Theory or the Practice of Econometrics - Simulated Dataset - Econometric Assessment Answer

Econometric Assignment 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.

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)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)?

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