Why Form 8865 Functional 2024

Up until now, we have only considered linear regressions where both the independent and dependent variables are linear. However, economic relationships are not always linear. For example, when considering the relationship between interest rate and GDP, we may encounter the problem of the liquidity trap. Therefore, the assumption of a linear relationship between interest rate and GDP does not hold. But before discussing that, let's first focus on the linear regression model we have been considering so far, of the form Y = alpha + betaX + Sigma. This model assumes a linear relationship between the variables, where a one unit change in X results in a beta unit change in Y, holding all other variables constant (ceteris paribus). Graphically, when representing this relationship on an XY plane, if beta is less than zero, we have a downward-sloping straight line, and if beta is greater than zero, we have an upward-sloping straight line. Now, let's discuss another functional form called the double log or the log-linear model. In this case, we take the logarithm of both the dependent and independent variables and run a regression, such as log(Y) = alpha + beta * log(X). This functional form is commonly used when examining price-quantity relationships, for example, log(Q) = alpha + beta * log(P) + Sigma. One interesting property of this log-linear functional form is that the elasticity, which represents the rate of change of Y with respect to the rate of change of X, is constant and equals beta. This is why it is referred to as a constant elasticity model. The slope, on the other hand, depends on the specific values of Y and X and is not constant for the entire functional form. The slope coefficient can be interpreted as the percentage change in Y caused by a percentage change in X,...