MASSIMILIANO MAZZANTI UNIVERSITY OF FERRARA CERIS CNR MILAN PALERMO, SEPTEMBER 12th 2012...

MASSIMILIANO MAZZANTI

UNIVERSITY OF FERRARACERIS CNR MILAN

PALERMO, SEPTEMBER 12th 2012

Environmental-Economic Performances in a

Dynamic Setting: Heterogeneous Slopes and Structural Breaks

Issues and Concepts

Usefulness of Slope heterogeneity analysis in environmental economics & policy

I will deal with examples under the umbrella of EKC and IPAT conceptual framework (structural change, decomposition analysis..)

Rationales Econometric rationale

(efficiency, correlation between units)

Better food for thought for policy and management (specific firm, sector, country effects)

More effective communication to non economist’s (the average coefficient problem..)

Econometric matters even (more) in policy and non economics fields…

A lawyier ‘expert’ for US Republicans on climate change recently affirmed in a congressional hearing on climate science:

“EPA cant declare GHG are a health problem, since emissions have been rising for a century, but public health has improved over the same period… “

Papers of Reference

Nicolli F. Mazzanti M. Iafolla V. 2012, Waste Dynamics, Country Heterogeneity and European Environmental Policy Effectiveness, J of Environmental Policy and Planning, i-first

Marin G. Mazzanti M., 2012, The relationship between environmental and labour productivities, J of Evolutionary Economics, i-first

Mazzanti M. Musolesi A., The heterogeneity of Carbon Kuznets Curves for advanced countries. Comparing homogeneous, heterogeneous and shrinkage/Bayesian estimators 2012, Applied Economics forth. and FEEM nota di lavoro 2010

Slope heterogeneity in the environmental economics applied literature

Recent advancements in EKC have focused on sub country and specific country heterogeneity in income-emission relationships

Seminal paper by List and Gallett (1999), Ecological Economics, on CO2 – income relationships at state level in the US

Recent working paper by Martinez Espineira on Bird abundance and GDP growth in a panel of Canadian regions

We already tried to focus on specific homogeneous areas rather than OECD or full sample

G7

0

0,5

1

1,5

2

8 8,5 9 9,5 10 10,5

log(y)

log

(co

2)

CANADA FRANCE GERMANY ITALYJAPAN UK USA FITTED VALUES (BAYES)FITTED VALUES (FE) FITTED VALUES (SWAMY)

Source: Mazzanti, Musolesi and Zoboli, 2010, Applied Economics

2040

6080

100

Em

issi

ons

(199

0=10

0)

1990 1995 2000 2005 2010Year

CO2 NOxSOxItaly Industrial emissions,

NAMEA (ISTAT)

01.

0e+0

72.

0e+0

73.

0e+0

74.

0e+0

75.

0e+0

7CO

2

DA DB DC DD DE DF DG DH DI DJ DK DL DM DN

1990 2007

CO2 emissions of manufacturing sectors: different dynamics

1.2

1.4

1.6

1.8

log(

CO

2 pe

r ca

pita

)

9 9.2 9.4 9.6 9.8 10log(GDP per capita)

AUSTRALIA

1.3

1.4

1.5

1.6

1.7

log(

CO

2 pe

r ca

pita

)


CANADA

.4.6

.81

1.2

log(

CO

2 pe

r ca

pita

)

8 8.5 9 9.5 10log(GDP per capita)

JAPAN

.8.9

11.

11.

2lo

g(C

O2

per

capi

ta)

9.2 9.3 9.4 9.5 9.6 9.7log(GDP per capita)

NEW ZELAND

.6.8

11.

21.

4lo

g(C

O2

per

capi

ta)

9 9.5 10log(GDP per capita)

NORWAY

1.6

1.7

1.8

1.9

log(

CO

2 pe

r ca

pita

)

9.4 9.6 9.8 10 10.2log(GDP per capita)

USA

EKC, CO2 diversity in long run trends, while most studies focus on average coefficient estimations (e.g. OECD)

.8.9

11.

11.

2lo

g(C

O2

per

capi

ta)

8.5 9 9.5 10log(GDP per capita)

AUSTRIA

.2.4

.6.8

11.

