On World Poverty: Causal Graphs from the 1990’s

On World Poverty: Causal Graphs from the 1990’s

David A. BesslerTexas A&M University

January 2003

Outline

I. Literature


II. Scatter Plots on Measures of Poverty and Related Variables

V. Regressions and Front Door

and Back Door Paths

III. Causal Modeling

IV. Directed Graphs

VI. Summary and Discussion

Measures of PovertyAlternatives are Discussed in Sen:Poverty and Famines, Oxford Press, 1981.


Biological Measures : e.g. deficits in calorie intake

Economic Measures: e.g., % of Population Living on One or Two Dollars per Day or Less

A Short List of Literature on Causes and Effects of Poverty

Agricultural Income (Mellor, 2000).

Freedom (Sachs and Warner 1997).

Income (Sen 1981).

Income Inequality (Sen 1981; Miller and Ruby 1971).

Child Mortality (Belete, et al 1977).


Literature Continued

Birth Rate (Sen, 1981) Rural Population (Rivers, et al 1976) Foreign Aid (World Bank, 2000) Life Expectancy (Rowntree 1901) Illiteracy (Huffman, 1989) International Trade (Bhagwati, 1996)


Data Sources

World Bank Development Indicators 80 Countries: % of Population Living off of One and Two Dollars per Day or Less.

Heritage Foundation Index of Economic and Political Freedom on 80 countries.

FAO % of Population that is Under-Nourished.


Algeria Armenia Azerbaijan Banglad Belarus Bolivia Botswana Brazil Bulgaria

Burkino C. Afr. Rep. Chile China Columbia Costa Rica Cote Divor Czech Domin Rep

Ecuador Egypt El Salvador Estonia Ethiopia Gambia Georgia Ghana Guatemala

Table 1.Countries Studied


Countries listed in this table were selected from 2001 World Bank Development Indicators for which $1/day and $2/day population figures were available.

Table 1.Countries Studied, ContinuedHonduras Hungry India Indonesia Jamaica Jordan Kazakhstan Kenya Korea S.

Lao Pdr Latvia Lesotho Lithuania Mdagscr Mali Mauritnia Mexico Moldova

Mongolia Morocca Mzambqe Namibia Nepal Niger Nigeria Pakistan Panama



Paraguay Peru Poland Portugal Romania Russia Rwanda Senegal Sierra Leon

Slovak Rep Slovenia So Africa Sri Lanka Tanzania Thailand Trinadad Tunisia Turkey

Turkmstan Ukraine Uruguay Uzzbekstn Venzuela Yemen Zambia Zimbabwe



Table 1.Countries Studied, Continued

Gini Index

% <

$2/

day

10 20 30 40 50 60 70 80

0

25

50

75

100

Figure 1. Scatter Plot of % of Population Living on $2/day or less and the Gini Index of Income Inequality, Eighty Low Income Countries, mid-1990’s data.

Index of Unfreedom

% <

$2/

day

2.0 2.5 3.0 3.5 4.0 4.5 5.0

0

25

50

75

100

Figure 2. Scatter Plot of % of Population Living on $2/day or less and the Heritage Foundation’s Index of Un-freedom on Eighty Low Income Countries, mid-1990’s data.

Ag Prod/Person ($/person)

% <

$2/

day

0 2000 4000 6000 8000 10000

0

25

50

75

100

Figure 3. Scatter Plot of % of Population Living on $2/day or less and Agricultural Income per Person on Eighty Low Income Countries, mid-1990’s data.

Life Expectancy (yrs)

% <

$2/

day

30 40 50 60 70 80

0

25

50

75

100

Figure 4. Scatter Plot of % of Population Living on $2/day or less and Life Expectancy on Eighty Low Income Countries, mid-1990’s data.

% Population Rural

% <

$2/

day

0 20 40 60 80 100

0

25

50

75

100

Figure 5. Scatter Plot of % Population Living on $2/day or less and the % of Population that is Rural, Eighty Low Income Countries, mid-1990’s data.

Child Mortality (deaths per 1000 live births)

% <

$2/

day

0 50 100 150 200 250 300

0

25

50

75

100

Figure 6. Scatter Plot of % Population Living on $2/day or less and Child Mortality, Eighty Low Income Countries, mid-1990’s data.

