Master APE & PPD Econometrics Professor: Karen Macours Marion Leturcq (leturcq@pse.ens.fr) Problem Set 1

STATA APPLICATIONSTask 1 last year- Computer assignmentThe data set busind.dta contains information on Gross National Income (GNI) per capita and the number of days to open a business and to enforce a contract in a sample of 135 countries. It was extracted from the Doing Business dataset, a dataset collected by the World Bank based on expert opinions in each country. The variable gnipc measures GNI per capita in thousand $. The variable daysopen measures the average number of days needed to open a business in that country, and daysenforce measures the average number of days needed to enforce a given type of contract. (i) Find the average GNI per capita and the average number of days to open a business, and the average number of days to enforce a contract.

2Answer to question (i)Stata command: use busind,clearsu daysenforce daysopen gnipc

(ii) In how many countries does it take on average less than 5 days to open a business? What is the maximum number of days to open a business in the dataset? In which countries does it take more than 200 days to open a business?

Answer to Question (ii)Stata command:su daysopen if daysopen=200

4Question (iii)Estimate the following simple regression model:

Give a careful interpretation of estimates b1 and b0. Are the signs what you expected them to be?

5Answer to Question (iii)Stata commands:reg gnipc daysopen

Question (iv)Question: What kind of factors are contained in u? Are these likely to be correlated with the number of days to open a business?

Answer: Factors contained in u are factors that explain the GNI par capita apart from the number of days to open a business. You might be conscious that there are many other factors, such as economic institutions, education, savings, consumption, R&D Some factors are likely to be correlated with the number of days to open a business, such as the quality of economic institutions.

Question (v)Question: What is according to this model the predicted income for a country where it takes 5 days to open a business? And the predicted income for a country where it takes 200 days to open a business? Show how you can calculate the answers by hand (once you have obtained the estimation results). Do the obtained levels of income seem reasonable? Explain.

. 8Answer to Question (v)You can compute predicted values for the dependent variable in two ways: by displaying when daysopen=5 and daysopen=200

Stata commands:display _b[daysopen]*5+_b[_cons]10.894018display _b[daysopen]*200+_b[_cons]-7.5347099

Answer to question (v)or by generating the fitted value of the dependent variable :reg gnipc daysopenpredict gnipc_hat

A problem arises with this second method as there is no observation with daysopen=200, so that it is impossible to get the value of gnipc_hat for daysopen=200.

To illustrate our fitted values, we can draw the OLS regression line: scatter gnipc daysopen||lfit gnipc daysopen

11Question (vi) Estimate the following simple regression model and give a careful interpretation of b1.

Answer to Question (vi)Stata command:reg gnipc daysenforce

13Question (viii)

14Question (vii)Comparing the estimates of the models in (iii) and (v), which one explains more of the variation in income per capita across countries. Can you infer whether the duration to open a business or the duration for enforcing contracts is more strongly correlated with income per capita? Answer: How much of the variation of GNI per capita (y) is explained by an independent variable is given by the R2. The greater the R2, the more variation of y is explained by x. The R2 of the regression of GNI per capita on the number of days to open a business is about 13% and the R2 of the regression of GNI per capita on the number of days to enforce a contract 21%. That means that this variable explains more of the variation of the gni per capita than the former. It means that the duration for enforcing contract is more strongly correlated with income per capita than the number of days to open a business. Here, the correlation between gnipc and daysenforce is equal to -0.46 and the correlation between gnipc and daysopen is equal to -0.36.

Question (viii)Estimate the following simple regression model and give a careful interpretation of b1.

Answer to Question (viii)Stata commands:gen lngnipc=ln(gnipc)reg lngnipc daysopen

Do these results allow you to draw conclusions regarding the desirability of policies aimed at reducing the number of days for opening a business in certain developing countries?The dataset contains 135 countries, and hence does not contain information about all the countries in the world. Do you think one should account for that when interpreting the regression results. Why?

