Dear Students of Prof. Vinod in
Econometrics II
Cheers, Let us have fun with econometrics II.
The assignments are not so much to judge you as to nudge you to do the work.
The name of the assignment suggests the date assigned. You are expected to prepare a neat diary of all assignments, which is collected near the end of the semester, about 2 weeks before the final exam. The directory structure for diaries is
c:\diary2009\Doe if the first few letters of your last name are Doe
Feel free to have further
directories inside the folder and separate files for each R program
snippet. I will copy and paste entire
code.txt or some such file into my R and expect that it will run without any
hitch, without syntax errors etc. Please
self-correct the diary and grade yourself (preferably in red ink on the hard
copy). Please fill column F of the template. Excel will automatically add
claimed points out of 120. (Like filing
our own 1040 tax return). If you claim points and my audit reveals that the
claimed work is missing, you will lose 2 points for every extra point
claimed as penalty.
http://www.fordham.edu/economics/vinod/ExeSummaryTemplate.xls
How will I check your work? The
most efficient way will be to select all (Control+A) copy and paste into R
(CTRL+C, CTRL+V) and look for syntax errors in R and compare with your
outptuts. Therefore, I recommend that
you use a campus computer (other than your own),
copy your stuff in the suitable directory and check if entire file works as
intended in R to avoid losing points for syntax errors. For your own sake if and when you look at it
several years from now, it is a good idea to have comments saying what the notation is, what you are doing, why, etc. I
will also reward such information by not cutting points.
MASTER LIST for Closed book part of final exam (worth 8%, subj to change).
1) Exercises 3.11 and 3.12, Sec 3.4.2, what is regressed on what in ECM (sec 3.4.3)
What is tested in non-causality testing? (eq. 3.5.1)
skip 2) Given a form f of the density f(x,q) to be normal or beta, write the likelihood function and score function.
3) Link between
4) Sec. 5.3 tests from eq 5.3.3
5) Wu-Hausman specification test Sec 6.2.2, discrepancy, its variance.
6) Use the delta method to find standard error for a squared coefficient. (Sec. 9.1.3)
7) Write the formula for GLS estimator used for correcting for first order autocorrelation among errors.
8) What is the relation between hazard and survival functions?
9) How are unanticipated values of macro variables computed by using a model based on past values of the variable?
10) Entropy is defined as expected value of -------. When the minimum and maximum of the support of f(x) is given and finite, what the form of the maximum entropy density?
MASTER LIST OF possible surprise quiz and Final Exam questions (worth 27%):
1) Discuss basic formulas and properties of k-class and LIML estimators.
2) Write the formula for 3SLS and explain the Kronecker product notation.
skip 1) Derive and plot the empirical distribution function for numbers (20, 12, 33, 50, 40).
skip
2) How are
3) Discuss parametric and nonparametric bootstraps and corresponding p-value computations for symmetric and asymmetric cases.
skip 4) What is the power of hypothesis tests? Why are noncentral (Chisq and F) distributions involved in power computations? What has exact test got to do with power under the null?
5) What is the difference between exact and asymptotic confidence intervals?
6) What are bootstrap t intervals?
12) Show how inversion of a test statistic leads to confidence intervals.
13) If b estimates β the estimation error is (b-β). What is the asymptotic variance of this? How can we make it finite?
14) At what rate does the estimation error tend to zero?
skip 15) which R package has covariance matrix of heteroscedasticity consistent errors?
16) What is the delta method for inference?
skip 17) Define all basic concepts of time series (e.g., stochastic process, arma models, (non)stationarity, MA(¥), green function) from my 33-page class notes.
skip 18) Distinguish between trend-stationary and difference stationary series.
skip 19) Derive the autocovariance of MA(1) model.
