handout13b_2010

handout13b_2010 - Econ 139: Introduction to Econometrics...

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Econ 139: Introduction to Econometrics Andrew Sweeting 1 1 Department of Economics Duke University Spring 2010 Econ 139 Handout 13b (Duke) Instrumental Variables Spring 2010 1 / 33
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Empirical Example: Demand for Cigarettes Policy debate over the health risks from smoking often revolves around government intervention. One policy option is to tax cigarettes heavily, so that smoking will be discouraged. But how big a tax hike is needed to make a dent in cigarette consumption? The answer depends on the elasticity of demand for cigarettes How much (by what %) will consumption decrease if price increases by 1%? Econ 139 Handout 13b (Duke) Instrumental Variables Spring 2010 2 / 33
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Empirical Example: Demand for Cigarettes Here, we will use 2SLS to estimate the elasticity of demand for cigarettes using state level data from 1995. Cigarette consumption ( Q i ) is the number of packs of cigarettes sold per capita in each state ( mean = 96). The price ( P i ) is the average real price per pack including all taxes ( mean = $ 1 . 20). Econ 139 Handout 13b (Duke) Instrumental Variables Spring 2010 3 / 33
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Empirical Example: Demand for Cigarettes Our model of demand is then ln Q i = β 0 + β 1 ln P i + u i Since this is a model of demand (which is determined simultaneously with supply), OLS will be inconsistent (ln P will be correlated with u ). To use 2SLS, we pick an instrument, SalesTax , which is the portion of the tax on cigarettes arising from the general sales tax (measured in dollars per pack). Econ 139 Handout 13b (Duke) Instrumental Variables Spring 2010 4 / 33
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Empirical Example: Demand for Cigarettes Is it relevant ( Cov ( Z i , X i ) 6 = 0 ) ? It seems good: taxes clearly increase the sales price. Is it exogenous ( Cov ( Z i , u i ) = 0 ) ? Maybe. Is SalesTax correlated with Q only through P ? That is, does it a/ect the demand for cigarettes only through price? Perhaps, but taxes can be a/ected by the same local conditions that However, this is probably more of a problem for cigarette speci±c taxes than sales taxes. Also, wealthy states might not need such high taxes (an omitted variables problem). Econ 139 Handout 13b (Duke) Instrumental Variables Spring 2010 5 ² 33
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Here are our estimation results: 1 First Stage Regression (i.e. X i = π 0 + π 1 Z i + v i ): d ln P i = 4 . 62 ( 0 . 03 ) + 0 . 031 ( 0 . 005 ) SalesTax i 2 Second Stage Regression (i.e. Y i = β 0 + β 1 b X i + u i ): d ln Q i = 9 . 72 1 . 08 d ln P i Econ 139 Handout 13b (Duke) Instrumental Variables Spring 2010 6 / 33
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Empirical Example: Demand for Cigarettes Can we test relevance? F = t 2 = . 031 . 005 ± 2 = ( 6 . 35 ) 2 = 38 . 44 > 10 , which looks quite good. Can we test exogeneity?
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handout13b_2010 - Econ 139: Introduction to Econometrics...

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