Note on positive lower bound of capital in the stochastic growth model

In the context of the classical stochastic growth model, we provide a simple proof that the optimal capital sequence is strictly bounded away from zero whenever the initial capital is strictly positive. We assume that the utility function is bounded below and the shocks affecting output are bounded. However, the proof does not require an interval shock space, thus, admitting both discrete and continuous shocks. Further, we allow for finite marginal product at zero capital. Finally, we use our result to show that any optimal capital sequence converges globally to a unique invariant distribution, which is bounded away from zero.     

Long-term forecasting and evaluation

Looking ahead thirty years is a difficult task, but is not impossible. In this paper we illustrate how to evaluate such long-term forecasts. Long-term forecasting is likely to be dominated by trend curves, particularly the simple linear and exponential trends. However, there will certainly be breaks in their parameter values at some unknown points, so that eventually the forecasts will be unsatisfactory. We investigate whether or not simple methods of long-run forecasting can ever be successful, after one takes into account the uncertainty level associated with the forecasts.     

The size distribution of ‘cities’ delineated with a network theory‐based method and mobile phone GPS data

We delineate “cities” independent of administrative boundaries in Japan by using a network theory‐based method and GPS‐based human mobility data. We divide the country into approximately 1 × 1 km² cells and detect the partition of cells that is optimal from the perspective of information theory. The resulting groups of cells are specified as cities. We find that the combination of two lognormal distributions better fits the city‐size distribution than a distribution with a Pareto upper tail. Moreover, we show that a jump diffusion process is the stochastic process of the city population underlying such a distribution.     

Another Look at the Equity Risk Premium Puzzle

The model of Mehra and Prescott (1985, J. Econometrics, 22, 145–161) implies that reasonable coefficients of risk‐aversion of economic agents cannot explain the equity risk premium generated by financial markets. This discrepancy is hitherto regarded as a major financial puzzle. We propose an alternative model to explain the equity premium. For normally distributed returns and for returns far away from normality (but still light tailed), realistic equity risk premia do not imply puzzlingly high risk aversions. Following our approach, the ‘equity premium puzzle’ does not exist. We also consider fat‐tailed return distributions and show that Pareto tails are incompatible with constant relative risk aversion.     

Convergence clustering in the Chinese provinces: New evidence from several macroeconomic indicators

In this paper, the convergence clustering in 31 Chinese provinces regarding several important economic indicators over the period 1952 to 2016 was empirically investigated. Several provincial clusters were identified in the per capita (real) gross domestic product (GDP), consumption–income ratio, retail price, and consumer price inflation rates, using a club convergence and clustering procedure. The empirical findings are as follows. First, it was found that all series of the original data contain a significant nonlinear component. Second, it was observed that there are five significant clusters for the per capita income in China. Third, it was found that there are four significant clusters for the consumption–income ratio. Fourth, it was observed that there are four significant clusters for the retail inflation rates and two significant clusters for the consumer inflation rates in China. These results will enable local and central planners to implement economic growth, savings and price adjustment policies for different groups of provinces.     

A note on the estimated GARCH coefficients from the S&P1500 universe

ABSTRACT

We employ 1440 stocks listed in the S&P Composite 1500 Index of the NYSE. Three benchmark GARCH models are estimated for the returns of each individual stock under three alternative distributions (Normal, t and GED). We provide summary statistics for all the GARCH coefficients derived from 11,520 regressions. The EGARCH model with GED errors emerges as the preferred choice for the individual stocks in the S&P 1500 universe when non-negativity and stationarity constraints in the conditional variance are imposed. 57% of the constraint’s violations are taking place in the S&P small cap stocks.     

Analytic moments for GJR-GARCH (1, 1) processes

For a GJR-GARCH(1, 1) specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moments for the most commonly used GARCH models are stated as special cases. We also derive the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments. A simulation study using these analytic moments produces approximate predictive distributions which are free from the bias affecting simulations. An empirical study using almost 30 years of daily equity index, exchange rate and interest rate data applies Johnson SU and Edgeworth expansion distribution fitting to our closed-form formulae for higher moments of returns.     

基于EGM2008模型确定的昆明地区似大地水准面精化

本文主要介绍了EGM2008模型与利用GPS水准点与EGM2008模型相结合进行大地水准面精化的方法。结合昆明市呈贡区部分GPS水准点数据在EGM2008模型的基础上利用GPS水准点与EGM2008模型结合计算出高程异常然后采用多项式拟合的方法拟合,最后对拟合后的结果进行了一个检验和精度评估。     

Bayesian median autoregression for robust time series forecasting

We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging is used to account for model uncertainty, including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulations and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performance compared to the selected mean-based alternatives under various loss functions that encompass both point and probabilistic forecasts. The proposed methods are generic and can be used to complement a rich class of methods that build on autoregressive models.     

Crop Insurance Valuation under Alternative Yield Distributions

Considerable disagreement exists about the most appropriate characterization of farm-level yield distributions. Yet, the economic importance of alternative yield distribution specifications on crop insurance valuation has not been well documented. The results of this study demonstrate that large differences in expected payouts from popular crop insurance products can arise solely from the parameterization chosen to represent yield distributions. The results suggest that the frequently unexamined yield distribution specification may lead to economically significant errors in crop insurance policy rating and assessment of expected payouts from policies.