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The missing data problem pervasively exists in statistical applications. Even as simple as the count data in mortality projections, it may not be available for certain age-and-year groups due to the budget limitations or diculties in tracing research units, resulting in the follow-up estimation and prediction inaccuracies. To circumvent this data-driven challenge, we extend the Poisson log-normal Lee-Carter model to accommodate a more exible time structure, and develop the new sampling algorithm that improves the MCMC convergence when dealing with incomplete mortality data. Via the overdispersion term and Gibbs sampler, the extended model can be re-written as the dynamic linear model so that both Kalman and sequential Kalman lters can be incorporated into the sampling scheme. Additionally, our meticulous prior settings can avoid the re-scaling step in each MCMC iteration, and allow model selection simultaneously conducted with estimation and prediction.

The proposed method is applied to the mortality data of Chinese males during the period 1995-2016 to yield mortality rate forecasts for 2017-2039. The results are comparable to those based on the imputed data set, suggesting that our approach could handle incomplete data well.

Keywords: Poisson log-normal Lee-Carter model, mortality projection, incomplete data, Kalman filter, sequential Kalman filter, dirac spike.

Under standard assumptions, the average price change of a security caused by a materially important announcement is zero. Event studies, used to test whether announcements are materially important, must therefore “bin” announcements into above or below market expectations. Otherwise, the approach would have no power to reject a null hypothesis of a no announcement effect. In situations where market expectations are unknown, we show a Wald statistic (the square of the standardized cumulative abnormal return found in standard event studies) is an easily implementable and powerful approach to test whether an event affects securities prices. We also provide three examples of its applicability.

Keywords: Event study, Wald statistic, efficient market hypothesis.

When modelling phenomena relating to the economy, dynamic panel models have proven to be a useful tool. Previous studies have modelled dynamic panel data using conventional methods of generalized method of moment, Instrumental variables and Maximum likelihood estimators among others. This study however focuses on modelling dynamic panel data using modern day approaches of deep-learning techniques. To this end, two macro-economic variables of Purchasing Power Parity (PPP) and Gross National Income (GNI) were employed to model the economic growth of twenty African countries. Dynamic panel information about these countries were sourced from UNESCO database between 1990 and 2019. Deep learning techniques of Long Term Short memory (LSTM), Bidirectional Long Short Term Memory (Bi-LSTM) and Gated Recurrent Units (GRU) were employed in the modelling process, and the findings revealed that LSTM having the least values of the adopted evaluation metrics, is the best and most suitable deep learning method for modelling dynamic panel data. Forecasts were also made for the next 20 years with the techniques, and the results show that LSTM gives the best predicting accuracy with its lowest Mean Absolute Error (MAE), MAPE, MSE and RMSE.

Keywords: Africa Economic Growth, Deep-Learning, Dynamic Panel Data, Evaluation Metrics, Forecast.

This paper examines different approaches for assessing causality as typically followed in econometrics and proposes a constructive perspective for improving statistical models elaborated in view of causal analysis. Without attempting to be exhaustive, this paper examines some of these approaches. Traditional structural modeling is first discussed. A distinction is then drawn between model-based and design-based approaches. Some more recent developments are examined next, namely history-friendly simulation and information-theory based approaches. Finally, in a constructive perspective, structural causal modeling (SCM) is presented, based on the  concepts of mechanism and sub-mechanisms, and of recursive decomposition of the joint distribution of variables. This modeling strategy endeavors at representing the structure of the underlying data generating process. It operationalizes the concept of causation through the ordering and role-function of the variables in each of the intelligible sub-mechanisms.

Keywords: structural modeling, exogeneity, causality, model-based and designbased approaches, recursive decomposition, history-friendly simulation, transfer entropy.

JEL Classification: C01, C03, C15, C18, C51, C54

A reinsurance contract should address the conflicting interests of the insurer and reinsurer. Most of the existing optimal reinsurance contracts only consider the interests of one party. This article combines the proportional and stop-loss reinsurance contracts and introduces a new reinsurance contract called proportional-stop-loss reinsurance. Using the balanced loss function, unknown parameters

of the proportional-stop-loss reinsurance have been estimated such that the expected surplus for both the insurer and reinsurer are maximized. Several characteristics for the new reinsurance are provided.

Keywords: Proportional reinsurance; Stop-loss reinsurance; Expected utility; Bayesian approach; Balanced loss function.