We construct simple macrodynamic models with policy lag by means of mixed difference and differential equations, and study how lags in policy response affect the macroeconomic (in)stability. Local dynamics of the prototype model are studied analytically, and the global dynamics of the prototype and the extended models are studied by means of numerical simulations. We show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system becomes locally unstable when the policy lag is too long. We also show the existence of cycles and complex behavior in some range of the policy lag.