A comparison of neural networks and econometric discrete dependent variable models in prediction of occupational attainment.

ABSTRACT

A number of recent studies have compared the performance of neural networks to a variety of statistical techniques for the classification problems. In this paper, we compared the prediction of occupational attainment using a backpropagation neural network model and a multinomial logit model Both techniques use variables related to education, experience minority status, disability status, marital status, sex, and geographic region as inputs to perform the prediction. The neural network training and performance evaluation is also discussed in detail Although a comparison of the predictive ability of both models showed similar results, this paper presents neural networks as a more robust alternative for occupational attainment prediction application.

1. INTRODUCTION

During the last two decades, several research studies have focused on investigating the determinants of occupational attainment, as well as the race and sex differences in occupational attainment for the determination of occupational segregation (Broom, Jones, McDonell, and Williams, 1980; Brown, Moon, and Zoloth, 1980a; Gabriel, Williams, and Schmitz, 1990; Meng and Miller, 1995; Miller and Volker, 1985; Schmidt, and Strauss, 1975). As defined by Brown, Moon, and Zoloth (1980a)"an individual's occupational attainment is a function of employer's willingness to hire that person and of the individual's desire to work in specific occupations. Willingness of employers to hire an individual depends on human capital. The individual's desire for a particular occupation can be expressed by at least three of the arguments in a utility function: income, taste for the work involved and family size. The interaction of these supply and demand factors leads to the individual's employment in a particular occupation." The most common technique employed in occupational attainment prediction involves the estimation of parameters using statistical models with discrete dependent variables, namely multinomial logit, and ordered probit. Although these qualitative response techniques are widely used in the social sciences, it is well known that the predictive power of these models is rather poor (Greene, 1993).

A useful and robust approach for solving applied business and engineering problems that are distinguished by lack of availability or applicability of any mathematical model is neural networks, also known as artificial neural networks, connectionist models, parallel distributed processing models, and neuromorphic systems. Neural networks are developed as generalizations of mathematical models of human cognition, based on the following assumptions (Fausett, 1994): (1) information processing occurs at many simple elements called neurons or neural processing elements (NPEs), (2) signals are passed between neurons over connection links, (3) each connection link has an associated weight, which, in a typical neural net, multiplies the signal transmitted, (4) each neuron applies an activation function (usually nonlinear) to its net input (sum of weighted input signals) to determine its output signal. Since neural networks utilize an architecture and information processing manner similar to the brain, some of the networks show similar characteristics that are associated with the brain, for example, the ability to learn from examples, to generalize from situations, to classify examples into categories, and to self organize information. It has been determined that while under ideal statistical conditions the neural network can perform as well as a multiple regression model, under less than ideal conditions (e.g. when the model is not correctly specified, existence of missing data, outliers, heteroscedasticity, or autocorrelation), neural networks' performance is superior (Denton, 1995).

The utility of neural networks in practical applications for a wide variety of problems has been documented extensively in engineering, management science, and financial management literature (Sharda, 1994). This paper describes how we developed a neural network model to predict occupational attainment. We also compare the accuracy of the neural network prediction with that obtained by a multinomial logit model. Utilizing a neural network software called NeuralWorks Professional II Plus (NeuralWare, 1993), we designed, developed, and validated a neural network that makes use of data from the Current Population Survey (CPS).

Section 2 is a review of literature detailing several practical applications of neural networks in business and engineering. Section 3 describes the various studies conducted in the area of occupational attainment. We also discuss in this section the motivation to use a neural network for the occupational attainment prediction problem. Section 4 explains the issues involving the multinomial logit model, and provides the basic architecture, training, and performance evaluation of the neural network. Results are discussed in Section 5, followed by conclusions in Section 6.

