Commodity is an important part of industrial production and financial investment, and accurate commodity price forecasting is of great significance to safeguard industrial production and help investors avoid risks. However, most of the existing commodity price forecasting models are point-value models based on closing prices, which ignores the volatility information. Therefore we propose a heteroskedasticity threshold autoregressive interval model with exogenous variables (HTARIX) and apply it to the commodity markets. We also construct a test statistic based on interval-valued data to test whether there is conditional heteroskedasticity in the model, and propose a generalized minimum $D_K$ distance estimation. The advantage of our model is that it can capture the conditional heteroskedasticity and nonlinear features of interval-valued time series models. Compared with the point-valued models, our method contains more information of the data. The empirical results imply that HTARIX model performs better than other comparative models in interval-valued commodity price forecasting.

This paper studies how environmental regulation affects the sustainable economic development through an angle of soft constrains of environmental regulation. We first develop a theoretical model, based on the threshold effect of innovation investment, to introduce the role of soft constrains of environmental regulation into the theoretical framework of Porter hypothesis, and analyze how the soft constraints of environmental regulation affect enterprise competitiveness. Using policy change of the SO₂ emission charges from 2007 to 2014, we examine the Porter hypothesis by adopting a DID estimation. We find evidence that state owned enterprises have more significant soft constraint problems than non-state owned firms, which weaken incentives for innovation investment, and then hurt enterprise competitiveness. However, we find strong evidence of the existence of Porter hypothesis for no-state owned firms.

To implement the instructions from General Secretary Xi Jinping regarding "enhancing the effciency of funding for the National Natural Science Foundation, " the Department of Management Sciences conducted a series of research activities, systematically analyzing the funding effectiveness of the distinguished young scholars and outstanding young scholars talent projects. A total of 556 survey questionnaires were designed and distributed, and 233 experts participated in the discussion. Utilizing statistical methods such as the coeffcient of variation, the difference-in-differences, and the natural language processing, the survey data were quantitatively analyzed. The statistical analysis of the survey data showed the following key findings: First, compared to other talent projects like outstanding young scholars, the comprehensive funding effectiveness of distinguished young scholars is relatively higher. After approval, there is a significant improvement in both academic achievements and academic influence. Second, there is heterogeneity in the funding effectiveness among talent projects like distinguished young scholars and outstanding young scholars. Third, scholars who receive distinguished young scholars funding before the age of 42 experience a greater improvement in comprehensive funding effectiveness. Based on these analysis, recommendations are proposed, emphasizing the need to "strengthen process management and project closeout management" for talent projects.

Large models, exemplified by ChatGPT, represent a significant breakthrough in general generative artificial intelligence technology. Their far-reaching implications extend into diverse facets of human production, lifestyle, and cognitive processes, prompting a transformative paradigm shift in the realm of economic research. Originating from the convergence of big data and artificial intelligence, these large models introduce a novel approach to systemic analysis, particularly adept at scrutinizing intricate human economic and social systems. We first discuss the fundamental characteristics and development paradigms of ChatGPT and large models, focusing on how these models effectively tackle the methodological challenges posed by the "curse of dimensionality". We then delve into how ChatGPT and large models will influence the paradigm of economic research. This includes a shift from the assumption of the rational economic man to an AI-driven "human-machine hybrid" economic agent, from the isolated economic individual to the socio-economic individual whose behaviors are measurable, from the separation of macroeconomics and microeconomics to their integration, from the separation of qualitative and quantitative analysis to their unification, and from the long-dominant "small-model" paradigm to a "large-model" paradigm in economic research. We also cover the increasing significance of computer algorithms as a prominent research paradigm and method in economics. Finally, we point out the limitations inherent in artificial intelligence technologies, including large models, when employed as a research method in economics and the broader social sciences.

Mixing plays a fundamental role in time series and spatial econometrics, and many time series papers assume that the variables in their models follow a mixing process. However, in the literature on spatial econometrics, there are no criteria to establish the mixing property for spatial econometric models. Following the general idea in Doukhan (1994), based on some common assumptions, we establish some criteria for a linear spatial process over an irregular lattice to be $\alpha $-mixing. We apply the criteria to establish the $\alpha $-mixing property generated by the spatial autoregressive model, the spatial error model, the matrix exponential spatial model, and spatial econometric models with qualitative and limited dependent variables based on latent dependent variables, such as a spatial sample selection model. Using the $\alpha $-mixing property, we establish large sample properties of estimators for the spatial sample selection model proposed in Flores-Lagunes et al. (2012).

