Introduction and Exam Overview

The professor introduces the lecture and provides an overview of the exam. He also mentions that the solution to the exam has been posted on the webpage.

• The professor encourages students to check their answers against the posted solution before approaching him with questions about grading.

• Students who believe they were not graded properly should first approach Chris, as he has a better sense of horizontal equity.

• The professor will read through exams himself and make an assessment of what grade each deserves.

Grading Procedure

The professor explains his grading procedure for exams.

• If a student disagrees with Chris's assessment, they can come see the professor.

• The null hypothesis is that Chris was correct in his grading, but if there is overwhelming evidence to the contrary, the professor will change it.

• When means are low, more students tend to search for ways to increase their score.

Lack of Preparation

The professor expresses disappointment in students' lack of preparation for the exam.

• Despite offering extra office hours and making research sources available, few students took advantage of these resources.

• Students who did not do the necessary work beforehand will struggle in this class.

Conclusion

The professor concludes by emphasizing that this is a difficult class that requires consistent effort throughout the semester.

• Watching videos alone without attending class or doing additional work will not be sufficient for success in this course.

Importance of Studying and Doing the Work

The professor emphasizes the importance of studying and doing the work before taking tests. He mentions that there are other opportunities to improve grades, such as homework and projects.

Need to Study for Tests

• Professor stresses the importance of studying before taking tests.

• Students who did not study had difficulty answering questions on previous tests.

• Students who did not do well on previous tests need to do better on future ones.

Other Opportunities to Improve Grades

• Homework and projects contribute to students' scores.

• Professor uses percentages to determine grades based on rank order, but encourages good scores to rise to the top.

Grading Distribution and Bias

The professor discusses grading distribution and potential bias in grading estimates.

Grading Distribution

• Professor will email students the grade distribution when all exams have been graded.

• Rank order is important for determining grades, but there are guidelines for how many A's and B's should be given.

Potential Bias in Grading Estimates

• Professor is hesitant to give a biased estimate of grades based on only 30 exams graded so far.

• If nobody is doing well, it may be due to lack of incentives or encouragement from the professor.

Test Timing and Format

The professor discusses test timing and format, including repeat questions from previous classes.

Test Timing

• Tests are usually given on Monday during week six so students have time over the weekend to prepare.

• Week five and seven are busy weeks with many tests.

Test Format

• Students usually have a choice of six questions, but there were only five this time.

• Professor grades all questions to ensure consistency.

Time Management

The professor talks about time management and how it relates to effectiveness. He mentions that there are only so many tests one can take in a week.

• The professor suggests moving on to more pleasant topics like Cochran Orkut procedures.

Feeling Good About Tests

The professor discusses the importance of feeling good about your test results, even if they are lower than the mean.

• Feeling bad about your test results means you are more likely to improve in the future.

• Lowering the mean is a good thing, even if it doesn't necessarily mean you did well on the test.

Serial Correlation

The professor explains serial correlation and its effects on efficiency.

• Serial correlation is when there is correlation among errors, not among exes. It's an efficiency issue, not a bias issue.

• To fix this problem, we need to isolate just one variable by subtracting models from each other.

Writing Models

The professor demonstrates how to write models for serial correlation problems.

• We can write models for serial correlation problems by lagging them once and multiplying through by Rho.

• By subtracting one model from another, we can isolate just one variable and avoid serial correlation issues.

Introduction

The speaker greets the audience.

• The speaker says "thank you Hey".

Quasi Differencing

The speaker explains quasi differencing and how it can be used to calculate a term in a regression model.

• Quasi differencing is taking some fraction of the difference between YT and YT minus 1.

• If we knew Rho, we could make this model just our model.

• We can form all the star variables and run this regression, which would be the best linear unbiased estimator that's linear. There still might be a non-linear estimator instead of a special in here.

• The problem is getting an estimate of Rho. Once we have an estimate of Rho, this is fully efficient as long as we know Rho exactly. If we don't know Rho exactly, but have a consistent estimate of Rho then in the limit as n goes to infinity, the Rho will be corrected as we fully look fully efficient.

Consistency

The speaker discusses consistency and what it means for estimating values.

• Consistency means that if T or n gets big enough, this row that we estimate will go to the true value. That's all that consistency means; it tells us that in the limit, we got exactly what we need to do this transformation perfectly and so it works perfectly. Then we know that convergence is well; however, there may still be some error present even though it will be small.

Cochran or Theil Procedure

The speaker explains the steps for the Cochran or Theil procedure.

• Estimate the model yg is beta 1 plus beta 2 X 2 T plus theta K X K T Plus u T with OLS. We're relying upon the fact that the betas are unbiased; they're not efficient because of the serial correlation of UT, but they're unbiased and consistent, and so therefore we get an estimate of you its unbiased and consistent that's important because step 2.

• Save all the residuals that you estimated there's tío.

• Estimate Rho by running a regression of UT on UT minus one. This is just a regression of that on that, and this is the estimator for that. Practically, take these u hats or guys you had on you hat minus 1, and that estimate of Rho comes out with no constant, which is what you need now.