2lo

g(C

O2

per

capi

ta)

8 8.5 9 9.5log(GDP per capita)

GREECE

.81

1.2

1.4

log(

CO

2 pe

r ca

pita

)


IRELAND

.4.6

.81

1.2

log(

CO

2 pe

r ca

pita

)


ITALY

.2.4

.6.8

1lo

g(C

O2

per

capi

ta)

8 8.5 9 9.5log(GDP per capita)

PORTUGAL

.4.6

.81

1.2

log(

CO

2 pe

r ca

pita

)

8 8.5 9 9.5 10log(GDP per capita)

SPAIN

EU South

1.2

1.3

1.4

1.5

1.6

log(

CO

2 pe

r ca

pita

)


BELGIUM

11.

11.

21.

31.

41.

5lo

g(C

O2

per

capi

ta)


DENMARK

.6.8

11.

21.

4lo

g(C

O2

per

capi

ta)


FINLAND.9

11.

11.

21.

3lo

g(C

O2

per

capi

ta)


FRANCE

1.3

1.35

1.4

1.45

1.5

log(

CO

2 pe

r ca

pita

)

9 9.2 9.4 9.6 9.8log(GDP per capita)

GERMANY

11.

11.

21.

31.

4lo

g(C

O2

per

capi

ta)


NETHERLANDS.9

11.

11.

21.

31.

4lo

g(C

O2

per

capi

ta)


SWEDEN

1.25

1.3

1.35

1.4

1.45

log(

CO

2 pe

r ca

pita

)


UK

EU North

The way to deal with heterogeneity are many, some pragmatic some more

technically refined

We here hold attention on SUR – Seemingly Unrelated Regression -

contexts

Some notes on SURE models (Zellner’s 1962)

Applied both in cross section and panel contexts Need to test Systems of equations (by OLS and GLS)

e.g. Household demand function (food, housing, clothing)…typical cross section example

Seminal Grunfeld and Zellner papers on firm data 10 firms observed over 20 years

SUR ‘deliveries’ Higher efficiency wrt Fixed effects (constrained SUR which

accounts for correlation between units) Slope heterogeneity based output

In a nut-shell

1. Fixed effect model (LSDV or better within if N high in the panel) Two ways or without T dummies (testparm) E.g. the latter likely to be more efficient…

2. Then what if you are unsatisfied with homogeneous slopes?

3. First, we may try to look at LSDV dummies sign stability and significance reg i f c mu1-mu10, nocons (STATA)

Then, we may try to investigate whether the non observable heterogeneity affects slopes as well

SUR

In case we face a pretty long time series and a limited number of covariates, we can try to go further

The issue is the contemporaneous correlation between cross sectional units

E.g. systems of 10 equations with T=20y1t = a1 + b1 x1t + 1t

y2t = a2 + b2 x2t + 2t

....y10t = a10 + b10 x10t + 10t

Unconstrained and Constrained SUR

SURE…. ‘Model of apparently not related individuals’ Common effects captured by error terms related to unobservable information

We need to reshape reshape wide y x1 x2, i(year) j(cod) (note: j = 1 2 3 4 5 6 7 8 9 10) We now have created new variables

STATA estimates ‘i equations’, 1 to 10. Say we have 2 for learning

global i3(i3 f3 c3), f and c covariates, y dep var

global i8(i8 f8 c8)

. sureg (i3 f3 c3) (i8 f8 c8), corr (estimate only two equations here, 3 and 8)

This is an unconstrained SURE command in STATA

Unconstrained and Constrained SUR

TESTS

1. Through (Chi2) Breusch Pagan I check the correlation between errors SUR consistent and more efficient than OLS systems (often similar estimates but

lower s.e) 2. Towards Het slopes..

test [i3]x13=[i8]x18 (accum) We test all slope’s equality, 3 and 8 are here 2 equations Null Hp is equality (poolability)

If Not rejected, Constr SUR, that accounts for correlation but still witness slope homogeneity

Define constraints – might be burdensome but just in terms of do file construction, then apply SUREG

Very similar to LSDV FE, but we have individual variance in the errors and we account for correlations

* the test on equality may give different results when picking up different ‘couples’

If we apply a constrained SURE when the null is eventually rejected, s.e. rise due to the imposition of a non valid constraint

Applications

Nicolli et al., JEPP 2012

Waste Kuznets curves in the EUEUROSTAT data for EU15 over 1995-2008

Slope heterogeneity highlights various performances on decoupling

Waste generated. SURE Model, constrained slopes.

