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.

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.

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.

scholarly journals Analysis of Indonesian Tax Revenue

2017 ◽  
Vol 1 (01) ◽  
pp. 71
Author(s):  
Amalia Wijayanti ◽  
Firmansyah Firmansyah
Keyword(s):  
Exchange Rate ◽  
Error Correction ◽  
Government Spending ◽  
Inflation Rate ◽  
Correction Term ◽  
Error Correction Model ◽  
Tax Revenue ◽  
Correction Model ◽  
Long Run ◽  
Short Run

<p>This study analyzes the long-run and short-run effect of macroeconomic factors, such as real Gross Domestic Product (GDP), inflation rate, exchange rate and government spending on Indonesia’s tax revenue during 1976-2013, by utilizing the Error Correction Model (ECM). The finding of the study demontrates that in the long-run; the real GDP, exchange rate, and government spending affect Indonesia’s tax revenue, except the inflation rate. In short-run, Indonesia’s tax revenue statisically affected by government spending, while others variable do not influence Indonesia’s tax revenue. Error Correction Term (ECT) coefficient is 0.221, explains incompatibility tax revenue occur in long-run is corrected of 22 percent in one period.</p><p><br />JEL Classification: E01, E20, H20<br />Keywords: Error Correction Model, Macroeconomic, Tax revenue</p>

Modeling and Forecasting Sales Data by Time Series Analysis

1981 ◽  
Vol 18 (1) ◽  
pp. 94-100 ◽  
Author(s):  
S. G. Kapoor ◽  
P. Madhok ◽  
S. M. Wu
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Time Series Modeling ◽  
Average Model ◽  
Sales Data ◽  
Autoregressive Moving Average Model ◽  
Deterministic Function ◽  
Modeling And Forecasting ◽  
Moving Average Model

Time series modeling technique is used to model a series of sales data in which seasonality causes distinct spike peaks. The analysis of actual sales data shows that the seasonality in the data can be approximated by a deterministic function and the stochastic component is a sixth-order autoregressive moving average model. Use of the combined deterministic and stochastic models to derive the minimum mean squared forecast yields reliable results.

Fractional Integration Methods and Short Time Series: Evidence from a Simulation Study

2016 ◽  
Vol 24 (1) ◽  
pp. 59-68 ◽  
Author(s):  
Agnar Freyr Helgason
Keyword(s):  
Time Series ◽  
Alternative Model ◽  
Fractional Integration ◽  
Short Time Series ◽  
Integration Methods ◽  
Correction Model ◽  
Long Run ◽  
Short Run ◽  
Short Time ◽  
General Error

Grant and Lebo (2016) and Keele, Linn, and Webb (2016) provide diverging recommendations to analysts working with short time series that are potentially fractionally integrated. While Grant and Lebo are quite positive about the prospects of fractionally differencing such data, Keele, Linn, and Webb argue that estimates of fractional integration will be highly uncertain in short time series. In this study, I simulate fractionally integrated data and compare estimates from the general error correction model (GECM), which disregards fractional integration, to models using fractional integration methods over thirty-two simulation conditions. I find that estimates of short-run effects are similar across the two models, but that models using fractionally differenced data produce superior predictions of long-run effects for all sample sizes when there are no short-run dynamics included. When short-run dynamics are included, the GECM outperforms the alternative model, but only in time series that consist of under 250 observations.

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.

Fractionally Integrated Data and the Autodistributed Lag Model: Results from a Simulation Study

2016 ◽  
Vol 24 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Justin Esarey
Keyword(s):  
Error Correction ◽  
Simulation Study ◽  
Fractional Integration ◽  
Error Correction Model ◽  
Exogenous Variables ◽  
Correction Model ◽  
Long Run ◽  
Lag Model ◽  
Fractional Error ◽  
Arfima Model

Two contributions in this issue, Grant and Lebo and Keele, Linn, and Webb, recommend using an ARFIMA model to diagnose the presence of and estimate the degree of fractional integration, then either (i) fractionally differencing the data before analysis or, (ii) for cointegrated variables, estimating a fractional error correction model. But Keele, Linn, and Webb also present evidence that ARFIMA models yield misleading indicators of the presence and degree of fractional integration in a series with fewer than 1000 observations. In a simulation study, I find evidence that the simple autodistributed lag model (ADL) or equivalent error correction model (ECM) can, without first testing or correcting for fractional integration, provide a useful estimate of the immediate and long-run effects of weakly exogenous variables in fractionally integrated (but stationary) data.

scholarly journals Comparing parametric and semiparametric error correction models for estimation of long run equilibrium between exports and imports

2017 ◽  
Vol 11 (1-2) ◽  
pp. 19-23
Author(s):  
Henry De-Graft Acquah ◽  
Lawrence Acheampong
Keyword(s):  
Least Squares ◽  
Error Correction ◽  
Correction Term ◽  
Error Correction Model ◽  
Ordinary Least Squares ◽  
Information Criteria ◽  
Least Squares Regression ◽  
Error Correction Models ◽  
Correction Model ◽  
Long Run

This paper introduces the semiparametric error correction model for estimation of export-import relationship as an alternative to the least squares approach. The intent is to demonstrate how semiparametric error correction model can be used to estimate the relationship between Ghana’s export and import within the context of a generalized additive modelling (GAM) framework. The semiparametric results are compared to common parametric specification using the ordinary least squares regression. The results from the semiparametric and parametric error correction models (ECM) indicate that the error correction term and import variable are significant determinants of Ghana’s exports. On the basis of Akaike Information Criteria and Generalized Cross-Validation (GCV) scores, it is found that the semiparametric error correction model provides a better fit than the widely used parametric error correction model for modeling Ghana’s export-import relationship. The results of the analysis of variance provide further evidence of nonlinearity in Ghana’s export and import relationship. In effect, this paper demonstrates the usefulness of semiparametric error correction model in the estimation of export – import relationship. JEL code: C14, C18, C22, F10, F14

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