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Enns et al. respond to recent work by Grant and Lebo and Lebo and Grant that raises a number of concerns with political scientists' use of the general error correction model (GECM). While agreeing with the particular rules one should apply when using unit root data in the GECM, Enns et al. still advocate procedures that will lead researchers astray. Most especially, they fail to recognize the difficulty in interpreting the GECM's "error correction coefficient." Without being certain of the univariate properties of one's data it is extremely difficult (or perhaps impossible) to know whether or not cointegration exists and error correction is occurring. We demonstrate the crucial differences for the GECM between having evidence of a unit root (from Dickey–Fuller tests) versus actually having a unit root. Looking at simulations and two applied examples we show how overblown findings of error correction await the uncareful researcher.

AbstractA unique sample of auditor error correction decisions made in practice is investigated to see what factors influenced the decisions. A general model of auditor behaviour is postulated, in which the auditors are expected to respond to materiality requirements, legal liability considerations, and pressures from managers to avoid disclosing material items. The results indicate that all three factors influence the correction decision.RésuméCette étude porte sur un échantillon unique de décisions de correction d'erreurs effectuées par des vérificateurs; elle vise à déterminer les facteurs influençant ces décisions. On a postule un modèle général de comportement des vérificateurs, selon lequel ils sont supposés avoir à prendre en compte les exigences de l'importance relative, les considérations de responsabilité face à la loi et les pressions exercées sur eux par les dirigeants afin d'éviter la révélation d'éléments significatifs. Les résultats obtenus indiquent que ces trois facteurs influencent les décisions de correction.

We show that a [Er–Ce–Er] molecular trinuclear coordination compound is a promising platform to implement the three-qubit quantum error correction code protecting against pure dephasing, the most important error in magnetic molecules. We characterize it by preparing the [Lu–Ce–Lu] and [Er–La–Er] analogues, which contain only one of the two types of qubit, and by combining magnetometry, low-temperature specific heat and electron paramagnetic resonance measurements on both the elementary constituents and the trimer. Using the resulting parameters, we demonstrate by numerical simulations that the proposed molecular device can efficiently suppress pure dephasing of the spin qubits. ; This work has received funding from the European Union's Horizon 2020 research and innovation programme (ERC Starting Grant 258060 FuncMolQIP, COST Action 15128 MOLSPIN, QUANTERA project SUMO, FET-OPEN grant 862893 FATMOLS), the Spanish MICINN (grants CTQ2015-68370-P, CTQ2015-64486-R, RTI2018-096075-B-C21, PCI2018-093116, PGC2018-098630-B-I00, MAT2017-86826-R), the Gobierno de Aragón (grants E09-17R-Q-MAD, and PLATON E31_17R), the Generalitat de Catalunya (ICREA Academia 2018 to GA), and from the Italian Ministry of Education and Research (MIUR) through the co-funding of SUMO and through the PRIN Project 2015 HYFSRT "Quantum Coherence in Nanostructures of Molecular Spin Qubits". Institució Catalana de Recerca I Estudis Avançats: ICREA Academia Prize 2018. ; Peer reviewed

AbstractGrant and Lebo (2016) and Keeleet al.(2016) clarify the conditions under which the popular general error correction model (GECM) can be used and interpreted easily: In a bivariate GECM the data must be integrated in order to rely on the error correction coefficient,$\alpha _1^\ast$, to test cointegration and measure the rate of error correction between a single exogenousxand a dependent variable,y. Here we demonstrate that even if the data are all integrated, the test on$\alpha _1^\ast$is misunderstood when there is more than a single independent variable. The null hypothesis is that there is no cointegration betweenyand anyxbut the correct alternative hypothesis is thatyis cointegrated with at least one—but not necessarily more than one—of thex's. A significant$\alpha _1^\ast$can occur when someI(1) regressors are not cointegrated and the equation is not balanced. Thus, the correct limiting distributions of the right-hand-side long-run coefficients may be unknown. We use simulations to demonstrate the problem and then discuss implications for applied examples.

While traditionally considered for non-stationary and cointegrated data, DeBoef and Keele suggest applying a General Error Correction Model (GECM) to stationary data with or without cointegration. The GECM has since become extremely popular in political science but practitioners have confused essential points. For one, the model is treated as perfectly flexible when, in fact, the opposite is true. Time series of various orders of integration–stationary, non-stationary, explosive, near- and fractionally integrated–should not be analyzed together but researchers consistently make this mistake. That is, withoutequation balancethe model is misspecified and hypothesis tests and long-run-multipliers are unreliable. Another problem is that the error correction term's sampling distribution moves dramatically depending upon the order of integration, sample size, number of covariates, and theboundednessofYt.This means that practitioners are likely to overstate evidence of error correction, especially when using a traditionalt-test. We evaluate common GECM practices with six types of data, 746 simulations, and five paper replications.

For political scientists who engage in longitudinal analyses, the question of how best to deal with nonstationary time-series is anything but settled. While many believe that little is lost when the focus of empirical models shifts from the nonstationary levels to the stationary changes of a series, others argue that such an approach erases any evidence of a long-term relationship among the variables of interest. But the pitfalls of working directly with integrated series are well known, and post-hoc corrections for serially correlated errors often seem inadequate. Compounding (or perhaps alleviating, if one believes in the power of selective perception) the difficult question of whether to difference a time-series is the fact that analysts have been forced to rely on subjective diagnoses of the stationarity of their data. Thus, even if one felt strongly about the superiority of one modeling approach over another, the procedure for determining whether that approach is even applicable can be frustrating.