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2021-9-26 published at HR&Recruiting category

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1.On World Poverty: Causal Graphs from the 1990’s David A. Bessler Texas A&M University January 2003
2. Outline I. Literature David A. Bessler Texas A&M University 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
3.Measures of Poverty Alternatives are Discussed in Sen: Poverty and Famines, Oxford Press, 1981. David A. Bessler Texas A&M University Biological Measures : e.g. deficits in calorie intake Economic Measures: e.g., % of Population Living on One or Two Dollars per Day or Less
4.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). David A. Bessler Texas A&M University
5.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) David A. Bessler Texas A&M University
6.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. David A. Bessler Texas A&M University
7.Table 1.Countries Studied David A. Bessler Texas A&M University
8.Table 1.Countries Studied, Continued David A. Bessler Texas A&M University
9.David A. Bessler Texas A&M University Table 1.Countries Studied, Continued
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21.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
22.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. David A. Bessler Texas A&M University
23.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.
24.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).
25.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.
26.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.
27.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 don’t know the "true" system that generated our data.
28.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.”
29.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.
30.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.
31.A Causal Fork For three variables X, Y, and Z, we illustrate X causes Y and Z as: David A. Bessler Texas A&M University 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 Z Y
32.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. David A. Bessler Texas A&M University
33.An Inverted Fork Common effects do not screen off the association 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: David A. Bessler Texas A&M University X Y Z
34.The Causal Inverted Fork: An Example Let Y be the event that my car won’t 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(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) David A. Bessler Texas A&M University
35.The Literature on Such Causal Structures has been Advanced in the Last Decade Under the Label of Artificial Intelligence Pearl , Biometrika, 1995 David A. Bessler Texas A&M University 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
36.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 David A. Bessler Texas A&M University
37.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 David A. Bessler Texas A&M University
38.Causal Sufficiency No two included variables (X and Y in diagram) are caused by a common omitted variable (Z): Z X Y David A. Bessler Texas A&M University
39.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) David A. Bessler Texas A&M University
40.Faithfulness There are no cancellations of parameters, eg: B A C b1 b2 b3 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). David A. Bessler Texas A&M University
41.David A. Bessler Texas A&M University
42.Table 2.Edges Removed Edge Removed Partial Correlation Corr. Prob. David A. Bessler Texas A&M University
43.Table 2.Edges Removed, Continued Edge Removed Partial Correlation Corr. Prob. David A. Bessler Texas A&M University
44.Edge Removed Partial Correlation Corr. Prob. Table 2.Edges Removed, Continued David A. Bessler Texas A&M University
45.Edge Removed Partial Correlation Corr. Prob. Table 2.Edges Removed, Continued David A. Bessler Texas A&M University
46.David A. Bessler Texas A&M University GDP/Person Agricultural Income/Person Illiteracy Unfreedom Gini Life Expectancy % Malnourished % Pop Rural % <$2/day Birthrate Child Mort Foreign Aid (+) (+) (+) (+) (-) (+) (+) (+) (-) (-) (-) Int. Trade (+)
47.David A. Bessler Texas A&M University GDP/Person Agricultural Income/Person Illiteracy Unfreedom Gini Life Expectancy % Under Nourished % Pop Rural % <$1/day Birthrate Child Mort Foreign Aid (+) (+) (-) (+) (+) (+) (-) (+) Int. Trade (+) (-)
48.“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)
49.“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)
50.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.
51.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)
52.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 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.
53.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)
54.Conclusions Illiteracy, Freedom, Income Inequality, and Agricultural Income are Exogenous movers of Poverty. David A. Bessler Texas A&M University Foreign Aid appears not to be a mover of Poverty. We are not able to direct causal flow among our four exogenous variables.
55.Caution Our methods assume Causal Sufficiency Markov Property Faithfulness Normality Failure of any of these may change results. David A. Bessler Texas A&M University Dynamic representation of poverty should be pursued. This will require a richer data set.
56.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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