2. LITERATURE REVIEW: NEURAL NETWORKS

A wide range of interesting applications of neural networks motivated and helped us in our research. Lu et al. (Lu, Chen, Kim, and Hwang, 1996) compared the effectiveness of neural networks and the multinomial logit model, and concluded that the ANNs perform better than logit regressions in franchising decision-making. Fletcher and Goss (1993) used back-propagation (BP) neural network model to predict the bankruptcy of a firm, and reported improvement in the prediction accuracy over the logit model. Salchenberger, Cinar and Lash (1992) used a neural network and the logit model to forecast bank failures using the bank's financial ratios as inputs. The neural network performed as well or better than the logit model. Wu, Fang, King, and Nuttle (1995) applied neural network technology for the decision surface modeling of apparel retail operations. Denton (1995) compared neural networks to linear regression forecasting models and used the mean square error of their forecasts as a measurement of their relative performance. The analysis was performed with, (1) an ordinary linear regression, (2) in the presence of an outlier, (3) in the presence of multicollinearity, and (4) with a misrepresentation of the model. Their results show that there was no significant difference in the performances in the first case, but the neural network performed better than the regression model in the last three cases. Kuo and Reitsch (1995) have compared the forecasting performance of neural networks and several conventional forecasting models. Neural networks showed a superior performance in almost all cases.

Numerous successful attempts have been made to use neural networks for managerial decision making. Hansen, McDonald, and Stice (1992) applied neural networks in two audit problems. In the first audit problem, the authors predicted the audit opinion rendered for specific firms from financial ratios and other predictors. The second audit problem investigated the neural network's ability to predict the likelihood of litigation presented to an auditor by a specific client. Tam and Kiang (1992) discussed a BP neural network application in predicting future bank bankruptcy based on financial ratios. Dutta and Shekhar (1988) applied neural networks to a generalization problem of predicting the corporate bond ratings. They used a BP network with one hidden layer and simultaneous weight adjustments to learn the weights. The authors reported that that the neural network resulted in a successful prediction rate of 88.3% compared to a success rate of 64.7% for the linear multivariate model. Surkan and Singleton (1990) later suggested that networks trained with two hidden layers outperform a network with only one hidden layer containing a comparable number of neurons. Successful application of various neural network training algorithms in forecasting of potable water demand is reported by Thind (1994). Chiang, Urban, and Baldridge (1996) discussed a BP neural network approach to mutual fund net asset value forecasting.

Hu, Zhang, and Haiyang (2004) found that the ANN performed better than logistic regression in the modeling of foreign equities. Collins, Ghosh, and Scofield. (1988) have built a neural network to make mortgage underwriting judgments. Their application made use of a Multiple Neural Network Learning System (MNNLS) to replicate the decisions made by mortgage insurance underwriters. The MNNLS used an array of coupled Restricted Coulomb Energy (RCE) sub-networks. Using a variant of the nonlinear least square method, neural networks have also been used to search and decode nonlinear regularities in asset price movements (White, 1988). Kimoto, Asakawa, Yoda, and Takeoda (1990) applied modular neural networks to develop a buying and selling timing prediction system for stocks on the Tokyo Stock Exchange. They developed a high-speed learning method called supplementary learning that is actually based on error backpropagation. Odom and Sharda (1990) developed a neural network model using backpropagation for prediction of bankruptcy. They claimed that their model performed better than discriminant analysis which is generally used for this class of problems. A study by Kattan (1993) applied the BP neural network to predict the self-reported usage of a popular graphics software package.

3. LITERATURE REVIEW AND BACKGROUND: OCCUPATIONAL ATTAINMENT

Gabriel, Williams, and Schmitz (1990) used the multinomial logit model to make comparisons of occupational attainment among ethnic and gender groups. They obtained logit coefficients for each variable and used the coefficients for white males in minority groups to make inferences about occupational segregation, and found the logit model appropriate for predicting the occupational attainment. Schmidt and Strauss (1975) analyzed occupational attainment using the multinomial logit model. Meng and Miller (1995) applied the multinomial logit and ordered probit models to the estimation of occupational attainment based on education, job experience, firm tenure and three regional dummies. Based on this study, the authors reported that the intricate linkages between independent variables and occupational outcomes are better captured by the multinomial logit model as it estimates a larger set of parameters--one set for each occupation. Miller and Volker (1985) compared the performance of the multinomial logit and ordered probit models to determine occupational attainment and mobility in a random sample of Australian males. They found that, while the ordered probit model is more consistent with previous notions of job hierarchies and requires less computational time, the multinomial logit model performed better in the prediction of the occupational distributions. Brown et al. (1980a) modeled occupational attainment with the multinomial logit model using data from the National Longitudinal Survey. The model allowed them to simulate the occupational distribution of women that would exist if they were treated as men. Brown et al. (1980b) used the multinomial logit model to estimate segregation by sex in occupational attainment, and tested the robustness of the model with multiple discriminant analysis, and reported that both approaches provides similar results.

