Statistical modelling of temporal and spatial causal effects with application to policy evaluation

Abstract

This thesis aims at developing temporal and spatial statistical causal inference methods applicable to policy evaluation problems. Specifically, we are interested in the problems of determining the causal effect of a certain intervention on the metric that is of our interest, such as the impact of a government policy on certain local financial or economic indicators. We propose two causal models in this thesis for such causal inference problems with their theoretical properties established.

For the first model, from the perspective of time series, we propose a modified synthetic control causal model for time series data with volatility in terms of absolute value of return outcomes taken into account to construct the inference of potential outcomes for time series causal analysis. The consistency property of the synthetic weight parameter estimators is developed theoretically under time series dependent conditions. Its application to evaluate the UK’s mini-budget policy, announced by the then Chancellor on 23 September 2022, which had significant implications for the stock market, is examined and analysed. Empirical comparison with conventional synthetic control and synthetic difference in difference (SDID) methods in evaluating the causal effect of the mini-budget policy on the UK’s stock market is also discussed.

For the second model, considering the existence of spatial dependence among the locations while determining the causal effect of some locally intervention on the treated location, we additionally take the spatio-temporal dependence into consideration to propose a spatio-temporal penalized synthetic error model for spatio-temporal causal inference problems. It borrows the synthetic idea from the synthetic control method but adopts a more generalized brand new synthetic error structure to deal with the unobserved factors including confounding factors and exogenous variables in causal inference problems. For the determination of synthetic weights in the error synthetic process, we make use of the adaptive Lasso penalization to obtain the sparse error synthetic weights so that the interpretation and good validation performance of this model can be ensured. Since the parameters of this model are estimated using a two step method, the asymptotic properties of the parameters in the two steps are developed separately under the spatio-temporal dependence conditions. We evaluate the causal effect of Kansas 2012 Tax Cuts on its GDP as the empirical study to assess the performance of our method empirically in comparison with other popular causal models. Simulation studies are also conducted to compare the spatio-temporal penalized synthetic error model with other methods. And the advantage of selecting the tuning parameter for adaptive Lasso penalization by cross-validation is also discussed in the simulation cases.

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Identifiers

ORCID for Yan Zhang: orcid.org/0009-0001-8003-4547

ORCID for Zudi Lu: orcid.org/0000-0003-0893-832X

ORCID for Wei Liu: orcid.org/0000-0002-4719-0345

ORCID for Chao Zheng: orcid.org/0000-0001-7943-6349

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