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Modelling the Evolution of Domestic Violence Occurrences in Portuguese Municipalities - What Causes Domestic Violence?

St. Aubyn, Ana Clara do Carmo · 2022

Abstract

Throughout the last years, domestic violence has been a widely discussed topic and an essential concern when building healthy communities. To fight the prevalence of this problem, its causes must be addressed. These causes can come from personal indicators, but they can also come from issues in society at large. It is important to shift the debate from micro-level to macro-level analyses, looking for structural factors in societies that contribute to the evolution of the number of domestic violence occurrences as these are the factors that can be addressed by regulatory bodies. When modeling domestic violence one can envisage two types of possible explanatory variables: risk factors and protective factors. The first ones, as the term suggests, increase the risk of domestic violence, causing a high number of occurrences when very prevalent. Protective factors do the opposite, buffing the risk for domestic violence. The identification of risk factors is very important for the prevention of violence and to guide policies. However, identifying protective factors is of the utmost importance as their presence in Societies can be promoted to avert the occurrences. The present document studies the evolution of domestic violence occurrences in the municipalities of the Portuguese mainland between 2009 and 2019 resorting to panel data analysis methods. The constant coefficients and the fixed effects approaches are employed to try and understand the relation between possible causes and domestic violence occurrences. While explaining a good proportion of the total variance encapsulated in the dependent variable was revealed to be a hard task, evidence of the importance of some variables in explaining domestic violence occurrences on a macro-level was found. These variables were the average number of children born to each woman in fertile age, the number of divorces per 100 marriages, the percentage of resident population with normal age for attending high school that is actually attending high school, the number of new marriages per 100 inhabitants, the percentage of men’s monthly gain that women receive on average, the number of people enrolled in employment and vocational training centers per 100 inhabitants and the number of doctors per 100 inhabitants according to the Doctors’ Professional Order. Most of these were shown to be risk factors, increasing the number of domestic violence occurrences.

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Modelling the Evolution of Domestic Violence Occurrences in Portuguese Municipalities - What Causes Domestic Violence?

Author: St. Aubyn, Ana Clara do Carmo
Year: 2022
Source: https://run.unl.pt/bitstream/10362/135684/1/TCDMAA0141.pdf
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Modelling he E olu ion o Domes ic Violence
Occu ences in Po uguese Municipali ies
Ana Cla a do Ca mo S . Aubyn
Wha Causes Domes ic Violence?
Disse a ion p esen ed as pa ial equi emen o ob aining
he Mas e ’s deg ee in Ad anced Analy ics
ii
NOVA In o ma ion Managemen School
Ins i u o Supe io de Es a ís ica e Ges ão de In o mação
Uni e sidade No a de Lisboa
MODELING THE EVOLUTION OF DOMESTIC VIOLENCE
OCCURRENCES IN PORTUGUESE MUNICIPALITIES
by
Ana Cla a do Ca mo S . Aubyn
Disse a ion p esen ed as pa ial equi emen o ob aining he Mas e ’s deg ee in Ad anced
Analy ics
Ad iso / Co Ad iso : Mau o Cas elli / Ma ia Jo dão
No embe 2021
iii
ACKNOWLEDGMENTS
Th oughou he w i ing o his s udy, I aced a lo o challenges ha could no ha e been o e come
wi hou he g ea deal o suppo and assis ance I ecei ed.
Fi s o all, I would like o hank my supe iso s, P o esso s Mau o Cas elli and Ma ia Jo dão o making
he w i ing o his hesis possible and o all he suppo p o ided when hings did no go he way I
wan ed hem o.
Secondly, I would like o hank my a he o his p ecious suppo and eadiness o enligh en me when
I was in doub . You we e a undamen al piece o his hesis.
I would also like o acknowledge my iends So ia, Ri a, Da id and Ped o, as well as my boy iend o
ne e le ing me gi e up and o sha ing he ups and downs o hese wo semes e s.
Finally, bu no leas impo an , I would like o hank my mo he , who unde s ands me like no o he
and always calms me down when needed. Thank you o always lis ening o me du ing he p ocess o
w i ing his hesis e en i you do no ha e a sligh knowledge o econome ics.
i
ABSTRACT
Th oughou he las yea s, domes ic iolence has been a widely discussed opic and an essen ial
conce n when building heal hy communi ies. To igh he p e alence o his p oblem, i s causes mus
be add essed. These causes can come om pe sonal indica o s, bu hey can also come om issues in
socie y a la ge. I is impo an o shi he deba e om mic o-le el o mac o-le el analyses, looking
o s uc u al ac o s in socie ies ha con ibu e o he e olu ion o he numbe o domes ic iolence
occu ences as hese a e he ac o s ha can be add essed by egula o y bodies.
When modeling domes ic iolence one can en isage wo ypes o possible explana o y a iables: isk
ac o s and p o ec i e ac o s. The i s ones, as he e m sugges s, inc ease he isk o domes ic
iolence, causing a high numbe o occu ences when e y p e alen . P o ec i e ac o s do he
opposi e, bu ing he isk o domes ic iolence. The iden i ica ion o isk ac o s is e y impo an o
he p e en ion o iolence and o guide policies. Howe e , iden i ying p o ec i e ac o s is o he
u mos impo ance as hei p esence in Socie ies can be p omo ed o a e he occu ences.
The p esen documen s udies he e olu ion o domes ic iolence occu ences in he municipali ies o
he Po uguese mainland be ween 2009 and 2019 eso ing o panel da a analysis me hods. The
cons an coe icien s and he ixed e ec s app oaches a e employed o y and unde s and he ela ion
be ween possible causes and domes ic iolence occu ences. While explaining a good p opo ion o
he o al a iance encapsula ed in he dependen a iable was e ealed o be a ha d ask, e idence o
he impo ance o some a iables in explaining domes ic iolence occu ences on a mac o-le el was
ound. These a iables we e he a e age numbe o child en bo n o each woman in e ile age, he
numbe o di o ces pe 100 ma iages, he pe cen age o esiden popula ion wi h no mal age o
a ending high school ha is ac ually a ending high school, he numbe o new ma iages pe 100
inhabi an s, he pe cen age o men’s mon hly gain ha women ecei e on a e age, he numbe o
people en olled in employmen and oca ional aining cen e s pe 100 inhabi an s and he numbe o
doc o s pe 100 inhabi an s acco ding o he Doc o s’ P o essional O de . Mos o hese we e shown
o be isk ac o s, inc easing he numbe o domes ic iolence occu ences.
KEYWORDS
Domes ic Violence; Econome ics; Panel Da a; Cons an Coe icien s; Fixed E ec s; Risk Assessmen ;
Explana o y Modelling
INDEX
1. In oduc ion ............................................................................................................................. 1
1.1. Thesis Objec i e and Resea ch Ques ions ........................................................................ 1
1.2. The E olu ion o Domes ic Violence in Po ugal .............................................................. 2
2. Li e a u e Re iew ..................................................................................................................... 4
3. Theo e ical Backg ound ........................................................................................................... 9
3.1. Panel Da a......................................................................................................................... 9
3.2. Econome ic P ime .......................................................................................................... 9
3.3. Causal Rela ionships and Ce e is Pa ibus ....................................................................... 13
3.4. Econome ic Assump ions .............................................................................................. 14
3.5. S a is ical Tes s ............................................................................................................... 16
3.6. He e oskedas ici y .......................................................................................................... 18
3.7. Model and Va iable Selec ion ........................................................................................ 19
3.8. Modelling Issues ............................................................................................................. 21
3.9. Models Fo Panel Da a ................................................................................................... 22
4. Da a Explo a ion ..................................................................................................................... 24
4.1. Dependen Va iable ........................................................................................................ 25
4.2. Explana o y Va iables ..................................................................................................... 28
5. Me hodology .......................................................................................................................... 32
5.1. Se ies B eaks ................................................................................................................... 32
5.2. Co ela ions .................................................................................................................... 32
5.3. Missing Values ................................................................................................................ 34
5.4. Summa y S a is ics ......................................................................................................... 36
5.5. Ou lie Analysis ............................................................................................................... 38
5.6. S a iona i y ..................................................................................................................... 39
5.7. Model Es ima ion ........................................................................................................... 42
5.7.1. Model 1 (CC – Cons an Coe icien s) ..................................................................... 43
5.7.2. Model 2 (CC) ........................................................................................................... 45
5.7.3. Model 3 (CC) ........................................................................................................... 47
5.7.4. Model 4 (CC) ........................................................................................................... 48
5.7.5. Model 5 (FE – Fixed E ec s) .................................................................................... 49
5.7.6. Model 6 (FE) ............................................................................................................ 50
5.7.7. Model 7 (FE) ............................................................................................................ 52
5.7.8. Model 8 (FE) ............................................................................................................ 53
5.7.9. Model 9 (FE) ............................................................................................................ 53
6. Resul s and Discussion ........................................................................................................... 55

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7. Conclusions ............................................................................................................................ 57
8. Limi a ions and Recommenda ions o Fu u e Wo ks ........................................................... 59
9. Bibliog aphy ........................................................................................................................... 60
10. Annexes .................................................................................................................................. 62
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LIST OF FIGURES
Figu e 1.1 - Domes ic Violence Occu ences (on a na ional le el) .......................................................... 2
Figu e 1.2 - Domes ic Violence Occu ences by Ca ego y (on a na ional le el) ..................................... 3
Figu e 1.3 - Domes ic Violence Agains Spouse o Analogous Occu ences (on a na ional le el) .......... 3
Figu e 2.1 - Age o Domes ic Violence Vic ims (2013-2017) ................................................................... 8
Figu e 3.1 - P obabili y Densi y Func ion o DVASA ............................................................................ 10
Figu e 3.2 - Condi ional P obabili y Densi y Func ion o DVASA (GER=70,16) .................................... 11
Figu e 3.3 - G aphical Rela ion Be ween GER and DVASA .................................................................... 11
Figu e 3.4 - Choosing Va iables and Func ional Fo ms o Models ....................................................... 19
Figu e 3.5 - Diagnos ic Residual Plo s (Example) .................................................................................. 21
Figu e 4.1 - Absolu e Change in To al and DVASA Occu ences (on a na ional le el) .......................... 26
Figu e 4.2 - A e Ma iages and DVASA Occu ences Rela ed? .............................................................. 30
Figu e 5.1 - A e age Con empo aneous Pea son Co ela ion .............................................................. 33
Figu e 5.2 - His og am o DVASA Dis ibu ion ..................................................................................... 37
Figu e 5.3 - E olu ion o GER, GER_Men, and GER_Women in Ba ancos ........................................... 39
Figu e 5.4 - Join Dis ibu ions o Explana o y Va iables wi h DVASA .................................................. 42
Figu e 5.5 - He e oskedas ici y Tes o Model 1 .................................................................................. 44
Figu e 5.6 - Residuals Agains Explana o y Va iables (Model 1) ........................................................... 45
Figu e 5.7 - He e oskedas ici y Tes o Model 2 .................................................................................. 46
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LIST OF TABLES
Table 4.1 - Da ase Va iable Desc ip ion ............................................................................................... 25
Table 4.2 - Desc ip i e S a is ics o he Dependen Va iable (on a na ional le el) ............................. 26
Table 4.3 - Missing Values by Domes ic Violence Ca ego y (Municipali ies) ........................................ 27
Table 4.4 - Missing Values o DVASA in Municipali ies and Di e ence Be ween Na ional To al and
Municipali y To al ......................................................................................................................... 27
Table 5.1 – O e all Summa y S a is ics ................................................................................................. 36
Table 5.2 - O e all, Be ween and Wi hin S anda d De ia ions ............................................................. 38
Table 5.3 - Pa ame e Es ima es o Model 1 ....................................................................................... 43
Table 5.4 - Pa ame e Es ima es o Model 2 ....................................................................................... 46
Table 5.5 - Pa ame e Es ima es o Model 3 ....................................................................................... 47
Table 5.6 - Pa ame e Es ima es o Model 4 ....................................................................................... 49
Table 5.7 - Pa ame e Es ima es o Model 5 ....................................................................................... 50
Table 5.8 - Pa ame e Es ima es o Model 6 ....................................................................................... 51
Table 5.9 - Pa ame e Es ima es o Model 7 ....................................................................................... 52
Table 5.10 - Pa ame e Es ima es o Model 8 ..................................................................................... 53
Table 5.11 - Pa ame e Es ima es o Model 9 ..................................................................................... 54
Table 6.1 - Model Compa ison .............................................................................................................. 55
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LIST OF ABBREVIATIONS AND ACRONYMS
AIC Akaike In o ma ion C i e ion
APAV Associação Po uguesa de Apoio à Ví ima
CC Cons an Coe icien s
DGEEC Di eção-Ge al de Es a ís icas da Educação e Ciência
DGPJ Di eção-Ge al da Polí ica de Jus iça
DVAM Domes ic Violence Agains Mino s
DVASA Domes ic Violence Agains Spouse o Analogous
FE Fixed E ec s
GAM Gene alized Addi i e Model
GBV Gende Based Violence
GER G oss En olmen Ra e
IPV In ima e Pa ne Violence
KNN K Nea es Neighbo s
OECD O ganiza ion o Economic Co-ope a ion and De elopmen
OMA Obse a ó io de Mulhe es Assassinadas da UMAR
RESET Reg ession Speci ica ion E o Tes
SC Schwa z C i e ion
SFI Syn he ic Fe ili y Index
WHO Wo ld Heal h O ganiza ion
YDI You h Dependency Index
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ac o , as a ound 34% o he ic ims we e ma ied. This is a ele an pe cen age when compa ed o
he 20.8% ha we e single, 16% whose ma i al s a us was unknown, 11.6% who we e in a non-ma i al
ela ionship, 8.7% who we e di o ced, 5.6% who we e sepa a ed and 3.3% who we e widowed.
The e o e, including a measu e o he numbe o ma ied people may be ele an .
S ill ega ding he ma i al s a us, (Bowlus & Sei z, 2006) inds ha women who a e se e ely abused by
hei husbands a e signi ican ly mo e likely o di o ce han women who do no ace his p oblem.
Howe e , i is impo an o no ice ha women may be mo e likely o epo iolence in a pas ma iage
han in a p esen one, causing an upwa d bias in his p obabili y. This s udy uses da a om all p o inces
o Canada, e ie ed in 1993. The ini ial analysis o his da a also e ealed ha women who
expe ienced abuse by hei pa ne s end o ha e lowe le els o educa ion and come om mo e
iolen backg ounds han women who did no ace abuse. The same applies o he pa ne s – husbands
who abuse hei wi es end o ha e lowe le els o educa ion. Ano he inding om his ini ial analysis
is ha women who a e no wo king a e mo e likely o ace abuse, which mee s he conclusions on
(Ande be g, Raine , Wadswo h, & Wilson, 2015). Acco ding o (WHO - Wo ld Heal h O ganiza ion,
2010), di o ces may no only be a consequence, bu also a cause o domes ic iolence. People who a e
sepa a ed o di o ced end o be mo e ulne able, inc easing hei p obabili y o becoming ic ims in
a u u e ela ionship.
