讲解：Econometrics、R、source-code、RR|Web

Advanced Econometrics: Homework 1October 23, 2019Instructions1:• Submit one file for each problem. “AdvEcox HW1 2018: Group surname1, surname2, surname3 ”.• Form groups of three yourself.• As a solution, provide 3 Jupyter Notebooks with R source-code. Code should be properly commented,interpretations of results as well as theoretical derivations2should be written in markdowncells.• Use “set.seed()“ function, so I can replicate your results.• Be concise (no lengthy essays please). Although, be sure to include all important things as Icannot second-guess your work.• The empirical problems do not necessarily have a unique solution in terms of numbers, you areassessed based on execution of the analysis not on the right numbers that you should get fromoutput. The emphasis is put mainly on meaningful presentation and extent of your knowledge.• The problem set is due on 6th November. Late submission automatically means 0points.Problem 1. For this problem, use data in file hw1 data.csv.Columns containing Y in their names correspond to dependent variables (4) and columns containingX are independent variables (2). Using following pairs of independent and dependent variables,(X1,Y1),(X1, Y2), (X1,Y3) and (X2,Y4) do the following:1. Estimate beta coefficients using OLS and MLE. Compare estimates from both methods, explaindifferences (if any). Discuss validity of necessary assumptions in individual cases.2. Show diagnostic plots (for OLS) and interpret them.1The contact person for this homework is Martin Hronec, the same mail as for submission of homeworks.2If you prefer not to write formulas in LATEX, you can send PDF with your derivations and interpretations in additionalfile and R code in Jupyte代写Econometrics、代写R程序语言、代做sourcr Notebook.13. Use LAD to estimate conditional median and compare it with the estimate of conditional meanfrom OLS for each of the pairs. Explain differences between them.4. Use quantile regression to estimate conditional quantiles (for tau 0.05,0.25,0.5,0.75,0.95) foreach of the pairs and discuss differences across quantiles.Problem 2. On the second seminar, we have talked about heteroskedasticity a lot and had an examplewhere data was generated according to the equationincomei = α + β · educi + educi,where ∼ N(0, 200), α = 4000, β = 200.1. Illustrate theoretically that this heteroskedasticity implies varying slopes in quantiles and elaboratehow to distinguish this kind of quantile dependency that arises purely from heteroskedasticity.2. Simulate data from such model and show empirically, that your finding holds.Hint: Derive the quantiles of income for given education first, i.e. qτ (income|educ) and thenthink how this relates to slope of quantile regression.Problem 3.1. Simulate 42, 168 and 672 data points from exponential distribution (λe−λx) with λ of your choice.2. Using all 3 samples, fit the λ parameter using MLE and exponential distribution as your assumeddistribution.3. Then, again using all 3 samples, fit the gamma distribution ( βαΓ(α)xα−1−βx) using MLE again.Report both estimates and their standard errors.4. Finally, as the exponential distribution is a special case of gamma distribution, use the threelikelihood-based tests you’ve seen during the lecture as well as seminar to test the null-hypothesisthat the data come from exponential distribution (again using all 3 samples).5. Compare results of your tests across all 3 samples and discuss whether they match your expectations.2转自：http://www.3daixie.com/contents/11/3444.html