代做ECON 20110/30370: Econometrics Semester 2 – Practical Session Worksheet 5帮做R编程

日期：2024-05-15 03:41

Semester 2 – Practical Session Worksheet 5

ECON 20110/30370: Econometrics

In this practical session, we aim to deepen our understanding of causal inference by estimating the causal effect of a policy mandating female politicians on policy outcomes. We will revisit essential statistical meth- ods for analysing randomised experiments, including t-tests and linear regression, and apply these to under- stand the implications of such policy interventions.

1    Data

Our analysis uses a simplified version of the dataset from Chattopadhyay and Duflo (2004), which examines the impact of a randomised policy experiment in India on public policy outcomes.  In the mid-1990s, one- third of local councils, known as Gram Panchayats (GPs), were randomly designated under this policy to be led by women, providing an opportunity to study the causal effects of policy-driven female leadership on policy-making.

Please download the ‘women.csv’ file from Blackboard to begin our analysis.

1.  Data Description & Background Information

Chattopadhyay and Duflo leverage this randomised policy experiment to explore whether female politi- cians, as a result of a policy initiative, promote different public policies than their male counterparts. The dataset includes 6 variables, where each observation is a village (i):

•  GP: Indicator for the level of local government studied.

•  village: Identifier for villages within a GP.

•  reserved:  Indicates whether the GP was randomly ‘reserved’ for a female council head (1=yes, 0=no), signifying the policy intervention.

•  female: Indicates the gender of the council head (1=female, 0=otherwise), which is a result of the reservation policy and other factors.

•  irrigation: Count of new or repaired irrigation systems since the new leader’s tenure.

•  water: Count of new or repaired drinking water systems since the new leader’s tenure.

2.  Load the Data

To load the ‘women.csv’ file, first save it to a directory on your computer.  Then set your working directory in R to this location and use the following commands:

setwd("~/path_to_your_data/")

women  =  read.csv("women.csv")

2    Loading the Required Packages

Before analysing the data, install and load the ‘estimatr’ package in R:

install.packages("estimatr")

library(estimatr)

This package includes the ‘lm_robust()’ function, which is crucial for conducting regression analysis with heteroskedasticity-robust standard errors.

3    Exercise: Female Politicians and Policy Outcomes

In this exercise, we will evaluate the impact of a policy that mandates female leadership on policy outcomes. This policy was operationalised in an experiment in India, where villages were randomly designated to have female council heads.

The critical variable of interest is the mandated reservation of council head positions for women (reserved), representing the policy intervention.  We will examine its effect on the number of new or repaired drinking  water facilities (water) in the villages.

1.  Identify the treatment and control groups within the context of the reservation policy experiment.

2.  Consider Y = water and D = reserved:

(a)  Define the potential outcomes Yi0  and Yi1  under the reservation policy.

(b)  For a village affected by the reservation policy (Di  = 1), identify the observed outcome and what the outcome would have been without the policy (the counterfactual).

(c)  For a village not affected by the policy (Di  = 0), identify the observed outcome and the counter- factual scenario under the policy.

(d)  Discuss whether we can directly compute the causal effect of the policy on the outcome for each village i, Yi1 − Yi0. Explain your reasoning.

3.  Discuss the potential issues with estimating causal effects of female leadership on policy outcomes through cross-sectional comparisons between male- and female-led political authorities in the absence of a randomised policy intervention.

4.  Calculate the difference in mean numbers of new or repaired drinking water facilities between policy- affected (treated) and non-policy-affected (control) villages using the ‘ mean ’ function. Describe your findings.

5.  Can the difference in means calculated above be causally attributed to the reservation policy as either the average treatment effect (ATE) or the average treatment effect on the treated (ATT)?Explain your rationale, considering the implications of random assignment.

6.  Test whether the ATE of the reservation policy is zero, using the ‘t.test’ function at the 5% significance level.

7.  Identify the 95% confidence interval for the ATE of the reservation policy. Compare these results with the hypothesis test and discuss the policy’s impact on drinking water facility outcomes.

8.  Estimate the ATE via linear regression with the ‘lm_robust()’ function, and compare the regression results with the difference in means analysis.

9.  Assess the implementation of the reservation policy by calculating the proportion of female leaders elected in both reserved and unreserved GPs.  Specifically, calculate the mean of the ‘female’ variable for each group.

Discuss your findings and consider whether the observed leadership composition suggests any potential bias in interpreting the earlier estimatedATE. Is there potential bias if we interpret the ATE as the effect of the policy (mandating female leadership) on water facility outcomes? What about interpreting the ATE as the effect of female leadership on water facility outcomes?