$8.$ Time series functional forms: Logarithmic form

Suppose an annual time series data set for the years $1950$ through $1987$ was analyzed using OLS to examine the relationship between U$.$S$.$ minimum wage levels and employment in Puerto Rico. The regression results are as follows, with standard errors in parentheses below the slope estimates:

log$($prepopt$)=1\mathrm{.}5(0\mathrm{.}63)0\mathrm{.}123(0\mathrm{.}05)$log$($mincovt$)0\mathrm{.}02(0\mathrm{.}017)$log$($usgnpt$)$

where

prepopt$=$ employment rate in Puerto Rico during year tmincovt$=$ a measure of the importance of the minimum wage relative to average wagesusgnpt$=$ real U$.$S$.$ gross national product $($in billions of dollars$)$ in year t$$R$2=0\mathrm{.}690$R$2=0\mathrm{.}660$

Note: Specifically, mincovt$=($avgmin$/$avgwage$)$avgcov, where avgmin$$is the average minimum wage, avgwage$$is the average overall wage, and avgcov$$is the average coverage rate $($proportion of workers actually covered by the minimum wage law$).$

True or False: Most functional forms used in OLS regressions on cross$-$sectional data cannot$$be used to analyze time series data.

True

False

The estimated elasticity of the employment rate in Puerto Rico, with respect to the variable mincov, is$.$

The t$$statistic for $1($assuming a null hypothesis that $1=0)$ is calculated as $()/(),$ which is$$how the t$$statistic would be calculated when analyzing cross$-$sectional data.