Diagnosing Failure: When is an Estimation Problem Too Large for a PC?

Sometimes numerical failure of an econometric software package is quite stark: a nonlinear procedure fails to converge; illegal arguments to a function cause an abnormal end; matrices cannot be inverted. Other times a package fails without warning, and these types of failures are particularly pernicious. One such failure in this latter class occurs when a problem simply exhausts the numerical limits of the computer, e.g., attempting to solve a problem that is larger than the computer can handle. In such situations, the user must be conscious that he is nearing the limits of the computer and test carefully to determine whether or not the problem has exhausted the computer's capabilities. Making use of the replication policy of the American Economic Review, we analyze just such a recently-published problem involving an attempt to maximize a 48 parameter nonlinear maximum likelihood problem. We show that the problem, as posed, cannot be reliably solved in double precision on a PC with a 32-bit word.