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**Unformatted text preview: **1 Economics 20 Lecture #2: Bivariate Regression 2 Today Brief Review of Last time Rubin Causal Model Simple Linear Regression Model Terminology Key assumption Derivation of Least Squares estimation Next Class: Multiple Regression The fundamental problem of causal inference is that: 3 1 2 3 4 5% 0% 5% 91% 1. People self-select into treatment, so we cant take differences in their outcomes as causal 2. We can never observe the counterfactual 3. Convincing natural experiments are difficult to find 4. Experiments are often not possible in economics No assumptions are necessary for experiments to produce causal estimates 4 0% 100% 1 2 1. True 2. False The assumptions necessary for experiments to produce causal estimates are plausible because of random assignment 5 86% 14% 1 2 1. True 2. False Causal inference always requires us to make untestable assumptions 6 76% 24% 1 2 1. True 2. False 7 Last Time Rubin Model of Causality: Individuals (i) have 2 potential outcomes: Y i1 = outcome if individual i gets treatment (last time: unemployed person gets a temp job ) Y i0 = outcome if i does not get the treatment = Average Treatment Effect (ATE) = E[Y i1 Y i0 ] = E[Y i1 ] E[Y i0 ] Fundamentally unobservable (why?) 8 What we can actually observe We observe T i = = E[Y i1 |T i = 1] - E[Y i0 |T i = 0] = + {E[Y i |T i = 1] - E[Y i0 |T i = 0]} What we can estimate, , represents the causal effect E ATE = true causal impact The counterfactual difference in outcomes between treated and non-treated groups absent the treatment (not observable!) 1 if person i gets the treatment 0 if does not 9 Econometric Models Econometric models = set of assumptions, relevant to a particular research question, describing the relationship between the outcome, treatment, and other observable and unobservable variables **No matter the model, some version of the independence assumption is required for causal inference** Today: simple linear regression model 10 The Simple Regression Model y i = + 1 x i + u i 11 Simple Linear Regression Model (SLRM) y i = + 1 x i + u i For situations where we believe there is a linear (straight line) relationship between two variables how much y rises with x is constant ( 1 ) 1 represents the causal effect of a one- unit change in x on y. This is: Always unknown (fundamental problem of causal inference) May be zero! 12 Terminology y i = + 1 x i + u i We typically refer to y as the Dependent Variable, or Left-Hand Side Variable, or Explained Variable, Outcome Variable Or Regressand 13 Terminology, cont....

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