GDP/Person ($)

% <

$2/

day

0 2000 4000 6000 8000 10000 12000

0

25

50

75

100

Figure 7. Scatter Plot of % Population Living on $2/day or less and GDP per Person, Eighty Low Income Countries, mid-1990’s data.

Illiteracy Rate (% of Population > 15 yrs)

% <

$2/

day

0 20 40 60 80 100

0

25

50

75

100

Figure 8. Scatter Plot of % Population Living on $2/day or less and Illiteracy Rate, Eighty Low Income Countries, mid-1990’s data.

Foriegn Aid (% GDP)

% <

$2/

day

0 25 50 75 100 125

0

25

50

75

100

Figure 9. Scatter Plot of % Population Living on $2/day or less and Foreign Aid, Eighty Low Income Countries, mid-1990’s data.

Under Nourished (% poplation)

% <

$2/

day

0 10 20 30 40 50 60

0

25

50

75

100

Figure 10. Scatter Plot of % Population Living on $2/day or less and % of Population that is Under Nourished, Eighty Low Income Countries, mid-1990’s data.

Birth Rate (per 1000 people)

% <

$2/

day

0 10 20 30 40 50 60

0

25

50

75

100

Figure 11. Scatter Plot of % Population Living on $2/day or less and Birth Rate, Eighty Low Income Countries, mid-1990’s data.

Figure 12. Scatter Plot of % Living on $2/Day or Less and Relative Importance of International Trade, Eighty Low Income Countries, mid-1990’s Data.

% <

$2/

day

25

50

75

100

International Trade

% <

$2/

day

0 25 50 75 100 125 150

0

25

50

75

100

Directed Acyclic Graphs

Recently Papineau (1985) has uncovered an asymmetry in causal relations which may prove to be every bit as helpful as Granger’s (Suppes’) time sequence in causal systems.


Motivation

Oftentimes we are uncertain about which variables are causal in a modeling effort.

Theory may tell us what our fundamental causal variables are in a controlled system; however, it is common that our data may not be collected in a controlled environment.

In fact we are rarely involved with the collection of our data.

Use of Theory

Theory is a good potential source of information about direction of causal flow. However, theory usually invokes the ceteris paribus condition to achieve results.

Data are usually observational (non-experimental) and thus the ceteris paribus condition may not hold. We may not ever know if it holds because of unknown variables operating on our system (see Malinvaud’s econometric text).

Observational Data

In the case where no experimental control is present in the generation of our data, such data are said to be observational (non-experimental) and usually secondary, not collected explicitly for our purpose but rather for some other primary purpose.

Experimental Methods

If we do not know the "true" system, but have an approximate idea that one or more variables operate on that system, then experimental methods can yield appropriate results.

Experimental methods work because they use randomization, random assignment of subjects to alternative treatments, to account for any additional variation associated with the unknown variables on the system.

Directed Graphs Can Be Used To Represent Causation with

Observational DataDirected graphs help us assign causal flows to a set of

observational data.

The problem under study and theory suggests certain variables ought to be related, even if we do not know exactly how.

With Observational Data we don’t know the "true" system that generated our data.

Causal Models Are Well Represented By Directed Graphs

One reason for studying causal models, represented here as X Y, is to predict the consequences of changing the effect variable (Y) by changing the cause variable (X). The possibility of manipulating Y by way of manipulating X is at the heart of causation.

Hausman (1998, page 7) writes: “Causation seems connected to intervention and manipulation: One can use causes to ‘wiggle’ their effects.”

We Need More Than Algebra To Represent Cause

Linear algebra is symmetric with respect to the equal sign. We can re-write y = a + bx as x = -a/b +(1/b)y.

Either form is legitimate for representing the information conveyed by the equation.

A preferred representation of causation would be the sentence x y, or the words: “if you change x by one unit you will change y by b units, ceteris paribus.” The algebraic statement suggests a symmetry that does not hold for causal statements.

Arrows Move InformationAn arrow placed with its base at X and head at Y indicates X

causes Y: X Y.

By the words “X causes Y” we mean that one can change the values of Y by changing the values of X.

Arrows indicate a productive or genetic relationship between X and Y.

