Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors

In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of mu* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when mu* is modelled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate mu*. In contrast, handling endogenous regressors in nonparametric models, where mu* is regarded as fully unknown, presents di±cult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification related properties of this model when the unknown function mu* belongs to a linear space. We also investigate underidentification of mu* along with the identification of its linear functionals. Several examples are provided in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.

Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors

Consider a nonparametric regression model Y=mu*(X) + e, where the explanatory variables X are endogenous and e satisfies the conditional moment restriction E[e|W]=0 w.p.1 for instrumental variables W. It is well known that in these models the structural parameter mu* is 'ill-posed' in the sense that the function mapping the data to mu* is not continuous. In this paper, we derive the efficiency bounds for estimating linear functionals E[p(X)mu*(X)] and int_{supp(X)}p(x)mu*(x)dx, where p is a known weight function and supp(X) the support of X, without assuming mu* to be well-posed or even identified.

Exact moment calculations for genetic models with migration, mutation, and drift

Using properties of moment stationarity we develop exact expressions for the mean and covariance of allele frequencies at a single locus for a set of populations subject to drift, mutation, and migration. Some general results can be obtained even for arbitrary mutation and migration matrices, for example: (1) Under quite general conditions, the mean vector depends only on mutation rates, not on migration rates or the number of populations. (2) Allele frequencies covary among all pairs of populations connected by migration. As a result, the drift, mutation, migration process is not ergodic when any finite number of populations is exchanging genes. in addition, we provide closed form expressions for the mean and covariance of allele frequencies in Wright's finite-island model of migration under several simple models of mutation, and we show that the correlation in allele frequencies among populations can be very large for realistic rates of mutation unless an enormous number of populations are exchanging genes. As a result, the traditional diffusion approximation provides a poor approximation of the stationary distribution of allele frequencies among populations. Finally, we discuss some implications of our results for measures of population structure based on Wright's F-statistics.

Empirical Analysis of Credit Risk Regime Switching and Temporal Conditional Default Correlation in Credit Default Swap Valuation: The Market liquidity effect

In this paper, we extend the debate concerning Credit Default Swap valuation to include time varying correlation and co-variances. Traditional multi-variate techniques treat the correlations between covariates as constant over time; however, this view is not supported by the data. Secondly, since financial data does not follow a normal distribution because of its heavy tails, modeling the data using a Generalized Linear model (GLM) incorporating copulas emerge as a more robust technique over traditional approaches. This paper also includes an empirical analysis of the regime switching dynamics of credit risk in the presence of liquidity by following the general practice of assuming that credit and market risk follow a Markov process. The study was based on Credit Default Swap data obtained from Bloomberg that spanned the period January 1st 2004 to August 08th 2006. The empirical examination of the regime switching tendencies provided quantitative support to the anecdotal view that liquidity decreases as credit quality deteriorates. The analysis also examined the joint probability distribution of the credit risk determinants across credit quality through the use of a copula function which disaggregates the behavior embedded in the marginal gamma distributions, so as to isolate the level of dependence which is captured in the copula function. The results suggest that the time varying joint correlation matrix performed far superior as compared to the constant correlation matrix; the centerpiece of linear regression models.

Moment Based Inference with Stratified Data

Many datasets used by economists and other social scientists are collected by stratified sampling. The sampling scheme used to collect the data induces a probability distribution on the observed sample that differs from the target or underlying distribution for which inference is to be made. If this effect is not taken into account, subsequent statistical inference can be seriously biased. This paper shows how to do efficient semiparametric inference in moment restriction models when data from the target population is collected by three widely used sampling schemes: variable probability sampling, multinomial sampling, and standard stratified sampling.

Total Factor Productivity and Monetary Policy: Evidence from Conditional Volatility

This paper empirically assesses whether monetary policy affects real economic activity through its affect on the aggregate supply side of the macroeconomy. Analysts typically argue that monetary policy either does not affect the real economy, the classical dichotomy, or only affects the real economy in the short run through aggregate demand new Keynesian or new classical theories. Real business cycle theorists try to explain the business cycle with supply-side productivity shocks. We provide some preliminary evidence about how monetary policy affects the aggregate supply side of the macroeconomy through its affect on total factor productivity, an important measure of supply-side performance. The results show that monetary policy exerts a positive and statistically significant effect on the supply-side of the macroeconomy. Moreover, the findings buttress the importance of countercyclical monetary policy as well as support the adoption of an optimal money supply rule. Our results also prove consistent with the effective role of monetary policy in the Great Moderation as well as the more recent rise in productivity growth.