Democracy, Dictatorship, and Infant Mortality

Thomas D. Zweifel and Patricio Navia

Journal of Democracy, April 2000

Statistical Explanations for the Technically Inclined Reader




The following tables and batch file detail our procedure, variables, and findings for our study on democracy, dictatorship, and infant mortality, published in the April 2000 issue of the Journal of Democracy.


Selection Model

We use a 2-stage procedure: (1) a selection model to regress exogenous variables (XREG) on regime (REG), using Pobit; and (2) a performance model to predict the effect of regime types (REG) on infant mortality (INFMORT) by regressing lambda and a set of exogenous variables (XIMR) on infant mortality using the Heckman Two-Step method.

A static Probit model was used to estimate the dichotomous selection equation,

yij = b' xij + eij

where y is the dependent variable REG, x is the set of independent variables XP, and e is the unobserved error term for country i and alternative j. In this multinomial Probit model, we assume that eij are normally distributed, and that ei and ej are independent.

For the selection model, we let y be the dependent variable IMR and d the selection mechanism of the two possible states of the world: democracy and dictatorship. yi1 is observed only when di = 1 (dictatorship); it is not observed otherwise. Likewise, yi0 is observed only when di = 0 (democracy), but unobserved when di=1.

The equation that determines the sample selection is: di* = a’ wi + ui , where
di = 1 if di* > 0 and di = 0 otherwise. As indicated above, d depends on a vector of exogenous variables w: selection is exogenous.

Assuming that ei and ui have a bivariate normal distribution with zero means and correlation r , then the model for the observations in the selected sample is the following, where dictatorship=1 and democracy=0:
E [yij | xi , in sample] = E [yij | xi , d=1]
= E [yij | xi, a’wi + ui > 0]
= b’ xi + E [ei | ui > -a’ wi]
= b’ xi + (r se su) {f (-a’ wi) / [1 - F (-f’ wi)]}
= b’ xi + (r se su) [f (a’ wi) / F (f’ wi)]}.


Then,
E [yij | xi, in sample] = b’ xi + (r se) li
= b’ xi + q li


where l = [f (a’ w)]/[F(a’ w)]

Likewise,
E [yi0 | xi , in sample] = E [yi0 | xi , d=0]
= E [yi0 | xi, a’wi + ui £ 0]
= b’ xi + E [ei | ui £ -a’ wi]


and analogously,

E [yi0 | xi, in sample] = b’ xi + q li0

where l = [-f (a’ w)]/[1-F(a’ w)]

The previous model is used to estimate the selection variable l. The Probit model calculates internally the Inverse Mill’s Ratio as
l = f / F if d = 1 , and l = - f / 1 - F if d = 0 .


Holding the Inverse Mill’s Ratio as l permits us to keep it for the performance model.

Finally, the corrected values were estimated by OLS regression of

Because we correct for auto-correlation, the estimation of the regression must use ordinary least squares (OLS). OLS produces inconsistent estimates of b: as long as l is omitted, the model suffers from the specification error of an omitted variable. Without some knowledge of x, it is impossible to determine how serious the bias will be. Thus, we write:

Yi = xbi + qi li + e .

The unbiased effect of REG, ceteris paribus, is the difference xb0 - xb1.

TABLE 1
Infant Mortality Rate (IMR) by Region
(1960–90 IMR is the mean of observations in the respective region.)

Region

1960–90 IMR

# Observations



Sub-Saharan Africa

133

221



South Asia

116

31



East Asia

61

28



South East Asia

57

50



Pacific Islands/Oceania

49

6



Middle East/North Africa

100

66



Latin America

74

127



Caribbean and Non-Iberian America

66

30



Eastern Europe/USSR

23

35



Industrial Countries

17

487



Total

60

1081



 

TABLE 2
Infant Mortality Rate (IMR) by Level of Development and by Regime Type

Level

Dictatorship

Democracy

 

