Testing for coefficient 0 < C < 1

[Riza Kuria]

Dear all,

I study the banking competition using panel data using xtreg command with 8 independent variables (x1, x2, .., x8).
We get the competition level by adding the first 3 coefficients of independent variables after executing the xtreg
(C = beta1 + beta2 + beta3), which is estimated coeff. of x1 x2 and x3.

C will be <=0 for monopoly, C=1 for perfect competition, and 0<C<1 for oligopoly.

I need to test that C is in an oligopoly or 0 < C < 1.
I tried to search and most use two-step of test
1. Test C=0
2. Test C=1
If these 2 tests reject H0, then we can not reject 0 < C < 1

Is there any other way to test that 0 < C < 1?

Note: C will always be in the range 0 - 1, usually 0.xxx for example 0.009 or 0.123 or 0.445 or 0.998 depend on the xtreg result

Thank you for your help

[Nick Cox]

Your procedure is fallacious for several reasons.

More positively, it would seem much simpler to focus on a confidence interval.

Alternative reading: as you assure us that C will always be in the range 0-1, what is there to test?

[Riza Kuria]

Yes, theoretically the C will be in the range 0 - 1, as also empirical result from previous study.
I read that other researchers use this way:
1. Test C = 0, if not rejected then monopoly
2. Test C = 1, if not rejected then perfect competition
3. If both rejected, then oligopoly

I just wonder how to test the oligopoly directly, which is test 0 < C < 1

Thank you

[Nick Cox]

I remember enough economics to know what monopoly and perfect competition mean. If you have only one seller, you should know that. Otherwise the problem is arguably better posed as one of measurement along a continuum, not testing. I wouldn't trust the empirical sum of three coefficients to behave well given the imperfections of data and a suspicion that a linear model here is purely a matter of convenience or convention. Hence, although not a researcher in this field, my advice remains to think in terms of confidence intervals.

People closer to your field might need references more precise than "other researchers" to comment in detail.

[Riza Kuria]

Yes we use Panzar Rosse to measure banking competition.

We measure the revenue (dependent var) by unit price of labour, fund, and capital (the first three in independent vars)
Then we test the C = coef. of unit price of labour, fund, and capital to determine whether the market in monopoly, perfect competition, or oligopoly

Thank you

[Nick Cox]

You need other advice, as Panzar Rosse means nothing to me, yet naturally means much to you, just as (say) Leopold, Wolman and Miller is to me a major work but I don't expect people to know about it outside those who have worked in one or two Earth sciences.

[William Lisowski]

Welcome to Statalist.

The real point here is that, if what you see in your subject literature is the approach you describe in posts #1 and #3, then that's a better approach for you to take than any alternative suggested by someone on what is largely a software-oriented, rather than finance-oriented, discussion forum. We are probably safe in assuming that, for a 30-year-old paper, any significant improvement in technique would have been long-since created by 30 years of graduate students looking for a dissertation topic.

With that said, while a web search did not turn up an accessible copy of

Panzar, J.C. and J.N. Rosse, "Testing for `Monopoly' Equilibrium," Journal of Industrial Economics, Vol. 35, pp 443-456, 1987.

(which is how you should have shown the reference in post #5 rather than leaving it to the reader to find), it did turn up the following summary of their work, which differs slightly from the approach you describe. (Beyond the fact that it writes Ψ where you write C.)

Basic economic theory suggests values of Ψ that are consistent with different market structures. In particular Ψ will equal unity for perfect competition and will be negative in the case of monopoly. ... Therefore two hypotheses can be tested on obtained values of Ψ. The first hypothesis test is the rejection of perfect competition by rejecting the null hypothesis that Ψ =1. The second hypothesis test refutes monopoly by rejecting a null hypothesis that Ψ<0.

[Riza Kuria]

Hi..
Thank you for your response

It means the approach is already correct
1. Test for Ψ (I called it C) = 1, if we reject then perfect competition is rejected
2. Test for Ψ = 0, if we reject then monopoly is rejected
3. If both rejected, then we are in oligopoly

Thank you

[William Lisowski]

There is a difference between testing for Ψ = 0 and Ψ <= 0. You can reject Ψ = 0 but actually have Ψ < 0 which would be monopoly not oligopoly.

[Riza Kuria]

Thank you for your correction

I think I can still use Stata and test for Ψ = 0, and convert the F test result into t test number and divide p/2 and do the one-tailed test

as explained here https://www.stata.com/support/faqs/s...-coefficients/