Econometrics

This paper improves the existing literature on the shrinkage of high dimensional model and parameter spaces through Bayesian priors and Markov Chains algorithms. A hierarchical semiparametric Bayes approach is developed to overtake limits and misspecificity involved in compressed regression models. Methodologically, a multicountry large structural Panel Vector Autoregression is compressed through a robust model averaging to select the best subset across all possible combinations of predictors, where robust stands for the use of mixtures of proper conjugate priors. Concerning dynamic analysis, volatility changes and conditional density forecasts are addressed ensuring accurate predictive performance and capability. An empirical and simulated experiment are developed to highlight and discuss the functioning of the estimating procedure and forecasting accuracy. Full article

In this paper, we address whether using a disaggregated series or combining an aggregated and disaggregated series improves the forecasting of the aggregated series compared to using the aggregated series alone. We used econometric techniques, such as the weighted lag adaptive least absolute shrinkage and selection operator, and Exponential Triple Smoothing (ETS), as well as the Autometrics algorithm to forecast industrial production in Brazil one to twelve months ahead. This is the novelty of the work, as is the use of the average multi-horizon Superior Predictive Ability (aSPA) and uniform multi-horizon Superior Predictive Ability (uSPA) tests, used to select the best forecasting model by combining different horizons. Our sample covers the period from January 2002 to February 2020. The disaggregated ETS has a better forecast performance when forecasting horizons that are more than one month ahead using the mean square error, and the aggregated ETS has better forecasting ability for horizons equal to 1 and 2. The aggregated ETS forecast does not contain information that is useful for forecasting industrial production in Brazil beyond the information already found in the disaggregated ETS forecast between two and twelve months ahead. Full article

In this paper, we investigate the relationship between the RavenPack news-based index associated with coronavirus outbreak (Panic, Sentiment, Infodemic, and Media Coverage) and returns of two commodities—Bitcoin and gold. We utilized the novel quantile-on-quantile approach to uncover the dependence between the news-based index associated with coronavirus outbreak and Bitcoin and gold returns. Our results reveal that the daily levels of positive and negative shocks in indices induced by pandemic news asymmetrically affect the Bearish and Bullish on Bitcoin and gold, and fear sentiment induced by coronavirus-related news plays a major role in driving the values of Bitcoin and gold more than other indices. We find that both commodities, Bitcoin and gold, can serve as a hedge against pandemic-related news. In general, the COVID-19 pandemic-related news encourages people to invest in gold and Bitcoin. Full article

I use the data on the COVID-19 pandemic maintained by Our Word in Data to estimate a nonstationary dynamic panel exhibiting the dynamics of confirmed deaths, infections and vaccinations per million population in the European Union countries in the period of January–July 2021. Having the data aggregated on a weekly basis I demonstrate that a model which allows for heterogeneous short-run dynamics and common long-run marginal effects is superior to that allowing only for either homogeneous or heterogeneous responses. The analysis shows that the long-run marginal death effects with respect to confirmed infections and vaccinations are positive and negative, respectively, as expected. Since the estimate of the former effect compared to the latter one is about 71.67 times greater, only mass vaccinations can prevent the number of deaths from being large in the long-run. The success in achieving this is easier for countries with the estimated large negative individual death effect (Cyprus, Denmark, Ireland, Portugal, Estonia, Lithuania) than for those with the large but positive death effect (Bulgaria, Hungary, Slovakia). The speed of convergence to the long-run equilibrium relationship estimates for individual countries are all negative. For some countries (Bulgaria, Denmark, Estonia, Greece, Hungary, Slovakia) they differ in the magnitude from that averaged for the whole EU, while for others (Croatia, Ireland, Lithuania, Poland, Portugal, Romania, Spain), they do not. Full article

A multivariate, non-Bayesian, regression-based, or feasible generalized least squares (GLS)-based approach is proposed to estimate time-varying VAR parameter models. Although it has been known that the Kalman-smoothed estimate can be alternatively estimated using GLS for univariate models, we assess the accuracy of the feasible GLS estimator compared with commonly used Bayesian estimators. Unlike the maximum likelihood estimator often used together with the Kalman filter, it is shown that the possibility of the pile-up problem occurring is negligible. In addition, this approach enables us to deal with stochastic volatility models, models with a time-dependent variance–covariance matrix, and models with non-Gaussian errors that allow us to deal with abrupt changes or structural breaks in time-varying parameters. Full article

Aggregate financial conditions indices (FCIs) are constructed to fulfil two aims: (i) The FCIs should resemble non-model-based composite indices in that their composition is adequately invariant for concatenation during regular updates; (ii) the concatenated FCIs should outperform financial variables conventionally used as leading indicators in macro models. Both aims are shown to be attainable once an algorithmic modelling route is adopted to combine leading indicator modelling with the principles of partial least-squares (PLS) modelling, supervised dimensionality reduction, and backward dynamic selection. Pilot results using US data confirm the traditional wisdom that financial imbalances are more likely to induce macro impacts than routine market volatilities. They also shed light on why the popular route of principal-component based factor analysis is ill-suited for the two aims. Full article

