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Register a new userEfficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve
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This paper develops the asymptotic theory of a Fully Modified Generalized Least Squares estimator for multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends and integer powers of stochastic trends to enter the cointegrating relations. Our fully modified estimator incorporates: (1) the direct estimation of the inverse autocovariance matrix of the multidimensional errors, and (2) second order bias corrections. The resulting estimator has the intuitive interpretation of applying a weighted least squares objective function to filtered data series. Moreover, the required second order bias corrections are convenient byproducts of our approach and lead to standard asymptotic inference. We also study several multivariate KPSS-type of tests for the null of cointegration. A comprehensive simulation study shows good performance of the FM-GLS estimator and the related tests. As a practical illustration, we reinvestigate the Environmental Kuznets Curve (EKC) hypothesis for six early industrialized countries as in Wagner et al. (2020).
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The Environment Kuznets Curve (EKC) predicts an inverted U-shaped relationship between economic growth and environmental pollution. Current analyses frequently employ models which restrict the nonlinearities in the data to be explained by the economic growth variable only. We propose a Generalized Cointegrating Polynomial Regression (GCPR) with flexible time trends to proxy time effects such as technological progress and/or environmental awareness. More specifically, a GCPR includes flexible powers of deterministic trends and integer powers of stochastic trends. We estimate the GCPR by nonlinear least squares and derive its asymptotic distribution. Endogeneity of the regressors can introduce nuisance parameters into this limiting distribution but a simulated approach nevertheless enables us to conduct valid inference. Moreover, a subsampling KPSS test can be used to check the stationarity of the errors. A comprehensive simulation study shows good performance of the simulated inference approach and the subsampling KPSS test. We illustrate the GCPR approach on a dataset of 18 industrialised countries containing GDP and CO2 emissions. We conclude that: (1) the evidence for an EKC is significantly reduced when a nonlinear time trend is included, and (2) a linear cointegrating relation between GDP and CO2 around a power law trend also provides an accurate description of the data.
We develop a distribution regression model under endogenous sample selection. This model is a semiparametric generalization of the Heckman selection model that accommodates much richer patterns of heterogeneity in the selection process and effect of the covariates. The model applies to continuous, discrete and mixed outcomes. We study the identification of the model, and develop a computationally attractive two-step method to estimate the model parameters, where the first step is a probit regression for the selection equation and the second step consists of multiple distribution regressions with selection corrections for the outcome equation. We construct estimators of functionals of interest such as actual and counterfactual distributions of latent and observed outcomes via plug-in rule. We derive functional central limit theorems for all the estimators and show the validity of multiplier bootstrap to carry out functional inference. We apply the methods to wage decompositions in the UK using new data. Here we decompose the difference between the male and female wage distributions into four effects: composition, wage structure, selection structure and selection sorting. After controlling for endogenous employment selection, we still find substantial gender wage gap -- ranging from 21% to 40% throughout the (latent) offered wage distribution that is not explained by observable labor market characteristics. We also uncover positive sorting for single men and negative sorting for married women that accounts for a substantive fraction of the gender wage gap at the top of the distribution. These findings can be interpreted as evidence of assortative matching in the marriage market and glass-ceiling in the labor market.
Dynamic model averaging (DMA) combines the forecasts of a large number of dynamic linear models (DLMs) to predict the future value of a time series. The performance of DMA critically depends on the appropriate choice of two forgetting factors. The first of these controls the speed of adaptation of the coefficient vector of each DLM, while the second enables time variation in the model averaging stage. In this paper we develop a novel, adaptive dynamic model averaging (ADMA) methodology. The proposed methodology employs a stochastic optimisation algorithm that sequentially updates the forgetting factor of each DLM, and uses a state-of-the-art non-parametric model combination algorithm from the prediction with expert advice literature, which offers finite-time performance guarantees. An empirical application to quarterly UK house price data suggests that ADMA produces more accurate forecasts than the benchmark autoregressive model, as well as competing DMA specifications.
We develop a novel method of constructing confidence bands for nonparametric regression functions under shape constraints. This method can be implemented via a linear programming, and it is thus computationally appealing. We illustrate a usage of our proposed method with an application to the regression kink design (RKD). Econometric analyses based on the RKD often suffer from wide confidence intervals due to slow convergence rates of nonparametric derivative estimators. We demonstrate that economic models and structures motivate shape restrictions, which in turn contribute to shrinking the confidence interval for an analysis of the causal effects of unemployment insurance benefits on unemployment durations.
We consider sparse estimation of a class of high-dimensional spatio-temporal models. Unlike classical spatial autoregressive models, we do not rely on a predetermined spatial interaction matrix. Instead, under the assumption of sparsity, we estimate the relationships governing both the spatial and temporal dependence in a fully data-driven way by penalizing a set of Yule-Walker equations. While this regularization can be left unstructured, we also propose a customized form of shrinkage to further exploit diagonally structured forms of sparsity that follow intuitively when observations originate from spatial grids such as satellite images. We derive finite sample error bounds for this estimator, as well estimation consistency in an asymptotic framework wherein the sample size and the number of spatial units diverge jointly. A simulation exercise shows strong finite sample performance compared to competing procedures. As an empirical application, we model satellite measured NO2 concentrations in London. Our approach delivers forecast improvements over a competitive benchmark and we discover evidence for strong spatial interactions between sub-regions.
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