Nonparametric Instrumental Variable Estimation in Practice

We provide general compactness results for many commonly used parameter spaces in nonparametric estimation. We consider three kinds of functions: (1) functions with bounded domains which satisfy standard norm bounds, (2) functions with bounded domains which do not satisfy standard norm bounds, and (3) functions with unbounded domains. In all three cases we provide two kinds of results, compact embedding and closedness, which together allow one to show that parameter spaces defined by a ║·║s-norm bound are compact under a norm ║·║c. We apply these results to nonparametric mean regression and nonparametric instrumental variables estimation.

Compactness is a widely used assumption in econometrics. In this article, we gather and review general compactness results for many commonly used parameter spaces in nonparametric estimation, and we provide several new results. We consider three kinds of functions: (1) functions with bounded domains which satisfy standard norm bounds, (2) functions with bounded domains which do not satisfy standard norm bounds, and (3) functions with unbounded domains. In all three cases, we provide two kinds of results, compact embedding and closedness, which together allow one to show that parameter spaces defined by a -norm bound are compact under a norm . We illustrate how the choice of norms affects the parameter space, the strength of the conclusions, as well as other regularity conditions in two common settings: nonparametric mean regression and nonparametric instrumental variables estimation.

The systematic risk estimation models: A different perspective

There is a long-standing debate in the statistical, epidemiological, and econometric fields as to whether nonparametric estimation that uses machine learning in model fitting confers any meaningful advantage over simpler, parametric approaches in finite sample estimation of causal effects. We address the question: when estimating the effect of a treatment on an outcome, how much does the choice of nonparametric vs parametric estimation matter? Instead of answering this question with simulations that reflect a few chosen data scenarios, we propose a novel approach to compare estimators across a large number of data-generating mechanisms drawn from nonparametric models with semi-informative priors. We apply this proposed approach and compare the performance of two nonparametric estimators (Bayesian adaptive regression tree and a targeted minimum loss-based estimator) to two parametric estimators (a logistic regression-based plug-in estimator and a propensity score estimator) in terms of estimating the average treatment effect across thousands of data-generating mechanisms. We summarize performance in terms of bias, confidence interval coverage, and mean squared error. We find that the two nonparametric estimators can substantially reduce bias as compared to the two parametric estimators in large-sample settings characterized by interactions and nonlinearities while compromising very little in terms of performance even in simple, small-sample settings.

In this thesis, using a finance lens, we investigate various aspects of political actions of the Chinese National Social Security Fund (CNSSF). The thesis comprises three empirical papers. In the first essay, we analyze the trading behavior of the CNSSF that operates in a highly political environment. We show that the CNSSF adopts a rebalancing strategy that maintains both portfolio liquidity and growth opportunities. Further, we find direct and indirect evidence that the CNSSF actively intervenes in the stock market by providing liquidity to mutual funds in distress. This liquidity provision can be primarily explained by public information quality. Most notably, CNSSF can profit by assisting distressed mutual funds, especially if such liquidity provision relates to private information. In addition, this bailout-like behavior is not speculative and can positively improve the performance of the distressed mutual funds. In essay 2, we propose a new measure of the policy information advantage available to the CNSSF. Specifically, we assess the impact of this policy-linked “information advantage” on stock performance. Our results show that in the short run, there is a positive and significant information advantage-stock performance linkage. Moreover, our findings support the view that CNSSF promotes the absorption of inside information into prices. In contrast, in the long run, the policy information advantage of the CNSSF negatively decreases the firm operation performance. Finally, we document that there is an information network spillover of the information advantage across the Chinese mutual fund industry, which also affects mutual fund performance. In the third essay, we propose a smooth non-parametric estimation to explore the safety-first portfolio optimization problem. As an empirical application, we simulate optimal portfolios and display return-risk characteristics using the CNSSF strategic stocks. We obtain a non-parametric estimation calculation formula for loss (truncated) probability using the kernel estimator of the portfolio returns’ cumulative distribution function, and embed it into two types of safety-first portfolio selection models. We numerically and empirically test our non-parametric method to demonstrate its accuracy and efficiency. Cross-validation results show that our non-parametric kernel estimation method outperforms the empirical distribution method.

