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Resilience in Italian Inner Areas
Alessandra Faggian, Marco Modica and Giulia Urso
Gran Sasso Science Institute, L’Aquila, Italy
1
Trento 7th February 2019
A very brief introduction of resilience...
• Since the economic crisis of 2009, the concept of “resilience” has
gained popularity
• Urban and regional scientists follow suit, highlighting the importance of
“urban” and “regional” resilience
– A couple of special issues on the theme appeared, in the years
following the crisis, in prominent economic geography/regional
science journals dedicated entirely to this topic (Cambridge Journal
of Regions, Economy and Society 2010; Journal of Economic
Geography 2012; Annals of Regional Science 2017)
• It is clear that different regions (even within the same country) have a
different level of resilience, but let us start by defining what
“resilience” means..
2
• As Hill and Atkins (2012) point out economic resilience is
a concept frequently used in recent years but rarely well
defined
• It is a concept borrowed by physical sciences and it
refers to
“…the ability of an entity or system to ‘recover form and
position elastically’ following a disturbance or
disruption of some kind” (Chambers Dictionary, quoted in
Martin, 2012, p. 4)
3
• For a region this translates into its ability to recover from the negative effects of an
external shock
• However, there are –at least - two different interpretations of what “recovery” means
– First approach -“Equilibrium” analysis: ability to return to a pre-existing state in a
single equilibrium system (Hill and Atkins, 2012)
– Second approach – “Adaptive” capacity: ability to ‘absorb’ a shock shifting
towards a new and different equilibrium and growth path. Martin (2013) talks
about:
adaptive changes… to maintain or restore its previous developmental path, or transit to a new
sustainable path characterized by a fuller and more productive use of its physical, human and
environmental resources (p. 15)
4
• Martin (2012, p. 12) and Martin and Sunley (2013) identify
different dimensions of regional economic resilience to a
recessionary shock
Resistance
Degree of sensitivity or depth of reaction of a regional economy to
a recessionary shock (How far has the state or dynamic being
disturbed by the shock?)
Recovery
Speed and degree of recovery
Reorientation and Renewal
Ability of a region to adapt in response to the shock and renew its
growth path
5
Why resilience of peripheral areas?
2007 was the year urban population surpassed rural
population.
“In 2014, 54 per cent of the world’s population is
urban. The urban population is expected to continue
to grow, so that by 2050, the world will be one- third
rural (34 per cent) and two-thirds urban (66 per
cent)” (United Nations, 2014)
6
So “why should we care about peripheral areas”?
Some recent events have
brought to the attention
of the whole world, the
fact that the rural-urban
divide is increasing with
serious implications for
the direction of national
elections.
7
1. Because recently peripheral areas have had an important impact on the
world...
USA
The 2016
Presidential
elections are
often cited as a
key example
(Goetz et al.
2017)
8
Big difference in the size of the
counties that voting Democrat
(blue) vs. Republican (red)
Scaling the sizes of counties
to be proportional to their
population
Newman (2016)
http://www-
personal.umich.edu
/~mejn/election/20
16/
UK
The other often-cited
example of rural-urban
divide is Brexit. In
England the polarization
between rural and urban
areas was evident.
Liverpool
London
Cambridge
Manchester
Oxford
Leeds & York
Leicester
Warwick
Exeter
Reading
Newcastle
Bristol &
Bath
9
Peripheral areas have increasingly had the feeling of being left
behind and most of them experienced only a weak recovery
(where there was a recovery at all) from the Great Recession.
As Capello et al. (2015) pointed out, although the crisis was a world-wide
phenomenon, “its costs are characterized by a high degree of spatial
heterogeneity”, hence the regional dimension is critical to employment
creation efforts in the wake of the crisis (OECD Regional Outlook, 2011,
p.20; Camagni and Capello, 2014)
10
Globalization, the Great Recession and the peripheries
Oct 21st 2017
11
2. Because in peripheral areas two different types of “challenges” are co-
existing...
Two categories of disturbance:
1. Acute shocks, one-time
challenges/discrete events
(such as the Great Recession...)
