lectures in applied econometrics ch. 1. amazonian...

Ch. 1. Amazonian Deforestation 2015-16

Lectures in Applied EconometricsCh. 1. Amazonian Deforestation

M1 E-Quant (Quantitative Economics)

Pr. Philippe Polomé, Université Lumière Lyon 2

2015 – 2016


Introduction

Outline

Introduction

Time-series Theory

Deforestation Data & Analysis

References


Introduction

Definition and scope

I United States Environmental Protection Agency definesdeforestation as the "permanent removal of standing forests."

I Amazonian Deforestation is monitored by Landsat since 1975I Google publishes some images

In pictures, from Landsat, Google Annual Timelapse


Introduction

Why is this an important issue ?

I Biodiversity reservoirI Habitat loss

I Carbon sinkholeI + deforesting emits carbon

I By burningI Released from soil

I Changes moisture in the airI Causes droughts down South


Introduction

Why is this an important issue ?

I Social issue 1 : not developementI Deforestation is mostly due to agricultureI Cattles mostly (about 80%), on planted pasture

I The Amazon basin appears generally not well-suited for crops,soy-bean in particular [9].

I 70% of formerly forested land in the Amazon, and 91% of landdeforested since 1970, is used for livestock pasture

I This in turns causes soil erosion and flash floods

I Social issue 2 : Indigenous people


Introduction

Deforestation Time Profile

Source: Landsat images interpreted by PRODES project of the Instituto de PesquisasEspaciais since 1975 - Values for some years linearly interpolated.

I This is the “Legal Amazon” deforestationI Why is it declining since the mid-2000’s ?


Introduction

Causes of Deforestation

Outline

IntroductionCauses of DeforestationEnvironnemental KuznetsCurves

Time-series TheoryTrendsI(0)Autorregressive Errors of Order1 AR(1)Stationnarity : integration oforder 1 I(1)Deciding if a time-series is I(1)

CointegrationErrors correction modelsJohansen Test of Cointegration

Deforestation Data & AnalysisAnalysis: EKC, I(1) tests andcointegrationAlternative TheoryOther Econometric IssuesThe Estimated RelationOther Explanatory variablesDiscussion and conclusionsDigression

References


Introduction



I Are certainly complexI but primarily driven by human actionI Hence economic might be a factorI And thus it may compete with other economic activities

I The 70’s and 80’s deforestation had been induced by governmentpolicies and subsidies

I Slash and burn agriculture appears much less prevalent than it was


Introduction


World Bank 2004 [9]: Deforestation in the 90s and early 00s

I Attributed mainly to cattle ranchingI Soybean to a much lesser extentI Grass does not deplete the soil so muchI The 1995 peak was attributed to accidental forest fire

I Agriculture and cattle ranching may be more profitable in theAmazon due to

I weak land titling, land grabbing, irregular labor contracts,I and the continuous process of opening up of new forest areas

I The later are carried out at low cost by small farmersI who prepare the land for medium- and large-scale cattle ranching

which follow them

I Small farmers are less blamed than they once were


Introduction


Causes of DeforestationI Weinhold and Reis [12]

I analyse the way roads creation induces deforestationI it turns out that is does only in areas that have not seen

deforestationI but it reduces deforestation in areas where land is already cleared

I Nasa Earth Observatory1 states:This pattern follows one of the most common deforestation

trajectories in the Amazon. Legal and illegal roads penetrate a remote partof the forest, and small farmers migrate to the area. They claim land alongthe road and clear some of it for crops. Within a few years, heavy rains anderosion deplete the soil, and crop yields fall. Farmers then convert thedegraded land to cattle pasture, and clear more forest for crops. Eventuallythe small land holders, having cleared much of their land, sell it orabandon it to large cattle holders, who consolidate the plots into largeareas of pasture.

1Anonymous, 2012 data, accessed October 2015 athttp://earthobservatory.nasa.gov/Features/WorldOfChange/deforestation.php


Introduction



I “Geography”: Kauppi et.al. 2006 [7]I Above a certain level of income, countries stop to deforestI Evidence is essentially a world-wide cross-section

I This points to an explanation economists are familiar with:I Deforestation as worldwide cross-section follows an

Environmental Kuznets Curve


Introduction

Environnemental Kuznets Curves

Outline





References


Introduction


Hypothesis: Environmental Kuznetz Curves EKC

I S. Kuznets (1955) suggested an inverted U-shaped relationshipbetween economic growth and income inequality

I At first, economic development induces major inequalitiesbetween the richs and the poors

I As income (per capita) rose, inequalities would become moreintolerable and disappear

I Possible because of money transfer, better opportunities or bettereducation / health care / public goods

I Environnemental KC suggested by Grossman & Kruger [4][5]I Environmental damage first worsen and then recover as income

per capita risesI Emissions, deforestation,...


Introduction


Formal EKC

I Larger levels of per capita income are associated with graduallylower levels of pollutants

yt = b0+b1GDPht +b2GDPh2t + gxt + et


Introduction


Evidence for EKC

I Cross-section or Panel studies found EKC on occasionI Is that causal or spurious?

I Stern 2004 [10]I EKC for CO2 and CO2eq emissions is an artefact (=spurious) of

the analysisI Instead, the apparent EKC is a mixture of effects:

1. Pollution increases roughly monotonically (linearly) with income2. But “time” reduces pollution, that is, income-independant policies3. In rapidly growing middle-income countries, the income effect (%

pollution) overwhelms the time effect4. In wealthy countries, growth is slower, and pollution reduction

efforts can overcome the income effect

I That is what causes an apparent EKC effect in cross-section orpanel data sets


Introduction


Time-series

I Stern 2004 [10] and others clearly identify EKC as a time-seriesissue

I as a cross-section forces all countries to the same pathI and a panel only allows a different starting point but the same

curvature

I In other words, Kauppi et.al. [7]I make the same mistake as earlier papers on identifying an EKC in

CO2 emissionsI Their results could then be an artefact


Introduction


Comparing Deforestation across Countries

I Barbier and Burges (2001)I Survey of the economics of tropical deforestationI Indicate that even if countries might follow an EKC,

I They are unlikely to follow all the same path

I Lambin & Meyfroidt 2011 [8]I using forest cover evidence in a more “geographical” studyI indicate that “there is no default forest transition pathway”

I Both these results are to be interpreted against resorting tocross-sections or even panel studies to test EKC


Introduction


Meta-analyses

I Lack of an EKC is generally NOT clearly established fordamages / emissions other than CO2

I For deforestation, mixed issue

I Choumert et.al. [2]I Review 69 papers on Environmental Kuznets Curve for

deforestationI They find only one paper using time-series

I Probably Shafik, N. & Bandyopadhyay, S., 1992I It is not cointegration

I The economics literature does not appear to supply anexplanation for the current decreasing trend in deforestation

I But a more “geography-oriented” literature does not hesitate topoint to economic factors


Introduction


Objectives

I This paper proposes to test EKC for Brazil deforestationI Because there is a well-documented and relatively long

time-seriesI Currently 40 years

I Regression analysis of Deforestation on GDPh and its square ?I Number of issuesI But the cointegration issue appears both essential and untreated


Introduction


EKC Econometric Issues in a NutshellI Deforestation is a time-series

I Non stationary “stochastic trend”I No stable expectation or varianceI Several well-known statistical tests

I But no “deterministic trend” yt = a +b t+ et

I So Deforestation decline cannot be “only time”

I GDPh is also a non stationary seriesI Regression of non-stationary on non-stationary is spuriousI Unless Cointegration

