Department of Economics
Spring 2011
University of California
Prof. Woroch
Economics 140
: 2
ND
MIDTERM ANSWER SHEET
Note:
There were versions of the exam that differed in terms of the order of questions and the numerical
values.
Below are suggested answers for one version, but with notes about answers to other versions.
I.
EVALUATE ECONOMETRIC RESEARCH
1.
“To understand the economic determinants of alcohol consumption, I estimated a log-log regression of
consumption of alcoholic beverages reported to me by 1,000 adults in California on the average price of
alcohol in their home town and their reported annual personal income.
All data are from 2010.
I know
that individuals typically err in reporting their income, and I also believe they will err in reporting their
true alcohol consumption.
If they randomly err in reporting both values, which I am willing to assume, I
would nevertheless expect that my estimate of the income elasticity of demand will be biased.
Specifically, I expect it will show excessive elasticity relative to the true value.”
Answer: This is a case of error in measurement of both the dependent variable and one of the
independent variables.
Assuming that the population regression has a positive coefficient on income
(i.e., alcoholic beverages is a “normal good”), then we would expect the estimated elasticity will be too
small because measurement error in an explanatory variable biases that variable’s coefficient towards
zero. The measurement error in the dependent variable, i.e., purchase of alcoholic beverages, will not
cause a bias, but it will increase the standard error of the regression relative to case where purchases are
accurately measured, e.g., using grocery store scanner data linked to a consumer.
Some people assumed alcoholic beverages to be inferior goods (negative coefficient on income), this is
less intuitive, but we accepted this assumption as well: Even if we think that richer people tend to drink
less alcohol
in quantity
, they still might spend more on it
in dollar terms
(as they tend to buy more
expensive drinks – e.g. cognac instead of beer) and consumption is measured in dollar terms. In this case,
the measurement error in income will bias the elasticity upward, but that still means a flatter than true
regression line, and hence smaller elasticity.
2.
“I wanted to model the effect of education on the earnings of U.S. workers.
To do so, using data from
the Census Bureau’s Current Population Survey in 2000, I ran a multivariate linear regression of
workers’ hourly earnings on their age and gender, as well as their level of educational attainment.
Unconvinced that these demographic variables fully explained a worker’s earnings, I ran a second
regression which included dummy variables for the state in which workers reside.
But, not wanting to
fall in the “dummy variable trap,” I excluded one state, Alabama, leaving 49 others.
Finally, recognizing
that labor market conditions outside the individual’s control affect earnings, I ran a third regression