A probit model to explain whether a firm is taken over by an

A probit model to explain whether a firm is taken over by another firm during a given year is:

where takeover is a binary response variable, avgprof is the firm’s average profit margin over several prior years, mktval is market value of the firm, debtearn is the debt-to-earnings ratio, and ceoten, ceosal, and ceoage are the tenure, annual salary, and age of the chief executive officer, respectively.

1)Question: Explicitly write down the null hypothesis that, other factors being equal, variables related to the CEO have no effect on the probability of takeover. What kind of test will you use to test this null hypothesis?

Suppose you suspect that the variable mktval is endogenous. The logic is that when a firm’s market valuation is very low, the market anticipates that the probability of this firm being taken over is high; after factoring in this expectation, the market valuation of the firm will increase. In other words, mktval depends on the probability of takeover.

In order to deal with this endogeneity issue, you decide to run an instrument variable regression on the probit model. The key is to find an instrument for the endogeneous variable mktval.

2)Question: What conditions should the proposed instrument satisfy?

Solution

Ho:there is no effect among the factors i.e., the variables related to CEO.

H1:there is an effect among the factors i.e., the variables related to CEO.

So we use ANOVA test i.e., F-test.