I A difference between the two series is stationaryI Large literature in econometrics / financeI But not used in Deforestation EKC studies (roughly 70 studies)

I Could EKC be the cointegration relation ?I Cointegration relation could be more complex

I Other series should be considered


Time-series Theory

Outline

Introduction

Time-series Theory


References


Time-series Theory

Time Series

I Are very commonI Most macroeconomic data : GDP, inflation, unemployement...I Individual (or population aggregate) employment, wage,

consumption ...I Stock quotes : yearly, monthly, daily, real-time. . .I Exchange rateI Sales / purchases in a firm

I Time-series are often considered autocorrelatedI The present is influenced by the past

I This section is mostly based onI Wooldridge [13]I the Gretl User’s Guide[3]


Time-series Theory

Time-series vs. cross-section

I Time-series observations are naturally orderedI Cross-section data has no natural order

I except geo-localised data

I Time-series observations proceed from a random stochasticprocess

I Cross-section data proceed from a random sample

I Time-series models are usually indexed by t :

yt = b0+b1x1t + . . .+bkxkt + et


Time-series Theory

Distributed lags model

I Model yt = b0+d0xt + et is said staticI Classical Phillips’ curve inflationt = b0+b1unemploymentt + et

I Finite distributed lags (of the regressor) modelsI one or several x impact y with one or more lagsI gft = b0+d0tet +d1tet�1+d2tet�2+ et

I gf “general (average) fertility” (re-used later)I te “tax exemption”I this an “order 2” distributed lag

Id0 = immediate impact (= short term) from x on y

I The set d0,d1, . . . ,dq describes the long-term relation between xand y


Time-series Theory

Shocks

I Order 2 model yt = b0+d0xt +d1xt�1+d2xt�2+ et

I Transient shock (1 t) � on constant x at time t

I yt = b0+d0 (x+�)+d1x+d2x+ etI yt+1 = b0+d0x+d1 (x+�)+d2x+ et+1I yt+2 = b0+d0x+d1x+d2 (x+�)+ et+2

I Permanent shock (starting from time t) � on constant xI yt = b0+d0 (x+�)+d1x+d2x+ etI yt+1 = b0+d0 (x+�)+d1 (x+�)+d2x+ et+1I yt+2 = b0+d0 (x+�)+d1 (x+�)+d2 (x+�)+ et+2


Time-series Theory

Trends

Outline





References


Time-series Theory

Trends

Trend models

I Model yt = b0+d0t+ et i s a trendI yt “follows” the time flow with a stochastic noise e

I Several specificationsI Computer-simulated on Trend and RndWalk.ods on websiteI Monte-Carlo


Time-series Theory

Trends

Linear trend yt = b0+b1zt +b2t+ et , t = 1,2 . . .T


Time-series Theory

Trends

Quadratic trend yt = b0+b1zt +b2t+b3t2+ et

I Not easy to spot or to differentiate from a ln


Time-series Theory

Trends

Exponential trend yt = exp(b0+b1zt +b2t+ et)

I � ln(yt) = ln(yt)� ln(yt�1)⇡yt � yt�1

yy�1I The log-differential approximately equals the growth rateI For rather small rates

I An expon. trend without regressor is then lnyt = b0+b2t+ et

I Happens when y has the same growth rate every tI �ln (yt) = b2+�et : cst growth rate + zero-expectation error


Time-series Theory

Trends

Spurious Regression

I Economic chronological variables may have a temporal trendI Regressing a trend on a trend often seems like a good idea :

I R2 & t are often highI However, unobserved (by the econometrician) variables may

actually be causing the trendsI 3 examples below

I The unobserved variables may be controled for introducing adeterministic time trend

I the significance of the other regressors might then be brought backto their correct levels

I the time trend maybe only a proxyI So: not explaining anything


Time-series Theory

Trends

Spurious Example 1: The storks and the babies

I Fisher, 1936, Copenhagen,post WWII decade

I B = b0+b1S+ e

Ib1 = .15 with t-stat 5.98

I What is up ?


Time-series Theory

Trends

Spurious Example 1: The storks and the babies

I Fisher, 1936, Copenhagen,post WWII decade

I More likely: reconstruction +rural migration to the city

I Assuming migration andconstruction are linear:time trend

I B = b0+b1S+b2t+ e

Ib1 = .03 with t-stat 0.34

I However low dof


Time-series Theory

Trends

Note on storks and babies

I Birds that leave Northern & Central Europe in autumn and comeback early april

I That is about 9 months after the summer solstice (21 of June /Saint John)

I The summer soltice was an important pagan (and later Christian)festival

I In which many people would marry...


Time-series Theory

Trends

Spurious Example 2 : property investment and pricesI Gretl

I File ! open data : sample fileI Wooldridge tab

I hseinv.gdtI data from [13]

I 1947-88 seriesI General info under Data ! Dataset infoI housing investment per capI housing priceI ...

I Data ! dataset structureI time-seriesI indicate

I periodicityI start period


Time-series Theory

Trends

Spurious Example 2 : property investment and pricesI model menu : OLS Regression

\ln(invpc) =�.55+1.24 ln(price)I Household property investment elasticity wrt price is

significantly different from zero but not from oneI A change in price appears completely passed on to the investmentI But both series follow a trend


Time-series Theory

Trends

Spurious Example 2 : property investment and prices

I Adding a trend (data menu)

\ln(invpc) =�.91� .38 ln(price)+ .0098t

I Price is not significant any moreI But the (real) investment grows of about 1% yearlyI Possibly, this might be due to omitted regressors

I The previous result was spuriousI If y and x have opposing trends

I Introducing a trend may increase the significance of xI The t-stat of a trend is not necessarily correct as we will see on

the section on I(1)


Time-series Theory

Trends

Spurious Example 3 : simulated data

I Trend and RndWalk.ods tab Trend on trend


Time-series Theory

Trends

De-trending

I To purge the data from the trend (detrend)I Instead of introducing a linear trend in the regression

1. Regress each variable from the model on a trend2. Use the residuals from each equation as new variables

I like a redefinition

I For example yt = b0+b1zt + et

1. Creation de-trended variables yt = g0+ g1t+zt 99K ydt = zt

zt = q0+q1t+xt 99K zdt = xt

2. Regress the de-trended variables ydt = lzdt +nt

I Intercept no more useful since E�ydt

�= E

�zdt

�= 0


Time-series Theory

Trends

De-trending (2)I Introducing a trend and using de-trended variables are in

principle equivalent approachesI But de-trending is a 2-step method

I introduces a measurement error in the 2nd stepI The de-trended variables are constructed on the basis of estimated

parametersI

xt is a measurement of zdt with errorI Thus the results are not identical

I Why use de-trending ?I Time-series regressions often have a high R2

I mostly because of the trend, which does not explain anythingI So such R2 does not reflect the real explanatory power of the

estimated modelI The R2 of the regression using de-trended variables is likely a

better measure of the true explanatory power of the model


Time-series Theory

I(0)

Outline





References


Time-series Theory

I(0)

Stationnarity

I A stochastic process is stationnaryI When its distribution does not change through time

I parameters included

I Stationnarity is similar to “identically distributed”

I A trend is not stationnary since its expectation changes with timeI A stochastic process is said covariance-stationnary

I If its expectation and its variance are constant through timeI And if the covariance between 2 periods depend only on the

number of periods between them

I Stationnary process are covariance-stationnaryI unless the covariance is •


Time-series Theory

I(0)

