The Effect of Family Life How Divorce affects Abortion

Domininkas Mockus

Contents 1 Introduction

1

2 Theoretical Framework

1

3 Econometric Methods

1

3.1

Relevant Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

3.2

Model Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

3.2.1

Fixed-Effects or First-Differencing? . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

3.3

4 Data

4

4.1

Abortion Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

4.2

Divorce Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

4.3

Employment

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

4.4

Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

4.5

Household Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

4.6

Race . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

4.7

Financial Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

4.8

Age and Sex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

5 Results 6 Conclusion

7 11

Domininkas Mockus

1

The Effect of Family Life

3

ECONOMETRIC METHODS

Introduction I am interested in the importance of the family to society. Specifically, I will look at how the divorce

rate, a quantifiable number that reflects the degradation of the family, affects the abortion rate. Since most people agree that abortion is a tragedy that should be avoided, I consider the abortion rate a measure of the degradation of society. There is a movement to outlaw abortions; opponents claim that this would only lead to illegal backalley abortions that do more harm. I believe that the most effective way to curb abortions is to attack the root of the problem. If society were diagrammed by a tree, abortion would only be a sick leaf; the family is, if not the root, at least the heartwood of this tree. The most effective way to heal a tree is not to pluck off its sick leaves but to cure the ailing heartwood. Hence, I would like to find evidence to support or refute my claim that divorce has an effect on abortions.

2

Theoretical Framework The family has always been a child’s first educator, and so if a family is abusive to each other (not

necessarily to the young child), generally the child will grow up and somehow reflect this abuse by making poor choices. Therefore, abortion should be positively correlated with abuses earlier in life (whether inside or outside an individual’s family; seeing hatred around also has an effect). Divorce is a form of this abuse that may occur early in life; consider the traumatic effect of divorce on a child. There should be a positive correlation between the divorce rate and the abortion rate.

3

Econometric Methods My primary variables of interest are my dependent variable, the abortion ratio, and my interesting

independent variable, the divorce rate. I use rates to eliminate the error caused by the number of abortions and divorces changing simply due to population growth.1 I will further define both of these below.2 There is a tradeoff for the abortion ratio between using the state of occurrence and state of residence. The former measure is more accurate than the latter; however, the latter is the measure that I am interested in because a person living in state x, even if she goes to state y for her abortion, is influenced by the environment of state x. The abortion ratio is defined as the number of abortions per 1000 births. By using the ratio, I capture 1I

use state-level data, so there should be no issue in having to “guess” the rates because there are not enough people. section 4 on page 4.

2 See

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Domininkas Mockus

The Effect of Family Life

3

ECONOMETRIC METHODS

a greater percentage of sexually active women3 but more importantly exclude sexually inactive women, as opposed to the abortion rate, which includes all sexually mature women. My primary concern is to make sure that the divorce rate is not correlated with anything else that also affects the abortion ratio and that is not controlled for in the model. I include controls for the standard measures of sex, age, and race as well as controls for education, employment, household characteristics, and financial status. If a person is educated, he probably has a better job and better living conditions and is generally happier and less prone to make poor decisions. Thus, education might affect both the divorce rate and abortion ratio and so I consider it a valid control. The problem of overcontrol lies in the fact that if a female divorces, she may seek higher education; thus, I only consider higher education for males. If a person is employed, he is happier and has less time to bum around all day and make poor choices because he or she has a sense of purpose in life. Thus, employment might affect both the divorce rate and abortion ratio. An increase in the divorce rate may cause former spouses to suddenly look for work (and hence may be an overcontrol), and so I consider specifically male employment. Household characteristics give a measure of other factors that are in the household that are correlated with the divorce rate and the abortion ratio. Good families have a certain amount of children, and bad families have another amount of children.4 Overcontrol may occur if I tried to include a measure of the size of the household. A divorce would tend to lower this number. Consider also the percentage of the population living as unmarried partners at home; this would also be affected by the divorce rate. I control for the percent of the population that is living as children at home. This should be less correlated with the divorce rate; granted over time I would expect to see a declining percentage of children living at home if families were to start breaking. However, since I only consider 7 years, there is not much room for lagged variables and so I consider pchild a good enough control.5 There is a correlation between divorce and wealth of the area; typically, richer areas are more conservative and have lower divorce rates. I consider variables such as state-level real and nominal GDP, state-level real and nominal per-capita income, state-level PCE, and the state-level poverty rate.

