The determinants of health status in Sub-Saharan Africa (SSA).

Fayissa, Bichaka ; Gutema, Paulos

I. Introduction

The health capital of nations serves both as an important means and a basic end in efforts aimed at improving human welfare. Consequently, development specialists and policy formulators have focused their attention on a viable and efficient mechanism for improving the health status of society, (Schultz, 2004). Over the years, such efforts have produced impressive results in many regions of the world.

Although some African development specialists and policy makers have also undertaken important measures for improving the quality of life for their citizens, the health status of SSA is still considerably low and exists below that of most parts of the world. Low life expectancy at birth, high infant and maternal mortality rates, malaria and tuberculosis afflictions, and the HIV/AIDS pandemic are some of the unique images of the health status of the African content. The World Bank (2002) data set shows that a new infant born in SSA has only 42 expected life-years to live. If the same infant were born in high-income countries of the world during the same period, however, it would have expected 70 years to live. The high-income groups aside, the infant would have 46 expected years had it been from other low-income countries. Not only is the level of expected life disappointing, but also its dynamics is equally alarming. In low and middle-income countries, the average life expectancy at birth has improved from about 13 to 15 life-years from the 1960s to the 1990s, respectively; in SSA, however, it has only changed by about 7 life-years during the same period. This change is also far below the world average of about 11 years.

A similar phenomenon can also be observed from other indicators. In the 1960s, the average number of infants dying before reaching one year of age per 1,000 live births was estimated to be 154, while it was only about 27 in high-income countries. From the 1960s to 1990s, the high income and middle income countries have reduced this figure by about 77 and 65 percent, respectively, while SSA only reduced infant mortality by only 38 percent which is also below the world's average of almost 50 percent. The intended progress might have been hampered by different socioeconomic, political, and environmental factors. This study, nonetheless, perceives that the health status of SSA can be substantially improved despite the prevailing distressing health records.

This paper estimates the determinants of health status for the region based on the Grossman (1972) theoretical model. The model treats economic, social, and environmental factors as inputs of the production system. The major advantages of identifying the determinants are that estimates of the over-all effect of medical care utilization on the health status of the population can be obtained (Thornton, 2002). Policy makers and practitioners can use the above information in their search for cost effective mechanisms for providing health services and the reallocation of health resources in such a manner that the gains from health spending could be optimized.

The remaining sections of the paper are organized as follows. The next section outlines the framework, hypotheses, and data. Section three describes the empirical method derived from the Grossman (1972) theoretical model. The econometric results and interpretations are given in section four. The last section summarizes and draws conclusions based on the results.

II. The Framework, Hypotheses, and Data

To determine responsiveness of the health status of SSA to the economic, social, and environmental factors, we specify a double log-linear Cobb-Douglas production function based on the Grossman (1972) model as:

Lnh = ln[OMEGA] + [SIGMA][[alpha].sub.i] (ln[y.sub.i]) + [SIGMA][[beta].sub.j] (ln[s.sub.j]) + [SIGMA][[gamma].sub.k](ln[v.sub.k]), (1)

Where Lnh is the natural log of individual's health status measured by life expectancy at birth, [y.sub.i] is a vector of per capita economic variables, [s.sub.j] is a vector of per capita social variables, [v.sub.k] is a vector of per capita environmental factors, and [y.sub.i], [s.sub.j], and [v.sub.k] are expressed in natural log (where i = 1, 2; j = 1, 2; and k = 1, 2). [OMEGA] is an estimate of the initial health stock of the region, [[alpha].sub.i], [[beta].sub.j], [[gamma].sub.k] are elasticities.

Estimation of the health status model given by equation (1) requires data on health status as well as on socioeconomic and environmental variables. However, measuring health status directly is somewhat difficult and, for aggregate studies, some researchers (1) suggest life expectancy at birth and mortality rate for infants and children as indicators of the health output. In our study, we employ life expectancy at birth as the dependant variable. It indicates the number of years a newborn infant would live if prevailing patterns of mortality at the time of its birth were to remain the same throughout its life. The explanatory variables and their expected coefficients are described below.

On the right hand side of the function, as indicated in equation (1), the health expenditure per capita to GDP ratio, per capita food availability index, illiteracy rate, adult alcohol consumption per capita, urbanization rate, and C[O.sub.2] emissions are used.