2. Slow burns occur in systems
undergoing transformation,
and systems that are arguably
long since out of equilibrium
Pendall et al. (2010: 81)
UVAL (2014: 26)
Inner Areas are defined by the National
Strategy for Inner Areas (SNAI) as
“territories substantially far from centres
offering essential services (schools,
hospital, trains) and characterized by
depopulation and degrade” (UVAL, 2014:
abstract)
They suffered both “slow burn” (e.g.
marginalization, deindustrialization,
depopulation) - that tend to be corrosive
of regional adaptability capacity - and
the acute “shock” of the Great Recession
Our (very preliminary...) contribution
13
We focus specifically on the different levels of
resilience along the urban hierarchy, exploting
the inner areas classification (6 categories
from core to ultra-peripheral).
Moreover, following the approach by Dauth
and Suedekum (2016) we are interested in the
relationship between their industrial
composition and their ability to be resilient.
The idea is to identify a possible re-
orientation, we know surprisingly little on
this, i.e. relationship between industrial
change and resilience
Data
• We are focusing on one variable to proxy resilience, i.e.
employment (no complex index)
• Statistical Archive of Active Enterprises (Asia) by ISTAT on
employment rate by industrial sector at the municipal level
(2004-2014)
• We use 80 two digit sectors. No information on public and
agriculture sectors were available
14
Empirical strategy: 1. Descriptives
Three-step empirical
analysis:
1. We start with a
descriptive analysis
of trends over time
to identify possible
differences between
different areas with
a different degree of
“peripherality”
15
Peripheral areas had a two-year
delay and a deeper recession
(double dip, two crises of different
nature? We’ll get back to this...)
16
Among the most central areas,
it is actually the areas
surrounding the big cities
(“cintura”) that performed the
best...compatible with Faggian
et al. (2017) but also Dijkstra
et al. (2015) who found that in
fact the intermediate regions
in Europe responded to the
crisis the best
Breaking the trends further using the Inner Areas categories
2. “Excess of change”
2. The second step, following Dauth and Suedekum (2016), is to look at the
changes in sectoral composition before and after the acute shock of the
Great Recession, defining a sort of the “excess of change” (Dm) of
municipality (m) level as compared to the national one for each
industrial sector (s)
17
% change of employment in
sector s in municipality m
% change of employment
in sector s in the country
18
Best performing sectors at
national level
Worts performing sectors
at national level
Difference in employment growth between the nation and the
areas (here urban areas)
Pre-crisis Post-crisis
Very similar to
the national
trends
This is a graphical representation of:
Weighted sectoral growth at
national level
National boom
industries
National declining
industries
Industrial composition
19
Difference in employment growth between the nation and the areas
Pre-crisis Post-crisis
In peripheral
areas the
differences start
appearing...
Industrial composition
20
Difference in employment growth between the nation and the areas
Pre-crisis Post-crisis
• It is a measure for the strength of the change in local industry
composition over time, compared with the average national
pattern of structural change. Yet, with Dm alone we cannot
disentangle the direction of the regional change, i.e., we cannot
distinguish whether the change, compared to the nation, were –
using Dauth and Suedekum terminology - ‘pro-trend’ or ‘anti-trend’.
• In other words, were the changes aligning more the local areas to
the national economy or moving them further away?
• In order to do so, we need a further step...
21
3. Definition of “pro-trend” or “anti-trend” areas
22
The graphs presented before can help us distinguish
the areas in pro-trend vs. anti-trend in this way.
• If the municipality grows more than the nation in
growing sectors at national level (Area A) and
declines in declining sectors at national level (Area
B’) then it is “pro-trend”.
• On the opposite, if most of the excess of change
lines are in the areas A’ and B, they are “anti-
trend”.
23
Examples of pro-
trend and anti-
trend (Dauth and
Suedekum, 2016)
Rule to define pro-trend and anti-trend
 Pro-trend:
- if g = + :𝛼 𝑚
{𝑎,𝑔}
> 𝛽 𝑚
{𝑎,𝑔}
and 𝛼 𝑚
{𝑎,𝑔}
> 𝛼 𝑔
{𝑎}
- if g = - :𝛽′ 𝑚
{𝑎,𝑔}
> 𝛼′ 𝑚
{𝑎,𝑔}
and 𝛽′ 𝑚
{𝑎𝑔}
> 𝛽 𝑔
′{𝑎}
 Anti-trend:
- if g = + :β 𝑚
{𝑎,𝑔}
> α 𝑚
{𝑎,𝑔}
and β 𝑚
{𝑎,𝑔}
> 𝛽 𝑔
{𝑎}
- if g = - :𝛼′ 𝑚
{𝑎,𝑔}
> 𝛽′ 𝑚
{𝑎,𝑔}
and 𝛼′ 𝑚
{𝑎,𝑔}
> 𝛼 𝑔
′{𝑎}
24
This is Am
standardised by the
share in similar
regions of the same
category a (one of
the six categories of
Inner Area)
Rationale of the rules...
