LT6: IV2

Sam Mardens.h.marden@lse.ac.uk

Question 1 & 2

We estimate the following demand equationln(packpc) = b0 + b1ln(avgprs) +u

What do we require for a consistent estimate of b1?

What is the biggest problem we are likely to face? What is the likely direction of bias?

Why might Sales Tax be a suitable instrument for ln(avgprs)? Why might it not?

Question 1 & 2

We estimate the following demand equationln(packpc) = b0 + b1ln(avgprs) +u

What do we require for a consistent estimate of b1?• Standard asummption: cov(ln(avgprs) , u)=0What is the biggest problem we are likely to face? What is the likely direction of bias?• Simultaneity: price and quantity are jointly determined. Other

biases exist.Why might Sales Tax be a suitable instrument for ln(avgprs)? Why might it not?• It’s clearly relevant. Exogeneity? Culture? Cross-price elasticities.

Sales tax in pence usually depends on pre-tax price etc.

Question 3

First Stage: What’s the interpretation? Why do I use the absolute value of sales tax?

Linear regression Number of obs = 528 F( 1, 526) = 305.54 Prob > F = 0.0000 R-squared = 0.3693 Root MSE = .1061

------------------------------------------------------------------------------ | Robust lnravgprs | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- rstax | .0275433 .0015757 17.48 0.000 .0244479 .0306388 _cons | 4.61418 .0087801 525.53 0.000 4.596932 4.631429------------------------------------------------------------------------------

. sum salestax,d

salestax------------------------------------------------------------- Percentiles Smallest 1% 0 0 5% 0 010% 0 0 Obs 52825% 1.315125 0 Sum of Wgt. 528

50% 6.36325 Mean 5.833128 Largest Std. Dev. 4.11370375% 8.548334 14.4290% 11.0575 14.68425 Variance 16.9225595% 12.37533 15.52892 Skewness .011235399% 14.36575 15.64267 Kurtosis 2.066596

Ln(0)=????

Question 4 & 5 (1) (2) (3) (4)VARIABLES lnpackpc lnravgprs lnpackpc lnpackpc lnravgprs -1.213*** -1.084*** (0.195) (0.319)rstax 0.0307*** (0.00484) lnravgprshat -1.084*** (0.334) Constant 10.34*** 4.617*** 9.720*** 9.720*** (0.935) (0.0289) (1.597) (1.528) Observations 48 48 48 48R-squared 0.406 0.471 0.152 0.401

Robust standard errors in parentheses*** p<0.01, ** p<0.05, * p<0.1

What is the price elasticity of demand for cigarettes?What is the implications of the different estimates for public policy?What do you notice about the estimates obtained manually copared to the estimates obtained by ivregress?What do the difference in IV and OLS results tell us?

Question 6Why should we include log per capita income? What might it have to do with the exogeneity assumption. On seeing the results what does it have to do with the exogeneity assumption?

Instrumental variables (2SLS) regression Number of obs = 48 F( 2, 45) = 8.19 Prob > F = 0.0009 R-squared = 0.4189 Root MSE = .18957

------------------------------------------------------------------------------ | Robust lnpackpc | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- lnravgprs | -1.143375 .3723029 -3.07 0.004 -1.893232 -.3935189 lnrincomepc | .2145154 .3117469 0.69 0.495 -.4133751 .8424059 _cons | 9.430659 1.259393 7.49 0.000 6.894111 11.96721------------------------------------------------------------------------------Instrumented: lnravgprsInstruments: lnrincomepc lnravgprshat------------------------------------------------------------------------------

Question 7

Maybe there are unobserved variables driving the sales tax and smoking? How could panel data help?

Question 7Maybe there are unobserved variables driving the sales tax and smoking? How could panel data help? Some of you estimated this in first differences instead of with FE and obtained different results; what’s up with that? Number of obs = 96 F( 2, 46) = 167.34 Prob > F = 0.0000Total (centered) SS = 1.930660947 Centered R2 = 0.8966Total (uncentered) SS = 1.930660947 Uncentered R2 = 0.8966Residual SS = .1996443998 Root MSE = .06449

------------------------------------------------------------------------------ | Robust lnpackpc | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- lnravgprs | -1.072459 .1683164 -6.37 0.000 -1.402354 -.7425654 lnrincomepc | -.0790036 .254929 -0.31 0.757 -.5786553 .420648------------------------------------------------------------------------------Underidentification test (Kleibergen-Paap rk LM statistic): 11.742 Chi-sq(1) P-val = 0.0006------------------------------------------------------------------------------

Question 8

Would excise duty on cigarettes likely be more or less exogenous than general sales taxes?

Question 8

Would excise duty on cigarettes likely be more or less exogenous than general sales taxes?- ‘More’ exogenous, because levied per-pack so

dollar value of exices taxes not effected by price

- ‘Less’ exogenous, because more specific to cigarettes (although sales taxes often different rates for cigs) so more likely to be driven by tastes/culture/politics

LATE, ITT and TOT

LATE: Local average treatment effect• When we do IV we are exploiting variation in x that is

caused by the instrument.• This means we discover the effect of x on people whose x’s

were changed– E.g. if x is education, and our instrument is living near a four year

college then there are1. People who would go to college whether they lived close to one or not2. People who won’t go to college regardless3. People who would only go to college if they live near one.

– It is the effect of education for the third group that we discover with IV.

LATE, ITT and TOT

When we run an experiment we typically randomise treatment and control groups. However, conditional on being in the treatment group, sometimes only a subset of people will actually take up the treatment. For instance suppose the treatment is random assignation of microfinance organisations to villages. Only some of the people will join the microfinance groups. This means we can talk about two effects:• ITT (Intention to Treat): this is the reduced form effect of being

in the treatment group. I.e. it is yT-yC

• TOT (Treatment on the Treated): this is the effect of the treatment on those who actually took up the treatment. – it is the LATE using assignment to treatment as an instrument