This paper considers a functional-coefficient spatial Durbin model with nonparametric spatial weights. Applying the series approximation method, we estimate the unknown functional coefficients and spatial weighting functions via a nonparametric two-stage least squares (or 2SLS) estimation method. To further improve estimation accuracy, we also construct a second-step estimator of the unknown functional coefficients by a local linear regression approach. Some Monte Carlo simulation results are reported to assess the finite sample performance of our proposed estimators. We then apply the proposed model to re-examine national economic growth by augmenting the conventional Solow economic growth convergence model with unknown spatial interactive structures of the national economy, as well as country-specific Solow parameters, where the spatial weighting functions and Solow parameters are allowed to be a function of geographical distance and the countries' openness to trade, respectively.

The new growth theories with an emphasis on fundamental determinants such as institutions suggest a non-linear cross-country growth process. In this paper, we investigate the public debt and economic growth relationship using the semi-parametric smooth coefficient approach that allows democracy to influence this relationship and parameter heterogeneity in the unknown functional form and addresses the endogeneity of variables. We find results consistent with the previous literature that identified a significant adverse effect of public debt on growth for the countries below a particular democracy level. However, we also find conclusive evidence that countries with high institutional quality have an adverse effect of public debt on growth for the period 1980–2009, as well as for the extended period including the years 2010–2014. A 10-percentage point increase in the debt-to-GDP ratio is associated with a 0.12% and 0.07% decrease in the subsequent 10-year period real GDP growth rate for the zero democracy countries and for the countries with a democracy score of 10, respectively.