A new Keynesian model with unemployment: The effect of on-the-job search

Although new Keynesian models with labor market frictions report an increase in unemployment and a decrease in labor market tightness in response to a positive technology shock, which appears to be in line with recent empirical findings, the volatilities of these variables are not as high as their empirical counterparts. This calls for the introduction of new modeling tools to amplify the volatilities of the unemployment rate and labor market tightness. Along this line, this paper contributes to the theoretical literature by studying the effect of employment-to-employment flow in a new Keynesian model with labor market frictions. We consider two types of firms that offer different wage levels, which incentivize low-paid agents to search on the job. Differently from the existing literature, the main source of wage dispersion is the difference between firms' bargaining powers. The proposed model generates a higher volatility of unemployment and labor market tightness in response to a positive technology shock compared to the model without on-the-job search, without causing a significant change in the responses of other variables.