As discussed above, despite the widespread use of statistical models in the domain of occupational attainment, several limitations of these models exist. The estimation of models with discrete dependent variables is a complicated statistical problem. Because of heteroskedasticity in the error terms and the need to keep probabilities within the 0-1 range, the ordinary least squares model is not appropriate, forcing modelers to use maximum likelihood estimation. Although more appropriate than ordinary regression models, maximum likelihood estimations have the following drawbacks:

(a) Independence of irrelevant alternatives property

According to Kennedy (1996), a limitation of the multinomial logit model is that when several alternatives with very similar utility are introduced in the model, the probabilities of choosing the other alternatives will be affected. This makes the model inappropriate when several alternatives are close substitutes of each other.

(b) Assumptions about error terms

In statistical models we must make some assumptions on the error terms. In the multinomial logit model, we assume that the error terms present a logistic distribution. In the ordered probit model, we assume that the error terms are normally distributed. We do not need to make any assumptions about error terms in the neural network.

(c) Determination of the functional form

In multinomial logit models some restrictive assumptions must be made about the functional form of the relationship between the explanatory variables and the probabilities of each of the alternative outputs. A Box-Cox transformation can be applied to the probit and logit models to determine if the regressors should be included in natural form or in logarithmic form. Greene, Greene, and Seaks (1995) described the effect of the Box-Cox transformation in a probit model. A neural network has the capability to select the parameters that best approximate the underlying functional form of the data. Therefore, a neural network can simulate the appropriate functional form with the data provided, resulting in the best forecast of the occupational attainment.

4. MODELS

4.1 Multinomial logit model

If we assume that individual workers select their occupations according to a number of individual specific variables (e.g., personal characteristics, taste, economic status, regional labor market), we can define the goodness of their occupation [Y.sub.i] as:

[Y.sub.i] = a + [X'.sub.i][beta] + [epsilon] [epsilon] ~ N(0,1)

where [X.sub.i] is a vector of personal characteristics of the individual i and [beta] is the corresponding vector of coefficients. [Y.sub.i] is not observed. Instead, we can observe whether or not the individual adopted a particular occupation. If we assume that the probability that an individual i is employed in the jth occupation follows the cumulative distribution of a logistic random variable, then it can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [P.sub.ih] is the conditional probability that individual i adopts occupation h', [[beta].sub.h] is the vector of coefficients that relate the characteristics X to the log probability ratio. This model can be estimated by maximizing the likelihood function of a sample of T independent observations on individual choices [Y.sub.i]. The likelihood function can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [LAMBDA](.) is the logistic cumulative distribution function.

4.2 Neural Network Model

This section describes the neural network model constructed to predict the occupational attainment. The inputs to the network are 10 decision variables (see Table I) that influence the decision regarding the occupational attainment. The output of the network is the classification of the occupation in one of the 9 categories (see Table III) that is best suited for the individual worker. The neural network model development starts with selecting appropriate neural network architecture. Different neural architectures are employed for different problems. We initially considered several neural network architectures such as Standard Backpropagation (BP), Fast Backpropagation, Quickprop, Cascade-Correlation, and Learning Vector Quantization (LVQ). We decided to use Standard BP network, as it is practical, easy to implement, and the most popular choice among management scientists for various research and application efforts (Sharda, 1994). The BP neural network was implemented using NeuralWorks Professional II/PLUS software (Neuralware, 1993).

