Reference no: EM132199950

Assignment 2 -

In this final exercise, we will think but about problems specific to time series. Goal is simply to introduce some issues, not to give you comprehensive set of tools. The goal is to give you a basic sense of some of the issues involved in working with time series, so that in the future if you continue doing empirical work you will have a better foundation to pick up specific tools and techniques.

For this assignment, we will work with the unemployment and GDP data as in the previous assignment, so you do not need to download any new data. We will work with the log of real GDP throughout.

Data tasks -

1. Plot the data and look for signs of serial correlation and nonstationarity.

2. Measure the variables' serial correlation.

3. Assess the variables' stationarity or nonstationarity.

4. Add a trend to the variables.

5. Plot GDP against the trend, and the residuals.

6. Regress actual unemployment on detrended GDP.

7. Take the first differences of the variables.

Write-up tasks -

Say where unemployment and log GDP appear to be strongly serially correlated and/or nonstationary on the basis of the plots you made in step 1. Describe the features of plots you made that lead you to these views.

Report the correlation coefficients from step 2. Discuss whether these confirm or contradict your visual impression from the plot. Discuss whether the variables can be used in their untransformed form, or whether first-differencing or some other correction is needed.

Report the results of the calculations in step 3. How likely does it appear that each of the two variables is nonstationary? Does this confirm or contradict your visual impression from step 1?

Describe the results of the regression in step 4. You do not need to give a full regression table. Just summarize the key results in plain English. What does the coefficient mean? What does the r-squared mean?

Show the plots produced in step 5. Say whether, visually, the trend appears to get rid of the serial correlation and/or the nonstationarity in each variable. (That is, do the residuals still seem to have these properties?) Does adding a trend to either or both of these variables appear potentially useful, in the sense of isolating the economically interesting variation?

Show the regression results from step 6. Are the results useful/interesting, in the sense of having a coefficient with a sensible value and a reasonably high t-statistic, and a reasonably high r-squared? Or are the standard errors too large and/or the r-squared too low for this regression to give useful information?

Show the plots from step 7. Describe them in terms of how well they seem to eliminate the serial correlation and/or nonstationarity of the untransformed variables. That is, do the new variables now look more or less white noise around a stable mean, or do high values still seem to be followed by other high values and low values by other low values? Report the correlation coefficient of each new variable with its own lagged values and the results of the nonstationarity test. Discuss whether these results confirm or contradict your visual impression. Discuss whether the variables now appear suitable for regression analysis.

Discuss your results from steps 7 and 9 of Assignment 3 in terms of the work you have done here. Are you now more or less confident of your results from Assignment 3? Are there any changes you would make to the results you reported there?

In this assignment, we explored two ways of dealing with serial correlation/nonstationarity: first differencing and detrending. Which approach worked better here? Can you think of any situation where the other one might work better?

Is there any difference in their economic interpretation?

Assignment 3 -

This assignment is an exploration of Okun's law, the relationship between output and unemployment discussed in the Michael Reich paper. We won't try to duplicate his analysis exactly, we will simply ask some questions about the relationship using national and state-level data.

In this assignment we will introduce regressions in R, using the lm function. (The name stands for linear model.) We will also introduce some other useful R techniques, including downloading macroeconomic data from the FRED website, basic techniques for working with time-series data, and some new plotting tools.

For this assignment, as for most assignments this semester, you will submit two files. The first is an R script that performs all the data tasks in the assignment. The second is a text file that answers all the questions. In RStudio, you can create a new script using the New File command. The script will appear in the upper left panel.

To get credit for the R script, it must (1) be possible to run the entire script once and generate answers to all the data questions; (2) be fully commented. The first requirement means that, once I download the data, I should simply be able to run the remainder of your script and generate all the dataframes, tables, figures, etc. the assignment requires. If the script generates some of the required outputs, I will give you partial credit. But I will not make any changes to your script to try to get it to work. You will be graded on exactly what you submit to me. You may need to experiment with different code, different formats for tables and figures, etc. All of this should go in a separate scratchpaper script. Do not submit this to me, only the finished script that generates the results. The second requirement means that each step in the script should have a comment line immediately before or after, explaining what it does and why. (Comments in R begin with the # sign.) You don't need to comment every single line - if several lines are needed to do one thing you can write one comment for the whole set. To write the comments, imagine you were reading the script for the first time. The comments should be sufficiently detailed that you would understand what it was doing and why it was written the way it was.

All figures and tables should be included in the text writeup, in a clear readable form. Always make sure your figures have axes labeled appropriately. In some cases, an axis requires no label; but never use the default R label unless it is easily understood. The text portion should be submitted as a separate document from the R script. The answers should be written in the form of one or more paragraphs.