This same epo by WHO lis s some o he causes o domes ic and sexual iolence included in he
li e a u e hey e iewed. Young age appea s o be a isk ac o o ei he becoming a ic im o in ima e
iolence o a pe pe a o . I is o eseeable ha popula ions wi h a highe p opo ion o young adul s
ha e highe a es o domes ic iolence occu ences. Lowe le els o educa ion a e also consis en ly
associa ed wi h bo h sides o he c ime ( ic im and pe pe a o ). A highe le el o educa ion may ac
as a p o ec i e ac o , since people wi h a highe le el o educa ion show lowe le els o in ima e
pa ne iolence. Ano he ac o associa ed wi h bo h he ic im and he pe pe a o is po e y. E en
hough domes ic iolence cu s ac oss all socioeconomic g oups, people wi h lowe incomes end o be
mo e a isk o becoming ei he a ic im o an agg esso . One explana ion o his, besides he
hopelessness, s ess and us a ion caused by his condi ion, is he ac ha sho age o money is a
common cause o ma i al a gumen s and makes i ha de o people o lea e oxic ela ionships, as
hey a e mo e inancially dependen on each o he . Some cha ac e is ics o he neighbo hood may
also in luence he numbe o IPV occu ences, such as a lowe p opo ion o women wi h highe le els
o educa ion, highe unemploymen a es, a highe p opo ion o illi e acy and a lowe p opo ion o
women wi h high le els o au onomy.
(Acke son, Kawachi, Ba beau, & Sub amanian, 2008) examined he ole o women’s educa ion and
p oxima e educa ional con ex on GBV in India. A sample o 83,627 ma ied women aged 15 o 49
yea s old om he 1998 o 1999 Indian Na ional Family Heal h Su ey was examined. The s udy
conside ed ha no only does he le el o educa ion o he woman he sel in luence he p obabili y o
becoming a GBV ic im, bu also does he gene al le el o educa ion o he communi y su ounding
he . The esul s o his pape show ha women wi h no educa ion a e 4.5 imes mo e likely o epo
ha ing su e ed om domes ic iolence a some poin in hei li e han women schooled o mo e han
12 yea s. Ano he ele an conclusion was ha he p obabili y o a woman who is li ing in he middle
and lowes e iles o emale li e acy o su e om domes ic iolence a some poin in he li e was
1.18 and 1.10 imes g ea e , espec i ely, han hose o women li ing in he highes e ile
neighbo hoods. This s udy shows he impac ha educa ion has on GBV.

8
Figu e 2.1 - Age o Domes ic Violence Vic ims (2013-2017)
9
3. THEORETICAL BACKGROUND
The heo e ical backg ound o he p esen s udy was mos ly w i en conside ing (Hill, G i i hs, & Lim,
2012) and (Woold idge, 2013).
3.1. PANEL DATA
Da a can be collec ed in mul iple o ma s. The mos widely discussed ones a e c oss-sec ional da a,
pooled c oss-sec ional da a, ime se ies da a and panel da a.
C oss-sec ional da a is da a collec ed o mul iple uni s ac oss he same pe iod. Each obse a ion
ep esen s a uni o he ele an popula ion. This is he “common” da ase s uc u e. When we
combine c oss-sec ional da a om di e en pe iods we c ea e a pooled c oss-sec ional da ase . In his
case, each obse a ion ep esen s a uni o he popula ion in a speci ic pe iod in ime. I is no
necessa ily ue ha he same uni s a e s udied o he di e en pe iods. I we a e s udying he same
uni ac oss di e en pe iods in ime, we c ea e a ime se ies. A ime se ies shows he e olu ion o ha
uni h ough a speci ied ime span. Finally, panel da a, also called longi udinal da a, is a combina ion
o c oss-sec ion and ime se ies da a. He e, we ha e one ime se ies o each included uni . The
iden i ie o he uni and he pe iod he da a e e s o a e shown as a iables in he da ase . The
p esen s udy ocuses on panel da a, as he e is one yea ly disc e e ime se ies o each Po uguese
municipali y. Panel da a analysis is a way o s udying a subjec in mul iple si es pe iodically obse ed
o e a ime ame.
Panel da a may be conside ed sho o long, balanced o unbalanced and ixed o o a ing. A panel
da a is conside ed sho when i s udies many uni s o a sho ime pe iod and i is conside ed long
when i s udies ew uni s o a long ime pe iod. In he case o he p esen s udy, a sho panel is being
examined as i has 11 ime pe iods and 278 uni s. A balanced panel has a numbe o obse a ions equal
o he numbe o uni s imes he numbe o pe iods, meaning ha all uni s a e obse ed o all pe iods.
I his is no he case, we ha e an unbalanced panel. The p esen s udy ocuses on a balanced panel as
all 278 municipali ies a e obse ed o all 11 yea s. Finally, i he same uni s a e obse ed o each
pe iod, he panel da a is ixed. I he se o uni s a ies om one pe iod o he nex he panel da a is
o a ing. In he case o his s udy, he 278 municipali ies a e ixed.
3.2. ECONOMETRIC PRIMER
Econome y s a s wi h a heo y abou how some ele an a iables a e ela ed o o he s. To exp ess
ou ideas ega ding hese ela ionships we use unc ions. Fo mos p oblems, i is no enough o know
in which di ec ion he a iables a e ela ed (i hey inc ease oge he , a y in opposi e di ec ions, e c.).
Ins ead, one needs o know he in ensi y o ha ela ion, which means how much a change in he alue
o one a iable will a ec he alue o he o he . To know hese pa ame e s o he ela ionship we
c ea e eg essions.
Be o e gene a ing an econome ic model, one mus keep in mind ha ela ions among a iables a e
no exac and, o his eason, no econome ic model explains he exac beha io o i s objec o s udy.
Ins ead, i desc ibes he a e age o sys ema ic beha io . This means ha when p esen ing esul s om
an econome ic model one mus always say “i is expec ed ha …”. Since he p edic ions a e no exac ,
he e is a di e ence be ween he ac ual alue and he p edic ed alue. This di e ence is he andom
10
componen o he model and is called he e o e m. I ep esen s all ac o s ha we e no included
in he model and includes he beha io unce ain y. The pa ha is explained by he model is he
sys ema ic componen o he o mula and i is decided by he in es iga o based on wha he heo y
al eady exis en s a es abou he p oblem ha is being s udied.
One can say ha he e o e m ep esen s all hings a ec ing he dependen a iable o he han he
explana o y a iables included in he model. I comp ises he e ec s o ele an a iables ha we e
excluded om he model, measu emen e o s in bo h he dependen and explana o y a iables, he
e ec s o using a linea o any o he o m o gene a e esul s ha do no ollow ha o m and, inally,
he na u al andomness o obse a ions.
To comple e a model speci ica ion, he esea che mus choose which a iables o include and how o
include hem, keeping in mind he algeb aic o m o he ela ions. This o m is also called he unc ional
o m and in he mos basic scena io, i is assumed o be linea . An econome ic model looks like he
o mula below whe e Y is he a iable being s udied (dependen a iable), Xi a e he a iables ha a e
assumed o a ec he beha io o Y (explana o y a iables), βi a e he coe icien s o he explana o y
a iables ha indica e how much hey a ec he dependen a iable and, inally, ei is he e o e m.
β0 is he expec ed alue o Y i all explana o y a iables a e 0 and is called he cons an o he model.
𝑌𝑖= 𝛽0+𝛽1𝑋1𝑖+𝛽2𝑋2𝑖+𝛽3𝑋3𝑖+𝑒𝑖
As i can be seen in he equa ion abo e ha ep esen s a mul iple eg ession linea model, he model
ela es a dependen a iable Y o a se o explana o y a iables (X1, X2 and X3) and o a andom e o
e m e. This emains ue o o he econome ic models, changing he se o explana o y a iables, he
unc ional o m, e c. The βs a e he pa ame e s ha a e es ima ed by he model and hey can be
in e p e ed o explain he ela ionships among a iables. In he example abo e, one can say ha a
change in X1 o one uni will ep esen a change o β1 uni s in Y, holding e e y hing else cons an . Taking
his in o accoun , one can s a o unde s and ha he alues calcula ed using an econome ic model
a e, in ac , a condi ional a e age. The p edic ed alue o Y is he a e age o Y i he explana o y
a iables assume a se o ixed alues. Le us conside he example o he p esen s udy: he p obabili y
densi y unc ion o Domes ic Violence Agains Spouse o Analogous (DVASA) is illus a ed in Figu e
3.1 below, wi h a g ay dashed line indica ing he a e age alue.
Figu e 3.1 - P obabili y Densi y Func ion o DVASA
Sys ema ic Componen
Random Componen
11
I we ha e a simple linea eg ession model, wi h only one explana o y a iable (le us conside
Educa ion as he only explana o y a iable), he p edic ed alue o DVASA in a gi en poin would be
he a e age alue o DVASA when Educa ion a ains a ce ain alue. The e o e, we can calcula e a
condi ioned p obabili y densi y unc ion and ind i s a e age o ind he p edic ed alue. Figu e 3.2
below shows he plo o he p obabili y densi y unc ion o DVASA condi ioned o when he a iable
GER (a measu e o educa ion – u he explana ion on Chap e 4.2) is a i s mos common alue. One
can see ha he a e age alue o his new dis ibu ion shi ed sligh ly o he igh when compa ed o
he gene al dis ibu ion o DVASA. These a e he di e ences ha will be e lec ed in an econome ic
model.
Figu e 3.2 - Condi ional P obabili y Densi y Func ion o DVASA (GER=70.16)
The e a e nume ous ypes o econome ic models. The simples one akes only one explana o y
a iable and is called he simple linea eg ession model. I we include mo e han one explana o y
a iable, we a e c ea ing a mul iple eg ession model. Econome ics also con empla es models o ime
se ies and panel da a.
To unde s and how an econome ic model is es ima ed he bes op ion is o i s s udy he simple
linea eg ession model. In he p e ious example we conside ed DVASA as ou dependen a iable and
GER as he only explana o y a iable. We can plo he ela ionship be ween hese a iables o see how
good o an app oach we ge . Figu e 3.3 below shows a sca e plo o he wo a iables on he le . On
he igh side o he same igu e, we added an app oxima ion line o p edic DVASA based on GER.
Howe e , adding a line is no gua an ee ha he expec ed alue o he e o s is 0, so he bes app oach
is o use he Leas Squa es Es ima o s.
Figu e 3.3 - G aphical Rela ion Be ween GER and DVASA
12
To es ima e he in e cep and he slope o he op imal line ha desc ibes he ela ionship be ween
he dependen a iable and he explana o y a iable we wan o make use o all obse a ions a ailable.
The leas squa es p inciple says ha we should add he line in a way so ha he sum o squa es o he
e ical dis ances be ween he obse a ions and he i ed line is minimized. I is impo an o squa e
hese dis ances so ha posi i e dis ances do no cancel nega i e ones. These e ical dis ances a e he
esiduals, hence he desi e o minimize hem. The sum o squa es we wish o minimize is gi en by:
𝑆(𝛽0,𝛽1)= ∑(𝑦𝑖−𝛽0−𝛽1𝑋1𝑖)2
𝑛
𝑖=1
The unc ion abo e is quad a ic in e ms o β0 and β1 and is shaped like a bowl. To ind i s minimum
alue we need o ind he bo om o he bowl, which occu s whe e he slope o he bowl in he
di ec ion o each axis is 0. This is he same as saying ha i occu s whe e he pa ial de i a i es o S
conce ning β0 and β1 a e 0. By calcula ing hese pa ial de i a i es, we ob ain:
𝜕∑(𝑦𝑖−𝛽0−𝛽1𝑥𝑖)2
𝑛
𝑖=1 𝜕𝛽0=0 ⇔𝛽0= 𝐸(𝑦𝑖)−𝛽1𝐸(𝑋1𝑖)
𝜕∑(𝑦𝑖−𝛽0−𝛽1𝑥𝑖)2
𝑛
𝑖=1 𝜕𝛽1=∑𝑦𝑖𝑋1𝑖 − 𝛽0∑𝑋1𝑖 −𝛽1∑𝑋1𝑖
2
We can hen eplace β0 as gi en by he i s equa ion in he second one and ob ain:
∑𝑦𝑖𝑥𝑖−(𝐸(𝑦𝑖)−𝛽1𝐸(𝑥𝑖))∑𝑥𝑖−𝛽1∑𝑥𝑖2=0 ⇔𝛽1=𝐸(𝑦𝑖)𝐸(𝑥𝑖)−∑𝑦𝑖𝑥𝑖
𝑛
𝐸(𝑥𝑖)2−∑𝑥𝑖2
𝑛
These a e he o mulas o he leas -squa es es ima o s in he simple linea eg ession model and hey
can be used ega dless o wha he dependen o explana o y a iables a e.
E en hough he simple linea eg ession model is he easies o unde s and, mos eal-li e
econome ic models ake wo o mo e explana o y a iables, c ea ing mul iple eg ession models.
Mos o he conclusions ega ding he simple linea eg ession model can be adap ed o his ype o
model, excep o some changes in he in e p e a ion o he coe icien s and in he deg ees o eedom
o he T dis ibu ions.
In a mul iple eg ession model, we ha e se e al explana o y a iables and we wan o quan i y he
impac o each o e he dependen a iable, while con olling he e ec s o he emaining ones. This
is he no ion o ce e is pa ibus (see Chap e 3.3). Le us con inue using he same example whe e DVASA
is he dependen a iable and GER is he explana o y a iable, excep ha his ime we a e adding
unemploymen as ano he explana o y a iable. We hen ob ain he ollowing heo e ical model:
𝐷𝑉𝐴𝑆𝐴𝑖= 𝛽0+𝛽1𝐺𝐸𝑅𝑖+𝛽2𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡𝑖+𝑒𝑖
The βs in he abo e model measu e he change in he dependen a iable DVASA gi en a change o
one uni in he espec i e explana o y a iable, while holding e e y hing else cons an . The expec ed
impac o an explana o y a iable in he dependen a iable is gi en by i s pa ial de i a e:
𝜕𝑦
𝜕𝑥

13
The objec i e in a mul iple eg ession model is he same as i was in he simple eg ession model – o
minimize he sum o squa es o he e ical dis ances be ween he obse a ions and he i ed line.
The di e ence is ha his ime we need o wo k wi h ma ices o ind he leas -squa es es ima o s. In
ma ix no a ion, he model is gi en by: 𝑌=𝑋𝛽+𝑒
In he p e ious equa ion Y is a ma ix wi h only 1 column and n (n being he numbe o obse a ions)
ows con aining he obse ed alues o he dependen a iable. X is a ma ix wi h n ows and k+1
columns (whe e k is he numbe o explana o y a iables). The i s column in he X ma ix only
con ains ones and will be used o calcula e β0. The emaining columns in X con ain he obse ed alues
o he explana o y a iables and will be used o calcula e he espec i e βs. The ma ix β has k+1 ows
and only one column, con aining he alues o he leas -squa es es ima o s. Finally, he ma ix e has n
ows and only one column con aining he esiduals o each obse a ion.
