Modeling (Optional) 345 where U = ln[Y], = ln[A], and V = ln[X]. So, if Y and X are related to each other by a power function, then the logarithm of Y is a linear function of the logarithm of X, and there is said to be a log-linear relationship between Y and X. For the Cobb-Douglas function, there is a log-linear relation between output, labor, and capital: Q = AK 1 L 2 ln½Q= ln½A + 1 ln½K + 2 ln½L This equation can be estimated by multiple regression procedures with the logarithm of output the dependent variable and the logarithms of capital and labor the explanatory variables. 11.6 Growth Models Many variables (such as income, prices, or population) change over time, and a useful model should take time into account. We can do so by using a variable t, which marks the passage of time. If time is measured in years, we might set t = 0 in 2000, t = 1 in 2001, and so on. If we want to measure time in months, then we might set t = 0 in January 1980 and t = 1 in February 1980. The variable t can be used as a subscript to show the value of a variable at different points