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Heckman Sampel Selection Model (PSSM) has been adopted widely in the study of labour work. This model contains exogenous, endogenous and standard error variables. However, this model is constantly exposed to high inaccuracy of estimation result. Therefore, to obtain an accurate and precise estimation, the bootstrap approach is introduced. The bootstrap approach will be hybrid with PSSM model known as BPSSM to achieve estimation result that is more precise. Then, the BPSSM is applied to Malaysian Population and Family Survey 1994 (MPFS-1994) data. The results showed that BPSSM provide a smaller standard error and shorter confidence intervals.

Sample selection model is part of the field of econometrics. The term “selection” or “select” is the term commonly used and it is mentioned in a number of different issues related with the econometric data. Sample selection was developed [

The earliest introduced model consists of female labour force and wage equality [

Model selection consists of two parts [

Therefore, to get the accurate and precise estimation, bootstrap approach was introduced. Through this method, Bootstrap approach will be hybridized with PSSM model called Bootstrap PSSM to get more accurate estimator result. The best model is the model contains of consistent and efficient.

Bootstrap introduced by [

In this study, a mean process is considered to monitor individual observations of

where

x and z = vectors of exogenous remaining variables

The standard approach is to assume that follow a bivarite normal distribution and then applied to the maximum likelihood estimation or a two-stage estimation procedure purposed by Heckman (1979). Firstly, how to estimate

In this study, the hybridization of bootstrap approach in base model (1). This hybridization produced a hybrid control charts where the basic model named by Bootstrap PSSM (BPSSM). The algorithm for this hybrid process is as follows:

Step 1: A sample data,

Step 2: Find bootstrap replication, B(c) by using:

where

Step 3: By continue from Step 2, the residual value will be used in sampling with replacement method to get a matrix of residual bootstrap,

Step 4: For each residual in Step 3, compute new data

Step 5: Compute average of column of

Step 6: By using bootstrap data,

Step 7: For complete PSSM model,

Step 8: After the both equation have bootstrap data, Heckman Two Step estimation was used base on model BPSSM;

In this study, we intend to examine the performance of BPSSM in terms of effectiveness and efficiency control. Numerical estimation was selected to be used in this study. For numerical estimation, basically it is used to examine effectiveness of base model where is evident in two kind of methods, i.e. confidence interval, bootstrap percentile (PB) and Biased Corrected and Accelerate (BCa). BP and BCa selection is motivated by the advantages of these two methods in which BP is the basic method for estimating bootstrap intervals while BCa is a method that can improve BP interval estimation [

Student’s-t:

Bootstrap Persentile (BP):

Bias Corrected and accelerated (Bca):

where

In this study,

For Equation (4), length of this interval based on percentile of mean estimation of bootstrap replication, B of

Mean Square Error (MSE) and Root Mean Square Error (RMSE) was used for error estimation in this study. In theory, a model that gives the smallest estimation value is said to be more efficient and automatically show the effectiveness of the model itself [

where for both MSE and RMSE refers to differences of real error,

A comparison of performance of the real model, PSSM and hybrid model, BPSSM in terms of effectiveness or efficiency base on model estimation. The data set used for this study is from the Malaysian population and family survey 1994 (MPFS-1994). This survey was conducted by National Population and Family Development Board of Malaysia under Ministry of Women, Family and Community Development Malaysia. This survey was specifically for married women, providing relevant and significant information for the problem of married women status regarding wages, educational attainment, household composition and other socioeconomic characteristics. The original MPFS-94 sample data comprises 4444 married women.

The whole data sets used in this study consisted of 2792 married women. The selection rules [

・ Married and aged below 60

・ Not in school or retired

・ Husband present in 1994

・ Husband reported positive earnings for 1994

The empirical results of the basic specification one are presented for the Heckman two-step approach. These approaches consider the probit estimates for the participation equation as a first step and OLS estimates for the wage equation as the second step. We discuss both the participation and wage equation on the estimated coefficient for interval method, the significant effect, and consistency and for PSSM, as well as BPSSM for comparison purposes.

Based on

In

Model | Lower | Upper | Length |
---|---|---|---|

PSSM-t | 22.8134200 | 23.9032400 | 1.0898210 |

BPSSM-t | 23.2661200 | 23.3284100 | 0.0622905 |

BPSSM-PB | 2.1398290 | 2.1136020 | 0.0262270 |

BPSSM-BCa | 23.3015500 | 23.2929800 | 0.0085664 |

Model | MSE | RMSE |
---|---|---|

PSSM | 0.000574969 | 0.023978510 |

BPSSM | 0.000394221 | 0.019855010 |

Next, estimation of the effectiveness of the real and hybrid models is seen in the results of the MSE and RMSE and the good performance of the model is based on the theory of effectiveness estimation model, as discussed in the previous section. Therefore, the results of this error can be referred to

Based on the results of

Based on such a significant error reduction in

strap approach in real base model of control charts fixing the estimation of real model and provide a more accurate estimation for the model. This small error values also indicate that the hybrid model is more effective and gives good performance compared to the real model, PSSM.

In this study, a PSSM model was hybrid with bootstrap method using an alternative algorithm. Using an alternative algorithm, the hybrid process was involved the construction of a standard error of PSSM confidence interval and proposed a new hybrid model of BPSSM. The data set Malaysian population and Family survey 1994 (MPFS-1994) was used. Participation and wage equation on the estimated coefficient for interval method, the significant effect, and consistency and for PSSM, as well as BPSSM for comparison purposes was discussed. The differences shown in these two models proved that the bootstrap approach fixed the interval estimation and gives a good performance for hybrid model. Estimation of the effectiveness of the real and hybrid models is seen of the MSE and RMSE. This small error value also indicates that the hybrid model is more effective.

A special gratitude for School of Informatics and Applied Mathematic (SIAM) and Research Management Centre (RMC), Universiti Malaysia Terengganu for supported this research paper.

Lola, M.S., Alwi, W.S.W. and Zainuddin, N.H. (2016) Sample Selection Model with Bootstrap (BPSSM) Approach: Case Study of the Malaysian Population and Family Survey. Open Journal of Statistics, 6, 741-748. http://dx.doi.org/10.4236/ojs.2016.65060