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Causal Impact and Statistics II

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Okay, I think I have a fix on this.

Suppose we want to test our hypothesis that otherwise comparable firms with high levels of indebtedness cut back on expenditures desired by employees in circumstances where their not-so-indebted cousins would not. (For a further explanation of that hypothesis, review Part I of this discussion from last week.) How do we do it?

We'll assume that we haven't found a smoking gun memo in which the company's Treasurer writes to the CEO and says, "we can't afford those darn safety vests any longer. Tell Human Resources to stop buying them so we can make the interest payments!" Assume we're looking at circumstantial evidence. What counts as evidence?

What we can't do is simply say: firm X buys safety vests for its employees and is mostly equity financed. Firm Y doesn't and isn't. No matter how many Xs and Ys we find compliant with our hypothesis, we will still have only correlation, not causation. The arrow of causation could go the other way. Maybe the fact that firm Y is a less desirable place to work leaves it with less desirable employees -- the talented ones go to firm X! This has had negative consequences for cash flow and THAT has made it difficult to issue stock successfully, forcing Y into debt. That is the opposite of the causal connection we're looking for, though on its face as plausible.

This is where the idea of a structural time-series model may help us. It involves creating a time series model of a particular firm that includes both changes. It also involves abandoning the idea of comparisons across firms. Just focus on one firm, and build a model of its history, the changes in its debt equity situation over time, and the changes in its labor policy, and which predicts which. Then create an inference based on that model, or what in Bayesian terms is then the "prior." Continue to follow both variables in the life of that firm...

But surely someone has attempted this.
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