2018SpringUN3213Lecture10Regressions.pdf

# 2018SpringUN3213Lecture10Regressions.pdf - Intermediate...

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Intermediate Macroeconomics Economics UN3213 Professor: Jón Steinsson Lecture 10 1

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Announcements Problem Set 2 due now Readings for Today: Jones ch 3, Levitt-Dubner, Mankiw, Thompson, Dell’Antonia, Hodgekiss. Steinsson (2017): Malthus and Pre-Industrial Stagnation Readings for Thursday: Steinsson (2018): How Did Growth Begin? The Industrial Revolution and Its Antecedents. 2
What is a Regression? “Best” line 𝑦𝑦 𝑖𝑖 = 𝛼𝛼 + 𝛽𝛽𝑥𝑥 𝑖𝑖 + 𝜀𝜀 𝑖𝑖 through a cloud of points 𝜀𝜀 𝑖𝑖 : “error” term Regression: Minimizes sum of squared “errors” (vertical distance from points to line) 3

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Multiple Regressors Say we have data on both investment and schooling for Farawayistan. What is our best prediction of growth? Assume linear relationship: 𝑦𝑦 𝑖𝑖 = 𝛼𝛼 + 𝛽𝛽 1 𝑥𝑥 1𝑖𝑖 + 𝛽𝛽 2 𝑥𝑥 2𝑖𝑖 + 𝜀𝜀 𝑖𝑖 Regression minimizes squared errors Each coefficient gives change in predicted 𝑦𝑦 𝑖𝑖 for a change in one particular regressor holding other regressors fixed. 4
Multiple Regression Way to calculate the correlation of growth and some particular factor holding fixed a bunch of other factors. In principle we would like to hold fixed all other factors If we could then we could claim to have causal relationships (Everything else is the same) 5

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Interpreting Regression Results Holding everything else fixed: Possible in biology, medicine, physics (randomized experiments) Impossible in macroeconomics (can’t do experiments on whole economies) Consequence: Hard to know whether some unobserved factor really is the underlying cause of differences in growth Unobserved factor could cause both 𝑥𝑥 𝑖𝑖 and 𝑦𝑦 𝑖𝑖 Conclusion: Often hard to make causal inference with simple regressions 6
Causal Inference Newspapers abound with statements like: Countries with more political freedom grow faster Children that are smacked at age five display more aggressive behavior at age nine (DailyMail article) Girls (and boys) exposed to Disney princesses display more female gender-stereotypical behavior (NYT article) Elderly people that walk fast have lower mortality rates (New York Magazine Article) 7

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“It’s not just that girly-girls like princesses,” said Sarah Coyne, a professor of family life at Brigham Young University and lead author of the study , which was published in the journal Child Development. “We were able to completely take that out of the equation, and look at whether there is really long-term growth” in female stereotypical behaviors in children with high levels of princess engagement.
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