Steps for Regression Analysis

In this section, the speaker explains the steps involved in regression analysis.

Transforming Data

• To get a good estimate, transform the data using YT minus Rho hat 1 2 minus 1 X 2 T star is X 2 T when it's throw hat X 2 t minus 1 it's K T star.

• Use Eviews to do those transformations for regress Y T score on a constant that's that theta one times one minus R over beta 1 star this is beta 1 star X T 2 star X K T store and use OLS here.

Getting Estimates

• Use these estimates to get a new estimate of you half so this is going to give you they go one scar at theta two hat up to beta K hat right when you run this you'll get beta one star and beta two up to beta K because those are the coefficients in front of the transform variables if you look at the regression.

• Beta one star is not beta one so divide by one minus Rho to get the right data one.

Repeating Steps

• Find UT hat as YT minus beta 1 hat - hey I'm sorry writing with a real -.

• Repeat steps two three months one time.

Iterative Procedure for Fully Efficient Consistent Estimates

In this section, the speaker explains an iterative procedure to obtain fully efficient consistent estimates.

Steps for Obtaining Fully Efficient Consistent Estimates

• Use new betas to get a new U hat.

• Repeat steps 6.2 through 6.5 until Rho changes by less than a preset tolerance value.

• Transform the data using the formula UT hat on UT minus 1/2 (no constant) to get Rho hat.

• Run YT star on theta 1 star X2T star XK T star plus UT star to get new betas.

• Use the new betas to get new U's and then use the new U's to get another Rho.

• Keep iterating until convergence is achieved.

Getting Residuals and Rho from Original Model

In this section, the speaker explains how to obtain residuals and Rho from the original model.

Steps for Obtaining Residuals and Rho

• Get residuals from original model by subtracting E t from Y t.

• Obtain Rho by transforming data using formula UT hat on UT minus 1/2 (no constant).

Tricky Steps in Obtaining Fully Efficient Consistent Estimates

In this section, the speaker highlights two tricky steps in obtaining fully efficient consistent estimates.

Two Tricky Steps

• The first tricky step is that beta one is missing in transformed data because it is a constant term.

• The second tricky step is that residuals obtained from regression are e t's and not u t's. To obtain u t's, one needs to go back to the original model.

Convergence of Fully Efficient Consistent Estimates

In this section, the speaker explains how convergence is achieved for fully efficient consistent estimates.

Steps for Achieving Convergence

• Run all steps until true values are obtained.

• Use new betas to get new U's and then use the new U's to get another Rho.

• Keep iterating until convergence is achieved.

Tolerance Value for Rho Hat

In this section, the speaker explains how to determine a tolerance value for Rho hat.

Determining Tolerance Value

• Look at absolute value of difference between Rho n minus Rho m minus 1.

• Set tolerance value as less than absolute value of difference.

Transforming Data

In this section, the speaker explains how to transform data.

Steps for Transforming Data

• Run regression on X2T star using X2T minus Rho hat X2T minus 1.

• Obtain point estimate from regression output.

• Calculate Y star by subtracting point estimate times Y t minus 1 from Y t.

• Calculate X2T star by subtracting point estimate times X2T minus 1 from X2T.

Regression Coefficients

The speaker explains how to calculate the coefficients from a regression.

Calculating Coefficients

• The coefficients from a regression are beta 1 hat, beta 2 hat through beta K hat.

• To calculate the coefficients, run a regression and look at the main statistics.

• Beta 1 hat is just one of the coefficients from the regression.

Iterative Procedure for Finding Maximum Likelihood Estimates

The speaker explains an iterative procedure for finding maximum likelihood estimates.

Steps for Iterative Procedure

• Start by finding beta 1 hat using step two of the iterative procedure.

• Repeat steps two to five until it converges.

• Calculate u hat using YT minus theta 1 hat minus beta 2 hat X 2 minus beta K hat XK ya.

• Each time you repeat steps two to five, you will get a new u and a new beta 1 each time.

Convergence of Maximum Likelihood Estimates

The speaker discusses convergence of maximum likelihood estimates.

Efficiency and Consistency

• The iterative procedure is consistent but not fully efficient.

• Once you have shown that this estimator converges to the maximum likelihood estimator, you know it's efficient and consistent.

• This estimator does converge after iteration.

Conditions for Convergence

The speaker discusses conditions for convergence.

Condition for Convergence

• When bro-hat-n-he-run-half-n-minus-one converges, that's also when it converges to the maximizer yesterday.

• You can start off with row that's like point eight this procedure and it very fast.

• You rarely have to go up to three or four or five iterations if it'll converge really fast.

Linear Regressions

The speaker discusses linear regressions and their limitations.

Finding Nonlinear Outcomes

• Old econometrics is about finding a series of linear regressions that converge to a nonlinear outcome.

• This iterative procedure finds a series of linear regressions that converge to the maximum likelihood estimator.

Learning Nonlinear Least Squares

In this section, the speaker discusses how to estimate nonlinear models using nonlinear least squares.

Estimating Nonlinear Models

• If the original equation is specified differently and is nonlinear, you can use a different version of transformation to estimate it.

