Here we investigate the relationship between stock returns and various economic indicators over the period January 1970 to December 1990. Consider the following static model used to explore this relationship: (C1) rsp500t = Bo + $1i3t + Bzip: + Bat + u, where rsp500 is the monthly return on the Standard & Poor's 500 stock market index, at annual rate. (This includes price changes as well as dividends.) 13 is the return on three-month T-bills ip is the industrial production index and t is the time trend. Results of the regression model are provided below: . reg rsp500 i3 ip t Source SS df MS Number of obs 252 F (3, 248) 1I 6.90 Model 39540.6474 3 13180.2158 Prob > F II 0. 0002 Residual 473630.247 248 1909 . 79938 R-squared II 0. 0771 Adj R-squared 0. 0659 Total 513170.895 251 2044.50556 Root MSE = 43.701 rsp500 Coef. Std. Err. t P>It| [95% Conf. Interval] 13 -2. 479809 1. 079766 -2.30 0. 022 -4. 606489 - . 3531288 ip -2. 880641 . 8118516 -3.55 0.000 -4.479644 -1. 281638 t . 6013797 . 1529905 3.93 0. 080 . 3000534 . 902706 cons 29 . 2411 17 . 82123 1.64 0. 102 -5. 859165 64. 341373.[4 points] The following STATA output reports results of a new Model (C2) adding two lags of ip to the equation (C1), as follows: (C2) rsp500, = Bo + 31i3t + Bzipt + Bzip-1 + BAipt-2 + Bst + u What is the estimated long-run propensity (LRP) for the effect of industrial production index on rsp500? Rewrite Model (C2) to directly estimate the LRP for the effect of industrial production index and its standard error. ip is ipt ip_1 is ipt-1 ip_2 is ipt-2 reg rsp500 13 ip ip_1 ip_2 t Source SS df MS Number of obs 11 250 F (5, 244) 4.35 Model 41760.9679 5 8352 . 19358 Prob > F 0. 0008 Residual 468629. 231 244 1920. 6116 R-squared 0. 0818 Adj R-squared 0. 0630 Total 510390. 199 249 2049.75983 Root MSE = 43. 825 rsp500 Coef. Std. Err. t P> It| [95% Conf. Interval] 13 - 2. 592402 1. 100566 -2.36 0. 019 -4. 760224 - . 4245788 ip -1. 67942 4.375525 -0. 38 0. 701 -10. 29804 6.9392 ip 1 -6.768582 7. 179914 -0.94 0. 347 -20. 9111 7. 373938 ip 2 5. 782985 4. 364614 1.32 0. 186 -2. 814143 14. 38011 t . 5589092 . 1563957 3.57 0.000 . 2508512 . 8669672 _cons 30. 1245 18. 02884 1. 67 0. 096 -5. 38751 65 . 63651 4.[2 points] Name two problems that can arise when estimating with OLS B2, B3, and 34 in Model (C2)?1.[2 points] Is there any evidence of a linear time trend. Explain. 2.[3 points] A time series plot of rspSOO is given below. What is the key feature of the time series plot in Figure 1? Propose a new regression to capture this feature of the series. Figure 1. Monthly return on the S&P500 stock market index January 1970 to December 1990 rsp500 -100 0 100 200 A A 200 1970m1 1975m1 1980m1 1985m1 1990m1