Correlation Ex.: Ex.: Causation: Ex.: Ex.: Ex.: Ex.: Randomized trials Treatment group Control group

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1 Ch. 3 1 Public economists use empirical tools to test theory and estimate policy effects. o Does the demand for illicit drugs respond to price changes (what is the elasticity)? o Do reduced welfare benefits lead to increased labor force participation? o Do school vouchers help or hurt public schools? o How much do quality public schools add to housing values? o Do scholastic chess programs lead to increased academic performance? The biggest challenge for empirical public economists is distinguishing between correlation and causation. o Correlation: two variables are correlated if they move together. Ex.: If the NFC wins the super bowl, the stock market will finish the year up, if the AFC wins it will finish down (correct 30/37 times through 2005). Ex.: Until 2004, the Washington Redskins last home game prior to a presidential election had correctly predicted the outcome of the winner since the teams inception in A loss meant the incumbent party would lose the white house and vice versa. o Causation: two variables are causally related if movement in one causes movement in the other. Ex.: Surface sea temperatures in the Atlantic are correlated with the intensity of a hurricane season. Scientists believe that higher SSTs in the Atlantic help cause hurricanes to develop and intensify. o When two variables, A and B, are correlated there are four possible explanations (discuss previous examples and decide which explanation applies): A causes B B causes A Some third factor, C is causing A and B The variables simply happen to be correlated o Ex.: Studies show that substance abuse is correlated with STD rates among teenagers (could be 1 or 3). o Ex.: The text talks about the Russian government sending doctors to areas ravaged by cholera. Locals noticed that areas with more doctors had a higher incidence of cholera. Thus they killed the doctors. o Ex.: Margulies chess study. o For policy purposes we want to know when two variables are causally related. Randomized trials: randomly assigns individuals to a treatment group and a control group. o Treatment group: the group of individuals who are affected by the policy being studied. o Control group: the group of individuals who are not affected by the policy being studied. o Suppose we observe that participation in a voluntary job training program is correlated with lower recidivism among inmates. What are the treatment and control groups? What are possible explanations for the correlation? If inmates who want to become productive members of society are more likely to participate, then there is selection bias.

2 Ch. 3 2 Bias: any difference between the control and treatment groups that is correlated with, but not a result of treatment. Selection bias: bias that is a result of people voluntary selecting into treatment and control groups. What if we clone one inmate, and use his clone as the control group? Then, the treatment and control groups are the same except for whether they receive treatment. Any differences in the probability the inmate reoffends must be a result of the program. But if the program only affects the probability of reoffence, we may not observe differences even though the program is effective. If we cloned 1000 inmates, then we could estimate the difference in recidivism between the two groups. o Note: by using much larger treatment and control groups we reduce the chances that explanation 4 applies. In practice, we might randomly select 1000 inmates to be the treatment group. The law of large numbers implies that as our sample size grows, the sample begins to look more and more like the population (excel example). o This implies that with a large enough sample, the treatment group will be virtually identical to the control group. o Then with a large enough sample, we can be confident that any differences in recidivism are the result of treatment. o The pharmaceutical industry often uses randomized trials. o Use California AFDC experiment from book: 15% reduction in benefits for randomly selected 2/3 of recipients. Found that a 15% reduction in benefits led to a 10% increase in the percentage of recipient employed. Elasticity of employment with respect to benefits is Emp Emp Benefits.15 Benefits o Problems with randomized trials: Sometimes they are impossible to implement (e.g. substance abuse and STD rates). The results may not hold for other populations. If we estimate the impact of the job training programs at a women s prison, the results may not generalize to male inmates.

3 Ch. 3 3 Medical studies usually have people volunteer to take part. These people may be less risk-averse than the general population. Attrition: people leave the study before it is finished. Okay as long as the attrition is random. If people who have negative outcomes are more likely to leave, then we will overstate the benefits of the program. Ethics Is it fair to reduce some people s AFDC benefits but not others? Is it right to provide potentially life-saving medications to some people but randomly deny them to others? Note the medical study for Parkinson s treatment o Involved injecting pig fetal cells directly into patient s brains. o In order to have a valid control group they had to drill holes in the heads of the control group for no medical reason. o Bottom line: In the real world we often do not have randomized trials, but must rely on observational data (e.g. the effect of gun control laws on crime rates; the effect of tort reform on legal settlements). Show how to adjust time-series data for inflation o Nominal prices: prices stated in today s dollars. o Real prices: prices stated in some constant year s dollars. o Consumer Price Index: shows the change in price, over time, of buying a typical bundle of goods. From 1982 to 2003 the CPI rose 91%. If the price of a good rose by less than 91% that good has a falling real price. Time-series analysis: analyzing the patterns of two or more data series over time. o Look at slide 1. Are the variables correlated? Does the data suggest causation? o Look at slide 2. Are the variables correlated? Does the data suggest causation? 1992 was the beginning of a price war. Beginning in 1997 manufacturers passed on significant legal costs to consumers. Cross-sectional regression analysis: statistically analyzing the behavior of many individuals at a single point in time. o Bivariate regression: regression that only looks at two variables. Essentially just a way of measuring the extent to which two variables are correlated.

