006).
In this paper we explicitly take into account the relationshipbetween suicide rates and social norms by proposing an index ofsocial conformity which refers to the religious sphere as an areaof conflict between individual and social behaviors. To our knowl-edge, the only indicator (at the aggregate level) of social conformityin the literature is the participation in religious rites (O’Dea, 1970)which has been considered a valid indicator in societies cultur-ally dominated by ecclesiastical institutions (and this is the caseof Italy). However, as pointed out by Corbetta (2003, p. 76) thisindicator would be “biased” to the extent that it captures not onlythe conformity-related aspects but also the “religious sentiment”.
In this reasoning, we define social conformity as the adoptedbehavior by individuals according to what they perceive asaccepted by their social group, regardless of their true belief, inthis case, with respect to religion. Consequently, we speculate thatthe religiousness manifested at the social level(social religiousness)
2009) find in the suicidal behaviour of migrants and ethnic minority a recurrentexample of fatalistic suicides.
2 Other proxies of social (dis-)integration extensively used are number of mar-riages, the average number of individuals per households, the average consumptionof alcohol and drugs, the population density and the average number of births (seeamong others Andrés et al., 2011; Yamamura et al., 2012).
3 Some papers suggest that divorce rates should be relatively high to manifestan effect on suicide rates (e.g., Fernquist, 2003) and that analyses need to be basedon relatively long time periods to detect such impact on the national suicide rate(Agerbo et al., 2011).
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to the ones accepted by their community or social group. Hence,we expect a positive sign of this variable, i.e. the higher the per-centage of religious marriages, the higher the value of committed
A. Bussu et al. / The Journal of
arriages) as proxy for the social religiousness and the churchttendance as proxy for individual religiousness which we considerhe true belief at the individual level. The difference between thewo indicates the extent to which social conformity characterizeshe society. To those who choose the route of social conformity, theesidue of resentment could be insidiously detrimental to some. Its to this group that the link between social conformity and sui-ide is addressed. Therefore, a positive relationship between socialonformity and suicide rates is expected.
. Empirical model and data description
.1. The basic model
Starting from the empirical literature on suicide, this study pro-oses the structural equation model illustrated below to explorehe relationship between suicide and socio-economic factors fortalian provinces in the time span 1996–2005:
SUICIDEit = ˇ0 + ˇ1GROWTHit + ˇ2INCOMEit + ˇ3DIVORCEit+
ˇ4MARRIAGEit + ˇ5HOUSE SIZEit + ˇ6DENSITYit + ˇ7MIGRATIONit + ˇ8GENDERit+
ˇ9AGEit + ˇ10DRUGit + ˇ11ALCOHOLit + ˇ12SOCIAL CONFORMITYit+
ˇ13SOCIAL FUNDSit + ˇ14LATITUDEi + ˇ15YEARt + εit
(1)
EL MARRIAGEit = ˛0 + ˛1RELIGIONit + ˛2SOCIAL CONFORMITYit + ˛3YEARt + �it
(2)
1) and (2) are the two equations of the system, where εit andit are the error terms; we assume that E(εit) = 0, E(�it) = 0, and(εit, �it) = 0. In Eq. (1) the suicide rate is function of a set ofovariates, among which we consider a latent variable, namelyOCIAL CONFORMITY, that determines, along with RELIGION, theariable REL MARRIAGE (Eq. (2)). Hence, all variables are observ-ble, with the exception of the variable of interest which is theatent variable SOCIAL CONFORMITY.
The previous system of equations can be solved by using theollowing strategy. Firstly, Eq. (2) can be re-arranged in order toake SOCIAL CONFORMITY as function of the observable variablesELIGION and REL MARRIAGE, as follows:
OCIAL CONFORMITYit = −˛0
˛2− ˛1
˛2RELIGIONit
+ 1˛2
REL MARRIAGEit˛3
˛2YEARt − ςit
˛2(3)
hen, substituting (3) into (1), we can estimate the following model:
SUICIDEit˜̌ 0 + ˇ1GROWTHit + ˇ2INCOMEit + ˇ3DIVORCEit + ˇ4MA
ˇ5HOUSE SIZEit + ˇ6DENSITYit + ˇ7MIGRATIONit + ˇ8GENDERit +
ˇ11ALCOHOLit + ˜̌ 12REL MARRIAGEit + ˜̌̃12RELIGIONit + ˇ13SOCIA
˜̌ 15YEARt + ε̃it
here ˜̌ 0 = ˇ0 − (˛0ˇ12/˛2), ˜̌ 12 = (ˇ12/˛2),
˜̌̃0 = −(˛1ˇ12/˛2), ˜̌ 15 = ˇ15 − (˛3ˇ12/˛2) and
ε̃it = εit − (ˇ12/˛2)ςit
UICIDEit is the number of committed suicides per 100,000 inhabi-ants in the i-th province at time t. GROWTH and INCOME indicate
he growth rate and level, respectively, of Gross Domestic ProductGDP) per capita at 1995 constant prices. As shown by Brainerd2001), Cheng et al. (2000) and Neumayer (2003), a negative corre-ation between suicide rate and economic performance is expected.-Economics 42 (2013) 67–78 69
GEit+GEit + ˇ10DRUGit+
NDSit + ˇ14LATITUDEi+(4)
However at the same time few4 studies highlight oppositefindings. For example, Jungeilges and Kirchgässnerb (2002), by per-forming a cross-section analysis for 30 countries, find that that realper capita income and real economic growth are positively associ-ated with suicide rates.