Integration

I A stationnary process is integrated of order zero I(0) ifI xt and xt+h are “nearly independant” when h! •I We also say weakly dependent for I(0)

I A similar definition exists for a non-stationary processI I(0) is similar to “independently distributed”

I A covariance-stationnary series is I(0) ifI its correlation between xt and xt+h ! 0 when h! •

I I(0) implies that some law of large numbers and central limittheorem may be applied

I It replaces the (simple) random sample hypothesis, that is “iid”I I(0) is a sufficient condition to use a time series in regression


Time-series Theory

I(0)

MA(1) : moving average process of order 1

I MA(1) xt = et +aet�1, t = 1,2, . . .I {et : t = 0,1, . . .} is an i.i.d. sequence with mean zero and

variance s

2e

I et is a White Noise

I An MA(1) is I(0)I Adjacent terms (in a sequence) are correlatedI As soon as there are 2 periods between 2 terms of an MA(1),

correlation falls to zero since et is i.i.d.I Since et is i.i.d., an MA(1) is stationnaryI Clearly an MA(1) is covariance-stationnary


Time-series Theory

Autorregressive Errors of Order 1 AR(1)

Outline





References

AR(1) : et = ret�1+µt autoregressive process of order 1

I AR(1) is said stable when |r|< 1 [vs. explosive]I

µt ⇠ iid�0,s2

µ

�white noise

I Expectation 0, constant variance and covariance 0

I We can write et = µt +rµt�1+r

2µt�2+ . . .

I So var (et) = s

2e

= s

2µ

+r

2s

2µ

+r

4s

2µ

+ . . .=s

2µ

1�r

2

I And cov (et ,et�1) = cov (ret�1+µt ,et�1) = rs

2e

=rs

2µ

1�r

2

I Substituting successively in the AR(1)

et = ret�1 +µt = r (ret�2 +µt�1)+µt = r

2et�2 +rµt�1 +µt = . . .= r

set�s +

s�1

Âi=0

r

iµt�i

Thus cov (et ,et�s) =r

ss

2µ

1�r

2 = r

ss

2e


Time-series Theory


Matrix of var-cov of AR(1) errors

⌃e

= s

2e

0

BBBBB@

1 r r

2 · · · r

T�1

1 r · · · r

T�2

. . ....

1 r

sym 1

1

CCCCCA

= s

2e

IT +s

2e

0

BBBBB@

0 r r

2 · · · r

T�1

0 r · · · r

T�2

. . ....

0 r

sym 0

1

CCCCCA

= s

2e

IT +s

2e

�

AR(1) stable is I(0)I Stationnary

since µt i.i.d.I Cov ! 0 when

time betweenperiods ! •


Time-series Theory


Var-cov matrix of the OLS coefficients MCO with AR(1)errors

I y = Xb + e with et = ret�1+µt

⌃b

=⇣X

0X⌘�1

X0⌃

e

X⇣X

0X⌘�1

=⇣X

0X⌘�1

X0 ⇥

s

2e

IT +s

2e

�⇤X⇣X

0X⌘�1

= s

2e

⇣X

0X⌘�1

+s

2e

⇣X

0X⌘�1

X0�X

⇣X

0X⌘�1

I It cannot be shown whether it is larger than ⌃b

= s

2e

⇣X

0X⌘�1

I Thus, it is not known whether the t-stats will be over- orunder-evaluated


Time-series Theory

Stationnarity : integration of order 1 I(1)

Outline





References


Time-series Theory


Random walk definition

I In an AR(1), the hypothesis |r|< 1 is crucial for the series to beI(0)

I Many economic time-series are better described with an AR(1)where |r|= 1 :

I yt = yt�1+ et : called a random walk

I PredictionI Since E

�et+j |yt

�= 0 8j � 1, we have E (yt+h|yt) = yt 8h � 1

I So that whatever the time difference h, the best prediction foryt+h is yt


Time-series Theory


yt = yt�1+ et with e ⇠ n (0,4) and y0 = 0

Computer-simulated data, to show random walk profileI Trend and RndWalk.ods tab Rnd walk


Time-series Theory


Random walk and OLS

I Variance of a random walk % linearly with time (in theory)I An AR(1) process is thus non-stationnary

I since its distribution changes with time

I It can be shown it is not I(0) eitherI xt and xt+h do not become nearly independents when h! •

I So the OLS hypotheses for time-series (i.i.d. equivalent) are notsatisfied

I OLS has unknown properties


Time-series Theory


I(1)

I A random walk is one particular case of unit root or I(1) processI Such an I(1) process is “strongly persistent” or “long memory”

I “Trend” 6= “strongly persistent”I Series like interests rates, inflation or unemployement are often

considered “long memory”I but have no clear trend

I But in many other cases, a long memory series also has a cleartrend

I e.g. a random walk with drift : yt = ⌦+ yt�1+ etI ⌦ is the driftI See plot next page


Time-series Theory


yt = ⌦+ yt�1+ et with e ⇠ n (0,4), y0 = 0 and ⌦= .05

Drift : yt = ⌦+ yt�1+ et = 2⌦+ yt�2+ et�1+ et = . . .

Computer-simulated data, to show random walk with drift profileI Trend and RndWalk.ods tab Rnd walk


Time-series Theory


Regression between I(1)

I A simple regression between 2 independent I(1) will often resultin a significant t-stat

I Even without trend in any variable

I Let 2 random walks yt = yt�1+ et and xt = xt�1+atI Specify yt = b0+b1xt +xt ,I Then H0 : b1 = 0 is true,I but xt contains yt�1 which is a random walk,I Then the t-stat associated with b1, t

b1! • when T ! •

I The limit distribution of tb1

is not normal

I So we are led to think x is a significant regressor for y

I Simulated ExampleI Trend and RndWalk.ods tab Spurious I(1)


Time-series Theory


Remark : the types of spurious regressions1. In a cross-section

I Spurious regression may be due to unobserved heterogeneityI 2 variables are unrelated, but are both correlated to a third

I Regressing the 1º on the 2º, it appears that the relation issignificant

I but inserting the 3º variable, then the 2º looses its significance

I This phenomenon may also occur in time-seriesI e.g. Storks & babies

2. A spurious relation also occurs between series who share a trendI Both series have a positive trend or a negative oneI This issue may be solved by inserting a trend in the model

I but not always

3. 2 I(1) series often appear in a spurious relation


Time-series Theory


First Differences

I The first difference of a unit root yt : yt � yt�1

I is I(0) : yt and yt+h become near independent when h! •I and is often stationnary

I its distribution does not change with time

I It is said that the series is difference-stationnary

I Many series yt that are > 08t are such that ln(yt) is I(1)I Then we often can use ln(yt)� ln(yt�1) in an OLS regressionI Since ln(yt)� ln(yt�1)⇡

yt � yt�1

yt�1the interpretation is in terms

of growth ratesI That is : groth rates are often I(0)

I Differenciating a time-series also remove any linear trend


Time-series Theory

Deciding if a time-series is I(1)

Outline





References


Time-series Theory


CorrelationI Let r1 = Corr (yt ,yt�1)

I Is called the 1º order autocorrelation of {yt}I

r1 can be estimated from the sample correlation between yt andyt�1

Ir1 = ÂT

t=2

⇣yt �ÂT

t=2 yt⌘⇣

yt�1�ÂTt=2 yt�1

⌘/(T �2)

I However, the sampling distributions of r1 are very differentwhen r1 is close to 1 than when r1 is far from 1

I When r1 is close to 1, r1 may have a large downwards biasI Otherwise, the sample correlation is unbiased and consistent