20) What are unit root tests? How are they used for testing cointegration?
skip 21) Derive the autocovariance generating function for AR(1) model.
skip 22) Describe the relation between AR(2) model and business cycles.
skip 23) What is a second order dynamic system and what is a general solution to its difference equation ? [Hint: Use eq (2.3.14) of Chapter 2 notes]
skip 24) State the four identification rules for ARIMA models. If acf has a spike at 1 lag and pacf has no distinctive spike it suggests what model?
skip 25) What is the purpose of ARIMA diagnostic checking? Normality testing is useful for residuals of the fitted model. True or False? If the p-value of Ljung-Box statistic is 0.25 what do you conclude?
skip 26) If a DGP follows a third order polynomial in time t, how would you make it stationary? What f(t) functions of time produce S-shaped curves and explosive curves?
skip 27) Describe the frequency, amplitude and phase angle of a sinusoid.
skip 28) What is the relation between AGF and the power spectrum?
skip 29) What is the motivation behind ARCH and GARCH models?
skip 30) What are chaotic non-iid series. What is BDS test? What are turning point and CUSUM tests?
skip 31) What are ARFIMA models? Discuss the advantages of the d parameter.
32) What are distributed lag models? Discuss the ARDL model encompassing eleven distinct economic models.
33) Discuss the Chan et al model for price dynamics in drift and volatility. Discuss a new use of nonlinear estimation in R for the discretized model.
34) What are the motivations and operations of 3 stages in 3 stage least squares?
skip 35) Discuss the macroeconomics without macro theory by using VAR models.
skip 36) Comment on the Identification problem in simultaneous equations estimation. [Hint going from reduced form to structure, particular sub matrix of P needed]
37) Distinguish between truncation, censoring, and between logit, probit and tobit models.
38) Describe the cancellation of individual-specific hazard in Cox proportional hazard model by using appropriate formulas.
39) Define amorphous partial derivative in nonparametric regression using K(w) to denote the kernel function.
40) In double bootstrap, how is the power of the computer is used to fix the bias of usual bootstrap confidence intervals?
41) Describe the motivation behind maximum entropy bootstrap (Hint sec. 9.5.2).
Research Paper
Assignment for spring 2009: TBD
Assignment 1=23i09
Task 1 worth 4pts) Read at least 30 pages excluding the first 40 from my notes on R software at my website
www.fordham.edu/economics/vinod/r-lang.doc
Check to see if any information is correct and/or needs to be updated. Feel free to suggest better organization or better color-typing for easier reading. I am assuming that in doing Econometrics I you have already learned the material from pages 1 to 40. If not, please read those pages also.
Task 2 worth 4pts) 1) We want to study the effect of sample size n on the accuracy of OLS estimate of the slope in the presence of autocorrelated errors. Use a seed of 50 and conduct a simulation of a regression model with 3 regressors created from one n by 3 matrix upon sampling random numbers from 100 to 2500 and make this a source for the regressor data in the simulation. Now let the sample sizes be: n= 100 to 500 in increments of 50. Pick the first 3*n numbers from the source and make the 3 columns out of these numbers as the three regressors x1 to x3. Set the true value of all three regression slopes as 2 and the true intercept as zero. Create the simulated y vector by using autocorrelated regression errors having their AR(1) coefficient of 0.7 by using 'arima.sim.' Estimate the OLS model and compute the (combined scalar) mean squared error of the least squares estimates of all three slopes. Plot the MSE values associated with each of the n values in a line plot with a heading. What does the overall shape of the plot indicate about the effect of n on MSE? Print second through fifth values of the MSE?
rm(list=ls())
set.seed(50);
x=sample(100:2500)
n= seq(100,500, by=50)
nn=length(n)
mse=rep(NA, nn)
for (i in 1:nn) {
err=arima.sim(list(order = c(1,0,0), ar = 0.7), n[i])
xx=x[1:(3*n[i])]
xx=matrix(xx, n[i], 3); x1=xx[,1]; x2=xx[,2]; x3=xx[,3];
y=2*x1+2*x2+2*x3+err
reg1=lm(y~x1+x2+x3)
b1=coef(reg1)[2]
b2=coef(reg1)[3]
b3=coef(reg1)[4]
mse[i]=(b1-2)^2+(b2-2)^2+(b3-2)^2}
plot(n, mse, typ="l")
mse[2:5]
task 1 worth 6pts) Write an R program to do Lagged Dependent variable inference 3 steps (including Vinod’s third step) and using Housing starts data available in textbook snippets
Task 2 worth 5pts) Study the answers to all chapter 3 exercises at Web page: http://www.fordham.edu/economics/vinod/exercises3.pdf
For each exercise pick 4 lines of R code and explain what the code does.