IMR

#Obs

IMR

#Obs



$0-1,999

1122.7

320

95.7

47



$2,000-2,999

84.1

57

59.6

38



$3,000-3,999

55.1

44

42.6

35



$4,000-4999

43.6

42

28.9

24



$5,000-5999

31.2

26

23.4

48



$6,000+

35

15

15.1

385



Total Observations
 

504

 

577



 

TABLE 3
Impact of Exogenous Variables on Regime Type (REG): Binomial Probit
Binomial Probit Model [where Democracy=0, Dictatorship=1]

Variable

Coefficients

Standard Errors

Constant

3.947**

0.704

STRA

0.173*

0.082

COMEX

-0.340*

0.147

NEWC

-0.253

0.228

BRITCOL

-0.735**

0.201

RELIGION

-0.0142**

0.004

CATH

0.626*

0.283

PROT

-0.385

0.430

MOSLEM

1.029**

0.313

ODRP

-2.734**

0.293

ODWP

-1.927

1.548

LEVEL

-0.000**

0.000



p<0.05, ** p<0.01. Degrees of Freedom =11.

Frequencies of actual & predicted outcomes:

Actual
Predicted
Total

0
1

0
496
81
577
1
50
454
504
Total
546
535
1081


TABLE 4
Impact of Exogenous Variables on Infant Mortality Rate (IMR) by Regime Type

Ordinary Least Squares Model [Democracy=0, Dictatorship=1]
(Standard errors in parentheses)
Parameter
Dictatorships
Democracies
Constant
134.437**
3.595

(10.087)
(0.520)
COMEX
1.278
4.662**

(2.686)
(1.861)
EDT
-14.087**
-1.847**

(0.690)
(0.362)
FERTIL
2.397*
10.169**

(1.171)
(0.764)
POP
-0.000**
0.000**

(0.000)
(0.000)
LFPW
0.461**
0.535**

(0.112)
(0.108)
LEVEL
-0.003**
-0.002**

(0.001)
(0.000)
LAMBDA
-15.940**
-8.547**

(3.960)
(1.926)

N
423
520
Degrees of Freedom
415
512
F
256.88
315.60
Fit:R-squared
0.81
0.81
Fit:Adj.R-squared
0.81
0.81
Durbin-Watson final
1.892
1.859
Final Rho
0.054
0.070


*p < .05, **p < .01.

 

TABLE 5
Predicted Independent Effect of Regime Type on Infant Mortality Rate (IMR)

Unbiased Values/Descriptive Statistics
(All results based on nonmissing observations)

Variable

Predicted Mean

Standard Deviation

Predicted Minimum

Predicted Maximum

# of Observations produced



IMR Dictatorship

52.6

58.5

-85.1

168.5

943



IMR Democracy

42.8

33.3

-4.52

141.6

943



Difference

9.8

33.9

-103.64

79.1

943

 

TABLE 6
Regime Type and Infant Mortality Rate (IMR) by Year in Selected Countries and Years

Country

Year

(a)

Regime

(b)

Observed IMR

(c)

Predicted IMR

Dictatorship

(d)

Predicted IMR

Democracy

(e)

Difference

f=(d-e)



Burkina Faso


1967

Dic

185

168.5

93.5

75.0

 

1982

Dic

149

162.5

93.8

68.8

 

1987

Dic

138

161.0

98.2

62.8



Brazil


1970

Dic

94.6

104.2

62.5

41.7

 

1977

Dic

79

88.7

54.5

34.3

 

1982

Dem

71

77.2

50.6

26.6

 

1987

Dem

63

63.8

43.5

20.3



China


1962

Dic

88

106.9

141.6

-34.7

 

1970

Dic

69

72.9

130.9

-57.9

 

1976

Dic

44

42.5

107.6

-65.0

 

1980

Dic

42

27.2

105.1

-77.9

 

1987

Dic

37

6.3

109.9

-103.6



Egypt


1970

Dic

158.0

103.1

62.4

40.7

 

1982

Dic

112.0

76.9

51.1

25.8

 

