Is investment always lower, if it precedes the wage bargain?

It is known from Grout (1984) that if the investment decision by the firm precedes the wage bargain, it will be unable implicitly to share the cost of capital with its workforce through negotiating a lower wage, and that this leads to under-investment. However, in a model, where there is asymmetric information of firms’ differing levels of productivity and where workers are mobile between firms before but not after the wage bargain, firms may invest also to signal their relative productivities in order to attract workers. Thus, asymmetric information leads to an additional over-investment effect that may outweigh the under-investment effect of the hold-up, so that the capital stock may be higher if investment precedes the wage bargain.