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Econ 240A

Econ 240A. Power 17. Outline. Review Projects. Review: Big Picture 1. #1 Descriptive Statistics Numerical central tendency: mean, median, mode dispersion: std. dev., IQR, max-min skewness kurtosis Graphical Bar plots Histograms Scatter plots: y vs. x

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Econ 240A

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  1. Econ 240A Power 17

  2. Outline • Review • Projects

  3. Review: Big Picture 1 • #1 Descriptive Statistics • Numerical central tendency: mean, median, mode dispersion: std. dev., IQR, max-min skewness kurtosis • Graphical • Bar plots • Histograms • Scatter plots: y vs. x • Plots of a series against time (traces) Question: Is (are) the variable (s) normal?

  4. Review: Big Picture 2 • # 2 Exploratory Data Analysis • Graphical • Stem and leaf diagrams • Box plots • 3-D plots

  5. Review: Big Picture 3 • #3 Inferential statistics • Random variables • Probability • Distributions • Discrete: Equi-probable (uniform), binomial, Poisson • Probability density, Cumulative Distribution Function • Continuous: normal, uniform, exponential • Density, CDF • Standardized Normal, z~N(0,1) • Density and CDF are tabulated • Bivariate normal • Joint density, marginal distributions, conditional distributions • Pearson correlation coefficient, iso-probability contours • Applications: sample proportions from polls

  6. Review: Big Picture 4 • Inferential Statistics, Cont. • The distribution of the sample mean is different than the distribution of the random variable • Central limit theorem • Confidence intervals for the unknown population mean

  7. Review: Big Picture 5 • Inferential Statistics • If population variance is unknown, use sample standard deviation s, and Student’s t-distribution • Hypothesis tests • Decision theory: minimize the expected costs of errors • Type I error, Type II error • Non-parametric statistics • techniques of inference if variable is not normally distributed

  8. Review: Big Picture 6 • Regression, Bivariate and Multivariate • Time series • Linear trend: y(t) = a + b*t +e(t) • Exponential trend: ln y(t) = a +b*t +e(t) • Quadratic trend: y(t) = a + b*t +c*t2 + e(t) • Elasticity estimation: lny(t) = a + b*lnx(t) +e(t) • Returns Generating Process: ri(t) = c + b*rM(t) + e(t) • Problem: autocorrelation • Diagnostic: Durbin-Watson statistic • Diagnostic: inertial pattern in plot(trace) of residual • Fix-up: Cochran-Orcutt • Fix-up: First difference equation

  9. Review: Big Picture 7 • Regression, Bivariate and Multivariate • Cross-section • Linear: y(i) = a + b*x(i) + e(i), i=1,n ; b=dy/dx • Elasticity or log-log: lny(i) = a + b*lnx(i) + e(i); b=(dy/dx)/(y/x) • Linear probability model: y=1 for yes, y=0 for no; y =a + b*x +e • Probit or Logit probability model • Problem: heteroskedasticity • Diagnostic: pattern of residual(or residual squared) with y and/or x • Diagnostic: White heteroskedasticity test • Fix-up: transform equation, for example, divide by x • Table of ANOVA • Source of variation: explained, unexplained, total • Sum of squares, degrees of freedom, mean square, F test

  10. Review: Big Picture 8 • Questions: quantitative dependent, qualitative explanatory variables • Null: No difference in means between two or more populations (groups), One Factor • Graph • Table of ANOVA • Regression Using Dummies • Null: No difference in means between two or more populations (groups), Two Factors • Graph • Table of ANOVA • Comparing Regressions Using Dummies

  11. Review: Big Picture 9 • Cross-classification: nominal categories, e.g. male or female, ordinal categories e.g. better or worse, or quantitative intervals e.g. 13-19, 20-29 • Two Factors mxn; (m-1)x(n-1) degrees of freedom • Null: independence between factors; expected number in cell (i,j) = p(i)*p(j)*n • Pearson Chi- square statistic = sum over all i, j of [observed(i, j) – expected(i, j)]2 /expected(i, j)

  12. Summary • Is there any relationship between 2 or more variables • quantitative y and x: graphs and regression • Qualitative binary y and quantitative x: probability model, linear or non-linear • Quantitative y and qualitative x: graphs and Tables of ANOVA, and regressions with indicator variables • Qualitative y and x: Contingency Tables

  13. Projects • Learning by doing • Learning from one another

  14. Control of Social Problems • HIV/AIDS

  15. HIV/AIDS What can we do to prevent it?! Group 4: Pinar Sahin Darren Egan David White Yuan Yuan Miguel Delgado Helleseter David Rhodes

