Much research studies US inflation history with a trend-cycle model with unobserved components, where the trend may be viewed as the Fed’s evolving inflation target or long-horizon expected inflation. We provide a novel way to measure the slowly evolving trend and the cycle (or inflation gap), by combining inflation predictions from the Survey of Professional Forecasters (SPF) with realized inflation. The SPF forecasts may be treated either as rational expectations (RE) or updating according to a sticky information (SI) law of motion. We estimate RE and SI state space models with stochastic volatility on samples of CPI and GNP/GDP deflator inflation and the associated SPF inflation predictions using a particle Metropolis-Markov chain Monte Carlo sampler. The trend converges to 2% and its volatility declines over time, two tendencies largely complete by the late 1990s.

Countries that specialize in commodity exports often exhibit a correlation between the relevant commodity price and the value of their currency. We explore an explanation for this correlation based on the present-value, monetary model of the exchange rate. An increase in the commodity price leads to an increase in the expected, future policy interest rate and so to an immediate appreciation. We test the model’s over-identifying restrictions for Canada, Australia, and New Zealand. There, controlling for the effect of commodity prices in predicting current and future monetary policy leaves those prices no significant, remaining role in statistically explaining exchange rates.

The all-gap Phillips curve (PC) explains inflation by expected inflation and an activity variable such as output or the unemployment rate, but with both inflation and the activity variable measured relative to their stochastic trends and thus as gaps. We study this relationship with minimal auxiliary assumptions and under rational expectations (RE). We show restrictions on an unobserved-components model that identify the Phillips curve, first with an autonomous output gap and second with output and inflation gaps following a VAR. For the US, UK, and Canada both cases yield all-gap PCs with slopes of the expected signs, but there is little support for the restrictions implied by RE.

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.