Under the influence of various factors such as politics, economics, and technology, global value chains are undergoing profound adjustments. Western countries and India itself are actively enacting a series of industrial policies aimed at positioning India as a focal point for the new phase of international industry relocation. This paper constructs a quantitative assessment framework to gauge a country/region's potential as a recipient of international industry relocation, and conducts a case study of India. Overall, the Modi government's realization of "Made in India" to replace "Made in China" can be described as a long and difficult road. We identified six sectors where India has potential advantages, including food, beverage and tobacco manufacturing; base metals; paper products and printing; other non-metallic mineral products; other transportation equipment; and computer, electronic and optical equipment. Among these, the food, beverage, and tobacco manufacturing, paper products and printing, and other non-metallic mineral products industries may be the first to undertake China's external industrial transfer. Vietnam, Thailand, and Bulgaria are competitive with India in the food, beverage, and tobacco manufacturing industry; Vietnam and Malaysia in paper products and printing; and Vietnam, Malaysia, Thailand, and Bulgaria in other non-metallic mineral products.

The main goal of macro prudential policies is to maintain financial stability. This paper proposes adopting the macro-econometric policy evaluation method under the Rubin causal effect framework to evaluate the impact of China's macro prudential policies on financial stability during the sample period 2007--2020. First, the paper constructs a macro prudential policy index to quantitatively measure the intensity of China's macro prudential policies. Second, the paper uses the systemic financial risk index, termed as SRISK to measure China's systemic financial risk. Finally, the paper evaluates the macro prudential policies' effects on the systemic financial risk, cross-sectoral contagion of systemic financial risk and important intermediate variables in the credit channel. Our empirical findings indicate that loose macro prudential policies can increase the risks of intermediate variables in the credit channel, and the risks lead to a significant rise in SRISK of house sector, but for the SRISK of financial and manufacturing sectors, the cumulative effects in 24 periods are not significant. However, in addition to a significant rise in commercial banks' capital adequacy ratio growth, tight macro prudential policies have no significant effects on the other intermediate variables in the credit channel, and further have no obvious effects on SRISK of financial, house and manufacturing sectors. Based on the conclusions, we suggest that systemic risk indicators should be further researched to provide more comprehensive and systematic targets for macro prudential authorities. Moreover, the transmission channel of macro prudential policies on financial stability should be improved to enhance the efficiency of regulation. Finally, more attentions should be paid to the cross-sectoral contagion of systemic financial risk so as to prevent systemic financial risk from a systemic perspective.

Improving and developing the green financial system is a vital tool to achieve emission peak and carbon neutrality, and the research on green incentive (GI) in Chinese securities market is conducive to further discovering the impacts of policies and green risk compensation on the market. First, based on the classical CAPM and α return, we construct brand-new GI indicators with distinct incentive factors by the index of environmental protection industry. Second, to investigate the characteristics of GI indexes, this work proposes a systematic hybrid analysis method by integrating the causality test, trend analysis and regression significance test, which can also reveal the advantages and merits of our established indicators. Third, the empirical results demonstrate that under different incentive factors, GIs can exhibit obvious leading trend, significant regression coefficient and predictive explanatory power, with regard to the environmental protection industry index. The conclusion points out that the trend of the environmental protection index is affected by the green risk compensation required by the market in a long term, and meanwhile, it also provides a valuable reference for tracking and predicting the index.

We conduct a two-stage extension of Ellsberg's two-urn experiment and find that ambiguity aversion and attitudes toward new information when learning under ambiguity are tightly associated. The first stage is a static extension of the Ellsberg's two-urn experiment, which is designed to test the degree of ambiguity aversion of decision makers. Instead of simply dividing subjects into ambiguity averse and ambiguity seeking, the sample is decomposed into four groups according to the first-stage experiment results. The second stage is a dynamic experiment, which allows the decision maker to obtain information by drawing the balls. And there is a trend in the second-stage experiment — subjects with a lower degree of ambiguity aversion are more likely to change their initial (ambiguity-averse) choices when faced with favorable information for the ambiguous prospect. When faced with information favorable to ambiguous prospects, decision makers with higher ambiguity aversion are more likely to underreact to the signal and show low confidence in the information.

This study investigates the recent development of financial research. We first summarize the up-to-date progress of research on asset pricing, corporate finance, and the economic development and finance market. Then we analyze emerging trends and challenges and show the following frontiers of financial research, including new monetary theory to accommodate financial crisis and digital currency, sustainable finance, finance safety, and climate finance. Among these topics, there are significant opportunities for China's finance research, especially in the area of preventing financial systemic risk, expanding and monetary theory, and developing inclusive finance.