4 Ch. 3 4 Slide 3 plots semester GPA and SAT scores for a group of college freshmen. Note there seems to be a correlation. Slide 4 fits a linear regression line through the scatterplot. o Regression line is the best linear fit for the data. Minimizes the sum of the squared residuals. The slope is positive because the correlation is positive. In this case we estimate that the slope (coefficient) of the line is This means that, on average, a 100 point difference in SAT is associated with a.19 increase in GPA. The standard error is a measure of the precision of the coefficient estimate. If the standard error is too big relative to the coefficient, then we can t be certain that the coefficient really is different from zero. How big is big? To be 95% sure that the coefficient is bigger/smaller than zero, the coefficient should be 1.96 times bigger than the std. error. The t-statistic is the coefficient divided by the std. error. Thus if the absolute value of the t-stat is bigger than 1.96, we can be 95% sure that our coefficient is bigger/smaller than zero. P shows the probability that the coefficient is not bigger/smaller than zero. The last two columns show the 95% confidence interval. Sometimes we use proxy variables because what we really want to measure is not available. o Control variables Suppose in the STD/drug use case we could divide people into two groups: risk-loving and risk-averse. Then, if all individuals in a group have the same risk preferences, we could estimate a coefficient for each group, and we wouldn t have to worry about risk preferences affecting our results. But if our measure of risk is a continuous variable dividing into groups doesn t solve the problem. However, with linear regression we can simply insert our measure into the regression to control for it (show slide 5). Dummy variables: variables that take on a value of zero or one depending on whether or not something is true. Using a dummy variable in a regression helps us to control for true/false variables that may have an effect on outcomes. We often use a dummy variable for treatment. We might use a dummy variable for race, sex, marital status, ect. (show slide 6). o Problems with linear regression:

5 Ch. 3 5 It is linear. It assumes that SAT scores have the same impact on GPA for smart kids and not so smart kids. Correlated regressors. If two explanatory variables are highly correlated we cannot distinguish between the two (e.g. ACT and SAT scores). Omitted variables bias. If we cannot measure risk preferences we cannot control for it. In reality there are virtually always factors that we cannot observe. Not including these factors can bias the results of our regression (we attempt to control for these factors using panel data). Panel data regression analysis o Panel data: data set containing multiple individuals over multiple years. o Allows us to see how an individual changes his behavior in response to changes in explanatory variables. o It uses a dummy variable for each individual, which essentially creates an individual fixed effect o The real benefit is that we no longer have to worry about individual-fixed unobservables. o Better than cross-sectional data in this regard, but unobservable characteristics of individuals still change over time. Difference-in-difference estimation: uses a natural-experiment (quasi-experiment) to estimate the impact of the policy/variable of interest. o Card Mariel Boatlift paper: In the summer of 1980, 125,000 Cuban immigrants arrived by boat in Miami. Half settled permanently, leading to a 7% increase in the labor force. We would expect this to lead to a (temporary) increase in unemployment and a decrease in wages. This effect should be particularly strong among low-skilled workers. Slide 7 shows unemployment rates in Miami and 4 other cities in 1979 and Calculate DID as ( ) ( ) = -1.2 Calculate the SE of the difference between two means by squaring them, adding the squares together, then taking the square root of the sum. o E.g. the SE of the difference between 1979 and 1980 Hispanic employment in Miami is o The SE of the difference between 1979 and 1980 Hispanic employment in the four other cities is

6 Ch. 3 6 o The SE of the difference between 1979 and 1980 Hispanic employment in the four other cities is Thus the SE of the DID estimate is 3.3, and the estimate is statistically no different from zero. Card finds virtually no impact of the boatlift on the unemployment rate or the wage rate of low-skill and Cuban workers. o Just like in the randomized trial we discussed previously, our observations are divided into a control and treatment group. Treatment group: Miami Control group: Tampa-St. Pete, Houston, Atlanta and L.A. However, the effectiveness of the strategy depends on whether the two groups are on the same trajectory over time. If unemployment was climbing faster in the control group anyway, we could miss a spike in unemployment that occurred as a result of the boatlift. Therefore, with DID estimates we need to pick treatment and control groups that are as similar as possible. Grossman, Kaestner, Markowitz; An Investigation of the Effects of Alcohol Policies on Youth STDs. o Recall that drug/alcohol use and STDs are correlated. How can we determine whether explanation 1 or 3 is appropriate to describe the relationship? We need an identification strategy. Talk about Mark s divorce paper. o GKM use the price (proxied by tax) and availability of alcohol rather than the actual rates of use. If the alcohol tax rate is correlated with the STD rate, which explanations could apply? The idea is: Lower taxes cause increased alcohol use. Increased alcohol use causes an increase in STD rates. Therefore lower tax rates cause an increase in STD rates. Note it does not seem plausible that lawmakers respond to high STD rates by increasing alcohol taxes, nor can I think of a third variable that might be correlated with both. This is what is called exogenous variation. Other examples include: Mariel boatlift. Alachua County Chess Challenge. What about state gun control laws? o Panel data Use the real state and federal excise tax on beer (proxy for price). Use the percentage of people living in a dry county (proxy for availability). Use dummy variables for BAC law and youth zero tolerance law. Control variables include religious affiliation and education (why?). Outcome variables: rate of gonorrhea and AIDS.

7 Ch. 3 7 o Results: Higher beer taxes associated with lower rates of gonorrhea and AIDS rates for males (elasticity = -.47 for males and -.41 for males 20-24) Availability had no statistically significant effect on STD rates. Some evidence that zero tolerance laws may lower gonorrhea rates among males under the legal drinking age by 7-8%. o In order for these results to be convincing they need to: Provide evidence that the price elasticity of alcohol among youths/young adults is not zero. Argue that lawmakers do not respond to high STD rates by increasing alcohol taxes. Argue that there is no third factor that is correlated with both alcohol taxes and STD rates.

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