In his case, minimizing he sum o squa es o he esiduals is he same as minimizing he ollowing
(whe e he T means ansposed):
∑ 𝑒𝑖2
𝑛
𝑖=1 = 𝑒𝑇𝑒=(𝑌−𝑋𝛽󰆹)𝑇(𝑌−𝑋𝛽󰆹)=𝑌𝑇𝑌−2𝑌𝑇𝑋𝛽󰆹+𝛽󰆹𝑇𝑋𝑇𝑋𝛽󰆹
To de e mine he alues o he es ima o s ha minimize he sum o squa es we need o di e encia e
he abo e exp ession and equal i o 0, as we did wi h he simple eg ession model. We hen ob ain:
𝜕(𝑌𝑇𝑌−2𝑌𝑇𝑋𝛽󰆹+𝛽󰆹𝑇𝑋𝑇𝑋𝛽󰆹)
𝜕𝛽󰆹=0⇔𝛽󰆹=(𝑋𝑇𝑋)−1𝑋𝑇𝑌
3.3. CAUSAL RELATIONSHIPS AND CETERIS PARIBUS
The goal in eg ession analysis is o ind causal ela ionships be ween a iables, ha is, o de e mine
whe he a change in X causes a change in Y. To exp ess ou ideas ega ding he ela ionships be ween
a iables we use unc ions. Fo example, o exp ess a ela ionship be ween domes ic iolence and
educa ion one can w i e:
𝐷𝑜𝑚𝑒𝑠𝑡𝑖𝑐_𝑉𝑖𝑜𝑙𝑒𝑛𝑐𝑒=𝑓(𝐸𝑑𝑢𝑐𝑎𝑡𝑖𝑜𝑛)
The p e ious unc ion is a possible no a ion o say ha he domes ic iolence occu ences in a ce ain
place a e a unc ion o he educa ion le el o he people esiding in ha same place. This is he same
as saying ha he places whe e domes ic iolence occu s depend on he p e alen educa ional le el in
hose places. Howe e , he occu ences may no depend only on educa ion, hey may depend on many
o he ac o s as well. Keeping his in mind, o unde s and he ela ionship be ween domes ic iolence
occu ences and educa ion i is impo an o se aside he impac s o he emaining ac o s on domes ic
iolence. The idea o ce e is pa ibus (c.p.) means o hold all o he ac o s cons an and is a key poin in
es ablishing causal ela ionships. Wi hou holding he emaining a iables cons an one does no show
ha he change obse ed in y is caused by he change in x. This is also he eason why a simple
co ela ion s udy is no enough o analyze causal ela ionships.
When we a e s udying he causal e ec o x on y, he emaining a iables ha in luence y a e called
he con ol a iables. The eason o con ol o hese a iables is simple: we belie e ha x is co ela ed
wi h o he ac o s in luencing y, which means ha no holding hese a iables cons an will make hei
14
e ec s e lec on he coe icien o x. Since we eed da a o he eg ession model, i is impo an o
co ec ly de e mine he con ol a iables ha need o be held ixed. This is a c i ical pa o eg ession
analysis bu may be ha d, as usually no all ac o s in luencing he dependen a iable a e obse able
o accessible. When one does no include an impo an con ol a iable, i s e ec s a e e lec ed on he
pa ial e ec s o o he ac o s, making he la e inco ec .
S a ing he di e ence be ween explana o y a iables and con ol a iables may be ha d. E en i some
a iables can be conside ed con ol a iables on all occasions, all explana o y a iables a e e en ually
con ol a iables when i comes o explaining he pa ial e ec s o ano he a iable. Fo panel da a,
he a iables ha de e mine he di e ence be ween obse a ions (in he case o his s udy:
municipali y and yea ) a e always con ol a iables as, e en i hey can explain pa o he a iance in
he da a, hei main goal is o dis inguish be ween obse a ions.
3.4. ECONOMETRIC ASSUMPTIONS
In e e y econome ic s udy, he e a e a leas wo models: he heo e ical model and he empi ical
one. The heo e ical model desc ibes a beha io bu is an abs ac ion o eali y. To con e he
heo e ical model in o an empi ical one, some assump ions mus be made. These assump ions a e e y
impo an because i hey a e e i ied ou conclusions a e wa an ed. Howe e , i ou model does no
mee hem, he conclusions may no be ue.
The i s assump ion is ha he a iance o he dependen a iable is a cons an o each alue o X.
This means ha in he case o he example using DVASA as he dependen a iable and GER as he
explana o y a iable, o each alue ha GER may ake, he a e age o DVASA may be di e en , bu
he measu e o how much i a ies a ound ha a e age mus be he same. This leads o a u he
assump ion ha he e o e m mus ha e a cons an a iance as well. When his condi ion is sa is ied,
he da a is said o be homoskedas ic. When his condi ion is iola ed, he da a is said o be
he e oskedas ic.
The second assump ion is ha he dependen a iable is no only andom bu also s a is ically
independen . This means ha he alue o one obse a ion is no dep,enden on he alue o ano he
obse a ion. In he DVASA example his means ha he alue o DVASA o one municipali y is no
dependen on he alues o o he municipali ies on he da ase . Ins ead o assuming he
independence o he a iables, we o en assume ha he co a iance o he a iable is 0. Again, in he
DVASA example, his means ha i 𝑌𝑗 and 𝑌𝑖 a e he alues o DVASA o wo di e en municipali ies,
𝑐𝑜𝑣(𝑌𝑗,𝑌𝑖)=0.
The hi d assump ion is also ela ed o a iance. Since he main goal o an econome ic s udy is o
unde s and how changes in he explana o y a iables a ec he dependen a iable, i is impo an
ha he explana o y a iables a e sca e ed enough. Ob iously, i he e is no a iance in he
explana o y a iables i is impossible o jus i y changes in he dependen a iable om changes in he
explana o y a iables. The e o e, i is assumed ha he explana o y a iables ake a leas wo alues.
The ou h assump ion is ela ed o he e o e m o he eg ession. Since he o al e o o he model
is he sum o he de ia ions be ween he ac ual alue o an obse a ion and he p edic ed alue o i
and he objec i e o a eg ession is o minimize hese de ia ions, i is assumed ha he expec ed alue
o he e o , e m is 0. Fu he mo e, in a simple eg ession model i is also assumed ha he expec ed
15
alue o he e o e m gi en he explana o y a iable is also 0. This is demons a ed in he equa ion
below. I is impo an o emembe ha he expec ed alue o he dependen a iable gi en he
explana o y a iable is he p edic ed alue so 𝐸(𝑦|𝑥)=𝛽0+𝛽1𝑋1.
𝐸(𝑒|𝑥)=𝐸(𝑦|𝑥)−𝛽0−𝛽1𝑋1=0
Finally, some imes i is also assumed ha he e o e m ollows a no mal dis ibu ion cen e ed a ound
0. This is an op ional assump ion, bu i is a s ong one as he p obabili y dis ibu ion o he pa ame e s
es ima ed in he eg essions (βs) depends on he dis ibu ion o he e o e m which means ha his
is an impo an assump ion o s a is ical analysis o he model. Howe e , i he e a e enough
obse a ions one can base he conclusions on he cen al limi heo em ha es ablishes ha i he
sample is la ge enough, he dis ibu ion o he sample means will be app oxima ely no mally
dis ibu ed.
These assump ions exis so ha we can de e mine he quali y o he leas -squa es es ima o s. These
es ima o s a e supposed o be cen e ed and e icien . An e icien es ima o is one wi h minimal
a iance.
When he expec ed alue o an es ima o equals he eal alue o he pa ame e i is ying o es ima e
we say ha we a e dealing wi h a cen e ed es ima o . This means ha he expec ed alues o he
es ima o s o he βs mus be equal o he βs. In he simple eg ession model his would mean ha :
𝐸(𝛽1
)=𝛽1 𝑎𝑛𝑑 𝐸(𝛽0
)=𝛽0
These equa ions a e only ue i he expec ed alue o he e o is 0, he e o is no co ela ed wi h
he a iables and he da a is coming om a andom sample.
The a iance o an es ima o is also key o e alua ing i s eliabili y. I measu es how much he alues
ha he es ima o may ake a e sp ead and, because o i , ends up measu ing he p ecision o he
es ima o . Keeping his in mind, he smalle he a iance o an es ima o , he mo e p ecise i will be.
Fo he simple eg ession model, when we calcula e he a iance o he es ima o s we ge :
𝑉𝑎𝑟(𝛽1
)= 1
∑(𝑥𝑖−𝑥)2𝜎2 𝑎𝑛𝑑 𝑉𝑎𝑟(𝛽0
)=𝜎2(∑𝑥𝑖2
𝑛∑(𝑥𝑖−𝑥)2)
No ice ha σ2 s ands o he a iance o he e o e m and appea s on bo h exp essions. We can see
ha he la ge he a iance o he e o e m, he la ge he a iance o bo h es ima o s and,
consequen ly, he mo e imp ecise he es ima ion. We can also conclude ha o he es ima o o be
e icien , he a iance o he e o e m mus be cons an . Fu he mo e, we can see ha he sum o
he squa ed dis ances o x o i s a e age is on bo h exp essions on he denomina o . This means ha
he la ge he dispe sion o he alues in x, he smalle he a iance o es ima o s, hus, he mo e
p ecise hey a e. This means ha choosing a sample ha is di e se in e ms o he alues in he
explana o y a iables con ibu es o a highe p ecision o es ima o s.
An impo an heo em ega ding he assump ions in an econome ic model is he Gauss-Ma ko
heo em. I s a es ha i he undamen al assump ions a e e i ied, he es ima o s o he βs a e he
ones wi h he leas a iance ou o all he cen e ed es ima o s. This means ha hey a e he BLUE (Bes
Linea Unbiased Es ima o s).
16
When one is applying a mul iple eg ession model, a new assump ion mus be e i ied. Tha is ha
none o he explana o y a iables is a pe ec linea combina ion o ano he . When his assump ion is
no e i ied, we a e acing pe ec mul icollinea i y and he leas -squa es es ima o s canno be
calcula ed.
3.5. STATISTICAL TESTS
When we es ima e he coe icien s o a eg ession, we a e making a punc ual es ima e o he
eg ession pa ame e s. These es ima es ep esen an in e ence o e he eg ession model because
a e we calcula e he alues o he pa ame e s o ou sample, we in end o make an in e ence o
he esul s o be applied o he popula ion.
To make in e ences we eso o in e al es ima ion and hypo hesis es s. Bo h hese p ocedu es a e
s ongly based on he assump ion ha he esiduals in he model ollow a no mal dis ibu ion. I his
assump ion is no e i ied, i is necessa y o gua an ee ha he sample is la ge enough o assu e ha
he leas -squa es es ima o s ollow an app oxima ely no mal dis ibu ion h ough he cen al limi
heo em. When eso ing o his heo em he es s and in e als can be calcula ed, bu hei esul s
a e only app oxima e.
A hypo hesis es allows us o e alua e he possibili y ha a pa ame e is equal o some alue. In each
hypo hesis es , he e mus be a null hypo hesis, an al e na i e hypo hesis, a es s a is ic, a c i ical
egion, and a conclusion. The null hypo hesis is deno ed as H0 and mos o he ime equals he
pa ame e being es ed o a speci ic alue. I is he hypo hesis ha we in end o accep o ejec
acco ding o he s a is ical e idence. Pai ed o any null hypo hesis he e is an al e na i e one, deno ed
as H1. I is usually he con a y o he null hypo hesis and is he one ha is accep ed i he null
hypo hesis is ejec ed.
To decide whe he he null hypo hesis is accep ed o ejec ed, we mus ake in o conside a ion he
alue o he es s a is ic. The dis ibu ion o his s a is ic is known i he null hypo hesis is ue bu is
unknown o he wise.
The c i ical egion o ejec ion egion o a hypo hesis es depends on he o m o he al e na i e
hypo hesis. I consis s o he alues ha ha e a uly low p obabili y o occu ing i he null hypo hesis
is ue. The logic behind his is ha i he es s a is ic alls in o he ejec ion egion i is e y unlikely
ha he null hypo hesis is ue. To de ine his egion we mus de ine a le el o signi icance o he es .
The le el o signi icance o a es is he p obabili y o ejec ing he null hypo hesis while i is ac ually
ue. This is also called a ype I e o . The le el o signi icance is commonly designa ed by α and is
usually ei he 0.01, 0.05 o 0.1. Ano he impo an concep when men ioning he signi icance o a es
is he p- alue. The p- alue is he minimal le el o signi icance wi h which we can ejec he null
hypo hesis. I he p- alue is less han he de e mined le el o signi icance we ejec he null hypo hesis.
I is impo an o always emembe while pe o ming a hypo hesis es ha hese es s a e no able o
p o e ha a null hypo hesis is ue o alse. We can only conclude i he da a is compa ible wi h ha
hypo hesis o no .
One o he mos impo an hypo hesis es s when i comes o econome ic models is abou he
indi idual signi icance o he es ima ed pa ame e s. Fo his, we es he hypo hesis o a pa ame e
being 0, which would mean ha he e is no signi ican ela ionship be ween he dependen a iable
23
impossible i he numbe o coe icien s o be es ima ed su passes he numbe o obse a ions o
each uni . One way o a oid his p oblem is by using an al e na i e e sion o he ixed e ec s model,
in which only he cons an in he model di e s om uni o uni . This can be w i en, conside ing h ee
explana o y a iables, as ollowing:
𝑦𝑖𝑡 = 𝛽0𝑖 +𝛽1𝑥1𝑖𝑡 +𝛽2𝑥2𝑖𝑡 +𝛽3𝑥3𝑖𝑡 +𝑢𝑖𝑡
One can see ha in he p e ious equa ion only he i s β has he subsc ip i, meaning ha all
di e ences be ween indi iduals a e assumed o be cap u ed by he in e cep in he model. One way
o es ima e his simple e sion o he ixed e ec s model is by c a ing a dummy a iable o each uni
ha se es as an iden i ie o which indi idual he obse a ion belongs o. By assuming he alue 0 o
1 acco ding o whe he he obse a ion e e s o he uni o no , he co esponding coe icien will be
igno ed o obse a ions ha do no belong o he espec i e uni (by being mul iplied by 0). In o de
o a oid p oblems ela ed o mul icollinea i y, one uni mus se e as he base o he o he s, which
means ha one uni does no ha e a co esponding dummy a iable and is hen ep esen ed by a
cons an in he model. The emaining coe icien s ep esen he di e ences in he cons an ega ding
he base uni o he emaining indi iduals. I is impo an o no ice ha , in sho panels, he
coe icien s o he dummy a iables a e calcula ed using as many obse a ions as he numbe o imes
pe iods con empla ed o each uni , meaning ha p obably he cen al limi heo em does no apply
anymo e. Keeping his in mind, in e ences on he coe icien s o he dummy a iables need no mally
dis ibu ed e o s in o de o be alid.
Fixed e ec s models can ha e di e en coe icien s o he c oss-sec ional uni s, o he ime pe iods
o o bo h. The base idea is always he same – o e lec he ixed e ec s o each o hese componen s
di e en ly.

24
4. DATA EXPLORATION
The da ase is composed by 19 explana o y a iables and he dependen a iable (DVASA occu ences).
The me hods used o calcula ing, ea ing, and s anda dizing all o hese a iables a e explained in he
nex pages o his s udy. The da ase ollows a panel da a s uc u e, ha ing a column o he spa ial
dimension (Municipali y) and one o he empo al dimension (Yea ). A summa y o he exis ing
a iables can be ound on Table 4.1, below:
Va iable Name
Desc ip ion
Municipali y
Spa ial Dimension o he Da ase .
Yea
Tempo al Dimension o he Da ase .
DVASA
Numbe o DVASA Occu ences Regis e ed
by Police Au ho i ies by 100
Inhabi an s.
Di o ces
Numbe o Di o ces o 100 Ma iages in
ha Ci il Yea .
Elde ly_Dependency
Numbe o People Aged 65 and O e o
E e y 100 People o Wo king Age, ha
is, Be ween 15 and 64 Yea s Old.
Female_Doc o s
Pe cen age o Doc o s En olled in he
Doc o ’s O de Who A e Female.
Fe ili y
A e age Numbe o Child en Bo n o
Each Woman in Fe ile Age (Be ween 15
and 49 Yea s Old).