3.1

Relevant Variables For some measures, I have more than one variable; for example, for financial status, I have six measures.

I wish to reduce the number of variables in a particular category to reduce the degrees of freedom that are 3 Though not all; contraception is a factor that theoretically should be controlled for (as suggesting sexual activity) but cannot be practically accounted for. Consider also how some women use birth-control pills solely for health reasons and not for contraceptive purposes. 4 The divorce rate between good and bad families should be different as well. 5 The ideal data set would include information for at least two generations.

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Domininkas Mockus

The Effect of Family Life

3

ECONOMETRIC METHODS

used up and possibly reduce the standard errors. I first correlate all the variables without fixing time to see generally how the data looks. I find that srpci and snpci; srGDP , snGDP , sP CE, and totpop; mage, pyoung, and pearlyadult; pmale and pyoungmales; have correlations of at least 0.8 in magnitude. I look at the correlations within a year6 and find that srGDP , snGDP , sP CE and totpop (minimum correlation 0.9804); srpci and snpci (minimum correlation 0.8639); mage and pyoung (average correlation above 0.85); pmale and pyoungmales (average correlation above 0.85); are highly correlated. From here I keep the few variables with the highest correlation with dr and the lowest correlation with the other independent variables. The point of a control variable is to be correlated with the variable of interest, so unless no variable has a significantly higher correlation than the others with dr, I will not worry about the second criteria that only reduces standard errors. Consider srGDP , snGDP , sP CE and totpop. sP CE, srGDP , and snGDP are the most correlated with dr, but sP CE is just barely less correlated with the other independent variables, so I keep sP CE only 7

Consider srpci and snpci. snpici is significantly more correlated with dr, so I keep only snpci. Consider

mage and pyoung. mage is the most correlated with dr so I will keep mage only. Consider pmale and pyoungmales. pmale is significantly more correlated with dr, so I keep pmale. I then have 17 variables.

3.2

Model Comparison I cannot choose which model is better, the level or log of ar and dr. Both make sense, but both

account for slightly different things. For example, in the level form of ar, ar would be expected to change by some θ. In the logarithmic form, ar would be expected to change by some δ%. Mathematically, I consider y = βx + µ

(1)

ln(y) = βx + µ

(2)

and

In addition, I look at the level and natural log form of dr for each of the models given above.8 I use fixed-effects estimation throughout. I first check for regression specification errors. Then, I run model (1) twice, once with dr and once with ldr, and use a Davidson-Mackinnon test to pick a better model. I repeat the process with model (2).9 6I

now look for correlations 0.85 and above within a category, 0.95 and above between two categories. the variables almost perfectly predict each other, it really does not matter which variable I pick. 8 The results are given in table 1 on page 10. 9 See the previous footnote. 7 Since

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Domininkas Mockus

The Effect of Family Life

4

DATA

It seems that models 1 and 2 ({ar, dr} and {ar, ldr}) are close to being misspecified;10 additionally, the errors are serially correlated, so fixed-effects is the wrong approach.11 Thus, I pick between models 3 and 4 ({lar, dr} and {lar, ldr}). Since there is no problem in interpretation or theory, I have the luxury of choosing models in this way. In addition, all the practically significant coefficients follow the same sign, and most importantly, the sign on the divorce rate is positive, as expected, and so I have not missed anything given the variables I have. The final model I consider is the fixed-effects regression given by the variables in (4) in table 1 on page 10 since the parameter estimate for ldr will be easier to interpret and since the errors are serially uncorrelated. 3.2.1

Fixed-Effects or First-Differencing? Given the nature of the panel data set, I have the option of using fixed-effects of first-differences

to eliminate time-invariant factors (such as state). There is a key difference for the assumptions: Firstdifferencing assumes that the differenced errors are serially uncorrelated (which happens if and only if the error follows a random walk), while fixed-effects assumes the errors are serially uncorrelated. Woolridge[2] proposed such a test12 I include the results for this as well in table 1 on page 10. Notice that the estimates for models 1 and 2 are incorrect because the errors are serially correlated.

