Economic homework

Economics 202 Homework #2 Due: October 7, 2019

1. Find the September 2019 “Employment Situation” released by the Bureau of Labor Statistics on October 3. What are the seasonally adjusted numbers of unemployed for August and September 2019? What are the seasonally unadjusted numbers of unemployed for the same months? Briefly discuss the magnitude of the seasonal adjustment.

2. Consider the model

𝑦" = 𝛽% + 𝛽'𝑇𝑖𝑚𝑒" + ,𝛾.𝐷." + 𝑒"

0

.1'

With estimates

𝛽2% =0.2

𝛽2'=0.01

𝛾3'=0.5

𝛾34 =0.8

𝛾30 =0.2

The time index at the end of the sample is Timen = n = 200, and the final observation is the second quarter of 2019. What are your point forecasts for the third and fourth quarters of 2019?

3. The following FRED codes are for monthly US unemployment rates, 1948m1 through 2019m8, not seasonally adjusted, for people aged 20 and over. Men: LNU04000025 Women: LNU04000026. Fit simple seasonal dummy models for the two series. Plot fitted values for one year. These fitted values are estimated seasonal patterns. Is the seasonality the same for men and women, or different? What is different?

4. Rewrite the following expressions without using the lag operator.

a. (1 − 𝜌𝐿)𝑦" = 𝑒" b. (1 + 0.2𝐿 − 0.8𝐿4)𝑦" = 𝑒" c. 𝑦" = (1 − 𝜃𝐿)𝑒" d. 𝑦" = (1 − 0.3𝐿 + 0.5𝐿4)𝑒"

5. Rewrite the following expressions in lag operator form. a. 𝑦" = 0.8𝑦"B' + 𝑒" b. 𝑦" = 0.2𝑦"B' + 0.3𝑦"B4 − 0.7𝑦"BD + 𝑒"

6. Consider the MA(1) process 𝑦" = 2.3 − 0.95𝑒"B' + 𝑒" a. What is the optimal forecast for time periods T+1, T+2, and T+3. Write

your answer as a function of 𝑦',𝑦4,𝑦0,…𝑦H IJK LM 𝑒',𝑒4,…𝑒H

b. Now suppose that eT = 0.4 and eT-1 = -1.2. Re-answer part (a). 7. The FRED codes for housing starts in the Midwest are HOUSTMW and

HOUSTMWNSA (seasonally adjusted and not seasonally adjusted, respectively). For the South they are HOUSTS and HOUSTSNSA. Graph the autocorrelation functions for these four series. Comment and discuss.

8. Use the real GDP growth data from FRED code A191RL1Q225SBEA. Run an AR(1) regression on these data (with constant). Save the residuals from that regression (predict e, residuals). Graph the time series of the residuals. Graph the autocorrelation function of the residuals. Comment and discuss.

9. Using the simulation instructions at the end of the homework, simulate T=100 observations from each of the four models below. For each series, graph the autocorrelation function, and estimate an MA(2) model. Comment and discuss. For estimation, use the command (where y is the name of the variable that you created): arima y arima(0,0,2)

a. yt = et (white noise) b. yt = et + 0.8et-1 c. yt = et – 0.6et-1 + 0.4et-2 d. yt = 0.5yt-1 - et