The parameterized shadow pricing framework has been widely used to estimate the marginal abatement costs of carbon dioxide (CO₂) emissions. However, in the context of China, there exists a large variation in the empirical estimations of the shadow price of CO₂ emissions in China by different studies, which affects the reliability of abatement costs for supporting decision making. This paper firstly summaries the studies of CO₂ abatement cost based on the parameterized shadow price analysis framework. It has been found that the variation in the shadow price estimates mainly comes from: whether the synergistic effects of carbon dioxide with other pollutants are considered, the difference in production technology, the difference in the characterization of distance function and the difference in constraints imposed by distance function. Based on that, this paper aims to standardize the setting of input and output variables, production technology characterization, explicit function selection of distance function and constraints imposed by distance function, derivation of shadow price. A focus is to consider the influence of heterogeneous production technology, heterogeneous technological progress and heterogeneous emission abatement strategy on shadow price estimates simultaneously. A unified parametric framework for estimating the shadow prices of CO₂ emissions is then provided. It is expected that the unified framework can provide a more scientific and reasonable research paradigm for evaluating the marginal abatement costs of CO₂ emissions, which helps improve the comparability and continuity of relevant applied research.

Based on the data of China Family Panel Studies (CFPS) in 2014 and 2018, this paper conducts a systematic study on the impact and its mechanisms of ecommerce development quality on residents' subjective well-being from the perspective of common prosperity. The results show that: First, the development of e-commerce can significantly improve the subjective well-being of residents, and it has a more significant effect on the residents in the late developing areas and economic-disadvantaged groups, which means that it can promote spiritual common prosperity of all residents. Second, the development of e-commerce can improve the subjective well-being of residents by promoting material common prosperity, that is, reducing income inequality between urban and rural areas and reducing living costs, but it will also worsen the well-being of urban residents and non-internet users by reducing their relative income. Third, under the comprehensive effect of various mechanisms, the relationship between the quality of e-commerce development and subjective well-being at this stage presents an inverted U-shaped relationship. Finally, the development of cross-border e-commerce can also significantly improve the subjective well-being of residents, and it plays a role of icing on the cake in the process of promoting spiritual common prosperity through the development of e-commerce. The practical significance of this paper is to analyze the multiple impacts of the development of e-commerce on people's real life, and deepen the understanding of the influencing factors of Chinese residents' subjective well-being, it also provides enlightenment for the formulation of corresponding policies.

It is urgent to develop systematic theories and methods to support the scientific research of innovation management and innovation policy. At the same time, the scientometric theories and methods of analyzing the upstream scientific and technological output of the innovation process fail to meet the needs of comprehensively analyzing the whole innovation process and systematically supporting the research of innovation management and innovation policy. This situation inevitably leads to a more comprehensive interdisciplinary "Innovation Metrology (Innovametrics)". Innovametrics is an emerging discipline that takes the entire innovation system as the research object, orients to the occurrence and development of innovation, and comprehensively analyzes the innovation system. Innovametrics constructs the theoretical and methodological system for analyzing the innovation process from the perspective of innovation system, so as to realize the systematic diagnosis and analysis of the innovation process. Based on the simultaneous development of innovation activity analyses and innovation models, this paper classifies Innovametrics into innovation input metrics, innovation output metrics, innovation profit metrics, innovation transformation metrics and innovation system metrics from five aspects: Input (I), output (O), profit (P), transformation (T) and system (S). Typical research problems and analysis techniques of Innovametrics are summarized from the perspectives of structural, development and dynamic problems. Finally, combined with the practice of innovation management in China, the urgent scientific problems of Innovametrics are prospected. The continuous enrichment of innovation statistics and surveys will inevitably promote the vigorous development of Innovametrics, and the development of Innovametrics will also make innovation management and innovation policy more scientific. The "I-O-P-T-S" five-dimensional Innovametrics system constructed in this paper not only provides a classification system for the analysis of innovation activities for the first time, but also provides a systematic whole-process analysis perspective for the design of research problems in the field of innovation.