According to Durkheim (1897), suicide rates are affected byfamily and social ties that reduce the egoistic suicidal propensity.DIVORCE and MARRIAGE are the number of divorces and mar-riages per 100,000 residents, respectively; HOUSE SIZE indicatesthe number of individuals per household. Following Neumayer(2003) and Yamamura (2010), we expect that higher numbers andlarger sizes of families decrease the suicide rate. Yamamura (2010)estimates also a positive impact of divorce on suicide rate.
DENSITY is the number of inhabitants per square kilometre. Thisvariable measures the level of urbanization of each province; we donot have an a priori hypothesis about the impact of urbanizationon suicidal behaviors. In fact, on the one hand, urbanization canincrease social ties reducing suicide rates (Otsu et al., 2004); on theother hand, especially in big municipalities and metropolitan areas,we can observe poverty and poverty-related phenomena of socialexclusion that lead to suicide.
REL MARRIAGE and RELIGION are the share of religious mar-riages over the total number of marriages and the churchattendance in a given province at time t, and represent the socialand individual religiousness respectively. As long we control forRELIGION, the former can be considered as a proxy of social normsthrough Eq. (2). As discussed in the previous section, Italy has aconservative culture with a strong religious component. In this con-test, such social-religious norms can stand for the degree of socialconvention in a given community or territory. Many analyses havealready investigated the relationship between religion and suicidalbehaviors at an individual level and an aggregate level, finding thata strong belief in God and church attendance have a positive effect(Helliwell, 2007). We believe that REL MARRIAGE, controlling forreligious sentiment, measures the level of social rules adopted by agiven community. Such norms tend to unify society (Durkheim,1897) but, at the same time, they may lead to social exclusionthrough different channels. A number of social practices and ritualsare generally accepted by many individuals in order not to violatethe system of rule in which they live. Such behaviors are caused byfear (and risk) that non-mainstream behaviors could lead to theirexclusion or marginalization. This effect can be stronger in Italydue to the low internal mobility, which reduces the incentive tomove from one territory to another. In this view, REL MARRIAGE isinserted in the model in order to capture such social aspects, to theextent that this index is correlated to the level of social convention(Eq. (2)). It is quite common in Italy to marry in church, whatever
the individual religious belief, and to keep to the old traditions. Suchcommon behaviors underline social convention and conformity,i.e. people who match their own attitudes, beliefs, and behaviors
4 By reviewing extensively the relationship between suicide and the socio-economic characteristics at an aggregate level, Rehkopf and Buka (2006) observethat only the 30% of 221 analyses reported in the literature reveal a positive associ-ation between the socio-economic character of a region and suicides.
7 Socio-Economics 42 (2013) 67–78
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Table 1Description of the variables.
Name Description Source
SUICIDES Number of committed suicide per100,000 inhabitants
Istat
INCOME GDP per capita in real terms (euro2000)
Tagliacarne
GROWTH GDP growth per capita in real terms(euro 2000)
Tagliacarne
DIVORCE Number of divorce per 100,000inhabitants
Istat
MARRIAGE Number of marriages per 100,000inhabitants
Istat
FAMILY SIZE Number of inhabitants per family IstatDENSITY Number of inhabitants per square
kilometresIstat
AGE Share of people aged over 80 years andbefore 20 years
Istat
GENDER Share of male inhabitants IstatMIGRATION Number of immigrants (both from
other Italian provinces and abroad),arrived in a given year, over totalinhabitants
Istat
ALCOHOL Share of people that consume alcoholbetween meals
Istat
DRUG Number of drug dealing offences per100,000 inhabitants
Istat
REL MARRIAGE Share of religious marriage IstatRELIGION Share of people that go to church at
least one time a weekIstat
SOCIALFUND Amount of resources per capita thatlocal governments allocate for direct
Istat
0 A. Bussu et al. / The Journal of
uicide per capita, controlling for the religious sentiment. In thisense, for a given level of church attendance, we expect that theigher the percentage of religious marriage in a given province, theigher the level of social convention and, consequently, of suicideate.
Unfortunately, Eq. (4) leads to biased and inconsistent estimates.n fact, the residuals ε̃it are correlated to REL MARRIAGE, due tohe presence of the component ςit. In order to solve this prob-em, a different strategy is also performed to hive off the socialonformity component from the REL MARRIAGE index. To do so, awo-stage approach is run. In the first step, Eq. (2) is run withouthe latent variable SOCIAL CONFORMITY, i.e. the share of religious
arriage is regressed on church attendance (RELIGION) along withear dummies. In the second step, the residuals of the first stagere used as index of SOCIAL CONFORMITY in Eq. (1). Such vector ofesiduals represents the choice to marry in church not explainedy religious sentiment. In this way, the residuals are a proxy ofOCIAL CONFORMITY as they measure, on average, the conflictetween individual (religious) preference and social convention.5
MIGRATION is the number Italian and foreign immigrantsrrived in the i-th province at time t. It measures the decay of socialapital in a given province (Yamamura, 2010). Its expected sign isositive.
AGE and GENDER6 indicate the share of people aged less than 20nd over 80 years old, and the share of males over total residents,espectively. Since suicide rates usually decrease among youngnd very old people and are higher among males than femalesHamermesh and Soss, 1974; Goldsmith et al., 2002; Rehkopf anduka, 2006; Noh, 2009; Kuroki, 2010), we take into account thege/gender composition of the provinces in order to control for theigher propensity to commit suicide of these sub-groups.