3.3

Model Analysis To check the linearity of my model, I look at a scatter plot of the actual values on the predicted

values.13 I notice how the data clusters. I find that if I remove New Mexico and Mississippi (outliers on the left and right, respectively), I get a better relation (call this model 5). The most precise model, model 6, excludes additionally Arizona, Texas, Alabama, Georgia, South Carolina, Maryland, and Louisiana. It is interesting to note the states excluded and the results of model 6, even though model 6 is not good due to data manipulation.

4

Data I use a (final) panel dataset consisting of 47 groups14 over a period of seven consecutive years (2005

to 2011). There are a total of 320 observations15 and 17 independent variables (excluding time and state). 10 With

90% confidence the model is misspecified. subsubsection 3.2.1. 12 Verified by and described in Drukker[1]. H : No first-order autocorrelation 0 13 See figure 1 on page 8. 14 Each of the 50 states less California, Florida, and New Hampshire. I did not use another estimate of abortion rates for these places for consistency; I stick with only the CDC’s estimates for abortion ratio. Other sources give different data. 15 DE is missing in the 2009 data; KY in the 2006 data; LA in the 2005 and 2006 data; MD is only in the 2005 and 2006 data. Using Planned Parenthood’s data, I would have only 250 observations (50 groups, five nonconsecutive years) 11 See

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Domininkas Mockus

4.1

The Effect of Family Life

4

DATA

Abortion Ratio The abortion ratio, ar, is the number of abortions per 1000 births by state of residence. This data

comes from the Morbidity and Mortality Weekly Report Abortion Surveillance Summaries of each respective year prepared by the Division of Reproductive Health, National Center for Chronic Disease Prevention and Health Promotion, CDC.16 The data is sent in voluntarily.

lar = ln(

ar ) 1000

(3)

Variable

Label

Obs

Mean

Standard Deviation

Minimum

Maximum

Abortion Ratio

ar

320

184.5437

81.24057

36

488

Natural Log Abortion Ratio

lar

320

-1.782307

0.4362574

-3.324236

-0.7174399

4.2

Divorce Rate The divorce rate, denoted dr, comes from data from the American Community Survey, Table S0201

from each respective year.17 Responses to the ACS are legally required. I define the divorce rate by:

dr =

Number of people divorced × 100 Number of people (formerly) married

(4)

Note how my divorce rate is in percentage terms.

ldr = ln(

dr ) 100

(5)

Variable

Label

Obs

Mean

Standard Deviation

Minimum

Maximum

Divorce Rate (%)

dr

320

15.71231

1.86133

11.34752

20.558

Natual Log Divorce Rate

ldr

320

-1.857904

0.1209054

-2.176171

-1.58192

4.3

Employment munemp is the male non-institutional civilian unemployment rate in percentage terms. The data

comes from the Bureau of Labor Statistics, “Employment status of the civilian noninstitutional population in states by sex, race, Hispanic or Latino ethnicity, marital status, and detailed age” from each respective year.

18

16 http://www.cdc.gov/reproductivehealth/data

stats/Abortion.htm

17 http://factfinder2.census.gov/faces/nav/jsf/pages/index.xhtml. 18 http://www.bls.gov/lau/#ex14

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Domininkas Mockus

The Effect of Family Life

4

DATA

Variable

Label

Obs

Mean

Standard Deviation

Minimum

Maximum

Male Unemployment Rate (%)

munemp

320

6.8

2.7884

2.4

15.8

4.4

Education pmbach is the percentage of the total population that is male and has a bachelor’s degree of hight.

I created the variable from data from the American Community Survey, Table S0201 from each respective year.19

pmbach = % of bachelor’s or higher that are male × % of population that has bachelor’s or higher

(6)

Variable

Label

Obs

Mean

Standard Deviation

Minimum

Maximum

Male, Bachelor’s or higher (%)

pmbach

320

7.48892

2.660336

2.8545

15.5618

4.5

Household Characteristics pchild is the percent of the population that is living as children at home. The data comes from the

American Community Survey, Table S0201 from each respective year.20 Variable

Label

Obs

Mean

Standard Deviation

Minimum

Maximum

Children Living at Home (%)

pchild

320

29.695

2.03728

25.1

37.4

4.6

Race prace is a percentage of the total population. I created the variable from data from the American

Community Survey, Table DP05 from each respective year.21 I define prace in the following way:22

prace =

Number of race Total Population

(7)

