Equation Balance and Dynamic Political Modeling

Abstract

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.

Social Investment, Employment Outcomes and Policy and Institutional Complementarities: A Comparative Analysis across 26 OECD countries

“…Only when using an average lag length of 0.69 in the ADF regressions following AIC the null-hypothesis cannot be rejected, meaning that at least some panels are stationary (̅̅̅ = -2.19; p = 0.01). If series are nonstationary Lebo and Grant (2016) argue that analysts should closely examine equation balance in order to determine whether the estimation of an error correction model is appropriate. Philips (2018) elaborates the solutions suggested by Lebo and Grant (2016) by using the bounds testing procedure developed by Pesaran, Shin and Smith (2001).…”

“…If series are nonstationary Lebo and Grant (2016) argue that analysts should closely examine equation balance in order to determine whether the estimation of an error correction model is appropriate. Philips (2018) elaborates the solutions suggested by Lebo and Grant (2016) by using the bounds testing procedure developed by Pesaran, Shin and Smith (2001). This procedure helps analysts to test the existence of a long run relationship between the dependent variable and a set of regressors when one is certain that the dependent variable is a unit root but uncertain about the dynamic properties of the regressors.…”

Beyond the Unit Root Question: Uncertainty and Inference

“…A recent flurry of articles has grappled with this problem. Grant and Lebo (), Lebo and Grant (), Keele, Linn, and Webb (, ), Esarey (), and Helgason () demonstrate when standard strategies are likely to be vulnerable to misclassification and when they may be fairly robust. Enns et al.…”

“…A recent flurry of articles has grappled with this problem. Grant and Lebo (2016), Lebo and Grant (2016), Webb (2016a, 2016b), Esarey (2016), and Helgason (2016) demonstrate when standard strategies are likely to be vulnerable to misclassification and when they may be fairly robust. Enns et al (2016), Lebo and Kraft (2017), contend with the different substantive conclusions that come from divergent interpretations of unit root test results.…”

“…In the next section, we describe the two central problems complicating tests for long-run relationships: the practical problems of pretesting and the ambiguities in extant tests for LRRs given this uncertainty. We then discuss concepts of equilibrium and show the problem 1 This is true whether we estimate the popular autoregressive distributed lag model (ADL), use the generalized error correction model (GECM; De Boef and Granato 1997;De Boef and Keele 2008;Engle and Granger 1987;Ericsson and MacKinnon 2002), or model the series as a fractionally integrated process (Box-Steffensmeier and Tomlinson 2000;Clarke and Lebo 2003;Lebo and Grant 2016). with tests commonly applied in the GECM framework. Following that, we present both the long-run multiplier (LRM) t-test as a general test for long-run relationships and a bounds framework for assessing the significance of the LRM test statistic that accommodates uncertainty about the univariate properties of the data.…”