This paper uses the randomized controlled trials method to evaluate the pilot effect of the category-specific review in 2021, which is composed of 1, 110 applications in Economic Sciences (G03) of Division Ⅲ in the Department of Management Sciences. These applications cover the General Program and the Young Scientists Funds. We find that category-specific review can effectively increase the consensus of peer-review on the Original Exploratory program, the Cutting-edge program, and Cross-category program. There is significant evidence that the rate for the applications being on the conference review and finally approved in the above three programs have increased. Furthermore, there is no significant difference in the distribution and mean value of the overall scores in the treatment and control groups, which implies that the category-specific review pilot has not systematically affected the results of the peer-review.

With the increasing global attention to carbon dioxide emissions, the carbon market price has become more and more important. Accurate and reliable carbon market price forecasts can not only provide a better reference for the government's macro-control to achieve the "Chinese carbon peak and carbon neutralization" goal, but also help enterprises can more effectively manage the risks brought by carbon emissions. This article uses empirical mode decomposition (EMD), convolutional neural networks (CNN) and long short-term memory networks (LSTM) to predict carbon emissions trading prices to propose different EMD-CNNs-LSTM combination strategy, and discussed the effect of the CNN-LSTM combination strategy, divide it into serial strategy and parallel strategy. This article uses the Guangdong, Shanghai, Hubei, and Chongqing carbon market price data to systematically compare the EMD-CNN-LSTM combination strategy with single prediction model and combination prediction model. The prediction effect of EMD-CNN-LSTM verifies the accuracy and robustness of the four combined strategy models of EMD-CNN-LSTM, demonstrated that parallel strategy forecasting is better for the universality of carbon market price series.

From the perspective of economics, we introduce the economic interpretations and applications of some basic concepts, ideas, methods and tools in probability and statistics. Examples include subjective probability, cumulative distribution function, stochastic dominance, quartile, expectation, Jensen's inequality, mean and variance, law of large numbers, variance of sample mean converging to zero, independence, martingale difference sequence, statistical significance, goodness of fit and model specification, spectral analysis of time series, machine learning and random sets. Economics applications consist of rational expectations, depicting income inequality, portfolio, efficient market hypothesis, capital asset pricing model, financial derivatives pricing, risk management, model risk, measuring economic causal relationships, identifying economic cycles, and macroeconomic interval management. These examples and applications are helpful in understanding the importance and usage of probability and statistics in economic research and analysis.

The value added of digital economy is an important statistical indicator reflecting the development scale of digital economy and its contribution to the overall economy. So far, the concept, scope and measurement methods of digital economy are still in the process of exploration, there's no unified opinions and consistent measurement methods. Thus, there are significant differences between the results of digital economy value added that calculated by different academic institutions and scholars. This paper systematically combs the definition of digital economy form narrow scope and wide scope; summarizes three method of digital economy value added: Production method in GDP accounting, method based on growth accounting framework and econometric method; compares the results of the value added of digital economy of the United States and China, which have relative importance in the world. Finally, this paper summarizes the challenges, and puts forward corresponding suggestions. Try to improve the calculation method of value added of digital economy and the comparability of calculation results, meanwhile, attempt to provide reference to formulate digital economy policies and promote the high-quality development of digital economy.

With the development of information technology, social media have gradually become an important channel for people to obtain information, share views, and vent feelings, and exerted a profound impact on information dissemination and sentiment contagion in the capital market, giving birth to a large body of literature focusing on social media and capital market. The extant literature has confirmed social media's information content and role in influencing the behaviors of investors, companies as well as other information intermediaries. This paper uses the method of bibliometrics to sort out and analyze the literature in this area. The main results are as follows: 1) This research area is in a stage of vigorous development, and the amount of publications exhibits an increasing trend over the years; 2) The core effects of journals for research in this area have not fully emerged; 3) The research team in this field has basically formed; 4) The research topic in this area can be divided into two parts: Social media and stock trading and social media and corporate governance. Based on these findings, this paper summarizes the possible research directions as well as issues worthy of attention in the hope of providing a valuable reference for scholars who are interested in this area.