1987

Dic

86.0

64.7

42.6

22.2



Ethiopia


1967

Dic

162

161.8

84.9

76.8

 

1972

Dic

155

160.0

84.8

75.2

 

1982

Dic

159

156.1

96.4

59.7



Greece


1961

Dem

39.8

83.6

27.6

56.0

 

1964

Dem

35.8

76.4

27.6

48.9

 

1970

Dic

34.3

58.1

24.0

34.1

 

1974

Dem

23.9

47.3

22.3

25.0

 

1984

Dem

14.3

28.4

13.2

15.3

 

1987

Dem

11.7

16.7

8.4

8.3



India


1967

Dem

145

97.3

108.8

-11.6

 

1972

Dem

132

82.6

106.4

-23.8

 

1982

Dem

108

53.3

104.0

-50.7

 

1987

Dem

96

37.0

101.1

-64.0



Indonesia


1970

Dic

118.0

110.5

76.3

34.1

 

1977

Dic

105.0

96.4

68.9

27.4

 

1982

Dic

95.0

84.3

61.1

23.2



Mexico


1970

Dic

72.4

91.8

69.2

26.9

 

1982

Dic

49.0

55.8

45.0

10.8

 

1987

Dic

41.0

42.1

38.7

3.4



Nicaragua


1967

Dic

115

110.7

81.8

29.0

 

1972

Dic

100

104.9

77.9

27.0

 

1982

Dic

68

87.5

66.6

20.9



Nigeria


1970

Dic

139.4

145.8

94.5

51.2

 

1972

Dic

135

144.1

93.3

50.8

 

1982

Dem

95.7

130.1

91.9

38.2

 

1987

Dic

87

115.4

83.3

32.2



Pakistan


1967

Dic

145

130.2

79.1

51.1

 

1982

Dic

120

116.0

80.3

35.8

 

1987

Dic

104

109.3

72.8

36.5



South Africa


1970

Dic

78.8

71.3

64.2

7.2

 

1977

Dic

72.0

65.2

58.4

6.8

 

1982

Dic

63.0

58.7

54.8

3.9



Switzerland


1961

Dem

21.0

10.2

14.1

-3.1

 

1970

Dem

15.4

14.1

7.7

6.3

 

1974

Dem

12.4

7.8

2.9

4.9



 

Appendix 1: Variables

The data set used for this paper was Alvarez, Cheibub, Limongi and Przeworski 1997, ACLP World Political / Economic Database. ACLP defines the variables used here as follows:

BRITCOL: British colony. Dummy variable coded 1 for every year in countries that had been a British colony any time after 1919, 0 otherwise.

CATH: Percentage of Catholics in the population.

COMEX: Primary commodity exporting country, as defined by the IMF.

EDT: Cumulative years of education of the average member of the labor force. (Bhalla-Lau-Louat series).

FERTIL: Total fertility rate (births per woman).

INFMORT: Infant mortality rate per 1,000 live births.

LEVEL: Level of economic development. Real GDP per capita, 1985 international prices, Chain index.

LFPW: Labor force, female (% of total).

MOSLEM: Percentage of Moslems in the population.

NEWC: New country. Dummy variable coded 1 for every year in countries that became independent after 1945, 0 otherwise.

ODRP: Democracies in the region (Percentage). Percentage of democratic regimes in the current year (other than the regime under consideration) in the REGION to which the country belongs.

ODWP: Democracies in the world (Percentage). Percentage of democratic regimes (other than the regime under consideration) in the world for the current year.

POP: Population, in thousands.

PROT: Percentage of Protestants in the population.

RELIGION: Percentage of population of the largest religious group, measured in the year for which data were available (roughly 1976-1985) as presented in The Economist (1988) and Vanhanen (1992). Time invariant variable.

STRA: Sum of transitions to authoritarianism. The sum of past transitions to authoritarianism in a country. If a country experienced a transition to authoritarianism before 1950, STRA was coded 1 in 1950.

