Interpretation of coefficient differences across sample groups (please help!?)


New Member

Before I start the whole story, I am going to sumamrize my main question beforehand so the story will hopefully make more sense.

Mainly, I want to now how to interpret the results of a regression which I ran in a manner requested by my professor. Next, I would want to know how to use the wald test in spss to test for significant difference in the coefficient of an independent variable across groups.

I am in despreate need of some help with my thesis. I am researching the effect of stock liquidity (iv) on the acquisition premium (dv) in takeovers. Next to stock liquidity, I have included a number of other independent variables (not sure if this is relevant but market-to-book, market-cap LOG , cash-to-assets, leverage and ROA are scale/numeric and toehold, lockup, equity consideration, and cash consideration are dummys).
Next to this I also run the regression year fixed and industry fixed ( so a dummy for each year and each industry, and I exclude one (my prfessor said it would then be included in the constant... :) )

My hypotheses are 1. to test wheteher overall higher liquidity causes higher acq. premium and 2. whether this relationship holds per different type of acquirer ( i have 3 type of acquirers: public firms, private operating and private equity).

so far so good, i have simply regressed the model 4 times, once for the whole sample and then for each type of acquirer.

Next, I wanted to compare the coeffiecient for liquiidty (others are less relevant) between the type of acquirers. to do so, I ran the regression for the whole sample and included a dummy for the public firm and a dummy for the private operating firm (excluded the dummy for the private equity as it would then be included in the constant). so then I thought the significance of the dummy's could be interpreted as that the groups really do differ (although in abstract, I was already struggling with the idea that this would not only include the effect of liquidity)

Now coems my struggle, the feedback from my prof. was that I need only to run the regression once and include the dummy's for private operating firm and public + also 2 new variables, dummy operating firm*liquidity and dummy public firm*liqudity.

then, to test for significant difference in coefifcients across groups, he said to perform a wald test (this I even could not find in SPSS hahahaha - he uses stata so could not help me)

I did so, however now I really do not know how to interpret the results and how to compute the coefficient for liquidity pre type of acquirer from this regression output? what number gives me the delta of acq. premium for 1 extra unit of liquidity for, say, a private equity firm? also, how to intepret the constants per type of acquirer?

I found this a bit helpfull: however it does not fully cover my interpretation problem (+ coputation is only described for 2 groups)

I have a gutfeeling the computation of constants & liquidity coefficients per type acquirer from this single regression might have something to do with covariance, so I do not want to go that far (actually, I was just wondering on the computation to crosscheck with the separate regression model runs).

So, to summarize my main question:

:wave: How do I interpret the results when running the regression as requested by my professor + how to perform the wald test? :wave:

I would be very thankfull for any help!