3. Instrumental Variables (IV) Natural experiment Look for ways the world creates the experiment we’d like to do. Lotteries, policy changes, other chance variations.

3. Instrumental Variables (IV) Example: ln(wage) = α + β*veteran + e Why might x (veteran) be correlated with e? Unobserved factors that lead you to join the military might also be correlated with wages. Key: Usually, veteran is a choice variable. But suppose we had something that was correlated with your likelihood of being a veteran, but not otherwise correlated with your wage?

3. Instrumental Variables (IV) Formally: y = α + βx + e Suppose we have a variable z such that: Corr (x, z) ≠ 0. Corr (z, e) = 0. Then z can be used as an instrument for x. Can show that estimates of β are consistent with this approach. In the case of veteran, can use your draft lottery number as an instrument. Does it satisfy our two conditions?

3. Instrumental Variables (IV) Other examples: Quarter of birth as instrument for education Sex mix as instrument for fertility.

5 Sex mix and fertility: Angrist and Evans Surveys reveal that parents have: – Slight preference for boys on the 1 st birth – Slight preference for more boys if they desire an odd number of children – Of those that want 2+ kids, most prefer a mix of boys and girls Suppose you prefer a mix but are endowed with same sex. How do you respond? – You could try again to obtain an optimal sex mix – Sex mix mimics random assignment – realization of sex mix changes the propensity to have an additional kid

6 Women w/ >=1 Kid, 1980 Census Sex of 1 st kid% of sample % that have a second kid Girl (0.001) Boy (0.001) Difference0.000 (0.002)

7 Women w/ >=2 Kids, 1980 Census Sex of 1 st 2 kids% of sample % that have a third kid 1 Boy/1 Girl (0.001) 2 B or 2 G (0.001) Difference0.060 (0.001)

8 Women w/ >=2 Kids, 1980 Census Sex of 1 st 2 kids% of sample % that have a third kid 1 Boy/1 Girl (0.001) 2 Girls (0.002) 2 Boys (0.002)

9 Are women who have a mix of boys/girls different? No difference in: – Years of education, age at first birth, % Hispanic, % Black, % White, Sex mix of children looks random

10 How to interpret? We know two facts – Sex composition is random – But sex composition alters the chance a mom will have another child Therefore, suppose we find that moms with 2 kids of the same sex are working less. What can we conclude? Since sex composition is random, the only reason labor supply is different is because of the fact that moms w/ 2 kids of the same sex have more kids

11 Table 5 Difference in Means between couples with Same sex and mixed sex kids Δ = Y 1 - Y o (standard error) Worked last year Weeks worked Hours/ Week Earnings (0.0016) (0.0709) (0.0602) (34.5) T-stat

12 Having two children of the same sex: Increases the chance of a third child by 6 percentage points – Δ x = X 1 - X o = 0.06 Reduces fraction working by 8 tenths of a percentage point – Δ y = Y 1 - Y o =

13 The sex composition is only impacting 6 percent of women So the change in labor supply should be for this group only So, if we divide by 0.06, we get /0.06 = Having a 3 rd child will reduce labor supply by 13.3 percentage points

3. Instrumental Variables (IV) Other examples: Quarter of birth as instrument for education Sex mix as instrument for fertility. Having a girl first as instrument for divorce. Miscarriage as instrument for fertility/birth spacing. Election cycle as instrument for police spending. Cigarette taxes as instrument for smoking.

3. Instrumental Variables (IV) Notes: IV estimates are consistent, but less precise than OLS estimates The weaker the link between the instrument (z) and x, the less precise the estimates will be. You can test the assumption that corr(x,z)≠0, but you (usually) can’t test that corr(z,e)=0. IV identifies the effect of x on y for people who’s value of x is affected by the instrument. This is the LATE that Angrist & Pischke discuss.

3. Instrumental Variables (IV) IV is estimated by a process known as two-staged least squares (2SLS). 1.Regress x on the instrument, z. This is the “first stage.” Can be used to test whether corr(x,z)≠0. Use the parameters (α, β) from this regression to predict a value of x for every observation (x-hat). 2.Regress y on x-hat. The coefficient on x-hat is the IV estimate of the effect of x on y. Use a statistical software package to get the correct standard errors.

4. Differences-in-Differences Another type of natural experiment Particularly useful for policy. When a policy is enacted, we can look at how the affected population responds (compare outcomes in t 1 to outcomes in t 2 ). However, because many other things might change from period 1 to period 2, can’t attribute the difference in outcomes entirely to the policy. With dif-in-dif, try to find a control group that is similar to the affected group but that did not experience the policy change.

A & P’s Monetary Policy Example This picture is intriguing, but we have to assume that sixth district would have moved exactly like the eighth in order to make a causal statement (the common trends assumption).

A & P’s Monetary Policy Example This picture is more convincing, because we can see that both before and after the policy change, the two districts were on similar paths.

