## Saturday, November 8, 2014

### Econometric Society World Congress

Every five years, the Econometric Society holds a World Congress. In those years, the usual annual European, North American, Latin American, and Australasian meetings are held over.

The first World Congress was held in Rome, in 1960. I've been to a few of these gatherings over the years, and they're always great events.

The next World Congress is going to be held in Montréal, Canada, in August of 2015. You can find all of the details right here.

Something to look forward to!

### A Reverse Regression Inequality

Suppose that we fit the following simple regression model, using OLS:

yi = βxi + εi   .                                                              (1)

To simplify matters, suppose that all of the data are calculated as deviations from their respective sample means. That's why I haven't explicitly included an intercept in (1). This doesn't affect any of the following results.

The OLS estimator of β is, of course,

b = Σ(xiyi) / Σ(xi2) ,

where the summations are for i = 1 to n (the sample size).

Now consider the "reverse regression":

xi = αyi + ui   .                                                             (2)

The OLS estimator of α is

a = Σ(xiyi) / Σ(yi2).

Clearly, a ≠ (1 / b), in general. However, can you tell if a ≥ (1 / b), or if a ≤ (1 / b)?

The answer is, "yes", and here's how you do it.