Author Archives: Andrew

One reason why plans are good

By Andrew · June 12, 2007 10:17 am · Comments (13)

One of the small puzzles of decision analysis is that:

(a) Plans have lots of problems–things commonly don’t go according to plan, plans notoriously exclude key possibilities that the planner didn’t think of, plans can encourage tunnel vision, etc.  But . . .

(b) Plans are helpful.  In fact, it’s hard to do much of anything useful without a plan.  (I’m sure people will come up with counterexamples here, but certainly in my own work and life, not much happens if I don’t plan it.  Serentipitous encounters are fine but don’t add up to much.

Beyond this, one could add that economic activity seems to work well with minimal planning (just enough structure and rules to set up "the marketplace") but individual actors plan, and need to plan, all the time.

This puzzle is particularly interesting to me as I do work in applied decision analysis.

So what’s the solution to the puzzle?

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Statistical inefficiency = bias, or, Increasing efficiency will reduce bias (on average), or, There is no bias-variance tradeoff

By Andrew · April 13, 2007 8:52 pm · Comments (2)

Statisticians often talk about a bias-variance tradeoff, comparing a simple unbiased estimator (for example, a difference in differences) to something more efficient but possibly biased (for example, a regression).  There’s commonly the attitude that the unbiased estimate is a better or safer choice.  My only point here is that, by using a less efficient estimate, we are generally choosing to estimate fewer parameters (for example, estimating an average incumbency effect over a 40-year period rather than estimating a separate effect for each year or each decade).  Or estimating an overall effect of a treatment rather than separate estimates for men and women.  If we do this–make the seemingly conservative choice to not estimate interactions, we are implicitly estimating these interactions at zero, which is not unbiased at all!

I’m not saying that there are any easy answers to this; for example, see here for one of my struggles with interactions in an applied problem—in this case (estimating the effect of incentives in sample surveys), we were particularly interested in certain interactions even thought they could not be estimated precisely from data.

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Truth is stranger than fiction

By Andrew · February 13, 2007 11:06 am · Comments (16)

Robin asks the following question here:

How does the distribution of truth compare to the distribution of opinion?  That is, consider some spectrum of possible answers, like the point difference in a game, or the sea level rise in the next century. On each such spectrum we could get a distribution of (point-estimate) opinions, and in the end a truth.  So in each such case we could ask for truth’s opinion-rank: what fraction of opinions were less than the truth?  For example, if 30% of estimates were below the truth (and 70% above), the opinion-rank of truth was 30%.

If we look at lots of cases in some topic area, we should be able to collect a distribution for truth’s opinion-rank, and so answer the interesting question: in this topic area, does the truth tend to be in the middle or the tails of the opinion distribution?  That is, if truth usually has an opinion rank between 40% and 60%, then in a sense the middle conformist people are usually right.  But if the opinion-rank of truth is usually below 10% or above 90%, then in a sense the extremists are usually right.

My response:

1.  As Robin notes, this is ultimately an empirical question which could be answered by collecting a lot of data on forecasts/estimates and true values.

2.  However, there is a simple theoretical argument that suggests that truth will be, generally, more extreme than point estimates, that the opinion-rank (as defined above) will have a distribution that is more concentrated at the extremes as compared to a uniform distribution.

The argument goes as follows:

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