We revisit the question about whether a larger public sector stabilizes or destabilizes the economy. Based on results from two causal identification approaches, we show that a higher rate of public-sector employment reduces volatility in, i.e. stabilizes, private-sector employment growth, with at most a slight crowding-out of private employment. Public wages, meanwhile, increase private wages but appear not to be destabilizing. The stabilizing effect of public employment with limited crowding out is at odds with standard search and matching models that contain a public sector, which predict 1:1 crowding out and strong destabilization. To improve the performance of such models, we follow Gomes (2015) and add a product market that can replicate what Gomes calls the Business Cycle Wealth Effect. We also point out that the government procures output directly from the private sector. When the model has these two features, then it can generate stabilizing effects of public employment on private employment, with reduced crowding out.