The first representative of an economic factor is the health expenditure to GDP ratio. It constitutes both public and private health expenditure and covers the provision of health services, family planning activities, and emergency aid designed for health. Generally, it is considered as a measure of availability of the health production facilities to a given society. Indeed, some empirical studies use stock of facilities like hospital beds per 1000 people, physician per 1000 people etc. instead of expenditures on health. However, Hadley (1982) states that using medical care expenditures as a measure of the provision of the facilities is more desirable than using a stock of providers because variation in expenditures across geographic areas better reflects the differences in quality and quantity of such services.

The expected relationship between health expenditure and life expectancy is, however, somewhat ambiguous. On the one hand, higher levels of per capita health expenditures may help to increase the provision of health facilities that in turn may improve life expectancy. However, this is only true if the increment in expenditure has no adverse effect on the individual's health status. An adverse effect may arise if the expenditures are financed by revenues collected from user fees, or taxes, and if the fees and tax payments are made at the expense of the individual preventive health cares such as food, clothing, and housing which may occur in subsistence societies. In this situation, unless the marginal effect of an increase in the facilities is so high to compensate the forgone benefits from preventive health care, it is normal to obtain a negative coefficient for the variable. Moreover, countries with poor initial health levels may allocate more resources to medical care than other countries. Therefore, the sign of the coefficient cannot be predicted a priori.

The second representative of an economic factor is the food availability index. Given that the problem of nutrition in poor economies is more of scarcity and not of over consumption, we expect a positive coefficient for food availability. Food production index is used as a measure of food availability. It covers food crops that are considered edible and contain nutrients.

Social factors are represented by variables of education and adult alcohol consumption per capita. In using education as a social factor, we recognize the argument of some writers that education is not an input by itself, as Wolfe and Behrman (1984) have argued; it is considered as a catalyst which increases the marginal efficiency of other inputs. Adult illiteracy rate is taken as a proxy for education. It is the percentage of people above 15 years who cannot read, write, and understand a simple statement on their daily activities. Grossman (1972) and other studies have argued that education influences many decisions that impact the quality of life (such as a choice of job, ability to select a healthy diet, and avoid unhealthy habits, efficient use of medical care). Grossman (2004), Fuchs (2004), Berger and Leigh (1989), Rosen and Taubau (1982) and others have provided empirical evidence in support of this argument. We, therefore, hypothesize that the more literate society is the healthier its people will be, and hence we expect a negative coefficient of adult illiteracy rate.

The second social factor is life style; among others, it is represented by adult alcohol consumption per capita. It is measured by the amount of pure ethanol in liters of total alcohol consumed per adult (15 years and older) in a country during a calendar year, as calculated from official statistics on production, sales, imports, and exports, taking into account stocks whenever possible. The source of the data is the World Health Organization's (WHO) alcohol consumption database. According to Fuchs (2004), Chick et al. (1986), and Choquent and Ledoux (1989), alcohol consumption is recognized as an important risk factor for most chronic illnesses such as diseases of the digestive system, cancer, cirrhosis etc. as well as for accidents and violent deaths. Thus, we expect a negative coefficient for this variable.

We consider urbanization rate or the share of the total population living in areas defined as urban in each country and carbon dioxide emissions per capita to capture the effect of environmental factors on life expectancy. Thornton (2002) states that urbanization is a proxy for a collection of potential negative and positive health related factors. On the positive side, he notes that it avails access to medical care and health information. In a slightly different context, Rosenzweig and Schultz (1983) argue that urban public health institutes are substitutes for health care knowledge and management capacity that an educated individual brings to his family. Moreover, it is argued that in urban areas clinics are more cost-effective. On the negative side, Thornton (2002) indicates that urbanization is associated with pollution and congestion that have adverse effects on health. Considering both sides of the issue, one can assert that the marginal effect of urbanization depends on the net effect of the two contradictory factors. Hence, the sign of urbanization rate cannot be predetermined.

Lastly, carbon dioxide emission per capita is another variable we considered as an environmental factor. Emissions from the burning of fossil fuels and the manufacture of cement are used as a proxy for the environmental factors. They include contributions to the carbon dioxide produced during consumption of solid, liquid, and gas fuels and gas flaring. Since emissions cause air pollution that results in health hazards, we expect a negative coefficient for the variable. Data for the above variables were taken from World Bank (2002), unless otherwise stated. The study is confined to the period of 1990-2000 for a cross-section of 33 Sub-Sahara African countries (2) due to data incompleteness.