Causal Statements are asymmetric: X Y is not consistent with Y X.

A Causal Fork For three variables X, Y, and Z, we illustrate X causes Y and Z as:


Here the unconditional association between Y and Z is non-zero, but the conditional association between Y and Z, given knowledge of the common cause X, is zero:

common causes screen off associations between their joint effects.

X ZY

An Example of a Causal Fork X is the event, the patient smokes. Y is the event, the patient (a light-skin person) has yellow fingers. Z is the event, the patient has lung cancer.

P (Z | Y) > P (Z) Here yellow fingers are helpful in forecasting whether a patient has lung cancer.

P (Z | Y, X) = P (Z | X) Here, if we add the information on whether he/she smokes, the influence of yellow fingers disappears.


An Inverted Fork

Common effects do not screen off theassociation between their joint causes.

Here the unconditional association between X and Z is zero, but the conditional association between X and Z, given the common effect Y is non-zero:

Illustrate X and Z cause Y as:


X Y Z

The Causal Inverted Fork: An Example

Let Y be the event that my car won’t startLet Z be the event that my gas tank is emptyLet X be the event that my battery is dead

My battery being dead and my gas tank being empty are independent: P(X|Z) = P(X)

Given I know my car is out of gas and it won’t start gives me some information about my battery: P(X|Y,Z) < P (X|Y)


The Literature on Such Causal Structures has been Advanced in the Last Decade Under the Label of Artificial Intelligence

Pearl , Biometrika, 1995


Pearl, Causality, Cambridge Press, 2000

Spirtes, Glymour and Scheines, Causation, Prediction and Search, MIT Press, 2000

Glymour and Cooper, editors, Computation, Causation and Discovery, MIT Press, 1999

Causal Inference Engine

1.Form a complete undirected graph connecting every variable with all other variables.

2.Remove edges through tests of zero correlation and partial correlation.

3.Direct edges which remain after all possible tests of conditional correlation.

- Use screening-off characteristics to accomplish edge direction

- PC Algorithm


Assumptions(for PC algorithm to give same causal model

as a random assignment experiment)

1. Causal Sufficiency

2. Causal Markov Condition

3. Faithfulness

4. Normality


Causal Sufficiency

No two included variables (X and Y in diagram) are caused by a common omitted variable (Z):

Z

X Y


Causal Markov Condition The data on our variables are generated by a Markov property, which says we need only condition on parents:

Z

X

Y

W

P(W, X, Y, Z) = P(W) • P(X|W) • P(Y) • P(Z|X,Y)


Faithfulness There are no cancellations of parameters, eg:

BA

C

b1

b2b3

A = b1 B + b3 CC = b2 B

It is not the case that: -b2 b3 = b1

So deep parameters b1, b2 and b3 do not form combinations that cancel each other (economist know this as a version of the Lucas Critique). David A. Bessler

Texas A&M University

<$2/day Gini Index Unfreedom Ag Income Life Exp % Pop Rural Child Mortality GDP/capita Illiteracy Foreign Aid % Under- Birthrate nourished International Trade


Table 2.Edges Removed

Edge Removed Partial Correlation Corr. Prob.Gini -- Ag Inc rho(Gini, Ag Inc) -0.1266 0.2612 Gini -- Life Exp rho(Gini, Life Exp) -0.0920 0.4157 Gini -- % Rural rho(Gini, % Rural) -0.0298 0.7921 Gini -- Child Mort rho(Gini, Child Mort) 0.1103 0.3283 Gini -- GDP/Person rho(Gini, GDP/Person) -0.0416 0.7131 Gini -- Illiteracy rho(Gini, Illiteracy) 0.0709 0.5315 Gini -- Foreign Aid rho(Gini, Foreign Aid) 0.0829 0.4637 Gini -- Health Exp. rho(Gini, Health Exp.) -0.1086 0.3356 Life Exp -- Birth Rate rho(Life Exp, Birthrate | Child Mort) 0.0093 0.9347 Life Exp -- Illiteracy rho(Life Exp, Illiteracy | Child Mort) 0.0312 0.7842 <$2/Day -- Life Exp rho(<$2/Day, Life Exp | Child Mort) -0.1199 0.2906