This article was prepared for the Special Issue “Celebrated Econometricians: Katarina Juselius and Søren Johansen” of Econometrics. It is based on material recorded on 30 October 2018 in Copenhagen. It explores Søren Johansen’s research, and discusses inter alia the following issues: estimation and inference for nonstationary time series of the I(1), I(2) and fractional cointegration types; survival analysis; statistical modelling; likelihood; econometric methodology; the teaching and practice of Statistics and Econometrics. Full article

This article was prepared for the Special Issue ‘Celebrated Econometricians: Katarina Juselius and Søren Johansen’ of Econometrics. It is based on material recorded on 30–31 October 2018 in Copenhagen. It explores Katarina Juselius’ research, and discusses inter alia the following issues: equilibrium; short and long-run behaviour; common trends; adjustment; integral and proportional control mechanisms; model building and model comparison; breaks, crisis, learning; univariate versus multivariate modelling; mentoring and the gender gap in Econometrics. Full article

This paper aims to better predict highly skewed auto insurance claims by combining candidate predictions. We analyze a version of the Kangaroo Auto Insurance company data and study the effects of combining different methods using five measures of prediction accuracy. The results show the following. First, when there is an outstanding (in terms of Gini Index) prediction among the candidates, the “forecast combination puzzle” phenomenon disappears. The simple average method performs much worse than the more sophisticated model combination methods, indicating that combining different methods could help us avoid performance degradation. Second, the choice of the prediction accuracy measure is crucial in defining the best candidate prediction for “low frequency and high severity” (LFHS) data. For example, mean square error (MSE) does not distinguish well between model combination methods, as the values are close. Third, the performances of different model combination methods can differ drastically. We propose using a new model combination method, named ARM-Tweedie, for such LFHS data; it benefits from an optimal rate of convergence and exhibits a desirable performance in several measures for the Kangaroo data. Fourth, overall, model combination methods improve the prediction accuracy for auto insurance claim costs. In particular, Adaptive Regression by Mixing (ARM), ARM-Tweedie, and constrained Linear Regression can improve forecast performance when there are only weak learners or when no dominant learner exists. Full article

The COVID-19 pandemic is a serious threat to all of us. It has caused an unprecedented shock to the world’s economy, and it has interrupted the lives and livelihood of millions of people. In the last two years, a large body of literature has attempted to forecast the main dimensions of the COVID-19 outbreak using a wide set of models. In this paper, I forecast the short- to mid-term cumulative deaths from COVID-19 in 12 hard-hit big countries around the world as of 20 August 2021. The data used in the analysis were extracted from the Our World in Data COVID-19 dataset. Both non-seasonal and seasonal autoregressive integrated moving averages (ARIMA and SARIMA) were estimated. The analysis showed that: (i) ARIMA/SARIMA forecasts were sufficiently accurate in both the training and test set by always outperforming the simple alternative forecasting techniques chosen as benchmarks (Mean, Naïve, and Seasonal Naïve); (ii) SARIMA models outperformed ARIMA models in 46 out 48 metrics (in forecasting future values), i.e., on 95.8% of all the considered forecast accuracy measures (mean absolute error [MAE], mean absolute percentage error [MAPE], mean absolute scaled error [MASE], and the root mean squared error [RMSE]), suggesting a clear seasonal pattern in the data; and (iii) the forecasted values from SARIMA models fitted very well the observed (real-time) data for the period 21 August 2021–19 September 2021 for almost all the countries analyzed. This article shows that SARIMA can be safely used for both the short- and medium-term predictions of COVID-19 deaths. Thus, this approach can help government authorities to monitor and manage the huge pressure that COVID-19 is exerting on national healthcare systems. Full article

The primary objective of this paper is to revisit DSGE models with a view to bringing out their key weaknesses, including statistical misspecification, non-identification of deep parameters, substantive inadequacy, weak forecasting performance, and potentially misleading policy analysis. It is argued that most of these weaknesses stem from failing to distinguish between statistical and substantive adequacy and secure the former before assessing the latter. The paper untangles the statistical from the substantive premises of inference to delineate the above-mentioned issues and propose solutions. The discussion revolves around a typical DSGE model using US quarterly data. It is shown that this model is statistically misspecified, and when respecified to arrive at a statistically adequate model gives rise to the Student’s t VAR model. This statistical model is shown to (i) provide a sound basis for testing the DSGE overidentifying restrictions as well as probing the identifiability of the deep parameters, (ii) suggest ways to meliorate its substantive inadequacy, and (iii) give rise to reliable forecasts and policy simulations. Full article