ALCOHOL and DRUG indicate the share of people that consumelcohol between meals and the number of drug dealing offenceser 100,000 inhabitants; since the consumption of drug and alcoholay be correlated to depression status, positive signs are expected
Noh, 2009).According to Minoiu and Rodríguez (2008) state fiscal pol-
cy, and in particular public spending on health and welfare,lays an important role in reducing the number of suicide deaths.OCIAL FUNDS indicates the amount of resources per capita thatocal governments allocate for direct social programmes, such asombating poverty and social exclusion. Unfortunately, we do notave any information about the effectiveness and efficiency of suchrogrammes across Italian provinces. Assuming that better resultsre obtained in preventing suicide behaviors with larger amountspent on social programmes, the expected sign is negative.
LATITUDE is the geographic coordinate that specifies the north-outh position on the Earth’s surface of the province capitals. It isproxy of climate difference between North and South of Italy.ccording to the empirical analysis,7 we expect a positive relation-hip between latitude and suicide rates.
Finally, YEAR is a set of time dummy variables; the inclusion
f time dummies makes the assumption of no correlation acrossndividuals in the idiosyncratic disturbances more likely to holdRoodman, 2009).5 Notice that this approach also leads to biased and inconsistent estimatesince the statistical analysis of the coefficient associated with the proxy ofOCIAL CONFORMITY shows that (see the Appendix for details): E( ˆ̌ 12) < ˇ12. Thisnequality represents the so-called attenuation biased (Wooldridge, 2002, pp. 75).owever, the advantage of such approach is that in large samples, on average, thestimated effect will be attenuated. So if ˇ12 > 0, ˆ̌ 12will tend to underestimate thenknown parameter ˇ12. In other word, through this strategy, we can identify theirection of the bias, which leads to (a kind of) parsimonious estimate.6 AGE, GENDER and LATITUDE are time-invariant.7 See Helliwell (2007) for a detailed review.
social programmesLATITUDE Latitude of each capital province Istat
Tables 1 and 2 provide detailed information and some descrip-tive statistics of the variables in use, respectively.
All data come from National Institute of Statistics (ISTAT), exceptfor the economic variables (INCOME and GROWTH) that come fromTagliacarne Institute. All variables are transformed in logarithmterm, so the coefficients can be interpreted as elasticities.
3.2. The dynamic panel data: GMM approach
As shown in Fig. 1, the four Italian macro-areas (North, Center,South and Islands) exhibit a similar downward pattern over time(as also highlighted by Preti, 2012), although differences in levelare easily detected; the highest and lowest number of suicides per100 thousands of residentsis observed in the North and South ofItaly, respectively. Fig. 1 indicates that suicide series show a stronginertia over time, indicating that in a given province the number ofsuicides at time t is correlated to the one at time t + 1. In order to con-firm this graphical evidence, we start our analysis estimating model(4) with an ordinary least squares (OLS) approach, both randomand fixed effect, and we apply the Wooldridge test (Wooldridge,2002) to check the presence of serial correlation in panel data.The null hypothesis of no serial correlation is rejected. These argu-ments strongly suggest the use of k lagged dependent variables(SUICIDEit−j for j = 1, . . ., k) to remove serial correlation in the resid-uals. A panel unit root test (Levin et al., 2002) is then performed tosee whether we have stationarity of the dependent variable in (4),and the null hypothesis of non-stationarity is rejected.8
Furthermore, a reverse causality between suicide and social
funds is strongly expected. For example, high suicide rates in a givenregion could motivate public intervention in order to reduce socialillness; as a result, by using OLS approach in models (1)–(2) and8 The statistics tests are provided by the authors upon request.
A. Bussu et al. / The Journal of Socio-Economics 42 (2013) 67–78 71
Table 2Descriptive statistics.
Obs. Mean Std. dev. Min. Max.
SUICIDES 1030 7.58 3.61 0.00 23.32GROWTH 1030 0.01 0.03 −0.48 0.12INCOME 1030 15,393.67 4005.42 7119.16 26,452.31DIVORCE 1030 129.24 56.37 0.17 441.93MARRIAGE 1030 456.30 65.33 232.20 978.42HOUSE-SIZE 1030 39,211.48 3611.65 31,217.34 50,329.55DENSITY 1030 244.30 330.80 36.54 2661.62MIGRATION 1030 0.03 0.01 0.00 0.05GENDER 1030 0.49 0.00 0.46 0.50AGE 1030 38.64 1.80 34.78 42.32DRUG 1030 57.68 45.19 10.30 907.70ALCOHOL 1030 0.25 0.07 0.11 0.55REL. MARRIAGE 1030 0.74 0.12 0.09 0.94RELIGION 1030 0.74 0.12 0.41 0.94SOCIAL FUNDS 1030 0.69 1.33 0.00 11.32LATITUDE 1030 178.9 10.91 153.9 193.8
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ig. 1. Suicide rates in Italy and its macro-areas (North, Center, South and Islands)iedmont, Trentino, Sudtirol, Veneto. Center regions: Abruzzi, Lazio, Marche, Tuscnd Sicily.
4), the coefficient associated to SOCIAL FUNDS can be downwardiased.
The presence of the lagged dependent variable and the lackf strict exogeneity between suicide rates and one explanatoryariable do not allow to use the OLS method to estimate model1) (Roodman, 2009). A possible solution is given by the general-zed method of moments (GMM) that gives a consistent estimatorf ˇ using the lagged value of the dependent and explanatoryariables as instruments. In this analysis, the System GMM esti-ator is applied, which seems to perform better than the linear
rst-differenced GMM in small samples (Blundell and Bond, 1998;oodman, 2009).
