Temporary replacement workers in a matching model with employment at will

In the US almost 3 per cent of employees are absent from their job for reasons other than vacation, but are still technically employed. We argue that firms may find optimal to use temporary replacement workers to fill these vacant positions. We set up a matching model with directed search and double-sided heterogeneity. When a workers is temporarily forced out of the labour market, firms can freely destroy the job, put it in "mothball", or look for a temporary worker to "keep the seat warm". When the latter option is optimal, a market for temporary replacement workers emerges in equilibrium. In a quantitative application to the US labor market, replacement workers represent 2.7 per cent of total employment.