Final Review Session

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Final Review Session

• January 16th, 2009
• Dainn Wie
• Arturo Aguilar

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I. Be sure to know

• Important topics covered before the midterm to
  review
• Interpreting coefficients (multivariate regs)
• Hypothesis tests (t stats F stats)
• Dummy variables
• Interactions (when to use them and how to
  interpret them)
• Non-linear regressions polynomial and logs
• Panel data analysis (fixed effects)
• HAC SEs
• Internal and external validity

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II. Final 2006 Part I

• Using regression (1) in Table 2
• Compute the estimated effect on the childs years
  of education of an increase of four years in the
  mothers education.
• Compute a 95 confidence interval for your
  estimated effect in (a).

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II. Final 2006 Part I

• Compute the estimated effect on the childs years
  of education of an increase of four years in the
  mothers education.

The coefficient implies Caeteris paribus (all
else equal), the childs years of education are
expected to increase in 4x0.097 (0.0388) for a 4
yr increase in mothers education
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II. Final 2006 Part I

• Compute a 95 confidence interval

• The new coefficient b4xb
• Var(b) Var(4xb) 16xVar(b)
• SE(b) sqrt(Var(b))sqrt(16xVar(b))4xSE(b)
• SE(b)4x0.027 0.108
• 95 CI 0.388 /- (1.96)(0.108)

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II. Final 2006 Part I

• Consider the relationship between the childs
  years of education and parental BMI, holding
  constant the regressors in Table 2, column (1)
  other than parental BMI.
• Suggest a reason why this effect might be
  nonlinear.
• Can you reject the null hypothesis that effect on
  the childs years of education of parental BMI is
  linear? Explain.

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II. Final 2006 Part I

• Can you reject the null hypothesis that effect on
  the childs years of education of parental BMI is
  linear? Explain.

Ho Mom BMI2 0 Dad BMI2 0 (Mom
BMI)x(DadBMI)0 We reject at a 5 level if
p-value is less than 0.05 gt Here we FAIL TO
REJECT
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II. Final 2006 Part I

• Consider the regressions in Table 1.
• Explain why these regressions can be used to
  examine the proposition that the assignment
  process of adoptees to families was in effect
  random.

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II. Final 2006 Part I

• Using regressions (1) and (2), can you reject the
  hypothesis of random assignment? Explain.
• Using regressions (3) and (4), can you reject the
  hypothesis of random assignment? Explain.

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II. Final 2006 Part I

• Explain what your answers to (b) and (c) imply
  about the program. Explain, in real-world,
  concrete terms, how you might reconcile any
  discrepancy between your answers to (b) and (c).
• Once year of adoption dummy variables are
  included, the variable of log parents income
  looses its significance.
• This might be the case if the log parents income
  variable was catching up a year effect.

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II. Final 2006 Part I

• The standard errors reported in Tables 1 and 2
  are clustered standard errors, clustered at the
  level of the household.
• Explain specifically what this means, that is,
  what are clustered standard errors, clustered at
  the level of the household? Be precise.
• Provide a reason why the clustered standard
  errors could be larger than the conventional
  heteroskedasticity-robust standard errors for the
  regressions in Table 2.

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II. Final 2006 Part I

• Important facts to have in mind about clustered
  SEs
• Coefficients do not change since you are not
  adding or subtracting regressors
• SEs of the coefficients change and this has an
  impact on t-stats, F-stats, CI, etc.
• Clustered SEs mean that errors (ui in the reg)
  within a cluster (in this case within adoptees in
  the same hhold) are correlated, but not across
  clusters

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II. Final 2006 Part I

• Adding clustered SEs usually makes the SEs
  increase with respect to the heteroskedastic SEs.
  This is the case when the correlation between the
  errors within the cluster is positive.
• In (b) this is the case if within adoptees
  living in the same household both get less
  attention for the presence of non-adoptee
  children or because the household received a
  negative shock (illness of a parent for example)

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III. Final 2006 Part II

• Consider a female adoptee whose med is 14, fed is
  16, parents income is 50,000, mBMI is 23, fBMI
  is 24, mom dad not drink. Also child was
  adopted in the initial program year.
• Using reg(2) in Tbl 3, compute predicted
  probability that the adoptee grows up to be a
  drinker.
• Using the coefficients
• E(zX) -1.3 (0.013)(14) (0.022)(16)
  (0.079)(log50,000) (0)(23) (0)(24)
  (0.374)(0) (0.211)(0) (0.203)(0) 0.089

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III. Final 2006 Part II

• Probit uses the normal cdf. What I am predicting
  is the value of z.
• So, to find the expected probability I need to
  find the cdf at z0.089 in the normal std tables.

