Applied Econometrics I
Assignment #1
I- Download the quarterly data on CPI for the period 2004.1-2009.4, find the following estimates and do the following tests.
1. Plot the variable over time. Explain the movements in your variable and mark the outliers and structural break, if any. Comment on the existence of time trend, seasonal trend, cyclical trend, and randomness in the variable.
2. Do the histogram of the CPI data and comment on the distribution of data.
3. Plot the natural logarithm of the variable. Explain movements in the natural log of the variable and mark the outliers and structural breaks.
4. Plot the histogram of the log of the variable and comment on its distribution.
5. Comment on the differences between the behavior of the variable and the natural log of the variable.
6. Find the summary statistics of the CPI variable.
7. Do a hypothesis test that the mean CPI during the 2004.1-2006.12 is statistically no different from the mean CPI during the 2007.1-2009.12.
8. Do a hypothesis test that the variation of CPI during the 2004.1-2006.12 is statistically no different from the mean CPI during the 2007.1-2009.12.
9. Create the lag of the CPI variable and use it as a naive forecast of your variable. Find the mean absolute deviation (MAD), mean absolute percentage error (MAPE), and mean squared error (MSE)for your forecast.
12. Divide the CPI data to three equal-size periods. Find the means and the variances of the first and the last periods.
13. Do a hypothesis test that the mean of the first period is the same as the mean of the third period.
14. Do a hypothesis testing that the variance of the first period is the same as the variance of the Third period.
15. Find the correlation coefficient between the first period and the third period data. Comment on the correlation coefficient.
16. Take time as an explanatory variable. Find the correlation between the CPI and the time. Comment on the correlation.
II- For the CPI variable find the following estimates and do the following tests.
1. Plot a scatter diagram of the variable and comment on the time trend of the variable.
2. Run a regression of the CPI variable on time and analyze the relationship (Comment on the significance of the coefficients and overall explaining power of the regression).
3. Find the estimated value of the dependent variable (y-hat) .
4. Graph the dependent variable (y) and the estimated y, (y-hat), on the same coordinate system and comment on the relationship between the two.
5. Find the histogram of the regression error. Comment on the distribution of the residuals.
6. Run a regression of the variable on a polynomial function on time and analyze the relationship. Fit the best model and decide on the degree of the polynomial.
7. Find the estimated value of the dependent variable (y-hat).
8. Graph the dependent variable (y) and the estimated y, (y-hat), on the same coordinate system and comment on the relationship between the two.
9. Find the MAD, MAPE, and RMSSE of the regression error.
10. Compare the MAD, MAPE, and RMSE of the two models.
11. Do a three period forecasting based on your best regression on time.
12. Find an explanatory variable based on economic theory. Run a regression of the dependent variable on time and other explanatory variable.
13. Decide on the significance and efficiency of the best model.
14. Find the MAD, MAPE, and RMSE of the regression error.
III
1. Convert the CPI variable to inflation. Define economic variables that would best explain inflation. Download data for those variables.
2. Write a regression model explaining inflation.
3. Run a regression of the dependent variable (inflation) on the independent variables and estimate the model. Comment on the significance of the coefficients, statistical output, and the overall explaining power of the regression.
4. Check whether the classical regression assumptions are satisfied or not. Do proper corrections to meet the required conditions.
5. Find the estimated value of the dependent variable (y-hat). Plot the actual value of the dependent variable y, estimated y, (y-hat), and the residuals. Comment on the relationship among the variables.
6. Find the MAD, MAPE, and RMSE of the regression error.
7. Plot the error of the regression. Comment on the randomness of the error term. Test for the existence of outliers, heteroscedasticity, and/or serial correlation.
8. Make the necessary adjustments for heteroscedasticity or serial correlation.
9. Find the MAD, MAPE, and RMSE of the new regression error. Compare the MAD, MAPE, and RMSE to the MAD, MAPE, and SE in item 6.
10. Do a three period forecasting of the dependent variable assuming that independent variables will be increasing by 10% each period for the next three periods.
11. Test your dependent variable (inflation) for time trend. If trend exists, detrend the variable.
12. Test your dependent variable (inflation) for the existence of seasonality. If seasonality exists, deseasonalize the variable.
IIII
1- Check your model in assignment #3 for the significance of using lagged dependent variable as an independent variable (argue for theoretical and application properties).
2- Extend the argument on using lagged dependent variable to polynomial distributed lag.
3- Assume one of the independent variables in your model is correlated with the error of the regression, (EUX) =/=
0. Find an instrumental variable and run an instrumental variable estimate of your model.
4- Compare the efficiency of the instrumental variable estimate with the OLS estimate.
