Spring 1998
GUO Gang
For this project I constructed a multivariate regression model to explain the infant mortality rates in different countries of the world. Using OLS estimation on the data set, I found that the infant mortality rates are influenced by the country's education level, adequacy of medical care, and people's affluence.
In my initial model, the infant mortality rate of a country depends on four factors: education level, adequacy of medical care, health level, and people's affluence. The data are from the file World95.sav in SPSS 8.0 for Windows. I used the variables literacy (people who read(%)), urban (people living in cities(%)) and death_rt (death rate per 1000 people), calories (daily calories intake), and log_gdp (Log (base10) of gross domestic product per capita) to measure these four factors, respectively. The summary of the dependent variable, babymort (infant mortality (deaths per 1000 live births)), and the independent variables are as follows:
. summarize babymort literacy urban death_rt calories log_gdp
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
babymort | 109 42.31294 38.07923 4 168
literacy | 107 78.33645 22.88319 18 100
urban | 108 56.52778 24.20337 5 100
death_rt | 108 9.557315 4.253231 2 24
calories | 75 2753.827 567.8277 1667 3825
log_gdp | 109 3.421814 .620055 2.08636 4.370587
Since the adequacy of medical care was measured by two variables, I used three different models to see the effects of the factors when I control for different variables. The formulas of the models are as follows:
Model I: babymort = α + β1literacy + β2urban + β4calories + β5log_gdp
Model II: babymort = α + β1literacy + β3death_rt + β4calories + β5log_gdp
Model III: babymort = α + β1literacy + β2urban + β3death_rt + β4calories + β5log_gdp
Here we expect to see positive coefficient for death_rt and negative coefficients for literacy, urban, calories, and log_gdp. The results of the OLS estimation of the parameters in the three models and the student's t statistics significance are shown in the table below:
| factors | variables | Model I | Model II | Model III | |||
|---|---|---|---|---|---|---|---|
| beta | P > |t| | beta | P > |t| | beta | P > |t| | ||
| Education level | literacy | -1.102333 | 0.000 | -.9213567 | 0.000 | -.9226064 | 0.000 |
| Adequacy of medical care | urban | -.1531617 | 0.131 | .0262324 | 0.767 | ||
| death_rt | 1.983066 | 0.000 | 2.019446 | 0.000 | |||
| Health level | calories | -.0107551 | 0.038 | -.0104902 | 0.014 | -.0105235 | 0.014 |
| People's affluence | log_gdp | -6.904975 | 0.194 | -11.20093 | 0.005 | -11.83477 | 0.009 |
| Constant | 191.6734 | 0.000 | 163.7471 | 0.000 | 164.2594 | 0.000 | |
| R square | 0.8970 | 0.9311 | 0.9312 | ||||
So all the parameters are in the expected direction except the one for urban, and all the R squares are very high. From the results in this table, we drew the following conclusions about the effects of the variables:
So far, so good. However, we still have other things to worry about. One of the most conspicuous problems is the possibility of multicollinearity. As the independent variables are all measurements of social development, we suspect that there can be very high correlation between the independent variables. The higher the correlation between the independent variables (the more severe the multicollinearity), the less information used by the OLS procedure in making its coefficient estimates, just as though it had a very small sample size, or a sample in which the independent variable did not vary much. In order to detect multicollinearity, we computed all the possible pairwise correlations between the variables. The results are as follows:
. pwcorr babymort literacy urban death_rt calories log_gdp, sig
| babymort literacy urban death_rt calories log_gdp
----------+------------------------------------------------------
babymort | 1.0000
|
|
literacy | -0.9005 1.0000
| 0.0000
|
urban | -0.7180 0.6496 1.0000
| 0.0000 0.0000
|
death_rt | 0.6304 -0.4858 -0.4828 1.0000
| 0.0000 0.0000 0.0000
|
calories | -0.7769 0.6816 0.6924 -0.3524 1.0000
| 0.0000 0.0000 0.0000 0.0019
|
log_gdp | -0.8236 0.7323 0.7542 -0.4015 0.8474 1.0000
| 0.0000 0.0000 0.0000 0.0000 0.0000
Just as we expected, some of the correlations between the independent variables are very high. The most disturbing one is the almost linear relationship between calories and log_gdp. The correlation, 0.8474, seems too high. According to Kennedy, here one of the feasible remedies for multicollinearity is to "[d]rop a variable. A popular means of avoiding the multicollinearity problem is by simply omitting one of the collinear variables. If the true coefficient of that variable in the equation being estimated is zero, this is a correct move."(Kennedy 1985:151). In the above models we have estimated, the coefficient for calories is almost zero, so we assumed that we could drop calories in the OLS estimation of the parameters of the models. In this way we came up with two new models:
Model IV: babymort = α + β1literacy + β3death_rt + β5log_gdp
Model V: babymort = α + β1literacy + β2urban + β3death_rt + β5log_gdp
The results of the OLS estimation of the parameters in these models are shown below:
| factors | variables | Model IV | Model V | ||
|---|---|---|---|---|---|
| beta | P > |t| | beta | P > |t| | ||
| Education level | literacy | -.9046475 | 0.000 | -.9049902 | 0.000 |
| Adequacy of medical care | urban | .0044465 | 0.956 | ||
| death_rt | 2.177427 | 0.000 | 2.182952 | 0.000 | |
| People's affluence | log_gdp | -20.18637 | 0.000 | -20.29549 | 0.000 |
| Constant | 161.7375 | 0.000 | 161.8307 | 0.000 | |
| R square | 0.9140 | 0.9140 | |||
Here all the coefficients are in the expected direction except the one for urban, and the effects of all the independent variables are statistically significant at 0.05 level.
In conclusion, in the first three models we have constructed, the effects of education level, adequacy of medical care, health level, and people's affluence all show up, although their effects are more evident if we control for death rate. Since there is high correlation between calories intake and logarithm of GDP per capita, we dropped calories and estimated the parameters in the new models. The coefficients are statistically significant. In terms of the "leverage" (King, Keohane, and Verba 1994:18) of the models, I would prefer Model IV, in which infant mortality rate is explained by three variables, literacy, death rate, and log of GDP per capita, and whose explanatory power is no less than the other models.
1998-05-03