In general, the GMM estimator assumes that residuals are seri-lly uncorrelated, i.e. E(εitεis) = 0 for i = 1, . . ., N and s /= t, and thathe initial conditions of the dependent and all explanatory vari-bles at time t0 are predetermined. In addition, the system GMMstimator requires a mean stationary restriction on the initial con-
ition of the variables in use, which implies that, in the time spannalyzed, the units are close enough to their steady-state: in otherords, changes in the instrumenting variables are assumed to bencorrelated with the individual-specific effect.h regions: Aosta Valley, Emilia-Romagna, Friuli-Venezia-Giulia, Liguria, Lombardy,mbria. South Regions: Apulia, Basilicata, Calabria and Campania. Islands: Sardinia
A crucial assumption for the validity of GMM estimates is thatthe instruments are exogenous. The Sargan (1958) test of over iden-tifying restrictions checks the overall validity of the instruments:failure to reject the null hypothesis gives support to the model. Inour case, since the robust standard errors are estimated, in orderto correct for heteroskedasticity or cross-correlation in the residu-als, the Sargan test is inconsistent. Hence, the Hansen (1982) test isperformed under the null hypothesis of the joint validity of theinstruments. Another important issue is the Arellano and Bond(1991) test for autocorrelation of the residuals, which tests whetherthe differenced error term is first and second order correlated. Fail-ure to reject the null hypothesis of no second-order autocorrelationindicates that the residuals are not serially correlated.
3.3. The spatial dynamic panel data approach
Besides the issue of the inertia over time, Fig. 2 indicates an inho-
mogeneous distribution of suicide rates in Italy, with some spatialclusters with similar level of suicides. A higher concentration ofsuicides is found in the North of Italy, especially along the Alpineregions, in Umbria-Tuscany and in Sardinia, while, in general, the
72 A. Bussu et al. / The Journal of Socio-Economics 42 (2013) 67–78
r 100,
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Fig. 2. Average number of suicides pe
outh and the Centre of Italy exhibit low suicide attitude. Suchisparities between North and South of Italy can be explained bytrong structural differences in terms of culture, social capital andconomic condition.
The spatial clusters of Fig. 1 could indicate the presence ofpatial autocorrelation, which is the case when the number ofuicides in a given province is correlated to the suicides observedn the neighboring areas. Unfortunately, spatial dependence canead to unbiased standard estimates (Elhorst, 2003) due to theon-diagonal structure of the disturbance term. By using theesiduals of the OLS regression of Eq. (1), the Moran I test is runor each year (Anselin, 1988). Notably, the null hypothesis of nopatial autocorrelation is always rejected.9
In order to take into account spatial autocorrelation, a newodel has to be implemented. The general spatial process is the
ollowing (Baltagi et al., 2007):
it = Xitˇ + uit (5)
here
t = m + εt (6)
t = �Wεt + �t (7)
t = ��t−1 + et (8)
= 2
2ε
(9)
he model considers serial correlation on each spatial unit overime (8), and spatial dependence between spatial units at each timeeriod (7). In the model, y is the dependent variables (SUICIDE),is the set of covariates in Eq. (1), W is the weighted matrix. In
his study, a row-standardized distance matrix is used; the dis-ance between two provinces is measured as the Euclidian metricetween their centroids.
9 The statistics tests are provided by the authors upon request.
000 inhabitants in Italy (1996–2005).
Depending on the restrictions on the parameters we can com-bine error features in different ways, giving rise to various nestedspecifications. For � /= 0 and � /= 0, we obtain a random effectsmodel and fixed effects model, respectively. For � /= 0 and � = 0,the model incorporates serial correlation. Finally, � = 0 and � /= 0,we have a spatial autoregressive model. For � /= 0 and � /= 0, weobtain a standard linear model.
Baltagi et al. (2007) proposes a set of tests in order to check thevalidity of spatial component, serial component and random effectscomponent in the dynamic spatial panel data approach, respec-tively. In this way, the statistical tests give a formal indication ofwhether one can estimate a simpler model than the general one.
4. Results
In a first stage, Eq. (4) is regressed by using the basic OLSapproach. Initially, random and fixed effects models are performed(from now on FE and RE, respectively) and the Hausman test indi-cates RE as the preferred model.
Table 3 shows the results of the OLS approach. As shown in col-umn (1), the economic variables (economic growth and income percapita) do not seem to have any effect on suicide rates. These resultsare analogous to the ones of Detotto and Sterzi (2011) for the Italiancase.
Then, we observe that a 1% increase in the number of marriagesand in the average size of households, ceteris paribus, reduces thenumber of suicide by 0.48% or 2.04%, respectively. Both phenomenalead to an increase in social ties and individuals could find benefitsfrom such family structures, in terms of financial and emotionalsupport. This findings support Durkheim theories whereby strongfamily ties reduce individual suicidal attitudes.
Interestingly, population density is negatively correlated to sui-cide rates. A 1% increase in population density decreases suicidesby 0.19%. Probably, low density urban areas suffer from low levels
of social contact, leading to a higher number of suicides. Further-more, on the one hand, small communities may invest less in socialprogrammes aimed at assisting people with discomfort; on theother hand, in small communities depressed people are unlikely
A. Bussu et al. / The Journal of Socio-Economics 42 (2013) 67–78 73
Table 3OLS regression results on suicide.
