Cumulative Density Function - Probabilities with Probit

[nickij]

Hello,

I am using a probit model to assess the predictive power on bond term-spreads in relation to real economic activity. I have estimated all the variables etc, and now I wish to construct a probability table which is intended to showcase the probability of a recession given a certain level of the term-spread.

However I am having trouble calculating this and I have no idea why as I am fairly used to utilize the Z-table.

In my econometrics book there is an example where the authors have estimated (Probit) two variables;

C = -1.0166
X = 0.04846

where X = Income. The idea of the example is to estimate the probability of owning a house given a certain income. The example continues with X = 6 (thousand dollars). They find the normal density function at f[-1.0166 + 0.04846*(6)] = f(-0.72548).

The authors then continues to state that "if you refer to the normal distribution table you will find that for Z = -0.72548, the normal density is about 0.3066. I am unable to get this value, even with interpolation.

From the Z-table I get
0.72 = 0,2642
0.73 = 0,2673

No matter how I treat the numbers I do not end up with 0.3066. Any help is appriciated as to how I am supposed to treat the numbers in order to get 0.3066.

After this it is straightforward as they take the normal density of 0.3066 and multiplies by the beta coeficient (X = 0.04846) and end up with a probability of 0.01485, i.e. starting with an income of $6000, if the income goes up by 1000, the probability of purchasing a house goes up by about 1.48%.

-Thanks

[EViews Glenn]

I'm not certain where you are getting your table results. I thought it might be that you were using the cumulative rather than the density, but the closest I can get to your result is...

Code: Select all

=@cnorm(-.73)

which equals 0.2327, which is close to, but not equal to your 0.26 result.

In any event, what you want to do is touse the @dnorm function. You should be able to verify that

Code: Select all

=@dnorm(-0.72548)

is 0.3066.

[nickij]

Thanks for the help Glenn!

Also I was using the NORMDIST command in excel to get my result.

Do you compute the @dnorm(-xxxx) in eviews? I am not really an advanced user so just wondering where I should type the command? Is there a similar command in excel?

What I have done, as explained above, was that I ran a probit on term-spreads with different quarterly lags to find the predictive power in the yield curve on real-economic growth. What I also wanted to do, was to calculate the probability of a recession for a given term-spread on a 4 quarter lagged basis.

So I estimated my probit model in Eviews, and once I had the coefficient values (bo and b1) I took these values and used different spreads which I put in the model. EX. if b0 = 1 and b1 = 2 and I wanted to check the probability of a recession given a 4% term spread I'd compute:

1 + 2*4 = 9

Then I'd do the NORMDIST(9) to compute the probability of a recession given a termspread of 4%. However I am somewhat uncertain if this is the way to do it, and if I am even using the correct distribution.

Thanks again, very much appriciated!

[EViews Glenn]

@dnorm is computed using... @dnorm... :)

The probabilities you are interested in are computed using the @cnorm function in a probit specification. You should take a look at the manual (or any good book describing probit models) for additional detail.

As to NORMDIST my quick firing up of Excel suggests that there are other arguments that need to be passed to Excel which would explain the discrepancies...

[nickij]

Cheers Glenn! You're a lifesaver