RAND Corporation and the Family Development Board of Malaysia - Econometrics Assessment Answer

Econometrics Assessment Task

Question 1: Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 points One purpose of this assignment is to improve on your econometric writing skills. Points will be allocated to (overall) clarity and quality of presentation. Hence, carefully consider the way you express yourself while writing down your answers. You may want to read Chapter 19 of Wooldridge. If you choose to use LaTeX, which is recommended but not required, you may consider using Stata’s table formatting tool, to export regression results as LaTeX formatted tables. ssc install estout, replace // Downloads and installs table formatting tools. eststo: regress y x // Stores the results of a regression.

 Question 2: Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 points When studying of the theory or the practice of econometrics, it is often useful to use simulated data to illustrate or understand a method or a problem. In this exercise, we will show how to generate a simulated dataset, and illustrate a number of issues discussed in the lectures: correlation between the covariates, the effect of a change in the variance of a covariate, and a change in the distribution of the error term. We are interested in a model of the form: y = β0 + β1x1 + β2x2 + u.

(2.1) The advantage of simulation is to start from a model where you know (or assume) the population parameter values, so you can see how well you can approximate these values with your estimations. Throughout this exercise, we will use the following values: ???? = ( ????0 ????1 ????2 ) = ( 5 4 3 ). (2.2) We need to generate values of x1, x2 and u, which result in a value for y given the model (2.1)-(2.2). In this exercise, we use a simple example to illustrate how to do so.

(a) (5 points) Let us start with a simple model generated as follows:

1. We start with an empty dataset.

2. We first fix the number of observations to 1,000 by using the following command: set obs 1000

3. For this simple case, we assume that the error term u follows a normal distribution with mean 0 and standard deviation of

2. That is, u ∼ N(0,4). To do so, use the following command line: gen u = rnormal(0,2) 4. We then generate values for the x-variables. For this, use the following commands: gen x1 = rnormal(3,6) gen x2 = rnormal(2,5) Note that generated in this way, x1 and x2 are independent. 5. Based on the values described above, generate the corresponding values of y. (b) (5 points) Regress y on x1 and x2. Create a table —not necessarily in Stata— where you put, in the first column, the true values of the parameters, and then, in the second and third columns, the estimated values and the corresponding standard errors. Briefly discuss these results.

(c)  Use the following command line replace x2 = 0.5*x1 + rnormal(5,4) Generate the new corresponding values for y = y(x new), and repeat exercise

(b). Add the results to the table you generated. Do the results confirm what you would have expected to change in your estimation results, compared to the estimation results in (b)?

(d) Use the following command line replace x1 = rnormal(3,8) 3 / 4 to generate new values for x1 , create the corresponding new values for y (using the original x2 generated in (a)), and repeat exercise (b) with the new variables. How does the estimated standard error of ????? 1 compare to the estimated standard error of ????? 1 in (b)? Is this in line what you expected? (e) (10 points) Using steps (a) and (b) described above, assess the impact of having an error with a χ 2- distribution with 3 degrees of freedom, u ∼ χ 2(3). You can generate new values for the error term using the following command line replace u = rchi2(3) According to theory, how should this unusual error term affect your estimation? In particular, are the estimates by OLS still unbiased in this case? If not, what is the predicted bias? Is this in line with the results from your simulation?

