EViews LOAD DATA • Click on EViews icon. • Click on File, New, Workfile. • In the dialog box specify annual data, and put 1871 2000 in the boxes for beginning and end. • The file is Shiller.xls in G:ems data; eviews courses is also on Ron Smith’s home page. • You will then get a box with two variables, C for the constant and Resid for the residuals. • Choose File, Import, Read Text Lotus Excel.
In the dialog box where it asks for Names or numbers type 5, and OK. Notice that it will start reading data at B2. This is correct, column A has years, which it already knows and row 1 has names, which it will read as names Five Variables will appear in the box. These are US data for ND nominal dividends for the year NE nominal earnings for the year NSP nominal standard and poors stock price index, January value PPI producer price index, January Value R average interest rate for the year Highlight ND and NE in the box. Click Quick, Graph, Line Graph, OK the two variables and you will get a graph of dividends and earnings. After looking at it, close it and delete it. You could save it if you want. ESTIMATE A LINEAR EQUATION Click, Quick, Estimate an Equation, Type in ND C NE Notice the default estimation method is LS (least squares) but there are other methods you could choose. There is an option box, which you can use to get Heteroskedasticity and Autocorrelation Consistent (HAC) Standard Errors if you want. Click OK and you will get the following output Dependent Variable: ND Method: Least Squares Date: 11/05/04 Time: 15:21 Sample(adjusted): 1871 1999 Included observations: 129 after adjusting endpoints Variable
Coefficient Coefficie nt
Std. Error
t-Statistic
Prob.
C NE
0.336833 0.421626
0.089865 0.008437
3.748188 49.97162
0.0003 0.0000
R-squared Adjusted R -squared squar ed S.E. of regression Sum squared resid Log likelihood Durbin-Watson Durbin-Watson stat
0.951604 0.951223 0.880097 98.37048 -165.5590 0.533942
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) Prob(F-statistic)
2.611163 3.984932 2.597813 2.642151 2497.163 0.000000
On the equation Window click View. Then click Actual, Fitted Residual and then Actual, Fitted Residual Graph. These do not look like random residuals. The DurbinDurbinWatson shows severe serial correlation. Close the equation and delete. GENERATE NEW VARIABLES Type Quick, Generate Series and type into box LND=LOG(ND) And OK. You will get a new series in the box LND. Similarly generate LNE=LOG(NE) LNSP=LOG(NSP) ESTIMATE LOGARITHMIC DYNAMIC EQUATION AND DO DIAGNOSTIC TESTS Click, Quick, estimate equation and type in LND C LNE LNE(-1) LND(-1) @TREND @trend, is a variable that goes 1,2,3, etc. You will get Dependent Variable: LND Method: Least Squares Date: 11/05/04 Time: 15:49 Sample(adjusted): 1872 1999 Included observations: 128 after adjusting endpoints Variable
Coefficient Coefficie nt
Std. Error
t-Statistic
Prob.
C LNE LND(-1) LNE(-1) @TREND
-0.188548 0.266954 0.619659 0.062857 0.000735
0.044679 0.031936 0.040208 0.043210 0.000655
-4.220087 8.359155 15.41149 1.454707 1.123130
0.0000 0.0000 0.0000 0.1483 0.2636 0.263 6
R-squared Adjusted R -squared squar ed S.E. of regression Sum squared square d resid Log likelihood Durbin-Watson Durbin-Watson stat
0.996177 0.996052 0.083107 0.849543 139.3414 1.765940
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) Prob(F-statistic)
0.037723 1.322725 -2.099085 -1.987677 8011.965 0.000000
This estimates d t = α 0 + β0 et +
β1et −1 + α1d t −1 + γ t + ut
Click View, Actual Fitted Residual Graph. This looks better than before, but there are still some outliers. Click View on the equation box, choose Residual Tests, Serial Correlation LM tests, and accept the default number of lags to include 2. You will get the LM serial correlation test. Note that neither nei ther lagged residual is individually significant si gnificant (t value less than 2, p value >0.05) nor are they jointly significant F stat p value is 0.19. So we do not have a serial correlation problem with this equation. On diagnostic tests, the null hypothesis is that they are well specified, p values below 0.05 indicate that there is a problem. Click View, Residual tests, histogram- normality test. You will get the histogram and in bottom right the JB test of 56.59 and a p value of 0.0000. There is clearly a failure of normality, caused by the outliers. Click View, residual, White Heteroskedasticity (no cross terms) p value is 0.24977, so no indication of heteroskedasticity.
