Hi I have a panel dataset (for 35 years and 200 panels). For a project I need to estimate a regression of the following form.
$Y_{it} = Y_{it-1}+[\int_{u∈i}\int_{min(T_{uz})}^{max(T_{uz})}h_i(T_{uz})dT_{u}d_{u}]$
Where Y is the dependent variable (denoting total production) and T is the independent variable (denoting temperature deviations during a period z within a longer time period t (i.e. ∈)) for a production unit u within a larger unit i (i.e. ∈). My problem is while I have run linear regressions in the past, I have not dealt with an independent variable that is an integral. I have the data for my temperature variable and need to know how I can calculate this variable?