To begin the assignment, set up a new R script, using the "New File" command in R Studio. You can run code from the script by selecting it and then hitting the "Run" button, or you can run the current line by hitting ctrl-return. Remember, all the code you have that does what you want it to do should go in this script, along with comments. Use the console window in the lower left for experimenting with commands, checking the properties (length, type, names, etc.) or objects, or other actions that aren't part of the project itself.

Data tasks -

1. Import real GDP and the unemployment rate from FRED.

2. Convert both series to annual.

3. Remove any years where you have data for only one of the variables.

4. Convert unemployment data from levels to changes.

5. Convert GDP from levels to percentage changes.

6. Plot the two series over time.

7. Run the regression.

8. Make a scaterrplot with years as points.

9. Run regression again, with dates split.

10. Download employment data.

11. Convert employment data to percentage change.

12. Regress employment growth on real GDP growth.

13. Plot employment growth and real GDP growth.

14. Run regression again, with dates split.

Write-up tasks -

Present the plot from step 6. Make sure it is clear and readable and has a title, and that it either has a legend (created with the legend command) or your writeup says clearly which line represents which variable. Write a few sentences about what the figure shows about the variables and the relationship between them.

Present the regression results from steps 6, 9, 12 and 14. For each one, present the results in a nicely formatted table, and write a few sentences explaining what the values mean.

For each regression, your table should include the estimates for the coefficient and the constant term, the standard errors for each, and the r-squared of the regression. You can combine several regressions in one table as long as it is easy to tell which results are where. Look at some of the regression results in papers we have read to get an idea of how to present these results.

Make a separate table with descriptive data - the overall period covered by the data, the years in each of the two subsamples. For each give the mean of each variable.

Discuss whether the results for the earlier and later periods are substantially different, and if so, how.

Discuss the difference between the results with unemployment as the dependent variable, and the results with employment as the dependent variable. In addition to the results themselves, try to explain the economic meaning of any differences between them. What do the two regressions together tell us about the operation of labor market. Can you think of any interpretation of them in terms of people's behavior?

Present the plots you did in steps 8 and 13. Write a sentence or two indicating whether they simply confirm the regression results, or whether there is some information in the plots that would not be present in the regressions. If there are extreme outlier years, you should mention them here.

Discuss whether your results are broadly similar to the ones in the Reich paper, or whether they are substantially different. If the latter, suggest some possible reason(s) for the difference.

Assignment 4 -

In this final exercise, we will think but about problems specific to time series. Goal is simply to introduce some issues, not to give you comprehensive set of tools. The goal is to give you a basic sense of some of the issues involved in working with time series, so that in the future if you continue doing empirical work you will have a better foundation to pick up specific tools and techniques.

For this assignment, we will work with the unemployment and GDP data as in the previous assignment, so you do not need to download any new data. We will work with the log of real GDP throughout.

Data tasks -

1. Plot the data and look for signs of serial correlation and nonstationarity.

2. Measure the variables' serial correlation.

3. Assess the variables' stationarity or nonstationarity.

3. Assess the variables' stationarity or nonstationarity.

4. Add a trend to the variables.

5. Plot GDP against the trend, and the residuals.

6. Regress actual unemployment on detrended GDP.

7. Take the first differences of the variables.

Write-up tasks -

Say where unemployment and log GDP appear to be strongly serially correlated and/or nonstationary on the basis of the plots you made in step 1. Describe the features of plots you made that lead you to these views.

Report the correlation coefficients from step 2. Discuss whether these confirm or contradict your visual impression from the plot. Discuss whether the variables can be used in their untransformed form, or whether first-differencing or some other correction is needed.

Report the results of the calculations in step 3. How likely does it appear that each of the two variables is nonstationary? Does this confirm or contradict your visual impression from step 1?

Describe the results of the regression in step 4. You do not need to give a full regression table. Just summarize the key results in plain English. What does the coefficient mean? What does the r-squared mean?

Show the plots produced in step 5. Say whether, visually, the trend appears to get rid of the serial correlation and/or the nonstationarity in each variable. (That is, do the residuals still seem to have these properties?) Does adding a trend to either or both of these variables appear potentially useful, in the sense of isolating the economically interesting variation?

Show the regression results from step 6. Are the results useful/interesting, in the sense of having a coefficient with a sensible value and a reasonably high t-statistic, and a reasonably high r-squared? Or are the standard errors too large and/or the r-squared too low for this regression to give useful information?

Show the plots from step 7. Describe them in terms of how well they seem to eliminate the serial correlation and/or nonstationarity of the untransformed variables. That is, do the new variables now look more or less white noise around a stable mean, or do high values still seem to be followed by other high values and low values by other low values? Report the correlation coefficient of each new variable with its own lagged values and the results of the nonstationarity test. Discuss whether these results confirm or contradict your visual impression. Discuss whether the variables now appear suitable for regression analysis.