I As a rule of thumb, to “counter” this downward bias, the seriesshould be differenciated as soon as r1 > .8, at worst r1 > .9

I When the series has a clear trendI it is first de-trended and then r1 is estimatedI Otherwise, r1 tends to be over-estimated


Time-series Theory


Unit Root Test

I AR(1) model yt = a +ryt�1+ etI Dickey-Fuller (DF) Test H0 : r = 1 against H1 : r < 1

I Subtract yt�1 on each sideI �yt = a +qyt�1+ et with q = r �1

I Under H0 : q = 0 (so r = 1), yt�1 is I(1)I So that the associated t-stat in an OLS regression does not

converge to a normalI but to a Dickey-Fuller distribution

I We test q = 0 (so r = 1) calculating the usual t-statI but compare it with the Dickey-Fuller distribution tabulated values


Time-series Theory


Augmented DF Test

I Same test as DF for r = 1 but in the modelI �yt = a +qyt�1+ g1�yt�1+ g2�yt�2+ · · ·+ gp�yt�p + etI This is most often used : “ADF” test

I The test can be specifiedI Without constant �yt = qyt�1+ g1�yt�1+ · · ·+ gp�yt�p + etI With a trend

�yt = a +b t+qyt�1+ g1�yt�1+ · · ·+ gp�yt�p + etI How to choose ?

Ia = 0 and b = 0 : “pure” random walk

Ia 6= 0 and b = 0 : random walk with drift

Ia 6= 0 and b 6= 0 : random walk with drift and trend

I These cases are discussed below


Time-series Theory


Trend and I(1)I For series that have clear time trends, the test is

I �yt = a +b t+qyt�1+ g1�yt�1+ · · ·+ gp�yt�p + et

I A trend-stationary processI which has a linear trend in its mean but is I(0) about its trendI can be mistaken for a unit root processI if we do not control for a time trend in the test [Wooldridge [13]]I Cfr how a random walk with drift looks like a trended I(0)

I The usual DF or ADF test on a trending but I(0) seriesI (that is not including a trend term)I has little power for rejecting a unit root

I power = probability of rejecting the null hypothesis of a unit rootwhen there is not one

I the trend makes us believe there is a unit rootI BUT, if we include a un-needed trend, we loose power

I So try to avoid including the trend as much as can be


Time-series Theory


Notes on DF

I When we include a time trend in the regression, the criticalvalues of the test change.

I Omitting the intercept a in the DF equation is rarely donebecause of biases induced if a 6= 0

I We can allow for more complicated time trends, such asquadratic, is also seldom used.


Time-series Theory


How many lags ?I The inclusion of the lagged changes is intended to “clean up”

serial correlation in ytI The more lags,

I the more initial observations we loseI the smaller the power of the test

I Too few lags,I the size of the test will be incorrect, even asymptotically,

I size = probability of rejecting the null hypothesis of a unit rootwhen there is one

I because the validity of the DF critical values relies on thedynamics being completely modeled

I Often,I annual data, one or two lags usually suffice [Wooldridge [13]]I monthly data, 12 lags may be usedI large sample size : you may experiment


Time-series Theory


One application of the DF test

I r3t (annualised) interest rate (or yield) on 3-month treasury billsI “Bond equivalent yields”, in the financial pages

I In Gretl, data in INTQRT.gdt, using Wooldridge [13]I Change structure of the dataset : monthly, initial date unknown

I Estimate �yt = a +qyt�1+ etI OLS cr3 against 0 r3_1I Coefficient of r3_1 is −0,0907, so r =0.9093I t-stat of r3_1 is -2.47, but does not follow a t distributionI On the r3 variable

I Menu “variable” ! “unit-root test” ! “Augmented...”I No lag (so : simple DF test), with constant, without trendI This produces the same results as the regression, with a correct

p-value of .12 so ¬R H0 : there is a unit root


Time-series Theory

Cointegration

Outline





References


Time-series Theory

Cointegration

Motivation & DefinitionI Taking first differences of I(1) series before regressing them is a

“safe strategy”I but limits the analysis to short term relations

I That is : one-period changes explained by one-period changesI Cointegration may give back its meaning to regressions between

I(1) series in levels (or logs)

I If {yt} and {xt} are I(1), then in general yt �bxt is I(1) 8b

I However, it is possible for some b 6= 0, yt �bxt to beI I(0) : Asymptotically un-correlated with its own pastI Stationnary : Constant expectation & variance

I When such a b exists, we say that {yt} and {xt} are cointegratedI

b is the cointegration parameter

I {yt} and {xt} cannot move much apart from each other in thelong run


Time-series Theory

Cointegration

Example : Treasury bills Interest RatesI r6t (annualised) interest rate series of 6-month treasury bill

I T-bill, r3t idem but 3-monthI Data in INTQRT.gdt from Wooldridge [13]

I We saw earlier that r3t had a unit rootI That is also true of r6t

I Let Sprt = r6t � r3t (spr for spread)I

b = 1 : we know the coint. param.I Test if Spr has a unit root

I DF stat -7.71 with a corresponding near-zero p-valueI thus RH0 : spr has unit root

I so r6t are r3t cointegrated with parameter 1I Interpretation : if the rates moved apart, one of the two would

become a relatively more attractive investment than the otherI therefore, investors would pay more for it, its price would riseI since the interest rate is the return of the bond divided by its price,

it would decrease automatically


Time-series Theory

Cointegration

Cointegration test

I When we know the value of the cointegration coefficient b

I then we test whether yt �bxt has a unit root : DF or ADF

I Usually, we do not know b

I If yt and xt are cointegratedI OLS is consistent for b in yt = a +bxt +utI otherwise, OLS yields spurious results and b is falsely significant

I Engle-Granger Test = Dickey-Fuller on ut = yt � a � bxtI Regress �ut on ut�1 with a constant, without lag

�ut = d + g ut�1+xtI If ut�1 is not significant, then ut is I(0)I Then yt and xt are cointegratedI Again, the test uses a special distribution, not a t


Time-series Theory

Cointegration

Engle-Granger Test

I If the lag order, k, is greater than 0,I then k lags of the dependent variable are included on the

right-hand side of the test regressionI Gretl allows "test down from maximum lag"

I From a selected lag order taken as a maximum,I the actual lag order used is obtained by testing downI AIC can be used to compare the different lag levels

I If yt or xt has a trend, it must be modeledI See Wooldridge 2012 p648 [13]

I Where the trend is improperly called a drift


Time-series Theory

Cointegration

Engle and Granger 2003 Nobel Prize in Economics

“for methods of analyzing economic time series

with time-varying volatility(ARCH)”

Robert F. Engle

with common trends(cointegration)”

Clive Granger


Time-series Theory

Cointegration

Example : cointegration between fertility and fiscality

I In the USA “personal exemption” is a tax break on householdincome

I Among others, the more the HH has children, the bigger the taxbreak

I The amount is relatively small, but changes arbitrarily throughtime

I One can then imagine testing a link between the exemption andthe number of births


Time-series Theory

Cointegration

Example : cointegration between fertility and fiscality

I Data in Gretl Fertil3.gdt from Wooldridge [13]I Modify the dataset structure for a time-series, annual, beginning

19 ? ?I gfr births / 1000 women 15-44 year-old

I DF : p-value .80 so ¬R H0 : unit root

I pe “personal exemption”, in real $I DF : p-value .45 so ¬R H0 : unit root

I RegressionsI In levels gfrt = a +bpet +utI In first differences �gfrt = a +b�pet +�ut


