Skip to content

Latest commit

 

History

History
85 lines (61 loc) · 5.04 KB

index.md

File metadata and controls

85 lines (61 loc) · 5.04 KB
Raw

INDEX OF THE PROJECT

1.INTRODUCTION

The aim of the present project is to develop a theory and empirical analysis using R as a programming language. To do so, we will answer the tasks given in the work guideline. The project structure is straight forward: Firstly, we will answer the theory tasks assigned in the guidelines, using the knowledge that we have acquired along the course. Secondly, using the dataset: “data_giulietti_etal.dta”, that quantifies the extent of racial discrimination in local public services in the U.S, we will work on the tasks assinged in the project guidelines. It is important to consider that, although there are many different ways to answer the questions given, we have decided to answer them in such a way that the output given is the most clear to interpret. Notice that, with the aim of distinguishing between the write-up assignment from the code we have decided that the best idea is that the code is given in a green color. Finally, there will be a brief subsection that will work with the monte carlo simulation.

2.THEORY TASKS

Suppose you want to quantify the extent of discrimination in public service provision in the U.S.. Your company has collected data on email queries of citizens to public offices (libraries, police, registry), whereby citizens were asked in a survey to provide the relevant information. In particular, the survey includes data on 1) a person’s race – whether the person is white or belongs to a minority (Black or Latinx), and 2) data on how many hours it takes for a public office to respond.

1.Suppose you want to estimate the effect of minority status (i.e. a dummy that equals one if a person belongs to a minority – either Black or Latinx – and zero if the person is white) on the response time to an email. Write down a regression equation that would allow you to estimate this effect.

2.Explain what parameter you are interested in estimating and provide an interpretation of this parameter. We are interested in the parameter ß1, which is the slope of the regression line but also the difference in means of two groups:

3.Discuss the random sampling assumption and the conditional independence assumption (in the lecture it was E(u|X) = 0). Are these assumptions fulfilled in this case (explain why or why not)? Explain intuitively the likely consequences of these assumptions (not) being fulfilled for estimating the effect of interest.

4.If you could run an experiment (regardless of ethical considerations) to estimate the effect of interest, what would this experiment look like and why? (N.B.: the ideal experiment asked for here is different from an experiment described further below.)

3.EMPIRICAL ANALYSIS

  1. Load the dataset into R and produce a table of summary statistics (number of observations, mean, sd, median, min, max, number of missing observations) for the variables listed in Table 1. Interpret the mean of reply, complexity,cordial_reply, length_reply and race.

  2. Produce a frequency table for the number of emails sent to each type of recipient. The table should include the number as well as the share of emails sent to each recipient.

  3. Produce a frequency table with senders on the horizontal and recipients on the vertical axis. Each cell should show the share of all emails that was sent by a given sender to a given recipient (hint: search for cross tabulation). What does the result tell you about the quality of the randomisation in the experiment?

  4. Run t-tests comparing the difference in means between Whites and Blacks for the following variables: reply, cordial_reply, length_reply, delay_reply. The results of the t-tests should be presented in a table that shows the following: each row is a variable; columns: mean of the variable for Whites, mean of variable for Blacks, difference in means between Whites and Blacks, p-value of t-test. Interpret your findings regarding magnitude and statistical significance.

  5. Regress the dummy reply on the dummy race. Interpret the coefficients of the slope and intercept, comment on statistical significance, and compare your results to those in the table produced in 4.

  6. Another way of analysing the results of an experiment like this is through bar charts with error bars. You plot the means for the treatment and control group and attach to each bar a so-called error bar(y ± sd(y)). The error bars give an indication of the variation in each group. Produce such a chart (separate bars for Black and White) for the following outcomes: reply, cordial_reply, length_reply.

  7. Not only did the researchers randomise whether the sender has a black-sounding name, but they also randomised whether an email had a complex or simple content. Run a regression of complexity on race and interpret your result. Comment on the meaning of this result for the experimental design.

  8. Now regress delay_reply on race and interpret the coefficients in terms of magnitude and statistical significance. Explain why your estimates are likely biased despite having run a clean experiment.

4. MONTE CARLO SIMULATION