III. The Empirical Estimation Method

For estimation of the parameters under consideration, a panel data analytic approach is employed. In forming the panel, time series data of each country were averaged over two years and a total of five periods were formed for each country; an econometric model is specified for equation (1) in its general form. In order to provide an empirical exposition of the model, the specification is given as follows:

h *(g,t) = [delta](g) + [GAMMA](t) + X *(g,t). [PHI] + [PSI](g,t) (2)

Where h *(g,t) is natural logarithm of life expectancy in country g at year t, and X *(g,t) is vector of explanatory variables ([y.sub.1],[y.sub.2],[s.sub.1],[s.sub.2],[v.sub.1],[v.sub.2]) for g = 1,2, ... m (number of countries), t = 1,2 ... T (number of years), [PHI] is vertical vector of parameters ([[alpha].sub.1], [[alpha].sub.2] [[beta].sub.1], [[beta].sub.2], [[gamma].sub.1],.[[gamma].sub.2]); [PSI](g,t) is a classical stochastic disturbance term with E[[PSI](g,t)] = 0 and var[[PSI](g,t)] = [[delta].sup.2.sub.[epsilon]], [delta](g) and [GAMMA](t) are country and time specific effects, respectively. Instead of an a priori decision on the behavior of [delta](g) and [GAMMA](t), five different types of the most common assumptions are separately imposed on the model and the one that gives a superior estimate is selected based on statistical rules.

The first assumption is that all of the country specific effects are constant and equal across the countries; and the time specific effects are not present, i.e. [delta](g) = [lambda] and [GAMMA](t) = 0, for some constant [lambda]. Under this assumption, model (2) is estimated by ordinary least squares (OLS) method and the results are reported as the Restricted OLS Model.

The second and third alternative specifications assume absence of time specific effects, which is basic attribute of One-Way specification. The second estimation technique assumes that country specific effects are constant like the first one, but not necessarily equal, i.e. [delta](g) = [lambda](g) and [GAMMA](t) = 0, for some constants [lambda](g). Under this case, equation (2) is estimated by a partitioned OLS. The estimates are reported under One-Way Fixed-Effects Model.

The third assumption type tested in the analysis is that country specific effects are not constants, but rather are disturbances; and the time specific effects are not present here again i.e., [delta](g) = [lambda] + w(g) and [GAMMA](t) = 0, where E[(w(g)] = 0, and var[w(g)] = [[sigma].sup.2.sub.w]. and cov[[PSI](g,t),w(g)] = 0. Unlike the previous cases, equation (2) is estimated by a feasible a 2-step Generalized Least Squares (GLS). The results of this estimation are given under the One-Way Random-Effects Model.

The fourth and the fifth assumptions differ from the first three in their time specific effects components (a basic feature of Two-Way specification). The fourth assumption requires that both country and time specific effects are constants, but are not necessarily equal; and there is an overall constant, i.e., [delta][delta](g) + [GAMMA](t) = [lambda]' + [lambda]'(g) + [gamma](t), where [lambda]', [lambda]',(g) and [lambda](t) are some constants. The results of this estimation are reported under the Two-Way Fixed-Effects Model.

The last assumption is that both the country and time specific effects are disturbances with [delta](g) + [GAMMA](t) = [lambda]" + w' (g) + [tau](t), where [lambda]" is some constant, and w' (g), [tau](t) are disturbances. In this case, just as in assumption three above, eq7uation (2) is estimated by 2-step GLS model. The results of the estimation are reported under Two-Way Random-Effects Model. After estimating the parameters based on the above five assumptions, the superior specification is selected on the basis of a suitable statistical test.

IV. Econometric Results and Interpretations

Equation (2) is estimated using the data and method described above. The empirical results are given in tables 1 and 2. To choose from One-Way and Two-Way specifications, we use the F-statistics. The statistics tests the significance of any time specific effect that is not included in One-Way regression specification. The test result given at the bottom of table 2, suggests that Two-Way error component regression model is superior to the One-Way, (p = 0.0016).