Time-series Theory

Cointegration

gfr and pe

gfrt coef (p-val) �gfrt coef(p-val)Cst 99.4 (0) 92.9 (0) 108.6 (0) Cst -.08 (.92) -.32 (.68) -3.45 (0)pet .05 (.40) -.06 (.36) .03 (.66) �pet -.05 (.27) -.05 (.17) -.05 (.19)pet�1 -.02 (.83) -.04 (.72) �pet�1 -.01 (.69) -.009 (.75)pet�2 .11 (.07) .13 (.11) �pet�2 .09 (0) .09 (0)pet�3 -.005 (.93) -.01 (.88) �pet�3 .04 (.17) .04 (.15)pet�4 .08 (.16) .02 (.04) �pet�4 -.04 (.04) -.36 (.05)

Pill (63) -27.8 (0) -30.9 (0) .38 (.97) Pill (63) -2.23 (.07) -1.78 (.14) -5.43 (.005)t -1.17 (0) t .11 (.01)

DW .12 .17 .25 1.44 1.34 1.57T 72 68 68 T 71 67 67

The differences between the model in levels and in first differencessuggest to test for cointegration because if the series are notcointegrated, the regressions in level are spurious


Time-series Theory

Cointegration

gfr and peI Cointegration test

I Gretl : “model” ! “Time Series” ! “Coint Test” !“Engle-Granger”

I Variables : gfr and pe, without lag since we test�ut = a +b ut�1+ et

I Complete outputI DF for gfr and pe : each is I(1)I MCO gfr on peI MCO residuals : ¬R H0 : b = 0I So ¬R H0 : 1�b = 1 : the residuals are I(1)I Thus gfr and pe are NOT cointegrated

I Control for a possible common trend between gfr and peI Same procedure, but select “constant and trend”I Same conclusion

I Thus, the relation in levels is spurious (Pill !)I The one in first differences reflects only the short run


Time-series Theory

Errors correction models

Outline





References


Time-series Theory


Definition

I If yt and xt are I(1)I One can only estimate a model in first differences

I a “VAR” : Vector Autoregressive Model

I e.g. �yt = a0+a1�yt�1+ g0�xt + g1�xt�1+ut

I But if yt and xt are cointegratedI We can introduce additional I(0) variablesI Let st = yt �bxt which is I(0)

I For simplicity, assume E (st) = 0

I In the simplest case, we insert a lag of stI �yt = a0+a1�yt�1+ g0�xt + g1�xt�1+d st�1+ut

I The d st�1 term is called error correctionI As is the whole model


Time-series Theory


Discussion

I An error correction model ECM allows us to analyse the shortrun dynamics between yt and xt

I Usually, b has to be estimatedI OLS is consistent under cointegrationI There are other models (Leads and Lags)

I For simplicity, a model without lags of �yt or �xtI �yt = a0+ g0�xt +d st�1+utI �yt = a0+ g0�xt +d (yt�1�bxt�1)+ut


Time-series Theory


Discussion

I Then it should be that d < 0I If yt�1�bxt�1 > 0 then y has overshoot the equilibrium in t�1I Cointegration imposes that we return to the equilibriumI Since d < 0 the error correction tends to reduce �yt

I Which brings us back to the equilibrium

I Likewise when yt�1�bxt�1 < 0

I However, ECM can also be seen as a context for an estimation ofa cointegration relation

I In which short-run terms in �yt or �xt are introduced to reducethe unexplained noise

I That is yt = p0+p1�xt +p2�yt +p3xt +xt


Time-series Theory


Vector Error Correction Models

I Consider an n-variate process of order p

I yt =

0

B@y1t...

ynt

1

CA that is n endog. variables

I yt = µt +A1yt�1+ . . .+Apyt�p + et

I In real life, we don’t know pI

µt may include exog. variables

I RewriteI tautology : yt�s = yt�1� (�yt�1+�tt�2+ . . .+�yt�s+1)I so �yt = µt +⇧yt�1+Âp�1

s=1 �s�yt�s + et

I with ⇧= Âps=1As � I and �s =�Âp

h=s+1AhI called the VECM representation of yt


Time-series Theory


Vector Error Correction Models

I The important things areI It looks like the expression for the Engel-Granger test yt�1I Plus terms that look like error corrections �yt�s

I Interpretation of �yt = µt +⇧yt�1+Âp�1s=1 �s�yt�s + et

I depends on the rank of ⇧I called r

I If r = 0 : all the elements of yt are I(1)I and not cointegrated

I If r = n : all the elements of yt are I(0)I s is the lag order of the VECM2

I Note �yt�s = yt�s �yt�s�1

2In Gretl, s is the chosen Lag-order minus 1 because Gretl first computes a VARof that lag order, while the VECM is with 1st differences, so one lag order less.


Time-series Theory


Cointegration

I Occurs when 0 < r < n

I Then ⇧ can be written as ab

0

I yt is I(1)I but zt = ab

0yt is I(0)

I For ex.I Assume b1 =�1 and r = 1I Then 9b s.t. zt =�y1t +b2y2t + . . .+bnynt is I(0)I That is y1t = b2y2t + . . .+bnynt + zt is a long run relation

I zt may be non-zero but is stationary

I In practiceI We do not know b

I We estimate it first and then the rest


Time-series Theory

Johansen Test of Cointegration

Outline





References


Time-series Theory


Johansen Test of CointegrationI Works by computing the eigenvalues of a matrix closely related

to ⇧I

l is the vector of (real) eigenvalues of ⇧ if det(⇧�l I ) = 0I So that ⇧n = 0 has a non-zero solutionI We can guess the relation with the VECM representation

I Count the number of eigenvalues different from zeroI If all are significantly 6= 0

I then all the processes are I(0) (stationary)I If there is at least one zero eigenvalue

I then yt is I(1)I but some linear combination b

0yt is stationary

I If no eigenvalues are significantly 6= 0I then yt is I(1)I also any linear combination b

0yt

I SO : no cointegration


Time-series Theory


Søren Johansen

Econometrician

Most cited economist in the world from 1990–2000


Time-series Theory


Johansen Test of Cointegration in Gretl

I Test : COINT2 P YLIST [ ; XLIST]I P is as above : order, so number of lags

I That we can only guess

I YLIST is the list of endog. var.I XLIST is a list of optional exog. var.

I that may enter µ

I From here r is the number of non-zero eigenvaluesI So the cointegration rank of ytI Or the number of cointegration relations in yt

I Estimation : VECM P R YLIST [ ; XLIST]I We have to give r the cointegration rank


Time-series Theory


Interpretation of the deterministic components

I The term µt is usually understood to take the form

µt = µ0+µ1t

where t is a deterministic trendI Assess whether the data follow a trend

I By visual inspectionI Following economic theoryI If it does, is it linear of quadratic ?

