Use knowledge about Selection on observables/Instrumental variables/Panel data to answer Questions:

The Agricultural Department of Country Z wants to know how to best manage the country's hydro systems, they need to understand how the cost of extracting groundwater -- which depends on (i) how efficient each factory's pump is, (ii) how

expensive their electricity is, and (iii) how deep the aquifer is -- will impact factory's groundwater usage.

1. Z is interested in answering the following question: What is the effect of average groundwater costs between Janunary and March (measured in dollars per acre-foot) on total groundwater consumption (measured in acre-feet) during the same time period? Describe what experiment you would like to design and the dataset that you'd like to have to carry out this ideal experiment

2. Z is 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 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.

3. Z is interested in this research design. 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.

4. It turns out that two of the Z's 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 Z 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.