Abstract. We propose confidence regions for the parameters of incomplete models
with exact coverage of the true parameter in finite samples. Our confidence region
inverts a test, which generalizes Monte Carlo tests to incomplete models. The test
statistic is a discrete analogue of a new optimal transport characterization of the
sharp identified region. Both test statistic and critical values rely on simulation
drawn from the distribution of latent variables and are computed using solutions
to discrete optimal transport, hence linear programming problems. We also pro-
pose a fast preliminary search in the parameter space with an alternative, more
conservative yet consistent test, based on a parameter free critical value.

Abstract:
We show that the identification problem for a class of dynamic panel logit models with fixed effects has a connection to the truncated moment problem in mathematics. We use this connection to show that the sharp identified set of the structural parameters is characterized by a set of moment equality and inequality conditions. This result provides sharp bounds in models where moment equality conditions do not exist or do not point identify the parameters. We also show that the sharp identified set of the non-parametric latent distribution of the fixed effects is characterized by a vector of its generalized moments, and that the number of moments grows linearly in T. This final result lets us point identify, or sharply bound specific classes of functionals, without solving an optimization problem with respect to the latent distribution. We illustrate our identification result with several examples, and an empirical application on modeling children’s respiratory conditions.

Abstract:
Quantile regression is a method that allows to access the effect of predictors on the conditional quantile of the response in a regression framework. In this talk, we will present some recent theoretical and methodology developments for quantile regression in a panel data setting where repeated observations on individuals are available. On the theory side, we will discuss conditions that guarantee unbiased asymptotic normality of quantile regression with individual-specific intercepts and common slopes. From a methodological standpoint, we will discuss approaches to relax the common slope assumption and allow for groups of individuals that share the same slopes while leaving the intercepts unrestricted.

高田保馬記念講演会ポスターＡ４

1) Daisuke Kurisu (U of Tokyo) 15:10 – 16:25

Title: Prediction and nonparametric inference on random objects
Abstract: In this presentation, I will talk about two topics on statistical analysis of non-Euclidean data.
Firstly, we extend the notion of model averaging for conventional regression models to Frechet regression, which has Euclidean predictors and a non-Euclidean output.
Specifically, we will introduce a cross-validation (CV) criterion for selecting model averaging weights and demonstrate its optimality in terms of the final prediction error.
Through simulation results, we will illustrate that CV outperforms AIC and BIC-type model averaging estimators.

Secondly, we consider statistical inference on the Frechet mean, which is a generalization of the conventional population mean.
In particular, we introduce empirical likelihood (EL) methods for the inference on Frechet means of Manifold-valued data and study asymptotic properties of the EL statistics.
We also discuss some extensions of our main results.
Simulation and real data analysis illustrate the usefulness of the proposed method.

2) Jiaying Gu (U of Toronto) 16:40 – 17:55

Title: Counterfactual Identification and Latent Space Enumeration (joint work with Thomas Russell and Thomas Stringham).

Abstract: This paper provides a unified framework for partial identification of counterfactual parameters in a general class of discrete outcome models allowing for endogenous regressors and multidimensional latent variables, all without parametric distributional assumptions. Our main theoretical result is that, when the covariates are discrete, the infinite-dimensional latent variable distribution can be replaced with a finite-dimensional version that is equivalent from an identification perspective. The finite-dimensional latent variable distribution is constructed in practice by enumerating regions of the latent variable space with a new and efficient cell enumeration algorithm for hyperplane arrangements. We then show that bounds on a certain class of counterfactual parameters can be computed by solving a sequence of linear programming problems, and show how the researcher can introduce additional assumptions as constraints in the linear programs. Finally, we apply the method to a mobile phone choice example with heterogeneous choice sets, as well as an airline entry game example.

Program

プログラム2022年度official

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Abstract: This study proposes a tying maximum likelihood estimation (TMLE) method to improve the performance of estimation of statistical and econometric models in which most time series have long sample periods, whereas the other time series are very short. The main idea of the TMLE is to tie the parameters of the long time series with those of the short time series together so that some useful information in the long time series which is related to the short time series can be transferred to the short time series. The information transferred from the long series can help improve the estimation accuracy of the parameters related to the short series. We first provide asymptotic properties of the TMLE and show its finite-sample risk bound with a fixed tuning parameter which determines the strength of tying. Further, we provide a method for selecting the tuning parameter based on a bootstrap procedure. A finite sample theory about this method is derived, which tells us how to conduct the bootstrap procedure effectively. Extensive artificial simulations and empirical applications show that the TMLE has an outstanding performance in point estimate and forecast.

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応用ミクロ経済学セミナーと共催
https://www.econ.kyoto-u.ac.jp/about/seminars/seminars-cat/seminar-micro/
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