Hypothesis testing with error correction models

2021 ◽  
pp. 1-9
Author(s):  
Patrick W. Kraft ◽  
Ellen M. Key ◽  
Matthew J. Lebo
Keyword(s):  
Hypothesis Testing ◽  
Error Correction ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Correction Coefficient ◽  
Correction Model ◽  
Long Run ◽  
Independent Variable ◽  
The Right ◽  
General Error

Abstract Grant and Lebo (2016) and Keele et 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 exogenous x and 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 between y and any x but the correct alternative hypothesis is that y is cointegrated with at least one—but not necessarily more than one—of the x's. A significant $\alpha _1^\ast$ can occur when some I(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.

scholarly journals An application of the error correction model in analyzing the long run equilibrium between Ghana’s exports and imports

2015 ◽  
Vol 9 (3) ◽  
pp. 57-62
Author(s):  
Henry de-Graft Acquah ◽  
Joyce De-Graft Acquah
Keyword(s):  
Error Correction ◽  
Trade Deficit ◽  
Error Correction Model ◽  
Correction Coefficient ◽  
Equilibrium Relation ◽  
Macroeconomic Policies ◽  
Correction Model ◽  
Long Run ◽  
Step Procedure ◽  
Long Run Equilibrium

This study investigates the long-run relationship between Ghana’s exports and imports for the period of 1948 to 2012. Using the Engle Granger two-step procedure we find that Ghana’s exports and imports are cointegrated. However, the slope coefficients from the cointegration equations were not statistically equal to 1. Furthermore, application of the error correction model reveals that 1% increase in the imports will significantly result in 0.56% increase in exports, suggesting that the exports’ responsiveness to imports is low. The estimated error correction coefficient suggests that 32% of the deviation from the long run equilibrium relation is eliminated, leaving 68% to persist into the next period. These results suggest persistence in the trade deficit and an option of curbing the deficit is to re-order the relationship between imports and exports with a view to reducing imports demand. These results imply that though Ghana’s past macroeconomic policies have been effective in bringing its imports and exports into a long run equilibrium, it is yet to satisfy the sufficient condition for sustainability of foreign deficit.

Error Correction Methods with Political Time Series

2016 ◽  
Vol 24 (1) ◽  
pp. 3-30 ◽  
Author(s):  
Taylor Grant ◽  
Matthew J. Lebo
Keyword(s):  
Time Series ◽  
Sample Size ◽  
Error Correction ◽  
Political Science ◽  
Correction Model ◽  
Long Run ◽  
Size Number ◽  
Political Time ◽  
True Time ◽  
General Error

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.

Equation Balance and Dynamic Political Modeling

2016 ◽  
Vol 24 (1) ◽  
pp. 69-82 ◽  
Author(s):  
Matthew J. Lebo ◽  
Taylor Grant
Keyword(s):  
Error Correction ◽  
Correction Term ◽  
Moving Average ◽  
Fractional Integration ◽  
Time Series Modeling ◽  
Average Model ◽  
Correction Model ◽  
Long Run ◽  
Moving Average Model ◽  
General Error

The papers in this symposium agree on several points. In this article, we sort through some remaining areas of disagreement and discuss some of the practical issues of time series modeling we think deserve further explanation. In particular, we have five points: (1) clarifying our stance on the general error correction model in light of the comments in this issue; (2) clarifying equation balance and discussing how bounded series affects our thinking about stationarity, balance, and modeling choices; (3) answering lingering questions about our Monte Carlo simulations and exploring potential problems in the inferences drawn from long-run multipliers; (4) reviewing and defending fractional integration methods in light of the questions raised in this symposium and elsewhere; and (5) providing a short practical guide to estimating a multivariate autoregressive fractionally integrated moving average model with or without an error correction term.

scholarly journals The general error correction model in practice

2017 ◽  
Vol 4 (2) ◽  
pp. 205316801771305 ◽  
Author(s):  
Matthew J. Lebo ◽  
Patrick W. Kraft
Keyword(s):  
Error Correction ◽  
Recent Work ◽  
Unit Root ◽  
Error Correction Model ◽  
Correction Coefficient ◽  
Correction Model ◽  
General Error

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.

scholarly journals ANALISIS NILAI TUKAR RUPIAH DAN IMPLIKASINYA PADA PEREKONOMIAN INDONESIA: PENDEKATAN ERROR CORRECTION MODEL (ECM)

2007 ◽  
Vol 8 (2) ◽  
pp. 146
Author(s):  
Imamudin Yuliadi
Keyword(s):  
Exchange Rate ◽  
Interest Rate ◽  
Error Correction ◽  
World Bank ◽  
Error Correction Model ◽  
Economic Factors ◽  
Correction Model ◽  
Long Run ◽  
Short Run ◽  
Independent Variable

The changing of exchange rate is due to interaction between economic factors and non-economic factors. The aim of this research is to analyse some factors that affect exchange rate and their implications on Indonesian economy. Analytical method used in this research is explanatory method is to test hypothesis about simultaneous relationship among variables that research by developing the characteristics of verificative research by doing some testing at every step of research. We used secon-dary data taken from BI, BPS, World Bank and IFS. We used error correction model (ECM) to analysis between independent variable and dependent variable in both the short run and long run. The result of this research shows that ratio between domestic interest rate and international interest rate did not affect negative and significantly to exchange rate. Capital flow affected negative and significantly. Balance of payment affected negative and significantly. Money supply affected positive and significantly. According ECM method that used in this research shows that the methodology is good to analyse because the magnitude of ECT is accept.

