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# lecture3 - Economics 10: Introduction to Statistical...

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Economics 10: Introduction to Statistical Methods Class #3 Looking at the Data-Relationships Bivariate Data

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Overview Last time: summary of univariate data Univariate data: one data series Description with graphs, statistics Today: summary of bivariate data Bivariate data: two potentially related data series Description with graphs, statistics
Today’s Lecture Motivations for analysis of bivariate data Terminology Summary of bivariate relationships G raphs : scatterplots, smoothing S tatistics (to characterize linear relationships): Covariance Correlation Least-squares regression

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Motivations for Analyzing Bivariate Data
Examples from Macro Phillips Curve (unit is year, t ): Inflation and unemployment Okun’s Law (unit is year, t ): %ΔGDP and Δ unemployment The "gap version" states that for every 1% increase in the unemployment rate , a country's GDP will be an additional roughly 2% lower than its potential GDP . According to Andrew Abel and Ben Bernanke , estimates based on data from more recent years give about a 2% decrease in output for every 1% increase in unemployment (Abel and Bernanke, 2005). Beveridge Curve (unit is year, t ): Job vacancies and unemployment

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Beveridge Curve (unit is year, t ): It typically has vacancies on the vertical axis and unemployment on the horizontal; it slopes downwards as a higher rate of unemployment normally occurs with a lower rate of vacancies.
Examples from Micro From labor economics (unit is person): Schooling/work experience and earnings From public economics (unit is person): Taxes/tax relief and labor supply From international trade (unit is area): K (or L) supply and K (or L) intensity of industry mix

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Terminology
Basic Notation Refer to the two variables as x and y x referred to as: an independent variable , an explanatory variable , a covariate , or a regressor y referred to as: a dependent variable , an outcome , or a response variable

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Association between Variables Two variables are measured on the same cases are “associated” if knowing the value of one of the variables tells you something about the values of the other variable that you would not know without this information. Example: Class attendance and test scores First test and final exam Happiness and being productive
Interpretation Causality often assumed to run from x to y ( x→y ) x and y come from economic theory But with observational data, methods/statistics only capture associations , not causal relationships Note: experiment useful in establishing causation The value of x would be manipulated “in the lab,” not determined by the choices of individuals Makes it possible to “hold other things constant” by design when changing the value of x

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Graphical Representation of Bivariate Relationships
Scatterplots: Definition A scatterplot plots the realizations of two

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## This note was uploaded on 05/05/2010 for the course ECON 010 taught by Professor Giummo during the Spring '08 term at Dartmouth.

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lecture3 - Economics 10: Introduction to Statistical...

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