I Once we are confidentI Impose consequent constraints on µ0 and µ1


Time-series Theory


Deterministic components exampleI Suppose the data do not exhibit a discernible trendI Thus �yt is on average 0

I Surely also its expectationI Consider the VECM representation

I �yt = µt +⇧yt�1+Âp�1s=1 �s�yt�s + et = 0

I Assume one lag s = 1I Assume cointegration so ⇧ can be written as ab

0

I and so zt = b

0yt is I(0)

I �1�yt�1 = µ0+µ1t+azt�1+ et

I Take expectationI 0 = µ0+µ1t+amz where mz = E (zt)I Since the LHS has no t, it should be that µ1 = 0I

µ0 =�amz , thus

I �1�yt�1 = a

⇥b

0 �mz

⇤ yt�11

�+ et

I The long-run relation has an intercept


Time-series Theory


Deterministic components exampleI For illustration, consider

I y2t =m+ y2t�1+ et a random walk with driftI y1t = k+ y2t +µt

I If µt is a white noise, y1t and y2t are cointegratedI Their difference zt = y1t �y2t = k+µt is I(0)

I In VECM✓�y1t�y2t

◆=

✓k+mm

◆+

✓�1 10 0

◆✓y1t�1y2t�1

◆+

✓µt + et

et

◆

I Write

I ⇧=

✓�1 10 0

◆=

✓�10

◆��1 1

�=�ab

0

I zt�1 =

✓y1t�1y2t�1

◆;✓

µt + et

et

◆= ht ; µ0 =

✓k+mm

◆

I y1t �y1t�1 = k+m�y1t�1+y2t�1+µt + etI since y2t =m+y2t�1+ et , we indeed get y1t

I So �zt = µ0+azt�1+ht

✓�y1t�y2t

◆=

✓k+mm

◆+

✓�1 10 0

◆✓y1t�1y2t�1

◆+

✓µt + et

et

◆

I If m 6= 0 : y2t has a driftI Thus y1t also since it must keep a constant distance k to y2t on

avg

Iµ0 =

✓k+mm

◆is unrestricted

I If m = 0 and k 6= 0I Neither y2t nor y1t have a driftI But the mean distance between them is kI Thus µ0 =

✓k0

◆is called “restricted constant”

I If m = 0 and k = 0I Neither y2t nor y1t have a driftI The mean distance between them is 0I This case is called “no constant”


Time-series Theory


Deterministic components : more general caseI If there are more lags, it’s the same ideaI If there is more than 2 variables

I The order of integration r can be > 1I

a is a matrix with rcolumnsI The “restricted constant” case is when µ0 is linear combination

of columns of a

I If a linear trend is included, we get two more casesI “restricted trend” : the cointegration relations include a trend

I but the first differences of the variables in question do not

I “unrestricted trend”I trend appears in both the cointegration relationships and the first

differencesI corresponds to a quadratic trend in the variables (in levels)

I In Gretl, the COINT and VECM menus have the 5 options



Outline

Introduction

Time-series Theory


References



Deforestation Data

I Projeto PRODES http ://www.obt.inpe.br/prodes/index.phpI Monitoramento da floresta amazônica brasileira por satéliteI Ministério da Ciência, Tecnologia e Inovação & Ministério do

Meio Ambiente

I LANDSAT images over “Legal Amazon”I Since 1975 (analogic) - 2003 (digital)

I This is no trivial processI Team of people identifying deforested areas between images at 2

different points in time in a year

Deforestation Data



Missing data : interpolation

I Some years are missingI for unspecified reasons

I Discarding these years implies using shorter series than availableI Thus poorer statistical propertiesI But also, regressions “believe” interpolated points are real

I Assume that at no point in time there was re-forestationI Thus deforestation at t must be between deforestation at t�1

and t+1



Interpolation : Deforestation.ods interpolation tab

I Piecewise LinearI Let yt and yt+2 be knownI Interpolation is the point on the straight line between those 2

pointsI yt+1 = (yt +yt+2)/2

I Piecewise because we do it between pairs of points

I OLS regression on time and time²I On time alone : constant deforestation rate of 19 459 km² year�1

I OLS induces more unexplained variation in the deforestation rateI so prefer piecewise interpolation.

I Several other techniques, but amount to similar results here



Interpolated Deforested Area (Left) & Deforestation (Right)



Analysis: EKC, I(1) tests and cointegration

Outline





References




Analysis

I Analysis is performed primarily in GretlI Stata & R are less explicit

1. Is deforestation linked to income in the Kuztnets (quadratic)sense ?

I Rem. Both GDPh and Deforestation are flows

1.1 Test I(1)1.2 Test cointegration

2. Is there an alternative theory ?3. Is deforestation cointegrated with other variables ?




Analysis - I(1) TestsI ADF test

I In principle, 1 or 2 lags because annual data (earlier)I Testing down using AIC criteriaI Table below show results with selected number of lags

I Drift a and trend b t are in principle allowed

I Phillips-Perron testI H0 the series is a unit rootI Like the ADF

I Also addresses the issue that the {yt} process might have a higherorder of autocorrelation

I Thus yt�1 is endogenous in the test equationI The ADF addresses this issue by introducing the �yt�pI Phillips–Perron test makes a non-parametric correction to the t-test

statisticI It is robust to unspecified autocorrelation & heteroscedasticity




I(1) Tests Results

Deforestation GDP/h Population Meat priceAsymp. p-value Lags Asymp. p-value Lags Asymp. p-value Lags Asymp. p-value Lags

ADF w/ constant .58 2 .99 2 0 2 .84 2ADF w/ constant & trend .65 2 .89 2 .60 2 .99 2Phillips-Perron w/ constant .24 - .98 - 0 - .71 -PP w/ constant & trend .31 - .90 - 1 - .98 -

I Trend does not appear to make a difference in the ADF I(1) tests




Cointegration Tests: Deforestation, GDPh and GDPh2

I Engle-Granger residual-based testI Gretl selects 1 lag for highest AIC, even starting from high lag

order 4

I Johansen 2 testsI “Trace” and lmaxI No test procedure for lag order

I Use 1 lag as selected from Engle-GrangerI cointegration remains w/ 2 lags, but not 3

I “Unrestricted constant” or “Restricted constant” cases depends onwhether GDPh can be seen to have a drift or not

I this is beyond the scope of the present studyI It turns out that the coefficients of the cointegrating relation do not

change in any significant way in either cases




Engle-Granger Cointegration Tests Results

Engel-Granger Without trend With linear trend Quadratic trendCoint. regression Coef. estimate p-value Coef. estimate p-value Coef. estimate p-value

Intercept −115 973 .001 -145 942 .003 -160 160 .002GDPh 60.36 <.001 72.47 .0005 81.72 .0003GDPh2 −0.0068 <.001 -0.0078 .0001 -0.0091 .0001Time - - -153 .37 -548 .16Time2 - - - - 13.2 .26

ADF on residuals Lags p-value Lags p-value Lags p-value1 .009 1 .028 1 .029




Johansen Tests Results




Conclusion Deforestation, GDPh and GDPh2 appearcointegrated

I “No trend” cases are preferredI as GDPh and Deforestation data do not appear to include a (linear

or quadratic) trendI as deterministic trend does not appear significant in the

Engle-Granger testI Thus including a trend makes us loose power in regressions

I Cointegration remains in tests with or without trend, restricted ornot

I Longer lags makes cointegration disappear

I Time itself cannot be seen as an alternative to GDPI A simple regression of Deforestation against time and its square

leads to significant (but spurious) results



Alternative Theory

Outline





References



Alternative Theory

Stern 2004 [10]

1. Pollution increases roughly monotonically (linearly) with income2. But “time” reduces pollution, that is, income-independant

policies3. In rapidly growing middle-income countries, the income effect

(% pollution) overwhelms the time effect4. In wealthy countries, growth is slower, and pollution reduction

efforts can overcome the income effect

I Stern 2004 does not refer explicitly to deforestationI But rather to emissions and “flow pollutants”

I Test whether this alternative theory applies to deforestationI Stern 2004 has not formalized it howeverI What formalization / model do you suggest ?



