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On World Poverty Causal Graphs from the 1990s

- David A. Bessler
- Texas AM University
- January 2003

Outline

- I. Literature

II. Scatter Plots on Measures of

Poverty and Related Variables

III. Causal Modeling

IV. Directed Graphs

- V. Regressions and Front Door
- and Back Door Paths

VI. Summary and Discussion

Measures of Poverty

- Alternatives are Discussed in Sen
- Poverty and Famines, Oxford Press, 1981.

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

Less

- Biological Measures e.g. deficits in
- calorie intake

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.

Table 1.Countries Studied

Table 1.Countries Studied, Continued

Table 1.Countries Studied, Continued

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100

75

50

lt 2/day

25

Figure 12. Scatter Plot of Living on 2/Day or

Less and Relative Importance of International

Trade, Eighty Low Income Countries, mid-1990s

Data.

Directed Acyclic Graphs

- Recently Papineau (1985) has
- uncovered an asymmetry in causal
- relations which may prove to be every
- bit as helpful as Grangers (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

Malinvauds 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 Data

- Directed 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 dont 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 Information

- An 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.

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) gt 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

- Illustrate X and Z cause Y as

- 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

Common effects do not screen off the association

between their joint causes.

The Causal Inverted Fork An Example

- Let Y be the event that my car wont start
- Let Z be the event that my gas tank is empty
- Let X be the event that my battery is dead
- My battery being dead and my gas tank being

empty are independent

P(XZ) P(X) - Given I know my car is out of gas and it wont

start gives me some information about my battery

P(XY,Z) lt P (XY)

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

- PC Algorithm

- 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

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)

Causal Markov Condition

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

P(W, X, Y, Z) P(W) P(XW) P(Y) P(ZX,Y)

Faithfulness

- There are no cancellations of
- parameters, eg

A b1 B b3 C C 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).

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Table 2.Edges Removed

Table 2.Edges Removed, Continued

Edge Removed

Partial Correlation

Corr.

Prob.

Table 2.Edges Removed, Continued

Edge Removed

Partial Correlation

Corr.

Prob.

Table 2.Edges Removed, Continued

Edge Removed

Partial Correlation

Corr.

Prob.

(-)

Agricultural Income/Person

Illiteracy

Unfreedom

()

()

Gini

()

GDP/Person

()

Birthrate

Child Mort

()

()

(-)

lt2/day

()

Foreign Aid

Pop Rural

Int. Trade

()

Malnourished

(-)

(-)

Life Expectancy

(-)

Agricultural Income/Person

Illiteracy

Unfreedom

()

()

Gini

()

GDP/Person

()

Birthrate

Child Mort

()

()

lt1/day

(-)

Foreign Aid

Pop Rural

Int. Trade

()

Under Nourished

(-)

Life Expectancy

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 PathConsider the Effect of

Agricultural Income on lt2/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 lt2/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 on GDP/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.

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

- Foreign Aid appears not to be a mover of
- Poverty.

Caution

- Our 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

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