GER
Pe cen age o he Residen Popula ion
wi h No mal Age o A ending High
School ha is Ac ually A ending High
School.
GER_Men
Pe cen age o he Male Residen
Popula ion wi h No mal Age o
A ending High School ha is Ac ually
A ending High School.
GER_Women
Pe cen age o he Female Residen
Popula ion wi h No mal Age o
A ending High School ha is Ac ually
A ending High School.
Ma iages
Numbe o New Ma iages pe 100
Inhabi an s.
Men65
Pe cen age o he To al Popula ion o
he Municipali y ha Rep esen s Men
Wi h 65 Yea s o Mo e.
Men al_Heal h
Pe cen age o To al_Doc o s ha a e
Specialized in Psychia y acco ding o
he Doc o ’s O de .
Middle_Aged_Women
Pe cen age o he To al Popula ion o
he Municipali y ha Rep esen s Women
Be ween 25 and 54 Yea s Old.
Mon hly_Gain
A e age G oss Amoun ha he Employees
in he Municipali y Recei e E e y Mon h
Including basic emune a ion and O he
Remune a ion Paid by he Employe
(O e ime, Holiday Pay o P emiums).
SS_Pensions
Numbe o Pensione s o Each Pe son
who Cashes o Social Secu i y. A
25
Pension is an Amoun A ibu ed Each
Mon h o Someone in he E en o
Disabili y, Old Age, Occupa ional
Disease o Dea h.
To al_Doc o s
Numbe o Doc o s by 100 Inhabi an s
Acco ding o he Doc o ’s O de .
Unemploymen _Female
Numbe o Women En olled in Employmen
and Voca ional T aining Cen e s pe 100
Inhabi an s.
Unemploymen _Male
Numbe o Men En olled in Employmen
and Voca ional T aining Cen e s pe 100
Inhabi an s.
Unemploymen _To al
Numbe o people En olled in Employmen
and Voca ional T aining Cen e s pe 100
Inhabi an s.
You h_Dependency
Numbe o Child en Unde 15 Yea s Old
o E e y 100 People o Wo king Age,
ha is, Be ween 15 and 64 Yea s Old.
Wage_Gap
Pe cen age o Men’s Mon hly Gain ha
Women Recei e on A e age.
Table 4.1 - Da ase Va iable Desc ip ion
4.1. DEPENDENT VARIABLE
Th ee da ase s con aining in o ma ion ega ding he dependen a iable we e e ie ed om he
o icial s a is ics websi e by DGPJ on he 4 h o Ma ch o 2021. One con aining in o ma ion abou he
numbe o domes ic iolence occu ences na ionwide, one wi h his da a spli by dis ic s and a las
one wi h he da a spli by municipali ies. All o hem con ained in o ma ion ega ding h ee ca ego ies
(as explained in Chap e 1. In oduc ion): domes ic iolence agains spouse o analogous (DVASA),
domes ic iolence agains mino s (DVAM) and o he s. Finally, o all h ee da ase s, he da a was
collec ed o he pe iod be ween 2008 and 2019, due o da a a ailabili y.
The Po uguese C iminal Code p o ides o and punishes he c ime o domes ic iolence. Domes ic
iolence assumes he na u e o a public c ime, which means ha he c iminal p ocedu e is no
dependen on a complain by he ic im, jus a complain o knowledge o he c ime is enough o he
Public Minis y o p omo e he p ocess. Thus, in Po ugal, he egis e ed numbe o occu ences o
domes ic iolence does no depend only on sel - epo by he ic im. Howe e , as i is a c ime ha
commonly akes place in he p i acy o a home, many cases may depend on sel - epo . The da ase
ob ained ocuses on da a egis e ed by police au ho i ies and, acco ding o (Ellsbe g, Heise, Peña,
Agu o, & Wink is , 2001), may su e om unde epo ing, as i depends on sel - epo o some
ex en .
The da a eco ded o Po ugal as a whole is a disc e e ime se ies. Fo each ca ego y he e is a se o
12 obse a ions eco ded a uni o mly spaced ime alues, in his case, yea s. This emains ue o he
da a ega ding dis ic s and municipali ies, excep ha , o he i s case, he e is one ime se ies pe
ca ego y and pe dis ic , and o he second case he e is one ime se ies pe ca ego y and pe
municipali y.
The e olu ion o he numbe o domes ic iolence occu ences in Po ugal can be seen abo e in Figu es
1.1 and 1.2. I becomes clea by he analysis o hese igu es and o he desc ip i e s a is ics on Table
26
4.2 ha domes ic iolence agains spouse o analogous is he mos p ominen ca ego y ou o he
h ee. One can see ha , be ween 2008 and 2019, he yea ly a e age o domes ic iolence occu ences
was 27,394. Conside ing he same pe iod, he yea ly a e age o he DVASA ca ego y was 22,977.8, a
alue ha clea ly shows how ele an his ca ego y is o he o al domes ic iolence occu ences. The
emaining ca ego ies ha e less signi ican yea ly a e ages.
DVASA
DVAM
O he s
To al
Occu ences
S d
1226.32
75.22
435.55
1612.36
Minimum
20394.00
430.00
3083.00
24157.00
Mean
22977.80
537.92
3879.17
27394.90
Maximum
25129.00
680.00
4651.00
30340.00
Q3
23382.80
599.00
4039.00
27877.00
Median
22851.50
515.50
3800.00
27155.00
Q1
22457.50
484.00
3647.75
26683.50
Table 4.2 - Desc ip i e S a is ics o he Dependen Va iable (on a na ional le el)
When compa ing he e olu ion o o al occu ences in Po ugal (Figu e 1.1) wi h he e olu ion o
occu ences o DVASA (Figu e 1.3), one can de ec he same pa e ns. By calcula ing he di e ence in
he numbe o occu ences o subsequen yea s, i is possible o no ice ha DVASA occu ences
almos always jus i y o e hal o he g ow h o dec ease in he numbe o o al occu ences. This is
only no ue o 2014, when he numbe o DVASA occu ences inc eased by 35 bu he numbe o
o al domes ic iolence occu ences dec eased by 48 due o a dec emen in he o he ca ego ies.
Figu e 4.1 shows exac ly his.
Figu e 4.1 - Absolu e Change in To al and DVASA Occu ences (on a na ional le el)
Since he da ase s only ha e 12 yea s wo h o da a, i would no be possible o pe o m a ime se ies
eg ession o Po ugal as a whole, as he e would no be enough deg ees o eedom o p o ide
powe ul es ima es. Keeping his in mind, a panel da a eg ession will be pe o med wi h da a
ega ding he yea s and municipali ies. Fo his pu pose, he da ase con aining in o ma ion abou
domes ic iolence occu ences by municipali y mus be analyzed.
Po ugal is di ided in o 18 dis ic s and 2 au onomous egions. Each o hese is subdi ided in o
municipali ies. Cu en ly, Po ugal has 308 municipali ies. The municipali y da a e ie ed om he
o icial s a is ics websi e by DGPJ measu ed he h ee domes ic iolence ca ego ies o he 308
Po uguese municipali ies and o an ex a N.E. one, meaning no speci ied (não especi icado in
Po uguese). Since i would no be possible o ind he explana o y a iables alues o his special
27
case, his ex a municipali y was elimina ed om he da ase . Fu he mo e, 12 o he 308
municipali ies did no ha e alues o all he ca ego ies. Co o, he smalles island in he Au onomous
Region o he Azo es, only had da a o he DVASA ca ego y. The emaining 11 municipali ies
(Pampilhosa da Se a, Golegã, Ribei a de Pena, Vila de Rei, Ba ancos, Vila Viçosa, Penela, Alcou im,
Al ândega da Fé, São Roque do Pico e Aguia da Bei a) we e missing da a o he DVAM ca ego y.
The s a is ical con iden iali y p inciple is s a ed in Diá io da República ( he Po uguese o icial gaze e)
in Law nº22/2008, he ac ha legisla es on he Na ional S a is ical Sys em. This p inciple, e e ed o
in a icle 6 o he men ioned law, aims o sa egua d ci izens' p i acy and secu e us in he S a is ical
Sys em. The e o e, in he e ie ed da ase s, in o de o espec he p i acy o he people in ol ed,
numbe s below 3 a e no p esen ed, being symbolized as missing alues. Keeping his in mind, he
numbe o missing alues was calcula ed o each ca ego y. As one can see om Table 4.3, he e we e
a o al o 4,356 missing alues among he h ee ca ego ies. The majo i y o hese can be ound in he
DVAM and O he s ca ego ies. The missing alues o DVASA ep esen only a ound 2.3% o he o al
missing alues in he dependen a iable da ase .
Ca ego y
Numbe o Missing Values
DVASA
100
DVAM
2,862
O he s
1,394
To al
4,356
Table 4.3 - Missing Values by Domes ic Violence Ca ego y (Municipali ies)
As men ioned be o e and seen on Figu e 4.1, DVASA is he mos p ominen ca ego y in he o al
domes ic iolence occu ences in Po ugal. Adding his o he ac s ha i is also he ca ego y wi h he
leas missing alues (Table 4.3) and ha i is he only ca ego y measu ed o all 308 municipali ies, one
can conclude ha his is he bes dependen a iable o he p esen s udy.
In o de o be e unde s and he missing alues and o ind he bes way o impu e hem, he
di e ence be ween he na ional alues o each yea and he sum o he alues o each municipali y
in each yea was calcula ed (including he alues o N.E.). This can be seen on Table 4.4. One can see
ha he numbe o missing alues o he municipali ies in each yea is always e y close o he numbe
o occu ences epo ed on he na ional le el bu un epo ed on a municipal le el. In o de o add ess
his, he missing alues we e eplaced by he alue 1 as i was conside ed be e o keep in o ma ion
abou municipali ies wi h low occu ences han o emo e hem al oge he om he s udy.
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Missing
Values
21
16
6
7
5
7
9
8
4
6
4
7
Di e ence
27
21
8
7
6
10
7
12
4
10
3
10
Table 4.4 - Missing Values o DVASA in Municipali ies and Di e ence Be ween Na ional To al and Municipali y To al
I is impo an o keep in mind ha he e ie ed da a was measu ed as an absolu e alue, which means
ha i did no conside he di e ences in he numbe o inhabi an s o each municipali y. Keeping he
da a as i was would ha e biased he u u e model, o cing i in o hinking ha he highe numbe o
domes ic iolence occu ences in municipali ies wi h he mos popula ion was caused by ac o s o he
han he numbe o inhabi an s. In o de o a oid his p oblem, he numbe o DVASA occu ences was
28
s anda dized acco ding o he esiden popula ion in each municipali y, as shown below. This way, he
dependen a iable is now he numbe o DVASA occu ences pe 100 inhabi an s.
𝐷𝑉𝐴𝑆𝐴𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑧𝑒𝑑 = 𝐷𝑉𝐴𝑆𝐴𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒
(𝑇𝑜𝑡𝑎𝑙 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
100 )
The da a ega ding esiden popula ion by municipali y used o s anda dize he dependen a iable
was e ie ed om he Po da a websi e on he 23 d o Ap il o 2021. The de ini ion o esiden
popula ion in his case is he g oup o people who, ega dless o being p esen o absen in a pa icula
accommoda ion a he ime o obse a ion, li ed in hei usual place o esidence o a con inuous
pe iod o a leas 12 mon hs p io o he ime o obse a ion, o who a i ed a hei usual place o
esidence du ing he pe iod co esponding o he 12 mon hs p eceding he momen o obse a ion,
wi h he in en ion o emaining he e o a minimum pe iod o one yea .
4.2. EXPLANATORY VARIABLES
When modelling domes ic iolence one can con empla e wo ypes o a iables: isk ac o s and
p o ec i e ac o s. The i s ones, as he name sugges s, inc ease he isk o domes ic iolence, causing
a high numbe o occu ences when e y p esen . P o ec i e ac o s do he opposi e, bu ing he isk
o domes ic iolence. The iden i ica ion o isk ac o s is e y impo an o he p e en ion o iolence
and o guide policies. Bo h ypes o ac o s can be di ided in o modi iable ( o example educa ion) and
non-modi iable ( o example gende and age) ac o s. The i s ones a e he mos impo an when i
comes o de ining p e en ion policies, o logical easons.
Acco ding o (Ellsbe g, Heise, Peña, Agu o, & Wink is , 2001) indi iduals belonging o amilies wi h
mo e child en a e mo e p one o su e assaul s. As a way o include his ac o in he p esen s udy,
he syn he ic e ili y index (SFI) was conside ed as an explana o y a iable. This index is he a e age
numbe o child en bo n o each woman in e ile age (be ween 15 and 49 yea s). In o de o he
gene a ion enewal o be assu ed, he syn he ic e ili y index mus be a 2.1. The da a ega ding his
a iable was e ie ed om he Po da a websi e on he 15 h o Ap il o 2021 and included da a om
2009 o 2019.
Ano he measu e o he numbe o child en is he you h dependency index. The da a o his a iable
was e ie ed om he Po da a websi e on he 6 h o May o 2021. The you h dependency index is he
numbe o child en unde 15 yea s old o e e y 100 people o wo king age, ha is, be ween 15 and
64 yea s old. A alue less han 100 means ha he e a e ewe young people han people o wo king
age. This a iable had da a o all he municipali ies (wi hou missing alues) o he pe iod be ween
2009 and 2019.
Heal hca e wo ke s play an impo an ole in unco e ing domes ic iolence occu ences and
suppo ing he ic ims. Acco ding o (Cann, Wi hnell, Shakespea e, Doll, & Thomas, 2001), among
heal hca e wo ke s, women, nu ses and men al heal h wo ke s end o espond be e o domes ic
iolence cases. Keeping his in mind, da a ega ding he o al numbe o doc o s and he numbe o
emale doc o s o each municipali y was e ie ed om he Po da a websi e on he 10 h o May o
2021 in o de o calcula e he pe cen age o emale doc o s as below. This da a co e ed he pe iod
be ween 2009 and 2019 and had missing alues o some yea s in Pampilhosa da Se a, Olei os and
Lajes das Flo es.

29
𝐹𝑒𝑚𝑎𝑙𝑒𝐷𝑜𝑐𝑡𝑜𝑟𝑠%= 𝐹𝑒𝑚𝑎𝑙𝑒𝐷𝑜𝑐𝑡𝑜𝑟𝑠𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 ∗100
𝑇𝑜𝑡𝑎𝑙𝐷𝑜𝑐𝑡𝑜𝑟𝑠𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒
Following he same logic, he numbe o men al heal h wo ke s (using psychia y specialis s as a p oxy)
was e ie ed om he Po da a websi e on he 10 h o May o 2021. The pe cen age o men al heal h
doc o s in he o al o doc o s was calcula ed as below. Once again, his a iable had missing alues
o some yea s in Pampilhosa da Se a, Olei os and Lajes das Flo es.
𝑀𝑒𝑛𝑡𝑎𝑙𝐻𝑒𝑎𝑙𝑡ℎ%= 𝑀𝑒𝑛𝑡𝑎𝑙𝐻𝑒𝑎𝑙𝑡ℎ𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 ∗100
𝑇𝑜𝑡𝑎𝑙𝐷𝑜𝑐𝑡𝑜𝑟𝑠𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒
Finally, he o al numbe o doc o s in each municipali y was also used o c ea e a a iable ha showed
he numbe o doc o s pe 100 inhabi an s o he municipali y. This a iable had da a o he pe iod
be ween 2009 and 2019 and had no missing alues.