Alternative Theory

Alternative Model

I Formalization :

yt = b0+b1GDPht +b2t+b3Growtht + et

where Growtht = (GDPht �GDPht�1)/GDPht�1

I We expectI Cointegration

I Time is not stochastic, so it is exogenous and not “cointegrated”I Thus cointegration is really between deforestation, GDPh and

Growth, and there is a time trend

Ib1 > 0, b2 < 0 and b3 > 0

I So that when Growth is large, deforestation would be moreimportant



Alternative Theory

Alt. theory: yt = b0+b1GDPht +b2t+b3Growtht + et

I ResultsI Cointegration tests applicability is delicate because of the trend t

I Engle-Granger and Johansen are both sensitive to the specificationof the constant and/or the trend

I Conclusions are therefore hard to draw

I Under cointegration, several estimators are consistentI We expected b1 > 0, b2 < 0 and b3 > 0I The results, across several estimators, are b1 < 0, b2 > 0 and

b3 > 0 (all significant)I That is : time and growth tend to increase deforestation while

income would decrease it

I Thus, even though the cointegration issue could be investigated inmore details

I The actual results are opposite the theory for 2 out of the 3coefficients

I Thus EKC theory more coherent with Brazilian deforestation



Other Econometric Issues

Outline





References




Stern 2004: the 4 issues identified in the literatureI Heteroskedasticity

I Stern 2004 was refering to panel or cross-section studiesI It is difficult to argue that heteroscedasticity can be a big issue in

the present time-seriesI Classical tests do not R homoscedasticity

I SimultaneityI In the present case, this amounts to asking whether deforestation

causes GDP?I Agriculture in Brazil is about 5 to 6% of GDP (World Bank data)

at the end of the series, about 12% at the beginningI Therefore, even if there was simultaneity, its relative size appears

small

I Omitted variablesI More generally : unobserved heterogeneity, discussed below

I Cointegration, which is the object of the present work




Unobserved HeterogeneityI Parameter Stability

I yt = b0t +b1tGDPht +b2tGDPh2t +µt

I Causes endogeneity

I Omitted regressor(s)I Might cause endogeneity

I If the omitted regressor is correlated with the included regressors

I It is difficult to argue that a cointegrated relation may still sufferfrom unobserved heterogeneity of a type that causes endogeneity

I Because then residuals might not be stationary and I(0) - i.e. closeto a white noise

I Also, Least Squares becomes “super consistent”I Error correction model of Stock and Watson 1993 [11]I Lags of yt (or of �yt ) account for the unobserved heterogeneity



The Estimated Relation

Outline





References




Cointegration (VECM) RelationI As shown by Engle and Granger (1987), see Wooldridge [13]

I the preliminary estimation of b in the cointegration relation doesnot affect the asymptotic efficiency of the estimators of theparameters in the VECM

I A number of estimators could be used including OLS

I The relation presented here is estimated in the VECM using gretlI In general, the ML estimator for the restricted VECM problem

has no closed form solutionI Numerical methods, by default (in Gretl) the “switching

algorithm”I It uses by default the “Phillips normalization”I gretl manual for details

I 1 lag as above3

I Restricted constant version, so assuming no drift in GDPhI Coefficients are similar to OLS

I Table next slide3Specifying lag-order 2 in the VECM since we mean to use �yt�1 as regressor.




Cointegration (VECM) Relation

Defort bOLS p-value bVECM p-valueIntercept -115 973 .0011 -130 170 .0010GDPht 60.36 .0001 64.41 .0002GDPh2

t -0.0068 .00003 -0.0069 .0001T 39 37

R2adj .56 -




Cointegration Regression

To create the plot see Deforestation.ods vecm tab




Does Legal Amazon follow forest “transition path” ?

I Similar to Kauppi et. al. 2006 [7] : about $4,600 GDP per capitaI Note

I how earlier deforestation (hence small effect of square GDPh)matches well deforestation

I Indicating the importance of as long a series as possible

I how later deforestation also matches well later GDPh in negativeI Indicating the quadratic relation




Lead of GDPh drive deforestation a little better ?

Defort bOLS p-value bVECM p-value Defort bOLS p-value bVECM p-valueIntercept -115 973 .0011 -130 170 .0010 Intercept −143 697 .00004 68 624 .1137GDPht 60.36 .0001 64.41 .0002 GDPht+1 71.43 .000003 41.28 .0281GDPh2

t -0.0068 .00003 -0.0069 .0001 GDPh2t+1 −0.0078 .000001 0.0049 .0130

R2adj .56 R2

adj .59T 39 T 37 T 38 T 36





I VECM with one lagI Deforestation and lead one period of GDPh (and its square) are

also cointegratedI following the same test methodology as outlined above

I Graphically, it appears that one lead of GDPh might drivedeforestation better

I OLS estimators (including lead and lag) perform better with onelead

I the VECM estimator does not fit as well

I In the end, the VECM model without lead is selected





I Interpretation: This evokes anticipations



Other Explanatory variables

Outline





References





I We are interested in testing an EKCI So, linking Deforestation and a quadratic function of Income

I Income appears causal for lower deforestationI but how does it operate ?I Agriculture, population, forestry, policy ?

I That is a more “structural” analysisI are there competing explanation ?




Action Plan

I Policy starts in 2005I Dummy

I Not significantI But not clearly exogenous regressor

I Since it is started in reaction to deforestationI and it might operate differently accordingly with deforestation

levels (changing parameter)

I So: hard to test

I However : not likely correlated to GDPhI Leaving it in the error term does not lead to endogeneity




Macroeconomic data

I Worldbank http://data.worldbank.org/I World Development Indicators

I Population; GDP; CO2

I Global Economic Monitor (GEM) CommoditiesI Prices data

I International Labor Organisation (ILO) dataI Labor force in agricultureI Employment in agriculture

http://data.worldbank.org/

http://databank.worldbank.org/data/reports.aspx?source=global-economic-monitor-%28gem%29-commodities




Cointegration Tests Strategies

I In the sequel, we introduce these additional regressorsI e.g. Population or Meat priceI and examine whether they alter the tests resultsI We also test whether these regressors are cointegrated with

deforestation without GDPh in the relation

I I (1) regressors should be excluded from the Deforestation modelI if they are not co-integrated

I induce a risk of spurious correlation

I are irrelevantI make the tests loose power

I I(0) regressor cannot be in a cointegration relationI But are legitimate in a regression




What drives agriculture ?

I It is well-known that in BrazilI Deforested land is turned mainly in pasture and some in soy fields

I Little is turned in urbanized area

I Deforestation is not likely driven by forestry as not much wood isused / exported

I Forestry would be driven by technical progress (see below)

I Whether agriculture proceeds more from small scale farming orlarger scale commercial farming

I is beyond the scope of this work




What drives agriculture ?