• E.g. the pro-trend rule has two parts to
be interpreted like this:
– First: Growth needs to be led mainly
by nationally booming sectors
– Second: Growth in the municipality is
stronger than the average in similar
municipalities (same peripherality
category)
25
26
Pre-Crisis
(2004 - 2008)
Post Crisis (2009 - 2014) Total
0 1 2
Anti Trend 69 494 46 609
Not significant 529 4,780 348 5,657
Pro Trend 163 1,257 130 1,550
Total 761 6,531 524 7,816
2004-2008 2009-2014
27
Freq. Percent
0 - No switch 4,979 63.7
1 - Switch 2,837 36.3
Total 7,816 100
4. Determinants of switching, anti-, pro-trend...
• We are now in the phase of understanding the characteristics of
municipalities pro-trend, anti-trend and those who “switched” between
the two periods...
• We started by looking at the switch with a logit model whose dependent
variable is simply 1 if switch; 0 otherwise.
• Control variables:
– Dummies of peripherality; Population: number of people (Census 2011); Institutional capacity:
Composite indicator (Atlante Prin-Postmetropoli) including Employees in the Public administration
over total population, Employees in state education over total population, Employees in public
health; Education: Ratio between people in the age 15-24 who does not attend a regular course of
study and population of 15-24 years (Census 2011); Poverty: Households with potential economic
discomfort (Census 2011); Income (log): Average income per household (Ministry of Economy and
Finance); Female Condition: Male employment rate over females employment rate (Census 2011);
Social Capital (Composite indicator from Nannicini et al. 2012); Density of business: Number of local
units per km2 (Atlante Prin-Postmetropoli); Affordability Index: Percentage of average annual
income needed to pay an average mortgage annual payment (own calculations on MEF data, 2011);
Inequality index: Gini index Atlante Prin-Postmetropoli
28
29
Controls: Places are
more likely to switch
if: smaller (pop), less
institutional capacity,
lower education,
lower social capitalThe more peripheral the areas, the more they
switch...(still to be understood: the different
directions!)
Further steps...
Aside from refining the model (controls?, IV?), some future steps include:
• Study the direction of the switch and all the possible combinations
• Progress further in the investigation of the characteristics of the different
areas and, in particular, the differences by sub-groups classified according
to peripherality
• Moreover, the post-crisis period is not so “post” in reality, so we could
divide that in two periods to test the effect of the “double dip” on
peripheries (economic crisis vs. financial crisis...) – it could also explain
then lag in the decline of peripheries after the first financial crisis
30
Thank you!
Marco Modica
marco.modica@gssi.it
31
 We apply this idea to the different municipalities classified by Inner
Area category (6 from A – Centre to F – Ultra peripheral)
 For each group a = {A, B, C, D, E, F} with above- and below-average
growth, g = {+,-} we compute the average excess change
𝐷+
𝑎
=
1
𝑁+
𝑎 ∗ 𝐷 𝑚𝑎+ ;
𝐷−
𝑎 =
1
𝑁−
𝑎
∗ 𝐷 𝑚
𝑎−
Where 𝑁𝑔
𝑎 is the number of municipalities in each group a, g
32
 Then we calculate the following shares for every municipality:
• 𝛼 𝑚
{𝑎,𝑔}
=
𝐴 𝑚
𝐷 𝑔
𝑎 ; 𝛼′ 𝑚
{𝑎,𝑔}
=
𝐴′ 𝑚
𝐷 𝑔
𝑎
• 𝛽 𝑚
{𝑎,𝑔}
=
𝐵 𝑚
𝐷 𝑔
𝑎 ; 𝛽′ 𝑚
{𝑎,𝑔}
=
𝐵′ 𝑚
𝐷 𝑔
𝑎
• With a = {A, B, C, D, E, F} and g = {+,-}.
• That is, we set the region-specific amplitudes |Am|; |A’m|; |Bm|; |B’m|; into perspective to the average excess
change level in comparable regions. Finally, we calculate the average of these shares 𝛼 𝑔
{𝑎}
, 𝛽 𝑔
{𝑎}
, 𝛼′ 𝑔
{𝑎}
, 𝛽 𝑔
′{𝑎}
.
