Kazumitsu Nawata

Estimation of sample selection bias models by the maximum likelihood estimator and Heckman's two-step estimator

Abstract In this paper, methods of estimating models with sample selection biases are analyzed. Finite sample properties of the maximum likelihood estimator (MLE) and Heckmans two-step estimator are compared using Monte Carlo experiments.

Estimation of sample selection bias models

Econometric models with sample selection biases are widely used in various fields of economics, such as labor economics. The Maximum Likelihood Estimator (MLE) is seldom used to estimate models because of computational difficulty, while Heckmans two-step estimator is widely used to estimate these models. However, Heckmans two-step estimator sometimes performs poorly. In this paper, methods of calculating the MLE are analysed, and finite sample properties of the MLE and Heckmans two-step estimator are compared using Monte Carlo experiments and empirical examples.

A note on the estimation of models with sample-selection biases

Abstract Econometric models with sample-selection biases are widely used in various fields of economics, such as labor economics. Heckmans two-step estimator is widely used to estimates these models. This paper points out some limitations and problems of Heckmans two step-estimator

Estimation of the female labor supply models by Heckman’s two-step estimator and the maximum likelihood estimator

The female labor supply models have been widely used in labor economics. The models are usually estimated by Heckman’s two-step estimator. However, Heckman’s two-step estimator often performs poorly. This paper considers an estimation of the models by the maximum likelihood method. An algorithm which makes calculation of the maximum likelihood estimator (MLE) possible is proposed. The finite sample properties are compared using Monte Carlo experiments.

An analysis of the length of hospital stay for cataract patients in Japan using the discrete-type proportional hazard model

We analyze the length of hospital stays of patients hospitalized for cataract and related diseases (Diagnosis Related Groups (DRG) 2041) in Japan, utilizing the data pertaining to 3436 patients on whom one-eye lens operations are performed. We use the discrete-type proportional hazard model to analyze variables that may affect the length of stay. We find that estimates of the Child and Other Facility Dummies are negative and significant. These variables affect the leaving rate and the length of stay. The length of stay also changes at age 40. With regard to the types of affiliated operations and treatments, the estimates of dummy variables are negative and significant at the 1% level. We also find large differences in the length of stay among hospitals, despite eliminating the influence of both the characteristics of the patient and the types of affiliated operations and treatments. The longest average length of stay is over 3.5 times as long as the shortest average length of stay. Finally, we analyze the factors pertaining to hospitals that may affect the length of stay. The estimates of the Profit and Cold Region dummies are negative and significant; in other words, the leaving rate is reduced and the length of stay is increased if the hospital becomes more profitable and is located in the cold regions of Hokkaido and Tohoku.

Size Characteristics Of Tests For Sample Selection Bias: A Monte Carlo Comparison And Empirical Example

The t-test of an individual coefficient is used widely in models of qualitative choice. However, it is well known that the t-test can yield misleading results when the sample size is small. This paper provides some experimental evidence on the finite sample properties of the t-test in models with sample selection biases, through a comparison of the t-test with the likelihood ratio and Lagrange multiplier tests, which are asymptotically equivalent to the squared t-test. The finite sample problems with the t-test are shown to be alarming, and much more serious than in models such as binary choice models. An empirical example is also presented to highlight the differences in the calculated test statistics.

Evaluation of the DPC-based inclusive payment system in Japan for cataract operations by a new model