Some examples from my research Effect of blood test requirements on marriage rate (BGP 2011).

Some examples from my research Effect of infertility insurance mandates on triplets (Buckles 2013).

Some examples from my research Effect of state age cutoffs for adoption subsidies on number of adoptions (Buckles 2013).

4. Differences-in-Differences In that last figure, hard to detect with naked eye. Plus, may want to control for omitted variables (especially other related policies). Regression setup (Eq. 5.3 from A&P): Y dt = α + β TREAT d + γ POST t + δ rDD (TREAT d x POST t ) + e dt Where the interaction term is a dummy for being in the treatment group after the change. The δ rDD coefficient gives us the effect of the treatment.

4. Differences-in-Differences Some calculus helps us see why: Y dt = α + β TREAT d + γ POST t + δ rDD (TREAT d x POST t ) + e dt Take the derivative of Y dt with respect to POST: dY dt /dPOST = γ + δ rDD x TREAT d So, the effect of being in the post-policy world is γ for the control group and γ + δ rDD for the treatment group. The difference is δ rDD.

4. Differences-in-Differences You can add covariates to this regression, and also controls for the trends the groups were already on. This allows us to relax the common trends assumption (but we still have to assume that we have correctly specified the form of the trend for each group).

Blood Tests and Marriage In my paper, I had the following equation (analogous to Eq. 5.5 in A&P): Where bloodtest is like the TREATxPOST variable, the α s term is like the TREAT variable, and the δ t term is the POST variable. The time t variable is the state-specific trends.

Blood Tests and Marriage Show what data look like. In Stata, I type: areg marrate bldtest _Iy* ts* t2* [fw=pop2], absorb(state) cluster(state) r Add controls for age of consent laws: areg marrate bldtest consentlt16 consent16 _Iy* ts* t2* [fw=pop2], absorb(state) cluster(state) r

Blood Tests and Marriage

Putting it together: Using econometrics to study the family First, Ribar. Literature review that addresses: * Why do we care? * What does theory predict? * How might we go about answering it? * What methods have researchers tried, and what have they found? * What can/should be done next?

Why do we care? Tremendous interest by both academics and the public. Public policy implications: Direct: Administration for Children and Family’s Healthy Marriage Initiative, waiting periods, covenant marriages Indirect: welfare policy, tax policy Ribar’s contribution: Summarize and evaluate (not all studies are created equal!) Compare across disciplines, who often ignore one another Includes recent developments

What does theory predict? Aside: Defense of the Rational Choice Model Rational behavior: adults make conscious decisions that maximize their well-being subject to their constraints. *or* People do the best they can with what they have. Many different models/perspectives can be incorporated into this framework. “Rational choice is the worst assumption except for all those other assumptions that have been tried from time to time.”

What does theory predict? How might marriage affect child well-being? Resources (time and money) Stability and stress Parents’ productivity (health, cooperation) Which of these require marriage (vs. cohabitation, for ex.)? When might marriage have a negative effect?

How might we answer this question? Great challenge to research in this area is establishing causality. The endogeneity problem: correlation between variable (marital status) and error term. * Reverse causality * Omitted variables (or the problem of selection into marriage) Endogeneity problems often arise when the independent variable of interest is a choice variable—in this case, marriage.

How might we answer this question? Cross-section strategies 1. Add omitted variables, or proxies. Disadvantages: May not have, may not know what they are. Cannot address reverse causality. Issues with interpretation and over-controlling. 2. Natural experiments: look for ways in which the world runs the experiment we want to run. Examples: “shot-gun” marriages, parental death Disadvantage: hard to find, generalizability. Potential IVs for marriage: state/local laws regarding marriage, like blood test requirements.

How might we answer this question? Panel-data strategies 1. Fixed Effects Add dummies for each individual, so effectively comparing the same individual to him/herself at different points in time. Advantage: eliminates OVB caused by permanent unobserved characteristics (ex: innate ability level). Disadvantages: cannot address OVB caused by changing characteristics (ex: health). Can also think of family, geographic, school fixed effects Control for pre-existing characteristics Ex: Child health before the divorce

What has been tried? What was found? Broadly: Children with married parents have higher living standards, better health, better development, more education, better behavior, less risky behavior, and more success as adults. Some structures may be better than marriage, e.g. single mom with grandparents Marriage associated with bad outcomes for some groups Causal or not?

What has been tried? What was found? Studies that add controls to address selectivity often find that doing so reduces or eliminates the beneficial effect of marriage. What do you make of this?

What has been tried? What was found? Interesting studies/convincing methods? Gruber (2000): uses variation in unilateral divorce laws to estimate effect of divorce on kids’ education & wages. Finds divorce decreases schooling and income and increases likelihood of early marriage.

What has been tried? What was found? Summary: Selectivity “more than a hypothetical concern” May be small direct causal effects What’s next Studies should more carefully address the selectivity issue. Natural experiments, like IV, most promising. Use policy variation? Relationship quality, rather than status