Constrained slope SUREConstrained slope SURE –

all variables

CONS 0.95*** 1.19***

CONS2 -0.03*** -0.038***

DENSPOP … -0.29***

POLIND … -0.002

TP [CONS per capita, millions of €]

7.521 6.311

Breusch-Pagan test of independence (p-value)

0.000 0.000

Note:. (…) means not included; significance at 10%, 5% and 1% denoted by *, ** and ***, respectively.

Note:. (…) means not included; significance at 10%, 5% and 1% denoted by *, ** and ***, respectively.

SUR: landfilled waste

Constrained SUR

Constrained SUR – all covariates

CONS 1.49*** 4.27***

CONS2 -0.10*** -0.19***

DENSPOP … -3.68***

POLIND … -0.82***

TP [€] 1,659.39 47,328.06

Breusch-Pagan test of independence (p-value)

0.000 0.000

Waste generated. SURE Model, unconstrained model

Countries CONS CONS2 TP [€] Delinking evidence

Austria 84.31*** -4.33*** 16,646.52 Absolute

Belgium -3.73 0.210 7,075.36 No delinking

Denmark -11.26 0.62 8,051.13 No delinking

France 3.57 -0.17 33,767.68 No delinking

Germany 1.89*** -0.12*** 1,633.113 Absolute

Greece 17.36*** -0.91*** 13,548.99 Absolute

Italy -8.73*** 0.487*** 7,842.28 No delinking

The Netherlands 9.28*** -0.47*** 16,578.1 Relative

Portugal 8.89*** -0.48*** 9,983.131 Absolute

Spain 24.03*** -1.29*** 10,885.79 Absolute

Sweden -17.5*** 0.96*** 8,700.899 No delinking

United Kingdom 5.09*** -0.25*** 21,529.84 Relative

Breusch-Pagan test of independence (p-value) = 0.000 F test of slope homogeneity (p-value) = 0.000

Marin and Mazzanti, JEE, 2012

Environmental and labour productivity dynamics in Italy

Sector based lensNAMEA (ISTAT) dataset on economic

and environmental accounts: sector branches (e.g. Food, coke & refinery) over 1992-2009

IPAT/EKC framework

SUR constrained estimates (manufacturing) - All emissions

SUR[manuf]

SUR[manuf]

SUR[manuf]

ln(CO2/L) ln(NOx/L) ln(SOx/L)

ln(VA/L) 2.8517***[0.03]

-3.4261***[0.17]

-11.6507***[0.41]

ln(VA/L)2 -0.2745***[0.003]

0.3455***[0.02]

1.1463***[0.04]

Stagnation 0.0189***[0.001]101.91%

-0.2257***[0.02]79.79%

-0.8337***[0.05]43.45%

Breusch-Pagan test of independence (Chi2)

448.746*** 376.77*** 632.504***

Test of aggregation bias (Chi2)

16589.74*** 19992.81*** 3418.68***

N*T 238 238 238

Period 1990-2006 1990-2006 1990-2006

Turning point(s) 180.3537***[1.94]

142.3858***[7.83]

161.0529***[3.52]

Shape (VA/L) Inverted U shape U shape U shape

What hides behind aggregate shapes?

s.e < FE case

SUR unconstrained estimates for CO2 (dependent variable: ln(CO2/L) )

Branch ln(VA/L) ln(VA/L)2 Shape(VA/L)

TP

VA/L

Stagn. Stagn. (%) ConstantMin Year Max Year

DA2.4189***

[0.23]- Linear - 37.99 1990 47.95 2000

0.1836***[0.05]

120.15%0.4785[0.87]

DB16.2782***

[1.46]-2.2945***

[0.21]Inv. U shape

34.7145***[0.55]

23.34 1990 34.78 2000-0.0533[0.03]

94.81%-

19.1502***[2.5]

DC45.1774***

[1.53]-6.5425***

[0.22]Inv. U shape

31.5834***[0.11]

25.11 1991 32.58 20010.0189[0.03]

101.91%-

69.4115***[2.6]