Since medical care expenses have been increasing rapidly with the ageing of the population, reducing the length of hospital stay (LOS) has become an important political issue in Japan. A new inclusive payment system based on the diagnosis procedure combination (DPC) was introduced in 82 special functioning hospitals in April 2003. Since April 2004, use of the DPC system has been gradually extended to general hospitals. As of July 2009, a total of 1,283 hospitals, about 14% of the 8,862 general hospitals in Japan, had joined the DPC system. These 1,283 hospitals have 434,231 beds, which is nearly half of the total beds (913,234 beds) of general hospitals in Japan. The DPC system is an original system developed in Japan. Inclusive payments based on the DPC system cover fees for the following categories only: basic hospital stays, medical checkups, image diagnosis, medication, injections, treatments under 1,000 points (10 yen per point has been paid to hospitals), and medicines used during rehabilitation treatments and related activities. Fees for all other categories, such as fees for operations, are paid on the basis of the conventional fee-for- service system. Unlike the diagnosis-related group/prospective payment system (DRG/PPS) used in the U.S. and other countries, the Japanese DPC system is a per diem prospective payment system. The per diem payment becomes less as the LOS becomes longer. Three periods, Period I, Period II, and Specific Hospitalization Period, are determined for each DPC code. For stays over the Specific Hospitalization Period, the per diem payment is determined through the conventional fee-for-service system. The introduction of the DPC system was one of the largest and most important revisions of the payment system since the Second World War. For the effective use of medical resources, improvement of the DPC system by thorough analyses of the system is absolutely necessary. In this paper, we first propose a new model that considers heterogeneity of variances. We then present our analysis of the LOS for cataract operations before and after the introduction of the DPC system using the proposed model. The number of cataract patients in Japan has been increasing rapidly with the ageing of the population. According to a survey conducted by the Ministry of Health, Labour and Welfare (2008), nearly 800,000 cataract operations are performed annually and nearly 2.5 billion yen are spent for cataract operations annually. We analyzed the influence of the DPC system and factors that might affect the LOS for cataract patients by examining data collected from 5 general hospitals before and after the introduction of the system. To eliminate the influences of types of operations and treatments, we used data strictly pertaining to the patients who underwent cataract operations and insertion of a prosthetic lens on one eye only. The number of patients was 2,533. The estimates of the Female, Age 50, Age 90, Not_Home dummies are significant and affect the LOS. We found large differences in the changes of average lengths of stay (ALOSs) among hospitals. In hospitals where the ALOSs were long, the ALOSs decreased significantly under the DPC system. On the other hand, in hospitals where the ALOSs were already short, the ALOSs did not decrease under the DPC system. The results of empirical study imply that the DPC system gave strong incentives to reduce the ALOSs for the former hospitals but it gave weak (or no) incentives for the latter hospitals, where the ALOSs were already short.

An analysis of hip fracture treatments in Japan by the discrete-type proportional hazard and ordered probit models

The length of stay and the effectiveness of medical treatment are analyzed using data from patients hospitalized for hip fractures in Japan. The influence of the Revision of the Medical Service Fee Schedule in April 2002 is evaluated, and factors which may affect the length of stay and the effectiveness of treatment (walking ability upon leaving the hospital) are also analyzed. The length of stay is analyzed by the discrete-type proportional hazard model, and the effectiveness of treatment is analyzed by the ordered probit models.

A comparative study on predicting influenza outbreaks

Worldwide, influenza is estimated to result in approximately 3 to 5 million annual cases of severe illness and approximately 250,000 to 500,000 deaths. We need an accurate time-series model to predict the number of influenza patients. Although time-series models with different time lags as feature spaces could lead to varied accuracy, past studies simply adopted a time lag in their models without comparing or selecting an appropriate number of time lags. We investigated the performance of adopting 6 different time lags in 6 different models: Auto-Regressive Integrated Moving Average (ARIMA), Support Vector Regression (SVR), Random Forest (RF), Gradient Boosting (GB), Artificial Neural Network (ANN), and Long Short Term Memory (LSTM) with hyperparameter adjustment. To the best of our knowledge, this is the first time that LSTM has been used to predict influenza outbreaks. As a result, we found that the time lag of 52 weeks led to the lowest Mean Absolute Percentage Error (MAPE) in the ARIMA, ANN and LSTM, while the machine learning models (SVR, RF, GB) achieved the lowest MAPEs with a time lag of 4 weeks. We also found that the MAPEs of the machine learning models were less than ARIMA, and the MAPEs of the deep learning models (ANN, LSTM) were less than those of the machine learning models. In all the models, the LSTM model of 4 layers reached the lowest MAPE of 5.4%, and the LSTM model of 5 layers with regularization reached the lowest root mean squared error (RMSE) of 0.00210.

Estimation of generalised regression models by the grouping method

Nawata [8–10] proposed a new estimator for the standard regression, censored regression, and binary choice models, based on grouping of observations. This paper shows that Nawatas grouping method can be generalised to various types of estimation problems and represents a new class of estimation methods.