Vector Error Correction Models (VECM) have become a standard tool in empirical economics for analyzing nonstationary time series data because they integrate two key concepts in economics: equilibrium and dynamic adjustment in a single model. The current standard VECM procedure is limited to time series data with the same degree of integration, i.e., all I(1) variables. However, empirical studies often involve time series data with different de‐grees of integration, necessitating the simultaneous handling of I(1) and I(0) time series. This paper extends the standard VECM to accommodate mixed I(1) and I(0) variables. The conditions for the mixed VECM are derived, and consequently, we present a test and estimation for the mixed VECM.

The precise prediction of carbon emissions trading prices is the foundation for the stable and sustainable development of the carbon financial market. In recent years, influenced by a combination of factors such as the pandemic, trading regulations, and policies, carbon prices have exhibited strong random volatility and clear non-stationary characteristics. Traditional single-perspective prediction methods based on conventional statistical models are increasingly inadequate due to the homogenization of features and are struggling to adapt to China's regional carbon emissions trading market. Therefore, this paper proposes a multi-perspective fusion-based prediction method tailored to the Chinese market. It leverages carbon emissions trading information from key cities as relevant features to predict the price changes in individual cities. Inspired by the development of artificial intelligence, this paper implements various time series models based on deep neural networks. The effectiveness of the multi-perspective approach is validated through multiple metrics. It provides scientific decision-making tools for domestic carbon emissions trading investors, making a significant contribution to strengthening carbon market risk management and promoting the establishment and rational development of a unified carbon market in China.

This paper analyses a model of private value auctions with symmetric risk-neutral bidders, where bidders' private values of an indivisible good are fuzzy. The auction is studied as a game with incomplete information. Fuzzy random variables, their quantile functions, and expressions for expectations through quantile functions are used. An explicit expression for the solution is found. Also, expected bidders' payments are studied.

This paper investigates the degree of inflation persistence across regions in Portugal by analyzing the Consumer Price Index (CPI) growth rates for NUTS II regions. The study employs the Augmented Dickey-Fuller (ADF) test to determine whether the CPI data for Portugal is stationary or non-stationary. The results of the ADF test reveal that the IPC data for Portugal is non-stationary, indicating that inflation exhibits persistence in the long run. The study further assesses the persistence of inflation by estimating an autoregressive integrated moving average (ARIMA) model for each region. The Ljung-Box test is used to test for autocorrelation in the time series data, and the Hurst exponent is calculated to evaluate the presence of long-term memory in the time series data. The study finds that there is significant autocorrelation in the time series data for all regions, supporting the presence of persistence in inflation at the regional level in Portugal. The Hurst exponent also shows that the time series data for each region exhibits a high degree of persistence in inflation. Finally, the study applies the ARIMA model to each CPI division's data and uses the Ljung-Box test to test for autocorrelation in the time series data. The results show that some CPI divisions exhibited higher levels of persistence compared to others. For example, the "Housing, water, electricity, gas and other fuels" division exhibited high persistence, while the "Communication" division exhibited low persistence. This study contributes to the existing literature by exploring regional inflation persistence in Portugal and its implications for policymaking. The results provide insights into the inflation persistence patterns across regional levels in Portugal, by emphasizing the need to consider regional differences in inflation dynamics when formulating effective policy interventions. Understanding the persistence of inflation is crucial for policymakers to ensure price stability and sustainable economic growth.

This study documents the relationship between economic freedom and unauthorized immigration to the U.S.A. and tries to answer a still-in-debate question, what motivates people to unauthorizedly migrate? Using the generated instrument variables methodology, and a data panel of 15 countries and 16 years, the endogenous variable is the gap in economic freedom between the country of origin and the U.S., and the dependent variable is the unauthorized immigrant’s growth rate. The results show that for each 10% improvement in economic freedom in the country-of-origin unauthorized immigration decreases around 7%. Estimations are robust even after using other covariates and external instruments. The main conclusion is that economic and social factors play a significant role in shaping migration patterns and that the difference in economic freedom between the country of origin and the U.S. plays a fundamental role in deciding to unauthorizedly migrate

