economic and statistic question

HOMEWORK 6 Econ 4400, Elementary Econometrics

Directions: Please follow the instructions closely. Completion of this assignment re- quires the data set rgdp.dta available on Carmen. Due: All problem sets have to be turned in at the beginning of the class. Due Date: April 20

1. (10)Explain the difference between time series data and cross-sectional data.

2. (10)Why do we detrend time series data?

3. (10)Define serial correlation and give an example of a time series model that could have serial correlation.

4. (10)What is the difference between consistent and unbiased β̂?

5. (10)What is the difference between a static and dynamic model? Give an example of each.

6. (40 points)The St. Louis Fed publicly provides a significant amount of time series data. (https://research.stlouisfed.org/fred2/). The data set rgdp.dta can be found on Carmen. It includes quarterly GDP (in 1996 dollars), a stata time variable (date), year, quarter, a time index (where 1 is the first included quarter), and a randomly generated variable. The random variable was constructed with a time trend. Use this data set to complete the following exercises. (Start by telling stata that you are using time series data by typing ”tsset date”) Include regression results and graphs in your homework.

• Regress GDP on random. Show the regression results. Does the random variable have a statistically significant affect on GDP?

• Create time series graphs of each variable. What trends seem to be present? (tsline rgdp)

• Detrend the data by generating ∆Random and ∆Log(GDP) • Repeat the regression from number 4 with your detrended data. Report and

describe the results. If they have changed, discuss why.

Some helpful commands in STATA:

• To create a time series graph of y, type ”tsline y” • To designate a lagged value you must first tell stata that the data is time

ordered by some variable t ”tsset t”. Then you can create a lagged value ”gen lagx=x[ n-1]

• To generate a new variable x where x is the log of y, type ”gen x=log(y)”