# Model specification with Deflators: methodological question on forecast model

I am trying to build a model to predict one year ahead Earnings per share $(t+1)$ based on variables in year $t$. I’ve seen a lot of models in practice that use the following methodology:

Earnings(t+1)/#_of_shares(t) ~ x1(t) +x2(t)+x3(t)


and I’m wondering whether

 Earnings(t+1)/#ofshares in (t+1) ~ x1(t) +x2(t)+x3(t)


would be the correct model. I’ve seen researchers doing that with Total Assets as well. Are they doing it because it is simpler and there is less variation when having only 1 variable t instead 2 or is my way of thinking wrong?

Don't mess with the second model--stick with the first one.

### Explanation:

With the first model you only have to worry about Expected Earnings in the next period. In contrast, (as you indicated) the second model is trying to predict two random variables (or, to be more precise, the ratio of two random variables, which complicates your issue even further).

Besides converting your statistical analysis from a "Hard Problem" to an "Incredibly Hard Problem", there are a couple of things to keep in mind:

• This approach has the added benefit of separating issues related to Business Risk from those related to Financing.
• Whereas the level of earnings in a given year will be a function of many different random variables (depending on things like the current state of the economy, consumer preferences, etc.) shares outstanding will entirely depend on the decisions of the board of directors. Hence, it's probably best to analyze these two issues separately.
• Also, keep in mind that you're forecasting the lefthand side of the equation so that you can use it in some model you have today (in period t) . For many of these models, next-period earnings is the missing link (in fact, dividing by shares outstanding is merely a convenience in these models so that you're speaking in terms of share price and not the entire market value of the company's equity).

 Think of, for example, the Gordon Growth Model (Specifically, when deriving "Justified" Price Multiples).

• Yes, I see it from the statistical perspective but judging from an economical perspective I believe the latter would be correct. What worries me is that I've seen models predicting earnings 5 years ahead and still use total assets from 5 years back. But as you said from a statistical point of view I can see why everyone does it. Jul 29, 2014 at 18:34
• @Gritti: Actually, could please you elaborate on why you think that--from an Economics perspective--the latter would be correct? Jul 29, 2014 at 18:57
• Next to the mentioned level regression (EPS) I also tried to forecast future profitability and intuitively you want to forecast actual future profitability (with the most recent deflator) and not a historical/lagged deflator. For instance the deflator doubles in value from year t to t+forecast horizon. To obtain the same profitability you would need earnings to double as well. However if you use lagged deflator your profitability is likely skewed. But that's just my argumentation. If I was totally sure I probably wouldn't have raised the question :D Jul 29, 2014 at 19:08
• @Gritti: As an aside, it's sort of funny because that second equation is, in effect, forecasting expected future trailing earnings and I can't say I've ever heard of that before! Jul 29, 2014 at 19:26
• @Gritti: That's part of the reason why it's not much of an issue--the number of shares outstanding is much more stable than earnings (and is determined by totally different forces). Jul 29, 2014 at 19:59