## The OPG Regression

By no means all interesting econometric models are regression models. It is therefore useful to see if artificial regressions other than the GNR exist for wide classes of models. One of these is the outer-product-of-the-gradient regression, or OPG

regression, a particularly simple artificial regression that can be used with most models that are estimated by maximum likelihood. Suppose we are interested in a model of which the loglikelihood function can be written as

n

€(9) = (0), (1.27)

t = 1

where €t() denotes the contribution to the loglikelihood function associated with observation t. This is the log of the density of the dependent variable(s) for observation t, conditional on observations 1,…, t – 1. Thus lags of the dependent variable(s) are allowed. The key feature of (1...

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