2. The output below reports the estimated regression for the TSX return and the independent variables are Canadian Gross Domestic Product (GDP), Industrial Producer Price (IPP) index, and the 5-year fixed mortgage rate (M ORT G 5Y ). (a) (2 marks) What are the order of integration for the variables ln(T SXt), ln(GDPt), ln(IP Pt), and M ORT G 5Y . (b) (5 marks) Test for cointegration of these four variables. (c) (8 marks) Write out the estimated equation and discuss the coefficients. Is this error correction model consistent with cointegration? (d) (5 marks) Given the following data, what is the forecast for ln(T SX2018Q4)? Date MORTG 5Y ln GDP new ln TSX ln IPP 2018Q3 4.99 14.37308 11.56228 4.729156 2018Q4 4.99 14.37806 - 4.743192 . gen ln_GDP_new=log(GDP_new) (805 missing values generated) . gen ln_TSX=log(TSX_val) (469 missing values generated) . gen ln_IPP=log(IPPI_CAN) (504 missing values generated) . dfuller ln_GDP_new, lags(4) Augmented Dickey-Fuller test for unit root Number of obs = 438 1---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -0.541 -3.445 -2.872 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.8838 . dfuller MORTG_5Y, lags(4) Augmented Dickey-Fuller test for unit root Number of obs = 535 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -1.253 -3.430 -2.860 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.6506 . dfuller ln_TSX, lags(4) Augmented Dickey-Fuller test for unit root Number of obs = 774 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -0.844 -3.430 -2.860 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.8057 . dfuller ln_IPP, lags(4) Augmented Dickey-Fuller test for unit root Number of obs = 739 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -1.351 -3.430 -2.860 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.6055 . dfuller D.ln_GDP_new, lags(4) Augmented Dickey-Fuller test for unit root Number of obs = 437 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -6.496 -3.445 -2.873 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0000 . dfuller D.MORTG_5Y, lags(4) 2Augmented Dickey-Fuller test for unit root Number of obs = 534 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -10.280 -3.430 -2.860 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0000 . dfuller D.ln_TSX, lags(4) Augmented Dickey-Fuller test for unit root Number of obs = 773 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -15.299 -3.430 -2.860 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0000 . dfuller D.ln_IPP, lags(4) Augmented Dickey-Fuller test for unit root Number of obs = 738 ---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -8.582 -3.430 -2.860 -2.570 ------------------------------------------------------------------------------ MacKinnon approximate p-value for Z(t) = 0.0000 . reg ln_TSX ln_GDP_new ln_IPP MORTG_5Y Source | SS df MS Number of obs = 443 -------------+---------------------------------- F(3, 439) = 1661.19 Model | 811.059066 3 270.353022 Prob > F = 0.0000 Residual | 71.4456728 439 .162746407 R-squared = 0.9190 -------------+---------------------------------- Adj R-squared = 0.9185 Total | 882.504739 442 1.99661706 Root MSE = .40342 ------------------------------------------------------------------------------ ln_TSX | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- ln_GDP_new | 2.547145 .4233445 6.02 0.000 1.715111 3.379179 ln_IPP | 1.554854 .6284877 2.47 0.014 .3196351 2.790072 MORTG_5Y | -.1023253 .0140215 -7.30 0.000 -.1298829 -.0747677 _cons | -31.2276 3.51152 -8.89 0.000 -38.12908 -24.32612 ------------------------------------------------------------------------------ . predict u, resid (805 missing values generated) . dfuller u, noconstant Dickey-Fuller test for unit root Number of obs = 442 3---------- Interpolated Dickey-Fuller --------- Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value ------------------------------------------------------------------------------ Z(t) -5.137 -2.580 -1.950 -1.620 . reg D.ln_TSX L.u D.MORTG_5Y D.ln_GDP_new D.ln_IPP Source | SS df MS Number of obs = 442 -------------+---------------------------------- F(4, 437) = 17.12 Model | 2.39660757 4 .599151891 Prob > F = 0.0000 Residual | 15.2920684 437 .034993292 R-squared = 0.1355 -------------+---------------------------------- Adj R-squared = 0.1276 Total | 17.688676 441 .040110376 Root MSE = .18706 ------------------------------------------------------------------------------ D.ln_TSX | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- u | L1. | -.1135267 .0222482 -5.10 0.000 -.1572535 -.0698 | MORTG_5Y | D1. | -.0932763 .0234231 -3.98 0.000 -.1393123 -.0472404 | ln_GDP_new | D1. | 10.45176 2.115373 4.94 0.000 6.294194 14.60933 | ln_IPP | D1. | .9947945 1.345402 0.74 0.460 -1.649467 3.639057 | _cons | -.0158769 .0101002 -1.57 0.117 -.0357279 .0039741 ------------------------------------------------------------------------------ . clear . end of do-file