As men ioned in he APAV epo ega ding male domes ic iolence ic ims (APAV - Associação
Po uguesa de Apoio à Ví ima, 2018), elde ly men (65 yea s o mo e) end o be mo e a isk. This can
be seen on Figu e 2.1. Taking his in o accoun , he pe cen age o elde ly men in he o al popula ion
was included in he p esen s udy as an explana o y a iable. The da a ega ding he absolu e numbe
o men wi h 65 o mo e yea s was e ie ed om he Po da a websi e on he 23 d o Ap il o 2021. This
da a was hen con e ed o a pe cen age o he esiden popula ion as ollowing:
𝑀𝑒𝑛65%= 𝑀𝑒𝑛65𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 ∗100
𝑇𝑜𝑡𝑎𝑙 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
S ill ocusing on he elde ly popula ion, bu his ime wi hou dis inguishing be ween gende s, he
elde ly dependency index was e ie ed om he Po da a websi e on he 6 h o May o 2021. The
elde ly dependency index is he numbe o people aged 65 and o e o e e y 100 people o wo king
age, ha is, be ween 15 and 64 yea s old. A alue less han 100 means ha he e a e ewe elde ly
people han people o wo king age. This a iable had da a o all he municipali ies (wi hou missing
alues) o he pe iod be ween 2009 and 2019.
Ano he way o measu ing he le el o dependency in a popula ion is o conside he numbe o Social
Secu i y pensione s. A pension is an amoun a ibu ed each mon h o someone in he e en o
disabili y, old age, occupa ional disease o dea h. Da a ega ding he numbe o pensione s o each
pe son who cashes o Social Secu i y was e ie ed om he Po da a websi e on he 11 h o May o
2021. This da a con empla ed he pe iod be ween 2009 and 2019 and had some missing alues o he
municipali ies o Alenque , Lagoa (Azo es), Lajes das Flo es, San a C uz das Flo es and Co o.
I is also men ioned in ano he APAV epo ega ding domes ic iolence ic ims in gene al (APAV -
Associação Po uguesa de Apoio à Ví ima, 2018) ha mos o he ic ims end o be women wi h ages
comp ehended be ween 26 and 55 yea s. Keeping his in mind and wi h he same a ionale as o he
elde ly men a iable, he pe cen age o he popula ion ep esen ed by women in hese ages was
included. The da a ega ding he absolu e numbe o women be ween 25 and 54 yea s was e ie ed
om he Po da a websi e on he 27 h o Ap il o 2021. The bounda ies o he age gap we e as close as
possible o he ones men ioned in he APAV epo . Howe e , hey a e no exac ly he same as his
da a was no a ailable. The pe cen age o middle-aged women was calcula ed as ollowing:
𝑀𝑖𝑑𝑑𝑙𝑒𝐴𝑔𝑒𝑑𝑊𝑜𝑚𝑒𝑛%= 𝑀𝑖𝑑𝑑𝑙𝑒𝐴𝑔𝑒𝑑𝑊𝑜𝑚𝑒𝑛𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 ∗100
𝑇𝑜𝑡𝑎𝑙 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
30
The same APAV epo men ioned ha a high pe cen age o he ic ims was ma ied, showing ha i
migh be ele an o include a measu e o ma iages as an explana o y a iable o he p esen s udy.
Howe e , he numbe o ma iages in a gi en yea does no di ec ly a ec he numbe o domes ic
iolence occu ences in ha same yea , as he ma iage o he ic ims happens in yea s be o e he
occu ence. Ne e heless, da a ega ding he numbe o ma iages na ional-wide was e ie ed om
he Po da a websi e on he 28 h o Ap il o 2021 o es o co ela ions wi h he numbe o DVASA
occu ences na ional-wide. When es ing o he co ela ion be ween absolu e alues o DVASA
occu ences and absolu e alues o he numbe o ma iages he esul was 0.48 which is nei he a
weak no a high co ela ion. Howe e , hese alues should be s anda dized acco ding o he
popula ion. This s anda diza ion was made esul ing in DVASA occu ences pe 100 inhabi an s and
he same o he numbe o ma iages. The co ela ion was hen 0.31. Also, he e olu ion o bo h
a iables was plo ed o check o common pa e ns (Figu e 4.2) which we e mos ly no ound. One
can conclude ha i migh no be ele an o include his a iable in he s udy. Howe e , i migh be
in e es ing o check how his a iable beha es when included in a eg ession and o ha pu pose da a
ega ding he numbe o ma iages by municipali y was also e ie ed om he Po da a websi e on
he same da e. This da a was hen s anda dized o e lec he numbe o new ma iages pe 100
inhabi an s.
Figu e 4.2 - A e Ma iages and DVASA Occu ences Rela ed?
Di o ces a e ye ano he con o e sial a iable o include. Howe e , hey migh be impo an as, i his
a iable wo ks as expec ed acco ding o (Bowlus & Sei z, 2006), i can be a good d i e o ac ion. Tha
is, e en hough di o ces a e a consequence o domes ic iolence occu ences, hey migh be able o
explain some o he expec ed unde epo ing in domes ic iolence occu ences. Also, i an inc ease in
di o ces is connec ed o an inc ease in domes ic iolence occu ences, he esponsible en i ies can
look o a ise in he numbe o di o ces and, in ha case, pay close a en ion o domes ic iolence.
(WHO - Wo ld Heal h O ganiza ion, 2010) men ions di o ces as a cause o domes ic iolence and no
only a consequence, as sepa a ed o di o ced people end o be mo e ulne able, hus becoming mo e
p one o being ic ims in a ollowing ela ionship. Da a ega ding di o ces was e ie ed om he
Po da a websi e on he 7 h o May o 2021 in he o m o di o ces pe 100 ma iages. The da a included
he pe iod om 2009 o 2019 and had some missing alues, namely he e we e no alues a all o
Odi elas, no da a o Cas anhei a de Pê a in 2013, no da a o Ba ancos in 2019, no da a o Po o
Moniz in 2016 and 2018, no da a o Co o in 2013, 2015, 2016, 2018 and 2019. This a iable is
calcula ed he ollowing way:
𝐷𝑖𝑣𝑜𝑟𝑐𝑒𝑠 𝑝𝑒𝑟 100 𝑀𝑎𝑟𝑟𝑖𝑎𝑔𝑒𝑠= 𝐷𝑖𝑣𝑜𝑟𝑐𝑒𝑠 𝑖𝑛 𝐶𝑖𝑣𝑖𝑙 𝑌𝑒𝑎𝑟
𝑀𝑎𝑟𝑟𝑖𝑎𝑔𝑒𝑠 𝑖𝑛 𝐶𝑖𝑣𝑖𝑙 𝑌𝑒𝑎𝑟∗100
Ano he ele an a iable acco ding o (Campbell, 2002) is a measu e o income, as he poo es s a a
o he popula ion end o wi ness mo e cases o domes ic iolence. Conside ing his, he mon hly gain
31
o employees was included in he s udy. This e e s o he amoun ha he employee ecei es e e y
mon h. In addi ion o he basic emune a ion, i includes o he emune a ion paid by he employe ,
such as o e ime, holiday pay o p emiums. I is calcula ed as a g oss amoun (be o e deduc ing any
discoun s). This da a was e ie ed om he Po da a websi e on he 26 h o Ap il o 2021, and i
con empla es he pe iod be ween 2009 and 2018. The e was no in o ma ion o his a iable when i
comes o all he 19 municipali ies in he Au onomous Region o he Azo es o he pe iod be ween
2010 and 2013, which causes a o al o 76 missing alues.
Using he same da ase used o he mon hly gain o employees, a measu e o he wage gap be ween
men and women was calcula ed. The da a om Po da a, e ie ed on he 26 h o Ap il o 2021, included
he a e age mon hly gain o all employees in a municipali y as well as he a e age mon hly gain o
women only and o men. Once again, his da a e e s o he pe iod be ween 2009 and 2018 and has
no alues o he municipali ies in Azo es o he pe iod be ween 2010 and 2013. The a iable he e
e e ed o as wage gap is he pe cen age o he men’s mon hly gain ha women ecei e on a e age
and was calcula ed as ollowing:
𝑊𝑎𝑔𝑒𝐺𝑎𝑝= 𝑀𝑜𝑛𝑡ℎ𝑙𝑦𝐺𝑎𝑖𝑛𝑤𝑜𝑚𝑒𝑛 ∗100
𝑀𝑜𝑛𝑡ℎ𝑙𝑦𝐺𝑎𝑖𝑛𝑚𝑒𝑛
Acco ding o (Ande be g, Raine , Wadswo h, & Wilson, 2015) unemploymen also in luences
domes ic iolence occu ences. Since he unemploymen a e by gende was only a ailable by egions
and no municipali ies, he numbe o people en olled in employmen and oca ional aining cen e s
was used as a p oxy. The alues we e calcula ed om a simple a i hme ic a e age o he unemployed
egis e ed mon hly in he employmen and oca ional aining cen e s, so hey a e no always whole
numbe s. This da a was e ie ed om he Po da a websi e on he 29 h o Ap il o 2021 and had alues
o he pe iod be ween 2009 and 2019. To es di e en possibili ies, h ee a iables we e c ea ed
om his da a – emale unemploymen , male unemploymen and o al unemploymen . All o hem
came in absolu e alues and had o be s anda dized by he numbe o inhabi an s in he municipali y.
This s anda diza ion was done in he same way as he s anda diza ion o he dependen a iable,
esul ing in he numbe o people en olled in employmen and oca ional aining cen e s by 100
inhabi an s. I is also impo an o no ice ha he e we e no alues ega ding unemploymen o he
Au onomous Regions o he Azo es (19 municipali ies) and Madei a (11 municipali ies), making i a
o al o 30 municipali ies wi h no in o ma ion.
Educa ion may also play an impo an ole in explaining he e olu ion o domes ic iolence
occu ences. Acco ding o (Bowlus & Sei z, 2006), ic ims o iolence end o ha e lowe le els o
educa ion and so do he pe pe a o s. Da a ega ding he g oss en olmen a e (GER) was e ie ed
om he DGEEC – Di eção-Ge al de Es a ís icas da Educação e Ciência – on he 23 d o June o 2021.
The da a was a ailable o he pe iod be ween 2003 and 2019 and did no ha e alues o he
municipali ies in nei he Azo es no Madei a. This indica o is calcula ed by DGEEC based on DGEEC
en ollmen da a and INE (Ins i u o Nacional de Es a ís ica) esiden popula ion da a. I is calcula ed he
ollowing way:
𝐺𝐸𝑅= 𝑆𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝐸𝑛𝑟𝑜𝑙𝑙𝑒𝑑 𝑖𝑛 𝐻𝑖𝑔ℎ 𝑆𝑐ℎ𝑜𝑜𝑙
𝑅𝑒𝑠𝑖𝑑𝑒𝑛𝑡 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑊𝑖𝑡ℎ 𝑁𝑜𝑟𝑚𝑎𝑙 𝐴𝑔𝑒 𝑓𝑜𝑟 𝐴𝑡𝑡𝑒𝑛𝑑𝑖𝑛𝑔 𝐻𝑖𝑔ℎ 𝑆𝑐ℎ𝑜𝑜𝑙∗100
Rega ding he GER, h ee a iables we e included: he o al GER and GER by gende .
32
5. METHODOLOGY
The second s ep o his s udy, igh a e he da a collec ion, was he da a ea men and explo a ion,
ollowed by modelling. Some o he da a ea men was al eady desc ibed in he p e ious chap e s,
bu he emaining pa will be desc ibed in he p esen chap e . All calcula ions and plo s we e made
using Py hon. The code used in he scope o his s udy can be ound on a Gi Hub eposi o y
11
.
5.1. SERIES BREAKS
A lo o he explana o y a iables had b eaks caused by changes in he s anda ds o de ining and
obse ing he indica o o e ime. Acco ding o he OECD (O ganiza ion o Economic Co-ope a ion
and De elopmen ) Glossa y o S a is ical Te ms, “ he speci ic causes o b eaks in a s a is ical ime se ies
include changes in: classi ica ions used, de ini ions o he a iable, co e age, e c.”.
The a iables GER, GER_Women and GER_Men did no ha e se ies b eaks.
Fe ili y, You h_Dependency, Female_Doc o s, Men al_Heal h, Men65, Elde ly_Dependency,
SS_Pensions, Middle_Aged_Women, Mon hly_Gain, Wage_Gap, Unemploymen _To al,
Unemploymen _Female, Unemploymen _Male and To al_Doc o s all had ou b eaks, all in 2013.
Those we e in Lisbon, Lou es, San a ém and Golegã. The b eaks in San a ém and Golegã a e caused by
he ac ha he pa ish o Pombalinho was conside ed, om 2013 on, a pa ish belonging o he
municipali y o Golegã, no longe being a pa o San a ém. Pombalinho is a small pa ish, wi h 7.7km2
and 448 inhabi an s, making his b eak neglec able. I was also a change in he pa ish con igu a ion
ha caused he b eaks o Lisbon and Lou es. In 2013 a new pa ish called Pa que das Nações was
c ea ed, which included a eas om bo h he municipali ies o Lou es and Lisbon. This pa ish is, om
2013 on, pa o he municipali y o Lisbon and i has 5.44km2 and 21,025 inhabi an s. Since only 34.2%
o his a ea and 23.7% o his popula ion belonged o Lou es be o e he change, he e ec o his b eak
is neglec able.
The a iable Ma iages also had he ou b eaks o 2013 desc ibed in he las pa ag aph. Howe e , i
also had a b eak o each municipali y in 2010 due o he ac ha as o his yea (inclusi e), wi h he
implemen a ion o Law 9/2010 on he 31s o May, ci il ma iage be ween pe sons o he same gende
became allowed. This las b eak canno be conside ed neglec able and, so, da a o he yea o 2009
had o be emo ed om he a iable in o de o cancel he e ec s o he b eak.
Once again, he a iable Di o ces had he ou b eaks in 2013 ela ed o he edis ibu ion o pa ishes.
Howe e , i also had a b eak o all municipali ies o he yea o 2010 o he same eason he a iable
Ma iages had a b eak in 2010 (Law 9/2010). F om 2010 on (2010 included), di o ces we e allowed o
pe sons o he same gende . Once again, his b eak canno be conside ed neglec able and, so, alues
o he yea o 2009 had o be emo ed o he sake o he cohe ence o he a iable.
5.2. CORRELATIONS
I is impo an o know wha he ela ion be ween a iables wi hin he da ase is. Fo his pu pose, he
co ela ion ma ix was calcula ed using he Pea son Co ela ion Coe icien . The Pea son co ela ion is
11
Tex is unde lined as i ep esen s a link o h ps://gi hub.com/anas aubyn/Mas e Thesis
39
Figu e 5.3 - E olu ion o GER, GER_Men and GER_Women in Ba ancos
The second scena io, sampling p oblems, is no applied o he p esen s udy, as i is s udying a
popula ion a he han a sample. Ou lie s caused by sampling mis akes migh occu when da a is
collec ed abou an indi idual who does no belong o he a ge o he s udy. In his case, he ou lie
is also conside ed an e o and should be emo ed om he da ase .
Finally, he las scena io is na u al a ia ion. These a e he ou lie s ha migh be impo an o he
s udy. Da a dis ibu ions a e cen e ed a ound some poin and sp ead om ha poin . This means ha
ex eme alues migh occu bu ha e a lowe p obabili y o happening. E en hough hese da a poin s
a e unusual, hey ep esen a na u al pa o he dis ibu ion and migh add alue o he da ase . Fo
example, ex eme alues in one explana o y a iable migh jus i y ex eme alues in he dependen
a iable. Fo his eason, ou lie s appa en ly caused by na u al a ia ion we e no emo ed om he
da ase .
