Empirical Analysis on U.S. Real Output

The relative importance of permanent (trend) versus cyclical shocks to GDP has been a central issue in macroeconomics since the work of Nelson and Plosser (1982). Morley et al. (2003) find large trend shocks. In contrast, Perron and Wada (2009) argue for a onetime change in the mean growth rate at 1973:1 to be the only trend shock to the post-war U.S. real output.;Chapter 1 presents a joint work with Richard Startz. We re-estimate the Perron and Wada (2009) model conditional on a trend break having occurred at any one quarter. We then average the conditional estimates of the trend variance over the probability that the break occurred in a specified quarter. We do this both by an approximate Bayesian model average in which the conditional estimates are done by maximum likelihood and the date probabilities are found using the Schwarz (1978) approximation to the Bayesian marginal likelihood, and an exact Bayesian analysis which incorporates break date uncertainty into a trend-cycle decomposition of U.S. real GDP. The weight of the evidence supports the Perron and Wada (2009)'s finding of a fairly small trend variance, but the data does not provide very strong evidence against the alternative.;As confirmed in Chapter 1, little evidence has been found for the stochastic trends when researchers allow for adequate number of structural breaks in the growth rates. Therefore deterministic (linear) trends with structural breaks are often proposed to describe the trend component for U.S. real output. In Chapter 2, we examine the effect of unknown structural breaks, including those in the mean growth rate and the covariance matrix, on the evidence of the stochastic trend for the U.S. postwar quarterly real GDP. We use Bayesian approach to compare the stochastic trend models with the deterministic (linear) trend models, allowing for up to four unknown structural breaks in the mean growth rate and/or up to one break in the shocks' covariance matrix. We find evidence for two structural breaks in mean: one around early 1970s, and the other after 2000. Data also identify early 1980s as the date for a volatility reduction. Conditional on the selected break dates, data favors the stochastic trend models over deterministic trend models. Exclusions of the stochastic trends and the effect of ongoing real shocks reported in the literature could be misleading if one ignores the structural breaks in the error variances and covariances.;In Chapter 3, we present evidence for the changing correlation between U.S. trend and cycle GDP in the post-WWII period. Researchers usually assume constant trend-cycle correlation when using unobserved component models to decompose U.S. real output. We introduce the time varying correlation into a UC model with a random walk mean growth rate and stochastic volatilities. We find that the estimated correlation is negative but could be close to zero before 1980s. And it has become more negative since the 1980s till the end of the sample (2012:4). By allowing the correlation to change over time, we are able to reconcile some of the debating results from earlier work. Through counterfactural studies, we show that the change in correlation contributes equally with the reduction in the cycle volatility to the great moderation. As a by-product, we find evidence for a stochastic trend and ongoing permanent shocks. We also find some signs of the grow rate slowdown around 1970 and further reduction around 2005.