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fimmtudagur, ágúst 14, 2003
Já góðan daginn og gleðilegt kvöld.
Einar Mar er um þessar mundir á fullu að skrifa BA ritgerð. Hann birtir stundum góða kafla úr ritgerðinni á blogginu sínu. Ekki vil ég vera eftirbátur hans í þessum efnum og birti því hér skemmtilegan kafla úr MSc ritgerð minni. Við grípum hér niður þar sem ég er að fjalla um Koyck umbreytinguna. Sú aðgerð er nauðsynleg til að geta metið seinkuð áhrif markaðsaðgerða á sölu. Ansi hreint magnaður kafli.
The Koyck transformation
The geometric lag model in equation has an infinite number of terms, and the parameters β and Ф are multiplied together, making the model nonlinear in the parameters. Thus, as the model looks in equation (3), estimation seems to be a rather difficult task. One way around the difficulties is to use the Koyck transformation (Leeflang et al., 2000, Hanssens et al., 2001). This involves, lagging equation (3) one period, multiplying by Ф, and subtracting the result from equation (3). Step one and two give,
yt - Фyt-1 = - Ф [α + β(xt-1 + Фxt-2 + Ф2xt-3 + Ф3xt-4 + … ) + νt-1]. (5)
Step three yields,
yt - Фyt-1 = α(1 - Ф) + βxt + (νt - Фνt-1). (6)
Solving for yt gives the Koyck form of the geometric lag,
yt = α(1 - Ф) + Фyt-1 + βxt + (νt - Фνt-1), (7)
or
yt = λ1 + λ2yt-1 + λ3xt + υt, (8)
where λ1 = α(1 - Ф), λ2 = Ф, λ3 = β, and the random disturbance term υt = (νt - Фνt-1).
Thus, the Koyck transformation gives equation (8), which is a linear estimating equation and only three parameters have to be estimated. The current effect of marketing effort is measured by λ3 = β, while λ2 = Ф measures how much of the marketing effort in one period is retained in the next. Thus, Ф is the retention rate. In the second period the cumulative effect has become β + βФ = β(1 - Ф). After t periods the effect is β(1 - Фt)/(1 - Ф), and the long-term effect of marketing effort is β/(1-Ф) (Pindyck and Rubinfeld, 1998; Leeflang et al., 2000).
Já. Þannig hljómaði það.
Skrifin ganga vel. Gagnavinnsla gengur þokkalega. 75% líkur á skilum á réttum tíma.
18:04
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