This appendix provides the following items: response surfaces to approximate p-values, mathematical proofs, additional results from Monte Carlo experiments for the small sample properties, and the results from examining the performance of the F-test and the SBC selection procedure in determining the number of cumulative frequencies of the Fourier function.
Appendix A. Response surfaces to approximate p-valuesThis section explains how we estimate the response surface function to find the p-values of the univariate test statistic τ in (13). Since the individual test statistic has a non-standard limiting distribution, the corresponding p-values, denoted as p, must be approximated to construct the panel statistics proposed in ( 20) and ( 21). As the model specification using the Fourier function is simpler, the response surface function using the frequency parameters is easy to estimate and it performs fairly well, even in finite samples. This feature can lead to good size and power properties since the uncertainty of estimating more parameters can be reduced.We follow MacKinnon (1996MacKinnon ( , 2002 and estimate response surfaces to approximate p for the τ statistic. 1 We conduct Monte Carlo simulations in order to obtain the empirical distribution of τ for a range of 26 sample sizes,
This study tests for convergence in economic freedom across the 50 U.S. states from 1981 to 2019. In particular, we test for stochastic convergence in overall economic freedom using unit root tests that account for structural breaks and bounded processes, two sources of parameter instability. We find limited evidence of stochastic convergence. Further analysis of relative (club) convergence and weak σ‐convergence rejects the presence of overall convergence in the panel of the U.S. states, but the emergence of two convergence clubs with respect to state‐level economic freedom. The logit analysis of the determinants of the convergence clubs reveals that more prosperous states and states with a higher initial level of economic freedom have a higher probability of being in the club with more economic freedom. However, more racially diverse states have a lower probability of being in the club with more economic freedom.
Background: Suicide has become a public mental health problem in Turkey, with the number of deaths increasing: in 1974, the suicide rate was 1.92% for males and 1.31% for females; in 2013 this had risen to 6.22% for males and 2.26% for females. Aims: This study attempts to empirically investigate the behaviour of suicide in Turkey by focusing on sex and cause. We pay special attention to the role of structural shifts in suicide ratios, which may have arisen from the structural changes in Turkish economy during last 2 decades. Methods: We used time series analysis and employed unit root and stationarity tests for the period 1974-2013. Results: The results show that disruption to female suicide and suicidal affairs stemmed from economic problems and business failures have a random walk process. This finding implies that shocks driven by economic issues and shocks toward the female sex have a permanent, long-term impact on suicide. Conclusions: The implication is that the social administration needs to implement relevant, necessary suicide prevention policies for suicides occurring in the female and economic problems groups.
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