Investment subsidies, in contrast, are paid immediately and therefore serve as a substitute for employment subsidies. This argument, however, has the weakness that it does not explain why the government should not pay out labour subsidies immediately as well, based on future employment as announced by the firms, and raise taxes later in case the firm does not fulfill its employment obligations.
In what follows, we develop a model which gives a different explanation. In this model, union-firm bargaining distorts both employment and investment decisions and leads to an inefficiently low number of active firms. To correct these distortions, the government may use investment and employment subsidies. Our key result is that investment subsidies strictly dominate employment subsidies in this framework.

A Model to Explain the Investment Subsidy Puzzle

In this section, we develop a model which will be used to provide an explanation for the investment subsidy puzzle. We proceed as follows. In 4.1., the basic structure of the model is presented. In 4.2., we discuss the benchmark case of a competitive labour market. In 4.3., we derive the equilibrium with union-firm bargaining.
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The Basic Structure of the Model

There are two groups of agents in the economy: entrepreneurs and workers. Each entrepreneur owns a firm which produces a homogenous numeraire good. The output of firm i is

where Ki and Li are capital and labour employed by firm i. Y is a strictly concave production
function satisfying the standard neoclassical properties. Y(K;L) is common to all firms whereas denotes a firm-specific random output shock; z is a positive parameter. For the economy as a whole, |i is assumed to be uniformly distributed with support [0;1]. For analytical convenience, we normalize the number of entrepreneurs and firms to unity.

Each entrepreneur is endowed with K0 units of capital. This endowment may be used either for investment in the firm or for investment in a foreign capital market where it yields the riskless exogenous interest rate r. The entrepreneurs are assumed to be risk-neutral to rule out potential effects of risk-aversion on investment behaviour. In addition, we asssume that K0 is always large enough to finance investment in the firm. While this assumption is not critical for our results, it simplifies the analysis by ruling out problems arising from the potential bankruptcy of firms.

Investment, employment and production decisions in this model are not taken simultaneously but in a sequence of three stages. At the first stage, the firms choose the optimal level of investment. At the time of this decision, is unknown. As firms are ex ante identical, all firms choose the same capital stock, which will be denoted by (K). At the second stage, the labour market transactions take place. At this time, is still unknown. The number of workers (L) and the wage rate (w) will therefore also be the same for all firms. Note that this particular timing of decisions, where labour market contracts are made after investment decisions have been taken, follows the sequence in the seminal paper of Grout (1984).