The purpose and scientific novelty of this work is to analyze the changes and features of economic agents’ behavior when incorporating wage rigidity into a new Keynesian model under cognitive constraints of agents. The working hypothesis is the assumption that the forecasting of the output gap, inflation of prices and wages occurs with the help of fundamentalist and extrapolation rules. The first rule is based on forecasting the variables under study on the basis of their stationary values. The second rule is based on extrapolation of the latest available data on inflation and the output gap. The weight shares of agents applying these heuristic rules change endogenously, which is the source of endogenous waves of optimism and pessimism. An analysis of the impulse responses of interest rate and technology shocks suggests that a more flexible economy (an economy with flexible wages and rigid prices) is less prone to a spike in the economic cycle caused by waves of optimism and pessimism than a more rigid economy (an economy with rigid prices and wages) due to the inability of agents to respond immediately to exogenous disturbances in rigid conditions. Thus, these shocks cause wave effects in the economy, i.e., cyclical movements, i.e., a rigid economy will be more prone to booms and busts caused by alternating optimism and pessimism than a flexible economy. The model with an imperfect labor market is characterized by an increased concentration of vital forces at the values of 0 and 1, as well as in the mid-distribution compared to the base model. This feature provides a key explanation for the abnormal dynamics of the evolution of variables in this model. It is concluded that the difference between the degree of optimism and pessimism in the base model and in the model with rigid wages and prices is the full trust of agents in the central bank in targeting wage inflation in the absence of the stabilization of this inflation by the bank.