Effects of Misspecification of Lag Structure in Certain Two- variable Distributed Lag Models.

Distributed lag models are a type of dynamic econometric model often used in demand analysis. Such models take account of the fact that consumers do not respond instantaneously to changes in their economic situation. The Koyck lag model q sub t = lambda q sub (t-1) + beta sub p P sub t + beta sub y Y sub t + epsilon sub t is a particularly simple model form often fitted to data. If Q sub t = log Q sub t, P sub t = log P sub t, Y sub t = log Y sub t where Q sub t, P sub t, Y sub t are quantity, price and income data, respectively, then beta sub p, beta sub y represent one-period price and income elasticities of demand, while {beta sub p} over {1 - lambda}, {beta sub y} over {1 - lambda} represent long-term price elasticities and income elasticities, respectively. This paper considers data generated by a model in which q sub t has different geometrically declining responses to changes in P sub t and Y sub t, specified by parameters lambda sub 1, lambda sub 2, respectively. It determines large sample biases in elasticity estimates arising from incorrectly fitting either a static model or a Koyck lag model to such data using ordinary least squares.