Identification and nonparametric estimation of a transformed additively separable model

Let r(x,z)$r(x,z)$ be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses the identification and consistent estimation of the unknown functions H$H$, M$M$, G$G$ and F$F$, where r(x,z)=H[M(x,z)]$r(x,z)=H\left[M(x,z)\right]$, M(x,z)=G(x)+F(z)$M(x,z)=G\left(x\right)+F\left(z\right)$, and H$H$ is strictly monotonic. An estimation algorithm is proposed for each of the model’s unknown components when r(x,z)$r(x,z)$ represents a conditional mean function. The resulting estimators use marginal integration to separate the components G$G$ and F$F$. Our estimators are shown to have a limiting Normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives. Their small sample performance is studied in a Monte Carlo experiment. We apply our results to estimate generalized homothetic production functions for four industries in the Chinese economy.     

Extending the regression-discontinuity approach to multiple assignment variables

The recent scholarly attention to the regression-discontinuity design has focused exclusively on the application of a single assignment variable. In many settings, however, exogenously imposed cutoffs on several assignment variables define a set of different treatments. In this paper, we show how to generalize the standard regression-discontinuity approach to include multiple assignment variables simultaneously. We demonstrate that fitting this general, flexible regression-discontinuity model enables us to estimate several treatment effects of interest.     

A nonparametric test of weak separability and consumer preferences

Two stochastic nonparametric procedures are developed to evaluate the significance of violations of weak separability. When the data have measurement error, we show that the necessary and sufficient weak separability conditions of Varian [Varian, H., 1983. Nonparametric tests of consumer behavior. Review of Economic Studies 50, 99–110] must also satisfy the Afriat inequalities. The tests detect weak separability with high probability for weakly separable data. In addition, the procedures correctly reject weak separability for both nonseparable and random utility simulated data sets. The tests also fail to reject weak separability for a monetary and consumption data set which suggests that measurement error may be the source of the observed violations.     

A consistent nonparametric test of affiliation in auction models

We propose a new nonparametric test of affiliation, a strong form of positive dependence with independence as a special, knife-edge, case. The test is consistent against all departures from the null of affiliation, and its null distribution is standard normal. Like most nonparametric tests, a sample-size dependent input parameter is needed. We provide an informal procedure for choosing the input parameter and evaluate the test’s performance using a simulation study. Our test can be used to test the fundamental assumptions of the auctions literature. We implement our test empirically using the Outer Continental Shelf (OCS) auction data.     

The efficiency of top agents: An analysis through service strategy in tennis

We consider the question whether top tennis players in a top tournament (Wimbledon) employ an optimal (efficient) service strategy. While we show that top players do not, in general, follow an optimal strategy, our principal result is that the estimated inefficiencies are not large: the inefficiency regarding winning a point on service is on average 1.1% for men and 2.0% for women, implying that–by adopting an efficient service strategy–players can (on average) increase the probability of winning a match by 2.4%-points for men and 3.2%-points for women. While the inefficiencies may seem small, the financial consequences for the efficient player at Wimbledon can be substantial: the expected paycheck could rise by 18.7% for men and even by 32.8% for women. We use these findings to shed some light on the question of whether economic agents are successful optimizers.     

Online forecast combinations of distributions: Worst case bounds

This paper considers forecasts with distribution functions that may vary through time. The forecast is achieved by time varying combinations of individual forecasts. We derive theoretical worst case bounds for general algorithms based on multiplicative updates of the combination weights. The bounds are useful for studying properties of forecast combinations when data are non-stationary and there is no unique best model.     

The influence of school size,principal characteristics and school management practices on educational performance: An efficiency analysis of Italian students attending middle schools

The aim of the paper is to identify which among the aspects that relate to the composition of the student body, school (district) size, management practices and the school principals' own characteristics are associated with the performance of Italian students at grade 8, measured through standardised test scores in reading and mathematics. The analysis makes use of a student-level efficiency model, and several school level variables are included as explanators for efficiency scores. The results show that, especially for reading, the most influential variables relate to the composition of the student body, while the students' performance in mathematics is partly correlated with the management practices adopted by the school principal/head teacher. Schools and schooling can only explain a minor part of the variance in achievement scores, however, and the characteristics of the students themselves play the most significant role.     

