This paper examines how intergenerational income dependence in the United States has evolved across birth cohorts from 1987 to 2021. We employ a time-varying mixed copula model that combines Clayton, Gumbel, and Frank copulas, with weights and dependence parameters varying smoothly over cohort years, to estimate the full joint dependence structure between parent and offspring permanent incomes. Intergenerational immobility is summarized by the normalized Hellinger distance between the observed joint distribution and the independence benchmark. This index remained stable through the 1990s but increased sharply after 2000, approximately tripling by the 2010s. The copula decomposition associates this increase with upper-tail tightening: the Gumbel copula weight rises substantially, indicating increasing affluence persistence among high-income families, while the Clayton copula coefficient shows no significant trend, implying that lower-tail persistence did not intensify. Subgroup analyses reveal heterogeneous changes in within-group rank dependence, with a particularly sharp increase in the West.

This paper surveys the literature for the optimization problems in both discrete and continuous time models in macroeconomics, and provides an overview over some related computational methods to solve the models linearly and nonlinearly, and to compute the transition dynamics and the impulse response functions. Also, the introduction of the financial sectors, the continuous time analysis, and the advanced mathematical tools into the general equilibrium framework expands greatly the scope of the interdisciplinary research to mathematics, statistics and econometrics, and creates further space for exploration and collaboration. Finally, some future research issues related to this topic are highlighted.

This article proposes a generalized conditional autoregressive expectile model, including autoregressive components in assessing tail risk, which can be treated as an infinite version of the conditional autoregressive expectile model proposed by and can be implemented as a vehicle for estimating the CAViaR model proposed in and studied by . Due to the unobservable latent components in the proposed model, the quasi-maximum likelihood estimation method is suggested and a HAC covariance matrix estimator is proposed. Furthermore, a dynamic expectile test is proposed for both in-sample model adequacy evaluation and out-of-sample forecasting for comparison purposes. Finally, Monte Carlo simulations and a real example are conducted to illustrate that the proposed methodology is practically useful. Our empirical study demonstrates that the tail risk characterized by the proposed model achieves a better performance in the period of the Covid-19 epidemic.

This article investigates the relative importance of internal and external sources of funds in financing activities across different levels of investment activities by proposing a panel data quantile regression model with correlated random effects, accounting for heteroscedasticity in both firm-specific individuals and distribution of investment. A new estimation method, which takes the influence of disturbance into account, is proposed by using the integrated quasi-likelihood function for the conditional quantile model and Laplace approximation. The large sample theory for the proposed estimator and the corresponding asymptotic chi 2 test are investigated. A Monte Carlo simulation is conducted to examine the finite sample performance of the proposed estimator. Finally, empirical results find strong evidence that the financing hierarchy of U.S. firms is in accordance with the first rung of the pecking order theory across all levels of investments from 10% to 90%, but for the second rung of the pecking order theory, only at 30% to 70% levels of investments.

The escalating trade war between China and the US, initiated in 2018, has significantly impacted the trade pattern of these two nations. This event can be treated as an intervention which has led to a series of retaliatory actions, resulting in substantial economic and trade frictions between the two largest economies. This paper aims to analyze the economic impacts of the trade war effects using advanced econometric techniques. Our empirical study employs panel data analysis combined with a factor model, inspired by the methodologies of Hsiao, Ching and Wan (2012) and Bai, Li and Ouyang (2014), to construct trade patterns for both China and the US. By using annual trade data from multiple countries as a control group, we construct counterfactual results for China's and the US's imports, exports, and trade balance, respectively. Under a nonstationary setting, the counterfactual results indicate a significant decline in China's exports and a notable reduction in its trade surplus with the US post-2018. Meanwhile, US imports from China decreased, aligning with the trade war's goal of reducing the trade deficit, while US exports to China unexpectedly increased, possibly influenced by the Phase One trade agreement. We also perform a dynamic permutation test on treatment effects over time, which ensures the rigor and significance of our analysis, reinforcing the reliability of the estimated effects. Finally, we conduct an empirical comparative analysis with alternative methods to demonstrate that our chosen is well-suited to the context of this

In this article, we investigate a functional coefficient vector autoregressive model for conditional quantiles, in which the interdependences among tail risks such as Value-at-Risk are allowed to vary smoothly with a variable of general economy. Methodologically, we develop an easy-to-implement two-stage procedure to estimate functionals in the dynamic network system based on the deep learning method of neural networks and the local linear smoothing technique. We establish the consistency and the asymptotic normality of the proposed estimator under geometrically beta-mixing time series settings. The simulation studies are conducted to show that our new methods work fairly well. The potential of the proposed estimation procedures is demonstrated by an empirical study of constructing and estimating a new type of nonparametric dynamic financial network.

