A classic application of instrumental variables regression is estimating the elasticity of demand for a product. In our case, the product of interest is cigaretts. In economics, the elasticity of demand is the ratio of the percentage change in quantity demanded to the percentage change in price of a commodity. To express percentage change, we transform the variables using natural logs, so the relationship can be written as follows: lnQ = α + βlnP + ε, where β is the estimate of the elasticity (percentage change in quantity for a 1% change in price). We have observations on price and quantity of cigaretts, and it seems like we could run an OLS regression of lnQ on lnP and obtain an estimate of the elasticity.However, there is a problem. Quantity demanded, apparently depends on price, but price is also determined by market demand. When customers have a high demand, the price tends to go higher. Therefore, because of the causaility going both ways, the elasticity of demand cannot be estimated by an OLS regression of log quantity on log price.
Which of the following best describes the problem as mentioned above?
1.Obmitted variabe bias
2.selection bias
3.endogeneity
Endogeneity is the correct answer. endogeneity refers to the mutual relationship between the variables.
The problem described above is best described as endogeneity. The issue arises because both price and quantity demanded are simultaneously determined by market forces. In this case, the relationship between price and quantity demanded is not a simple one-way causal relationship. Instead, it is a two-way relationship where changes in price affect quantity demanded, and changes in quantity demanded also affect price.
This endogeneity makes it problematic to estimate the elasticity of demand using a regular OLS regression of log quantity on log price. The endogeneity violates one of the key assumptions of OLS regression, namely the exogeneity of the independent variables. Exogeneity assumes that the independent variables are unrelated to the error term in the regression equation. However, in this case, the error term is likely to be correlated with the price variable due to the reverse causality.
To address this endogeneity problem, instrumental variables regression can be used. Instrumental variables are used to "instrument" or substitute the endogenous variable in the regression equation. These instruments are chosen based on their correlation with the endogenous variable and their lack of correlation with the error term.
In the case of estimating the elasticity of demand for cigarettes, an instrumental variable could be something that affects price (such as changes in tobacco taxes) but does not directly affect quantity demanded. By using instrumental variables regression, the bias caused by endogeneity can be minimized, allowing for a more accurate estimation of the elasticity of demand.