The next step will be selecting an appropriate estimator from the three given estimators. To start with, the poolability or appropriateness of the constrained model, or OLS estimator is tested. In other words, this test helps us to examine the hypothesis of absence of country specific effects. With N = 33 T = 5 and k = 7, a Lagrange-multiplier test for significance of country specific effects yields a [chi square]-value of 155.86, p = 0.0000. This is distributed as [[chi square].sub.(2)] under the null hypothesis of zero country specific effects. The null is soundly rejected, and the within or the random effect model is preferred to OLS estimator. That is, the test does not support the poolability of the data set, suggesting that there are strong country-specific effects.

Next, for the choice between random-effects (GLS estimator) and the within effect estimator a Hausman-test is performed. The basic assumption associated with random-effect is that there is no correlation between the regressor and country specific effects. If such assumption is violated, then the GLS estimator will be biased and inconsistent. The test shows a [chi square] value equal to 3.88, (p = 0.6935). This is distributed as [[chi square].sub.(2) under the null hypothesis of absence of the indicated correlation. The null hypothesis of no correlation between the country specific effect and the regressor is strongly accepted. This implies that the GLS estimator in this case is unbiased and consistent. As a result, the preferable estimates of the parameters in equation (2) can be given by the two-way random-effects models.

Accordingly, the coefficient of the per capita food availability is found to be positive and statistically significant, suggesting that the variable favorably influences the health status of the region in the periods of good economic performance. The results suggest that a one per cent increment in food availability per capita can generate a 0.13 percentage improvement in health status. The estimate further suggests that if the region's economies are able to repeat their food production performance during the second half of 1980s (about 0.53% growth on food production per capita), then it is possible to improve life expectancy by about 2.5 life-years, other things remaining unchanged. In short, the parameter estimate of this variable suggests that successful policies directed towards increasing food availability of the region can have an impressive impact on the health status of the region.

On the other hand, the table reports a negative and statistically significant coefficient for the health expenditures variable. Such a relationship could occur if the society is close to subsistence, i.e. has meager, or no savings, and if the expenditures are financed through fees or taxes collected from the users. In this case, an increase in the expenditures will have a consumption reducing effect of life nurturing and sustaining goods such as food, clothing, housing etc, as it competes for the budget allocated for such types of amenities. If the marginal effect of the latter types of goods exceeds that of the former types (the health facilities to be provided by increased expenditures), then it is not surprising to get a negative coefficient for the health expenditures variable.

The analytical argument given in above suggests that the negative coefficient is due to the cost ineffective provision of health facilities, when seen from its opportunity cost perspective. In other words, the facilities could not restore the forgone health benefits that arise in the process of obtaining them. Moreover, the negative relationship between life expectancy and the per capita medical expenditures may be attributed to the fact that countries with poor initial health levels may allocate more resources to medical care than others. Thus, we argue that reversing the existing trend is one of the areas that deserves a special attention in efforts directed to the improvement of the health status of the region.

Table 2 also reports that the coefficient of the illiteracy ratio has a statistically strong impact on health status, (P = 0.0000), suggesting that a one percent reduction in the illiteracy ratio (which is an approximation of the 1990s educational performance of 1.17 percent) would lead to 0.004% increment in life expectancy. As previously discussed, this is possible as more education gives the people more awareness about their own health status and of what preventive measures would improve their own health.

Furthermore, the table indicates that alcohol consumption has a statistically strong negative impact on health status (p = 0.0308). Lastly, the table indicates that an increase in urbanization rate and a decrease in carbon dioxide emissions may contribute to the improvement of health status. This suggestion is, however, not supported by a statistical test of significance.

V. Summary and Conclusion

The study has investigated the determinants of health status in Sub-Sahara Africa in line with the Grossman (1972) theoretical model using socioeconomic and environmental factors as determinants of health status. The main data source for the study is the World Bank (2002) data set, with the exception of the alcohol consumption data which were drawn from the WHO's database. To overcome data limitation, we used pooled cross-section time series for 33 SSA countries covering the 1990-2000 periods.

The results obtained from two-way random-effect regression model suggest that an increase in food availability per capita and literacy rate and a decrease in alcohol consumption have a significant favorable effect on life expectancy. Health expenditure has shown a strong negative relationship with life expectancy, which possibly arises from the inefficient health service provision systems. Moreover, an increase in urbanization and a decrease in Carbon dioxide emissions per capita are found to improve life expectancy, though this argument cannot be supported based on the statistical significance of the tests.

