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BUS 10123 Lecture Notes - Lecture 33: Dependent And Independent Variables, Probit, Normal DistributionExam


Department
Business Administration Interdisciplinary
Course Code
BUS 10123
Professor
Eric Von Hendrix
Study Guide
Final

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Ordered Probit Results for the Determinants of Credit Ratings
Analysis of Ordered Probit Results
The key finding is that the SOL variable is positive and statistically significant in Model 1
(and it is positive but insignificant in Model 2).
This indicates that even after accounting for the financial characteristics of the firms,
unsolicited firms receive ratings on average 0.359 units lower than an otherwise
identical firm that had requested a rating.
The parameter estimate for the interaction term between the solicitation and Japanese
dummies (SOL*JP) is positive and significant in both specifications, indicating strong
evidence that Japanese firms soliciting ratings receive higher scores.
On average, firms with stronger financial characteristics (higher interest coverage,
higher return on assets, lower debt to total capital, or a lower ratio of short term debt
to long term debt) have higher ratings.
The Heckman 2-Step Procedure
A major flaw that potentially exists within the above analysis is the self-selection bias or
sample selection bias that may have arisen if firms that would have received lower
credit ratings (because they have weak financials) elect not to solicit a rating.
If the probit equation for the determinants of ratings is estimated ignoring this potential
problem and it exists, the coefficients will be inconsistent.
To get around this problem and to control for the sample selection bias, Heckman
(1979) proposed a 2-step procedure.
In this case would involve first estimating a 0-1 probit model for whether the firm
chooses to solicit a rating and second estimating the ordered probit model for the
determinants of the rating. The first stage probit model is
where Yi = 1 if the firm has solicited a rating and 0 otherwise, and Yi* denotes the latent
propensity of issuer i to solicit a rating, Zi are the variables that explain the choice to be
rated or not, and
are the parameters to be estimated.
The Heckman 2-Step Procedure
When this equation has been estimated, the rating Ri as defined above in will only be
observed if Yi = 1.
The error terms from the two equations,
i and
i follow a bivariate standard normal
distribution with correlation

.
The table on the following page shows the results from the two-step estimation
procedure, with the estimates from the binary probit model for the decision concerning
whether to solicit a rating in panel A and the determinants of ratings for rated firms in
panel B.
The Heckman 2-Step Procedure: Results
The Heckman 2-Step Procedure: Analysis
A positive parameter value in panel A indicates that higher values of the associated
variable increases the probability that a firm will elect to be rated.
Of the four financial variables, only the return on assets and the short term debt as a
proportion of total debt have correctly signed and significant (positive and negative
respectively) impacts on the decision to be rated.
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The parameters on the sovereign credit rating dummy variables (SOVAA, SOVA and
SOVB) are all significant and negative in sign, indicating that any debt issuer in a country
with a high sovereign rating is less likely to solicit its own rating from S&P, other things
equal.
The Heckman 2-Step Procedure: Analysis (Cont’d)
These sovereign rating dummy variables have the opposite sign in the ratings
determinant equation (panel B) as expected, so that firms in countries where
government debt is highly rated are themselves more likely to receive a higher rating.
Of the four financial variables, only ROA has a significant (and positive) effect on the
rating awarded.
The dummy for Japanese firms is also positive and significant, and so are three of the
four financial variables when interacted with the Japan dummy, indicating that S&P
appears to attach different weights to the financial variables when assigning ratings to
Japanese firms compared with comparable firms in other countries.
Finally, the estimated correlation between the error terms in the decision to be rated
equation and the ratings determinant equation,

, is significant and negative (-0.836),
indicating that the results in table 11.3 above would have been subject to self-selection
bias and hence the results of the two-stage model are to be preferred.
Censored and Truncated Variables
Censored or truncated variables occur when the range of values observable for the
dependent variables is limited for some reason.
Unlike the types of limited dependent variables examined so far, censored or truncated
variables may not necessarily be dummies.
A standard example is that of charitable donations by individuals.
It is likely that some people would actually prefer to make negative donations (that is, to
receive from the charity rather than to donate it), but since this is not possible, there
will be many observations at exactly zero.
So suppose, for example that we wished to model the relationship between donations
to charity and peoples' annual incomes, in pounds.
Censored and Truncated Variables (Cont’d)
Given the observed data, with many observations on the dependent variable stuck at
zero, OLS would yield biased and inconsistent parameter estimates.
An obvious, but flawed, way to get around this would be just to remove all of the zero
observations altogether, since we do not know whether they should be truly zero or
negative.
However, as well as being inefficient (since information would be discarded), this would
still yield biased and inconsistent estimates.
This arises because the error term in such a regression would not have an expected
value of zero, and it would also be correlated with the explanatory variable(s).
For both censored and truncated data, OLS will not be appropriate, and an approach
based on maximum likelihood must be used, although the model in each case would be
slightly different.
We can work out the marginal effects given the estimated parameters, but these are
now more complex than in the logit or probit cases.
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