Problem 3
Due: Thursday, May 13, at 11AM

Instructions:
This problem set consists of two files: (1) this document with instructions and questions; and (2)
a dataset which you will use to answer the questions below.

You can work in groups of up to three. Please identify your group members. Groups can share
code, but each group member must turn in their own problem set and must have separate
written answers to the questions. You should submit both written answers—which should be
parsimonious, as excessive length will be penalized—and your code and results for the data
analysis in a single file. You must use R. I recommend that you use R Markdown or knitr, which
will allow you to intersperse your code and written answers. Note that you are primarily being
graded on your written answers. Problem sets must be submitted in PDF format. Problem sets
must be turned in via Gradescope; no late submissions will be considered.

Questions:
The California Agricultural Lobby’s Bureau for Evidence-based Aquifer Recharge Sustainability
(CALBEARS) is very concerned about the upcoming drought year, which looks to be one of the
worst on record. In order to know how to best manage the state’s water systems, they need to
understand how the cost of extracting groundwater --which depends on (i) how efficient each
farmer’s pump is, (ii) how expensive their electricity is, and (iii) how deep the aquifer is --will
impact farmers’ groundwater usage. Their analysts are a bit in over their heads, so they’ve
called you in to help.

1. CALBEARS are interested in answering the following question: What is the effect of
average groundwater costs between April and September (measured in dollars per acre-
foot) on total groundwater consumption (measured in acre-feet) during the same time
period? To make sure everybody is on the same page, explain to them what the ideal
experiment would be for answering this question. Describe the dataset that you’d like to
have to carry out this ideal experiment, and use math, words, and the potential
outcomes framework to explain what you would estimate and how you would do so.
Make sure to be clear about the unit of analysis (ie, what is “i” here?).
2. CALBEARS are on board with your explanation, but, as they’ve discussed with you, they
won’t be able to implement your preferred solution. They don’t think that a selection-
on-observables approach will work (they’re very sophisticated). They’re also limited by
state privacy laws: they will only be able to give you one wave of data (no repeated
observations). Given these limitations, describe the type of research design you would
try to use to answer their question of interest. Be explicit about the assumptions
required for this design to work, describing them in both math and words.
3. CALBEARS are interested in this research design. It sounds promising. They’d like you to
propose a specific approach. Please describe a plausible instrumental variable you could
use to evaluate the effect of the cost of groundwater pumping on acre-feet of
groundwater consumption. Why is your proposed instrument a good one? Do you have
any concerns about your ability to estimate the treatment effect using your instrument?
If yes, why? If no, why not?
4. CALBEARS is intrigued by your approach. After an internal discussion, they’ve come back
to you with great news! It turns out that two of the California utilities ran a small pilot
program where they randomly varied electricity prices to different farms as part of a
new policy proposal. With this new information, please describe to CALBEARS how you
would estimate the impacts of electricity prices on groundwater consumption, and how
you would estimate the impacts of groundwater costs on groundwater consumption.
Use both words and math.
5. CALBEARS agree that your approach is a good one. So good, in fact, that they’d like to
see it in action! They are willing to share some data with you, in the form of
ps3_data.csv. Please report the results of an analysis of the impact of electricity prices
on groundwater costs, using electricity_price_pilotas the price variable and
groundwater_costas the cost variable. What parameter does this regression estimate?
Interpret your estimate. Will this utility pilot be a helpful way forward to estimating the
impacts of groundwater costs on groundwater usage? Why or why not?
6. CALBEARS wants you to use the pilot in youranalysis (they are ignoring any opinion you
gave in (5), good or bad). Please report the results of an analysis of the impact of
electricity prices on groundwater consumption, using electricity_price_pilotas the price
variable and groundwater_useas the usage variable. What parameter does this
regression estimate? Interpret your estimate. Is this estimate useful for policy? Why or
why not?
7. CALBEARS would like you to use their pilot to estimate the effect of groundwater costs
on groundwater consumption. For full transparency, make sure to show all of your
analysis steps. CALBEARS cares about your standard errors, so using a canned routine is
a good idea here. Interpret your effect. Do groundwater costs matter for consumption?
8. CALBEARS like your analysis, but they’re a bit worried about the quality of their data on
groundwater consumption. The way they normally collect these data is by surveying the
farmers. However, they went and did some back-checks in a subsample of data that
they gave you and noticed that the farmer reports seem to be off. They would like you
to make a graph showing the relationship between their back-checks
(groundwater_use_backchecks) and the farmers estimates (groundwater_use). Describe
to them what you find. Is this likely to be a problem for your analysis? Why or why not?
Next, estimate the impacts of groundwater costs on groundwater consumption using
the backcheck data instead of the farmer estimates. Report what you find. Do your
estimates differ? If no, explain why not. If yes, explain why.
9. The challenge with back-checks is that they’re very expensive to do. Fortunately,
CALBEARS realized that they have another dataset on groundwater consumption which
seems to match the back-checks much better. They’d like you to make a graph showing
the relationship between their back-checks and this new measurement
(groundwater_use_v2). Describe to them what you find. Is this likely to be a problem for
your analysis? Why or why not? Next, estimate the impacts of groundwater costs on
groundwater consumption using the backcheck data and using the new estimates.
Report what you find. Do your estimates differ? If no, explain why not. If yes, explain
why.
10. CALBEARS comes back to you again with yet another data problem. This time, they’re
worried that the utilities aren’t reporting electricity prices very well. They’d like you to
focus on the effect of electricity price on groundwater consumption (you can ignore
groundwater costs for the remainder of the problem set). CALBEARS explain to you that,
in one utility (labeled iou == 1in the data, because #privacy), something was going
wrong with the price information they were using. Farms facing low prices had these
prices recorded correctly in the data, but the higher the price, the more inflated utility
1’s record is. In the other utility (labeled iou == 2), there are still imperfect
measurements, but CALBEARS is convinced that the measurement problems are
random. Explain the implications of these data issues in each utility to CALBEARS. Are
these measurement issues going to be a problem for your analysis? Use words and math
to explain why or why not. Despite any misgivings you might have, run your analysis
anyway, separately for each utility this time (using your preferred groundwater
consumption variable from the three described above), and report your findings.
11. CALBEARS conducted a survey of farmers to understand their experience with the
pricing pilot, and asked the farms to report their electricity prices (survey price).
Describe how you could use these data to correct any issues you reported in (10). What
conditions need to be satisfied in order for this to work? Are these conditions satisfied
in utility 1, utility 2, both, or neither? Carry out your proposed analysis in the sample
where it will work (utility 1, utility 2, both, or neither). Report your results, and describe
how they compare to your estimates in (10), or explain why you didn’t produce any.
Which estimates would you send to CALBEARS as your final results?

欢迎咨询51作业君