4.3 Data description

The data needed to train the BP neural network as well as the multinomial logit model was obtained from the 1996 edition of the Current Population Survey (CPS). Each data set consisted of 10 input values corresponding to each decision variable and a specific output corresponding to one of the nine actual occupational categories. These 10 variables are specified and described in Table I and a statistical summary of is provided in Table I1. The same set of decision variables was used in the multinomial logit model and the BP neural network. A total of 4,982 cases were available to train the neural network and a hold-out sample of 1,452 cases was used for testing the network performance. For achieving best results, the training data set was selected in such a way that (1) the data was evenly divided among the various outcomes, and (2) it reasonably represented the entire universe.

Since the purpose of the models tested was to predict occupation of workers, observations within the age group 16-65 working for the private sector, federal, state or local government were selected. Both self-employed and Armed Forces related occupations were excluded from the sample. The categorical variables (minority, disability, sex, geographic region and marital status) were recoded in multiple dummy fields, mapped to 1 or 0. The education variable (highest grade achieved) was remapped to a continuous variable reflecting the years of education completed.

All subjects not belonging to the white race, Mexican American, Chicano, Mexican, Puerto Rican, Cuban, Central or South American, or other Spanish descent, were considered to be minorities. Experience was computed as age minus years of education minus five. Respondents who declared to "have a health problem or a disability which prevents work or which limits the kind or amount of work" were considered disabled. Marital status was coded to "married" if so declared and "single" if never married, widowed, divorced, or separated.

Table III describes the classification of occupations used in the models. The nine possible outputs were recoded to dichotomous variables containing the value 1 if the individual had the occupation represented by that variable or 0 if the individual had a different occupation. Therefore, the mean represents the proportion of observations corresponding to each occupation.

4.3 Neural Network Architecture and Training

Relevant design parameters for BP network include the number of hidden layers, the number of nodes in the hidden layer, the number of training cycles, epoch size (number of times examples are presented before the weights are updated), initial and final learning rate and momentum terms. These are important decisions in modeling the network and can significantly affect the performance of the network. There exists almost no sound theoretical basis for selecting model parameters. Therefore, modelers must rely on heuristic guidelines that seem to provide good performance (Jain and Nag, 1995). For example, literature suggests that while at least one hidden layer is mandatory, there is no evidence of any advantage by adding multiple hidden layers (Dutta and Shekhar, 1988; Salchenberger et al., 1992). In our application we experimented with various combinations of the design parameters. The final basic architecture of the neural network model is shown in Figure 1. For simplicity, some of the links and processing elements have been omitted in Figure 1.

[FIGURE 1 OMITTED]

The system is a feedforward backpropagation neural network with 10 input nodes or Neural Processing Elements (NPEs), one hidden layer with 15 NPEs, and an output layer with 9 NPEs, each corresponding to one of the decision categories. The network is presented a training file containing records corresponding to 4,982 observations from the training data set. The 4,982 observations of the training set were presented to the network randomly, and the network was trained for 50,000 cycles, when the error stabilizes and additional training did not yield any improvement in performance (refer to Gupta, 1995; Wasserman, 1989; and Wu et al., 1995 for background, details, and mathematical equations for the BP neural network).

A hyperbolic tangent function was chosen as transfer function. This choice was straightforward, since the hyperbolic tangent is the most popular transfer function for classification problems. An initial set of random weights was generated and gaussian noise was assumed at the input stage. A weighted sum of the inputs was computed for each processing element of the next layer, and the resulting values were again transformed by the transfer function and weighted until the data reached the output layer. After the resulting values have been compared to the desired ones and the weight corrections have been calculated, the connection weights are updated. The process of updating network weights constitutes the basis of the learning process.

