WEEK 13 & 14 ACTIVITY 9

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University of the Cumberlands *

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Economics

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Feb 20, 2024

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docx

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WEEK 13 & 14 ACTIVITY 9 Name: Akul Patel UC ID: 005011924 Activity I - Suppose Y is a dichotomous dependent variable, and the data-generating process for Y can be expressed as: Y i =0.1+0.03X1 i −0.02X2 i +U i Interpret the coefficients on X1 and X2 Coefficient of X1 and X2 is 0.03 and 0.02 respectively. If coefficient of X1 is positive, there will be a positive relationship between X1 and Y. For a one-unit increase in X1, the log-odds of Y being 1 increase by 0.03 while X2 is constant because Y is a dichotomous variable. Coefficient of X2 is negative therefore there will be a negative relationship between X2 and Y. Increase of X2 by 1 unit will decrease Y by 0.02 unit while X1 is constant. Activity II - Suppose you are trying to learn the relationship between the prices you charge for your product and the likelihood of purchase by individuals offered that price. You offer your product online and for one month have randomly posted prices between $10 and $30. Using data on purchases and prices, you get the following estimates for a linear probability model: Purchase i =1.7−0.06×Price i You are interested in the effect of a $20 price increase (i.e., moving from the lowest price to the highest) on the likelihood of Purchase. Why is answering this question problematic using this model? For 10 dollars: Purchase = 1.7−0.06×10 = 1.1 For 20 dollars: Purchase = 1.7−0.06×20 = 0.5 For 30 dollars: Purchase = 1.7−0.06×30 = -0.01
Thus we can conclude from the above result that for $20 purchase will decline. However, this model does not include other relevant variables that could affect purchase decisions, such as product features, customer demographics, marketing efforts, etc. Omitting important variables can lead to omitted variable bias. Also, for 10 dollar price model gives probability above 1 which shows it is not a meaningful value. For 30 dollar price model gives probability in negative value and it is meaning less thus we can say that answering by using above model is problematic as it does not include various other factor and it violates the probability range of 0 to 1.
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