scholarly journals Asymptotic relative submajorization of multiple-state boxes

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Gergely Bunth ◽  
Péter Vrana
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Standard Form ◽  
Point Of View ◽  
State Discrimination ◽  
Simple Alternative ◽  
Multiple State ◽  
Error Probabilities

AbstractPairs of states, or “boxes” are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde in Phys Rev Res 1(3):033170, 2019. 10.1103/PhysRevResearch.1.033170), where free operations are arbitrary quantum channels that are applied to both states. From this point of view, hypothesis testing is seen as a process by which a standard form of distinguishability is distilled. Motivated by the more general problem of quantum state discrimination, we consider boxes of a fixed finite number of states and study an extension of the relative submajorization preorder to such objects. In this relation, a tuple of positive operators is greater than another if there is a completely positive trace nonincreasing map under which the image of the first tuple satisfies certain semidefinite constraints relative to the other one. This preorder characterizes error probabilities in the case of testing a composite null hypothesis against a simple alternative hypothesis, as well as certain error probabilities in state discrimination. We present a sufficient condition for the existence of catalytic transformations between boxes, and a characterization of an associated asymptotic preorder, both expressed in terms of sandwiched Rényi divergences. This characterization of the asymptotic preorder directly shows that the strong converse exponent for a composite null hypothesis is equal to the maximum of the corresponding exponents for the pairwise simple hypothesis testing tasks.

scholarly journals A Critical Evaluation of the FBST ev for Bayesian Hypothesis Testing

2021 ◽  
Author(s):  
Alexander Ly ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Critical Evaluation ◽  
Significance Test ◽  
Bayesian Hypothesis Testing ◽  
Absence Of Evidence ◽  
Evidence Of Absence ◽  
Foregone Conclusion

AbstractThe “Full Bayesian Significance Test e-value”, henceforth FBST ev, has received increasing attention across a range of disciplines including psychology. We show that the FBST ev leads to four problems: (1) the FBST ev cannot quantify evidence in favor of a null hypothesis and therefore also cannot discriminate “evidence of absence” from “absence of evidence”; (2) the FBST ev is susceptible to sampling to a foregone conclusion; (3) the FBST ev violates the principle of predictive irrelevance, such that it is affected by data that are equally likely to occur under the null hypothesis and the alternative hypothesis; (4) the FBST ev suffers from the Jeffreys-Lindley paradox in that it does not include a correction for selection. These problems also plague the frequentist p-value. We conclude that although the FBST ev may be an improvement over the p-value, it does not provide a reasonable measure of evidence against the null hypothesis.

Concluding Comments

2016 ◽  
Vol 24 (1) ◽  
pp. 83-86 ◽  
Author(s):  
Luke Keele ◽  
Suzanna Linn ◽  
Clayton McLaughlin Webb
Keyword(s):  
Error Correction ◽  
Political Science ◽  
Fractional Integration ◽  
Error Correction Model ◽  
Costs And Benefits ◽  
Significant Progress ◽  
Integration Methods ◽  
Correction Model ◽  
General Error

This issue began as an exchange between Grant and Lebo (2016) and ourselves (Keele, Linn, and Webb 2016) about the utility of the general error correction model (GECM) in political science. The exchange evolved into a debate about Grant and Lebo's proposed alternative to the GECM and the utility of fractional integration methods (FIM). Esarey (2016) and Helgason (2016) weigh in on this part of the debate. Freeman (2016) offers his views on the exchange as well. In the end, the issue leaves readers with a lot to consider. In his comment, Freeman (2016) argues that the exchange has produced little significant progress because of the contributors' failures to consider a wide array of topics not directly related to the GECM or FIM. We are less pessimistic. In what follows, we distill what we believe are the most important elements of the exchange–the importance of balance, the costs and benefits of FIM, and the vagaries of pre-testing.

The Methodology of Cointegration

1992 ◽  
Vol 4 ◽  
pp. 237-247 ◽  
Author(s):  
Nathaniel Beck
Keyword(s):  
Error Correction ◽  
Political Attitudes ◽  
Error Correction Model ◽  
Correction Model ◽  
Long Run ◽  
Economic Circumstance ◽  
Economics Department ◽  
Technical Area

It is hardly surprising that I applaud the fine work of both Durr and Ostrom and Smith. I am on record in favor of the utility of the error correction model (e.g., Beck 1985) and it is impossible to obtain a visa to visit the economics department at UCSD without swearing an oath of loyalty to the methodology of cointegration. The two works here are notable for their methodological sophistication, their exposition of a relatively unknown and highly technical area, and, most important, their substantive contributions. Both articles show that political attitudes (approval and policy mood) adjust, in the long run, to changes in objective and subjective economic circumstance. Both articles are good examples of the synergy of methods and theory, since it is the methodology of cointegration that leads to this type of theorizing, and this type of theorizing can most easily be tested in the context of cointegration or error correction.

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