Before a connection weight is adjusted, the new increment is multiplied by a learning rate or learning coefficient. The adjustment of the learning rates is a critical step in network training. The learning rates were selected through trial and error, starting with a relatively high rate of 0.2. The initial learning rate was reduced until the network was able to learn without saturated cells. A cell saturates when the value received by a processing element is beyond the transfer function range. When a cell is saturated, it always yields the same output and becomes unable to learn from additional training. As the learning process progressed, the learning rates were reduced from 0.2 to 0.15 after 10,000 cycles and to 0.10 from 20,000 to 50,000 cycles. This allowed the network to continue learning and slowly achieving stability, minimizing its mean squared error. A higher learning coefficient would have allowed for faster learning, but the fluctuations would have made it more difficult to reach convergence. To minimize the effect of oscillations in the weight adjustments, a momentum factor was included in the calculation of the weight adjustments. The momentum factor is a proportion of the previous weight adjustment that is added to each weight adjustment. A momentum factor increases stability in the learning process and allows the network to advance faster toward convergence. A momentum rate of 0.5 proved most effective to avoid oscillations at the beginning, and it was also reduced as training progressed.

5. RESULTS

The multinomial logit model yields a coefficient for each variable and each occupation. These coefficients express how the independent variable affects the natural logarithm of the likelihood that an individual adopts a particular occupation over the executive/managerial (base) occupation. Logit coefficients are shown in Table IV.

The [chi square] statistic of 3561.87 is significant at [alpha]=0.01 level, meaning that the multinomial logit model is a good predictor of occupational attainment. Since this test of goodness of fit cannot be performed in the neural network, in order to compare the forecasting performance of both models we chose two procedures: (1) percentage of cases correctly forecasted by the model, and (2) mean squared error. The percentage of cases correctly forecasted is a good measure because the ultimate objective of the models is to accurately forecast the occupational attainment. It was calculated by counting the cases for which the occupation with the highest calculated probability was the actual occupation adopted. In the neural network, the probability matrix is extracted as an output file from the software. In the multinomial Iogit model, the probability matrix is calculated by applying the coefficients estimated with the training data set to the test data set.

The mean square error (MSE) is another good measure of performance because both models minimize MSE and therefore, it is a standard measurement for performance of forecasting techniques. The MSE was calculated with the formula:

MSE = [H.summation over h=1][T.summation over i=1][([A.sub.ih] - [F.sub.ih]).sup.2]/T * H

where [A.sub.ih] is the actual value of the occupation h dummy variable for individual i (1 or 0) and [F.sub.ih] is the forecasted probability that individual i adopts occupation h. The forecast errors are squared to avoid offsetting effects of errors with different signs. The results of both tests are shown in Table V.

The column labeled SQR(MSE) shows the square root of the mean squared error, and it is useful because it is expressed in the same units as the actual observation (probability). This means that the average deviation between forecasted and actual probabilities is very close to 30% in both cases. The percentage of cases correctly forecasted is also very close to 30% in both cases.

6. CONCLUSIONS

The review of the literature shows several studies of occupational attainment using statistical models, as well as applications of neural networks to other forecasting problems, such as linear regression. This study is a first attempt to systematically apply an ANN to the problem of forecasting occupational attainment. We found that the neural network is an alternative to the discrete dependent variable models. Since the neural network is capable of emulating virtually any functional form, it can perform better in cases where the errors are not normally distributed, or where there are several occupations with very similar utility.

Training a neural network can be, however, a very expensive procedure, and it is difficult, in general, to know how good the parameters generated in the training are until the network has been tested. Because of the lack of theoretical foundations, training a neural network requires a long trial and error process, experimenting different combinations of learning rates, momentum terms, transfer functions, and network architectures. The determination of the learning rates and other network parameters is fundamental to train the network successfully.

As previously reported, genetic algorithms can reduce the arbitrary nature of the determination of the training parameters, improving the training process and, therefore, the forecasting performance of the network. The results of this study can be extended to many other classification problems, especially to those with discrete dependent variables.

The results of the study show that, although the training of the network was less than optimal, there was no significant difference in the number of accurate forecasts between the neural network and the multinomial logit model. Likewise, there was no significant difference in mean square error between both models. A network trained by specialized and experienced neural network engineers can yield better results than the statistical model, allowing more accurate forecasts and fast re-estimations with different populations, from different geographic areas or different sampling criteria. However, a limitation of the ANN is that it does not allow for the statistical analysis often performed with multinomial logit estimates. Standard errors are not available in neural networks, making it impossible to perform confidence intervals, tests for significance for variables, tests for differences between data sets, etc.

