GMM with Many Moment Conditions

This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak or uninformed) instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter, and conditions for consistent GMM estimation are given. A general framework for the GMM limit distribution theory is developed based on epiconvergence methods. Some illustrations are provided, including consistent GMM estimation of a panel model with time varying individual effects, consistent limited information maximum likelihood estimation as a continuously updated GMM estimator, and consistent IV structural estimation using large numbers of weak or irrelevant instruments. Some simulations are reported.     

Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain

We develop results for the use of Lasso and post‐Lasso methods to form first‐stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post‐Lasso in the first stage is root‐n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well‐approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic “beta‐min” conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso‐based IV estimator with a data‐driven penalty performs well compared to recently advocated many‐instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso‐based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post‐Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non‐Gaussian, heteroscedastic disturbances that uses a data‐weighted ℓ₁‐penalty function. By innovatively using moderate deviation theory for self‐normalized sums, we provide convergence rates for the resulting Lasso and post‐Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that logp = o(n^1/3). We also provide a data‐driven method for choosing the penalty level that must be specified in obtaining Lasso and post‐Lasso estimates and establish its asymptotic validity under non‐Gaussian, heteroscedastic disturbances.     

Testing for Causal Effects in a Generalized Regression Model With Endogenous Regressors

A unifying framework to test for causal effects in nonlinear models is proposed. We consider a generalized linear‐index regression model with endogenous regressors and no parametric assumptions on the error disturbances. To test the significance of the effect of an endogenous regressor, we propose a statistic that is a kernel‐weighted version of the rank correlation statistic (tau) of Kendall (1938). The semiparametric model encompasses previous cases considered in the literature (continuous endogenous regressors (Blundell and Powell (2003)) and a single binary endogenous regressor (Vytlacil and Yildiz (2007))), but the testing approach is the first to allow for (i) multiple discrete endogenous regressors, (ii) endogenous regressors that are neither discrete nor continuous (e.g., a censored variable), and (iii) an arbitrary “mix” of endogenous regressors (e.g., one binary regressor and one continuous regressor).     

Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors

We propose two new methods for estimating models with nonseparable errors and endogenous regressors. The first method estimates a local average response. One estimates the response of the conditional mean of the dependent variable to a change in the explanatory variable while conditioning on an external variable and then undoes the conditioning. The second method estimates the nonseparable function and the joint distribution of the observable and unobservable explanatory variables. An external variable is used to impose an equality restriction, at two points of support, on the conditional distribution of the unobservable random term given the regressor and the external variable. Our methods apply to cross sections, but our lead examples involve panel data cases in which the choice of the external variable is guided by the assumption that the distribution of the unobservable variables is exchangeable in the values of the endogenous variable for members of a group.     

不完全信息下发电商竞价策略贝叶斯博弈分析

电力竞价是一个不完全信息下的博弈问题.论文假定竞争对手的报价服从已知区间[a,b]上的独立同分布,基于贝叶斯博弈原理,分别对容量相同的双寡头市场、容量相同与不同情况下的多个发电商的竞价进行了模型化分析,并给出了发电商的最优报价.最后,给出了简单算例分析.     

金融数学模型

数学模型对于金融市场中的交易者有着非常重要的作用,数学模型应用于金融市场研究的重大突破是证券组合投资模型和金融衍生工具定价模型的出现,资本资产定价模型是由此发展起来的具有重大应用价值的金融数学模型。这些模型的发展和应用仍是当今金融领域的研究热点问题。本文将概括性地介绍一些模型和它们的应用。     

Large Market Asymptotics for Differentiated Product Demand Estimators With Economic Models of Supply

IO economists often estimate demand for differentiated products using data sets with a small number of large markets. This paper addresses the question of consistency and asymptotic distributions of instrumental variables estimates as the number of products increases in some commonly used models of demand under conditions on economic primitives. I show that, in a Bertrand–Nash equilibrium, product characteristics lose their identifying power as price instruments in the limit in certain cases, leading to inconsistent estimates. The reason is that product characteristic instruments achieve identification through correlation with markups, and, depending on the model of demand, the supply side can constrain markups to converge to a constant quickly relative to sampling error. I find that product characteristic instruments can yield consistent estimates in many of the cases I consider, but care must be taken in modeling demand and choosing instruments. A Monte Carlo study confirms that the asymptotic results are relevant in market sizes of practical importance.     