A theory-consistent CVAR scenario describes a set of testable regularities capturing basic assumptions of the theoretical model. Using this concept, the paper considers a standard model for exchange rate determination with forward-looking expectations and shows that all assumptions about the model’s shock structure and steady-state behavior can be formulated as testable hypotheses on common stochastic trends and cointegration. The basic stationarity assumptions of the monetary model failed to obtain empirical support. They were too restrictive to explain the observed long persistent swings in the real exchange rate, the real interest rates, and the inflation and interest rate differentials. Full article

Most factor-based forecasting models for the term structure of interest rates depend on a fixed number of factor loading functions that have to be specified in advance. In this study, we relax this assumption by building a yield curve forecasting model that learns new factor decompositions directly from data for an arbitrary number of factors, combining a Gaussian linear state-space model with a neural network that generates smooth yield curve factor loadings. In order to control the model complexity, we define prior distributions with a shrinkage effect over the model parameters, and we present how to obtain computationally efficient maximum a posteriori numerical estimates using the Kalman filter and automatic differentiation. An evaluation of the model’s performance on 14 years of historical data of the Brazilian yield curve shows that the proposed technique was able to obtain better overall out-of-sample forecasts than traditional approaches, such as the dynamic Nelson and Siegel model and its extensions. Full article

We propose a method to explore the causal transmission of an intervention through two endogenous variables of interest. We refer to the intervention as a catalyst variable. The method is based on the reduced-form system formed from the conditional distribution of the two endogenous variables given the catalyst. The method combines elements from instrumental variable analysis and Cholesky decomposition of structural vector autoregressions. We give conditions for uniqueness of the causal transmission. Full article

Misclassification of a binary response variable and nonrandom sample selection are data issues frequently encountered by empirical researchers. For cases in which both issues feature simultaneously in a data set, we formulate a sample selection model for a misclassified binary outcome in which the conditional probabilities of misclassification are allowed to depend on covariates. Assuming the availability of validation data, the pseudo-maximum likelihood technique can be used to estimate the model. The performance of the estimator accounting for misclassification and sample selection is compared to that of estimators offering partial corrections. An empirical example illustrates the proposed framework. Full article

Missing data or missing values are a common phenomenon in applied panel data research and of great interest for panel data unit root testing. The standard approach in the literature is to balance the panel by removing units and/or trimming a common time period for all units. However, this approach can be costly in terms of lost information. Instead, existing panel unit root tests could be extended to the case of unbalanced panels, but this is often difficult because the missing observations affect the bias correction which is usually involved. This paper contributes to the literature in two ways; it extends two popular panel unit root tests to allow for missing values, and secondly, it employs asymptotic local power functions to analytically study the impact of various missing-value methods on power. We find that zeroing-out the missing observations is the method that results in the greater test power, and that this result holds for all deterministic component specifications, such as intercepts, trends and structural breaks. Full article

The green bond market is emerging as an impactful financing mechanism in climate change mitigation efforts. The effectiveness of the financial market for this transition to a low-carbon economy depends on attracting investors and removing financial market roadblocks. This paper investigates the differential bond performance of green vs non-green bonds with (1) a dynamic portfolio model that integrates negative as well as positive externality effects and via (2) econometric analyses of aggregate green bond and corporate energy time-series indices; as well as a cross-sectional set of individual bonds issued between 1 January 2017, and 1 October 2020. The asset pricing model demonstrates that, in the long-run, the positive externalities of green bonds benefit the economy through positive social returns. We use a deterministic and a stochastic version of the dynamic portfolio approach to obtain model-driven results and evaluate those through our empirical evidence using harmonic estimations. The econometric analysis of this study focuses on volatility and the risk–return performance (Sharpe ratio) of green and non-green bonds, and extends recent econometric studies that focused on yield differentials of green and non-green bonds. A modified Sharpe ratio analysis, cross-sectional methods, harmonic estimations, bond pairing estimations, as well as regression tree methodology, indicate that green bonds tend to show lower volatility and deliver superior Sharpe ratios (while the evidence for green premia is mixed). As a result, green bond investment can protect investors and portfolios from oil price and business cycle fluctuations, and stabilize portfolio returns and volatility. Policymakers are encouraged to make use of the financial benefits of green instruments and increase the financial flows towards sustainable economic activities to accelerate a low-carbon transition. Full article

This note studies the criterion for identifiability in parametric models based on the minimization of the Hellinger distance and exhibits its relationship to the identifiability criterion based on the Fisher matrix. It shows that the Hellinger distance criterion serves to establish identifiability of parameters of interest, or lack of it, in situations where the criterion based on the Fisher matrix does not apply, like in models where the support of the observed variables depends on the parameter of interest or in models with irregular points of the Fisher matrix. Several examples illustrating this result are provided. Full article