THIS SECTION PROVIDES additional details on the data construction and estimation procedure for the empirical evidence from Section 2 of the main text. We estimate our baseline VAR using data on the VXO, GDP, consumption, investment, hours worked, the GDP deflator, the M2 money stock, and the Wu and Xia (2016) shadow rate. To match the concept in the model, we measure consumption in the data as the sum of non-durable and services consumption. Then, we use the sum of consumer durables and private fixed investment as a measure of investment in our baseline empirical model. To match the quarterly frequency of the macroeconomic data, we average a weekly VXO series for each quarter. Thus, our measure of uncertainty captures the average implied stock market volatility within a quarter. We convert output, consumption, investment, and hours worked to percapita terms by dividing by population. Except for the shadow rate, all other variables enter the VAR in log levels.We include four lags in the estimation of the VAR and generate our confidence intervals using the Bayesian method outlined in Sims and Zha (1999).2 Figure A.1 plots the VXO over time as well as the series of identified, structural uncertainty shocks from the VAR. The empirical model identifies large uncertainty shocks after the 1987 stock market crash, the failure of Lehman Brothers, and the euro area sovereign debt crisis.To generate the unconditional moments in Table II of the main text, we detrend the log of each empirical data series using the HP filter with a smoothing parameter of 1600. We measure the unconditional volatility using the sample standard deviation of the detrended variable. We compute the empirical moments over the 1986-2014 sample period, which is the same time frame used in our empirical VAR. In Appendix Section D.3, we provide further analysis of the unconditional moments predicted by the model.We estimate stochastic volatility using a simple model-free and nonparametric method based on rolling sample standard deviations. Given an empirical data series, we estimate a rolling 5-year standard deviation. This procedure provides a time-series of realized volatility estimates for the given data series. Then, we compute the standard deviation of this time-series of estimates. This simple measure provides an estimate of the stochastic volatility in the data series. If the actual data were homoscedastic, the estimates of the 5-year rolling standard deviations should show little volatility and the resulting statistic would be near zero.