Besides he usual summa y s a is ics, his og ams and boxplo s a e common ways o explo ing he
p esence o ou lie s. The his og ams o bo h he dependen a iable and he explana o y ones we e
p esen ed in Figu e 5.2. and Annex II be o e. Howe e , o a be e unde s anding o he dis ibu ions
o all a iables, a g id o boxplo s is p esen ed in Annex III. A boxplo is a summa y o he da a
dis ibu ion whe e he sides o he cen al ec angle ep esen he i s and hi d qua iles, he line in
he middle o he ec angle ep esen s he median and he “whiske s” ep esen a measu e o 1.5
imes he in e -qua ile ange. Theo e ically, all da a poin s ha all ou side he “whiske s” o he plo
a e conside ed ou lie s.
One can see by he analysis o he boxplo s ha mos o he supposed ou lie s all e y close o he
dis ibu ion, as hey a e no a away om he end o he “whiske ”. Howe e , some a iables ha e
mo e ex eme alues: Di o ces, GER_Women, Ma iages, Men al_Heal h and Mon hly_Gain. These
ex eme alues may be impo an in jus i ying he a iance in DVASA.
5.6. STATIONARITY
When dealing wi h ime se ies da a (panel da a has mul iple ime se ies encapsula ed inside o i ) one
can ind ime-dependen s uc u es such as end o seasonali y. When hese s uc u es a e p esen a
ime se ies is conside ed o be non-s a iona y, as he summa y s a is ics do no emain ixed o all
ime pe iods. This causes a ia ions in da a ha a e caused by na u al e olu ion o he numbe s bu
ha he model may y o cap u e anyway, adding bias o he esul s. Time se ies ha a e ee o ime-
dependen s uc u es a e conside ed s a iona y. I he ime se ies is s a iona y, he co a iance

40
be ween wo alues o he se ies depends only on he amoun o ime sepa a ing hose alues and he
summa y s a is ics a e ixed independen ly o he ime pe iod. This means ha a s a iona y ime se ies
e i ies he ollowing condi ions:
(a) E(y ) = μ;
(b) Va (y ) = σ2;
(c) Co (y , y +s) = γs.
Since he p esen s udy is dealing wi h annual da a, seasonali y is o he able, as i is mos ly ound on
mon hly da a, o example. Howe e , end may s ill be a p oblem. The wo mos common ways o
de ec he p esence o ime-dependen s uc u es a e isualizing plo s o he a iables o in e es o
using a Dickey-Fulle es . Changes in he a iables o e pe iods o ime a e impo an o isualizing
whe he a ime se ies is s a iona y o no . I we ha e a a iable y ha is measu ed o e some ime
pe iods (y ), he di e ence (Δy ) gi en by y – y -1 is he change in he alue o a iable y om pe iod
-1 o pe iod and is called he i s di e ence.
The plo s in Annex IV show he a e age (yea ly mean alues conside ing all municipali ies) ime se ies
o all explana o y a iables plus he dependen one side by side wi h he ime se ies o he changes
o he same a iables. Since he mean and a iance o a s a iona y ime se ies a e cons an , i s
changes o i s di e ences mus luc ua e a ound a cons an alue, which does no seem o be he
case o he plo ed a iables. Howe e , as his is a esul based on a e age e olu ion and changes i
may no be he mos eliable one. Keeping his in mind, i is necessa y o eso o a mo e alid me hod,
he Dickey-Fulle es .
The Dickey-Fulle es is based on he i s o de au o eg essi e model in which he e a e no ex e nal
explana o y a iables and he dependen a iable is used as an explana o y a iable o i sel . This
means ha he dependen a iable is ela ed o pas alues o i sel which means ha each alue o
he a iable con ains pa o he las pe iod’s alue plus an e o e m. I he coe icien o he las
pe iod’s alue is less han one i means ha he a iable is s a iona y. This can be demons a ed as
ollows: 𝑦𝑡= 𝛽0+ 𝜌𝑦𝑡−1 + 𝑢𝑡 ⇔𝑦𝑡− 𝑦𝑡−1 = 𝛽0+(𝜌−1)𝑦𝑡−1 + 𝑢𝑡
One can see om he equa ion abo e ha when ρ is less han one, he e ec s o y -1 on y will dec ease
o e ime o he poin in which a p edic ion o a pe iod a om will be un ela ed o he alue o y .
Howe e , i ρ is equal o mo e han one, he e ec s o y -1 on he alues o y o any pe iod will ne e
be annula ed, which means ha he e a e ime-dependen s uc u es and ha he alues o y ely
hea ily on he alues o y o pas pe iods. Keeping his in mind, he hypo heses o a Dickey-Fulle es
a e as ollowing: 𝐻0: 𝜌≥1 𝑣𝑠. 𝐻1: 𝜌<1
I is impo an o no e ha he null hypo hesis is ha o he se ies no being s a iona y, meaning ha
i we ail o ejec i , we a e assuming non-s a iona i y. This causes a sligh di e ence in he es s a is ic
as non-s a iona y se ies ha e di e en p ope ies al e ing he dis ibu ion o he usual -s a is ic. To
ecognize his ac he s a is ic is called τ ( au) and i s alues a e compa ed o speci ically gene a ed
c i ical alues.
A p oblem may a ise when pe o ming a simple Dickey-Fulle es as he e o e m may be
au oco ela ed. To a oid his, we should add as many lagged di e ences as needed. This numbe o
41
di e ences is de e mined by examining he au oco ela ion unc ion (ACF) o he esiduals. This a ian
o he Dickey-Fulle es is called he Augmen ed Dickey-Fulle es and i s equa ion is as ollowing:
𝑦𝑡− 𝑦𝑡−1 = 𝛽0+(𝜌−1)𝑦𝑡−1 +∑𝛽𝑠(𝑦𝑡−𝑠 −𝑦𝑡−𝑠−1)
𝑚
𝑠=1 +𝑢𝑡
The da ase ha is he objec o his s udy con ains 5,560 ime se ies (278 municipali ies imes 20
a iables). The Augmen ed Dickey-Fulle es was applied o all o hese se ies and i was possible o
conclude ha o 1,238 o hem he null hypo hesis was ejec ed wi h a signi icance le el o 5%. I he
signi icance le el we e o be pushed o 10%, he numbe o s a iona y se ies would be 1,502. Using
ei he signi icance le el i becomes clea ha mos o he se ies in he da ase a e non-s a iona y. One
way o a oid he p oblems caused by his condi ion is by emo ing he end om he se ies. Howe e ,
ixed e ec models con empla e he possibili y ha he in e cep may change o e di e en ime
pe iods which can also be a solu ion. Finally, i is also possible o use di e ences as he a iables.
Ne e heless, since he e is a much highe p e alence o he c oss-sec ional componen in he p esen
da ase han o he ime se ies one his is no a se e e p oblem. The p esen s udy is also wo king wi h
sho ime se ies, making he powe o Dickey-Fulle es s dubious, as i becomes ha d o ejec he
null hypo hesis e en i i is alse. One o he main p oblems o non-s a iona y se ies is ha he e is a
dange o ob aining appa en ly signi ican esul s om un ela ed da a, which is called a spu ious
eg ession. Howe e , he highe p e alence o he c oss-sec ional componen a oids his p oblem.
42
5.7. MODEL ESTIMATION
Be o e es ima ing any models, i is impo an o unde s and how he explana o y a iables and he
dependen a iable a e ela ed in e ms o he unc ional o m o be used. This can be analyzed isually
wi h he aid o sca e plo s. Keeping his in mind, a se o sca e plo s showing he join dis ibu ion
o each explana o y a iable wi h DVASA was plo ed, as shown in Figu e 5.4 below.
Figu e 5.4 - Join Dis ibu ions o Explana o y Va iables wi h DVASA
F om he analysis o he plo s abo e, one can conclude ha i migh help o include some o he
a iables in di e en unc ional o ms. Some explana o y a iables, such as he ones ela ed o
unemploymen and he ones ela ed o educa ion, exhibi a slowly inc easing pa e n, in a cu ilinea
o m. This means ha o highe alues o he explana o y a iable, he alues o he dependen
a iable inc ease slowly. This ype o ela ionship can be summed up h ough a log-log model (wi h he
espec i e pa ame e being g ea e han one) o h ough a log-linea model (wi h he espec i e
pa ame e being g ea e han 0). Ei he way, i migh be bene icial o u n he dependen a iable in o
a loga i hmic o m.
43
5.7.1. Model 1 (CC – Cons an Coe icien s)
To es ima e he i s model a cons an coe icien s app oach was used. All 19 explana o y a iables
we e used o his model in a simple linea o m. F om now on his model will be called Model 1. The
heo e ical model is as ollows:
𝐷𝑉𝐴𝑆𝐴𝑖𝑡 = 𝛽0+𝛽1𝐹𝑒𝑟𝑡𝑖𝑙𝑖𝑡𝑦𝑖𝑡 +𝛽2𝑀𝑒𝑛65𝑖𝑡 +𝛽3𝑀𝑜𝑛𝑡ℎ𝑙𝑦_𝐺𝑎𝑖𝑛𝑖𝑡 +𝛽4𝑊𝑎𝑔𝑒_𝐺𝑎𝑝𝑖𝑡
+𝛽5𝑀𝑖𝑑𝑑𝑙𝑒_𝐴𝑔𝑒𝑑_𝑊𝑜𝑚𝑒𝑛𝑖𝑡 +𝛽6𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡_𝑇𝑜𝑡𝑎𝑙𝑖𝑡 +𝛽7𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡_𝑀𝑎𝑙𝑒𝑖𝑡
+𝛽8𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡_𝐹𝑒𝑚𝑎𝑙𝑒𝑖𝑡 + 𝛽9𝑀𝑎𝑟𝑟𝑖𝑎𝑔𝑒𝑠𝑖𝑡 + 𝛽10𝐸𝑙𝑑𝑒𝑟𝑙𝑦_𝐷𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑐𝑦𝑖𝑡
+ 𝛽11𝑌𝑜𝑢𝑡ℎ_𝐷𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑐𝑦𝑖𝑡 +𝛽12𝐹𝑒𝑚𝑎𝑙𝑒_𝐷𝑜𝑐𝑡𝑜𝑟𝑠𝑖𝑡 +𝛽13𝑇𝑜𝑡𝑎𝑙_𝐷𝑜𝑐𝑡𝑜𝑟𝑠𝑖𝑡
+𝛽14𝑀𝑒𝑛𝑡𝑎𝑙_𝐻𝑒𝑎𝑙𝑡ℎ𝑖𝑡 + 𝛽15𝑆𝑆_𝑃𝑒𝑛𝑠𝑖𝑜𝑛𝑠𝑖𝑡 +𝛽16𝐺𝐸𝑅𝑖𝑡 +𝛽17𝐺𝐸𝑅_𝑀𝑒𝑛𝑖𝑡
+𝛽18𝐺𝐸𝑅_𝑊𝑜𝑚𝑒𝑛𝑖𝑡 +𝛽19𝐷𝑖𝑣𝑜𝑟𝑐𝑒𝑠𝑖𝑡 +𝑢𝑖𝑡
Model 1 was es ima ed using clus e - obus s anda d e o s ha allow o a elaxa ion o he
assump ion ega ding he co a iance o he e o e m. This means ha he e o o obse a ions o
he same municipali y may be co ela ed bu he co a iance o e o e ms o di e en municipali ies
mus be 0. The R-squa ed o his model was 0.1342 meaning ha 13.42% o he a iabili y in DVASA
is ep esen ed by he se o explana o y a iables chosen o his model. The esul o he o e all
signi icance es o Model 1 was e y posi i e, wi h a p- alue o 0. Table 5.3 sums up he pa ame e
es ima es and hei signi icance o his model.
Pa ame e
S anda d
E o
T-s a
P- alue
Cons an
0.4115
0.1620
2.5409
0.0111
Fe ili y
0.0282
0.0105
2.6893
0.0072
Men65
-0.0103
0.0065
-1.5837
0.1134
Mon hly_Gain
0.0000413
0.000027
1.5278
0.1267
Wage_Gap
-0.0003
0.0004
-0.6158
0.5381
Middle_Aged_Women
-0.0088
0.0044
-1.9877
0.0469
Unemploymen _To al
4.5520
2.2377
2.0342
0.0420
Unemploymen _Male
-4.5526
2.2369
-2.0352
0.0419
Unemploymen _Female
-4.5356
2.2386
-2.0261
0.0428
Ma iages
0.0368
0.0186
1.9731
0.0486
Elde ly_Dependency
0.0010
0.0012
0.8918
0.3726
You h_Dependency
-0.0031
0.0013
-2.3648
0.0181
Female_Doc o s
-0.0000685
0.0002
-0.3551
0.7226
To al_Doc o s
0.0393
0.0178
2.2053
0.0275
Men al_Heal h
-0.0006
0.0011
-0.6031
0.5465
SS_Pensions
-0.0460
0.0225
-2.0474
0.0407
GER
-0.0008
0.0005
-1.7929
0.0731
GER_Men
0.0006
0.0003
2.0282
0.0426
GER_Women
0.0004
0.0002
1.5352
0.1248
Di o ces
0.0002
0.0000647
2.6329
0.0085
Table 5.3 - Pa ame e Es ima es o Model 1
The las wo columns o Table 5.3 show he esul s o he indi idual signi icance es o each
pa ame e . P- alues ha exceed he signi icance le el o 5% a e highligh ed in ed. In his es , i he
null hypo hesis is ejec ed, one can say ha he e is s a is ical e idence ha he pa ame e is no 0,
44
which means ha he co esponding a iable has an ac ual impac on he dependen a iable.
Conside ing a le el o signi icance o 5%, one can see om Table 5.3 ha he e is no s a is ical e idence
o some o he pa ame e s being ele an o he model. I is he case o he pa ame e s co esponding
o GER_Women, GER, Men al_Heal h, Female_Doc o s, Elde ly_Dependency, Wage_Gap,
Mon hly_Gain and Men65. I one we e o conside a signi icance le el o 10%, only GER would be
emo ed om he p e ious lis . In u u e models his conclusion will be conside ed.
In o de o es o he e oskedas ici y in Model 1, a g aphical app oach was used i s , plo ing he
esiduals agains he p edic ed alues. I any pa e n is de ec ed in he plo (inc easing o dec easing
a iance), he e is he e oskedas ici y in he model. The plo is shown in Figu e 5.5.
Figu e 5.5 - He e oskedas ici y Tes o Model 1
Acco ding o Figu e 5.5, he e does no seem o be any e idence o he e oskedas ici y in he model.
Howe e , o gua an ee his esul , a o mal es mus be made. The B eusch-Pagan es is mean o
de ec he e oskedas ici y. I akes he squa es o he esiduals c ea ed by he model and makes a
eg ession on i wi h he same dependen a iables as he o iginal model. Then, an o e all signi icance
es is pe o med o see i all he coe icien s can be 0. The esul s o his es show a eally low p-
alue (1.27825047691774e-16), indica ing ha he e is s a is ical e idence ha a leas one o he
coe icien s is no equal o 0, which means ha he e is he e oskedas ici y in he model. Consequen ly,
he es ima o s a e no e icien . Howe e , since clus e - obus s anda d e o s we e used, he esul s
o s a is ical es s can be e alua ed. No o he es s on he e oskedas ici y we e pe o med o Model 1
due o he ex emely low p- alue o he B eusch-Pagan es .