Breaking the curse of dimensionality in nonparametric testing

For tests based on nonparametric methods, power crucially depends on the dimension of the conditioning variables, and specifically decreases with this dimension. This is known as the “curse of dimensionality”. We propose a new general approach to nonparametric testing in high dimensional settings and we show how to implement it when testing for a parametric regression. The resulting test behaves against directional local alternatives almost as if the dimension of the regressors was one. It is also almost optimal against classes of one-dimensional alternatives for a suitable choice of the smoothing parameter. The test performs well in small samples compared to several other tests.     

Asymptotically distribution-free tests for the volatility function of a diffusion

This paper develops two tests for parametric volatility function of a diffusion model based on Khmaladze (1981)’s martingale transformation. The tests impose no restrictions on the functional form of the drift function and are shown to be asymptotically distribution-free. The tests are consistent against a large class of fixed alternatives and have nontrivial power against a class of root-n$n$ local alternatives. The paper also extends the tests of volatility to testing for joint specifications of drift and volatility. Monte Carlo simulations show that the tests perform well in finite samples. The proposed tests are then applied to testing models of short-term interest, using data of Treasury bill rate and Eurodollar deposit rate. The empirical results show that the commonly used CKLS volatility function of Chan et al. (1992) fits volatility function poorly and none of the parametric interest rate models considered in the paper fit data well.     

Efficient estimation of the semiparametric spatial autoregressive model

Efficient semiparametric and parametric estimates are developed for a spatial autoregressive model, containing non-stochastic explanatory variables and innovations suspected to be non-normal. The main stress is on the case of distribution of unknown, nonparametric, form, where series nonparametric estimates of the score function are employed in adaptive estimates of parameters of interest. These estimates are as efficient as the ones based on a correct form, in particular they are more efficient than pseudo-Gaussian maximum likelihood estimates at non-Gaussian distributions. Two different adaptive estimates are considered, relying on somewhat different regularity conditions. A Monte Carlo study of finite sample performance is included.     

A semiparametric panel model for unbalanced data with application to climate change in the United Kingdom

This paper is concerned with developing a semiparametric panel model to explain the trend in UK temperatures and other weather outcomes over the last century. We work with the monthly averaged maximum and minimum temperatures observed at the twenty six Meteorological Office stations. The data is an unbalanced panel. We allow the trend to evolve in a nonparametric way so that we obtain a fuller picture of the evolution of common temperature in the medium timescale. Profile likelihood estimators (PLE) are proposed and their statistical properties are studied. The proposed PLE has improved asymptotic property comparing the sequential two-step estimators. Finally, forecasting based on the proposed model is studied.     

Pitfalls in the estimation of a cost function that ignores allocative inefficiency: A Monte Carlo analysis

In the stochastic frontier literature, it is a widely held view that allocative inefficiency can be lumped together with technical inefficiency in the estimation of cost frontiers. Therefore, a one-sided error term in the cost function is believed to capture the cost of overall (technical plus allocative) inefficiency. In this paper we challenge that view through a detailed Monte Carlo investigation. The results show that failure to include the cost of allocative inefficiency explicitly in the cost function biases the estimates of: (i) the cost function parameters, (ii) returns to scale, (iii) input price elasticities, and (iv) cost-inefficiency.     

Random walk or chaos: A formal test on the Lyapunov exponent

A formal test on the Lyapunov exponent is developed to distinguish a random walk model from a chaotic system, which is based on the Nadaraya–Watson kernel estimator of the Lyapunov exponent. The asymptotic null distribution of our test statistic is free of nuisance parameter, and simply given by the range of standard Brownian motion on the unit interval. The test is consistent against the chaotic alternatives. A simulation study shows that the test performs reasonably well in finite samples. We apply our test to some of the standard macro and financial time series, finding no significant empirical evidence of chaos.     