Most occupational attainment models are used to compare among ethnic groups, ages, male and female, or other criteria. The usual approach is to estimate the statistical model for a group and then use the coefficients in another group to yield the expected occupational attainment. The difference between the predicted and the real attainment can be attributed to occupational segregation, geography or other factors. The use of neural networks easily allows training the network with a group, e.g., males, and testing with a different group, e.g., females, to make inferences about occupational segregation. Once the training algorithm is established, the neural network is in general easier to use than the standard statistical software packages.

The promising results of this study suggest that the performance of the neural network can be greatly improved with advanced training techniques such as genetic algorithms. This good performance can be generalized to other discrete dependent variable forecasting problems. In terms of future work in this area, it might be worthwhile to consider how other types of neural network architectures might be used in the application domain. It would also be interesting to optimize the neural network using a genetic algorithm and to test the use of the neural network and the multinomial Iogit model in a combined approach for predictive reinforcement.

TABLE I. DESCRIPTION OF NEURAL NETWORK INPUT VARIABLES

Neural Network         Description
Input Variables

[X.sub.1] (EDU)        Educational attainment, transformed to
                       equivalent years
[X.sub.2] (MINO)       Minority Status (not white, or Mexican, Chicano,
                       Puerto Rican, Cuban, Central or South American,
                       other Spanish: 1=minority, 0=not a minority.
[X.sub.3] (EXP)        Experience (Age minus EDU minus 5).
[X.sub.4] (DISA)       Respondent has a health problem or a disability
                       that prevents work or limits the kind or amount
                       of work: 1=disabled, 0=not disabled.
[X.sub.5] (SEX)        Self declared sex: 1=female, 0=male.
[X.sub.6] (NEAST)      Geographic region: 1=northeast, 0 otherwise.
[X.sub.7] (MIDW)       Geographic region: 1=Midwest, 0 otherwise.
[X.sub.8] (SOUTH)      Geographic region: 1=South, 0 otherwise.
[X.sub.9] (WEST)       Geographic region: 1=West, 0 otherwise.
[X.sub.10] (MARITL)    Marital status: 1=married, 0=single.

TABLE II. DESCRIPTIVE STATISTICS: INDEPENDENT VARIABLES

Variable    Mean     Std Deviation    Minimum    Maximum    N

DISA         0.02     0.15             0          1         4982
NEAST        0.20     0.40             0          1         4982
MIDW         0.24     0.43             0          1         4982
WEST         0.26     0.44             0          1         4982
MINO         0.28     0.45             0          1         4982
SOUTH        0.30     0.46             0          1         4982
SEX          0.45     0.50             0          1         4982
MARITL       0.60     0.49             0          1         4982
EDU         12.99     2.99             0         21         4982
EXP         19.38    11.76            -1         58         4982

TABLE III. OUTPUT VARIABLES (OCCUPATIONAL CLASSIFICATIONS)

Occupation                                        Mean    Std. Dev.

O[C.sub.1] (Executive, Admin, and Managerial)     0.11    0.31
O[C.sub.2] (Professional Specialty)               0.12    0.32
O[C.sub.3] (Technicians and Related Support)      0.11    0.32
O[C.sub.4] (Sales)                                0.11    0.31
O[C.sub.5] (Admin. Support Occupations, Incl.
  Clerical)                                       0.12    0.33
O[C.sub.6] (Services)                             0.11    0.32
O[C.sub.7] (Precision Prod., Craft and Repair)    0.10    0.31
O[C.sub.8] (Machine Operator, Assembler,
  Inspector)                                      0.10    0.30
O[C.sub.9] (Farming, Forestry and Fishing)        0.11    0.32