DD15.94***

[2.41]-2.2944***

[0.36]Inv. U shape

32.2564***[0.68]

22.94 1990 32.99 2001-0.0056[0.03]

99.44%-

18.8895***[4.04]

DE-25.5248*

[15.32]3.6168*

[2]U shape

34.0792***[5.65]

40.95 1990 51.46 20010.1121***

[0.03]111.86%

54.5399*[29.3]

DF0.1429***

[0.02]- Linear - 96.92 2006 266.04 1995

0.0237[0.03]

102.40%12.9344***

[0.09]

DG22.4233***

[5.2]-2.6966***

[0.61]Inv. U shape

63.9241***[1.46]

57 1990 82.71 2004-0.1081***

[0.03]89.75%

-35.1641***

[11.01]

DH38.0536***

[7.09]-4.9565***

[0.94]Inv. U shape

46.4664***[0.55]

40.12 1990 49.18 20060.027[0.02]

102.74%-

63.5661***[13.41]

DI-

38.0085***[2.6]

5.2095***[0.35]

U shape38.3977***

[0.32]37.13 1991 50.17 2006

-0.0098[0.02]

99.02%81.1714***

[4.86]

DJ42.916***

[6.9]-6.0225***

[0.94]Inv. U shape

35.2677***[0.6]

32.65 1990 43.03 2002-0.1531***

[0.04]85.80%

-65.9376***

[12.6]

DK110.5257**

*[14]

-14.156***[1.81]

Inv. U shape

49.5927***[0.29]

42.19 1993 50.09 2000-0.0151[0.05]

98.50%

-206.9535**

*[27.11]

DL30.8633***

[2.75]-3.8026***

[0.36]Inv. U shape

57.8702***[1.42]

37.38 1990 49.21 20010.0064[0.02]

100.64%-

54.1085***[5.24]

DM-

85.8531***[7.86]

11.4303***[1.04]

U shape42.7552***

[0.19]38.02 1993 47.11 2000

0.0817**[0.04]

108.51%170.497***

[14.86]

DN44.0742***

[8.46]-6.1415***

[1.22]Inv. U shape

36.1696***[0.87]

28.91 1991 36.11 20000.07***[0.02]

107.25%-

70.8135***[14.68]

Breusch-Pagan test of independence (Chi 2): 186.514***

constrained SUR estimates for manufacturing confirm the result of FE estimates. It is worth noting that as expected SUR estimates are more efficient than FE, with lower standard error and ‘Stagnation’ structural break that becomes significant.

This gain in efficiency depends on the high correlation among the disturbances of the different sectors

Unconstrained SUR estimates highlight an high degree of heterogeneity of the slopes across sectors, as confirmed by the test of the aggregation bias.

sectors that are robustly associated to absolute delinking are DG and DJ, both included in the EU ETS, and quite critical manufacturing sectors as far as pollution effects are concerned.

All other sectors show either linear (as DF, highly critical sector for GHG related environmental effects, with regional hot spots) or U shaped

false inference

The use of heterogeneous estimators can be motivated by the possible heterogeneity bias associated with the use of pooled estimators. As pointed out by Hsiao (2003), if the true model is characterised by heterogeneous intercepts and slopes, estimating a model with individual intercepts but common slopes could produce the false inference that the estimated relation is curvilinear.

Homogeneous slope models tend to capture EKC shapes even in presence of some outliers, they generally provide better

fits….

….but may hide the average structural relationship characterising the countries

Emerging Methodological issue

WE defined 39 constraints, I am not showing the do file…

Mazzanti and Musolesi, 2010, 2012

EnvKuznetsCurves Focus on advanced countries Looking at country / regions heterogeneity, income-time effects, structural breaks due to time related events

Structural breaks in a panel

Environmental Policy shocksOil shocks

Those can be captured by the time related component of the income-environmental relationship..

