Problems with a simple regression.

[Miskolak]

Hello all.

I'm a final year Economics student writing my dissertation.
The question is : To what extent is the change in growth of a macroeconomic variable ( CPI , GDP growth, Unemployment Rate) dependent on the growth of WTI ( Crude oil price)

I have problems when regressing the United states CPI. In my regression I include the constant variable, fist difference of the logarithm of WTI together with 4 lags of both the first difference of logged WTI and first difference of logged CPI.

Although when I checked the information criterion and AIC suggests a single lag period for this regression. However, after speaking to my lecturer I used 4 lags in the regression.

information criterion

VAR Lag Order Selection Criteria
Endogenous variables: DLNCPI DLNWTISPLC
Exogenous variables: C
Date: 04/08/20 Time: 09:26
Sample: 1960Q1 1973Q4
Included observations: 41

Lag LogL LR FPE AIC SC HQ

0 52.93978 NA 0.000286 -2.484867 -2.401279* -2.454429
1 58.83098 10.92027* 0.000261* -2.577121* -2.326354 -2.485805*
2 61.52966 4.739155 0.000278 -2.513642 -2.095698 -2.361450
3 63.32449 2.976777 0.000311 -2.406072 -1.820950 -2.193003
4 64.93517 2.514242 0.000352 -2.289521 -1.537221 -2.015574
5 65.74477 1.184776 0.000417 -2.133891 -1.214413 -1.799068
6 66.85284 1.513463 0.000489 -1.992821 -0.906166 -1.597121
7 69.98797 3.976263 0.000523 -1.950633 -0.696799 -1.494056
8 71.29336 1.528258 0.000618 -1.819188 -0.398177 -1.301734


The regression results look like this:

Dependent Variable: DLNCPI
Method: Least Squares
Date: 04/08/20 Time: 10:24
Sample (adjusted): 1962Q4 1973Q4
Included observations: 45 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 0.122697 0.108074 1.135307 0.2640
DLNWTISPLC 1.588654 3.945035 0.402697 0.6896
LAG1DLNWTI -0.085133 4.153612 -0.020496 0.9838
LAG2DLNWTI 2.761915 7.120546 0.387880 0.7005
LAG3DLNWTI -8.111154 7.148078 -1.134732 0.2642
LAG4DLNWTI 0.478346 7.096993 0.067401 0.9466
LAG1DLNCPI -0.608564 0.166232 -3.660944 0.0008
LAG2DLNCPI -0.596343 0.178036 -3.349561 0.0019
LAG3DLNCPI -0.434088 0.174115 -2.493114 0.0175
LAG4DLNCPI -0.268308 0.153444 -1.748576 0.0891

R-squared 0.358551 Mean dependent var 0.036708
Adjusted R-squared 0.193607 S.D. dependent var 0.657840
S.E. of regression 0.590736 Akaike info criterion 1.978236
Sum squared resid 12.21392 Schwarz criterion 2.379716
Log likelihood -34.51030 Hannan-Quinn criter. 2.127904
F-statistic 2.173775 Durbin-Watson stat 1.891174
Prob(F-statistic) 0.048707

The problem comes down to the WTI being statisitcally insignificant. Is there any way to fix this ?
Any help/advice is greatly appreciated.
Thank you.

[startz]

Do an F-test on all the WTI variables. One possibility is that they are jointly significant even though the timing of the effect is unclear. This number of lags is asking a lot from 45 observations.

[Miskolak]

Do an F-test on all the WTI variables. One possibility is that they are jointly significant even though the timing of the effect is unclear. This number of lags is asking a lot from 45 observations.

Hi.

Thank you for answering.
I've performed the F-test :

Both with the lagged CPI variables and without.

With:
Wald Test:
Equation: Untitled

Test Statistic Value df Probability

F-statistic 3.400585 (9, 39) 0.0036
Chi-square 30.60526 9 0.0003


Null Hypothesis: C(2)=0, C(3)=0, C(4)=0, C(5)=0, C(6)=0,
C(7)=0, C(8)=0, C(9)=0, C(10)=0
Null Hypothesis Summary:

Normalized Restriction (= 0) Value Std. Err.

C(2) 2.962592 0.739124
C(3) 0.673987 0.999427
C(4) 1.421426 0.846617
C(5) -0.430390 0.846766
C(6) -1.080226 0.781683
C(7) -1.230150 0.330308
C(8) -1.106052 0.418544
C(9) -1.043725 0.424922
C(10) 0.111140 0.328871

Restrictions are linear in coefficients.

---------------------------------------------------------
Only WTI variables F-test:

Wald Test:
Equation: Untitled

Test Statistic Value df Probability

F-statistic 3.634809 (5, 39) 0.0085
Chi-square 18.17405 5 0.0027


Null Hypothesis: C(2)=0, C(3)=0, C(4)=0 , C(5)=0 , C(6)=0
Null Hypothesis Summary:

Normalized Restriction (= 0) Value Std. Err.

C(2) 2.962592 0.739124
C(3) 0.673987 0.999427
C(4) 1.421426 0.846617
C(5) -0.430390 0.846766
C(6) -1.080226 0.781683

Restrictions are linear in coefficients.

Representations:
Estimation Command:
=========================
LS DLNCPI C DLNWTI LAG1DLNWTI LAG2DLNWTI LAG3DLNWTI LAG4DLNWTI LAG1DLNCPI LAG2DLNCPI LAG3DLNCPI LAG4DLNCPI

Estimation Equation:
=========================
DLNCPI = C(1) + C(2)*DLNWTI + C(3)*LAG1DLNWTI + C(4)*LAG2DLNWTI + C(5)*LAG3DLNWTI + C(6)*LAG4DLNWTI + C(7)*LAG1DLNCPI + C(8)*LAG2DLNCPI + C(9)*LAG3DLNCPI + C(10)*LAG4DLNCPI

Substituted Coefficients:
=========================
DLNCPI = -0.145886149217 + 2.96259158172*DLNWTI + 0.67398719433*LAG1DLNWTI + 1.4214262122*LAG2DLNWTI - 0.430390321252*LAG3DLNWTI - 1.08022561159*LAG4DLNWTI - 1.23015026663*LAG1DLNCPI - 1.10605172439*LAG2DLNCPI - 1.04372451875*LAG3DLNCPI + 0.111139899233*LAG4DLNCPI



In both F-tests the probabilities are less than 5% , which means that I should reject the null hypothesis.
Meaning that the variables do not affect CPI, which would further on mean that I constructed a regression in which the independent variables (WTI) have no influence on the dependent variable (CPI).

Is there any way to fix this ?

Thank you.

[startz]

I think you misunderstand what the null hypothesis is.

[Miskolak]

I think you misunderstand what the null hypothesis is.

Yeah... sorry about that. I need more sleep.

Coming back to the results.

If I'm thinking right this time. In the F-test I have checked if the coefficient of WTI is equal to 0 which means that the effect on CPI is 0 ( unaffected).
The results from the F-test concludes that I should reject the null ( coefficient = 0 ) meaning that the WTI does in fact affect CPI.

Is my thinking correct ?
Sorry about such a simple mistake.

[startz]

Sounds to me like you've got it!

[Miskolak]

Sounds to me like you've got it!

Thank you so much.
Sorry for wasting your time on something so simple.