Using the China CFPS database, this paper measures the degree of intra-occupational inequality in China with the Pareto coefficient and uses the generalized entropy index to decompose the top income gap by region as well as by industry. The empirical results show that, firstly, the degree of income inequality between occupations in China has increased significantly in recent years. The provinces with a higher degree of income inequality between occupations are mostly located in the more economically developed regions in the central and eastern parts of the country, while the degree of inequality between occupations in the western part is lower. Secondly, the highest-income occupations are mainly in the manufacturing industry, with relatively high levels in the construction industry, the education sector, the wholesale and retail trade, and public administration and social organizations, while the levels in other occupations are relatively low. Lastly, the top income gap primarily originates from within industries. However, the contribution rate of the top income gap between industries is gradually increasing, while the contribution rate of the top income gap within industries is gradually decreasing.

In this paper, we propose utilizing machine learning methods to determine the expected aggregated stock market risk premium based on online investor sentiment and employing the multifold forward-validation method to select the relevant hyperparameters. Our empirical studies provide strong evidence that some machine learning methods, such as extreme gradient boosting or random forest, show significant predictive ability in terms of their out-of-sample performances with high-dimensional investor sentiment proxies. They also outperform the traditional linear models, which shows a possible unobserved nonlinear relationship between online investor sentiment and risk premium. Moreover, this predictability based on online investor sentiment has a better economic value, so it improves portfolio performance for investors who need to decide the optimal asset allocation in terms of the certainty equivalent return gain and the Sharpe ratio.

The estimation and model selection of the conditional autoregressive value at risk (CAViaR) model may be computationally intensive and even impractical when the true order of the quantile autoregressive components or the dimension of the other regressors are high. On the other hand, conventional automatic variable selection methods cannot be directly applied to this problem because the quantile lag components are latent. In this paper, we propose a two-step approach to select the optimal CAViaR model. The estimation procedure consists of an approximation of the conditional quantile in the first step, followed by an adaptive Lasso penalized quantile regression of the regressors as well as the estimated quantile lag components in the second step. We show that under some regularity conditions, the proposed adaptive Lasso penalized quantile estimators enjoy the oracle properties. Finally, the proposed method is illustrated by a Monte Carlo simulation study and applied to analyzing the daily data of the S& P 500 return series.

This paper explores theoretically and empirically the issue of time-varying relative risk aversion. We analytically solve a parsimonious life-cycle portfolio choice model with the preferences given by Greenwood, Hercowitz and Huffman (1988, GHH). Our analytical solution identifies four partial equilibrium effects in our model with GHH preferences on risky shares through two channels, and two net effects whose signs hinge on the value of a key structural parameter. With household-level micro data, our mean and quantile regression results show that wealth negatively affects risky shares and the estimated effects are statistically significant and robust. This finding provides strong evidence to support our theoretical prediction. Thus, we show successfully that our portfolio choice model with GHH preferences provides a plausible underlying mechanism in understanding the wealth effect on risky shares in the microdata. Furthermore, we conclude that such a mechanism alone is not sufficient in explaining how risky shares respond to labor income and labor income risks in the microdata.

This paper investigates model specification problems for nonlinear stochastic differential equations with delay (SDDE). Compared to the model specification for conventional stochastic diffusions without delay, the observed sequence does not admit a Markovian structure so that the classical testing procedures may not be applicable. To overcome this difficulty, a moment estimator is newly proposed based on the ergodicity of SDDEs and its asymptotic properties are established. Based on the proposed moment estimator, a testing procedure is proposed for our model specification testing problems. Particularly, the limiting distributions of the proposed test statistic are derived under null hypotheses and the test power is examined under some specific alternative hypotheses. Finally, a Monte Carlo simulation is conducted to illustrate the finite sample performance of the proposed test.

In this paper, we propose a new procedure to test conditional independence assumption in studying casual inference for time series data. The conditional independence assumption is transformed to a nonparametric conditional moment test with the help of auxiliary variables which are allowed to affect policy choice but the dependence can be fully captured by potential outcomes and observable controls. When the policy choice is binary, a nonparametric statistic test is developed further for testing the conditional independence assumption conditional on policy propensity score. Under some regular conditions, we show that the proposed test statistics are asymptotically normal under the null hypotheses for time series data. In addition, the performances of the proposed methods are illustrated through Monte Carlo simulations and a real example considered in Angrist and Kuersteiner (2011).

