We have a case of the classic debate.

**Are sustainable companies rewarded for their good deeds by grateful stakeholders who bestow revenues, profits and lofty stock prices? Or, are profitable companies eager to give back because they are grateful for their good fortune?**

Before you think “*who cares?” *let me remind you that Clive Granger received a Nobel Prize for his efforts developing a causality test that could statistically answer the chicken or the egg debate.

**Correlation vs. Causation:**

*Post Hoc, Ergo Propter Hoc* is Latin for *“after this, therefore because of this*“. In fact, *Post Hoc, Ergo Propter Hoc* is the logical fallacy that occurs when one assumes that because one event precedes another, the first event causes the second. It is the exact mistake of assuming causation because of correlation.

Nine times out of ten, sustainability is correlated with profitability. But what about causation?

The implications are tremendous.

Should an “average” company employ methods used by **Patagonia**, **CVS Health** or any of the myriad of sustainable exemplars in attempt to mimic results? Or will they fail to be amply rewarded for these efforts, given that they are “only average”?

I have touched on this before: **are we only seeing sustainable efforts from those who can afford to implement?**

Here’s why this is important. If stakeholders do not reward sustainability, then implementation of corporate sustainability will be restricted to a small set of companies that can afford to be generous. The average company will not be motivated, or able, to implement sustainability, because in a competitive environment the extra costs could very well run that company out of business.

We must determine causation.

Mathematics is limited, as the field deals with relationships of certainty: known cause and effect. Two plus two always equals four. But if we venture into the field of statistics, we open doors to uncertainty.

This may sound simple. All one needs to do is compare a company’s profitability before said company implements sustainability with the company’s profitability after. For the more statistically-inclined, a regression would look something like this: [You will notice we are transforming P(t) with natural logs so as to model percentage change.]

LN P(t) = a + b LN P (t-1) + c (Sustainability Effort) + d (Industry/company factors) + e.

Ceteris paribus, if profitability rises proportionately in response to sustainability, and there is no autocorrelation, (an absence of autocorrelation would imply profitability growth in the preceding period is not related to profitability growth in the current period), then we can reasonably conclude that the causation of increased profitability is sustainable efforts. In fact, this is exactly what many academic studies have attempted to prove.

Given the above scenario, if we examined our database and found that “average” companies’ bottom lines increased atypically, we would have our answer.

But it’s not so simple.

**Consider the notion that “doing good” and making money are simultaneous events.**

Perhaps management expects to exceed targets and therefore invests a small portion of the “extra” in sustainable efforts. *Is it possible that a company anticipating 20% earnings growth might decide to spend 2% on “giving back” in the interim, especially if the average company may only be delivering 10%? *Absolutely.

This scenario would replicate what we saw above, yet the implication is vastly different. The former represents a company that increased profitability *as a result of* sustainability. The latter represents a company that only implemented sustainability because it believed such implementation would augment profits at an above average rate. The 20% growth company’s profits would have increased with or without sustainable initiatives. In fact, the 20% growth company only grew 18% after giving back.

One could even point to principal-agency theory: management’s preference was to invest in sustainability and accept an 18% return, whereas the shareholders might have preferred a 20% return. Yet, had this company been included in our regression, it would appear a poster-child for sustainability with abnormally high 18% growth and a healthy sustainable effort. We would have erroneously concluded that profitability was due to sustainability, when in reality it was the exact reverse.

If only we could adjust for expectations.

Oh wait. We can.

By and large, management owns company shares for one reason: expectation of above average share price growth.

If we insert some variable (i.e. percentage of management ownership) into our regression and find that companies with large management stock ownership pursue superior sustainable efforts, we might conclude that these companies are investing excess profits in sustainability. This would suggest that profitability is causing sustainability. And vice versa.

I throw down the gauntlet to my readers. Is it possible an expectations theory could shine light on causality of sustainable actions?

We already know the study of expectations and causality has resulted in Nobel Prizes, so your time won’t be wasted.

Excellent post, TSI! I’m not quantitatively inclined (not that much, anyway). So what do the variables “a”, “b” and “e” represent?

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Greensportsblog: The TSI post is entirely correct in its Model. The coefficients a and b represent the percentage change of the independent variable for which they precede. In a log-log transformation, as correctly stated, the underlying variables are converted to a percentage, so a coefficient of 4 in front of the variable P(t-1) would indicate that a 1 percent change in a previous year’s profitability would yield a 4 per cent change in P(t). The (a) coefficient can be thought of as the level of profit increase in the system. The e is the unexplained variance in the system. To be concrete, let us say the predicted equation looks like this:

LN P(t) = 5 + 2LN P(t-1) + 1LNS(t-1) – this would indicate that for a company which has a 3% growth in Profits in the preceding period and a 2 percent growth of sustainable spending, that one would expect a 5 + 2×3 + 2 or a 13 percent profit growth in the current period. One might also conclude that the sustainability efforts suggest increased profits if the coefficient in front of the sustainability variable is positive and statistically significant.

The robust form of this model might have several previous years of profit growth and several previous years of sustainable expenditures. The test to run would be an F test as to whether the sustainability variaiables are significant in their entirety – and then that would say you could not rule out causality of sustainability. That is the basis of the Granger causality test as I understand it.

Hope that helps

Peter

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Peter: thank you for the detailed response! You hit the nail on the head. And yes, I 100% agree with you, a multi-factor model and lagged time periods would be helpful to ascertain causality for the sustainability proxies. In my post, I was attempting to portray the most simplified regression possible.

Does Peter’s explanation make sense greensportsblog?

Thank you both for following along.

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