In my probit model I have a DV measured in t and several independent variables lagged up to 5 years. There also some other independent control variables which are not lagged.

The results do not make any sense as the signs of coefficients of the independent lagged variables vary and only in some of the years the variables have a significant influence. I guess the reason is multicollinearity from the lagged variables.

How do i deal with that problem? Is a specific distributed lag model appropriate even if i can not assume any specific relationship (linear etc.) between the independent variables and the DV over time?