In this paper, we adopt a smooth non-parametric estimation to explore the safety-first portfolio optimization problem. We obtain a non-parametric estimation calculation formula for loss (truncated) probability using the kernel estimator of the portfolio returns’ cumulative distribution function, and embed it into two types of safety-first portfolio selection models. We numerically and empirically test our non-parametric method to demonstrate its accuracy and efficiency. Cross-validation results show that our non-parametric kernel estimation method outperforms the empirical distribution method. As an empirical application, we simulate optimal portfolios and display return-risk characteristics using China National Social Security Fund strategic stocks and Shanghai Stock Exchange 50 Index components.

The first key objective of this thesis is to estimate a set of econometric models of Australian broadacre agricultural production by applying the duality theory in production economics. Models of Australian broadacre agriculture are estimated using alternative formulations of econometric modelling of producer decision-making, in which cost minimisation, revenue maximisation and profit maximisation are assumed. A unique, large quasi-micro pooled cross-sectional farm dataset drawn from the Australian Agricultural and Grazing Industries Survey over a sixteen year period, from 1990 to 2005, is used for model estimation. Key policy-relevant outcomes of this investigation are estimates of price elasticities and elasticities of transformation and substitution between broadacre inputs and outputs in Australia. Multi-product dual cost, revenue and profit functions are specified for Australian broadacre agriculture. The multi-product functions are specified to accommodate the prevalent multi-enterprise operation on Australian broadacre farms. The restricted versions of the dual functions are chosen to account for quasi-fixity and the lumpiness of some capital used in broadacre production. The translog and normalised quadratic, the two most popular flexible functional forms in empirical duality applications, are used to specify the dual functions. In addition, impacts of climatic conditions, production focuses, production scales and rainfall on production are also allowed for in the estimated models. Systems of demand and/or supply equations are derived from the specified dual cost, revenue and profit functions and estimated using the quasi-micro dataset available. The estimated systems obtained have reasonable statistical goodness-of-fit with high percentage of statistically significant system coefficients. Price variables are also found to significantly influence input demand and output supply. Importantly, using the normalised quadratic form, the estimated system of input demand derived from the cost function and the estimated system of output supply derived from revenue functions satisfy the theoretical curvature conditions implied by rational economic behaviour. The estimated supply and demand system derived from the profit function violates the curvature condition but the violation is not severe. Input demand and output supply in broadacre farming are found to be fairly inelastic with respect to price changes in the short run. However, demand for fertilisers and crop and pasture chemicals are found to be sensitive to changes in their own prices and in general production costs. The second key objective of this thesis is to investigate three significant issues concerning the application of the duality theory in empirical agricultural production research using data from Australian broadacre agriculture. First, the results obtained from the dual cost, revenue and profit functions are contrasted according to goodness-of-fit, the satisfaction of theoretical regularity conditions and the sensibility of the generated elasticity estimates. The estimation result obtained under the cost minimisation assumption conforms more to economic theory than results obtained under revenue maximisation or profit maximisation. Second, the estimation results are more in line with expectations based on prior economic reasoning when the normalised quadratic functional form is used than when the translog is used. Third, results using data of Australian broadacre farming at two aggregate levels indicate that data aggregation across firms can have a significant impact on research findings, depending on the assumption made regarding the economic behaviour of producers