In o de o es o au oco ela ion among esiduals, he Du bin-Wa son es was applied. The Du bin-
Wa son s a is ic is calcula ed using he esidual sum o squa es and he sum o squa es o di e ences
be ween consecu i e esiduals. I akes a alue be ween 0 and 4 whe e he middle alue (2) indica es
no au oco ela ion. Values be ween 0 and 2 indica e posi i e au oco ela ion and alues be ween 2
and 4 indica e nega i e au oco ela ion. The s a is ic o Model 1 was 1.8941, which indica es a small
le el o posi i e au oco ela ion.
Conside ing he esul s o he wo es s, i migh be a be e op ion o use a ixed-e ec s o a andom-
e ec s model. Ne e heless, he plo s o he esiduals e sus he explana o y a iables o which he
indi idual signi icance es showed s a is ical e idence o impo ance we e plo ed o check o w ong
unc ional o ms. These plo s can be seen on Figu e 5.6.

45
Figu e 5.6 - Residuals Agains Explana o y Va iables (Model 1)
A e analyzing he plo s in Figu e 5.6 he e does no seem o be any e idence o he exis ence o a
be e unc ional o m o any o he a iables.
To allow be e u u e model compa ison, he adjus ed R-squa ed was calcula ed o Model 1, using
he ollowing o mula whe e N is he o al numbe o obse a ions and k is he o al numbe o
explana o y a iables:
𝑅
2=1−(1−𝑅2)(𝑁−1)
𝑁−𝑘−1
Using he o mula abo e, he adjus ed R-squa ed o Model 1 is 0.1288.
5.7.2. Model 2 (CC)
Taking in o accoun he esul s om Model 1, and s ill using a cons an coe icien s app oach, a new
model was es ima ed keeping all a iables in a simple linea o m and emo ing a iables ha do no
seem o be ele an . This model will om now on be e e ed o as Model 2.
Model 2 was also es ima ed using clus e - obus s anda d e o s. I s R-squa ed was 0.1205, lowe han
Model 1. This is expec ed since 8 a iables we e emo ed. The p- alue o he o e all signi icance es
was s ill 0, meaning ha he e is eally s ong s a is ical e idence o he impo ance o he se o
explana o y a iables used in jus i ying he alues o DVASA. Table 5.4 sums up he pa ame e
es ima es and hei signi icancy o his model.
F om Table 5.4 below, one can see ha , conside ing a le el o signi icance o 5%, he null hypo hesis
o he indi idual signi icance es canno be ejec ed o some pa ame e s. These a e he ones
co esponding o Middle_Aged_Women, Ma iages, You h_Dependency and GER_Men. Howe e , i a
le el o signi icance o 10% was o be conside ed, he only pa ame e s o which he null hypo hesis
46
could no be ejec ed would be he ones co esponding o Middle_Aged_Women and Ma iages.
These alues a e highligh ed in ed on he p e ious able.
Pa ame e
S anda d
E o
T-s a
P- alue
Cons an
0.2479
0.0734
3.3766
0.0007
Fe ili y
0.0307
0.0108
2.8491
0.0044
Middle_Aged_Women
-0.0042
0.0028
-1.5342
0.1251
Unemploymen _To al
4.8803
2.2706
2.1493
0.0317
Unemploymen _Male
-4.8805
2.2698
-2.1502
0.0316
Unemploymen _Female
-4.8643
2.2716
-2.1414
0.0323
Ma iages
0.0306
0.0194
1.5812
0.1139
You h_Dependency
-0.0021
0.0011
-1.8705
0.0615
To al_Doc o s
0.0451
0.0170
2.6548
0.0080
SS_Pensions
-0.0536
0.0184
-2.9112
0.0036
GER_Men
0.0001
0.000058
1.7544
0.0795
Di o ces
0.0002
0.000067
2.6164
0.0089
Table 5.4 - Pa ame e Es ima es o Model 2
In a simila way o wha was done o Model 1, a g aphical app oach was used o es Model 2 o
he e oskedas ici y. The plo is shown in Figu e 5.7 and, once again, no pa e n o inc easing o
dec easing a iance was de ec ed.
Figu e 5.7 - He e oskedas ici y Tes o Model 2
To ha e a mo e o mal esul ega ding he p esence o he e oskedas ici y in Model 2, a B eusch-Pagan
es was applied. The esul s o his es o his es show a eally low p- alue o he F- es
(1.6751524272085239e-16), indica ing ha he e is s a is ical e idence ha a leas one o he
coe icien s is no equal o 0, which means ha he e is he e oskedas ici y p esen in he model.
Consequen ly, he es ima o s a e no e icien . Howe e , since clus e - obus s anda d e o s we e
used, he esul s o s a is ical es s can be e alua ed. No o he es s on he e oskedas ici y we e
pe o med o Model 2 due o he ex emely low p- alue o he B eusch-Pagan es .
Simila ly o wha happened ega ding Model 1, o es o au oco ela ion among esiduals he Du bin-
Wa son es was applied. The s a is ic o his es o Model 2 was 1.9072, which indica es a e y small
le el o posi i e au oco ela ion. Since his is a close enough alue o 2, one can assume ha he e is
no signi ican au oco ela ion.
47
The alue o he adjus ed R-squa ed o Model 2 is 0.1173, lowe han he alue o Model 1.
5.7.3. Model 3 (CC)
Acco ding o he conclusions aken om Figu e 5.4, some ans o ma ions we e applied o he
a iables, namely con e ing DVASA in o a na u al loga i hmic o m. A model wi h all a iables used
o Model 1 was es ima ed, bu his ime he a iables we e included as log-linea ela ionships. This
model will om now on be add essed o as Model 3. Once again, Model 3 used a cons an coe icien s
app oach wi h clus e - obus s anda d e o s.
The R-squa ed o Model 3 was 0.1396. This means ha 13.96% o he a iabili y in ln(DVASA) is
ep esen ed by his model. We can also ge in o ma ion on he be ween and wi hin R-squa ed, which,
simila ly o he wi hin and be ween s anda d de ia ions, ep esen he pa o he di e ences be ween
municipali ies ha is explained by he model and he pa o he di e ences wi hin municipali ies ha
is explained by he model. Fo Model 3 he be ween R-squa ed was 0.2711 and he wi hin R-squa ed
was 0.0320. F om hese numbe s, one can easily unde s and ha a much la ge pa o he a iance
being add essed by he model is jus i ied by di e ences be ween municipali ies.
The esul o he o e all signi icance es o Model 3 was e y posi i e, wi h a p- alue o 0. Howe e ,
acco ding o he T- es s o indi idual signi icance, conside ing a signi icance le el o 5%, he e was no
s a is ical e idence o he ele ance o many a iables, including he cons an . The esul s o Model 3
can be seen on Table 5.5 below, whe e he p- alues g ea e han he in ended signi icance le el (5%)
a e highligh ed in ligh ed.
Pa ame e
S anda d
E o
T-s a
P- alue
Cons an
-0.2051
0.9792
-0.2094
0.8341
Fe ili y
0.1422
0.0682
2.0849
0.0372
Men65
-0.0653
0.0441
-1.4818
0.1385
Mon hly_Gain
0.0002
0.0002
1.5164
0.1295
Wage_Gap
-0.0020
0.0028
-0.7318
0.4643
Middle_Aged_Women
-0.0539
0.0275
-1.9602
0.0501
Unemploymen _To al
42.762
18.404
2.3235
0.0202
Unemploymen _Male
-42.749
18.398
-2.3236
0.0202
Unemploymen _Female
-42.685
18.410
-2.3185
0.0205
Ma iages
0.1801
0.1138
1.5828
0.1136
Elde ly_Dependency
0.0055
0.0080
0.6889
0.4909
You h_Dependency
-0.0191
0.0080
-2.3778
0.0175
Female_Doc o s
0.0006
0.0013
0.4505
0.6524
To al_Doc o s
0.1949
0.0875
2.2265
0.0261
Men al_Heal h
-0.0028
0.0068
-0.4125
0.6800
SS_Pensions
-0.3451
0.1494
-2.3097
0.0210
GER
-0.0037
0.0027
-1.3367
0.1814
GER_Men
0.0029
0.0015
1.8992
0.0576
GER_Women
0.0013
0.0015
0.8358
0.4033
Di o ces
0.0010
0.0004
2.4794
0.0132
Table 5.5 - Pa ame e Es ima es o Model 3
48
The a iables ha we e no s a is ically signi ican we e analyzed one by one, in o de o check i he e
we e possible imp o emen s o he unc ional o m by con e ing he a iables in a na u al loga i hmic
o m as well, c ea ing log-log ela ionships. This was done by analyzing he plo s in Figu e 5.4. Men65
is included in Model 3 as a log-linea ela ionship in which he co esponden pa ame e is smalle han
0. Howe e , i seems o esemble mo e he shape o a log-log ela ionship wi h he co esponden
pa ame e being equal o -1 o below i . Thus, Men65 will be included in he nex model as a log-log
ela ionship. Mon hly_Gain can also bene i om a log-log ela ionship wi h he co esponding
pa ame e being smalle han 0. Wage_Gap does no exhibi any clea pa e n and has oo high o a p-
alue, meaning ha i will be excluded om he nex model. Middle_Aged_Women was included in
Model 3 as a log-linea ela ionship wi h he co esponding coe icien lowe han 0. Howe e , i seems
o be bes desc ibed as a log-log ela ionship wi h he co esponden coe icien g ea e han 0. I will
hen be included in he nex model as a log-log ela ionship. Ma iages does no exhibi a clea pa e n
and will be excluded om he nex model. Elde ly_Dependency also seems o bene i om a log-log
ela ionship and will be included in his way in he nex model. Bo h Female_Doc o s and
Men al_Heal h do no exhibi clea pa e ns and ha e e y high p- alues, being excluded om he nex
model. GER and GER_Men will also be included as log-log ela ionships in he nex model.
The adjus ed R-squa ed o Model 3 was 0.1342.
5.7.4. Model 4 (CC)
Model 4 was, once again, es ima ed using a cons an coe icien s app oach wi h clus e - obus
s anda d e o s. The a iables used we e desc ibed in he inal pa ag aph o Chap e 5.7.3. This model
p esen ed a R-squa ed o 0.1395, wi h a wi hin R-squa ed o 0.0336 and a be ween R-squa ed o
0.2687. Once again, di e ences be ween municipali ies a e much be e explained han di e ences
wi hin municipali ies. The p- alue o he o e all signi icance F- es was 0. The pa ame e es ima es a e
summed up in Table 5.6 below. The dependen a iable o his model is he na u al loga i hm o
DVASA.
Pa ame e
S anda d
E o
T-s a
P- alue
Cons an
-2.2822
2.0980
-1.0878
0.2768
Fe ili y
0.1445
0.0675
2.1413
0.0323
Ln_Men65
-0.6080
0.4721
-1.2878
0.1979
Ln_Mon hly_Gain
0.3882
0.1351
2.8737
0.0041
Ln_Middle_Aged_Women
-0.6790
0.5012
-1.3547
0.1756
Unemploymen _To al
42.802
18.588
2.3026
0.0214
Unemploymen _Male
-42.794
18.581
-2.3031
0.0213
Unemploymen _Female
-42.718
18.596
-2.2972
0.0217
Ln_Elde ly_Dependency
0.3086
0.3816
0.80088
0.4187
You h_Dependency
-0.00168
0.0081
-2.0704
0.0385
To al_Doc o s
0.1848
0.0805
2.2963
0.0217
SS_Pensions
-0.3240
0.1416
-2.2876
0.0222
Ln_GER
0.0064
0.0659
0.0974
0.9224
Ln_GER_Men
0.0792
0.0538
1.4707
0.1415
GER_Women
-0.0003
0.0004
-0.775
0.4384
55
6. RESULTS AND DISCUSSION
Nine models we e c ea ed in he scope o his s udy. Fou o hem used he cons an coe icien s
app oach and he emaining i e used he ixed e ec s app oach. The objec i e was o build a model
ha is subs an ia ed by s a is ical e idence. Fo his pu pose, esul s o o e all signi icance es s and
indi idual signi icance es s mus by analyzed.
The R2 o coe icien o de e mina ion o a eg ession is a measu e o he p opo ion o a iabili y in
he dependen a iable ha is jus i ied by changes in he explana o y a iables. Howe e , he R2 may
no always be he bes measu e o compa e models as i always becomes la ge when adding new
a iables, e en i he a iables added a e comple ely i ele an . Keeping his in mind, he R2 can only
be used o compa e models wi h he exac same numbe o explana o y a iables. When he models
ha e a di e en numbe o explana o y a iables, he adjus ed R2 can be used as an al e na i e.
Table 6.1 below shows a summa y o he measu es calcula ed o he models c ea ed o acili a e
compa ison be ween hem. In his able, one can see he dependen a iable used o each model, he
numbe o explana o y a iables included in each model, he alues o he o e all R-squa ed, be ween
R-squa ed, wi hin R-squa ed and adjus ed R-squa ed o each model, he numbe o he a iables
included as explana o y a iables ha had a p- alue lowe han 0.1 and we e, he e o e, conside ed
ele an based on a 10% signi icance le el, he p- alue o he o e all signi icance F- es , he p- alue
o he B eusch-Pagan es and he alue o he Du bin-Wa son s a is ic.
Model
1
Model 2
Model 3
Model 4
Model
5
Model
6
Model
7
Model
8
Model 9
Dependen
Va iable
DVASA
DVASA
Ln(DVASA)
Ln(DVASA)
DVASA
DVASA
DVASA
DVASA
DVASA
Nº
Explana o y
Va iables
19
11
19
15
29
24
19
17
15
Nº
Obse a ions
3,058
3,058
3,058
3,058
3,058
3,058
3,058
3,058
3,058
R-squa ed
0.1342
0.1205
0.1396
0.1395
0.1664
0.1657
0.1607
0.1577
0.1566
Be ween R-
squa ed
0.2592
0.2460
0.2711
0.2687
0.2957
0.2941
0.2918
0.2882
0.2877
Wi hin R-
squa ed
0.0181
0.0040
0.0320
0.0336
0.0462
0.0463
0.0389
0.0365
0.0349
Adjus ed R-
squa ed
0.1288
0.1173
0.1342
0.1353
0.1584
0.1591
0.1556
0.1530
0.1524
Nº Rele an
Va iables
(10%)
10
9
10
9
19
16
19
14
15
O e all
Signi icance
0
0
0
0
0
0
0
0
0
B eusch-
Pagan
≈0
≈0
≈0
≈0
≈0
≈0
≈0
≈0
0.00196
Du bin-
Wa son
1.8941
1.9072
1.9151
1.9068
1.9245
1.9259
1.9443
1.9396
1.9416
Table 6.1 - Model Compa ison
Model 1, he i s one c ea ed, included all e ie ed possible explana o y a iables in a simple linea
o m. I showed p omising esul s conce ning he alue o he be ween R-squa ed. Howe e , almos

56
hal o he a iables could no be conside ed ele an and he alue o he wi hin R-squa ed was
ex emely low, exposing om he s a he p oblem o low a iance o he da a wi hin municipali ies.