Pr(Zlt0.089)0.535
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III. Final 2006 Part II

• What is the difference in the predicted
  probabilities of drinking for the adoptee in (a),
  compared with an adoptee whose parents have the
  same characteristics as those in (a) except that
  the mother drinks?
• The predicted z will be the same, except here we
  add the 0.374 coefficient of Mother Drinks.
• z2 0.0890.374 0.463
• E(Zlt0.463)0.678
• DProb 0.678 0.535 0.143

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III. Final 2006 Part II

• Remember you cannot directly interpret the
  coefficient in the Probit regression, but you can
  interpret the sign.
• In this case the Mother Drink coefficient is
  positive which tells you z will increase. Since z
  increases, the expected proba will also increase

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III. Final 2006 Part II

• In the probit you will care also if the
  coefficient is significant, since this will tell
  you if the increase (or decrease) in probability
  is significant.
• The logit is completely the same, the only
  difference is that it uses another cdf the
  cumulative standard logistic distrib fn.

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III. Final 2006 Part II

• Now use the LPM from Table 2 to estimate the
  change in predicted probabilities for the
  comparison in 1(b).
• In the LPM case the coefficients can be directly
  interpreted as the change in probability of Y for
  an increase in X equal to 1.
• Hence, the result is just to look at the Mother
  Drinks coefficient 0.135

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III. Final 2006 Part II

• Using the results in Tables 2 and 3, do you agree
  or disagree with the following statements?
  Explain.
• Tables 2 and 3 show that high parental BMI and
  low parental education both are associated with
  worse outcomes for adoptees.
• Since the assignment of children to parents
  seems to be as good as random, the statement
  seems to be truth since parents BMI and education
  happens to be significant towards adoptees
  education.

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III. Final 2006 Part II

• The results show that dieting by overweight
  mothers has benefits for children. Caeteris
  paribus, we would expect to see this weight loss
  lead to an increase in the childs education and
  probability of graduating from college.
• Watch out with the wording!!!
• In (a) we said yes to high parental BMI is
  associated with worse outcomes for adoptees, but
  here we are saying lowering parent BMI will CAUSE
  an increase in outcomes for adoptees.
• It is not clear there is causality think in
  OVB. Example might not be BMI but family intake
  of iron

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III. Final 2006 Part II

• The results in Table 3 show that paternal
  characteristics are transmitted primarily through
  a genetic path, whereas maternal characteristics
  seem to be transmitted primarily through a
  non-genetic (environmental) path.
• Solution key says yes since fathers coefficients
  turn out to be significant when using
  non-adoptees while mothers coefficients change
  very little from adoptees to non-adoptees.
• However, you could argue that it is not a
  fathers genetic inheritance, but rather a
  distinction on how they treat adoptees vs
  non-adoptees, while mothers dont make much of a
  distinction.

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III. Final 2006 Part II

• Aside question
• How would you need to modify this regression to
  see if Dad and Mom Drinking differently affects
  Male and Female adoptees? What would you test?
• Answer You would need to add an two interaction
  terms Male x Dad Drinks Male x Mom Drinks
• Then, you would carry an F test on the
  coefficients of these two interactions

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IV. Final 2006 Part III

• Suggest a reason why TV exposure might be
  endogenous in regression (1).
• One possibility A kid that is lazy tends to do
  less sports and sit more to watch TV. Also, since
  he does less sports he has higher BMI.
• Here TV exposure is not the problem, its laziness
  which is in the error term (since we dont
  include it in the regression)

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IV. Final 2006 Part III

• Regression (3) uses three variables as
  instrumental variables for TV exposure. For each
  instrument, explain whether, in your judgment,
  the instrument plausibly is exogenous
• The Price of TV advertising in the county

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IV. Final 2006 Part III

• To see if a variable is a good instrument we
  need to check two conditions
• Relevance cov(Z,X)0
• Exogeneity cov(Z,u)0
• Remember you need to think exogeneity in two
  ways
• The instrument cannot be correlated with an
  omitted error, which in turn affects Y, since you
  would only replicate OVB
• The instrument should not directly affect the
  dependent variable (Y), only through X

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IV. Final 2006 Part III

• Price of TV advertising in the county
• Number of households with TV in the county
• Average annual county Temperature.
• Check for Relevance and exogeneity, where
• X TV exposure (fast food ads seen by child)
• Y Child BMI

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IV. Final 2006 Part III

• Consider regression (3).
• Suppose the instruments in regression (3) are
  weak. If so, what would the consequence be for
  interpreting the results in column (3),
  specifically the coefficient on TV exposure and
  its SE?
• Having weak instruments causes the estimates to
  be biased.
• Weak instruments mean that the instruments are
  not relevant, that is, in your first stage
  regression, the coefficients for the instruments
  are not significant enough.