(1) (2) (3) (4)OLS OLS OLS OLS-two stagea
Growth −0.12 −0.10 −0.08 −0.09(0.37) (0.37) (0.37) (0.37)
Income 0.30 0.27 0.30 0.27(0.20) (0.20) (0.20) (0.20)
Divorce 0.00 0.00 0.01 0.00(0.02) (0.02) (0.02) (0.02)
Marriage −0.48*** −0.46*** −0.46*** −0.45***
(0.16) (0.16) (0.17) (0.16)Household-size −2.04*** −1.86*** −1.86*** −1.76***
(0.55) (0.50) (0.54) (0.49)Density −0.19*** −0.18*** −0.20*** −0.18***
(0.05) (0.05) (0.05) (0.05)Migration −0.06 −0.07 −0.07 −0.07
(0.07) (0.07) (0.07) (0.07)Gender −0.19 −0.16 −0.59 −0.24
(2.36) (2.35) (2.37) (2.36)Age −0.92 −0.79 −0.94 −0.75
(0.87) (0.84) (0.87) (0.84)Drug 0.05 0.05 0.05 0.05
(0.03) (0.03) (0.03) (0.03)Alcohol 0.30** 0.32** 0.26* 0.31**
(0.14) (0.13) (0.14) (0.14)Rel. marriage 0.22* 0.24**
(0.12) (0.11)Religion 0.16 0.20
(0.14) (0.14)Social conformity 0.20
(0.13)Social funds −0.12 −0.11 −0.11 −0.11
(0.08) (0.08) (0.08) (0.08)Latitude −0.01 0.17 0.05 0.24
(0.85) (0.82) (0.84) (0.81)Constant 0.19 −0.56 −0.41 −1.22
(5.95) (5.78) (5.89) (5.73)Year dummies Yes Yes Yes YesNumber of observation 1030 1030 1030 1030R2 0.75 0.74 0.74 0.75
Robust standard errors are in parenthesis.a OLS-two stage indicates the two stage approach. In the first step, REL MARRIAGE is regressed on RELIGION, controlling for year dummies. In the second step, the residuals
of the first stage are added to the model.* Significance at the 10%.
tbc
iml
c10
eSenci
cmNps
sentiment. Then, we re-estimate Eq. (1) inserting the obtained vec-tor of residuals, which could be a proxy of social conformity, thelatent variable in Eq. (1). Column (4) in Table 3 indicates that the
** Significance at the 5%.*** Significance at the 1%.
o be helped to recover by medication. In fact, they stay invisibleecause they fear feeling unwanted and unaccepted by their ownommunity.
MIGRATION, GENDER and AGE do not have any significantmpact on the number of suicides; it is reasonable that these factors
ight play a role at an individual level, while at an aggregate level,ike in present analysis, they might not have any descriptive power.
The consumption of drug and alcohol positively affects the sui-ide rates, although only the ALCOHOL coefficient is significant. A% increase in heavy alcohol consumers causes a rise in suicides by.30%.
Then, SOCIAL FUNDS and LATITUDE coefficients have thexpected sign, even if they are not significant. However, theOCIAL FUNDS estimate can be downward biased due to the exist-nce of a bidirectional causality between this variable and theumber of suicides. In fact, we guess that as a higher number of sui-ides is observed, more resources are spent by local governmentsn social programmes.
Finally, the REL MARRIAGE coefficient is positive and signifi-ant: according to our results, an increase in the share of religious
arriages leads to a 0.22%. Increase in the number of suicides.otably, RELIGION is not significant, while REL MARRIAGE isositive and significant at 10% level. As discussed above, thehare of religious marriage, controlling for the aggregate religiousattendance, becomes a proxy of social conformity in a givenprovince. Such result confirms the impact of social norms on sui-cidal behaviors.
In order to check the robustness of our results, we eliminate,in turn, REL MARRIAGE and RELIGION from our model and re-estimate it (columns 2 and 3). As expected, column (3) in Table 3indicates that religious attendance has still no effects on suiciderates.
Finally, we apply a two-stage approach in order to separatethe two driving factors, conformity and religious sentiment, fromthe REL MARRIAGE variable and identify a proxy of the latentvariable in Eq. (1). In the first stage, we regress RELIGION onREL MARRIAGE.10 The residuals of such model represent the com-ponent of the religious marriages series not explained by religious
10 The coefficient associated to RELIGION is positive and highly significant (it values0.24 with a standard deviation of 0.04). Furthermore, the adjusted R squared equalsto 0.41, which means that the model is able to capture a significant portion of thevariation in REL MARRIAGE. Such results indicates that the residuals can be wellinterpreted as a (weak) proxy of the latent variable SOCIAL CONFORMITY.
74 A. Bussu et al. / The Journal of Socio-Economics 42 (2013) 67–78
Table 4System-GMM regression results on suicide.
(1) GMM (2) GMM (3) GMM (4)GMM-two stagec
Suicide (−1) 0.18*** 0.18*** 0.17*** 0.18***
(0.07) (0.07) (0.06) (0.07)Suicide (−2) 0.09** 0.09** 0.09** 0.09**
(0.04) (0.04) (0.04) (0.04)Growth 0.01 0.00 0.09 0.01
(0.34) (0.34) (0.35) (0.35)Income 0.37* 0.36* 0.33 0.33
(0.21) (0.20) (0.21) (0.21)Divorce −0.01 −0.01 −0.01 −0.01
(0.02) (0.02) (0.02) (0.02)Marriage −0.37 −0.36 −0.38 −0.36
(0.24) (0.23) (0.27) (0.23)Household-size −1.58*** −1.51*** −1.28** −1.36**
(0.58) (0.54) (0.59) (0.54)Density −0.15*** −0.14*** −0.16*** −0.14***
(0.05) (0.05) (0.05) (0.05)Migration −0.11 −0.11 −0.12 −0.11
(0.09) (0.09) (0.09) (0.09)Gender −1.86 −1.86 −1.69 −1.83
(2.83) (2.85) (2.85) (2.89)Age −0.94 −0.87 −0.99 −0.81
(0.93) (0.92) (0.90) (0.91)Drug 0.04 0.04 0.04 0.03
(0.03) (0.03) (0.03) (0.03)Alcohol 0.34** 0.35** 0.25 0.35**
(0.16) (0.15) (0.15) (0.16)Rel. marriage 0.38*** 0.40***
(0.12) (0.11)Religion 0.07 0.12
(0.12) (0.12)Social conformity 0.36***
(0.13)Social funds −0.21** −0.21** −0.19** −0.20**
(0.09) (0.09) (0.09) (0.09)Latitude −0.68 −0.61 −0.46 −0.46
(0.85) (0.84) (0.85) (0.84)Constant 1.53 1.23 0.77 0.21
(5.89) (5.83) (5.75) (5.77)Year dummies Yes Yes Yes YesNumber of observation 824 824 824 824Arellano and Bond (1) −5.11*** −5.12*** −5.14*** 302.72***
Arellano and Bonda (2) −0.13 −0.18 −0.04 −0.19Hansen testb 66.99 71.55 73.13 70.62
Robust standard errors are in parenthesis.a Arellano and Bond (1991) statistic test under the null hypothesis of no second-order autocorrelation in the residuals.b Sargan (1958) and Hansen (1982) statistic tests under the null hypothesis of the joint validity of the instruments.c GMM-two stage indicates the two stage approach. In the first step, REL MARRIAGE is regressed on RELIGION, controlling for year dummies. In the second step, the
residuals of the first stage are added to the model.* Significance at the 10%.
