This paper is about the labour market consequences of creative destruction with on-the-job search. We consider a matching model in an economy with embodied technological progress and show that its dynamics are profoundly affected by allowing on-the-job search. We obtain that the elasticity of unemployment with respect to growth shrinks from 1.63 to 0.13. Moreover, the underlying transmission channels change as the flow of obsolete jobs practically disappears and is replaced by a flow of job-to-job transitions. These effects persist even if employed job seekers are significantly less efficient in the search process than the unemployed. Thus, we show that, rather than contributing to unemployment, creative destruction induces a direct reallocation of workers from low to high productivity jobs. These results could be strengthened by assuming that search efforts are unobservable by firms which induces more on-the-job search. However, the action of worker is no longer surplus maximizing and, hence, the worker’s welfare is increasing in the cost of search which acts as a commitment device. Finally, we show that the model could be extended by allowing for variable search intensity
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