March 9, 2009

Statistics and Economics

I am taking a statistics course this semester. In today's class, we encountered some typical sample inference question like this:

Direct Mailing Company sells computers and computer parts by mail. The company claims that at least 90% of all orders are mailed within 72 hours after they are received. A recently taken sample of 150 orders showed that 129 of them were mailed within 72 hours. Do you think the company’s claim is true? Use the 2.5% significance level.

The method to solve such problems is not difficult, by setting a hypothesis test. The conclusion would look something like “we cannot say that the company’s claim is false”. Ambiguous, isn’t it? The problem is neither can we assure that the company’s claim is true. Actually even the company themselves do not know for sure the integrity of their statement, without incurring ridiculously large costs. It is all theoretical, only depending on what model you believe would be suitable to the particular situation.

In a recent blog post by Greg Mankiw, Are fiscal multipliers now big or small, he pointed out Richard Clarida's and Christy Romer's different conclusions about the current fiscal multiplier in the economy, also citing his own argument previously made. He immediately admits,

that all of these arguments--Clarida's, Romer's, and mine--are essentially theoretical. I don't know of much empirical work on state-dependent fiscal multipliers to establish convincingly which side of this debate is correct.

Again it is a question of what kind of model and intuition are being applied, or chosen, in constituting the argument. We cannot say which hypothesis is correct and which is not.

This is some similarity I found in these two subjects. Not a big statistics fan myself, I still look for the virtues that interest me in this subject. The characteristic stated above is definitely not exclusive for statistics and economics. It is shared by all academic realms which try to make use of speculative methods to explain events in the real world.

p.s.: I came across an interesting quotation today on the newly-acquired mathematical economics textbook:

If you want literal realism, look at the world around you;
if you want understanding, look at the theories.
- R. Dorfman (1964)

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