Click View, coefficient tests, redundant variables, enter LNE(-1) @trend OK, you will get Redundant Variable s: LNE(-1) LNE(-1) @TREND F-statistic Log likelihood ratio
1.499934 3.084352
Probability Probab ility Probability Probab ility
0.227198 0.213915
Test Equation: Dependent Variable: LND Method: Least Squares Date: 11/12/04 Time: 14:52 Sample: 1872 1999 Included observations: 128 Variable
Coefficient Coefficie nt
Std. Error
t-Statistic
Prob.
C LNE LND(-1)
-0.128696 0.301918 0.670366
0.014681 0.023779 0.027273
-8.766476 12.69656 24.57990
0.0000 0.0000 0.0000
R-squared Adjusted R -squared squar ed S.E. of regression Sum squared resid Log likelihood Durbin-Watson Durbin-Watson stat
0.996083 0.996021 0.083439 0.870263 137.7992 1.847807
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) Prob(F-statistic)
0.037723 1.322725 -2.106238 -2.039394 15895.29 0.000000
The F stat has a p value of 0.227, so the two variables are jointly insignificant, as well as being individually insignificant in the previous regression, so we can drop them. This equation estimates *
d t = θ 0 + θ1et ∆ dt =
λ (d t
*
− d t −1 ) + ε t
λθ0 + λθ1et + (1 − λ ) d t −1 + ε t So the implied estimate of λ = 1 − 0.670366 = 0.329634 and of θ1 = 0.3019 0.301918/ 18/0. 0.329 329634 634 = 0.91 0.9159 5919 19. Rather than working them out directly we can dt =
use EViews non-linear options to get them directly. ESTIMATE A NON-LINEAR NON-LINEAR VERSIO N Close the equation and click, quick, estimate an equation again, type in
D(lnd)=c(1)*(c(2)+c(3)*lne-lnd(-1)) The D(…) first differences the data. This estimates the partial adjustment model giving estimates of the long-run parameters and speed of adjustment directly:
∆dt = λ (θ0 + θ1et −dt −1 ) + ut
You might get results almost identical to those above Dependent Variable: D(LND) Method: Least Squares Date: 11/05/04 Time: 16:13 Sample(adjusted): 1872 1999 Included observations: 128 after adjusting endpoints Convergence achieved after 9 iterations D(LND)=C(1)*(C(2)+C(3)*LNE-LND(-1)) C(1) C(2) C(3) R-squared Adjusted R -squared squar ed S.E. of regression Sum squared resid Log likelihood
Coefficient Coefficie nt
Std. Error
t-Statistic
Prob.
0.329634 -0.390422 0.915917
0.027273 0.024387 0.015889
12.08651 -16.00940 57.64370
0.0000 0.0000 0.0000
0.567105 0.560178 0.083439 0.870263 137.7992
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat
0.032515 0.125815 -2.106238 -2.039394 1.847807
Notice the R squared is lower because here we are explaining the change in log dividends (the growth rate of dividends) not the level of log dividends. The long-run elasticity of dividends to earnings is 0.91 and significantly different from unity, the speed of adjustment is 33% a year. Notice that this is the same equation as we had above, with exactly the same standard error of regression. MULTIPLE MAXIMA However, you might get Dependent Variable: D(LND) Method: Least Squares Date: 11/12/04 Time: 14:42 Sample (adjusted): 1872 1999 Included observations: 128 after adjustments Convergence achieved after 2 iterations D(LND)=C(1)*(C(2)+C(3)*LNE-LND(-1))
C(1) C(2) C(3) R-squared Adjusted R -squared squar ed S.E. of regression Sum squared resid Log likelihood
Coefficient Coefficie nt
Std. Error
t-Statistic
Prob.
