{ "cells": [ { "cell_type": "markdown", "id": "d8bd02f6", "metadata": {}, "source": [ "# The Great Moderation: dating a fall in US growth volatility\n", "\n", "One of the most studied facts in modern macroeconomics is the *Great Moderation*: starting in the mid-1980s, the volatility of US real-GDP growth fell sharply and stayed low for two decades. Kim & Nelson (1999) and McConnell & Perez-Quiros (2000) dated the variance break to 1984:Q1, and Stock & Watson (2002) catalogued the breadth of the decline. Here we recover this pattern from the growth series alone, dating the break, quantifying the drop, and tracking the renewed rise in volatility in 2008, without telling the model in advance when anything happened.\n", "\n", "This is a natural application for *bayesloop*, and it makes use of a feature not exercised by the other examples: two parameters that vary in time simultaneously. We model quarterly growth as Gaussian and let both its mean (trend growth) and its standard deviation (volatility) drift in time, driven by two independent random walks that are combined with a `CombinedTransitionModel`. A `HyperStudy` then marginalises over both random-walk step sizes at once, a two-dimensional hyper-parameter inference that is visualised below as a joint posterior, while a `ChangepointStudy` scans every quarter to date the variance break and attach a credible interval to it.\n", "\n", "