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### econ120c_iv0

Course: ECON 120C, Spring 2011
School: UCSD
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Word Count: 946

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120C Consider Randomization Econ y = 0 + 1x + , Earnings = 0 + 1 * (military service) + ! However, most applied research in economics uses observational data instead of experiment data. So x is not randomly assigned. y 1 Econ 120C Earnings = 0 + 1 * (military service) + ! However, service in Vietnam was determined by more than simple random chance. ! Some men voluntarily enlisted; others received draft...

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120C Consider Randomization Econ y = 0 + 1x + , Earnings = 0 + 1 * (military service) + ! However, most applied research in economics uses observational data instead of experiment data. So x is not randomly assigned. y 1 Econ 120C Earnings = 0 + 1 * (military service) + ! However, service in Vietnam was determined by more than simple random chance. ! Some men voluntarily enlisted; others received draft deferments (or simply evaded the draft). ! Thus, a study of Vietnam War veterans would be more random than a study of veterans from the more recent all-volunteer American army. Yixiao Sun Randomization (cont.) 2 Econ 120C ! Military service in Vietnam, then, consists of two elements: 1. A clean random element determined by the draft lottery, that would be uncorrelated with in an earnings regression; and 2. An unclean element, determined by active decision-making on the agents part, that could easily be correlated with . ! The decision to volunteer, or to avoid being drafted, would undoubtedly be correlated with many other variables that may help explain Earnings Yixiao Sun x ! During the Vietnam War, the draft lottery was a largely random process. ! Fortunately, Nature often provides a certain degree of randomization. Randomization (cont.) Econ 120C ! For example, suppose we are studying the effect of military service on earnings. ! From last lecture, we know that x and are uncorrelated if x is randomly assigned. Yixiao Sun Randomization (cont.) 3 Yixiao Sun 4 1 Randomization (cont.) Econ 120C ! Vietnam War military service is partially determined by an obviously random process. ! Unfortunately, this method requires the data to include an instrumental variable with certain key properties. ! Military service is also partially determined nonrandomly. Instrumental Variables 5 Econ 120C ! An Instrumental Variable is a variable that is correlated with X but uncorrelated with . Yixiao Sun Instrumental Variables (cont.) 6 Econ 120C ! For example, a Vietnam War lottery number is: 1. Correlated with X (winning the lottery is highly correlated with military service), but ! If Zi is an instrumental variable: cov( Zi , Xi ) 0, the instrument must be correlated with the endogenous variable X cov(Zi , i ) = 0, the instrument must be exogenous. Yixiao Sun Econ 120C ! Fortunately, econometricians have discovered a method for separating out the random elements of explanators from the elements that may be correlated with . ! Nonetheless, a simple OLS estimate of the effect of military service on earnings would be inconsistent. Yixiao Sun Randomization (cont.) 2. Is uncorrelated with (the lottery number is not connected to cultural, psychological, or economic factors that might affect the decision to join the military, and that might also affect earnings). 7 Yixiao Sun 8 2 Instrumental Variables (cont.) Econ 120C ! The econometrician can use an instrumental variable Z to estimate the effect on Y of only that part of X that is correlated with Z. Instrumental Variables (cont.) Econ 120C ! An instrumental variable lets the econometrician find a part of X that behaves as though it had been randomly Because assigned. ! Z is uncorrelated with , any part of X that is correlated with Z must also be uncorrelated with . Yixiao Sun Instrumental Variables (cont.) 9 Econ 120C ! When the economist is worried about measurement error, a good choice of instrument is simply a different measure of the same variable. ! The new measure may have its own errors, but these errors are unlikely to be correlated with the mistakes in the first measure, or with any other component of . Yixiao Sun 11 Yixiao Sun Instrumental Variables (cont.) 10 Econ 120C ! For example, Ashenfelter and Rouse were studying the effect of education on earnings. ! Their data came from a survey of twins. ! They were concerned that individuals might misreport their own years of schooling, leading to measurement error biases. Yixiao Sun 12 3 Instrumental Variables (cont.) Econ 120C ! However, Ashenfelter and Rouse had two separate measures for each individuals years of schooling. Checking Understanding Econ 120C ! Suppose you are studying the effect of price on the demand for cigarettes, using a cross-section of different states cigarette consumption and average price. ! You would like to regress ! The survey asked each individual to list both his/her own years of schooling, and also the years of schooling for his/her twin. CigarettesSoldi = 0 + 1 Pricei + i ! The twins report of an individuals schooling served as an instrumental variable for the individuals selfreport. where i indexes each state In attempts to estimate the demand for cigarettes Yixiao Sun Checking Understanding (cont.) 13 Econ 120C CigarettesSoldi = 0 + 1 Pricei + i where i indexes each state ! Because Pricei is endogenous, you need to instrument. Which of these variables would be suitable? 1. Each states cigarette excise tax 2. A measure of each states anti-smoking laws 3. Each states sales tax Yixiao Sun 15 Yixiao Sun Checking Understanding (cont.) 14 Econ 120C 1. Each states cigarette excise tax Cigarette excise taxes are surely correlated with cigarette prices. However, they also reflect the level of anti-smoking sentiment in the state (MA has a tax of \$1.51 per pack, NC has a tax of \$0.05 per pack). Anti-smoking sentiment is an omitted determinant of consumption, so excise taxes are correlated with . Excise taxes are not a valid instrument. Yixiao Sun 16 4 Checking Understanding (cont.) Econ 120C 2. A measure of state anti-smoking laws State anti-smoking laws might be correlated with price, but only through their effect on cigarette demand in the state. Such measures are an explanator of cigarette consumption; moreover, they are also a proxy for state anti-smoking sentiment. Anti-smoking laws are a component of , and would make a terrible instrument. Yixiao Sun 17 Checking Understanding (cont.) Econ 120C 3. Each states sales tax State sales taxes are correlated with cigarette prices. Higher sales taxes raise the prices of all goods. There is no reason to expect sales taxes to have any other effect on cigarette consumption, or to be correlated with any other determinant of consumption. State sales taxes are a reasonable instrument. Yixiao Sun 18 5
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