The time-varying parameters vector autoregression models with exogenous variables (TVP-VARX) have become an indispensable tool for modeling time-varying relationships between macroeconomic indicators. At the same time, TVP-VARX models are often outperformed in forecasting by simpler benchmarks due to large parameter space. In order to reduce the number of parameters, we assume long-run monetary policy neutrality for the influence of exogenous shocks on endogenous variables. We propose a novel modification of TVP-VARX incorporating the time-invariant long-run multipliers. We present a Gibbs sampling scheme for Bayesian model estimation. The empirical analysis of quarterly data of real GDP, exchange rate, and real oil prices from Norway and Russia demonstrates significantly better forecasting performance of the proposed model compared to VAR, VARX, and TVP-VARX without multipliers, thus giving indirect support to the long-term neutrality assumption.