33
34

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Resilience in Italian Inner Areas - Alessandra Faggian, Marco Modica and Giulia Urso

  • 1. Resilience in Italian Inner Areas Alessandra Faggian, Marco Modica and Giulia Urso Gran Sasso Science Institute, L’Aquila, Italy 1 Trento 7th February 2019
  • 2. A very brief introduction of resilience... • Since the economic crisis of 2009, the concept of “resilience” has gained popularity • Urban and regional scientists follow suit, highlighting the importance of “urban” and “regional” resilience – A couple of special issues on the theme appeared, in the years following the crisis, in prominent economic geography/regional science journals dedicated entirely to this topic (Cambridge Journal of Regions, Economy and Society 2010; Journal of Economic Geography 2012; Annals of Regional Science 2017) • It is clear that different regions (even within the same country) have a different level of resilience, but let us start by defining what “resilience” means.. 2
  • 3. • As Hill and Atkins (2012) point out economic resilience is a concept frequently used in recent years but rarely well defined • It is a concept borrowed by physical sciences and it refers to “…the ability of an entity or system to ‘recover form and position elastically’ following a disturbance or disruption of some kind” (Chambers Dictionary, quoted in Martin, 2012, p. 4) 3
  • 4. • For a region this translates into its ability to recover from the negative effects of an external shock • However, there are –at least - two different interpretations of what “recovery” means – First approach -“Equilibrium” analysis: ability to return to a pre-existing state in a single equilibrium system (Hill and Atkins, 2012) – Second approach – “Adaptive” capacity: ability to ‘absorb’ a shock shifting towards a new and different equilibrium and growth path. Martin (2013) talks about: adaptive changes… to maintain or restore its previous developmental path, or transit to a new sustainable path characterized by a fuller and more productive use of its physical, human and environmental resources (p. 15) 4
  • 5. • Martin (2012, p. 12) and Martin and Sunley (2013) identify different dimensions of regional economic resilience to a recessionary shock Resistance Degree of sensitivity or depth of reaction of a regional economy to a recessionary shock (How far has the state or dynamic being disturbed by the shock?) Recovery Speed and degree of recovery Reorientation and Renewal Ability of a region to adapt in response to the shock and renew its growth path 5
  • 6. Why resilience of peripheral areas? 2007 was the year urban population surpassed rural population. “In 2014, 54 per cent of the world’s population is urban. The urban population is expected to continue to grow, so that by 2050, the world will be one- third rural (34 per cent) and two-thirds urban (66 per cent)” (United Nations, 2014) 6 So “why should we care about peripheral areas”?
  • 7. Some recent events have brought to the attention of the whole world, the fact that the rural-urban divide is increasing with serious implications for the direction of national elections. 7 1. Because recently peripheral areas have had an important impact on the world...
  • 8. USA The 2016 Presidential elections are often cited as a key example (Goetz et al. 2017) 8 Big difference in the size of the counties that voting Democrat (blue) vs. Republican (red) Scaling the sizes of counties to be proportional to their population Newman (2016) http://www- personal.umich.edu /~mejn/election/20 16/
  • 9. UK The other often-cited example of rural-urban divide is Brexit. In England the polarization between rural and urban areas was evident. Liverpool London Cambridge Manchester Oxford Leeds & York Leicester Warwick Exeter Reading Newcastle Bristol & Bath 9
  • 10. Peripheral areas have increasingly had the feeling of being left behind and most of them experienced only a weak recovery (where there was a recovery at all) from the Great Recession. As Capello et al. (2015) pointed out, although the crisis was a world-wide phenomenon, “its costs are characterized by a high degree of spatial heterogeneity”, hence the regional dimension is critical to employment creation efforts in the wake of the crisis (OECD Regional Outlook, 2011, p.20; Camagni and Capello, 2014) 10 Globalization, the Great Recession and the peripheries Oct 21st 2017