To y and achie e a mo e s a is ically ele an model, Model 2 was c ea ed, emo ing eigh o he
non- ele an a iables exposed in Model 1 while keeping all ela ionships in a simple linea o m. The
emaining wo non- ele an a iables om Model 1 we e kep in Model 2 o see i hei beha io
changed when included in a mo e es ic ed se o explana o y a iables. Howe e , hei co esponding
indi idual signi icance es s con inued o show hem non- ele an . As he alue o he R-squa ed was
e y low, Model 3 was c ea ed using di e en unc ional o ms (log-linea ) o check o imp o emen s
in explainabili y. This model showed p omising esul s bu many a iables had high p- alues o hei
indi idual signi icance es , causing he model o be no e y eliable. A u he a emp wi h he
na u al loga i hm o DVASA as he dependen a iable was made in Model 4, bu his ime including
some o he a iables in a log-log o m and emo ing he ones ha did no show appa en pa e ns
when plo ed agains DVASA. Once again, his model showed p omising esul s bu many a iables had
high p- alues o hei indi idual signi icance es s. As all he p e ious models we e showing clea
e idence o he e oskedas ici y, a change in he model app oach was conside ed, esul ing in Model 5,
es ima ed using ixed e ec s o he ime componen . In his model, di e ences be ween cons an s
o di e en yea s we e included using dummy a iables o all yea s excep 2009, o a oid
mul icollinea i y. F om Model 5 o Model 9, di e en combina ions o a iables we e ied in o de o
op imize in e p e abili y and eliance o he model.
All o he es ima ed models ended up showing e idence o he p esence o he e oskedas ici y. This
means ha he es ima o s a e no e icien and ha , i clus e - obus s anda d e o s had no been
used in all es ima ions, s a is ical in e ence would no be alid.
As al eady men ioned, alid s a is ical e idence is he main c i e ia when i comes o choosing he inal
model. Thus, all a iables o ha model mus be signi ican and he model i sel mus pass he o e all
signi icance es . The only wo models ha mee hese c i e ia a e Model 7 and Model 9. Since he
numbe o a iables o hese wo models is di e en , he R-squa ed mus no be used as a compa ison
measu e. Ins ead, he compa ison measu e o be used is he adjus ed R-squa ed. Howe e , e en i
Model 7 shows a highe alue o his measu e, Model 9 has be e in e p e abili y, making i a se ious
con es an o inal model. A choice was made o alue in e p e abili y in his case as he di e ence
be ween R-squa ed alues is no much signi ican . Tha being said, Model 9 was chosen as he inal
model.
57
7. CONCLUSIONS
As s a ed in he In oduc ion, he p esen disse a ion p oposed o answe he ollowing ques ions:
▪ How did he numbe o domes ic iolence occu ences in Po ugal e ol e be ween 2009 and
2019?
▪ How well can panel da a eg ession explain his e olu ion?
▪ Wha a e he main causes o domes ic iolence?
▪ How does each explana o y a iable a ec he numbe o domes ic iolence occu ences?
In o de o achie e he p oposed goal, se e al models we e es ima ed using he numbe o domes ic
iolence occu ences agains spouse o analogous o a ia ions o his as he dependen a iable. Fi s
o all, i is possible o conclude ha explaining he e olu ion o domes ic iolence occu ences is a
di icul p ocess as a iables on he indi idual le el canno be included o explain occu ences in a
municipali y. Due o his, he models es ima ed ended up jus i ying app oxima ely 15 o 16% o he
o al a iance in he dependen a iable. The model selec ed as inal can be w i en as ollowing:
𝐷𝑉𝐴𝑆𝐴𝑖=0.1188+0.0180𝐷2010𝑖+0.0106𝐷2011𝑖+0.0133𝐷2014𝑖+0.0175𝐷2015𝑖+0.0222𝐷2016𝑖
+0.0345𝐷2017𝑖+0.0477𝐷2018𝑖+0.0697𝐷2019𝑖+0.0303𝐹𝑒𝑟𝑡𝑖𝑙𝑖𝑡𝑦𝑖
+0.0002𝐷𝑖𝑣𝑜𝑟𝑐𝑒𝑠𝑖+0.0001𝐺𝐸𝑅𝑖+0.0414𝑀𝑎𝑟𝑟𝑖𝑎𝑔𝑒𝑠𝑖−0.0011𝑊𝑎𝑔𝑒_𝐺𝑎𝑝𝑖
+0.0125𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡_𝑇𝑜𝑡𝑎𝑙𝑖+0.0364𝑇𝑜𝑡𝑎𝑙_𝐷𝑜𝑐𝑡𝑜𝑟𝑠𝑖+𝑒𝑖
This means ha in 2009, 2012 and 2013, i all he o he a iables a e se o 0 and holding e e y hing
else cons an , on a e age, he numbe o DVASA occu ences egis e ed by police au ho i ies pe 100
inhabi an s was 0.1188. In 2010, i is es ima ed ha municipali ies had, on a e age and holding all
o he ac o s cons an an ex a 0,018 DVASA occu ences egis e ed by police au ho i ies when
compa ed o 2009, 2012 and 2013. Acco ding o he same a ionale, o 2011, 2014, 2015, 2016, 2017,
2018 and 2019, i is expec ed ha municipali ies, holding all o he ac o s cons an , ha e an ex a
0.0106, 0.0133, 0.0175, 0.0222, 0.0345, 0.0477 and 0.0697, espec i ely, DVASA occu ences
egis e ed by police au ho i ies o 100 inhabi an s when compa ed o 2009, 2012 and 2013.
Fe ili y ep esen s he a e age numbe o child en bo n o each woman in e ile age. The coe icien
o his a iable is 0.0303, which means ha , holding all o he ac o s cons an , i is expec ed ha an
inc ease o one child pe woman in e ile age causes an inc ease o 0.0303 DVASA occu ences pe
100 inhabi an s in ha same municipali y. This co obo a es he idea s a ed in (Ellsbe g, Heise, Peña,
Agu o, & Wink is , 2001) ha claims ha women wi h mo e child en a e mo e likely o become
ic ims o domes ic iolence.
The a iable Di o ces ep esen s he numbe o di o ces pe 100 ma iages. Simila ly o Fe ili y, his
a iable has also p o en o be a isk ac o . As he numbe o di o ces inc eases, he numbe o DVASA
occu ences is also expec ed o inc ease, which can be seen in he posi i e coe icien associa ed o
his a iable in he model. One can say ha , i he numbe o di o ces by 100 ma iages inc eases by
10, holding all o he ac o s cons an , i is expec ed ha he numbe o DVASA occu ences pe 100
inhabi an s inc eases by 0.002. This co obo a es he heo y s a ed in (WHO - Wo ld Heal h
O ganiza ion, 2010), a i ming ha di o ces canno only be a consequence o domes ic iolence, bu
also a cause. People who a e sepa a ed o di o ced end o be mo e ulne able, inc easing hei
p obabili y o becoming ic ims o domes ic iolence.
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GER ep esen s he pe cen age o esiden popula ion wi h no mal age o a ending high school ha
is ac ually a ending high school. The coe icien o his a iable being posi i e was an as onishing ind.
I goes agains all p econcei ed ideas and all ideas exposed in he li e a u e e iew. I shows ha as
he pe cen age ep esen ed in GER inc eases, i is expec ed ha so does he numbe o DVASA
occu ences pe 100 inhabi an s. This a iable was e ie ed due o lack o da a ega ding he
educa ion le el o he popula ion by municipali y, so i migh be in e es ing o y he same eg ession
using a mo e app op ia e a iable, i made a ailable.
The a iable Ma iages ep esen s he numbe o new ma iages pe 100 inhabi an s and has a posi i e
coe icien associa ed, which makes i a isk ac o . This was expec ed as mos o domes ic iolence
ic ims a e ma ied. Howe e , his was a con o e sial a iable as i should be added in a way ha
e lec s pas ma iages. Ne e heless, municipali ies wi h mo e ma iages may also be mo e
conse a i e, which adds a new hypo hesis on he able. F om he model one can see ha i is expec ed
ha o each new ma iage by 100 inhabi an s, he numbe o DVASA occu ences by 100 inhabi an s
inc eases by 0.0414, holding all o he ac o s cons an .
Wage_Gap ep esen s he pe cen age o men’s mon hly pay ha women ecei e on a e age. The
coe icien o his a iable is nega i e, which mee s he heo y o exposu e educ ion, explained in
(Aize , 2010) which s a es ha , as he wage gap dec eases, he labo o ce pa icipa ion o women
inc eases and, consequen ly, domes ic iolence agains hem declines because women spend less ime
wi h iolen pa ne s. Acco ding o he model buil , o each pe cen ual poin ha women sala y gains
when aced wi h men mon hly gain, i is expec ed ha he numbe o DVASA occu ences by 100
inhabi an s dec eases by 0.0011, holding all o he ac o s cons an .
Unemploymen _To al ep esen s he numbe o people en olled in employmen and oca ional
aining cen e s pe 100 inhabi an s. As expec ed, he coe icien o his a iable is posi i e, making
unemploymen a isk ac o . Acco ding o he model, i is expec ed ha o each 10 addi ional pe sons
en olled in employmen and oca ional aining cen e s, he numbe o DVASA occu ences pe 100
inhabi an s inc eases by 0.0125.
Finally, To al_Doc o s was added o he da ase o y and igh unde epo ing, as doc o s a e he
p o essionals who deal di ec ly wi h he consequences o domes ic iolence and can epo
occu ences o he au ho i ies. This a iable ep esen s he numbe o doc o s pe 100 inhabi an s
acco ding o he Doc o s’ P o essional O de . I has a posi i e associa ed coe icien , as expec ed.
Acco ding o he model buil , i is expec ed ha each new doc o pe 100 inhabi an s leads o an
inc ease o epo ed DVASA occu ences by 100 inhabi an s o 0.0364, holding all o he ac o s
cons an .
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8. LIMITATIONS AND RECOMMENDATIONS FOR FUTURE WORKS
Explaining a good p opo ion o he o al a iance encapsula ed in he dependen a iable was
e ealed o be a ha d ask. When choosing o s udy domes ic iolence occu ences using a social
s uc u al heo y, i is almos ine i able ha explana o y a iables a e mos o he imes e y s a ic. A
lo o mac o-le el a iables end o e ol e e y slowly, causing a p oblem o low a iance in sho ime
se ies. This is wha happened wi h da a ga he ed o each municipali y and his is he eason why, o
e e y model c ea ed, much highe alues we e p esen ed o he be ween R-squa ed han o he
wi hin R-squa ed. Ne e heless, he main goal o a model like he ones buil in he p esen documen
is o allow au ho i ies o ac on he p oblem and, o ha ma e , di e ences on a spa ial le el a e
mo e impo an han on a empo al le el. Ne e heless, i is my opinion ha s udies ocused on he
indi idual-le el should be done o ind mo e p ominen causes o domes ic iolence.
Fu he mo e, i is impossible o know o su e whe he he a iance in he dependen a iable e lec s
eali y. As men ioned be o e, domes ic iolence is a c ime ha commonly akes place in he p i acy o
a home and, o ha eason, many cases may depend on sel - epo . This means ha acco ding o
(Ellsbe g, Heise, Peña, Agu o, & Wink is , 2001), he numbe o occu ences egis e ed may su e
om unde epo ing. Explana o y a iables also ha e hei own issues. Due o una ailabili y o da a,
some explana o y a iables a e no exac ly hose o iginally hough o he heo e ical model. I is he
case o all a iables ela ed o unemploymen , a iables ela ed o educa ion, among o he s. The
a iables ha ended up being used a e as close as possible o he o iginal idea, bu hey migh ha e
led o a no so ideal se o independen a iables in he inal model.
Finally, he only wo panel da a analysis app oaches used we e he cons an coe icien s and he ixed
e ec s. The e was an a emp o apply a andom e ec s app oach, bu i did no show e y p omising
esul s and, conside ing he scope o his wo k, was no pu sued. Howe e , I belie e ha i may be
possible o build in e es ing models on his subjec using andom e ec s. Ano he op ion would be o
y di e en slopes o di e en yea s by c ea ing in e ac ions be ween he dummy a iables al eady
c ea ed and o he explana o y a iables.
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9. BIBLIOGRAPHY
Acke son, L., Kawachi, I., Ba beau, E., & Sub amanian, S. (2008). E ec s o Indi idual and P oxima e
Educa ional Con ex on In ima e Pa ne Violence: A Popula ion-Based S udy o Women in
India. Ame ican Jou nal o Public Heal h, 507-514.
Aize , A. (2010). The Gende Wage Gap and Domes ic Violence. Ame ican Economic Re iew, 1847-
1859.
Ami halingam, K. (2005). Women's Righ s, In e na ional No ms, and Domes ic Violence:. Human
Righ s Qua e ly,, 683-708.
Ande be g, D., Raine , H., Wadswo h, J., & Wilson, T. (2015). Unemploymen and Domes ic
Violence: Theo y and E idence. The Economic Jou nal, 1947-1979.
APAV - Associação Po uguesa de Apoio à Ví ima. (2018). Homens Ví imas de Violência Domés ica
2013 - 2017. Lisboa: Associação Po uguesa de Apoio à Ví ima.
APAV - Associação Po uguesa de Apoio à Ví ima. (2018). Ví imas de Violência Domés ica 2013 -
2017. Lisboa: Associação Po uguesa de Apoio à Ví ima.
APAV - Associação Po uguesa de Apoio à Ví ima. (2020). Ví imas de Homicído Rela ó io APAV 2019.
Lisboa: Associação Po uguesa de Apoio à Ví ima.
Ba be , C. (2008). Domes ic Violence Agains Men. Nu sing S anda d, 35-39.
Bowlus, A., & Sei z, S. (2006). Domes ic Violence, Employmen and Di o ce. In e na ional Economic
Re iew, 1113-1149.
B asil, E., Al es, F., & Soa es, S. (2018). Dados 2017. Almada: OMA - Obse a ó io de Mulhe es
Assassinadas da UMAR.
B asil, E., Al es, F., & Soa es, S. (2019). Dados 2018. Almada: OMA - Obse a ó io de Mulhe es
Assassinadas da UMAR.
Campbell, J. (2002). Heal h Consequences o In ima e Pa ne Violence. The Lance , 1331-1336.
Cann, K., Wi hnell, S., Shakespea e, J., Doll, H., & Thomas, J. (2001). Domes ic Violence: A
Compa a i e Su ey o Le els o De ec ion, Knowledge and A i udes in Heal hca e Wo ke s.
Public Heal h, 89-95.
De ies, M., Mak, T., Ga cia-Mo eno, C., Pe zold, M., Child, C., Falde , G., . . . Wa s, H. (2013). The
Global P e alence o In ima e Pa ne Violence Agains Women. Science, 1527-1528.
Ellsbe g, M., Heise, L., Peña, R., Agu o, S., & Wink is , A. (2001). Resea ching Domes ic Violence
Agains Women: Me hodological and E hical Conside a ions. S udies in Family Planning.
Hill, R. C., G i i hs, W. E., & Lim, G. C. (2012). P inciples o Econome ics. John Wiley and Sons.

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Soa es, S., B anco, E., & Al es, F. (2020). Rela ó io Anual 2019. Almada: OMA - Obse a ó io de
Mulhe es Assassinadas da UMAR.
WHO - Wo ld Heal h O ganiza ion. (2010). P e en ing In ima e Pa ne and Sexual Violence Agains
Women: Taking Ac ion and Gene a ing E idence. Gene a: Wo ld Heal h O ganiza ion.
Woold idge, J. M. (2013). In oduc o y Econome ics: A Mode n App oach. Michigan: Sou h-Wes e n.
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10. ANNEXES
Annex I. Con empo aneous Co ela ion Ma ixes
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Annex II – His og ams o Explana o y Va iables