cs
piFsd
Hsir
tcla
Controlling for endogenous factors, the SOCIAL FUNDS coeffi-cient becomes significant; a rise in the annual budget spent in socialprogrammes reduces the suicide by 0.21% (0.29% in the long run).
** Significance at the 5%.*** Significance at the 1%
oefficient associated to the vector of first stage residuals is notignificant.
However OLS estimates may suffer from the omitted variableroblem: as we noted in Section 3.2, all suicide series have a sim-
lar downward trend and seem to have a strong inertia over time.or this reason, a GMM approach is applied in order to obtain con-istent estimators of ˇ in Eq. (4) inserting the lagged values of theependent in our model.
Table 4 shows the results of the System GMM estimation. Theansen (1982) test for the joint validity of the instruments gives
upport to the model. In addition, the Arellano and Bond test (1991)ndicates that residuals are not serially correlated. The first twoows indicate the first and second lagged dependent variable.
Coefficients in column (1) are quite similar to those of
he basic OLS estimation, with the exception of income perapita, whose coefficient is now positive and significant at 10%evel, and the number of marriages, which is not significantnymore.According to our estimates, if the long-run equilibrium isassumed, the elasticities may be obtained by dividing each of theestimated coefficients by (1 − ˇ1 − ˇ2)−1, where ˇ1 and ˇ2 arethe coefficients of the lagged dependent variables. Following thisreasoning, the long run impact of income per capita and alcoholconsumption on suicide in Italy is about 0.51% and 0.47%, respec-tively, while the long run impact of household-size and density is−2.16% and −0.20%, respectively.11
11 The long run effect of income per capita on suicide rates is calculated by mul-tiplying the coefficient of such covariate (0.37) by the factor (1 − �1 − �2)−1. Hence,solving the following formula (0.37) × (1 − 0.18 − 0.09)−1 = 0.51, we are able to findthe long run elasticity associated to income per capita. The same procedure can beapplied to all coefficient in Table 4 to calculate the long run effects.
Socio
aaibomR
aofia
TS
S
r
A. Bussu et al. / The Journal of
REL MARRIAGE is still positive and highly significant. Its shortnd long run impact is 0.40% and 0.55%, respectively. In other words,1% increase in the share of religious marriages leads to an increase
n suicides by 0.40% in the short run, and 0.55% in the long run. Asefore, in order to separate the religion effect from the conformityne, we eliminate, in turn, RELIGION and REL MARRIAGE from ourodel (columns 2 and 3). REL MARRIAGE is still significant, while
ELIGION is not.In the last column of Table 4 we apply a two-stage approach
s before. The residuals of the first stage regression of RELIGION
n REL MARRIAGE are included in the model; the associated coef-cient (SOCIAL CONFORMITY) is positive (0.36% in the short run,nd 0.49% in the long run) and significant at 1% level.able 5patial dynamic panel data (SDPD) regression results on suicide.
(1) SDPD (2) SD
Growth −0.09 −0.07(0.09) (0.08)
Income 0.34 0.31(0.24) (0.22)
Divorce −0.01 −0.01(0.02) (0.02)
Marriage −0.39** −0.38(0.18) (0.18)
Household-size −2.08*** −1.90(0.67) (0.66)
Density −0.19*** −0.18(0.06) (0.06)
Migration −0.04 −0.05(0.04) (0.04)
Gender −0.46 −0.45(1.61) (1.62)
Age −0.86 −0.74(0.74) (0.77)
Drug 0.06* 0.07(0.04) (0.05)
Alcohol 0.30** 0.31**
(0.14) (0.15)Rel. marriage 0.25** 0.27**
(0.11) (0.12)Religion 0.17
(0.13)Social conformity
Social funds −0.05 −0.11(0.08) (0.08)
Latitude −0.03 0.17(0.46) (0.53)
Constant 6.28 5.32(7.21) (7.23)
Year dummies Yes YesNumber of observation 1030 1030� 0.14** 0.14**
(0.07) (0.07)� 0.19*** 0.19**
(0.04) (0.04)� 0.46*** 0.46**
(0.09) (0.09)LM(C1) testa 48.62*** 48.25LM(C2) testb 10.14*** 10.10LM(C3) testc 8.95*** 8.78**
LM(J) testd 334.17*** 332.4
tandard errors are in parenthesis.a Baltagi et al. (2007) LM test under the null hypothesis of no serial correlation.b Baltagi et al. (2007) LM test under the null hypothesis of no spatial correlation.c Baltagi et al. (2007) LM test under the null hypothesis of no random effects.d Baltagi et al. (2007) LM jointed test under the null hypothesis of no serial correlation,e SDPD-two stage indicates the two stage approach. In the first step, REL MARRIAGE
esiduals of the first stage are added to the model.* Significance at the 10%.
