### Here's what Harold Pollack's been tweeting about

**Matthew Martin**1/23/2014 10:23:00 PM

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To a certain extent, we're just witnessing an example of the prosecutor's fallacy--people are looking at the probability of an Obamacare enrollee was previously insured as evidence that it isn't working, without taking into account the prior probability of any individual, enrolling or not, having insurance. As Pollack points out nearly 80 percent of the population is previously insured, so the fact that most of the Obamacare enrollees are insured is, in fact, nothing out of the ordinary.

Pollack's actual rebuttal is a bit more mathematical, however:

If reporters would explain that individual coverage status is a continuous-time Markov process we would have a much better discussion.

— Harold Pollack (@haroldpollack) January 23, 2014

I don't know why he jumps to continuous time here--in my experience almost any continuous-time model can be turned into a substantially more tractible discrete-time model (and by the way, data reports aren't generated in real time, so discrete time really is more realistic). So, let's illustrate Pollack's point with a discrete-time markov process. It's discrete time, so we will talk in terms of "periods" of time, which may correspond to weeks or months or years or whatever. In each period, each individual exists in exactly one of three possible states: they either have employer sponsored health insurance (employer), are enrolled in an obamacare exchange (exchange), or else they have no insurance (uninsured). In reality, other possibilities exist, but they don't really change anything here so lets stick to those for simplicity. Now, let's specify a transition matrix:

Period t State | ||||

Period t+1 State | Employer | Exchange | Uninsured | |

Employer | 0.8 | 0.8 | 0.1 | |

Exchange | 0.2 | 0.1 | 0.1 | |

Uninsured | 0 | 0.1 | 0.8 |

So the bottom line is that Pollack is absolutely right: the high percentage of "previously insureds" isn't an aberration to be worried about--it's not only consistent with Obamacare's goal to increase insurance coverage, it's exactly what everyone should have expected in the first place.