Econometrics, Volume 8, Issue 3 (September 2020) – 12 articles

In this paper the theory on the estimation of vector autoregressive (VAR) models for I(2) processes is extended to the case of long VAR approximation of more general processes. Hereby the order of the autoregression is allowed to tend to infinity at a certain rate depending on the sample size. We deal with unrestricted OLS estimators (in the model formulated in levels as well as in vector error correction form) as well as with two stage estimation (2SI2) in the vector error correction model (VECM) formulation. Our main results are analogous to the I(1) case: We show that the long VAR approximation leads to consistent estimates of the long and short run dynamics. Furthermore, tests on the autoregressive coefficients follow standard asymptotics. The pseudo likelihood ratio tests on the cointegrating ranks (using the Gaussian likelihood) used in the 2SI2 algorithm show under the null hypothesis the same distributions as in the case of data generating processes following finite order VARs. The same holds true for the asymptotic distribution of the long run dynamics both in the unrestricted VECM estimation and the reduced rank regression in the 2SI2 algorithm. Building on these results we show that if the data is generated by an invertible VARMA process, the VAR approximation can be used in order to derive a consistent initial estimator for subsequent pseudo likelihood optimization in the VARMA model. Full article

This paper studies long economic series to assess the long-lasting effects of pandemics. We analyze if periods that cover pandemics have a change in trend and persistence in growth, and in level and persistence in unemployment. We find that there is an upward trend in the persistence level of growth across centuries. In particular, shocks originated by pandemics in recent times seem to have a permanent effect on growth. Moreover, our results show that the unemployment rate increases and becomes more persistent after a pandemic. In this regard, our findings support the design and implementation of timely counter-cyclical policies to soften the shock of the pandemic. Full article

Building on arguments by Joshua Angrist and Jörn-Steffen Pischke arguments for how the teaching of undergraduate econometrics could become more effective, I propose a redesign of graduate econometrics that would better serve most students and help make the field of economics more relevant. The primary basis for the redesign is that the conventional methods do not adequately prepare students to recognize biases and to properly interpret significance, insignificance, and p-values; and there is an ethical problem in searching for significance and other matters. Based on these premises, I recommend that some of Angrist and Pischke’s recommendations be adopted for graduate econometrics. In addition, I recommend further shifts in emphasis, new pedagogy, and adding important components (e.g., on interpretations and simple ethical lessons) that are largely ignored in current textbooks. An obvious implication of these recommended changes is a confirmation of most of Angrist and Pischke’s recommendations for undergraduate econometrics, as well as further reductions in complexity. Full article

The econometric data to which autoregressive moving-average models are commonly applied are liable to contain elements from a limited range of frequencies. If the data do not cover the full Nyquist frequency range of $[0,\pi ]$ radians, then severe biases can occur in estimating their parameters. The recourse should be to reconstitute the underlying continuous data trajectory and to resample it at an appropriate lesser rate. The trajectory can be derived by associating sinc fuction kernels to the data points. This suggests a model for the underlying processes. The paper describes frequency-limited linear stochastic differential equations that conform to such a model, and it compares them with equations of a model that is assumed to be driven by a white-noise process of unbounded frequencies. The means of estimating models of both varieties are described. Full article

The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study. Full article

Recent research in financial economics has shown that rare large disasters have the potential to disrupt financial sectors via the destruction of capital stocks and jumps in risk premia. These disruptions often entail negative feedback effects on the macroeconomy. Research on disaster risks has also actively been pursued in the macroeconomic models of climate change. Our paper uses insights from the former work to study disaster risks in the macroeconomics of climate change and to spell out policy needs. Empirically, the link between carbon dioxide emission and the frequency of climate related disaster is investigated using a panel data approach. The modeling part then uses a multi-phase dynamic macro model to explore the effects of rare large disasters resulting in capital losses and rising risk premia. Our proposed multi-phase dynamic model, incorporating climate-related disaster shocks and their aftermath as a distressed phase, is suitable for studying mitigation and adaptation policies as well as recovery policies. Full article