Manipulation of the running variable in the regression discontinuity design: A density test

Standard sufficient conditions for identification in the regression discontinuity design are continuity of the conditional expectation of counterfactual outcomes in the running variable. These continuity assumptions may not be plausible if agents are able to manipulate the running variable. This paper develops a test of manipulation related to continuity of the running variable density function. The methodology is applied to popular elections to the House of Representatives, where sorting is neither expected nor found, and to roll call voting in the House, where sorting is both expected and found.     

The performance of estimators based on the propensity score

We investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required, like inverse probability weighting, kernel and other variants of matching, as well as different parametric models. The simulation design used is based on real data usually employed for the evaluation of labour market programmes in Germany. We vary several dimensions of the design that are of practical importance, like sample size, the type of the outcome variable, and aspects of the selection process. We find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators. A conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall, in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property.     

Time and causality: A Monte Carlo assessment of the timing-of-events approach

We present new Monte Carlo evidence regarding the feasibility of separating causality from selection within non-experimental duration data, by means of the non-parametric maximum likelihood estimator (NPMLE). Key findings are: (i) the NPMLE is extremely reliable, and it accurately separates the causal effects of treatment and duration dependence from sorting effects, almost regardless of the true unobserved heterogeneity distribution; (ii) the NPMLE is normally distributed, and standard errors can be computed directly from the optimally selected model; and (iii) unjustified restrictions on the heterogeneity distribution, e.g., in terms of a pre-specified number of support points, may cause substantial bias.     

Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior

We propose a quasi-Bayesian nonparametric approach to estimating the structural relationship φ$\phi$ among endogenous variables when instruments are available. We show that the posterior distribution of φ$\phi$ is inconsistent in the frequentist sense. We interpret this fact as the ill-posedness of the Bayesian inverse problem defined by the relation that characterizes the structural function φ$\phi$. To solve this problem, we construct a regularized posterior distribution, based on a Tikhonov regularization of the inverse of the marginal variance of the sample, which is justified by a penalized projection argument. This regularized posterior distribution is consistent in the frequentist sense and its mean can be interpreted as the mean of the exact posterior distribution resulting from a Gaussian prior distribution with a shrinking covariance operator.     

The Feldstein-Horioka puzzle and capital mobility: The role of the recent financial crisis

The Feldstein-Horioka (FH) puzzle has long been debated as it relates to the important topics of capital mobility and how to determine levels of investment. Adopting a recursive approach and panel techniques, this paper explores the impacts of the recent financial crisis on the validity of the puzzle. The OECD’s saving-investment correlation dropped to a record low just before the 2008 crisis began, reflecting the perceived ‘end’ of the FH puzzle in some studies. But since the onset of the crisis, our results indicate that this correlation has increased, suggesting the puzzle’s return. The puzzle for net capital-importing and net capital-exporting countries differs, with the relationship being more significant for the exporters compared to the importers, reflecting the asymmetry in terms of the degree of shocks across countries.     

A spatio-temporal model of house prices in the USA

This paper provides an empirical analysis of changes in real house prices in the USA using State level data. It examines the extent to which real house prices at the State level are driven by fundamentals such as real per capita disposable income, as well as by common shocks, and determines the speed of adjustment of real house prices to macroeconomic and local disturbances. We take explicit account of both cross-sectional dependence and heterogeneity. This allows us to find a cointegrating relationship between real house prices and real per capita incomes with coefficients (1,−1)$(1,-1)$, as predicted by the theory. We are also able to identify a significant negative effect for a net borrowing cost variable, and a significant positive effect for the State level population growth on changes in real house prices. Using this model we then examine the role of spatial factors, in particular, the effect of contiguous states by use of a weighting matrix. We are able to identify a significant spatial effect, even after controlling for State specific real incomes, and allowing for a number of unobserved common factors. We do, however, find evidence of departures from long run equilibrium in the housing markets in a number of States notably California, New York, Massachusetts, and to a lesser extent Connecticut, Rhode Island, Oregon and Washington State.