Lecture 15 - PAM 3300 Midterm Review Where weve been...

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PAM 3300: Midterm Review
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Where we’ve been Overview of Program Evaluation and Program Theory (ln2) Statistics Review (ln3) Causality - FPCI, counterfactual reasoning, statistical approach to ‘solving’ FPCI, drawbacks of PF causal effect estimator, attributes as causes, SUTVA (ln4) Regression Review, description, uses of R 2 , causal interpretations of coefficients, omitted variable bias, multiple regression (ln5-7) Research designs and validity, randomized controlled trials (ln8) Rand Health Insurance Experiment (ln8-9) NYC Voucher Experiment (ln9-10) Non-experimental designs (ln10-11) Munnel et al. Study of Mortgage Lending in Boston (ln 11) Krueger vs. DiNardo & Pischke Studies of Returns to computer use (ln12) Assessment of non-experimental designs by LaLonde (ln13)
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Regression Regression as a linear approximation to graph of averages
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Summarizing the relationship: Regression of Earnings on Years of Education E[ Y i | X i ]=-19,280+4,157 X i Regression line: linear approximation to graph of averages
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Regression Language - Interpreting coefficients (1) Y and X are continuous (regress wage on years education) Interpretation of constant: The average hourly wage of those with 0 years of school is -15.25. Interpretation of coefficient on school: Each additional year of education is associated with an extra $2.67 in hourly wages on average. Avoid words like “each additional year of school causes/increases/leads to ”… unless you believe the relationship is causal. . reg hrwagely school Source | SS df MS Number of obs = 1000 -------------+------------------------------ F( 1, 998) = 127.30 Model | 53501.4245 1 53501.4245 Prob > F = 0.0000 Residual | 419437.138 998 420.277693 R-squared = 0.1131 -------------+------------------------------ Adj R-squared = 0.1122 Total | 472938.562 999 473.411974 Root MSE = 20.501 ------------------------------------------------------------------------------ hrwagely | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- school | 2.670268 .2366684 11.28 0.000 2.205843 3.134693 _cons | -15.25841 3.230216 -4.72 0.000 -21.5972 -8.919613 ------------------------------------------------------------------------------
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Regression Language - Interpreting coefficients (2) Y and X are continuous, Y in logs (regress log wages on years education) Interpretation of constant: The average log hourly wage of those with 0 years of school is 1.31989. Interpretation of coefficient on school: Each additional year of education is associated with about 10.61% higher hourly wages on average. . reg lnw school Source | SS df MS Number of obs = 1000 -------------+------------------------------ F( 1, 998) = 210.91 Model | 84.5172482 1 84.5172482 Prob > F = 0.0000 Residual | 399.919216 998 .400720658 R-squared = 0.1745 -------------+------------------------------ Adj R-squared = 0.1736 Total | 484.436465 999 .484921386 Root MSE = .63303 ------------------------------------------------------------------------------ lnw | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- school | .1061316 .0073079 14.52 0.000 .091791 .1204723 _cons | 1.31989 .0997434 13.23 0.000 1.124159 1.515621 ------------------------------------------------------------------------------
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Regression Language - Interpreting coefficients (3) Y continuous but X is a dummy (regress wages on dummy for finished college or did not finish college) Interpretation of constant: The average hourly wage of those who didn’t finish college is $15.62. Interpretation of coefficient on college: Individuals who finish college make an average of $16.70 more than individuals who do not finish college. Note this is just like comparing sample means between two groups (X=1 vs. X=0) . reg hrwagely college Source | SS df MS Number of obs = 1000 -------------+------------------------------ F( 1, 998) = 137.59 Model | 57301.8122 1 57301.8122 Prob > F = 0.0000 Residual | 415636.75 998 416.469689 R-squared = 0.1212 -------------+------------------------------ Adj R-squared = 0.1203 Total | 472938.562 999 473.411974 Root MSE = 20.408 ------------------------------------------------------------------------------ hrwagely | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- college | 16.69938 1.423666 11.73 0.000 13.90566 19.49311 _cons | 15.61962 .7653444 20.41 0.000 14.11775 17.12149 ------------------------------------------------------------------------------
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  • Fall '08
  • MATSUDAIRA
  • Regression Analysis, Coef, bOLS, Adj R-squared Root, R-squared Root MSE, R-squared Adj R-squared

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