Disentangle income and time effects… Further look at separated effects by country Back to the heterogeneity issue

EU south

-.5

0.5

1lo

g(C

O2 p

er

capita)

1960 1970 1980 1990 2000year

lco2pc fitted_step93fitted_ramp93 fitted_step97

fitted_ramp97

North America and Oceania

.6.8

11.2

1.4

log(C

O2 p

er

capita)

1960 1970 1980 1990 2000year


fitted_ramp97

EU North.7

.8.9

11.1

1.2

log(C

O2 p

er

capita)

1960 1970 1980 1990 2000year


fitted_ramp97

Basic Model

(1) it ity f x

(2) 20 1 2it i it it ity x x

1,... , 1,...,i N t T yit is the logarithm of CO2 emissions per capita, xit is the logarithm of per capita GDP, i is individual effects and εit is the error term

Similar to many other studies (Azhomau et al 2006, JPE) we do not control for other possible determinants There are reasons for this specification. The first is data availability over long time series Second, this specification allows for a greater comparability with existing studies.

Homogeneous panel estimations (SURE, DOLS) We implement several tests of cross section

independence and in all cases they strongly reject the null hypothesis that the errors are independent across countries..

Heterogeneous panel estimations (MG, PMG, Bayes) This situation corresponds to our empirical framework

where: (i) per capita GDP presents high variation across countries, (ii) the different groups of countries cannot be characterised by a common slope and, consequently, there is a high risk of estimating a false curvilinear relation

Semi parametric Income and time effects

Homogeneous Panel estimators

Least Square Dummy (LSD) estimator allowing for individual fixed effects

The Dynamic ordinary least squares (DOLS) estimator The PMG estimator proposed by Pesaran et al. (1999)

which can be considered as an ‘intermediate’ estimator since it allows intercepts, short-run coefficients and error variances to differ freely across cross-sections while holding long-run coefficients the same The first three estimators (FEM, DOLS, PMG) assume

that all cross-section units are independent.

The Driscoll-Kraay (DK) (1998) non-parametric

estimator, which corrects the variance-covariance matrix for the presence of spatial as well as serial correlation

Seemingly Unrelated Regressions (SUR) specification proposed by Zellner (1962) allowing cross section correlation

Heterogeneous Panel estimators

the Swamy (1970) random coefficient, which is a weighted average where the weights are inversely proportional to their variance-covariance matrices

Mean Group (MG) estimator proposed by Pesaran and Smith (1995) for dynamic random coefficient models.

Bayesian approaches the hierarchical Bayes approach (Iterative) Empirical Bayes

benchmark (homogeneous)

Table 3 –Estimators allowing for cross sectional dependence: DK, SUR, DSUR

ModelDC SUR DSUR

coef. t-stat

.

coef.

t-stat.

coef.

t-stat.

coef.

t-stat

.

coef. t-stat

.

coef.

t-stat

.

coef.

t-stat

.

coef.

t-stat

.

coef.

t-stat

.

Group of countries

Umbrella EU north EU south Umbrella EU north EU south Umbrella EU north EU south

GDPpc (linear) 3.716 5.97

16.888

9.96

2.862

4.87

3.072

15.133

15.202

26.165

2.498

13.287

3.253

5.667

10.996

6.062

3.337

4.654

GDPpc (quadratic)

-0.173 -5.23

-0.890

-9.89

-0.132

-4.14

-0.138

-12.54

-0.796

-25.67

-0.113

-11.30

-0.031

-4.613

-0.096

-5.979

-0.038

-4.211

EKC shape inverted U inverted U inverted U inverted U inverted U Inverted U inverted U inverted U inverted U

Turning point ($1995)

46,160.715 13,195.623 51,067.782 68,216.025 14,030.586 63,139.216 87,040.245 14,449.242 33,796.922

Turning point range

out in out out in out out in Out

Table 4 – Heterogeneous estimators: Swamy, MG, Hierarchical Bayes Model Swamy MG Hierarchical Bayes

Group of countries Umbrella EU north EU south Umbrella EU north EU south Umbrella EU north EU south

coef. t-stat.

coef. t-stat. coef. t-stat.

coef. t-stat.

coef. t-stat. coef. t-stat.

coef. t-stat. coef. t-stat. coef. t-stat.

