Econometrics

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

We use data on the following climate variables for the period of the last 798 thousand years: global ice volume (${\mathrm{Ice}}_t$), atmospheric carbon dioxide level (${\mathrm{CO}}_{2,t}$), and Antarctic land surface temperature (${\mathrm{Temp}}_t$). Those variables are cyclical and are driven by the following strongly exogenous orbital variables: eccentricity of the Earth’s orbit, obliquity, and precession of the equinox. We introduce score-driven ice-age models which use robust filters of the conditional mean and variance, generalizing the updating mechanism and solving the misspecification of a recent climate–econometric model (benchmark ice-age model). The score-driven models control for omitted exogenous variables and extreme events, using more general dynamic structures and heteroskedasticity. We find that the score-driven models improve the performance of the benchmark ice-age model. We provide out-of-sample forecasts of the climate variables for the last 100 thousand years. We show that during the last 10–15 thousand years of the forecasting period, for which humanity influenced the Earth’s climate, (i) the forecasts of ${\mathrm{Ice}}_t$ are above the observed ${\mathrm{Ice}}_t$, (ii) the forecasts of ${\mathrm{CO}}_{2,t}$ level are below the observed ${\mathrm{CO}}_{2,t}$, and (iii) the forecasts of ${\mathrm{Temp}}_t$ are below the observed ${\mathrm{Temp}}_t$. The forecasts for the benchmark ice-age model are reinforced by the score-driven models. Full article

This paper studies the performance of machine learning predictions for the counterfactual analysis of air transport. It is motivated by the dynamic and universally regulated international air transport market, where ex post policy evaluations usually lack counterfactual control scenarios. As an empirical example, this paper studies the impact of the COVID-19 pandemic on airfares in 2020 as the difference between predicted and actual airfares. Airfares are important from a policy makers’ perspective, as air transport is crucial for mobility. From a methodological point of view, airfares are also of particular interest given their dynamic character, which makes them challenging for prediction. This paper adopts a novel multi-step prediction technique with walk-forward validation to increase the transparency of the model’s predictive quality. For the analysis, the universe of worldwide airline bookings is combined with detailed airline information. The results show that machine learning with walk-forward validation is powerful for the counterfactual analysis of airfares. Full article

In linear regression analysis, the estimator of the variance of the estimator of the regression coefficients should take into account the clustered nature of the data, if present, since using the standard textbook formula will in that case lead to a severe downward bias in the standard errors. This idea of a cluster-robust variance estimator (CRVE) generalizes to clusters the classical heteroskedasticity-robust estimator. Its justification is asymptotic in the number of clusters. Although an improvement, a considerable bias could remain when the number of clusters is low, the more so when regressors are correlated within cluster. In order to address these issues, two improved methods were proposed; one method, which we call CR2VE, was based on biased reduced linearization, while the other, CR3VE, can be seen as a jackknife estimator. The latter is unbiased under very strict conditions, in particular equal cluster size. To relax this condition, we introduce in this paper CR3VE-$\lambda$, a generalization of CR3VE where the cluster size is allowed to vary freely between clusters. We illustrate the performance of CR3VE-$\lambda$ through simulations and we show that, especially when cluster sizes vary widely, it can outperform the other commonly used estimators. Full article