Question 3: A study of wages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 points Econometrics is an important part of labor economics, a sub-discipline of economics interested in various questions such as determinants of wages or unemployment. In this exercise, we will study the determinants of wages in a developing country: Malaysia. For this exercise, we will use the dataset contained in as2019.dta. The data are taken from the Second Malaysian Family Life Survey (MFLS-2). The MFLS-2 was developed by the RAND Corporation and the Family Development Board of Malaysia, with the support from the National Institute of Child Health and Human Development and the National Institute of Aging. The survey was conducted between August 1988 and January 1989 in Peninsular Malaysia. The sample consists of members of 8,748 different households. Respondents to the survey are women aged between 19 and 49 (regardless of marital status) or ever married women under the age of 18, husbands of married women, and one individual aged 50 or more per household. More information on the sample is available in Haaga et al. (1993). Detailed information about the survey can be found on RAND’s website, at the following address. We are interested in the variable lwage, the (natural) logarithm of the wage of the respondents. The following variables are included in the dataset: paidwork 1 if individual is a wage sector worker, 0 otherwise; lwage Natural logarithm of real hourly wage rate (in Malaysian Ringgits); men 1 if individual is a man, 0 otherwise; malay 1 if individual is Malay, 0 otherwise; chinese 1 if individual is Chinese, 0 otherwise; indian 1 if individual is Indian, 0 otherwise; age Age (in years); agesq Age squared / 100; yprim Years of primary schooling; ysec Years of secondary schooling & above; urban 1 if individual lives in an urban area, 0 otherwise. An urban area is defined to have 1000 or more inhabitants; unearn Household income from dividends, interest and rents received on property and land / 10000 (in Malaysian Ringgits); househ Actual house ownership (dummy) multiplied by the cost of housing / 100000 (in Malaysian Ringgits); amtland Household landholding (in hundreds of acres); unearnx 1 if data on unearned household income is missing, 0 otherwise. (a) (5 points) Load the data into Stata. Because we try to determine how variables such as schooling, experience or ethnicity affect hourly wage rates in Malaysia, the population under consideration contains the inhabitants of Malaysia with a wage rate. Delete all observations who do not do any paid 4 / 4 work and are therefore without observed wage. How many observations do you retain? In order for all of you to work on a different sample, we will only work on 50% of the sample. To do so, use the command sample 50 Remember to include the command set seed as explained on the first page of the assignment. (b) (5 points) Create the variables: school Years of (primary and secondary) schooling; wage Hourly wage rate. Delete the variables urban, unearn, househ, amtland and unearnx, which will not be used below. Present some descriptive statistics of the variables that you now have in your dataset. (c) (5 points) Draw histograms of wage and lwage, and discuss briefly what you obtain.

(d)Find the mean and median for both wage and lwage. Do you find that the mean (median) of lwage equals the log of the mean (median) of wage? Why or why not?

(e)We are first interested in the effect of schooling on wage for these employed respondents. We want to perform a regression of wage on school and a constant term. Consider the following model: wage = α0 + α1school + u. (3.1) List the assumptions under which the estimates obtained by OLS are unbiased. Estimate the model and present the results of the estimation. What is the interpretation of the estimated parameters? What is the interpretation of the R2?

(f) A common practice in labor economics is to use log-wages instead of wages. Consider the following model: lwage = β0 + β1school + u.

(3.2) What are now the assumptions for the OLS estimates to be unbiased? Estimate this new model. Interpret carefully the results. What is the difference between the model presented here and the model discussed in the previous question? How do you interpret the new parameter estimates?

(g) (5 points) Suppose that you had the variable lschool = log(school). Consider the following model: lwage = γ0 + γ1lschool + u.

(3.3) What is the interpretation of the parameter γ1 in this setting?

(h) (5 points) Show formally how a small change in school (say dx) changes the variable wage (call this dy) for both specifications (f) and (g).

How do these marginal effects relate to the coefficients β1 and γ1?

(i)  Estimate a linear regression model by OLS where you explain lwage with a constant term, age, school (not log(school)), chinese, indian and men. Interpret the coefficient estimates and the R2. For the remainder of the questions, the specification above is the specification that we will use.

(j) (5 points) Construct a 95% confidence interval for the percentage return to an additional year of schooling. What is the interpretation of this confidence interval?

(k) (5 points) Test the null hypothesis that the effect of schooling on a person’s log wage rate is at least 6%.

(l) (5 points) Test the null hypothesis that ethnicity (the dummies Chinese and Indian) does not play a role in explaining a person’s log-wage rate.

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