Phase and wave dependent analysis of health expenditure efficiency during pandemic: A sample of OECD evidence

This study focuses on evaluating and improving the effectiveness of healthcare expenditures in the public health system during the pandemic. A novel indirect measurement method is employed to examine the effectiveness of healthcare expenditures, using daily case numbers as a proxy. The hypothesis tested suggests that healthcare expenditures are effective when daily case numbers are stationary, whereas they are ineffective when case numbers are non-stationary. The analysis of data reveals that daily case numbers exhibit nonlinear periodic behavior in each country. To forecast the long-term periodic movement, a nonlinear cumulative Fourier function (discrete cumulative Fourier function) is proposed. Previous studies have addressed the issue of overfitting under an ad-hoc assumption, while this study proposes a mathematical solution with a constraint to determine the optimal frequency (n). In the second stage, to measure effectiveness according to waves and phases, the first and second derivatives of the case numbers' trend, represented by the reproduction number (R), are used to identify inflection points indicating changes in speed, which in turn determine wave and phase intervals. In the third stage, the Augmented Dickey-Fuller (ADF) unit root test is conducted to examine the stationarity of case numbers, assessing whether each country's healthcare expenditures are effective based on waves and phases. The stationarity of phase series implies predictability of cases and effectiveness of healthcare expenditures during that phase. The study provides insights into the effectiveness of healthcare expenditures based on daily case numbers during the Covid-19 pandemic in six OECD countries. It also addresses the challenges of inter-country comparisons and sample homogeneity. The findings aim to assist countries in developing effective short and long-term policies against pandemics. Furthermore, the proposed method offers a fresh perspective on the effectiveness of healthcare expenditures and can be utilized as a helpful tool in decision-making processes across various sectors such as energy, agriculture, and tourism.