Cointegration and control: Assessing the impact of events using time series data

Abstract

Summary Control groups can provide counterfactual evidence for assessing the impact of an event or policy change on a target variable. We argue that fitting a multivariate time series model offers potential gains over a direct comparison between the target and a weighted average of controls. More importantly, it highlights the assumptions underlying methods such as difference in differences and synthetic control, suggesting ways to test these assumptions. Gains from simple and transparent time series models are analysed using examples from the literature, including the California smoking law of 1989 and German reunification. We argue that selecting controls using a time series strategy is preferable to existing data‐driven regression methods.

Time Series Modelling of Epidemics: Leading Indicators, Control Groups and Policy Assessment

“…Let t ¼ m denote the date of divergence and let b δ t denote the values of δ t estimated for the lockdown growth path using the data on UK and Italy. Since the moving averages are quite smooth, b δ t was constructed as a simple average of the two countries, rather than by restricted least squares (RLS) as 11 in Harvey and Thiele (2021). Then,…”

“…The impact of lockdowns is explored further by developing the ideas associated with balanced growth to try to estimate the number of coronavirus deaths in Sweden had a more stringent lockdown been imposed. The methodology draws on the study of control groups in time series by Harvey and Thiele (2021). It is argued that the fact that death rates in Sweden were roughly 10 times those in neighbouring countries could be misleading; the growth paths of the UK and Italy provide more relevant information.…”

Estimating the Effect of an EU-ETS Type Scheme in Australia Using a Synthetic Treatment Approach

“…Ideally, the EU-ETS participants (donors) used to construct the Australian counterfactuals would be similar to Australia with respect to features that characterise the behaviour of the target variable. Harvey and Thiele (2021) formalise this concept in a time series setting by suggesting that relevant donors might share a common stochastic trend with the target variable of interest. We adopt a similar approach in our synthetic treatment analysis, but use a less stringent interpretation of trend that is based on work in Phillips (1998).…”

Structural time series models and synthetic controls—assessing the impact of the euro adoption

“…Recently, a new SCM based on structural time series models (STMs) and cointegration has been developed by Harvey & Thiele (2021) (HT hereinafter). The approach of the HT-SCM is to identify control series that are comoving to the target series prior the intervention, i.e., the euro adoption.…”

“…The code used to estimate the models is able to replicate the results inHarvey and Thiele (2021) who apply a different computer package (STAMP byKoopman et al (2008)). …”