Occupation                                        Min    Max    Code

O[C.sub.1] (Executive, Admin, and Managerial)     0      1      0
O[C.sub.2] (Professional Specialty)               0      1      1
O[C.sub.3] (Technicians and Related Support)      0      1      2
O[C.sub.4] (Sales)                                0      1      3
O[C.sub.5] (Admin. Support Occupations, Incl.
  Clerical)                                       0      1      4
O[C.sub.6] (Services)                             0      1      5
O[C.sub.7] (Precision Prod., Craft and Repair)    0      1      6
O[C.sub.8] (Machine Operator, Assembler,
  Inspector)                                      0      1      7
O[C.sub.9] (Farming, Forestry and Fishing)        0      1      8

TABLE IV. MULTINOMIAL LOGIT ESTIMATES OF OCCUPATIONAL ATTAINMENT
(STANDARD ERRORS IN PARENTHESES)

Variable     ln(P1/P0)    ln(P2/P0)      ln(P3/P0)      ln(P4/P0)

Constant      -3.996        2.365          5.811          5.067
              (0.499)      (0.479)        (0.502)        (0.506)
EDUC           0.267       -0.126         -0.351         -0.379
              (0.028)      (0.0286)       (0.315E-01)    (0.0315E-01)
MINORI         0.271        0.452          0.319          0.636
              (0.169)      (0.162)        (0.166)        (0.159)
EXPER         -0.018       -0.318E-02     -4.12E-01      -0.262E-01
              (0.006)      (0.589E-02)    (0.604E-02)    (0.579E-02)
DISA           0.600E-01    0.389          0.663          0.33419
              (0.521)      (0.474)        (0.46019)      (0.475)
SEX            0.622        0.202         -0.164          1.022
              (0.128)      (0.125)        (0.127)        (0.134)
MIDW           0.488E-02    0.198          0.207          0.118
              (0.181)      (0.181)        (0.190)        (0.187)
SOUTH         -0.181       -0.226          0.269E-01      0.601E-01
              (0.172)      (0.174)        (0.178)        (0.173)
WEST          -0.699E-02    0.937E-02      0.106         -0.376E-02
              (0.183)      (0.181)        (0.189)        (0.187)
MARITL        -0.315E-02   -0.139         -0.311         -0.400E-01
              (0.140)      (0.136)        (0.139)        (0.136)

Variable     ln(P5/P0)     ln(P6/P0)     ln(P7/P0)     ln(P8/P0)

Constant       9.375         9.662        10.815        12.355
               0.518         0.530         0.524         0.535
EDUC          -0.661        -0.659        -0.758        -0.901
               0.335E-01     0.342E-01     0.338E-01     3.42E-01
MINORI         1.037         0.243         0.859         0.378
               0.161         0.178         0.170         0.177
EXPER         -0.297E-01    -0.109E-01    -0.122E-01    -0.368E-01
               0.597E-02     0.624E-02     0.616E-02     0.642E-02
DISA           0.560         0.663         0.845        -0.135
               0.476         0.475         0.465         0.554
SEX            0.999E-01    -2.642        -1.507        -1.854
               0.132         0.186         0.147         0.158
MIDW           0.280         0.198         0.408         1.026
               0.195         0.200         0.199         0.235
SOUTH         -0.184        -0.185        -0.271         0.578
               0.184         0.189         0.191         0.225
WEST           0.252E-01    -0.828E-01    -0.284         1.165
               0.194         0.201         0.205         0.229
MARITL        -0.513         0.352E-01    -0.451        -0.447
               0.141         0.154         0.149         0.153

Chi-squared                  3561.87

TABLE V. PERCENTAGES ACCURATELY FORECASTED AND MEAN SQUARED ERRORS

                    % correct forecasts   MSE        SQR(MSE)

Multinomial Logit   31.25%                0.089792   0.299653
Neural Network      30.04%                0.090417   0.300694

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Author Profile

Dr. Jose V. Gavidia earned his Ph.D. at the University of Texas--Pan American in 2001. Currently, he teaches global management of technology and international business at the College of Charleston in Charleston, South Carolina.

Dr. Vipul Gupta earned his Ph.D. from the University of Houston in 1995. He teaches decision support systems at Saint Joseph's University, in Philadelphia, Pennsylvania.