In general, the results suggest that a health policy which mainly focuses on provision of health services, family planning programs, and emergency aids and ignores the marginal efficiencies of the services, and other socio-economic aspects may serve little in efforts directed to improve the existing health status of the region. Lastly, from the analyses and the region's past socioeconomic performances, we observe the fact that making substantial improvements of the health status of SSA are within the realm of possibility.

References

Auster, R, Levenson, I., and Sarachek, D. (1969), "The Production of Health, an Exploratory Study," Journal of Human Resources, 4:411-36.

Berger, M. and Leigh, J. (1989), "Schooling, Self-selection, and Health," Journal of Human Resources, 24: 433-55.

Behrman, Jere R. and Anil B. Deolalikar (1988), "Health and Nutrition," in Hollis Chenery and T. N. Srinivasan, eds., Hand-book of Development Economics, Volume I: 1988, Amsterdam: North-Holland.

Chick J., J. Duffy, G. Lloyd, B. Ritson (1986), "Medical Admissions in Men: The Risk Among Drinkers," The Lancet, ii: 1380-83.

Chistiansen, T. (1994), "Distribution of Health Status by Income. Result from Denmark," in A. Mielck and R. Maria, eds., Health inequalities: Discussion in Western European countries, Waxmann, Munster/New York.

Choquet, M. and S. Ledoux (1989), "Alcohol Related Problems in France" in WHO EURO Reports and Studies, 109: 45-63.

Fuchs, V., (1994), The Future of Health Policy, Harvard University Press: Cambridge.

--. (2004), "Reflections on the Socio-Economic Correlates of Health," Journal of Health Economics, 23 (2004): 653-661.

Grossman, M. (1972), The Demand for Health." A Theoretical and Empirical Investigation, NBER: New York.

--. (2004), "The Demand for health, 30 Years Later: A Very Personal Retrospective and Prospective Reflection," Journal of Health Economics, 23 (2004):629-636.

Hadley, J. (1982), More Medical Care, Better Health, Urban Institute: Washington DC.

Rogers, G. B. (1979), "Income and Inequality as Determinants of Mortality: An International Cross- Section Analysis," Population Studies, 33(2): 343-52.

Rosen S. and Taubman, P. (1982), "Some Socioeconomic Determinants of Mortality," in J. Van der Gagg, W. B. Neeman and T. Tsukahara, eds., Economics of Health Care: 1982, New York, Preager Publishers.

Rosenzweig, M. R. and T. P. Schultz (1983), "Estimating a Household Production Function: Heterogeneity, the Demand for Health Inputs, and Their Effects on Birth Weight," Journal of Political Economy, 91 (1983):723-746.

Schultz, T. P. (2004), "Health Economics and Applications in Developing Countries," Journal of Health Economics, 23 (2004): 637-641.

Thornton, J. (2002), "Estimating a Health Production Function for the US: Some New Evidence," Applied Economics, 34: 59-62.

Wilkinson, R. G. (1992), "Income Distribution and Life Expectancy," British Medical Journal, 304:165-68.

Notes

(1.) See, for example, Beherman and Deolalikar (1988: 698-701)

(2.) Benin, Botswana, Burkina Faso, Burundi, Cameroon, Cape Verde, Central African Republic, Chad, Cote d'Ivoire, Equatorial Guinea, Ethiopia, Gambia, Ghana, Kenya, Madagascar, Malawi, Mall, Mauritania, Mauritius, Mozambique, Namibia, Niger, Nigeria, Rwanda, Senegal, South Africa, Sudan, Swaziland, Tanzania, Togo, Uganda, Zambia and Zimbabwe

Bichaka Fayissa, Department of Economics and Finance, Middle Tennessee State University, Murfreesboro, Tennessee 37132, Tel. (615) 898-2385, Fax: (615) 898-5596, e-mail: bfayissa@mtsu.edu

Paulos Gutema, Addis Ababa University, Ethiopia, E O. Box 33229, Tel. (251-1) 55 68 22, Fax 251-1-55 13 33, e-mail: pgutema@hotmail.com

TABLE 1
One-Way Error Component Regression Model Estimates for Equation (2)

 Estimate of St. error of
Estimators Parameters the parameter the parameter

Restricted [[alpha].sub.1] -0.0206 0.0064
Model OLS [[alpha].sub.2] 0.2122 0.0682
 [[beta].sub.1] -0.0032 0.0006
 [[beta].sub.2] -0.0160 0.0071
 [[gamma].sub.1] 0.0029 0.0010
 [[gamma].sub.2] 0.0122 0.0081
 Constant 3.1046 0.3125