Table 2.Edges Removed, Continued

Edge Removed Partial Correlation Corr. Prob.Life Exp -- % Rural rho(Life Exp, % Rural | Child Mort) -0.1183 0.2973 Child Mort -- Health Exp. rho(Child Mort, Health Exp. | Birthrate) -0.1156 0.3084 % Rural -- Health Exp. rho(% Rural, Health Exp | <$2/Day) -0.1106 0.3300 GDP/Person -- Birthrate rho(GDP/Person, Birthrate | <$2/Day) -0.0615 0.5896 GDP/Person -- % Maln rho(GDP/Person, % Maln | Health Exp.) 0.0374 0.7425 % Rural -- GDP/Person rho(% Rural, GDP/Person | <$2/Day) -0.1314 0.2464 Life Exp -- Foreign Aid rho(Life Exp, Foreign Aid | Child Mort) -0.0317 0.7808 Child Mort -- GDP/Person rho(Child Mort, GDP/Person | Birthrate) -0.1385 0.2217 <$2/Day -- Ag Inc rho(<$2/Day, Ag Inc | Health Exp) 0.0079 0.9446 Ag Inc -- Birthrate rho(Ag Inc, Birthrate | <$2/Day) -0.1158 0.3075 Unfree -- Life Exp rho(Unfree, Life Exp | Health Exp.) -0.1195 0.2922


Edge Removed Partial Correlation Corr. Prob.


Ag Inc -- Child Mort rho(Ag Inc, Child Mort | Birthrate) -0.0234 0.8369 Ag Inc -- % Malnourish rho(Ag Inc, % Malnourish | Birthrate) -0.1202 0.2894 Ag Inc -- % Rural rho(Ag Inc, % Rural | <$2/Day) -0.0319 0.7793 GDP/Person -- Foreign Aid rho(GDP/Person, Foreign Aid | Child Mort) -0.1096 0.3344 Unfree -- Ag Inc rho(Unfree, Ag Inc | Illiteracy) -0.1368 0.2272 Ag Inc – Foreign Aid rho(Ag Inc, Foreign Aid | Child Mort) -0.0529 0.6426 Unfree -- Foreign Aid rho(Unfree, Foreign Aid | Child Mort) -0.0546 0.6317 Gini -- % Malnourish rho(Gini, % Malnourish | Child Mort) 0.1357 0.2306 <$2/Day -- Gini rho(<$2/Day, Gini | % Malnourish) 0.1075 0.3438 Unfree -- Birthrate rho(Unfree, Birthrate | Child Mort) -0.0754 0.5078 % Rural -- Foreign Aid rho(% Rural, Foreign Aid | <$2/Day) 0.0313 0.7832


Edge Removed Partial Correlation Corr. Prob.


<$2/Day -- Unfree rho(<$2/Day, Unfree Child Mort) 0.0940 0.4086 Unfree -- Child Mort rho(Unfree, Child Mort | Life Exp) -0.0038 0.9730 Unfree -- % Malnourish rho(Unfree, % Malnourish | Health Exp) 0.1043 0.3583 <$2/Day -- Foreign Aid rho(<$2/Day, Foreign Aid | Birthrate) -0.0254 0.8232 Illiteracy -- Foreign Aid rho(Illiteracy, Foreign Aid | Child Mort) -0.0441 0.6988 Foreign Aid -- % Malnourish rho(Foreign Aid, % Malnourish | Child Mort) 0.1036 0.3618 Ag Inc -- Life Exp rho(Ag Inc, Life Exp | Health Exp) 0.0079 0.9444 Foreign Aid -- Birthrate rho(Foreign Aid, Birthrate | Child Mort) 0.0955 0.4012 Life Exp -- GDP/Person rho(Life Exp, GDP/Person | Health Exp.) -0.0313 0.7833 Illiteracy -- % Malnourish rho(Illiteracy, % Malnourish | Child Mort) -0.0606 0.5949 Child Mort -- % Malnourish rho(Child Mort, % Malnourish | Life Exp) 0.0926 0.4155



GDP/Person

Agricultural Income/Person

Illiteracy Unfreedom

Gini

Life Expectancy

% Malnourished

% Pop Rural

% <$2/day

BirthrateChild Mort

Foreign Aid

(+)