  16. The Problem is Controllable Control Curve Morbidity Per capita Abatement Expenditure Per Capita

  17. Is there a relationship? • Both the t and F statistics are significant • R^2 is .61, which is decent Group 4

  18. HIV/AIDS cases vs. per capita funding per state Group 4

  19. Controlling Social Problems • This same analytical framework works for various social ills • Morbidity per capita • Offenses per capita • Pollution per capita

  20. The Problem is Controllable Control Curve Morbidity Per capita Offenses Per Capita Pollution Per Capita Abatement Expenditure Per Capita

  21. Source: Report to the Nation on Crime and Justice

  22. Causal factors control Source: Report to the Nation on Crime and Justice

  23. The Problem is Not Controllable Morbidity Per capita Control Curve Controllability is an empirical question that we want to answer Abatement Expenditure Per Capita

  24. Optimizing Behavior • Cost Curve: • Cost = Damages from Morbidity + Abatement Expenditures • C = p*M + Exp

  25. Cost Curve C = p*M + Exp Exp=0, M=C/p Morbidity M M=0, Exp=C Abatement Exp

  26. Family of Cost Curves Higher Cost Morbidity M Lower Cost Abatement Exp

  27. The Problem is Not Controllable: Don’t Throw Money At It Morbidity Per capita Control Curve Optimum: Zero Abatement Higher Cost Lowest Cost Abatement Expenditure Per Capita

  28. The Problem is Controllable: Optimum Expenditures Control Curve Morbidity Per capita Higher Cost Curve Optimum Lowest Attainable Cost Abatement Expenditure Per Capita

  29. The Problem is Controllable: Optimum Expenditures Control Curve Morbidity Per capita Higher Cost Curve Optimum Spend too Much But Morbidity Is Low Lowest Attainable Cost Abatement Expenditure Per Capita

  30. The Problem is Controllable: Optimum Expenditures Spend Too Little, Morbidity Is Too High Morbidity Per capita Higher Cost Curve Control Curve Optimum Lowest Attainable Cost Abatement Expenditure Per Capita

  31. Economic Paradigm • Step One: Describe the feasible alternatives

  32. The Problem is Controllable Control Curve Morbidity Per capita Abatement Expenditure Per Capita

  33. Economic Paradigm • Step One: Describe the feasible alternatives • Step Two: Value the alternatives

  34. Cost Curve C = p*M + Exp Exp=0, M=C/p Morbidity M M=0, Exp=C Abatement Exp

  35. Economic Paradigm • Step One: Describe the feasible alternatives • Step Two: Value the alternatives • Step Three: Optimize, pick the lowest cost alternative

  36. The Problem is Controllable: Optimum Expenditures Control Curve Morbidity Per capita Higher Cost Curve Optimum Lowest Attainable Cost Abatement Expenditure Per Capita

  37. The Problem is Controllable: Family of Control Curves Control Curve Morbidity Per capita Control Curve Another Time Or Another Place Abatement Expenditure Per Capita

  38. Behind the Control Curve • Morbidity Generation • M = f(sex-ed, risky behavior) • M = f(sex-ed, RB) • Producing Morbidity Abatement • Sex-ed = g(labor) • Sex-ed = g(L) • Abatement Expendtiture • Exp = wage*labor = w*L

  39. Morbidity Generation Morbidity, M M = f(Sex-ed, RB) Sex-ed

  40. Morbidity Generation Riskier behavior Morbidity, M M = f(Sex-ed, RB) Sex-ed

  41. Production Function Sex-ed Labor, L

  42. Expenditure On Wage Bill (Abatement) Exp Exp = w*L Labor, L

  43. Control Curve Morbidity Generation Morbidity, M M = f(Sex-ed, RB) Sex-ed Exp Sex-ed = g(L) Exp = w*L Expenditure function Labor,L Production function

  44. Control Curve Morbidity, M M = f(Sex-ed, RB) Sex-ed Exp Sex-ed = g(L) Exp = w*L Labor,L

  45. Control Curve Morbidity, M M = f(Sex-ed, RB) Sex-ed Exp Sex-ed = g(L) Exp = w*L Labor,L

  46. Control Curve Morbidity, M M = f(Sex-ed, RB) Sex-ed Exp Sex-ed = g(L) Exp = w*L Labor,L

  47. Control Curve Morbidity, M Higher Risky Behavior M = f(Sex-ed, RB) Sex-ed Exp Sex-ed = g(L) Exp = w*L Labor,L

  48. Exercise • Derive the control curve for the jurisdiction with more risky behavior

  49. Expansion Path • Assume the family of control curves is nested, i.e. have the same slope along any ray from the origin • Assume all jurisdictions place the same value, p, on morbidity • Assume all jurisdictions are optimizing • Then the expansion path is a ray from the origin

  50. The Problem is Controllable: Family of Control Curves Control Curve Morbidity Per capita Control Curve Another Time Or Another Place Expansion path Abatement Expenditure Per Capita

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