  • 11. 11 2. Because in peripheral areas two different types of “challenges” are co- existing... Two categories of disturbance: 1. Acute shocks, one-time challenges/discrete events (such as the Great Recession...) 2. Slow burns occur in systems undergoing transformation, and systems that are arguably long since out of equilibrium Pendall et al. (2010: 81)
  • 12. UVAL (2014: 26) Inner Areas are defined by the National Strategy for Inner Areas (SNAI) as “territories substantially far from centres offering essential services (schools, hospital, trains) and characterized by depopulation and degrade” (UVAL, 2014: abstract) They suffered both “slow burn” (e.g. marginalization, deindustrialization, depopulation) - that tend to be corrosive of regional adaptability capacity - and the acute “shock” of the Great Recession
  • 13. Our (very preliminary...) contribution 13 We focus specifically on the different levels of resilience along the urban hierarchy, exploting the inner areas classification (6 categories from core to ultra-peripheral). Moreover, following the approach by Dauth and Suedekum (2016) we are interested in the relationship between their industrial composition and their ability to be resilient. The idea is to identify a possible re- orientation, we know surprisingly little on this, i.e. relationship between industrial change and resilience
  • 14. Data • We are focusing on one variable to proxy resilience, i.e. employment (no complex index) • Statistical Archive of Active Enterprises (Asia) by ISTAT on employment rate by industrial sector at the municipal level (2004-2014) • We use 80 two digit sectors. No information on public and agriculture sectors were available 14
  • 15. Empirical strategy: 1. Descriptives Three-step empirical analysis: 1. We start with a descriptive analysis of trends over time to identify possible differences between different areas with a different degree of “peripherality” 15 Peripheral areas had a two-year delay and a deeper recession (double dip, two crises of different nature? We’ll get back to this...)
  • 16. 16 Among the most central areas, it is actually the areas surrounding the big cities (“cintura”) that performed the best...compatible with Faggian et al. (2017) but also Dijkstra et al. (2015) who found that in fact the intermediate regions in Europe responded to the crisis the best Breaking the trends further using the Inner Areas categories
  • 17. 2. “Excess of change” 2. The second step, following Dauth and Suedekum (2016), is to look at the changes in sectoral composition before and after the acute shock of the Great Recession, defining a sort of the “excess of change” (Dm) of municipality (m) level as compared to the national one for each industrial sector (s) 17 % change of employment in sector s in municipality m % change of employment in sector s in the country
  • 18. 18 Best performing sectors at national level Worts performing sectors at national level Difference in employment growth between the nation and the areas (here urban areas) Pre-crisis Post-crisis Very similar to the national trends This is a graphical representation of: Weighted sectoral growth at national level National boom industries National declining industries
  • 19. Industrial composition 19 Difference in employment growth between the nation and the areas Pre-crisis Post-crisis In peripheral areas the differences start appearing...
  • 20. Industrial composition 20 Difference in employment growth between the nation and the areas Pre-crisis Post-crisis
  • 21. • It is a measure for the strength of the change in local industry composition over time, compared with the average national pattern of structural change. Yet, with Dm alone we cannot disentangle the direction of the regional change, i.e., we cannot distinguish whether the change, compared to the nation, were – using Dauth and Suedekum terminology - ‘pro-trend’ or ‘anti-trend’. • In other words, were the changes aligning more the local areas to the national economy or moving them further away? • In order to do so, we need a further step... 21
  • 22. 3. Definition of “pro-trend” or “anti-trend” areas 22 The graphs presented before can help us distinguish the areas in pro-trend vs. anti-trend in this way. • If the municipality grows more than the nation in growing sectors at national level (Area A) and declines in declining sectors at national level (Area B’) then it is “pro-trend”. • On the opposite, if most of the excess of change lines are in the areas A’ and B, they are “anti- trend”.