-4.91E-05 -433.8815 -422.9887
0.040166 354883.5 354883.5 347035.4 347035.4
-0.001221 -0.001223 -0.001219
0.9990 0.999 0 0.9990 0.9990
0.061042 0.046019 0.122886 1.887615 88.24569
Mean dependent depend ent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat
0.032515 0.125815 -1.331964 -1.265119 1.547143
This is clearly rubbish. What has happened is that the likelihood function has multiple maxima and when the starting values are set at c(1)=0 c(2)=0 c(3)=0, it goes to this
local maximum. To get the global maximum we need to set other starti s tarting values. The T he minimum is quite close to zero, so even starting the coefficients a little bit positive will solve the problem. To do this type param c(1) 0.05 c(2) 0.0 c(3) 0.05 in the command window at the top under the toolbar. With these starting values it will get to the global maximum. When doing non-linear estimation, try to start with sensible starting values, using the economic interpretation or preliminary OLS regressions to give you sensible values. ESTIMATE AN ARIMA(1,1,1) Estimate an ARIMA(1,1,1) model for log stock prices. Click quick, estimate equation, equation, set the sample to 1871 1990 and type in D(LNSP) C AR(1) MA(1) Notice that both the AR (t=-3.06) and MA (t=5.50) terms are significant. Click forecast on the equation box. Set the forecast period to 1990 2000 look at the graph. It will save the forecast as LNSPF. Close the equation and graph LNSP and LNSPF. This is clearly a terrible forecast, you will see that the actual and predicted steadily diverge over the 1990s.
ESTIMATE A VECM FOR REAL INTEREST RATES Use quick generate and type in INF =100*(PPI(+1)-PPI)/100 =100*(PPI(+1)-PPI)/100 To get a series for inflation. We define it this way because PPI is the January figure. Graph the data, note that PPI inflation is more volatile than CPI inflation. Use Quick, Estimate a VAR enter in the box for endogenous variables R INF Set the sample to 1950 1999 Click the Vector Error Correction button, accept the default lags. Click the cointegration box at the top, leave the treatment of intercepts and trends as option 3, if there might have been a trend in the cointegrating vector you would have chosen option 4. There is also a box that allows you to impose restrictions on the adjustment coefficients A or the cointegrating vector B. Click OK and you will get the output below. The coefficient on inflation in the cointegrating vector is is almost exactly exactly –1 as it should be (I chose a sample that gave a nice result), and we cannot reject the hypothesis h ypothesis that the coefficient c oefficient is 1; t= (1.04-1)/0.32=0.125. (1.04-1)/0.32=0.125. From the View, Representations option you can find out that the long-run real interest rate is 2.76. Below the cointegrating equation are given the equation for the change in interest rate (first column) and change in inflation rat e (second column). The adjustment adjus tment coefficient on CointEq1 CointEq1 for the th e interest rate is negative as it should be and quite rapid 21% a year, the adjustment coefficient on inflation is positive, as it should be, but quite small 5% a year, and insignificant. All the adjustment is being done by interest rates. Lagged inflation is insignificant in the interest rate equation, but lagged interest rates are significant. Vector Error Correction Estimates Date: 11/26/04 Time: 11:24 Sample (adjusted): 1950 1999 Included observations: 50 after adjustments Standard errors in ( ) & t-statistics in [ ] Cointegrating Cointegrati ng Eq:
CointEq1
R(-1)
1.000000
INF(-1)
-1.040971 (0.32255) [-3.22729]
C
-2.765076
Error Correction:
D(R)
D(INF)
CointEq1
-0.208518 (0.07251) [-2.87589]
0.048463 (0.20009) [ 0.24221]
D(R(-1))
-0.046797 (0.13040) [-0.35888]
0.044142 (0.35985) [ 0.12267]
D(R(-2))
-0.298532 (0.12601) [-2.36916]
-0.954033 (0.34773) [-2.74358]
D(INF(-1))
-0.032239 (0.07111) [-0.45339]
-0.452509 (0.19623) [-2.30601]
D(INF(-2))
-0.002217 (0.05242) [-0.04229]
-0.415934 (0.14467) [-2.87504]
C
0.109011 (0.24247) [ 0.44959]
0.136277 (0.66912) [ 0.20367]
0.339613 0.264569 127.9183 127.9183 1.705061 4.525527 -94.43115 4.017246 4.246689 0.077400 1.988242