** Significance at the 5%.*** Significance at the 1%.
-Economics 42 (2013) 67–78 75
Finally, as described in Section 3.3, spatial clusters and Moran I’stest indicate the presence of spatial autocorrelation that could leadto biased estimates. A dynamic spatial panel data is run in orderto correct for both spatial and serial autocorrelation. Such modelstake into account serial correlation on each spatial unit over time aswell as spatial dependence between the spatial units at each pointin time. In addition, the model allows for heterogeneity across thespatial units using random effects. Baltagi et al. (2007) propose aset of tests for serial correlation, spatial autocorrelation and ran-dom effects, as well as a joint test, in a spatial error correlation
framework.Table 5 shows the results. The last four rows represent theLagrange Multiplier tests as proposed by Baltagi et al. (2007). The
PD (3) SDPD (4) SDPD-twostagee
−0.05 −0.07(0.08) (0.09)0.33 0.27(0.22) (0.19)−0.01 −0.01(0.02) (0.02)
** −0.37** −0.38**
(0.17) (0.18)*** −1.87*** −1.75***
(0.60) (0.67)*** −0.20*** −0.18***
(0.06) (0.06)−0.05 −0.04(0.04) (0.04)−0.73 −1.04(1.62) (1.65)−0.84 −0.65(0.77) (0.76)0.06* 0.06(0.04) (0.05)0.26* 0.29**
(0.15) (0.15)
0.19(0.14)
0.35***
(0.12)−0.11 −0.10(0.08) (0.08)0.03 0.18(0.47) (0.49)5.51 5.55(7.25) (7.25)Yes Yes1030 10300.15** 0.14*
(0.07) (0.08)* 0.18*** 0.19***
(0.04) (0.03)* 0.44*** 0.45***
(0.09) (0.10)*** 52.51*** 52.37***
*** 10.27*** 10.07***
* 8.95*** 8.78***
5*** 333.38*** 337.18***
spatial correlation and random effects.is regressed on RELIGION, controlling for year dummies. In the second step, the
7 Socio
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saCmPab
atoca
5
rstvsaoac
slaetctlno
nPribtSpasqatsar
r
6 A. Bussu et al. / The Journal of
iagnostic tests confirm the use of a dynamic spatial panel datapproach. The statistical significance of �, � and � is a furtherheck of the goodness of the model. All the estimates are obtainederforming a Maximum Likelihood method.12
The four estimation procedures (columns 1–4) yield similaresults to the previous ones, indicating that our results are quiteobust and do not depend on the estimation method in use.
In conclusion, we observe serial and spatial correlation in suicideeries. Such findings could indicate the presence of latent vari-bles that might drive the suicidal behaviors over time and space.ontrolling for these factors, we see that family plays a funda-ental role in explaining differences in suicide rates among Italian
rovinces. To be more precise, the higher the number of marriagesnd the average family size in a given province, the lower the num-er of suicides observed.
Population density is negatively correlated to suicides, whilelcohol consumption positively affects suicidal behaviors. Finally,he share of religious marriages has a positive impact on the numberf suicides. This result is robust to the inclusion of a religion index,onfirming our hypothesis that the enforcement of social normsnd the presence of conformity may have an effect on suicide rates.
. Conclusions
The relationship between socio-economic variables and suicidalates has been widely analyzed by scholars, under the hypothe-is of the sociological and economic model of suicide. Followinghis approach, suicide rates react to changes in the economicariables, like income per capita and unemployment, and in theocio-demographic factors, like number of marriages, divorces, andverage number of family members. According to Durkheim’s the-ry, such aspects are just one side of the coin. In fact, society playsfundamental role in driving suicidal incidents through different
hannels.To our knowledge, the impact of social norms, and in particular
ocial conformity, on suicidal behaviors have not been fully ana-yzed, despite their importance in the theoretical literature. Thedoption of social norms can produce two opposite effects on soci-ty. On the one hand, social norms could increase social cohesion,hereby reducing suicidal behavior, but, on the other hand, theyould seemingly fail to stop individual suicidal impulses and atti-udes, thus resulting in an increase in suicides. According to theatter point, changes in rules or deviation from the establishedorms could create a conflict that might lead to the marginalizationf those who deviate from “standard” behaviors.
Unfortunately, social norms are a complex phenomenon, and aumber of formal and informal rules may govern the individuals.robably, the measurement and identification complexities haveepresented a limit to the implementation of social norms indicesn the econometric models (Stutzer and Lalive, 2004). We try toridge this gap by using a panel data at Italian provincial level in theime span 1996–2005. We identify a type of social norm that we callocial Conformity and that directly concerns the religious sphere. Inarticular, we consider the religiousness expressed at social levels the consequence both of personal religious orientation and ofocial conformity. These two aspects are approximated by the fre-uency of religious marriages over the total number of marriagesnd church attendance, respectively. We speculate that the greaterhe difference between the two components, the higher the level of
ocial conformity. Performing GMM and dynamic spatial panel datapproaches, which control for serial and spatial autocorrelation, ouresults show that social conformity increases suicide rates.12 Unfortunately, such approach does not allow to control for the endogenouselationship between suicides and social funds.