GDPpc (linear) 0.473 4.778 17.492 4.135 0.464 6.705 0.475 3.006 12.262 4.966 0.436 4.955 3.600 36.327 17.494 201.080 2.178 25.326

GDPpc (quadratic) … … -0.922 -4.229 … … … … -0.654 -5.070 … … -0.163

-3.630 -0.922 -36.888 -0.088

-2.667

EKC shape monotonic inverted U monotonic monotonic inverted U monotonic inverted U inverted U inverted U

Turning point ($1995) 13,172.68 11,785.41 62,501.4 13,159.87 236,806.82

Turning point range in in out in out

(…) means not included given not significance

Benchmark (heterogeneous)

for both the Umbrella group and southern European countries, most heterogeneous estimators provide evidence of a linear CO2-GDP

relationship. The estimated elasticity is always slightly lower than 0.5, which is a sign of relative de-linking.

Modelling income and time

A more general and, at the same time, an identifiable EKC specification is given by assuming that the income effect, the effect of (time invariant) unobserved heterogeneity, the effect of time and the idiosyncratic effect are separable:

y_{it}= c{i} + f(x_{it})+ g(t,i)+ ε{it}

where the effect of the time invariant unobserved variables is captured by introducing individual- fixed effects,

HOW THE ISSUES OF SLOPE HETEROGENEITY, NON CONSTRAINED

FUNCTIONAL FORM AND TIME RELATED UNOBSERVED FACTORS AFFECT THE

ESTIMATION OF THE EKC

f(x_{it}) and g(t,i).

Moving on…two steps…

Non constrained functional form and common time effect

we estimate the model with common nonparametric trend in order to avoid the omitted time related factors bias

A nonparametric random growth model

we include individual time trends by adopting a nonparametric extension of the random growth model

''

' ( )it i it iti

y i i s x f t 1

''

' ,it i it iti

y i i s x t 1

Semi parametric models

(relative fit tested by F tests)

Joint factor

GAM Model types

One can cope with fixed effects by applying differences and then use GAM (Azhomau et al. Wp2009)

Analogy: within vs LSDV model

We estimate ai+ f(xit)+uit considering ai as dummies to estimate in the non parametric part (e.g. Basile and Girardi, JEG10; Criado, Valente and Stengos, wp2009)

With N low the estimation is efficient and properly designed

You can also implement your model treating the subject intercepts as random effects (sample population). computationally inefficient if you have large numbers of random effects

GAM individual fixed effects (eq 8 with f(t)=0)

Eu south

Eu NorthUmbrella

These results, thus, are on the one hand quite similar to those commented on above for parametric panel models, in terms of economic significance, but on the other hand at the same time highlight the limits of parametric formulations.

Unobserved common time trends

introducing a common (non parametric) trend of the kind:

y_{it}= c{i} + f(x{it})+ g(t)+ ε{it}

GAM with individual fixed effects and nonparametric common trend (eq 8)

EU southEU North

Umbrella

overall time evolution of per capita emissions is driven more by the unobserved common factors related to various time effects

We believe that the issue is not what penalizes northern EU with regard to income related dynamics, but what has advantaged northern EU regarding the time related effects (over the all period, from the energy shock in the 70's 80's to the environmental policy era in the 90's).

Random growth model

We finally propose a nonparametric variant of the random growth model:

y_{it}= c{i} + f(x{it})+ g{i}(t) + ε{it}

which consists at generalising GAM by making interacting the country's indicator variable with the nonparametric trend.

One main reason is that even countries belonging to similar geographical/economic groups tend to `specialize' with respect to innovation, energy and also policy.

1. Including individual time effects

It is interesting to note that, beyond the economic policy's insights, including individual time effects is also important from a statistical point of view.

Indeed, both the Akaike/Bayesian Information Criterion - AIC and BIC strongly support such specification against the common time effects specification

(non linear) CO2-time shapes, inverted U North America, monotonic Oceania and South EU, Negative for EU NORTH

2. Individual time and income effects

A more general specification can be obtained by considering both individual time effects and individual income effects

it does improve very marginally upon the random growth -- homogeneous income effect specification.

Nevertheless, on the side of economic significance, we highlight that the only two countries showing an inverted U EKC / negative shape for both the income-carbon and CO2-time relationships are Sweden and Finland.

Main evidence

Overall, the countries differ more on their carbon-time relation than on the carbon-income relation which is in almost all cases monotonic positive.

Just a few Nordic countries show a bell curve in both income and time related factors.

MASSIMILIANO MAZZANTI UNIVERSITY OF FERRARA CERIS CNR MILAN PALERMO, SEPTEMBER 12th 2012...

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