On World Poverty: Causal Graphs from the 1990’s

1. On World Poverty: Causal Graphs from the 1990’s David A. Bessler Texas A&M University January 2003

2. David A. Bessler Texas A&M University Outline II. Scatter Plots on Measures of Poverty and Related Variables I. Literature III. Causal Modeling IV. Directed Graphs • V. Regressions and Front Door • and Back Door Paths VI. Summary and Discussion

3. David A. Bessler Texas A&M University 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

4. David A. Bessler Texas A&M University 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).

5. David A. Bessler Texas A&M University 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)

6. David A. Bessler Texas A&M University 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.

7. David A. Bessler Texas A&M University Table 1.Countries Studied

8. David A. Bessler Texas A&M University Table 1.Countries Studied, Continued

9. Table 1.Countries Studied, Continued David A. Bessler Texas A&M University

21. 100 75 50 % < $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-1990’s Data.

22. David A. Bessler Texas A&M University 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.

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. Y X Z David A. Bessler Texas A&M University 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.

32. David A. Bessler Texas A&M University 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.

33. X Y Z David A. Bessler Texas A&M University 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.

34. David A. Bessler Texas A&M University 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)

35. David A. Bessler Texas A&M University 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

36. David A. Bessler Texas A&M University 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

37. David A. Bessler Texas A&M University 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

38. Z X Y David A. Bessler Texas A&M University Causal Sufficiency • No two included variables (X and Y in diagram) are caused by a common omitted variable (Z):

39. W X Z Y David A. Bessler Texas A&M University 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(X|W) • P(Y) • P(Z|X,Y)

40. b1 A B b3 b2 C David A. Bessler Texas A&M University 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).

41. David A. Bessler Texas A&M University

42. Edge Removed Partial Correlation Corr. Prob. David A. Bessler Texas A&M University Table 2.Edges Removed

43. David A. Bessler Texas A&M University Table 2.Edges Removed, Continued Edge Removed Partial Correlation Corr. Prob.

44. David A. Bessler Texas A&M University Table 2.Edges Removed, Continued Edge Removed Partial Correlation Corr. Prob.

45. David A. Bessler Texas A&M University Table 2.Edges Removed, Continued Edge Removed Partial Correlation Corr. Prob.

46. David A. Bessler Texas A&M University (-) Agricultural Income/Person Illiteracy Unfreedom (+) (+) Gini (+) GDP/Person (+) Child Mort Birthrate (+) (+) (-) % <$2/day (+) Foreign Aid % Pop Rural Int. Trade (+) % Malnourished (-) (-) Life Expectancy

47. David A. Bessler Texas A&M University (-) Agricultural Income/Person Illiteracy Unfreedom (+) (+) Gini (+) GDP/Person (+) Child Mort Birthrate (+) (+) % <$1/day (-) Foreign Aid % Pop Rural Int. Trade (+) % Under Nourished (-) Life Expectancy

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.