F-test

[sofitel_a]

Hello,

Could you suggest me a way of testing the null of: a1=a2=0 against the alternative of: a1+a2<0 using an F-test?

Thanks a lot!

[TomDoan]

F-tests aren't designed to do that. An F test rejects outside an ellipse. If you try to intersect that with a half-space defined by the adding-up constraint, you get a region whose probability can't be calculated using closed form expressions.

[sofitel_a]

Hello Tom,

I'm afraid I've lost you from the second sentence. What is "adding-up constraint" and a "half-space". I know it is possible to define the restrictions on the null, but I was wondering whether it is possible to set up restrictions on the alternative. Is it possible to do this in eViews or using a command in RATS?

Thank you!

[TomDoan]

Your adding-up constraint is a1+a2<0. That defines half the plane if you graph it.

What you're trying to do is highly non-standard---there is no formula which will give the probability of the type of critical region that you need. You would have to figure out exactly what type of critical region you want (which isn't simple since you have to combine two measures of "failure", a1=.01, a2=-.02 is different from a1=10.01,a2=-10.02) and do some type of bootstrapping or simulation to evaluate the critical value.

[naseem]

I am using RATS std 8.0 software. Recently I was reading the RATS Programming Manual to study hypothesis testing section. Sir, at page 11 of this book I got confused in interpretations of the example. The copied example is attached below. Sir, can we reject the null hypothesis, F-statistic (with three degrees of freedom in the numerator and 153 in the denominator) is 2.25276 with a significance level of 0.08449735 at the 5% level of significance or accept the null hypothesis at 10% significance.
The complete example is given below. Please can you guide me in the interpretation which is highlighted in following paragraphs. Thank you.

restrict(create) 3 resids
# 2 3
# 1 1 0
# 4 5
# 1 1 0
# 5 6
# 1 1 0
F(3,153)= 2.25276 with Significance Level 0.08449735
Variable Coeff Std Error T-Stat Signif
***************************************************************************
****
1. Constant 0.015301284 0.056541363 0.27062 0.78704020
2. DRS{1} 0.386719181 0.068502626 5.64532 0.00000008
3. DRS{2} -0.386719181 0.068502626 -5.64532 0.00000008
4. DRS{3} 0.288370925 0.079736678 3.61654 0.00040262
5. DRS{4} -0.288370925 0.079736678 -3.61654 0.00040262
6. DRS{5} 0.155835311 0.074036283 2.10485 0.03690688
7. DRS{6} -0.155835311 0.074036283 -2.10485 0.03690688
8. DRS{7} -0.198914927 0.078523550 -2.53319 0.01229020
Notice that the F-statistic (with three degrees of freedom in the numerator and 153 in the
denominator) is 2.25276with a significance level of 0.08449735. Hence, at the 5%
significance it is possible to reject the null hypothesis and conclude that the restriction is
binding. At the 10% significance,we accept the null hypothesis.

[naseem]

Could you guide me in the testing of equality constraints; the null of: a1=a2 using a F-test?

[TomDoan]

I am using RATS std 8.0 software. Recently I was reading the RATS Programming Manual to study hypothesis testing section. Sir, at page 11 of this book I got confused in interpretations of the example. The copied example is attached below. Sir, can we reject the null hypothesis, F-statistic (with three degrees of freedom in the numerator and 153 in the denominator) is 2.25276 with a significance level of 0.08449735 at the 5% level of significance or accept the null hypothesis at 10% significance.
The complete example is given below. Please can you guide me in the interpretation which is highlighted in following paragraphs. Thank you.

restrict(create) 3 resids
# 2 3
# 1 1 0
# 4 5
# 1 1 0
# 5 6
# 1 1 0
F(3,153)= 2.25276 with Significance Level 0.08449735
Variable Coeff Std Error T-Stat Signif
***************************************************************************
****
1. Constant 0.015301284 0.056541363 0.27062 0.78704020
2. DRS{1} 0.386719181 0.068502626 5.64532 0.00000008
3. DRS{2} -0.386719181 0.068502626 -5.64532 0.00000008
4. DRS{3} 0.288370925 0.079736678 3.61654 0.00040262
5. DRS{4} -0.288370925 0.079736678 -3.61654 0.00040262
6. DRS{5} 0.155835311 0.074036283 2.10485 0.03690688
7. DRS{6} -0.155835311 0.074036283 -2.10485 0.03690688
8. DRS{7} -0.198914927 0.078523550 -2.53319 0.01229020
Notice that the F-statistic (with three degrees of freedom in the numerator and 153 in the
denominator) is 2.25276with a significance level of 0.08449735. Hence, at the 5%
significance it is possible to reject the null hypothesis and conclude that the restriction is
binding. At the 10% significance,we accept the null hypothesis.

The conclusions on that are backwards. You would accept at the .05 and reject at the .10.