  Time-Varying Parameters Vector Autoregressive (TVP-VAR) models are frequently
used in economics to capture evolving relationships among the macroeconomic
variables. However, TVP-VARs have the tendency of overfitting the data,
resulting in inaccurate forecasts and imprecise estimates of typical objects of
interests such as the impulse response functions. This paper introduces a
Theory Coherent Time-Varying Parameters Vector Autoregressive Model
(TC-TVP-VAR), which leverages on an arbitrary theoretical framework derived by
an underlying economic theory to form a prior for the time varying parameters.
This "theory coherent" shrinkage prior significantly improves inference
precision and forecast accuracy over the standard TVP-VAR. Furthermore, the
TC-TVP-VAR can be used to perform indirect posterior inference on the deep
parameters of the underlying economic theory. The paper reveals that using the
classical 3-equation New Keynesian block to form a prior for the TVP- VAR
substantially enhances forecast accuracy of output growth and of the inflation
rate in a standard model of monetary policy. Additionally, the paper shows that
the TC-TVP-VAR can be used to address the inferential challenges during the
Zero Lower Bound period.
