Problem Set 3
ECO3121 - Fall 2024
Due ****3 ****PM , ****November ****28, ****2024
No ****late ****submission ****is ****allowed
Please combine your answer, Stata code and requested output in one pdf file and upload it to Blackboard
Question ****1
Download aghousehold.dta and village rainfall.dta datasets from the blackboard site and load into Stata. The main data we use is the National Fixed Point Survey (NPFS), which is a nationally representative panel dataset (unbalanced) of roughly 5000 households in 88 villages between 1995 and 2002. It is collected by the Ministry of Agriculture and Rural Afairs of China.
On the blackboard, we also uploaded a second dataset regarding precipitation records in each village in 2001. See the variable list below. Write up the answers to 1) - 6) below. In addition, also attach the do file that you used to answer the following questions.
| variable name | type | format | label |
|---|---|---|---|
| vl id | int | %8.0g | village ID, consistent with household data |
| lat o | float | %8.0g | latitude of each village |
| lon o | float | %8.0g | longitude of each village |
| provname | str24 | %24s | province name in Chinese |
| cityname | str33 | %33s | city name in Chinese |
| countyname | str33 | %33s | county name in Chinese |
| av rain | float | %9.0g | average precipitation in 2001, measured by mm |
| sd rain | float | %9.0g | standard deviation of precipitation across months in 2001 |
| z rain | float | %9.0g | zero score of precipitation in 2001 |
First, limit the sample to households in ****the ****year 2001 by running code “keep if year==2001” in Stata. You can generate variable yield (output per unit of land)
via , and variable fertilizer (fertilizer application per unit of land) through
nh6 3 hx95 nh112 .
1. The variable h95 nh269 indicates how many days for household members in each
household had been working as temporal migrants (measured by days) in 2001.
Generate a binary variable regarding household migration decision. It takes the value of 1 if h95 nh269 is greater than zero, otherwise it is 0. Generate the natu- ral log of yield and fertilizer application intensity (using log ( fertilizer + 1) ****and log ( yield ****+ ****1) ****to smooth zero values.). (2 points)
2. Run a linear probability model of household migration decision in question (1) on the natural log of yield.
Interpret the result and comment on its statistical significance. (2 points)
3. List three plausible arguments why the point estimate in question (2) could be biased, and the corresponding bias directions (upwards ****or downwards) relative to the true causal efect of household’s agricultural production on household migration decision. (3 points)
4. Now your professor suggests that the rainfall (precipitation) could be a valid in- strumental variable (IV) for your measure of household’s yield. Try to merge the household’s production dataset and precipitation dataset via vl id, the specific vil- lage identifier, using stata command merge (Many-to-one merge, type “help merge” in Stata for assistance).
You decide to use the natural log of average rainfall in 2001 (log(av rain)) as the IV for the natural log of yield. Verify if the assumption of instrument relevance is satisfied using the first stage regression, and obtain the results in Stata. Write down ****the ****first ****stage ****regression ****model ****and interpret the result and statistical significance of your result. (2 points)
5. Now use Stata to estimate the 2nd stage IV point estimate (using linear probability model) as suggested by the professor, and export your result. Write ****down ****the second ****stage ****regression ****model ****and interpret the result and statistical signifi- cance of your result. (2 points)
6. Now your professor tells you that you can use ivregress 2sls command directly to replicate the results in question (5).
(a) Do you find any diference in the IV estimations (βIV ) using ivregress 2sls command regarding ****the ****coe cients ****and ****s tandard ****errors ****relative to (5). (2 points)
(b) In reference to 代写ECO3121 Problem Set 3 your answer to questions (2) and (3), is the diference between the linear probability model and IV point estimates as you expected or rather not? (2 points)
Question ****2
Consider the two-way relationship between crop yield and fertilizer usage Crop = α0 + β0 Fertilizer + u
Fertilizer = α 1 + β1 Crop + v
The first equation models the determinant of crop yield given the amount of fertilizer usage. The second equation models the amount of fertilizer the farmer chooses to apply given the crop yield in the area.
1. What do you expect the signs of β0 and β1 are? Explain. (2 points)
2. Explain why the OLS estimator for β0 and β1 are biased. If we use the OLS estimator to estimate β0 and β1 , what directions are the biases? Explain. (4 points)
3. Suppose the only variables available are Crop, Fertilizer , Sunshine (the sunshine of the area), and Budget (the budget constraint of the farmer). To estimate β0 and β1 by the two-stage least squares estimator, which variables among the data you have should be used as instruments? Be specific, what IV is for Fertilizer and which IV is for Crop. Explain. (4 points)
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