task 1 worth 4pts) Write eq. (3.4.2) for the case when the variables are fygm3 and fygt1.
task 2 worth 2pts) Are these two variables cointegrated?
task 3 worth 2pts) test the Granger causality between these variables.
task 4 worth 4pts) do first 4 items of the first exercise 4.1 of "exercises4.pdf".
task 1 worth 7pts) do items 5 to 11 of the first exercise 4.1 of "exercises4.pdf".
task 2 worth 6pts) do all items of exercise 4.2 of "exercises4.pdf".
task 3 worth 4pts) do all items of exercise 4.3 of "exercises4.pdf".
task 1 worth 4pts) do the take home test as a diary assignment.
task 2 worth 6pts) do all the remaining exercises from Chapter 4. Choose two different small cap portfolios than the ones illustrated in the answers
task 1 worth 7pts) do exercises 5.3 to 5.9.
task 2 worth 4pts) do exercise 5.6 using the package `meboot' using snippet #R5.2.3.
March 5, Thursday, First part of your replication paper in the form of one piece of paper (hard copy) is due. Please provide your name, possible Title, Your e-mail address, exact article you plan to replicate. You will be allowed to modify the choice for a reason.
LATENESS PENALTY: Diary and replication (software + hard copy) are due on Thursday, April 23, 2009 by 7pm in my office before class. Lateness penalty is 2% per day till Monday, May 4, 5:30pm. No submissions will be accepted after May 4 (you will get a zero). 40% of your grade is for the Diary, 20% for Replication, 5% for quiz, 8% for the Closed book part and 27% for open book part of the Final exam on May 7, 2009.
task 1 worth 3 points] Do exercise 6.6
In Class test:
Define 2 endogenous and 3 exogenous variables
where we denote the (dot dot dot) by -99.
Assume that T=50 is the sample
size.
en1=c(1,2,-99,3)
en2=c(4,5,-99,6)
ex1=c(7,8,-99,9)
ex2=c(10,12,-99,13)
ex3=c(14,15,-99,16)
Structural equations are given as:
en1= a + b en2 + q ex1
en2= e + f ex1 + g ex2 + h ex3 + k en1
Write out all matrices of structural equations. Y2 and Z2
M1 , K1 , and
X1*
task 1 worth 3 points] Do exercise 6.10
task 2 worth 3 points] Do exercise 6.11
6.10 Exercise (k-class)
Describe the various special cases of the
k-class estimator. Discuss the eigenvalues
and eigenvectors of a matrix involved in LIML
estimation.
6.11 Exercise (LIML for food market model)
Describe the food market demand model and its
LIML estimation Explicitly
show the matrices involved for eigenvalues
and eigenvectors of in LIML estimation.
Explicitly show the numbers for W0j ,W1j
matrices with sufficient
detail showing that you understand their
composition.
task 1 worth 3 points] Do exercise 6.12
task 2 worth 3 points] Do exercise 6.13
task 3 worth 3 points] Do exercise 6.16
task 4 worth 3 points] Do exercise 6.17
task 1 worth 2 points] Do exercise 7.1 except that do not plot the all data line.
task 2 worth 3 points] Do exercise 7.5 .
task 3 worth 2 points] Do exercise 7.7 .
task 4 worth 2 points] Do exercise 7.8 .
task 1 worth 2 points] Do exercise 7.9
task
1 worth 2 points] Do exercise 7.10
task
1 worth 2 points] Do exercise 7.11
task 1 worth 2 points] Do exercise 7.12
(if
full answer is provided, try to tweak the code/data a bit and state what
happens)