• You can estimate a regression with rows and 1 minus Rho thin using nonlinear least squares to get a fully efficient consistent estimator that's better than what we did before.

• The technology has advanced so much that there is no need to learn linear regression anymore.

Limited Information Maximum Likelihood

• There is a way to transform the first two variables so that you don't lose any observations. This is called limited information maximum likelihood.

• Transforming the first two variables using this method gives you full information maximum likelihood.

Robert Engle's ARCH Test

In this section, the speaker talks about Robert Engle's ARCH test and how it mixes up autoregressions and Tuscan as DISA T.

Autoregressive Model of Variance

• US GDP was pretty variable until March of 1984 when some of the GD ball Atilla T and GDP fell by 50 percent just literally dropped by 50% in 1984.

• The latest crisis shows more variability in variance over time, which looks like an autoregressive model of variance.

Modeling Autoregressive Conditional Heteroscedasticity (ARCH)

The speaker discusses modeling the variance of macroeconomic series as an autoregressive process, and how to test for this using a non-linear estimator.

Autoregressive Process

• Variance of macroeconomic series can be modeled as an autoregressive process.

• This allows the variance to change smoothly over time.

• There are many models for this, including ARCH, GARCH, and AMARCH.

Non-Linear Estimator

• If the autoregressive process is present, a non-linear estimator should be used.

• OLS is still the best linear estimator if it is not present.

• The package "arch" can be used to estimate this non-linear model.

Testing for ARCH

• To test for ARCH, run a regression with white noise errors on constant X variables.

• Use LM test statistic t-P to determine if alpha 1 to alpha P are zero or not.

• Null hypothesis is that alpha 1 to alpha P are zero. Alternative hypothesis is that at least one of them is nonzero.

Project Discussion

The speaker briefly discusses the project and homework assignments.

Homework Assignment

• For lab homework, complete steps one through three by next lab session.

• A new homework assignment will be posted tomorrow.

Project Discussion

• Speaker wants to start discussing the project.

• No further details provided in this section.

Project Requirements

The professor explains the requirements for the project and emphasizes that it needs to have economic content. He gives an example of a sports-related project that could work if it has some economic questions related to it.

Economic Content

• The project needs to have economic content.

• A sports-related project is fine as long as it has some economic questions related to it.

• Theoretical predictions and economic theories need to be explained in detail.

• An econometrics model needs to be specified, including variables used, transformations made, and tests conducted.

Data Collection

The professor discusses the importance of data collection and how difficult it can be to find relevant data for a project.

Finding Relevant Data

• It's important to find relevant data for the project.

• Some projects may require specific types of data that are difficult to find.

• Sources of data need to be listed in the project report.

Macro and Micro Data

The speaker discusses the availability of macro and micro data, where to find them, and how to extract them.

Finding Macro Data

• Fred Federal Reserve Economic Data is a good source for macro data.

• Extracting data from Fred is easy. There's a button that dumps it into an Excel spreadsheet.

Finding Micro Data

• Micro data is harder to find than macro data.

• The book uses a dataset that can be helpful in finding micro data.

Importance of Knowing Your Data

• Knowing your data will be the hardest part of the project.

• It's important not to gloss over this step as it may require an iterative process.

• Running regressions early on can help identify problems with the data.

Estimation Techniques and Forecasting Information

The speaker discusses what estimation techniques to use, what problems to test for, how to correct for problems if found, and forecasting information.

Estimation Techniques

• The next steps in the project will involve deciding what estimation technique to use.

• Hypotheses need to be tested and significance levels should be picked in advance.

Correcting Problems

• If problems are found during testing, corrections need to be made immediately.

• Benchmarks will be set along the way so students don't fall behind.

Forecasting Information

• Students should take a liberal estimate of how long the project will take and triple it.

• The goal of the project is to illustrate that students know how to use the tools and techniques in the course.

Importance of Starting Early

The speaker emphasizes the importance of starting early on the project.

Time Management

• Students should get started early and get their data as soon as possible.

• The project will take longer than expected, so students need to plan accordingly.

Final Project Outcome

• The final outcome may not turn out as expected, but what's important is showing that students know how to use the tools and techniques in the course.

• It's not necessary for the project to be flashy or groundbreaking, but rather that it demonstrates knowledge of testing for heteroscedasticity, autocorrelation, and other problems.

Homework Assignments and Benchmarks

The speaker discusses the importance of completing weekly homework assignments or benchmarks to stay on track with the project.

Completing Homework Assignments

• Completing weekly homework assignments or benchmarks is important to stay on track with the project.

• One of the problems in the next homework is to complete steps one through three. There's also a problem in the book that will be part of your next homework.

Post Para Homework

• The next homework called "Post Para" has a problem that requires doing steps one through three on the empirical project outline, as well as another problem and another completely different from the project.

Importance of Turning Things In

• The speaker emphasizes turning things in at the lab to stay on track with the project, as it's easy to discount push things into the future if left to hit your own benchmarks.

More on Project Questions

The speaker talks about starting a new section for project questions that they hope will be easier.

New Section for Project Questions

• The speaker plans to start a brand new section for project questions that they hope will be easier.