-Economics 42 (2013) 67–78
Our study indicates also that family structure, alcohol con-sumption and population density drive suicide rates in Italy, whilethe economic variables, namely income per capita and economicgrowth, do not seem to produce any effects.
When interpreting these results, one should be aware of somecaveats. The most important is that we focus on a specific aspectof social conformity, the adherence to social norms in the religioussphere. Although religion is an all-pervasive force in Italy, this callsfor complementary analysis using different aspects of social confor-mity. The second caveat is that the proxy of individual religiousnessmight hide an aspect of conformity too, to the extent that people goto church not for religious belief but to conform to social behavior.
Both aspects can be linked to the use of aggregate data, whichreduce the availability of some important information and theexplanative power of our models. In light of this limitation, futureresearch requires preferably individual-level data and opportunesurveys analyses.
Acknowledgments
We are fully grateful to Claudio Lolli, Fausto Galli, Juan de DiosTena Horrillo, Antonello Preti and Andrea Vezzulli for their usefulcomments and suggestions. The support of the Regional LombardyOffice of the Italian Institute of Statistics (ISTAT) for this researchis gratefully acknowledged. C. Detotto thanks GREThA (Universitéde Bordeaux) and KITES (Bocconi University) fot the hositality. V.Sterzi acknowledges the financial support by the “Visiting ProfessorProgram” of the University of Sassari (Act of 29.12.2009 n.56/21).The authors would like to thank an anonymous referee for helpfuland valuable comments and suggestions.
Appendix A.
Suppose to have the following structural equation model:
y = ˇz + � (1A)
w = ˛0 + ˇ0x + ı0z + ε (2A)
where ε∼N(0, 2ε ), �∼N(0, 2
�)), cov(ε,�) = 0, cov(z,�) = 0,cov(x,z) /= 0, and Eq. (1A) for simplicity has no constant term.w, x and y are observable while z is a latent variable. Our goal isto measure the impact of z on y. Let’s start estimating Eq. (2A)without the latent variable z:
w = ˛∗0 + ˇ∗
0x + ε∗ (3A)
where ˛∗0, ˇ∗
0 and ε* are the new elements. As well known, ˛∗0 and
ˇ∗0 are biased given the so-called omitted value problem. Follow-
ing Wooldridge (2002), we can calculate the bias of ˇ∗0, given the
following relationship between z and x:
z = ˛1 + ˇ1x + u (4A)
where u∼N(0, 2u ), cov(u,ε) = cov(u,�) = 0. Hence, the coefficients ˛∗
0and ˇ∗
0, and the residuals ε* are as follows (Wooldridge, 2002, pp.61–62):
˛∗0 = ˛0 + ı0˛1 (5A)
ˇ∗0 = ˇ0 + ı0ˇ1 (6A)
ε∗ = ε + ı0u (7A)
The vector of residuals ε* is used as weak instrument of z in Eq.
(1A). We can re-write Eq. (1A) by substituting the vector z with z*,which corresponds to the vector of residuals ε*.y = ˇ ∗ z ∗ +� (8A)
Socio
ˇ
Lw
E
E
E
E
G
E
E
E
G
E
E
t
E
S
E
E
E
Eleu
R
A
A
A
A
A
A
B
B
A. Bussu et al. / The Journal of
We can observe that the OLS estimate of ˆ̌ ∗ in (8A) yields to:
ˆ ∗ = (z∗′z∗)−1(z∗′y) (9A)
et’s start with the statistical analysis of ˆ̌ ∗ in order to establishhether it is unbiased or not:
( ˆ̌ ∗) = E[(z∗′z∗)−1(z∗′y)]
( ˆ̌ ∗∗) = E[(z∗′z∗)−1(z∗′(ˇz + �))]
( ˆ̌ ∗∗) = E[(z∗′z∗)−1(z∗′z)] + E[(z∗′z∗)−1(z∗′�)]
( ˆ̌ ∗∗) = ˇE[(z∗′z∗)−1(z∗′z)] + E[(z∗′z∗)−1(ε′� + ı0u′�)]
iven cov(ε,�) = cov(u,�) = 0, then E(ε ’ �) = 0 and E(u ’ �) = 0, so:
( ˆ̌ ∗∗) = ˇE[(z∗′z∗)−1(z∗′z)]
( ˆ̌ ∗∗) = ˇE[((ε + ı0u)′(ε + ı0u))−1((ε + ı0u)′z)]
( ˆ̌ ∗∗) = ˇE[(ε′ε + nı0u′ε + nı0ε′u + ı2
0u′u)−1
(ε′z + ı0u′z)]
iven cov(ε,u) = cov(ε,z) = 0, we obtain E(u′z) = 0 and E(ε′z) = 0, so:
( ˆ̌ ∗) = ˇE[(ε′ε + ı20u′u)
−1(ı0u′z)]
( ˆ̌ ∗) = ˇı0E(u′z)
E(ε′ε) + ı20E(u′u)
hat is
( ˆ̌ ∗) = ˇı0cov(u, z)
2ε + ı2
02u
(10A)
ubstituting (4A) into (10A), we find:
( ˆ̌ ∗) = ˇı0cov(u, ˛1 + ˇ1x + u)
2ε + ı2
02u
( ˆ̌ ∗) = ˇı0cov(u, u)
2ε + ı2
02u
( ˆ̌ ∗) = ˇı02
u
2ε + ı2
02u
< ˇ (11A)
q. (11A) indicates that the above-presented two-stage approacheads to a downward biased estimate of ˇ, and such bias increas-swith increasing variance of ε(2
ε ) and decreasing variance of(2
u ).
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