Fixed Effect [[alpha].sub.1] -0.0350 0.0092
Model [[alpha].sub.2] 0.1511 0.0675
 [[beta].sub.1] 0.0019 0.0021
 [[beta].sub.2] -0.0331 0.0221
 [[gamma].sub.1] -0.0036 0.0032
 [[gamma].sub.2] 0.0164 0.0204

Random [[alpha].sub.1] -0.0337 0.0069
Effect [[alpha].sub.2] 0.1645 0.0486
Model [[beta].sub.1] -0.0018 0.0010
 [[beta].sub.2] -0.0165 0.0118
 [[gamma].sub.1] -0.0018 0.0015
 [[gamma].sub.2] 0.0448 0.0125
 Constant 3.5110 0.2322

Estimators Parameters T-ratio p-value

Restricted [[alpha].sub.1] -3.2135 0.0016
Model OLS [[alpha].sub.2] 3.1115 0.0022
 [[beta].sub.1] -5.4849 0.0000
 [[beta].sub.2] -2.2335 0.0269
 [[gamma].sub.1] 2.9619 0.0035
 [[gamma].sub.2] 1.5163 0.1315
 Constant 9.9342 0.0000

Fixed Effect [[alpha].sub.1] -3.8227 0.0002
Model [[alpha].sub.2] 2.2376 0.0266
 [[beta].sub.1] 0.9025 0.3682
 [[beta].sub.2] -1.4960 0.1366
 [[gamma].sub.1] -1.1300 0.2602
 [[gamma].sub.2] 0.8081 0.4203

Random [[alpha].sub.1] -4.8924 0.0000
Effect [[alpha].sub.2] 3.3841 0.0007
Model [[beta].sub.1] -1.8298 0.0673
 [[beta].sub.2] -1.3919 0.1639
 [[gamma].sub.1] -1.1976 0.2311
 [[gamma].sub.2] 3.5923 0.0003
 Constant 15.1220 0.0000

Lagrange Multiplier test of RM vs. FE/RE
[[chi square].sub.(1)] = 139.24, p = 0.0000

Hausman test of FE vs. RE; [[chi square].sub.(6)] = 0.00, p = 1.0000

TABLE 2
Two-Way Error Component Regression Model Estimates for Equation (2)

 Estimate of St. error of
Estimators Parameters the parameter the parameter

Fixed Effect [[alpha].sub.1] -0.0343 0.0079
Model [[alpha].sub.2] 0.1147 0.0515
 [[beta].sub.1] -0.0105 0.0042
 [[beta].sub.2] -0.0294 0.0218
 [[gamma].sub.1] 0.0016 0.0034
 [[gamma].sub.2] 0.0120 0.0259
 Constant 3.9852 0.3464

Random [[alpha].sub.1] -0.0302 0.0067
Effect [[alpha].sub.2] 0.1337 0.0474
Model [[beta].sub.1] -0.0042 0.0010
 [[beta].sub.2] -0.0255 0.0118
 [[gamma].sub.1] 0.0026 0.0016
 [[gamma].sub.2] 0.0115 0.0135
 Constant 3.5610 0.2279

Estimators Parameters T-ratio p-value

Fixed Effect [[alpha].sub.1] -4.3539 0.0000
Model [[alpha].sub.2] 2.2283 0.0273
 [[beta].sub.1] -2.4819 0.0141
 [[beta].sub.2] -1.346 0.1802
 [[gamma].sub.1] 0.4735 0.6365
 [[gamma].sub.2] 0.4624 0.6444
 Constant 11.5032 0.0000

Random [[alpha].sub.1] -4.5223 0.00001
Effect [[alpha].sub.2] 2.8211 0.0048
Model [[beta].sub.1] -4.1052 0.0000
 [[beta].sub.2] -2.1603 0.0308
 [[gamma].sub.1] 1.6058 0.1083
 [[gamma].sub.2] 0.8555 0.3923
 Constant 15.6230 0.0000

F-test of One-Way vs Two-Way F[4.122] = 4.633, p = 0.0016

Lagrange Multiplier test of RM vs. FE/RE
[[chi square].sub.(2)] = 155.86, p = 0.0000

Hausman test of FE vs. RE; [[chi square].sub.(6)] = 3.88 p = 0.6935