Identification of Nonseparable Models Using Instruments With Small Support

I consider nonparametric identification of nonseparable instrumental variables models with continuous endogenous variables. If both the outcome and first stage equations are strictly increasing in a scalar unobservable, then many kinds of continuous, discrete, and even binary instruments can be used to point‐identify the levels of the outcome equation. This contrasts sharply with related work by Imbens and Newey, 2009 that requires continuous instruments with large support. One implication is that assumptions about the dimension of heterogeneity can provide nonparametric point‐identification of the distribution of treatment response for a continuous treatment in a randomized controlled experiment with partial compliance.     

On optimal control and macroeconomic policy

Control theory has important contributions to make to the theory of macro-economic policy. These include a unified view of estimation, forecasting and control and a consequently clearer focus in identifying performance criteria. Further, the methods of control theory imply objectivity and a need for assumptions to be made explicit. By contrast, the UK lacks a research body for forecasting and policy evaluation detached from doctrinal or methodological commitment. Engineering control methods, however, diverge from those wholly acceptable to economic systems in that, in the latter, the controller is himself part of the system he controls and some of his controls operate only indirectly. A further difference is that economics cannot as yet furnish the controller with reliable models of system behaviour linking policy instruments to set targets.     

Hierarchical control of semi-automated production systems

An integrated control model of a hierarchical production system is presented where the output can be measured only at preset control points as it is impossible or costly to measure it continuously. Three levels are considered—company, section, production unit—each level faces stochastic optimization problems. Each unit produces a given target amount by a given due date (common to all units) and has several possible speeds, which are subject to disturbances. On the unit level, at each control point, decision-making centres on determining both the next control point and the speed to proceed with up to that point. The section level is faced with problems of either reallocating resources among the section's units or reassigning the remaining target amounts among the units so that the faster one will help the slower one. The company level is faced with similar problems, i.e. reallocating resources or reassigning target amounts among the sections. Two different cases are considered: (1) cost parameters are not taken into account, i.e. there are two conflicting objectives, namely to maximize the probability of completing the production on the due date and to minimize the number of control points, but the first objective is dominant; (2) the objective is to maximize the expected net profit. Various optimization problems at each level are presented. Examples from steel, construction and mining industries are given.     

Nonparametric Identification under Discrete Variation

This paper provides weak conditions under which there is nonparametric interval identification of local features of a structural function that depends on a discrete endogenous variable and is nonseparable in latent variates. The function delivers values of a discrete or continuous outcome and instruments may be discrete valued. Application of the analog principle leads to quantile regression based interval estimators of values and partial differences of structural functions. The results are used to investigate the nonparametric identifying power of the quarter‐of‐birth instruments used in Angrist and Krueger's 1991 study of the returns to schooling.     

Efficient Tests Under a Weak Convergence Assumption

The asymptotic validity of tests is usually established by making appropriate primitive assumptions, which imply the weak convergence of a specific function of the data, and an appeal to the continuous mapping theorem. This paper, instead, takes the weak convergence of some function of the data to a limiting random element as the starting point and studies efficiency in the class of tests that remain asymptotically valid for all models that induce the same weak limit. It is found that efficient tests in this class are simply given by efficient tests in the limiting problem—that is, with the limiting random element assumed observed—evaluated at sample analogues. Efficient tests in the limiting problem are usually straightforward to derive, even in nonstandard testing problems. What is more, their evaluation at sample analogues typically yields tests that coincide with suitably robustified versions of optimal tests in canonical parametric versions of the model. This paper thus establishes an alternative and broader sense of asymptotic efficiency for many previously derived tests in econometrics, such as tests for unit roots, parameter stability tests, and tests about regression coefficients under weak instruments.     

Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets

We develop an econometric methodology to infer the path of risk premia from a large unbalanced panel of individual stock returns. We estimate the time‐varying risk premia implied by conditional linear asset pricing models where the conditioning includes both instruments common to all assets and asset‐specific instruments. The estimator uses simple weighted two‐pass cross‐sectional regressions, and we show its consistency and asymptotic normality under increasing cross‐sectional and time series dimensions. We address consistent estimation of the asymptotic variance by hard thresholding, and testing for asset pricing restrictions induced by the no‐arbitrage assumption. We derive the restrictions given by a continuum of assets in a multi‐period economy under an approximate factor structure robust to asset repackaging. The empirical analysis on returns for about ten thousand U.S. stocks from July 1964 to December 2009 shows that risk premia are large and volatile in crisis periods. They exhibit large positive and negative strays from time‐invariant estimates, follow the macroeconomic cycles, and do not match risk premia estimates on standard sets of portfolios. The asset pricing restrictions are rejected for a conditional four‐factor model capturing market, size, value, and momentum effects.     