5- Use all you data except the last five observations. Run your best model (include all the corrections for stationarity, serial correlation, multicolinearity …..). Use the model for an ex-post forecasting of the last five periods. Find the MA, Mean, MAPE, and RMSE of the forecast. Comment on the efficiency of your forecast.
6- Write a 95% confidence interval for the estimated forecast values.
7- Use all of your data, run the best estimate of the model, and do a five period ex-ante forecasting.
8- Write a 95% confidence interval for the forecasted values.
| Title: | Consumer Price Index for All Urban Consumers: All Items |
| Series ID: | CPIAUCSL |
| Source: | U.S. Department of Labor: Bureau of Labor Statistics |
| Release: | Consumer Price Index |
| Seasonal Adjustment: | Seasonally Adjusted |
| Frequency: | Monthly |
| Units: | Index 1982-84=100 |
| Date Range: | 2004-01-01 to 2010-09-01 |
| Last Updated: | 2010-10-15 8:01 AM CDT |
| Notes: | Handbook of Methods – |
| (http://stats.bls.gov:80/opub/hom/homch17_itc.htm) Understanding the | |
| CPI: Frequently Asked Questions – | |
| (http://stats.bls.gov:80/cpi/cpifaq.htm) | |
| DATE | VALUE |
| 2004-01-01 | 186.300 |
| 2004-02-01 | 186.700 |
| 2004-03-01 | 187.100 |
| 2004-04-01 | 187.400 |
| 2004-05-01 | 188.200 |
| 2004-06-01 | 188.900 |
| 2004-07-01 | 189.100 |
| 2004-08-01 | 189.200 |
| 2004-09-01 | 189.800 |
| 2004-10-01 | 190.800 |
| 2004-11-01 | 191.700 |
| 2004-12-01 | 191.700 |
| 2005-01-01 | 191.600 |
| 2005-02-01 | 192.400 |
| 2005-03-01 | 193.100 |
| 2005-04-01 | 193.700 |
| 2005-05-01 | 193.600 |
| 2005-06-01 | 193.700 |
| 2005-07-01 | 194.900 |
| 2005-08-01 | 196.100 |
| 2005-09-01 | 198.800 |
| 2005-10-01 | 199.100 |
| 2005-11-01 | 198.100 |
| 2005-12-01 | 198.100 |
| 2006-01-01 | 199.200 |
| 2006-02-01 | 199.400 |
| 2006-03-01 | 199.700 |
| 2006-04-01 | 200.600 |
| 2006-05-01 | 201.400 |
| 2006-06-01 | 201.900 |
| 2006-07-01 | 202.900 |
| 2006-08-01 | 203.700 |
| 2006-09-01 | 202.900 |
| 2006-10-01 | 201.800 |
| 2006-11-01 | 202.000 |
| 2006-12-01 | 203.100 |
| 2007-01-01 | 203.372 |
| 2007-02-01 | 204.258 |
| 2007-03-01 | 205.312 |
| 2007-04-01 | 205.959 |
| 2007-05-01 | 206.850 |
| 2007-06-01 | 207.202 |
| 2007-07-01 | 207.651 |
| 2007-08-01 | 207.671 |
| 2007-09-01 | 208.503 |
| 2007-10-01 | 209.073 |
| 2007-11-01 | 210.740 |
| 2007-12-01 | 211.434 |
| 2008-01-01 | 212.225 |
| 2008-02-01 | 212.703 |
| 2008-03-01 | 213.543 |
| 2008-04-01 | 214.106 |
| 2008-05-01 | 215.287 |
| 2008-06-01 | 217.279 |
| 2008-07-01 | 219.102 |
| 2008-08-01 | 218.779 |
| 2008-09-01 | 218.846 |
| 2008-10-01 | 216.832 |
| 2008-11-01 | 212.923 |
| 2008-12-01 | 211.339 |
| 2009-01-01 | 211.959 |
| 2009-02-01 | 212.877 |
| 2009-03-01 | 212.643 |
| 2009-04-01 | 212.810 |
| 2009-05-01 | 213.050 |
| 2009-06-01 | 214.558 |
| 2009-07-01 | 214.774 |
| 2009-08-01 | 215.566 |
| 2009-09-01 | 215.911 |
| 2009-10-01 | 216.357 |
| 2009-11-01 | 216.859 |
| 2009-12-01 | 217.224 |
| 2010-01-01 | 217.587 |
| 2010-02-01 | 217.591 |
| 2010-03-01 | 217.729 |
| 2010-04-01 | 217.579 |
| 2010-05-01 | 217.224 |
| 2010-06-01 | 216.929 |
| 2010-07-01 | 217.597 |
| 2010-08-01 | 218.150 |
| 2010-09-01 | 218.372 |
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