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According to this article, calculating elasticity of demand for different models is:

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I generate data for 5% reduction in prices with a corresponding 10% increasing in sales: price elasticity = (+10%/-5%)=-2 and get different result coefficient from linear model.

price <- double(length = 10L)
price[1] <- 200
for(i in 2:10)price[i] <- price[i-1]*.95 # price sequence with step =  -5% of last value
sales <- numeric(10)
sales[1] <- 1000
for(i in 2:10)sales[i] <- sales[i-1]*1.1 # sales sequence with step =  +10% of last value
plot(price,sales,type="b")
+.1/-.05 #price elastic = -2
m <- lm(log(sales)~log(price))
coef(m) #price elastic = -1.858141 it's not equal -2
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  • $\begingroup$ The data you constructed used the Level-Level transformation, while the model you estimated used the Log-Log transformation. Therefore, your model is not the same as the data-generating process, which implies that you are not estimating the parameters of the data generating process. $\endgroup$
    – jbowman
    Commented Feb 4 at 2:07

1 Answer 1

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If $P2=P1*0.95$ then $P3=P2*0.95=P1*(0.95)^2$. So if $P1=100$ then $P2=95$ and $P3=90.25$ which isn't a 5% price step. I think your data generating process is incorrect which leads to a price elasticity from the model that doesn't match what you think it ought to be ($\frac{0.1}{-0.05}=-2$). As for the latter question, I do not have an answer for the price elasticity extraction in trend-seasonality problem.

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  • $\begingroup$ Ok, as @Brennan suggests: (price.index <- seq(from=1,by=-.05,length.out =20)) (price <- 200 * price.index) # price sequence with step = -5% of BASE(!) value (sales.index <- seq(from=1,by=.1,length.out =20)) (sales <- 1000*sales.index) # sales sequence with step = +10% of BASE(!) value plot(price,sales,type="b") +.1/-.05 #price elastic = -2 m <- lm(log(sales)~log(price)) coef(m) #price elastic = -0.3516593 it's not equal -2 $\endgroup$
    – Edvardoss
    Commented May 18, 2021 at 9:33

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