Task 2 last year- Computer exerciseThe dataset nepalind.dta contains data from 706 children of 15 years old in Nepal. The data come from the 2003 Nepal Living Standard Survey (NLSS) Living Standard Measurement Survey (LSMS). We want to analyze this data to understand the number of years of education. Illiteracy and low levels of education are a major concern in Nepal, so it would be good to know which type of factors could be explaining education of the present generation, to know what type of policies to implement. The dataset has some information on household characteristics and characteristics of the child, and of the household head. The NLSS is a LSMS-type survey, which are country-wide representative surveys that statistical offices in developing countries conduct with the support of the World Bank to determine poverty levels, determinants of poverty, etc. See www.worldbank.org/lsms for more info.

Question 1Write a paragraph describing the dataset using the standard descriptive statistics (also called summary statistics, or D-stats). Add a table with the d-stats.

Question (1)Child characteristicsMale (%)52Health status (%)Good69.5Fair30Poor0.5Years of education5.5 (3.6)Question (1)Household characteristicsNumber of household members6.8 (2.73)under 18 years old3.5 (1.74)between 18 and 593.0 (1.49)60 or older0.3 (0.63)Age of the head46 (10.5)Education of the head2.8 (4.1)Land owned (in ha)0.74 (1.05)Value of jewelries (in rupees)13985 (26726)Distance to school (in hours)0.29 (0.31)Number of observations706Standard errors into parenthesisQuestion 2: Show the distribution of the different values of years of education in the dataset. Drop the variables that have values higher than 10. Explain why that might be a smart thing to do, before doing any regression analysis.

. hist educ,discrete(start=0, width=1)Question (3): Specify a model that allows explaining the number of years of education as a function of fathers age, the number of active adults (between 18 and 60 years old) and the number of elderly (60 or older) and all other variables you think are interesting and appropriate.Make sure only to include variables that are exogenous and discuss why the variables you include can be considered exogenous. Estimate the model and give a careful interpretation of each of the coefficients (sign, size, and significance!). Do you find any of your results counterintuitive?Tips to answer question (3)Each variable that you add into the model must be related to educ in some way, and should not violate the ZCM assumption=>they must be exogenous=>ask yourself:x caused by y? i.e. possibility of reverse causality?One third factor determines both x and y? in this case correlation is not causation, and x is not exogenous.u and x related for some other reason?Gender? Heads age? Nb of active adults? Number of elderly? Heads education? Land owned? distance to school? Value jewelry? Nb of children? Health?

A reasonable model to estimate:Expected signs of coefficients? Argue.

Question 4:What is the minimum significance level at which one can reject that hypothesis that age of the household head does not affect education levels?The p-value gives the smallest significant level at which an hypothesis H0 can be rejected. In other words, a low p-value indicates that the tested hypothesis is unlikely. The minimum significance level at which one can reject the hypothesis that the age of the household head does not affect education levels is given by the p-value of the test 1 =0. Then, one can directly read on the stata output that this minimum significance level is 1.4%.Question (5)Do your results allow you to conclude that the effects of the number of active adults in the household is different than the effect of elderly? State the null hypothesis and the alternative hypothesis you are testing, and the significance level you are considering. Does your answer differ depending on which significance level you consider?Answer to Question (5)Need to test null hypothesis: H0: 3=4 against H1:34 You just need command "test".

Question (6)Test whether the characteristics of the household head are jointly significant. Show how to do this in stata, and calculate the test by hand in 2 different ways. What can you conclude about the role of household head characteristics on education of the children?

Answer to Question (6)

Question 6: compute F-testRun the unrestricted and restricted models, and compute either SSR or R2 form of the F-statistic.

reg educ head_age head_educ nractad nrold r2_supown distschool malescalar r2_ur=e(r2)scalar df=e(df_r)reg educ nractad nrold r2_supown distschool male scalar r2_r=e(r2)

Question (9)Child characteristicsNon missingMissingMale (%)5348Health status (%)Good69.574Fair3026Poor0.5.Years of education5.36.8Question (9)Household characteristicsNon missingMissingNumber of household members6.96.1under 18 years old3.52.8between 18 and 593.02.960 or older0.30.4Age of the head46.548.2Education of the head2.65.5Land owned (in ha)0.770.29Value of jewelries (in rupees)1221235488Distance to school (in hours)0.29.Number of observations60046