Understanding Fama Macbeth Regressions of Returns

Question

I'm trying to understand what the Fama-Macbeth regressions of returns actually mean. The source of confusion is a 2013 Novy-Marx paper, in which he states the following:

"The first specification of Panel A shows that gross profitability has roughly the same power as book-to-market predicting the cross section of returns ... The second and third specifications replace gross profitability with earnings-to-book equity and free cash flow-to-book equity, respectively. These variables have much less power than gross profitability"

The corresponding table is here, with info highlighted. Up to this point, my understanding is that the highlighted numbers are the monthly (annual?) Fama-Macbeth regressions of returns.

He then goes on to state the following:

Appendix A.2 performs similar regressions employing alternative earnings variables. In particular, it considers earnings before interest, taxes, depreciation, and amortization (EBITDA)... These regressions show that EBITDA-to-assets [has] significant power predicting the cross section of returns, but that gross profits-to-assets subsumes [its] predictive powers

However, Table A2 (pic 2) shows a different story, with the value of EBITDA/assets greater than GP/assets.

Can someone explain where I'm having a gap in understanding? It seems that EBITDA/assets in his study results in stronger returns, yet his wording and explanation makes it seem the opposite. I am also not sure what the highlighted numbers even mean. Do they signify abnormal returns from certain variables? Or something totally different?

"The other side of value: The gross profitability premium" is the study in question.

Answer 1

First, you are right that monthly return data is used. Table 1 concludes, that a one unit increase of gross profitability accounts for an additional 0.75% stock return per month after controlling for book-to-market ratio, size, stock reversal ($r_{1,0}$) and momentum ($r_{12,2}$).

Table A2 is based on the following statement on p.17:

Table A2 shows results of Fama and MacBeth regressions employing gross profits-to-assets into EBITDA-to-assets and XSGA-to-assets. [...] The table shows that both variables have power explaining the cross section of average returns, either individually or jointly. [...] The table also shows that while XSGA-to-assets has no power to predict returns in regressions that include gross profits-to-assets, EBITDA-to-assets retains incremental power after controlling for gross profitability.

So in fact, Earnings before interest, taxes, depreciation, and amortization (EBITDA) is gross profits minus operating expenses, which largely consist of selling, general, and administrative expenses. Table A2 shows this decomposition, that EBITDA-to-assets drives profitability more than XSGA-to-assets does, but both are economically and statistically very significant drivers of the profitability anomaly.

The first specification (1) in Table A2 is the same is shown in Table 1. Specification (2) and (3) show the decomposition of gross profitability from specification (1) (which is EBITDA minus operating expenses. The latter mainly consists of selling, general, and administrative expenses (XSGA); all scaled by assets). The 0.75% increase in monthly stock returns can therefore be subsumed in an underlying increase of 1.42% (accounting for EBITDA-to-assets) and an underlying decrease of 0.65% (accounting for XSGA-to-assets). Both account for the shown gross-profitability effect from specification (1).