The Oswald hypothesis is that home ownership reduces mobility and through that channel results in poorer labor market outcomes. There has been only limited previous evidence on the Australian case. Here we use data from the first four Australian censuses of the twenty-first century, aggregated at the smallest geographical areas for which statistics are released. We propose testing the Oswald hypothesis by estimating the effect of home ownership on the full-time employment rate. Modelling the unemployment rate, as is often done in testing the hypothesis, produces implausible results with respect to the control variables, most likely due to the limitations of the official definition of unemployment. We find that, in modelling the full-time employment rate, the control variables for educational and demographic factors have the theoretically plausible effects, while variables capturing rates for both outright home ownership and with mortgage home ownership are positively related to full-time employment rates, with the effect of the former stronger than the latter. Our findings strongly contradict the Oswald hypothesis.

The vigorous development of the digital economy has brought new opportunities and challenges to the construction of local fiscal revenue efficiency. Based on the panel data from 2011 to 2020, this paper uses the fixed effect model, instrumental variable method and other empirical studies to investigate the impact of the development of the digital economy on the efficiency of local fiscal revenue. The research results show that the development of the digital economy has directly improved the efficiency of local fiscal revenue, and the regression results of instrumental variables are still significant. The mechanism analysis shows that the development of digital economy mainly promotes local fiscal revenue such as efficiency improvement by cultivating tax sources.

Using data from the Japanese government bonds and stock markets, this study examines the predictability of Japanese recessions based on a probit model with instrument variables. By decomposing the term spread into the expected short-term interest rate and the term premium, this study analyzes the relationship between the components of the term spread and recessions. The results show that the predictive power of the term spread for recessions has declined since 1999—when Japan began employing an unconventional monetary policy. Additionally, stock market capitalization relative to nominal GDP is a useful predictor of recessions.

We propose an open-access innovation index for the U.S. states. This index was built by classifying into four core areas the twelve more important indicators, inputs, and outputs, that are widely accepted in the literature as the most relevant for measuring innovation. We consider the indicators aggregated in the areas of human capital and business environment as the inputs that create knowledge and influence the promotion of innovation, while those in areas of engagement and efficiency as the outputs that are all those outcomes and improvements related to the innovation process. As an example of potential uses of our index, we ran a basic econometric experiment using the economic growth rate as the dependent variable. Despite the results being qualitatively consistent with the literature, we suggest further research using our index and other methodologies. We included in the appendix the overall index score and ranking from 2000 to 2015.

The use of digital technologies like artificial intelligence, robotics, or smart devices can be expected to go hand in hand with higher productivity and lower trade costs, and, therefore, to be positively related to export activities. This paper uses firm level data for manufacturing enterprises from the 27 member countries of the European Union to shed further light on this issue by investigating the link between the digitalization intensity of a firm and extensive margins of exports. We use a new machine-learning based regression method, Kernel-Regularized Least Squares (KRLS), which effectively handles non-linear relationships in models and does not impose any restrictive assumptions for the functional form of the relation between margins of exports, digitalization intensity, and any control variables. We find that firms which use more digital technologies do more often export, do more often export to various destinations all over the world, and do export to more different destinations.

This paper employs a two-way fixed effects model and uses panel data from 31 provinces of China between 2012 and 2022 to empirically analyze the impact of digital inclusive finance on China's Outward Foreign Direct Investment (OFDI). The study finds that, overall, the development of digital inclusive finance in China significantly promotes OFDI. Its sub-dimensions, including coverage breadth and usage depth, have a significant positive impact on OFDI across Chinese provinces. Further analysis reveals that the sub-dimensions of usage depth, such as credit and payment, also have a significant effect on OFDI in various provinces. In addition, the control variable of economic development level significantly positively influences OFDI in China. Regional regression results indicate that the development of digital inclusive finance in central and western China significantly promotes OFDI in these regions, while the effect is not significant in the eastern region. Policy Recommendations: China should accelerate the development of a digital inclusive finance system and promote financial innovation. It is crucial to focus on the coordinated development of various digital inclusive finance indicators, narrow the financial service gap between regions, and thus foster the long-term development of China's outward foreign direct investment.