Historians have suggested there were waves of inflation or price revolutions in the UK (and earlier England) in the 13th, 16th, and 18th centuries,
prior to the ongoing inflation since 1935. We study retail price inflation since 1251 and model its dynamics.
The model is an AR(n) but allows for gradually evolving or drifting parameters and stochastic volatility.
The long-horizon forecasts suggest only one inflation wave, that of the 20th century.
We also use the model to measure inflation predictability and price-level instability from the beginning
of the sample and to provide measures of real interest rates since 1695.
An SVAR in US federal spending, federal revenue, and GDP is
a standard setting for the study of the impact of fiscal shocks.
An appealing feature of identifying a fiscal shock with an external instrument
(proxy variable) is that one can find the effects of that shock without fully identifying the SVAR.
But we show that fully or almost fully instrumenting the SVAR allows one to
overidentify the model by incorporating the condition that
the structural shocks are uncorrelated (via GMM).
Over 1948-2019 the overidentifying restrictions are not rejected. The overidentified SVAR yields (a) greater precision in estimating impulse response functions and multipliers
and (b) measures of the effects of output shocks even when there is no instrument for them.