Variable

Label

Obs

Mean

Standard Deviation

Minimum

Maximum

White (%)

pwhite

320

78.96075

12.42177

24.60823

96.61027

Black (%)

plack

320

9.867618

9.308136

.3019521

37.51736

Asian (%)

pasian

320

3.35612

5.659065

0.4496684

42.04342

Hispanic or Latino (%)

phisp

320

9.329175

9.187864

0.5722591

46.73133

19 http://factfinder2.census.gov/faces/nav/jsf/pages/index.xhtml 20 http://factfinder2.census.gov/faces/nav/jsf/pages/index.xhtml 21 DP1 22 I

for 2005. http://factfinder2.census.gov/faces/nav/jsf/pages/index.xhtml only used pure races and did not consider those who were both Black and Hispanic, for example, in the numerator.

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Domininkas Mockus

4.7

The Effect of Family Life

5

RESULTS

Financial Status This data comes from the Bureau of Economic Analysis23 and the U.S. Census Bureau.24

Variable

Label

Obs

Mean

Standard Deviation

Minimum

(BEA) State-level nominal per capita income ($1)

snpci

320

38103.4

5863.921

26415

57547

(BEA) State-level PCE ($1)

sP CE

320

167359.5

158369.5

15276

794698

(USCB) State-level poverty rate (%)

spr

320

12.80969

3.296469

7.1

22.7

4.8

Age and Sex The data is a percent of the total population. The data comes from the American Community Survey,

Table S0201 from each respective year.25

Variable

Label

Obs

Mean

Standard Deviation

Minimum

Maximum

25 - 34 years of age (%)

pearlyadult

320

13.10375

0.9846399

10.9

17.3

35 - 44 years of age (%)

pmidadult

320

13.62125

1.076677

11

16

45 - 54 years of age (%)

plateadult

320

14.67781

0.9540418

10.8

17.3

More than 65 years of age (%)

pretired

320

12.91125

1.655162

6.6

16.4

Median age

mage

320

37.17125

2.218641

28.4

43.2

Male (%)

pmale

320

49.33563

0.75116

48.1

52.3

5

Results As expected, looking across figures 1, 2, and 3 (on pages 8, 9, and 11), I see that I get better at

predicting the abortion ratio. However, looking at the corresponding models in table 1, I see that the divorce rate is only a statistically insignificant factor (although the variables are jointly significant; see table 1 on page 10). I have not been able to show that divorces cause abortions. I have shown that I can predict the abortion ratio, especially in model 6. This means that the abortion ratio is not completely random but is influenced; however, it seems that no single factor can be singled out as a cause.26 I take model 4 to be the best model since it uses all the data points and since it is the most convenient to interpret, passes RESET and Woolridge’s test for serial correlation, and it is only marginally different 23 http://www.bea.gov/regional/ 24 http://www.census.gov/hhes/www/poverty/data/historical/hstpov21.xls 25 http://factfinder2.census.gov/faces/nav/jsf/pages/index.xhtml 26 I

only considered the divorce rate, but perhaps another measure would do better.

7

Maximu

Domininkas Mockus

The Effect of Family Life

5

RESULTS

statistically from model 3. Model 4 tells me that, cet par, if the divorce rate were to increase by 1%, the abortion ratio is expected to increase by 0.05%. However, this result is statistically (and economically) insignificant; I cannot support the claim that the divorce rate causes a change in the abortion ratio (nor can anyone refute the claim that the divorce rate does not cause a change in the abortion ratio). However, since all the variables were jointly significant, it seems that everything together is important, but not one thing by itself.

Figure 1: Actual vs. Predicted Values, Model 4

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Domininkas Mockus

The Effect of Family Life

Figure 2: Actual vs. Predicted Values, Model 5

9

5

RESULTS

Domininkas Mockus

VARIABLES dr

The Effect of Family Life (1) ar

(2) ar

(3) lar

0.534 (2.442)

ldr snpci sPCE spr pearlyadult pmidadult plateadult pretired mage pmale pchild pmbach munemp pwhite pblack pasian phisp Constant

Observations R-squared F-Test (p) RESET (p) Woolridge (p) Davidson-Mackinnon (p) Number of id

