Uncertainty Shocks in a Model of Effective Demand

Abstract

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.

Uncertainty shocks in a model with mean-variance frontiers and endogenous technology choices

“…2 The basic neoclassical model is not particularly conducive to studying the effects of second moment shocks. For small values of household risk aversion the effects of second moment shocks are negligible in the basic neoclassical model, while for high levels of risk aversion (as in Basu and Bundick, 2012 ) the effects are not negligible, but then investment and consumption do not comove in response to these shocks -a result which is at odds with the data where there exists strong comovement between consumption and investment. Basu and Bundick (2012) provide an explanation for why the incorrect comovement occurs in the basic neoclassical model.…”

“…For small values of household risk aversion the effects of second moment shocks are negligible in the basic neoclassical model, while for high levels of risk aversion (as in Basu and Bundick, 2012 ) the effects are not negligible, but then investment and consumption do not comove in response to these shocks -a result which is at odds with the data where there exists strong comovement between consumption and investment. Basu and Bundick (2012) provide an explanation for why the incorrect comovement occurs in the basic neoclassical model. It should be noted here that many models in this literature inherit the negative comovement problem and are either unable to solve it or have to appeal to nominal rigidities or additional real rigidities to generate comovements between consumption and investment.…”

“…In both cases the negative correlation is due to a reallocation of inputs across firms with heterogeneous productivity levels. This is in contrast to my model, where the negative correlation is mainly due to 2 Papers in this category include: ( Basu and Bundick, 2012;Bloom, 2009;Bloom et al, 2012;Leduc and Liu, 2012;Mericle, 2011;Narita, 2011 ), andSchaal (2012) who all look at the role of various nominal and real rigidities in transmitting second moment shocks to business cycles. Arellano et al (2012) ; Christiano et al (2013) ; Dorofeenko et al (2008) ; Gilchrist et al (2010) and Fernandez-Villaverde et al (2011) who focus primarily on rigidities and frictions in the financial channel as a way for second moment shocks to have first moment effects.…”

Endogenous fluctuations, markups, capacity and credit constraints

“…First of all, the countercyclical pattern of the markup is also assumed by Basu and Bundick (2012) within an exogenous driven business cycle model. 8 In the second place, (average) fixed costs fall as output expands and this relaxes the borrowing constraints disproportionately more.…”

The consequences of an unknown debt target

“…That literature is mixed on the impact of volatility shocks. Some papers find that higher volatility reduces output (Alexopoulos and Cohen, 2009;Basu and Bundick, 2014;Bloom, 2009;Bloom et al, 2014), while others report little or no impact (Bachmann and Bayer, 2013;Chugh, 2013).…”