(+)

(+)

(+)

(-)

(+)(+)

(+)

(-)

(-)

(-)

Int. Trade

(+)


GDP/Person

Agricultural Income/Person

Illiteracy Unfreedom

Gini

Life Expectancy

% Under Nourished

% Pop Rural

% <$1/day

BirthrateChild Mort

Foreign Aid

(+)

(+)

(-)

(+)(+)

(+)

(-)

(+)

Int. Trade

(+)

(-)

“Rising Tide Lifts All Boats?”Regressions Based on $1/day Graph

% $1/Day = 27.45 - .004 GDP/Person ; R2 =.60 (2.65) (.001) (std. errors in parentheses)

Here merely regressing % $1/day on GDP/Person gives us the expected negative and significant estimate!

Notice from the graph however that no line connects GDP and $1/day. We removed the edge by conditioning on Child Mortality.

% $1/Day = 2.75 - .0004 GDP/Person + .237 Child Mort ; R2 =.84 (2.82) (.001) (.022)

“Rising Tide Lifts All Boats?”Regressions Based on $2/day Graph

% $2/Day = 57.96 - .007 GDP/Person ; R2 =.81 (3.39) (.001)

Here regressing % $2/day on GDP/Person gives us the expected negative and significant estimate!

Notice from the $2/day graph that we have a connection between GDP and $2/day. So conditioning on Child Mortality does not eliminate GDP as an actor in explaining %$2/day.

% $2/Day = 28.42 - .0033 GDP/Person + .287 Child Mort ; R2 =.91 (4.22) (.001) (.034)

Regression Analysis: Backdoor and Front Door Paths

The previous results on the “rising tide” argument are generalized as necessary conditions for estimating the magnitude of the effect of a causal variable.

•To estimate the effect of X on Y using regression analysis, one must block any “backdoor path” from X to Y via the ancestors of X. We “block” backdoor paths by conditioning on one or more ancestors of X.

•To estimate the effect of X on Y using regression analysis one must not condition on descendants of X. One must “not block” the front door path.

Front Door Path:Consider the Effect of Agricultural Income on %<$2/day

From above we have the following causal chain:

Ag Income/Person GDP/Person %2/Day

Since GDP/Person is caused by AG Income/Person, we cannot have GDP/Person in the regression equation to measure the effect of Agricultural Income/Person on %2/Day – do not block the front door!

Biased Regression: %2/Day = 57.99 - .0007 Ag Inc. - .0068 GDP ; R2 =.37 (3.60) (.0014) (.0018)

Unbiased Regression:%2/Day = -51.73 - .0038 Ag Inc. ; R2 =.23 (4.34) (.0018)

Backdoor paths: Consider the Effect of GDP/Person on %<$2/Day

We have the following sub-graph: GDP/Person Un-Freedom | %$2/Day Birth Rate Gini

The front door path would suggest that we regress $2/Day onGDP/Person. But there exists a backdoor path, through freedom to Gini and Birth Rate. We must “block” the backdoor path by conditioning on either Un-Freedom, Gini or Birth Rate.

Comparison of $2/Day on GDP Regressions

Biased Regression (fails to block the backdoor)

$2/Day = 57.98 - .0077 GDP/Per ; R2 = .37 (3.62) (.001)

Unbiased Regression (blocks the backdoor)

$2/Day = 4.97 - .0031 GDP/Per + 1.635 Birth Rt ; R2 = .71 (3.62) (.001) (.148)

Conclusions Illiteracy, Freedom, Income Inequality, and Agricultural Income are Exogenous movers of Poverty.


Foreign Aid appears not to be a mover of Poverty.

We are not able to direct causal flow among our four exogenous variables.

CautionOur methods assume

Causal Sufficiency Markov Property Faithfulness Normality

Failure of any of these may change results.


Dynamic representation of poverty should be pursued. This will require a richer data set.

Acknowledgements

Motivation for the study Aysen Tanyeri-Abur, FAO

Motivation on our study of Directed Graphs Clark Glymour, CMU

Judea Pearl, UCLA

PowerPoint Presentation Todd D. Bessler, COB, TAMU

On World Poverty: Causal Graphs from the 1990’s

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