This paper proposes a nonparametric test to assess whether there exist heterogeneous quantile treatment effects (QTEs) of an intervention on the outcome of interest across different sub-populations defined by covariates of interest. Specifically, a consistent test statistic based on the Cramér–von Mises type criterion is developed to test if the treatment has a constant quantile effect for all sub-populations defined by covariates of interest. Under some regularity conditions, the asymptotic behaviors of the proposed test statistic are investigated under both the null and alternative hypotheses. Furthermore, a nonparametric Bootstrap procedure is suggested to approximate the finite-sample null distribution of the proposed test; then, the asymptotic validity of the proposed Bootstrap test is theoretically justified. Through Monte Carlo simulations, we demonstrate the power properties of the test in finite samples. Finally, the proposed testing approach is applied to investigate whether there exists heterogeneity for the QTE of maternal smoking during pregnancy on infant birth weight across different age groups of mothers.

This paper proposes a novel approach to offer a robust inferential theory across all types of persistent regressors in a predictive quantile regression model. We first estimate a quantile regression with an auxiliary regressor, which is generated as a weighted combination of an exogenous random walk process and a bounded transformation of the original regressor. With a similar spirit of rotation in factor analysis, one can then construct a weighted estimator using the estimated coefficients of the original predictor and the auxiliary regressor. Under some mild conditions, it shows that the self-normalized test statistic based on the weighted estimator converges to a standard normal distribution. Our new approach enjoys a good property that it can reach the local power under the optimal rate T with nonstationary predictor and T for stationary predictor, respectively. More importantly, our approach can be easily used to characterize mixed persistency degrees in multiple regressions. Simulations and empirical studies are provided to demonstrate the effectiveness of the newly proposed approach. The heterogeneous predictability of US stock returns at different quantile levels is reexamined.

This article considers predictive regressions in which a structural break is allowed on an unknown date. We establish novel testing procedures for asset return predictability using empirical likelihood (EL) methods based on weighted score equations. The theoretical results are useful in practice because our unified framework does not require distinguishing whether the predictor variables are stationary or non-stationary. Monte Carlo simulation studies show that the EL-based tests perform well in terms of size and power in finite samples. Finally, as an empirical analysis, we test the predictability of the monthly S&P 500 value-weighted log excess return using various predictor variables.

We establish the asymptotic distribution for rolling linear regression models using various window widths. The limiting distribution depends on the width of the rolling window and on a "bias process" that is typically ignored in practice. Based on the asymptotic distribution, we tabulate critical values used to find uniform confidence intervals for the average values of regression parameters over the windows. We propose a corrected rolling regression technique that removes the bias process by rolling over smoothed parameter estimates. The procedure is illustrated using a series of Monte Carlo experiments. The paper includes an empirical example to show how the confidence bands suggest alternative conclusions about the persistence of inflation.

With the increase of economic environment uncertainty, it is of great importance to study the linkage and spillover effects of economic policy uncertainty among countries. Especially, this article selects eight countries along the Belt and Road as the core countries (China, Korea, Croatia, India, Russia, Greece, Pakistan, and Singapore) and four countries (Germany, France, Japan, and UK) as the peripheral countries, and then copula technique and mixed-frequency global vector autoregressive model are employed to analyze the correlation and the spillover effect of the economic policy uncertainty (EPU) for the twelve selected countries, respectively. The proposed empirical findings show clearly that the EPU correlation among the eight core Belt and Road countries is stronger and the spillover effect of the core countries to the peripheral countries is statistically significant. As a result, for harmonious and win-win development, the Belt and Road countries should pay a close attention to the EPU, because the stability of the EPU promotes greatly the economy development.

This article investigates two test statistics for testing structural changes and thresholds in predictive regression models. The generalized likelihood ratio (GLR) test is proposed for the stationary predictor and the generalized F test is suggested for the persistent predictor. Under the null hypothesis of no structural change and threshold, it is shown that the GLR test statistic converges to a function of a centered Gaussian process, and the generalized F test statistic converges to a function of Brownian motions. A Bootstrap method is proposed to obtain the critical values of test statistics. Simulation studies and a real example are given to assess the performances of the proposed tests.