Using a polynomial cointegration technique, this paper shows that the bilateral US current account balance with China has a U-shaped relationship with the life expectancy gap between the US and China. A narrowing gap initially increases the US deficit with China, but eventually, this increased US deficit falls with the further catching-up of Chinese life expectancy. The life expectancy gap between the two countries has been below the threshold level since 2013, and this demographic trend has the potential to improve the US deficit with China. This U-shaped relationship can be theoretically reproduced. A two-country overlapping generations model indicates that the effect of life expectancy is decomposed into four components: retirement savings, social security burden, the number of elderly workers, and the productivity of elderly workers. The total effect of foreign life expectancy on the home current account balance exhibits a sign change in the catching-up of foreign life expectancy.

This paper explores the shape of the Japanese money demand function in relation to the historical path of the Bank of Japan's policy rate by employing Saikkonen and Choi's [Econometric Theory 20, 301–340 (2004)] cointegrating smooth transition model. The nonlinear model provides a unified econometric framework, not only for pursuing the time profile of interest elasticity, but also to test the linearity of the Japanese money demand function. The test results for the linearity of the Japanese money demand function provide evidence of nonlinearity with a semilog model and linearity with a double-log model. Using a nonlinear semilog model, the analysis also finds that Japanese money demand comprises three regimes and that the interest semielasticity began to increase in the early 1990s when the Bank of Japan set the policy rate below 3%.

This paper explores single-equation nonlinear error correction (NEC) models with linear and nonlinear cointegrated variables. Within the class of semiparametric NEC models, we use smoothing splines. Within the class of parametric models, we discuss the interesting properties of cubic polynomial NEC models and we show how they can be used to identify unknown threshold points in asymmetric models and to check the stability properties of the long-run equilibrium. A new class of rational polynomial NEC models is also introduced. We found multiple long-run money demand equilibria. The stability observed in the money-demand parameter estimates during more than a century, 1878 to 2000, is remarkable.