Econometrics, Volume 10, Issue 1 (March 2022) – 12 articles

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

In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing methodology relies on the characteristic function of the population probability distribution being tested and is attractive in that, regardless of the null hypothesis being tested, it provides a unified framework for conducting such tests. The testing procedure is also computationally tractable and relatively straightforward to implement. In contrast to some alternative test statistics, the proposed entropy test is free from user-specified kernel and bandwidth choices, idiosyncratic and complex regularity conditions, and/or choices of evaluation grids. Several simulation exercises were performed to document the empirical performance of our proposed test, including a regression example that is illustrative of how, in some contexts, the approach can be applied to composite hypothesis-testing situations via data transformations. Overall, the testing procedure exhibits notable promise, exhibiting appreciable increasing power as sample size increases for a number of alternative distributions when contrasted with hypothesized null distributions. Possible general extensions of the approach to composite hypothesis-testing contexts, and directions for future work are also discussed. Full article

The age–period–cohort problem has been studied for decades but without resolution. There have been many suggested solutions to make the three effects estimable, but these solutions mostly exploit non-linear specifications. Yet, these approaches may suffer from misspecification or omitted variable bias. This paper is a practical-oriented study with an aim to empirically disentangle age–period–cohort effects by providing external information on the actual depreciation of housing structure rather than taking age as a proxy. It is based on appraisals of the improvement values of properties in New Zealand to estimate the age-depreciation effect. This research method provides a novel means of solving the identification problem of the age, period, and cohort trilemma. Based on about half a million housing transactions from 1990 to 2019 in the Auckland Region of New Zealand, the results show that traditional hedonic prices models using age and time dummy variables can result, ceteris paribus, in unreasonable positive depreciation rates. The use of the improvement values model can help improve the accuracy of home value assessment and reduce estimation biases. This method also has important practical implications for property valuations. Full article

We propose a simple and reproducible methodology to create a single equation forecasting model (SEFM) for low-frequency macroeconomic variables. Our methodology is illustrated by forecasting annual real GDP growth rates for 52 African countries, where the data are obtained from the World Bank and start in 1960. The models include lagged growth rates of other countries, as well as a cointegration relationship to capture potential common stochastic trends. With a few selection steps, our methodology quickly arrives at a reasonably small forecasting model per country. Compared with benchmark models, the single equation forecasting models seem to perform quite well. Full article

By its emissions of greenhouse gases, economic activity is the source of climate change which affects pandemics that in turn can impact badly on economies. Across the three highly interacting disciplines in our title, time-series observations are measured at vastly different data frequencies: very low frequency at 1000-year intervals for paleoclimate, through annual, monthly to intra-daily for current climate; weekly and daily for pandemic data; annual, quarterly and monthly for economic data, and seconds or nano-seconds in finance. Nevertheless, there are important commonalities to economic, climate and pandemic time series. First, time series in all three disciplines are subject to non-stationarities from evolving stochastic trends and sudden distributional shifts, as well as data revisions and changes to data measurement systems. Next, all three have imperfect and incomplete knowledge of their data generating processes from changing human behaviour, so must search for reasonable empirical modeling approximations. Finally, all three need forecasts of likely future outcomes to plan and adapt as events unfold, albeit again over very different horizons. We consider how these features shape the formulation and selection of forecasting models to tackle their common data features yet distinct problems. Full article

This paper presents a method for estimating the average treatment effects (ATE) of an exponential endogenous switching model where the coefficients of covariates in the structural equation are random and correlated with the binary treatment variable. The estimating equations are derived under some mild identifying assumptions. We find that the ATE is identified, although each coefficient in the structural model may not be. Tests assessing the endogeneity of treatment and for model selection are provided. Monte Carlo simulations show that, in large samples, the proposed estimator has a smaller bias and a larger variance than the methods that do not take the random coefficients into account. This is applied to health insurance data of Oregon. Full article