ON THE UNIDENTIFIABILITY OF THE FIXED-EFFECTS 3PL MODEL

Networks and Spatial Economics, 2008

The flexible structure of the mixed logit (ML) model is at the root of the difficulties associated to its estimation. Major problems are parameter identification and the distinction between different substitution patterns. In this paper we focus on the empirical identification problem and investigate the effect of low information richness in the data on the capability of estimating a correct ML model (i.e. with identifiable parameters and free of confounding effects). In particular, we analyse to which extent the empirical identification problem depends on the variability of the data among alternatives, on the degree of heterogeneity of the taste parameters, on the dimension of the sample and on the number of choice tasks for each individual. To test for information richness of the data and its effect on the capability of the ML model to reproduce random heterogeneity in tastes, a collection of datasets was generated varying systematically (a) the standard deviation (SD) of the distribution of travel time differences between the two alternatives, (b) the SD of the random parameter, (c) the number of choice tasks for each individual and (d) the number of individuals in relation to the number of choice tasks. Then, several ML models allowing for random travel time parameters were estimated using different number of draws and results were compared in terms of model goodness of fit and, also, on the capability of reproducing the real parameters used to generate each dataset. Our results suggest that identification problems depend only on the (low) variability of the associated data and disappear as the richness of the data associated to the random parameter increases. However, rich enough data only allows obtaining good statistics but the estimated parameters do not always reproduce the correct values, as the capability of the ML to reproduce random heterogeneity depends on the random Netw Spat Econ (parameter distribution (degree of variability and symmetry). Moreover, the capability of the ML to reproduce random heterogeneity increases when more than one choice is available for each individual and the effect of sample size on the empirical identification reduces considerably.

Annals of Economics and Statistics, 2019

This paper investigates identification in binary response models with panel data. Conditioning on sufficient statistics can sometimes lead to a conditional maximum likelihood approach that can be used to identify and estimate the parameters of interest in such models. Unfortunately it is often difficult or impossible to find such sufficient statistics, and even if it is possible, the approach sometimes leads to conditional likelihoods that do not depend on some interesting parameters. Using a range of different data generating processes, this paper calculates the identified regions for parameters in panel data logit AR(2) and logit VAR(1) model for which it is not known whether the parameters are identified or not. We find that identification might be more common than was previously thought, and that the identified regions for non-identified objects may be small enough to be empirically useful.

Journal of Econometrics, 2013

In semiparametric binary response models, support conditions on the regressors are required to guarantee point identification of the parameter of interest. For example, one regressor is usually assumed to have continuous support conditional on the other regressors. In some instances, such conditions have precluded the use of these models; in others, practitioners have failed to consider whether the conditions are satisfied in their data. This paper explores the inferential question in these semiparametric models when the continuous support condition is not satisfied and all regressors have discrete support. I suggest a recursive procedure that finds sharp bounds on the parameter of interest and outline several applications. After deriving closed-form bounds on the parameter, I show how these formulas can help analyze cases where one regressor's support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I also propose three approaches to address the problem of empty identification sets when a model is misspecified. Finally, I present a Monte Carlo experiment and an empirical illustration to compare several estimation techniques.

Economics Letters, 1990

In case of sample selectivity the maximum likelihood estimator of the parameters in a model with fixed effects will not be consistent when the number of time periods is small. In this paper, we present a transformation to eliminate the fixed individual effects and show that the corresponding marginal maximum likelihood estimator is computationally feasible and can be used to estimate the remaining parameters consistently even if the number of time periods is finite.

Structural equations models one the most important models in the field of economic and social science, artificial intelligence and so, because of its ability to analyze the relationship between Observed variables and Latent variables compared to many other models such as; regression models and Path Analysis models, that measure Observed variables only, and Confirmatory factor analysis models that measure Observed variables and Latent variables. There is a fundamental problem when applying structural equations models has been nearly half a century is non-identification problem, and summed up the non-identification problem in the inability of the researcher in obtaining single values of the parameters of the model. The non-identification problem arises from the under identified models that we cannot get them any values for the coefficients equation to be identified and therefore difficult to move to the next steps in the process of analyzing the data because it cannot rely on the results of non-identified model. Some recent studies have provided a set of criteria to determine whether the structural equations models identified or under-identified and some of them deals with the models is non-identified to become identified. And these new criteria mainly depend on the graph so it was renamed graphic criteria. There are two entrances to identified structural equations models; two well-known classical entrance and graphical modern entrance. The problem study concentrated of knowing whether these graphic criteria lead to the same results that have already been provided by the classical entrance or whether they offer the best results, and the order of these graphic criteria by preference according to the results reached them. The study aims to use mathematical (classical) and graphic entrances to treat the of non-identification problem through an econometric study to identified structural equations models, through knowing structural equations models and their relation to the of non-identification problem, and also to identify a software used in structural equation modeling Amos program to analysis data, which is used the maximum likelihood to

2008

2008

Essays on Identification in Econometric Models Tatiana Komarova This dissertation consists of three essays on the identification analysis of econometric models.

2003

In this study, the robustness of item parameter estimates with respect to the underlying distribution of abilities was explored. Using simulated datasets, item parameters were derived from a large sample representing the population versus samples representing a subset of ability and subsequently compared for possible mismatch. Comparisons were made under these conditions: (1) increasing differences between ability of examinees in the pilot sample and those of the population; and (2) the size of the pilot sample. All datasets were generated using DIFSUM, a computer program that permits the creation of dichotomous test data according to prespecified characteristics. In general, the study shows that item parameter estimates derived from a sample contain more errors when ability differences exist

Measurement: Interdisciplinary Research & Perspective, 2009

The goal of this commentary is to provide some additional results to the interesting and provocative paper of Maris and Bechger (this issue). More specifically, we have three aims. First, we want to distinguish between three fundamental concepts that are important in studying identification in statistical models: the statistical model, the identified parametrization, and the parameters of interest. Second, we want to take the analysis of Maris and Bechger (this issue) one step further by showing what restrictions are needed to identify the 3PL with discriminations equal to 1 (which, following San Martín, Del Pino, and De Boeck, 2006, we term 1PL-G) in a meaningful way. Third, we want to point to an implicit problem in the analysis of Maris and Bechger (this issue), but one that has much broader consequences than appear at first sight.