The basic classification is an important basis for GDP accounting and an important tools of reflecting the structure of the economy and its changes, which is of great significance for economic analysis and policy making. This paper systematically studies the changes in the basic classification of China's GDP accounting, and comprehensively compares the changes of industry classification and three industry classifications in China's production-based GDP accounting, as well as the changes of demand item classification in China's expenditure-based GDP accounting since China's GDP accounting system established. The industry classification of China's production-based GDP accounting is based on industrial classification for national economic activities promulgated by the national standards administration, while responding to the needs of economic management and taking into account the actual situation of the data sources. The classification of the three industries in China's production-based GDP accounting directly adopts the regulations on the division of the three industries set by the National Bureau of Statistics (NBS). Since the establishment of China's GDP accounting system in 1985, there have been four important changes in the industry classification and two important changes in the classification of the three industries. The classification of demand items in China's expenditure-based GDP accounting is based on the relevant classification standards set by the NBS, and is also determined in response to the needs of economic management and the actual situation of the data sources. Since the establishment of the expenditure-based GDP accounting system in 1989, most of the demand item classifications in expenditure-based GDP accounting have undergone several changes. Understanding the changes in the basic classification of China's GDP accounting is conducive to a comprehensive understanding of the changes in China's GDP accounting and to the accurate understanding and correct use of historical data on China's GDP accounting for academic and policy research.

This paper proposes a new model, termed as the partially conditional quantile treatment effect model, to characterize the heterogeneity of treatment effect conditional on some predetermined variable(s). We show that this partially conditional quantile treatment effect is identified under the assumption of selection on observables, which leads to a semiparametric estimation procedure in two steps: First, parametric estimation of the propensity score function and then, nonparametric estimation of conditional quantile treatment effects. Under some regularity conditions, the consistency and asymptotic normality of the proposed semiparametric estimator are derived. Furthermore, the finite sample performance of the proposed method is illustrated through Monte Carlo experiments. Finally, we apply our methods to estimate the quantile treatment effects of a first-time mother's smoking during the pregnancy on the baby's weight as a function of the mother's age, and our empirical results show substantial heterogeneity across different mother's ages with a significant negative effect of smoking on infant birth weight across all mother's ages and quantiles considered.

To prevent local government debt risks, it is not only necessary to strictly control the red line for local government debt, but more importantly, to straighten out and standardize the behavioral motives of debtors. Based on the panel data set of 264 prefecture-level cities in China, this paper studies the causes behind the expansion of local implicit debt from the perspective of behavioral economics, aiming to address, in addition to the passive influence of the mismatch of financial power and administrative power, whether local governments have active debt-raising behavior and the underlying motives. We find that there are significant "peer effects" in the binary choice of whether prefecture-level cities issue municipal investment bonds. Further, after removing the factors of passive issuance of municipal investment bonds by prefecture-level cities, using quasi-maximum likelihood estimation method, we apply spatial econometric methods to show that there are also significant "peer effects" in the scale of active issuance of municipal investment bonds by prefecture-level cities. Economic development motivation (pressure) and promotion motivation (pressure) would enhance the "peer effects". There are external demonstration learning mechanism and competitive imitation mechanism, and "followers" with lower level of economic development prefer to imitate "leaders" with higher level of economic development to issue bonds. The analysis of regional heterogeneity shows that since the eastern region has more space for active borrowing, the "peer effects" of competing bond issuance are stronger in the prefecture-level cities of eastern China. The "peer effects" under the behavioral motives of local government debtors provide a new perspective for explaining why the scale of municipal investment bonds continues growing, broaden the understanding of China's municipal investment bonds, and provide policy implications for controlling local government borrowing behavior to reduce local implicit debt risk.

There are considerable nonstationary time series in economics, finance, climate science and related areas. In last two decades or so, in order to improve theoretical research in these disciplines, asymptotic theory on nonstationary time series has captured close attention and well developed; on the other hand, classical series estimation often requires the values of variables considered fall into a bounded compact interval that in some circumstance suppresses the development and application of the method in nonparametric context, especially in the present of nonstationary time series. In order to break through the bottleneck of the conventional sieve method, the authors and their coauthors use orthogonal series expansion to achieve some theoretical results and their applications, in particular in nonparametric and nonstationary time series. These studies lay a foundation for the use of the series estimation in economics, finance, climate science and related disciplines.

Starting from the macroeconomic production function, we establish a theoretical framework of human capital measurement and form the linkage between individual and aggregate measures. Our focus is on the human capital measurement based on earnings. Because wage represents an individual's marginal productivity, wage-based measurement provides a comprehensive measure of human capital that cover all observed and unobserved aspects. We discuss three wage-based aggregate human capital measures, efficiency units, generalized division of labor (GDL) and the Jorgenson-Fraumeni lifetime income. The traditional measure of efficiency units reflects labor quantity and relative quality. Additionally, for efficient units, all labor is aggregated in a linear fashion, implicitly assuming perfect substitution among different skills. However, GDL aggregation takes into substitutability and complementarity of different skills with a given technology. The J-F human capital is based on lifetime-income but maintains the perfect substitution assumption in the aggregation. We further investigate the impact of individual life-time human capital dynamics on the J-F calculation and show that incorporating the dynamics will improve the J-F measurement. Using data from China, we calculate these three human capital measures from 1985 to 2018 and discuss their differences in dynamics. We further compare their importance in regional income disparity. The results show that the GDL human capital account for a much larger portion of income gap compared to the efficiency units. Additionally, J-F human capital also accounts for a large portion of income difference but appears to be falling below the GDL. Our results demonstrate that for aggregate human capital measurement, both the concepts and aggregations play an important role and will affect the study of human capital.

