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In this paper, we examine the results of GDP trend–cycle decompositions from the estimation of bivariate unobserved components models that allow for correlated trend and cycle innovations. Three competing variables are considered in the bivariate setup along with GDP: the unemployment rate, the inflation rate, and gross domestic income. We find that the unemployment rate is the preferred variable to accompany GDP in the bivariate setup to obtain accurate estimates of its trend–cycle correlation coefficient and the cycle. We show that the key feature of the unemployment rate that allows for reliable estimates of the cycle of GDP is that its nonstationary component is small relative to its cyclical component. Using quarterly GDP and unemployment rate data from 1948:Q1 to 2019:Q1, we obtain a trend–cycle decomposition of GDP that resembles the conventional CBO estimates; we find positively correlated trend and cycle components.

This paper develops a macroeconomic uncertainty index based on the multistage procedure that combines maximum likelihood and Bayesian estimation methods proposed by Jurado et al. (Am Econ Rev 105(3):1177–1216, 2015). Our approach streamlines the computation of the macroeconomic uncertainty index by specifying a state-space model estimated by maximum likelihood that allows us to obtain in one step the parameters of the model, the dynamic factors, and the forecast errors of the macroeconomic variables used to construct the index. Moreover, we estimate stochastic volatility models on the forecast errors also by maximum likelihood using a density filter that proves to be faster than a Bayesian estimation. After showing that our methodology produces reasonable results for the USA, we apply it to compute a macroeconomic uncertainty index for Ecuador, becoming the first index of this kind for a small developing or middle-income country. The results show that the Ecuadorian economy is more volatile and less predictable during recessions. We also provide evidence that macroeconomic uncertainty is detrimental to economic activity, finding that the responses of non-oil output, employment in the formal sector, and consumer prices to macroeconomic uncertainty shocks are sizable and persistent. Supplementary Information The online version contains supplementary material available at 10.1007/s00181-021-02069-5.

We estimate the natural rate of interest (r*) using a semi-structural model of the U.S. economy that jointly characterizes the trend and cyclical factors of key macroeconomic variables such as output, the unemployment rate, inflation, and short- and long-term interest rates. We specify a monetary policy rule and an equation that characterizes the 10-year Treasury yield to exploit the information provided by both interest rates to infer r*. However, the use of a monetary policy rule with a sample that spans the Great Recession and its aftermath poses a challenge because of the effective lower bound. We devise a Bayesian estimation technique that incorporates a Tobit-like specification to deal with the censoring problem. We compare and validate our model specifications using pseudo out-of-sample forecasting exercises and Bayes factors. Our results show that the smoothed value of r* declined sharply around the Great Recession, eventually falling below zero, and has remained negative since then. Our results also indicate that obviating the censoring would imply higher estimates of r* than otherwise.

We propose a model to nowcast the annual growth rate of real GDP for Ecuador, whose economy lacks timely macroeconomic information for some key variables and has gone through unstable periods due to its dependence on oil exports. Our specification combines monthly information for 30 macroeconomic and financial variables with quarterly information for real GDP in a mixed-frequency approach. Our setup includes a time-varying coefficient on the mean annual growth rate of output to allow the model to incorporate prolonged periods of low or high growth. The model produces more accurate nowcasts of real output growth in pseudo out-of-sample exercises than a nowcasting model that assumes a constant mean real GDP growth rate. We also conduct sensitivity analyses on our nowcasting model within the time-varying mean setup and find that including financial variables can be detrimental to the performance of the proposed model.

This paper develops a method to estimate the U.S. output gap by exploiting the cross‐sectional variation of state‐level output and unemployment rate data. The model assumes that there are common output and unemployment rate trend and cycle components, and that each state's output and unemployment rate are subject to idiosyncratic trend and cycle perturbations. I estimate the model with Bayesian methods using quarterly data from 2005:Q1 to 2018:Q2 for the 50 states and the District of Columbia. Results show that the U.S. output gap reached about negative 4.6% around the years of the Great Recession and was about 0.9% in 2018:Q2.

This paper proposes a framework to estimate the effects of exogenous fiscal policy and oil revenue shocks on the macroeconomic activity of price-taking oil producers. We use a structural vector autoregressive model estimated with Bayesian methods and apply it to the Ecuadorian economy. Specifically, we investigate the effects of unanticipated changes in taxes, government consumption spending, government investment spending, and oil revenues on economic activity. The results show that unanticipated expansive fiscal policy either through taxes or government investment can have positive effects on output. However, contrary to most studies in the literature, consumption spending shocks do not significantly affect gross domestic product. We also find that oil revenue shocks influence all the variables in the model, evidencing the vulnerability of the Ecuadorian economy to fluctuations of oil revenues. Historically, oil revenue shocks have been the most important driving force to move output above or below trend.

This paper proposes a model to nowcast the annual growth rate of real GDP for Ecuador. The specification combines monthly information of 28 macroeconomic variables with quarterly information of real GDP in a mixed-frequency approach. Additionally, our setup includes a time-varying mean coefficient on the annual growth rate of real GDP to allow the model to incorporate prolonged periods of low growth, such as those experienced during secular stagnation episodes. The model produces reasonably good nowcasts of real GDP growth in pseudo out-of-sample exercises and is marginally more precise than a simple ARMA model.

In this paper, we formulate and solve a New Keynesian model with monetary and fiscal policy rules whose coefficients are time-varying and interdependent. We implement time variation in the policy rules by specifying coefficients that are logistic functions of correlated latent factors and propose a solution method that allows for these characteristics. The paper uses Bayesian methods to estimate the policy rules with time-varying coefficients, endogeneity, and stochastic volatility in a limited-information framework. Results show that monetary policy switches regime more frequently than fiscal policy, and that there is a non-negligible degree of interdependence between policies. Policy experiments reveal that contractionary monetary policy lowers inflation in the short run and increases it in the long run. Also, lump-sum taxes affect output and inflation, as the literature on the fiscal theory of the price level suggests, but the effects are attenuated with respect to a pure fiscal regime.

In this paper, we examine the results of GDP trend-cycle decompositions from the estimation of bivariate unobserved components models that allow for correlated trend and cycle innovations. Three competing variables are considered in the bivariate setup along with GDP: the unemployment rate, the inflation rate, and gross domestic income. We find that the unemployment rate is the best variable to accompany GDP in the bivariate setup to obtain accurate estimates of its trend-cycle correlation coefficient and the cycle. We show that the key feature of unemployment that allows for precise estimates of the cycle of GDP is that its nonstationary component is "small" relative to its cyclical component. Using quarterly GDP and unemployment rate data from 1948:Q1 to 2015:Q4, we obtain the trend-cycle decomposition of GDP and find evidence of correlated trend and cycle components and an estimated cycle that is about 2 percent below its trend at the end of the sample.