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.

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.

The primary justification for the expectation that political time series may be fractionally integrated is based upon the aggregation theorem of Granger (1980), which has been demonstrated empirically with public opinion data by Box-Steffensmeier and Smith (1996) as well as Byers, Davidson, and Peel (1997). This chapter investigates a secondary justification for the presence of fractional integration - the error duration model (EDM) of Parke (1999). The variable of interest in such a model is the sum of shocks which survive to a specific time point, T. Given a process that generates a sequence of stochastic shocks, which are themselves stochastic in terms of duration and magnitude, a process can exhibit long-memory if a small percentage of shocks survive for long durations. Such a representation potentially explains the presence of fractionally integrated political time series that are not the product of aggregation. If events generate shocks of varying duration, it is possible for these shocks to then transmit long-memory to other political variables. The EDM representation is applied to a data set capturing the post-enactment history of federal domestic spending programs from 1971 to 2004. The survival rates of federal policies are demonstrated to be fractionally integrated.

The finite sample properties of various parametric and semiparametric estimators of fractional integration are determined using Monte Carlo simulations. Previous work investigating the performance of fractional estimators relied on large sample sizes typical of economic and finance data sets. Here, the simulations are run with sample sizes representative of data sets commonly found in political science - between 40 and 100. Simulations are run on three different data generating processes (0, d, 0), (1, d, 0), and (0,d,1), with the AR and MA parameters and the order of fractional integration, d, varying with the order of fractional integration. The results indicate that semiparametric methods and the parametric frequency domain Whittle estimator are consistent across all ranges of observations with a purely fractional, (0,d,0) process, while the parametric time domain estimator exhibits a negative bias in its estimates. In the presence of a higher-order process the time domain estimator suffers dramatically and the semiparamteric estimators also exhibit bias that is potentially alleviated with proper choice of bandwidth. Throughout, the frequency domain maximum likelihood estimator outperforms other estimators, even in the presence of significant higher frequencies. The results indicate that fractional integration can be reliably estimated with lag lengths of 80 observations, but caution is still urged, particularly with the time domain estimator.

Pay-for-performance, where healthcare remuneration is linked to prescribed key performance indicators (KPIs) rather than units of service delivery, is currently popular with healthcare administrators in many Organisation for Economic Co-operation and Development (OECD) countries as a tool for managing the complex balance of healthcare costs, quality, and outcomes. Where is the evidence? There is, at best, equivocal evidence that pay-for-performance is an effective way to improve service efficiency and quality. A 2013 article in the Harvard Business Review stated: Overall, evidence of the effectiveness of pay-for-performance in improving health care quality is mixed, without conclusive proof that these programs either succeed or fail. Some evaluations of pay-for-performance programs have found that they can modestly improve adherence to evidence-based practice. There is little evidence, however, that these programs improve patient outcomes, suggesting that to the extent that health care providers have responded to pay-for-performance programs, that response has been narrowly focused on improving the measures for which they are rewarded . . .1 So, why do healthcare administrators persist with pay-for-performance?