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IV. Final 2006 Part III

• Based on the results in Table 4, are the
  instruments weak, strong, or do you need more
  information before you can decide? Explain.
• The steps are
• Look at the first stage regression
• Carry out an F test on the instruments (if only
  one instrument, the square of the t stat is the F
  stat)
• If F-stat gt10 gt strong instruments

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IV. Final 2006 Part III

• Consider the J-statistic in column (3).
• Suppose you were to reject the null hypothesis
  using this J-statistic. What would you conclude?
• Ho cov(Z,u)0
• gt Rejecting the null hypothesis means rejecting
  exogeneity (i.e. at least one of the instruments
  is not exogenous, which is one of the key
  assumptions
• Note To be able to test for exogeneity you need
  to have overidentification (i.e. more instruments
  than endogenous variables)

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IV. Final 2006 Part III

• To test exogeneity you need to (just if over-id)
• Estimate the errors of the regression using the
  instruments (errors from reg (3) in this case)
• Regress the estimated errors vs the instruments
• Calculate an F-stat with the coefficients of the
  instruments
• Jstat (instruments) x (F-stat)
• Look for the p-value using the obtained J-stat in
  the chi-square fn with degrees of freedom equal
  to (instrum endog variables).

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IV. Final 2006 Part III

• Note that in the previous test you are testing
  the exogeneity of m-k instruments (where m is
  instruments and k of endogenous variables).

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IV. Final 2006 Part III

• Using the J-statistic actually reported in column
  (3), do you reject the null hypothesis at the 5
  significance level? Explain how you reached this
  conclusion (be precise).
• Jstat 0.308
• Look in the chi-squared with (3-1) d.o.f.
• The critical value at 5 is equal to 5.99
• gt 0.308 lt 5.99, hence FAIL TO REJECT

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IV. Final 2006 Part III

• A researcher suggests using as instruments a full
  set of county binary variables (county dummy
  variables). What would be the effect of adding a
  full set of county dummy variables to regression
  (2)?
• Problem Temperature, Price of TV advertising,
  and num. of hhs are all variables established at
  a county level
• Hence, adding county dummy variables would
  generate perfect multicollinearity

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IV. Final 2006 Part III

• Perfect multicollinearity is when one of the
  regressors can be expressed as a linear function
  of the other regressors
• Simplified example
• Think you have 3 counties A has an avg
  temperature of 50, B of 60, and C of 70
• Temperature could be expressed as a linear
  function of two of the dummies
• Temperature 50 10 Dummy B 20 Dummy C

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V. Final 2007 Part II

• At the start of the semester half the students in
  Ec1010a are randomly selected and told they will
  receive a cash payment of 250 if they attend at
  least 90 of the lectures.
• The objective is to estimate the causal effect of
  attendance on grades.
• Regression of interest
• Grade b0 b1 Attendance b2 Female
• b3 Prior GPA b4 SAT b5 HS quality
• Dummies for concentration

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V. Final 2007 Part II

• Provide a reason why the coefficient on
  Attendance could be a biased
• Need to make up an OVB history
• Example Having a job
• Having a job is likely to be negatively
  correlated with attendance
• If we add Having a job on the grades
  regression we would probably get a negative
  coefficient
• gt This would make the attendance coefficient to
  be positively biased

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V. Final 2007 Part II

• Let Cash denote a binary variable that equals 1
  if the student is chosen to be eligible for a
  cash enticement and equals 0 otherwise. Is Cash
  plausibly a valid instrument for Attendance in
  the 2SLS regression of Grade on Attendance and W?
  Explain.
• Relevant? Yes, I will be likely to attend if I
  get money for it
• Exogenous? Since it was randomly distributed it
  should not be correlated with any of the other
  regressors
• Watch out for Placebo effects here!! (John Henry)

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V. Final 2007 Part II

• Are the control variables W needed or useful in
  this regression? If not, should they be dropped
  from this regression? Explain.
• The coefficient on attendance will be consistent
  either way (if you include W or not)
• However, including W will allow you to get a
  better fit in the regression and reduce its SE

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VI. Final thoughts

• Two more things
• A piece missing here is Panel data and Fixed
  effects
• Advice Take a look at 2005 Final Part II
• GOOD LUCK IN THE EXAM!