I Agricultural prices ?I Primarily of beef, and soy to a lesser extentI Beef and Soy prices are quite correlated (65%)

I Employment elsewhere in the economy ?I Kauppi et.al. [7] interpretation is that as income rises,

deforestation becomes less interesting than other alternatives

I We present results on both in the sequel




Agricultural Prices Series

I Even though Brazil is a major meat producer, it is difficult toargue that world agricultural prices are in an endogenous relationwith deforestation

I Soybean / Meat pricesI Both display unit roots

I Thus possibly spurious results in some econometric analyses

I None in a cointegration relation with DeforestationI Quadratic or not

I With or without GDPh

I Regressing the first difference of Deforestation on the firstdifference of Meat price

I also fails to produce any significant result





Annual prices, real 2010 US$





I The present resultsI are in contrast with the belief that cattle ranching is a causal factor

I e.g. World Bank [9] or Nasa Earth Observatory4

I suggest rather that cattle ranching developped in the Amazonbecause of lack of better opportunities elsewhere

I These opportunities may currently be presentI or alternatively, the cost of deforestation has risenI If anything, beef prices have gone up in the decade in which

deforestation decreased

4Anonymous, 2012 data, accessed October 2015 athttp://earthobservatory.nasa.gov/Features/WorldOfChange/deforestation.php




Agricultural Labor, Opportunities, PovertyI Even though rural population declines smoothly, labor force in

agriculture appears to fall more sharplyI Reinforces the idea that higher income create more attractive jobs

in other sectorsI Higher incomes also induce higher government resources

I Concurently, higher spending in education per head...I More opportunities for children

I Possibly also poverty reductionI Even though the data appears widely varying until the mid-90’sI where it remains roughly stable until about the mid-00’sI After that, poverty reduction clearly acceleratesI It is possible that deforestation declines in response to that

acceleration

I These series are however much less documented than GDPI Not possible to use them in a formal time-series regressionI See plot next slide




Agricultural Labor, Opportunities, Poverty




Population

I Properties of population seriesI I(1)

I ADF “testing down from highest lag”I At most two lags only as annual data (Wooldridge [13])

I same results when testing with constant or with constant and trend

I Note that first difference is also I(1)I Often pollution is measured per h

I Doing that is in fact imposing a cointegration relation withcoefficient 1

I That makes sense wih CO2 emissions, since people are emittersI Clearly, we do not want to impose such restriction with

deforestation




Engel-Granger Cointegration Test on Population

Coint. regression Coef. estimate p-valueIntercept -61 178 .04pop 1.08 .007pop2 -3.7E-06 .004

ADF on residuals Lags p-value1 .23

Deforestation, pop and pop2 are not cointegrated

I Adding population to the EKC relationI Does not change the results regarding GDPhI Makes Population non significant

I Similar results hold when using population first differences(“pressure”) instead of levels




Engel-Granger “Cointegration” Test on TimeI Time is a pure (non-stochastic) trend

I it cannot be cointegrated

I But regressing Deforestation against time and squared-timecould leave an I(0) residual

I if deforestation was simply following a quadratic trendI That is not the case

Regression Coef. estimate p-valueIntercept 12 390 0

t 793 .01t2 -23.6 .001

ADF on residuals Lags p-value1 .14

Deforestation, t and t2 are not “cointegrated”




Population and Technological Progress

I No apparent effect of population pressureI Population change Trending, not StationaryI Relatively little of the deforested area goes to urbanisation

(NASA)

I Total population increases smoothlyI Not consistent with Deforestation seriesI Whatever the test results

I Smaller rural population sizeI True, but decline is smooth

I Likewise not consistent with Deforestation series

I Same argument for technological progressI Usually treated as time, so “smooth”: does not fit




Population Paths



Discussion and conclusions

Outline





References




Discussion

I Political importance of EKCI It is easy to interpret evidence of EKC as a “laissez-faire success”

I i.e. why bother about deforestation ? only income matters

I There is no evidence that the process will “naturally” continuefollowing a quadratic relation

I Obviously, it could not be the case in the long run (>100% forestcover)

I Meyfroidt et. al. 2011 “The onset of a possible forest recovery in acountry is not automatic and can nowhere be taken for granted.”

I However, it may indicate that better economic opportunities willhave a side-effect on deforestation




Discussion

I Not easy to test the effect of Action Plan at such an aggregatelevel

I But decline in deforestation roughly matches its existenceI and President’s Lula arrival in power (2002)I As do expenses in educationI and poverty reduction

I Changing driversI e.g. subsidies (70s) then meat (80-90s) then Action Plan since

mid-00sI But it remains deforestation matches well GDPh in an EKC sense




Forecast

I “Turning point” not reachedI i.e. when deforestation would reach zeroI When will it be reached ?

I When GDPh is about 6300-6400 in $20055

I Using GDPh forecast from the IMF[6] up to 2020I Using linear interpolation for the missing yearsI This is called “conditional forecast”

I We do as if we knew GDPh in the future

I Deforestation will go back up to about 2009 levels until about2018 when growth returns

I The turning point might be reached a little after 2020

I Plot next slide

5It is possible to compute a confidence interval for such measure following [1].




Forecast




ConclusionsI The conclusion of the present study are humbleI The path of deforestation in Brazil appear causaly linked to

incomeI This coincides with assertions by a more geography-oriented

literatureI The results are arrived at using only publicly available aggregate

dataI and a purely time-series methodologyI They are therefore additional evidence to previous results

I Deforestation causes are likely more complexI Yet, the present results suggest that income is a powerful driverI Global agricultural prices and population pressure may not play

an important roleI The effect of the Action Plan policy remains un-assessedI Yet policies on Poverty and Education might play a role,

I but aggregate data are not rich enough



Digression

Outline





References



Digression

A Digression about CO2

I Strict CO2

I Not equivalent CO2eq, w/o LULUCF

I Often studied for EKCI CO2/hI Not stationary, not trendingI Deforestation ! econ. activity ? ! CO2 ?I Population ?

I CO2, GDPh and GDPh2 may be cointegratedI The tests (Engle-Granger and Johansen) are conflictingI Adding Population or Deforestation does not alter the tests

I CO2 and Deforestation are not cointegratedI Thus Deforestation is not causal for strict (not LULUCF) CO2



Digression

A Digression about CO2


References

Outline

Introduction

Time-series Theory


References


References

References I

J.-T. Bernard, M. Gavin, L. Khalaf, and M. Voia.The environmental kuznets curve: tipping points, uncertainty and weak identification.Cahier de recherche/Working Paper, page 4, 2011.

J. Choumert, P. Combes Motel, and H. K. Dakpo.Is the environmental kuznets curve for deforestation a threatened theory? a meta-analysisof the literature.Ecological Economics, 90:19–28, 2013.

A. Cottrell and R. Lucchetti.Gretl user’s guide.Included in Gretl Econometrics Package, October 2014.

G. M. Grossman and A. B. Krueger.Environmental impacts of a north american free trade agreement, 1991.

G. M. Grossman and A. B. Krueger.Economic growth and the environment, 1995.

IMF.Adjusting to lower commodity prices.In World Economic Outlook. International Monetary Fund, October 2015.


References

References IIP. E. Kauppi, J. H. Ausubel, J. Fang, A. S. Mather, R. A. Sedjo, and P. E. Waggoner.Returning forests analyzed with the forest identity.Proceedings of the National Academy of Sciences, 103(46):17574–17579, 2006.

E. F. Lambin and P. Meyfroidt.Global land use change, economic globalization, and the looming land scarcity.Proceedings of the National Academy of Sciences, 108(9):3465–3472, 2011.

S. Margulis.Causes of deforestation of the Brazilian Amazon, volume 22.World Bank Publications, 2004.

D. I. Stern.The rise and fall of the environmental kuznets curve.World development, 32(8):1419–1439, 2004.

J. H. Stock and M. W. Watson.A simple estimator of cointegrating vectors in higher order integrated systems.Econometrica: Journal of the Econometric Society, pages 783–820, 1993.

D. Weinhold and E. Reis.Transportation costs and the spatial distribution of land use in the brazilian amazon.Global Environmental Change, 18(1):54 – 68, 2008.


References

References III

J. M. Wooldridge.Introductory Econometrics.Cengage Learning, 2012.

lectures in applied econometrics ch. 1. amazonian...

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