0.393428 0.324500 974.1651 974.1651 4.705328 5.707769 -145.1859 6.047435 6.276878 0.190440 5.725023
Determinant resid covariance (dof adj.) Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion
59.84696 46.34549 -237.7970 10.07188 10.60724
R-squared Adj. R-squared R-squ ared Sum sq. resides S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent depend ent S.D. dependent depend ent
Click View, Cointegration Tests and you will get the output below. There are two tests, the Trace statistic, which is more reliable and the max eigenvalue statistic. Both indicate no cointegration at the 5% level. It then gives you the Johansen estimates of the cointegrating vector based on the eigenvector identification, and the corresponding adjustment coefficients; then the normalized estimates treating the first variable as the dependent variable, which are the same as the ones given above. On the cointegration test box you can change the size of the test. At the 10% level the trace shows 2 cointegrating vectors. You can also get the tests summarized for all the options about trend and intercept. The results are often sensitive to these assumption, but in this case there is no cointegration at the 5% level under all assumptions. Date: 11/26/04 Time: 11:44 Sample (adjusted): 1950 1999 Included observations: 50 after adjustments Trend assumption: Linear deterministic trend Series: R INF Lags interval (in first differences): 1 to 2 Unrestricted Cointegration Rank Test (Trace) Hypothesized No. of CE(s) None At most 1 *
Eigenvalue
Trace Statistic
0.05 Critical Value
Prob.**
0.175343 0.175343 0.090016 0.090016
14.35576 14.35576 4.716393 4.716393
15.49471 3.841466 3.841466
0.0737 0.0299
Trace test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p -values -values Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized No. of CE(s)
Eigenvalue
Max-Eigen Statistic
0.05 Critical Value
Prob.**
None At most 1 *
0.175343 0.175343 0.090016 0.090016
9.639367 9.639367 4.716393 4.716393
14.26460 3.841466 3.841466
0.2367 0.0299
Max-eigenvalue test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p -values -values Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I): R -0.300688 0.221839
INF 0.313007 0.137724
Unrestricted Adjustment Coefficients (alpha): D(R)
0.693471 0.693471
-0.163405
D(INF)
-0.161174
1 Cointegrating Equation(s):
-1.320153
Log likelihood
-237.7970
Normalized cointegrating coefficients (standard error in parentheses) R INF 1.000000 -1.040971 (0.32255) Adjustment coefficients (standard error in parentheses) D(R) -0.208518 (0.07251) D(INF) 0.048463 (0.20009)
Click View Cointegration Graph and it will plot the cointegration relation or error, the deviation of the real interest in terest rate from fr om its long-run value. There are long-periods long-periods away from equilibrium, which is why we get little evidence of cointegration. Click View, lag structure, Granger Causality, you will get the output below, which shows that inflation is not Granger Causal for interest rates, but interest rates is Granger Causal for inflation. The null hypothesis is that the coefficients are zero, No Granger Causality. VEC Granger Causality/Block Exogeneity Wald Tests Date: 11/26/04 Time: 11:56 Sample: 1950 2000 Included observations: 50
Dependent variable: D(R) Excluded
Chi-sq
Df
Prob.
D(INF) D(INF)
0.273535 0.273535
2
0.8722
All
0.273535 0.273535
2
0.8722
Dependent variable: D(INF) Excluded
Chi-sq
Df
Prob.
D(R)
7.527378 7.527378
2
0.0232
All
7.527378 7.527378
2
0.0232
Under the lag structure option, you can also get a graph of the inverse roots of the lag polynomial. The VAR has three lags and there are two variables, so there are six roots one of which lies on the unit circle corresponding to the stochastic trend. You can also test for excluding lags under this option. You can do the usual diagnostic tests under the residual tests option of View. There does not seem to be any serial correlation but the interest rate equation shows non-normality. Under View residuals you can get the covariance or correlation matrix, the correlation between the errors of the two equations is 0.26. You can also get impulse response functions, which show the effect on the system of shocks to each variable.