-6.36e-06 (0.00139) -8.96e-05 (9.33e-05) 0.295 (0.575) -3.265 (3.740) 9.234* (5.489) 11.71* (6.391) 3.507 (8.849) -8.940 (5.444) -7.095 (6.792) 4.606* (2.619) 4.678 (4.157) -0.177 (1.252) 1.531 (1.421) 8.563* (4.969) -0.754 (3.880) -10.62*** (3.786) 282.7 (410.9)

5

RESULTS

(4) lar

(5) lar

(6) lar

0.00914 (0.275) -1.13e-05 (9.75e-06) 7.61e-08 (6.48e-07) 0.00489 (0.00401) -0.00249 (0.0261) 0.0680* (0.0383) 0.0470 (0.0447) 0.0438 (0.0618) -0.0440 (0.0380) -0.0105 (0.0473) 0.0149 (0.0184) 0.0459 (0.0289) -0.00550 (0.00873) 0.00250 (0.00990) 0.0655* (0.0347) 0.00112 (0.0271) -0.0568** (0.0264) -2.569 (3.039)

-0.00296 (0.286) -1.13e-05 (1.01e-05) -8.59e-08 (6.80e-07) 0.00534 (0.00426) 0.00257 (0.0272) 0.0678* (0.0402) 0.0462 (0.0465) 0.0576 (0.0650) -0.0419 (0.0397) -0.00569 (0.0500) 0.0190 (0.0195) 0.0406 (0.0302) -0.00764 (0.00909) 0.00854 (0.0116) 0.0699* (0.0365) 0.00503 (0.0279) -0.0499* (0.0294) -3.778 (3.268)

0.0289 (0.305) -3.83e-06 (1.07e-05) 2.38e-07 (8.82e-07) 0.00644 (0.00480) 0.000991 (0.0289) 0.0384 (0.0435) -0.00191 (0.0511) 0.0473 (0.0712) 0.00126 (0.0435) 0.00200 (0.0537) 0.0363* (0.0207) 0.0479 (0.0324) -0.00731 (0.0101) 0.00430 (0.0158) 0.0226 (0.0450) 0.00233 (0.0292) -0.0127 (0.0327) -4.749 (3.553)

306 0.139 0.0312 0.1892 0.1273

264 0.165 0.0229 0.0082 0.1527

45

38

-0.00225 (0.0170) 18.92 (39.38) -9.29e-05 (0.00140) -8.70e-05 (9.28e-05) 0.299 (0.575) -3.298 (3.739) 9.153* (5.490) 11.39* (6.414) 3.686 (8.854) -9.119* (5.441) -7.068 (6.781) 4.401* (2.632) 4.734 (4.139) -0.160 (1.251) 1.513 (1.419) 8.562* (4.968) -0.868 (3.879) -10.55*** (3.787) 345.6 (435.6)

-1.11e-05 (9.66e-06) 5.91e-08 (6.51e-07) 0.00487 (0.00401) -0.00241 (0.0261) 0.0683* (0.0383) 0.0480 (0.0446) 0.0433 (0.0617) -0.0432 (0.0380) -0.0102 (0.0474) 0.0158 (0.0183) 0.0453 (0.0290) -0.00555 (0.00873) 0.00262 (0.00991) 0.0655* (0.0347) 0.00161 (0.0271) -0.0570** (0.0264) -2.649 (2.865)

320 320 320 0.224 0.225 0.147 0.0000 0.0000 0.0111 0.0937 0.0930 0.2327 0.0297 0.0289 0.1325 0.156 0.176 0.385 47 47 47 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

320 0.147 0.0111 0.2490 0.1291 0.380 47

Table 1: Results of various models (fixed-effects estimation, time dummies not shown).

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Domininkas Mockus

The Effect of Family Life

REFERENCES

Figure 3: Actual vs. Predicted Values, Model 6

6

Conclusion

I looked for causation between the abortion ratio and the divorce rate, but I have not found that the divorce rate has a statistically or economically significant effect on the abortion ratio. While this is not what I expected to find, we must remember that there are a multitude of factors that constitute a family, and using the divorce rate is using only one (and extreme) measure of the degradation of the family. Since so many things constitute a family, most notably the level of love between the parents, I should not be surprised that it is near impossible to single out a cause of abortion. Everything together is important, but not one thing by itself.

References [1] D. M. Drukker. Testing for serial correlation in linear panel-data models. Stata Journal, 3(2):168–177(10), 2003. [2] Jeffrey M. Woolridge. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press, 2002.

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