In the preceding analysis, both models were harmonised so that the steady state of both models was identical. In addition, the Hosios condition Hosios (1990) has been imposed, so that the real friction due to search should be neutralised in the steady state.19
In this section, we explore the role of search frictions and labour market volatility on the outcomes of the permanent increase in government investment. We do so by exploiting the findings of Hagedorn and Manovskii (2008), who show that - in the presence of sticky wages - a smaller labour firm surplus helps overcome the Shimer puzzle (Shimer, 2005).20 By lowering the labour firm surplus, we can investigate whether making the labour market more reactive in terms of the extensive margin materially affects the outcomes of our experiment. We consider three cases: the benchmark case that we compared with the standard model above, a case with labour firm surplus halved (we call it a "Low surplus" case), and a case with labour firm surplus of approximately 20% of the surplus in the benchmark case ("Very low surplus" case)21
The reason why this experiment is interesting is because a delayed increase in (productive) public investment is akin to a news shock about future productivity, which has been a subject of a number of papers in the past, both in terms of empirics (Beaudry and Portier (2006)) and theory (Jaimovich and Rebelo (2009), Den Haan and Kaltenbrunner (2009), Den Haan and Lozej (2011)). One of the main issues in that literature was whether a news shock about future productivity can cause a so-called Pigou cycle, where output, consumption, investment, and labour jointly increase in the period before the shock materialises. In our setting, this question is particularly interesting when we have planning delays, because such a delay is closest to a news shock: households and firms find out today that productive public capital will be higher in the future, but only after some time. During this time there will be no demand stimulus because of the planning delay (construction delay is different, as there is a demand stimulus during this period; we consider this case in Appendix C).
The results of planning delays with varying degrees of search frictions are shown in Figures 5 and 6. Figure 5 shows the main macroeconomic aggregates and Figure 6 shows the main labour market variables. In each figure, the first column shows the benchmark results and the remaining two columns show the results of alternatives. First, note that in the benchmark case, there is no "Pigou cycle", as output and labour services (the latter due to the fall in hours worked) do not increase during the delay period, and the increase in private investment is meager. If the labour market is more volatile than in the benchmark case, then we do observe a small increase in output and labour services (the
19Note that our model features the choice of hours worked (see Appendix B, in particular equation 70). Because in equation 70 αH is less than 1, the hours production function is concave, and the marginal revenue for the firm from an additional hour supplied is αHxs,t(hs,t)αH-1. This nonlinearity matters, see e.g. Kudoh and Sasaki (2011) or Mangin and Julien (2021). In the model used here, this nonlinearity is not very strong, as αH is already close to 1.
20Recall, Shimer (2005) pointed out that a standard search model has difficulties generating realistic volatility in unemployment and vacancies.
21We implement the lowering of surplus by raising the number of hours worked in the steady state towards 1, which reduces the labour firm's surplus, as it reduces the margin it earns from buying labour from households and selling it to intermediate goods firms.