Impact of investing in quality improvement on (Q,r, L) model involving the imperfect production process

This paper investigates the impact of quality improvement on the modified lot size reorder point models involving variable lead time and partial backorders. The formulated models include the imperfect production process and an investing option of improving the process quality. The objective is simultaneously optimizing the lot size, reorder point, process quality level and lead time. We first assume that the lead time demand follows a normal distribution, then relax this assumption to consider the distribution-free case where only the mean and standard deviation of lead time demand are known. An algorithm procedure of finding the optimal solution is developed, and two numerical examples are given to illustrate the results.     

不确定条件下公司负债的利息抵税效应分析

在不确定条件下,以公司息前税前收益服从均匀分布为假设,基于静态权衡理论,不考虑除利息抵税效应以及破产成本之外的其他因素对融资决策的影响,我们建立了负债抵税价值期望值模型和破产成本期望值模型,然后在统一的负债区间内分析负债的利息抵税净收益,以确定存在利息抵税净效应最高时的最优负债数额和最优资本结构。     

“减规模”还是“增绿色”?异质性环保政策工具下的企业环保行为响应

市场机制和绿色投资型环保政策工具既是对命令控制型工具的有益补充,也可能在企业层面引致更加复杂的环保行为响应,企业“减规模”抑或“增绿色”还存在不确定性。为此,本文借助计量模型,基于2011-2019年重污染上市公司的微观数据,探讨企业在不同政策工具下的环保行为响应。研究发现：各类环保政策工具的“增绿色”属性突出;环境监管和排污收费均引致企业环保支出和绿色创新水平提升的“增绿色”响应;环保补助则带来企业以环保支出为主的“增绿色”响应;环境监管和排污收费两种政策工具并不相容,互相阻滞了对环保支出的激励效应;宽松的融资约束和富有的企业家精神将放大排污收费的“增绿色”效果,而环保补助对引导融资约束下的“增绿色”响应更加有效。本文结论启示环保部门需了解不同政策工具的异质性后果,合理进行工具组合,并面向不同特征企业精准施策。     

Timing and Self‐Control

The standard dual‐self model of self‐control, with a shorter‐run self who cares only about the current period, is excessively sensitive to the timing of decisions and to the interpolation of additional “no‐action” time periods in between the dates when decisions are made. We show that when the shorter‐run self is not completely myopic, this excess sensitivity goes away. To accommodate the combination of short time periods and convex costs of self‐control, we introduce a cognitive resource variable that tracks how the control cost depends on the self‐control that has been used in the recent past. We consider models with both linear and convex control costs, illustrating the theory through a series of examples. We examine when opportunities to consume will be avoided or delayed, and we consider the way in which the marginal interest declines with delay.     

ROBUSTNESS OF VARIOUS PRODUCTION CONTROL POLICIES IN SEMICONDUCTOR MANUFACTURING

This paper compares several different production control policies in terms of their robustness to random disturbances such as machine failures, demand fluctuations, and system parameter changes. Simulation models based on VLSI wafer fabrication facilities are utilized to test the performance of the policies. Three different criteria, namely, the average total WIP, the average backlog, and a cost function combining these measures, are used to evaluate performance. Among the policies tested, the Two‐Boundary Control policy outperforms the others.     

Returns to Schooling in Spain: How Reliable are Instrumental Variable Estimates?

This paper studies the ordinary least–squares (OLS) and instrumental variable (IV) estimates of the returns to schooling for male workers in Spain. OLS estimates are often biased due to the endogeneity of schooling, measurement errors or omitted variables. Proper IV estimates correct this bias. The reliability of family background, natural experiments (based on changes in the education system and season of birth) and the availability of a college in the province is checked using Spanish data. The results suggest that background and college availability are valid instruments and that the IV estimates of the returns to schooling are higher than OLS estimates. These results are in line with the majority of previous results in the literature.     

Identification of Nonseparable Triangular Models With Discrete Instruments

We study the identification through instruments of a nonseparable function that relates a continuous outcome to a continuous endogenous variable. Using group and dynamical systems theories, we show that full identification can be achieved under strong exogeneity of the instrument and a dual monotonicity condition, even if the instrument is discrete. When identified, the model is also testable. Our results therefore highlight the identifying power of strong exogeneity when combined with monotonicity restrictions.