Answering my Blog Mail
Every week I receive some very reasonable e-mail from blog readers. I'd like to try to answer two questions I've received. One is on Jim Heckman's work on "Essential heterogeneity" and its impact on estimating treatment effects. The other is about making cross-country environmental performance comparisons.
First a "simplified" Heckman Model:
A researcher wants to know how much weight do people gain when they eat a single Twinkee. So, the treatment here is eating the twinkee and the weight gain is the treatment effect. There is an asymmetry here. People KNOW their own twinkee effect before they eat the twinkee. To keep this really simple, if your last name begins with a "A" you gain 1 pound, if your last name begins with a "B" you gain 2 pounds, and so on such that if your last name begins with a "Z" you gain 26 pounds.
Assume that each letter is equally likely (so there are as many Adams as Quartz).
The researcher observes your weight and whether you ate a twinkee but the researcher doesn't know your last name or your treatment effect.
The researcher estimates using OLS: Weight = constant + B*1(Eat Twinkee) + U
where 1(Eat Twinkee) is a dummy variable that equals one if you eat the twinkee and it equals zero if you don't eat the twinkee.
Note that if a random set of people were forced to eat the twinkee, then the researcher would estimate a AVERAGE TREATMENT EFFECT = 13.5 pounds.
One of HECKMAN's points is that people self select (sounds familiar?) into whether they eat the twinkee or not.
To keep things simple, let everyone have the same utility function. People gain utility from eating a twinkee but they don't like to gain weight and they don't like to pay a high price for the twinkee.
Utility for person with last name starts with a B = 10 - Weight - Price = 10 - 2 - Price
Now assume that a twinkee is $2. Let's define an instrumental variable such that half the population is offered a twinkee for a price of $0. Note this "exogenous" reduction in the price of a twinkee.
When the price of a twinkee is $2, the marginal person who chooses to buy it and eat it (given the weight gain) has a B = 8 (so last name of Gonzales)
When the price of a twinkee is $0 , the marginal person who chooses to buy it and eat it (given the expected weight gain) has a B = 10 (so a last name of Igloo)
This instrumental variable (the cheap twinkee) gets people who will gain more weight to participate in the program (relative to who would have participated had the price of a twinkee remained at $2). Only if the twinkee price were negative would the real weight gainers (the Zebras) participate.
Heckman makes the point that the IV estimator may not be reflective of any interesting sub-population of the entire population. The mean treatment effect for this group at the margin may bear little resemblence to the Average Treatment Effect of 13 or other interesting percentiles of the treatment distribution.
Heckman also makes the point that the LATE estimator is instrument dependent in the presence of essential heterogeneity. For example, the LATE estimator would have been smaller had the instrument been a reduction in price of a twinkee from $2 to $1 rather than from $2 to $0 because in the former case the marginal person would have had a B=9 rather than a B=10.
Tomorrow I will answer this question:
"Environmental Performance Index (EPI) and the
Environmental Sustainability Index (ESI). I am interested in learning
about the following: the creators? motivations behind the indexes, the
refinements in methodology that attributed to England?s rather quick
jump in the ranking, the consequences of each indicator being weighted
equally, etc. Other key questions include: Do countries point to the
empirical data as leverage in environmental treaty negotiations? Have
governments approached other countries performing well on a particular
indicator to inform themselves about potential strategies they can
apply? Can the rankings generate enough international shame to mobilize
countries? Wh
at is being done to raise the awareness of citizens around the world of
their countries? performance?"
First a "simplified" Heckman Model:
A researcher wants to know how much weight do people gain when they eat a single Twinkee. So, the treatment here is eating the twinkee and the weight gain is the treatment effect. There is an asymmetry here. People KNOW their own twinkee effect before they eat the twinkee. To keep this really simple, if your last name begins with a "A" you gain 1 pound, if your last name begins with a "B" you gain 2 pounds, and so on such that if your last name begins with a "Z" you gain 26 pounds.
Assume that each letter is equally likely (so there are as many Adams as Quartz).
The researcher observes your weight and whether you ate a twinkee but the researcher doesn't know your last name or your treatment effect.
The researcher estimates using OLS: Weight = constant + B*1(Eat Twinkee) + U
where 1(Eat Twinkee) is a dummy variable that equals one if you eat the twinkee and it equals zero if you don't eat the twinkee.
Note that if a random set of people were forced to eat the twinkee, then the researcher would estimate a AVERAGE TREATMENT EFFECT = 13.5 pounds.
One of HECKMAN's points is that people self select (sounds familiar?) into whether they eat the twinkee or not.
To keep things simple, let everyone have the same utility function. People gain utility from eating a twinkee but they don't like to gain weight and they don't like to pay a high price for the twinkee.
Utility for person with last name starts with a B = 10 - Weight - Price = 10 - 2 - Price
Now assume that a twinkee is $2. Let's define an instrumental variable such that half the population is offered a twinkee for a price of $0. Note this "exogenous" reduction in the price of a twinkee.
When the price of a twinkee is $2, the marginal person who chooses to buy it and eat it (given the weight gain) has a B = 8 (so last name of Gonzales)
When the price of a twinkee is $0 , the marginal person who chooses to buy it and eat it (given the expected weight gain) has a B = 10 (so a last name of Igloo)
This instrumental variable (the cheap twinkee) gets people who will gain more weight to participate in the program (relative to who would have participated had the price of a twinkee remained at $2). Only if the twinkee price were negative would the real weight gainers (the Zebras) participate.
Heckman makes the point that the IV estimator may not be reflective of any interesting sub-population of the entire population. The mean treatment effect for this group at the margin may bear little resemblence to the Average Treatment Effect of 13 or other interesting percentiles of the treatment distribution.
Heckman also makes the point that the LATE estimator is instrument dependent in the presence of essential heterogeneity. For example, the LATE estimator would have been smaller had the instrument been a reduction in price of a twinkee from $2 to $1 rather than from $2 to $0 because in the former case the marginal person would have had a B=9 rather than a B=10.
Tomorrow I will answer this question:
"Environmental Performance Index (EPI) and the
Environmental Sustainability Index (ESI). I am interested in learning
about the following: the creators? motivations behind the indexes, the
refinements in methodology that attributed to England?s rather quick
jump in the ranking, the consequences of each indicator being weighted
equally, etc. Other key questions include: Do countries point to the
empirical data as leverage in environmental treaty negotiations? Have
governments approached other countries performing well on a particular
indicator to inform themselves about potential strategies they can
apply? Can the rankings generate enough international shame to mobilize
countries? Wh
at is being done to raise the awareness of citizens around the world of
their countries? performance?"
posted by Matthew Kahn at 9:04 PM
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