Public Lectures on Structural Econometrics - CEMMAP masterclass - Shared screen with speaker view
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Quick question: the "weights" are simply the probability of reaching state x_tau in period t+tau when you are in state x and make decision j in period t?
@Emilio: not quite. these weights in principle can be negative (see slide 23 and their definition based on kappa_t and kappa_tau)
@Emilio: these weights "subsume" possibly positive or negative differences between conditional continuation values and the ex ante value which no longer "appear" in the expression for a conditional value. this way you no longer need to compute any value, that is, only static utility and weighted transitions appear in all expression so no maximization is necessary
Arcidiacono and Miller (ECTA, 2011) have a very nice leading example based on Rust (ECTA, 1987) in which this logic is transparently spelled out. Highly recommended!
so in short while normalisation in static discrete choice is wlog, it is not in dynamic discrete choice right?
@GIuseppe: yes, that's right. In fact normalizations in the dynamic case, as normally invoked, are not quite normalizations in the usual sense (ie immaterial level/scale anchoring) since the normalization factors usually depend on endogenous model objects.