  • 23. 23 Examples of pro- trend and anti- trend (Dauth and Suedekum, 2016)
  • 24. Rule to define pro-trend and anti-trend  Pro-trend: - if g = + :𝛼 𝑚 {𝑎,𝑔} > 𝛽 𝑚 {𝑎,𝑔} and 𝛼 𝑚 {𝑎,𝑔} > 𝛼 𝑔 {𝑎} - if g = - :𝛽′ 𝑚 {𝑎,𝑔} > 𝛼′ 𝑚 {𝑎,𝑔} and 𝛽′ 𝑚 {𝑎𝑔} > 𝛽 𝑔 ′{𝑎}  Anti-trend: - if g = + :β 𝑚 {𝑎,𝑔} > α 𝑚 {𝑎,𝑔} and β 𝑚 {𝑎,𝑔} > 𝛽 𝑔 {𝑎} - if g = - :𝛼′ 𝑚 {𝑎,𝑔} > 𝛽′ 𝑚 {𝑎,𝑔} and 𝛼′ 𝑚 {𝑎,𝑔} > 𝛼 𝑔 ′{𝑎} 24 This is Am standardised by the share in similar regions of the same category a (one of the six categories of Inner Area)
  • 25. Rationale of the rules... • E.g. the pro-trend rule has two parts to be interpreted like this: – First: Growth needs to be led mainly by nationally booming sectors – Second: Growth in the municipality is stronger than the average in similar municipalities (same peripherality category) 25
  • 26. 26 Pre-Crisis (2004 - 2008) Post Crisis (2009 - 2014) Total 0 1 2 Anti Trend 69 494 46 609 Not significant 529 4,780 348 5,657 Pro Trend 163 1,257 130 1,550 Total 761 6,531 524 7,816 2004-2008 2009-2014
  • 27. 27 Freq. Percent 0 - No switch 4,979 63.7 1 - Switch 2,837 36.3 Total 7,816 100
  • 28. 4. Determinants of switching, anti-, pro-trend... • We are now in the phase of understanding the characteristics of municipalities pro-trend, anti-trend and those who “switched” between the two periods... • We started by looking at the switch with a logit model whose dependent variable is simply 1 if switch; 0 otherwise. • Control variables: – Dummies of peripherality; Population: number of people (Census 2011); Institutional capacity: Composite indicator (Atlante Prin-Postmetropoli) including Employees in the Public administration over total population, Employees in state education over total population, Employees in public health; Education: Ratio between people in the age 15-24 who does not attend a regular course of study and population of 15-24 years (Census 2011); Poverty: Households with potential economic discomfort (Census 2011); Income (log): Average income per household (Ministry of Economy and Finance); Female Condition: Male employment rate over females employment rate (Census 2011); Social Capital (Composite indicator from Nannicini et al. 2012); Density of business: Number of local units per km2 (Atlante Prin-Postmetropoli); Affordability Index: Percentage of average annual income needed to pay an average mortgage annual payment (own calculations on MEF data, 2011); Inequality index: Gini index Atlante Prin-Postmetropoli 28
  • 29. 29 Controls: Places are more likely to switch if: smaller (pop), less institutional capacity, lower education, lower social capitalThe more peripheral the areas, the more they switch...(still to be understood: the different directions!)
  • 30. Further steps... Aside from refining the model (controls?, IV?), some future steps include: • Study the direction of the switch and all the possible combinations • Progress further in the investigation of the characteristics of the different areas and, in particular, the differences by sub-groups classified according to peripherality • Moreover, the post-crisis period is not so “post” in reality, so we could divide that in two periods to test the effect of the “double dip” on peripheries (economic crisis vs. financial crisis...) – it could also explain then lag in the decline of peripheries after the first financial crisis 30
  • 32.  We apply this idea to the different municipalities classified by Inner Area category (6 from A – Centre to F – Ultra peripheral)  For each group a = {A, B, C, D, E, F} with above- and below-average growth, g = {+,-} we compute the average excess change 𝐷+ 𝑎 = 1 𝑁+ 𝑎 ∗ 𝐷 𝑚𝑎+ ; 𝐷− 𝑎 = 1 𝑁− 𝑎 ∗ 𝐷 𝑚 𝑎− Where 𝑁𝑔 𝑎 is the number of municipalities in each group a, g 32
  • 33.  Then we calculate the following shares for every municipality: • 𝛼 𝑚 {𝑎,𝑔} = 𝐴 𝑚 𝐷 𝑔 𝑎 ; 𝛼′ 𝑚 {𝑎,𝑔} = 𝐴′ 𝑚 𝐷 𝑔 𝑎 • 𝛽 𝑚 {𝑎,𝑔} = 𝐵 𝑚 𝐷 𝑔 𝑎 ; 𝛽′ 𝑚 {𝑎,𝑔} = 𝐵′ 𝑚 𝐷 𝑔 𝑎 • With a = {A, B, C, D, E, F} and g = {+,-}. • That is, we set the region-specific amplitudes |Am|; |A’m|; |Bm|; |B’m|; into perspective to the average excess change level in comparable regions. Finally, we calculate the average of these shares 𝛼 𝑔 {𝑎} , 𝛽 𝑔 {𝑎} , 𝛼′ 𝑔 {𝑎} , 𝛽 𝑔 ′{𝑎} . 33
  • 34. 34