This paper estimates the drift parameters in the fractional Vasicek model from a continuous record of observations via maximum likelihood (ML). The asymptotic theory for the ML estimates (MLE) is established in the stationary case, the explosive case, and the boundary case for the entire range of the Hurst parameter, providing a complete treatment of asymptotic analysis. It is shown that changing the sign of the persistence parameter changes the asymptotic theory for the MLE, including the rate of convergence and the limiting distribution. It is also found that the asymptotic theory depends on the value of the Hurst parameter. Full article

The relation between causal structure and cointegration and long-run weak exogeneity is explored using some ideas drawn from the literature on graphical causal modeling. It is assumed that the fundamental source of trending behavior is transmitted from exogenous (and typically latent) trending variables to a set of causally ordered variables that would not themselves display nonstationary behavior if the nonstationary exogenous causes were absent. The possibility of inferring the long-run causal structure among a set of time-series variables from an exhaustive examination of weak exogeneity in irreducibly cointegrated subsets of variables is explored and illustrated. Full article

We discuss some conceptual and practical issues that arise from the presence of global energy balance effects on station level adjustment mechanisms in dynamic panel regressions with climate data. The paper provides asymptotic analyses, observational data computations, and Monte Carlo simulations to assess the use of various estimation methodologies, including standard dynamic panel regression and cointegration techniques that have been used in earlier research. The findings reveal massive bias in system GMM estimation of the dynamic panel regression parameters, which arise from fixed effect heterogeneity across individual station level observations. Difference GMM and Within Group (WG) estimation have little bias and WG estimation is recommended for practical implementation of dynamic panel regression with highly disaggregated climate data. Intriguingly, from an econometric perspective and importantly for global policy analysis, it is shown that in this model despite the substantial differences between the estimates of the regression model parameters, estimates of global transient climate sensitivity (of temperature to a doubling of atmospheric CO${}_2$) are robust to the estimation method employed and to the specific nature of the trending mechanism in global temperature, radiation, and CO${}_2.$ Full article

Wage coordination plays an important role in macroeconomic stabilization. Pattern wage bargaining systems have been common in Europe, but in different forms, and with different degrees of success in terms of actual coordination reached. We focus on wage formation in Norway, a small open economy, where it is custom to regard the manufacturing industry as the wage leader. We estimate a model of wage formation in manufacturing and in two other sectors. Deciding cointegration rank is an important step in the analysis, economically as well statistically. In combination with simultaneous equation modelling, the cointegration analysis provides evidence that collective wage negotiations in manufacturing have defined wage norms for the rest of the economy over the period 1980(1)–2014(4). Full article

The goal of this paper is to search for conclusive evidence against the stationarity of the global air surface temperature, which is one of the most important indicators of climate change. For this purpose, possible long-range dependencies are investigated in the frequency-domain. Since conventional tests of hypotheses about the memory parameter, which measures the degree of long-range dependence, are typically based on asymptotic arguments and are therefore of limited practical value in case of small or medium sample sizes, we employ a new small-sample test as well as a related estimator for the memory parameter. To safeguard against false positive findings, simulation studies are carried out to examine the suitability of the employed methods and hemispheric datasets are used to check the robustness of the empirical findings against low-frequency natural variability caused by oceanic cycles. Overall, our frequency-domain analysis provides strong evidence of non-stationarity, which is consistent with previous results obtained in the time domain with models allowing for stochastic or deterministic trends. Full article

When using the Focused Information Criterion (FIC) for assessing and ranking candidate models with respect to how well they do for a given estimation task, it is customary to produce a so-called FIC plot. This plot has the different point estimates along the y-axis and the root-FIC scores on the x-axis, these being the estimated root-mean-square scores. In this paper we address the estimation uncertainty involved in each of the points of such a FIC plot. This needs careful assessment of each of the estimators from the candidate models, taking also modelling bias into account, along with the relative precision of the associated estimated mean squared error quantities. We use confidence distributions for these tasks. This leads to fruitful CD–FIC plots, helping the statistician to judge to what extent the seemingly best models really are better than other models, etc. These efforts also lead to two further developments. The first is a new tool for model selection, which we call the quantile-FIC, which helps overcome certain difficulties associated with the usual FIC procedures, related to somewhat arbitrary schemes for handling estimated squared biases. A particular case is the median-FIC. The second development is to form model averaged estimators with weights determined by the relative sizes of the median- and quantile-FIC scores. Full article