计量经济作业代写 Econometrics Assignment

Econometrics Assignment

计量经济作业代写 For this problem, joint work with up to 3 other students who are currently enrolled in this course is possible. Please state……

Problem I (10 Points)  计量经济作业代写

For this problem, joint work with up to 3 other students who are currently enrolled in this course is possible. Please state the student matriculation numbers of your co-authors in your solution. Load the datafile THdata.csv. It contains a cross-section of 1040 working individuals with the following variables:

You would like to model the relationship between individuals potential human capital accumulation through work experience and labor market earnings. You may treat potential experience as a continuous random variable. Your econometric model is given by  计量经济作业代写

Yi = m(Xi3) + εi

where m(·) is a smooth function. You assume that E[εi |Xi3] = 0.
1. Assume that m(Xi3) = β0+β1Xi3. Estimate the model via ordinary least squares and provide a scatterplot with the regression line. Why might you be worried about your model choice?

1. Assume that m(·) is twice continuously differentiable. Estimate the model and provide multiple scatterplots with the regression curves using the following methods:
   • Nadaraya-Watson regression with 2nd order Gaussian kernel and Silverman’s bandwidth,
   • local constant regression with 2nd order Gaussian kernel and leave-one-out cross-validated bandwidth,
   • local linear regression with 2nd order Gaussian kernel and leave-one-out cross-validated bandwidth.

Always report your bandwidth estimates. Interpret your results. Remark: If your optimization procedure has problems with initial values, standardize Xi3 and start at a bandwidth of 1.
You want to test the hypothesis that the linear model is correctly specified, i.e. H0 : E[Yi |Xi3] = β0 +β1Xi3, using a conditional moment test (Li and Racine, p. 355–356). The test statistic is given by

with

and ˆui = Yi − βˆ 0 − βˆ 1Xi3 being the residuals from question 1.), k being the kernel function and h being the bandwidth parameter.  计量经济作业代写

1. Test at a 1% level whether the true mean function is linear. Use the approach with theoretically superior boundary properties and the corresponding bandwidth from question 2). What do you conclude? Interpret your result.




2. Repeat question 3.) for the H0 that E[Yi |Xi3] = β0 + β1Xi3 + β2X2 i3 . What do you conclude? Interpret your result.

Problem II (5 Points)  计量经济作业代写

You are not permitted to collaborate on this problem. Hand in your own, unique solution. Min./max. number of words: 750/1500. You may use a limited amount of equations and formula.

Let ˆf(x) be the kernel density estimator at an interior point x and z1−α/2 be the (1−α/2)-quantile of the standard normal distribution. Discuss the following paragraph:

“The choice of the bandwidth h is almost as important as the choice of the right kernel function. Choosing an integrated mean squared error optimal bandwidth over leave-one-out cross-validation for estimating a density function has several desirable properties: It assures that the variance converges to zero and that the bias of the kernel density estimator is zero. Moreover, one can use the bandwidth directly to construct two-sided (1-α) confidence intervals at x as

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