Using the data of 38 economies, we provide the most recent evidence that trumpets the importance of internet penetration on the efficiency of the financial market in fostering the innovativeness and long-term growth of the economy. Additionally, we find that the effect varies for the intermediary-based financial system and market-based financial system. We document that internet penetration improves the intermediary-based financial system by removing the physical limitations of banks, enhancing the depth of the banking system, and promoting market competition. By contrast, internet-based technology provides support for a highly active stock market and maintains market efficiency during uncertain periods by providing information advantages.

This survey paper highlights some recent developments in estimating treatment effects for panel data. First, this paper begins with a brief introduction of the basic model setup in modern econometric analysis of program or economic policy evaluation for panel data. Second, the primary attention goes to the focus on estimating both the average and quantile treatment effects for panel data. Finally, it concludes the paper by addressing theoretically, methodologically and empirically some possible future research directions for young scholars in econometrics and statistics, particularly, some interesting and challenging research topics related to a combination of machine learning and casual inference for panel data.

The socio-economic field is one of the main occasions for data science applications. How to grasp the disciplinary pattern and focus of data science in this field is a basic problem in formulating and implementing discipline development strategies. Based on the practical needs of China's economic statistics and the important points in the "HMYW 2019 Statistics Report", this paper discusses the disciplinary pattern of data science applications in the socio-economy. We propose that "data processing methods", "ambiguity uncertainty phenomenon" and "problem-driven pattern" are the three focuses of the application of data science in the socio-economy in the era of big data, analyzing their respective importance and key points. Finally, we discuss the future development direction and strategic adjustment of data science.

This paper aims to introduce the philosophy, theories, fundamental content systems, models, methods and tools of modern econometrics based on its development history. We first review the classical assumptions of the linear regression model and discuss the historical development of modern econometrics by various relaxations of the classical assumptions to further illustrate the modern theoretical system and fundamental contents. We also discuss the challenges and opportunities for econometrics in the Big Data era and point out some important directions for the future development of econometrics.

We selectively review some literature on prediction in the presence of big data. Issues of data based approach versus causal approach, micro versus macro modeling, homogeneity versus heterogeneity, model uncertainty versus sampling errors, constant parameter versus time-varying parameter modeling, model evaluation and cross-validation as well as aggregation, etc. are considered.

In the era of digital economy, economic activities based on Internet, mobile Internet and artificial intelligence are generating massive data, which have promoted economic growth in return. Big data have various sources and forms, including structured and unstructured data. Unstructured data can be text, images, audio and video, and new structured data can be functional data, interval data, symbolic data, etc. Most Big data has a huge volume, and some is Tall Big data, whose dimensionality of potential explanatory variables is larger than its sample size. The rise of Big data together with machine learning, a main computer-based automatic analytic tool for Big data, has profound implications on statistical science. Based on the characteristics of Big data and the nature of machine learning, the paper discusses the challenges and opportunities brought by Big data and machine learning to statistical modeling and inference, including sample inference, sufficiency principle, data reduction, variable selection, model specification, out-of-sample prediction and causality. We also explore the theory and methodology foundation of machine learning and its integration with statistics.

This paper provides an overall view on the SAR model, which generalizes the autoregessive time series model to a spatial setting. It is the most popular model in spatial econometrics with broad applications in empirical economics as it captures interactions and spilled over effects across economic agents. We first provide some economic justification of such a model in an complete information static game setting, of which observed outcomes are Nash equilibria. Comparative statics analysis in economics provides economic implications on direct and indirect effects and multiplier effect on outcomes. The traditional ML estimation and its extension in terms of QML estimation are discussed. Recent developments on concavity of its log likelihood function are established, and alternative estimation methods, GMM and GEL, are presented. The construction of best GMM estimation with linear-quadratic moments is feasible. The GEL approach on estimation and testing for the SAR model can be robust against unknown heteroskedasticity.