YEAR: From 1950 or date of independence to 1990.

 

Appendix 2: LIMDEP Batch File

The statistical program used for this paper was LIMDEP Version 7.0, Econometric Software 1985–1997. A copy of the batch file follows:

TITLE; ********** INFMORT PROBITSEL 5-8-99 ****************** $

LOAD; FILE=c:\statscom\WORLDSRT.INT $

READ; file=c:\statscom\demogr.wk1; format=wks; names $

TITLE; ********** REJECT MISSING VALUES ********************* $

SAMPLE; 1-4126 $

REJECT; INFMORT < 0 $ REJECT; INFMORT = 0 $

REJECT; EDT = -9 $ REJECT; FERTIL = -9 $

REJECT; LFPW = -9 $ REJECT; STRA = -9 $

NAME; XIMR= ONE, comex, edt, fertil, pop, lfpw, level $

REGRESS; LHS=infmort;RHS=XG,REG $

NAME; XREG= one, stra, comex, newc, britcol, religion, cath, prot, moslem, odrp, odwp, level $

CALC; LIST; KXIMR=COL(XIMR) $

TITLE; ************ PROBIT WITH SELECTION ***************** $

PROBIT; LHS= REG ;RHS= XREG ;HOLD(IMR=LAMBDA) $

TITLE; ************ HECKMAN TWO-STEP METHOD *************** $

TITLE; ************ OLS FOR DICTATORSHIPS ***************** $

REJECT; REG=0 $

CREATE; CL=COUNTRY [-1] $ (lags country)

CREATE; IF (CL # COUNTRY) FLAGD=1 $

CREATE; IF (CL # COUNTRY) FLAGA=0 $

CREATE; IF (FLAGA=-999) FLAG1=0; ELSE FLAG1=FLAGA $

CREATE; IF (FLAGD=-999) FLAG2=0; ELSE FLAG2=FLAGD $

CREATE; FLAGN=FLAGA+FLAGD $

REJECT; FLAGN=1 $

REGRESS; LHS=infmort; RHS=XIMR,LAMBDA; AR1 $

MATRIX; BAUT=PART(B,1,KXIMR) $

TITLE; ************* OLS FOR DEMOCRACIES ****************** $

SAMPLE; 1-4126 $

REJECT; INFMORT = -9 $ REJECT; INFMORT = 0 $

REJECT; EDT = -9 $ REJECT; FERTIL = -9 $

REJECT; LFPW = -9 $ REJECT; STRA = -9 $

REJECT; REG=1 $

CREATE; CL=COUNTRY [-1] $ (lags country)

CREATE; IF (CL # COUNTRY) FLAGA=1 $

CREATE; IF (CL # COUNTRY) FLAGD=0 $

CREATE; IF (FLAGA=-999) FLAG1=0; ELSE FLAG1=FLAGA $

CREATE; IF (FLAGD=-999) FLAG2=0; ELSE FLAG2=FLAGD $

CREATE; FLAGN=FLAGA+FLAGD $

REJECT; FLAGN=1 $

REGRESS; LHS=infmort; RHS=XIMR,LAMBDA; AR1 $

MATRIX; BDEM=PART(B,1,KXIMR) $

TITLE; ************** CALCULATE UNBIASED VALUES *********** $

SAMPLE; 1-4126 $

REJECT; INFMORT < 0 $

REJECT; INFMORT = 0 $

REJECT; EDT = -9 $

REJECT; FERTIL = -9 $

REJECT; LFPW = -9 $

REJECT; STRA = -9 $

REJECT; FLAGN=1 $

CREATE; IMR1 = DOT(XIMR,BAUT) $ (IMR1 is infmort under dic)

CREATE; IMR0 = DOT(XIMR,BDEM) $ (IMR0 is infmort under dem)

CREATE; DIMR=IMR1-IMR0 $ (DIMR is the difference)

DSTAT; RHS=IMR1,IMR0,DIMR $

STOP