Three-stage semi-parametric inference: Control variables and differentiability

Demand analysis is a key element of economics. It has the attractive feature of being important in theory as well as in application. Its purpose is to explain consumer behavior in the market place, i.e., demand analysis is designed to explain what commodities the consumer will purchase and in what quantities and how the consumer can be expected to respond to changes in commodity prices and income. Since the parameters of demand functions can be extremely valuable for both public and private decision makers, it is important to obtain concise and accurate estimates of them. Public policy makers must have reliable estimates of demand parameters for the scientific study of economic growth and development and for the rational formulation of economic policies. Farm policies directed towards commodity programs like price supports, production controls, and payment programs for the major farm crops, would no doubt benefit from more accurate information in regard to market demand functions. Private business models for forecasting future markets, planning merchandising and advertising, and devising promotional programs can be improved with demand analysis. Traditionally, most of the estimates of demand parameters in empirical analysis were based on single equation least squares approach. Theoretically, however, the estimation of demand parameters calls for the complete set of demand functions to be considered as a whole. One of the major reasons for the relatively few studies devoted to the estimation of the full set of demand parameters is the existence of a gap between demand theory and empirical analysis, i.e., the classical theory of consumer behavior has not provided workable relationships for estimation purposes due to the fact that available data is insufficient for the estimation of a large number of the required parameters. Recent studies of the theory of consumer behavior have provided a number of empirically useful hypotheses concerning the separability of the consumers utility functions. These hypotheses imply certain empirically meaningful conditions on the parameters of demand functions. More specifically, these conditions reduce the number of parameters to be estimated in a complete system of demand functions and thus make estimation of all the parameters more feasible. In this study an attempt is made to examine consumer behavior in the United States for the period 1929-1969, by assuming an additive preference specification and by using a complete system of demand functions. Briefly, the plan of this study is as follows: a historical note on demand analysis is given below. In Chapter II a review of the classical theory of consumer demand is presented. The assumptions of additivity and separability are then introduced and examined in terms of their consequences for estimation. Chapter III provides a statistical model for obtaining estimates of demand parameters under the assumption of an additive preference specification. Chapters IV, V, and VI contain the main results of this study. In Chapter IV estimates of demand elasticities (price and income) for major commodity groups, e.g., food, clothing, etc. are reported. Chapter V contains estimates of price and income elasticities of demand for food and non-food commodity groups. The statistical information available is then used to obtain estimates of demand elasticities (price and income) for nine food groups. The empirical evidence which suggests that the demand for food at retail level is becoming more elastic is examined in Chapter VI. Concluding remarks are offered in Chapter VII.

Nonparametric identification and estimation of transformation models

On the Estimation of Supply and Demand Elasticities of Agricultural Commodites

In estimating demand elasticities for food, we must choose a functional form for the statistical model. Because this choice can have untoward consequences for the user (King), we seek a form which does not impose undue restrictions on the estimated demand elasticities. Statistically, we seek a functional form which gives close approximations to the elasticities of interest. In this connection, Gallant (1981, 1982) points out that the key consideration is the method of approximation. There are two: Taylor's series and Fourier series methods. The problem with Taylor's theorem is that it applies only locally on a region of unspecified size. This method can yield testable implications of the theory at the point of approximation; but this point is in general unknown and may not even be in the range of the data (Caves and Christensen, White). Moreover, the approximation error from Taylor's series can be large for small departures from the (unspecified) point of expansion (White). In short, there is nd guarantee that Taylor's theorem will give close approximations at any point in the sample (Gallant 1981). Thus there is no assurance that even the recently popularized locally flexible functional forms (translog, generalized Leontief, almost ideal demand system) will give close approximations to the true demand system.

This paper is concerned with inference about a function g that is identified by a conditional moment restriction involving instrumental variables. The paper presents a test of the hypothesis that g belongs to a finite-dimensional parametric family against a nonparametric alternative. The test does not require nonparametric estimation of g and is not subject to the illposed inverse problem of nonparametric instrumental variables estimation. Under mild conditions, the test is consistent against any alternative model and has asymptotic power advantages over existing tests. Moreover, it has power arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is O(n-1/2), where n is the sample size.

Registry data typically report incident cases within a certain calendar time interval. Such interval sampling induces double truncation on the incidence times, which may result in an observational bias. In this paper, we introduce nonparametric estimation for the cumulative incidences of competing risks when the incidence time is doubly truncated. Two different estimators are proposed depending on whether the truncation limits are independent of the competing events or not. The asymptotic properties of the estimators are established, and their finite sample performance is investigated through simulations. For illustration purposes, the estimators are applied to childhood cancer registry data, where the target population is peculiarly defined conditional on future cancer development. Then, in our application, the cumulative incidences inform on the distribution by age of the different types ofcancer.

In this article we study the semiparametric estimation of the Tobit model simultaneously jointed with an endogenous regressor. The model usually is estimated by maximum likelihood method and two-stage estimation under the normality assumption of the error terms. The possible misspecification motivates our semiparametric study. We first construct a semiparametric estimator for the parameters in the reduced form equations and prove its consistency and asymptotical normality. Then the parameters in the structural models are recovered by system minimum distance estimator. The simulation shows that our estimator performs well in different designs in finite samples. Finally, an empirical application is given to show the usefulness of the estimator.