Discuss your results from steps 7 and 9 of Assignment 3 in terms of the work you have done here. Are you now more or less confident of your results from Assignment 3? Are there any changes you would make to the results you reported there?

In this assignment, we explored two ways of dealing with serial correlation/nonstationarity: first differencing and detrending. Which approach worked better here? Can you think of any situation where the other one might work better?

Is there any difference in their economic interpretation?

Final Exam -

Part I -

A common question in macroeconomics is how much trade flows respond to changes in exchange rates. In this exercise, we will do a simple test of this, using historical US data.

The goal of this exercise is to answer the question, how responsive are US exports and imports to changes in the value of the dollar? Based on historical data, how much is a weaker dollar likely to raise exports and lower imports? And, how much of the historical variation in exports and imports is explained by exchange rates?

Note: All the tasks here are things you did in one or more of the assignments. If you're not sure how to proceed, go back and look at the assignments. As with the assignments, you should submit both R code and a writeup.

For the analysis, do the following: Download the following series from FRED:

TWEXBPA

EXPGSCA

IMPGSCA

GDPCA

The first is an index of the real exchange rate of the dollar against a group of other currencies; the second and third are real exports and imports; and the last is real GDP. ("Real" here means adjusted for inflation.)

Check that all the series are annual. Convert any series at other frequencies to annual, using the earliest values for each year.

Check to see that the series all cover the same years. If not, remove any years that are not present in one or more of the series.

Convert all the values into percentage changes.

Now run two regressions: the percent change in imports on the percent change in the dollar index, and the percent change in exports on the percent change in the dollar index.

It's sometimes argued that imports respond more to income changes than to exchange rate changes. To investigate this:

Run another regression, of the percent change in imports on both the percent change in the exchange rate and the percent change in GDP. (In other words, two independent variables.)

Write up a discussion of your findings, presenting basic descriptive statistics (number of observations, mean, median, and standard deviation for each variable) as well as all three sets of regression results. For each regression, explain what it shows about the questions we are interested in. Discuss all the relevant coefficients or other results, and explain clearly what each means. Then compare the different results with each other. What do they tell you about the behavior of imports and exports - are they similar or different, and if different, how? What do the results suggest about the relative importance of exchange rates versus income in explaining changes in imports?

Note: Before writing up your results, take a moment to think if they make sense. You should plot your data to confirm that the values are reasonable, and that the regressions are capturing the relationship you are interested in.

As with the assignments you should submit both working R code that produces your results; and a clearly written, properly formatted writeup that incorporates your regression tables. In addition to summarizing the results, the writeup should discuss their implications for the substantive economic questions posed at the beginning. You may also include one or more plots in your writeup, if you think it will help communicate your results. If you do include plots, make sure they are are easy to understand, with appropriate labels and captions.

Part II -

Pick two of the following articles, one from group A and one from group B:

Group A:

Gould and Kimball 2015, "Right to Work States Still Have Lower Wages"

Mishel and Gee 2012, "Why Aren't Workers Benefiting from Productivity Growth?"

Wilson 2015, "The Impact of Full Employment on African American Employment and Wages"

Group B:

Marglin and Spiegler 2014, "Did the States Pocket the Obama Stimulus Money?"

Herndon 2017, "Liar's Loans, Mortgage Fraud, and the Great Recession"

Note: You do not have to read all the articles. I suggest you quickly skim them and decide which look most accessible and/or interesting to you/ For the longer articles (group B), you do not need to read every word or make sense of every table or equation. Your goal should be to identify the central results and then read only as much as you need to in order to understand and explain them.

For each article, write a short summary or review that addresses the following questions:

What is the central question(s) that the article addresses?

What kind(s) of data does the article draw on? Are there reasons it uses the specific data it does?

What methodology or methodologies does it use?

What challenges, obstacles or limitations to the data does the paper have to overcome to get a meaningful answer to its question(s), and how does it do so?

What are the most important results?

Are there alternative answers/explanations that the paper considers and rejects? Is there a position the paper is arguing against?

Are there any aspects of the question(s) that the paper is unable to answer, or answers unconvincingly?

Your answer should be a well-organized short essay, not simply a set of answers to the bullets. You should present key quantitative results; make sure to translate any parameter estimates or other numerical results that you discuss into concrete answers to the substantive questions the paper addresses. Imagine you are writing a memo to a policymaker, advocate or journalist who wants to understand the empirical literature on the topic. Your job is to give a comprehensive and precise, but also readable and nontechnical, summary of the key findings and possible limitations of the paper.

Attachment:- Assignment Files.rar