The expanding/contracting behavior of monetary macroeconomic models is largely driven by government deficits. Their monetary effects on inflation and monetary growth determine the real value of money (or of government debt) in the long run. Only positive stationary (constant) real values of money guarantees stationary positive levels of output and employment in the long run. Within a generalized class of nonlinear monetary macroeconomic models of the AD-AS type derived from a microeconomic structure with OLG consumers, such economies generically have no stationary equilibria under perfect foresight/rational expectations when tax revenue is income dependent and endogenous (no lump sum taxes) and when the government follows a stationary spending rule. They usually have two balanced stochastic equilibria, an unstable one with positive levels of employment, output, and positive real value of money plus a stable nonmonetary one under hyperinflation (or a monetary bubble). Under the hypothesis of the model, only the stable ones are empirically observable. The paper shows that these properties are true for a large class of AD-AS models including those with a random budget policy rule whose deficit is zero on average. In contrast, such economies have positive stable balanced stationary equilibria if the government policy has a small strictly positive nonrandom demand component in all cases of uncertainty. Among other things, this confirms the long run effectiveness of deficit spending in random economies under rational expectations known from Keynesian theories. The results are derived using techniques from the theory of random dynamical systems which allows a complete theoretical and numerical analysis of the dynamics of random time series and their stability of the nonlinear stochastic model.