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An Optimal Statistical Model for Extrapolation of the Maryland Child Support Guidelines

May 15, 2012, 03:05:00 PM
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An Optimal Statistical Modelfor Extrapolation of the Maryland Child Support Guidelines
by Hans R. Dutt:

I. Purpose:

The purpose of this work is to develop a statistical model which will most accurately extrapolate past the current child support guideline schedule. This statistical model should be able to predict total support necessary to raise a given number of children based on parent's combined gross income and the precision of the model should be able to be objectively defined and quantifable2. This will allow the model to objectively reflect the legislatures intent.

The objective of this analysis is not theoretical academic work, but to provide extrapolation of the child support tables which would likely reflect the intent of the legislators when developing the guidelines. The most important contribution of this work is not the fact that extrapolation tables are provided, but extrapolation tables are provided that are objective and whose accuracy is quantifiable.

In order to justify the efficacy of the model, some amount of statistical theory was required. Every effort was made to keep this to a minimum.

II. Background:

Maryland has adopted child support guidelines, in part, to streamline the determination of child support within the family court system. Maryland Family Law 12-201 states:

"...It was the intent of the legislature that the guidelines and accompanying statutory provisions limit the necessity of the court to make those findings of fact required in existing case law,..."

Examination of the guidelines reveals several intentions of the legislature:

Intention (1): Both parents are responsible for contributing to the total support (basic child support obligation, adjusted basic child support obligation) of their children and the responsibility for that support will be assigned in a manner prorated in accordance with their gross income.

Intention (2): The greater amount of gross income parents earn between them, the greater amount of total support that will be required to raise their children.

Intention (3): Although total support will generally increase as combined gross income increases, the incremental (marginal) increase in child support will decrease as combined gross income grows.

However, the Maryland Child Support Guidelines are only applicable up to $10,000 per month in combined gross income. Maryland Family Law 12-204 states:

"...If the combined adjusted actual income exceeds the highest level specified in the schedule in subsections (e) of this section [(i.e., the Maryland Child Support Guidelines)], the court may use discretion in setting the amount of child support."

In cases where the combined gross income of the parents exceeds the child support schedule, it leads parties to define what is appropriate by extrapolating on what the guidelines would have been, had the Maryland legislature decided to continue the schedule. Hence the underlying argument which these parties make is that the extrapolated amount was the intent of the legislature. However, different extrapolation techniques can emphasize intention (2) or alternatively, intention (3). Thus, the choice of extrapolation techniques can yield vastly different results.

Three major methods of extrapolation are3:

  • non statistical methods of extrapolation
  • nonlinear statistical methods
  • linear statistical methods
Non statistical techniques are deterministic models which make no reference to the underlying randomness of the data. 'Forecasts' using these techniques are simply extensions of whatever data is being estimated. The major benefit of these methods are that they are inexpensive to employ.



However depending upon the method of extrapolation, the 'forecasts' can change dramatically. Since these methods are not rooted in statistical theory, there is no way to evaluate how reasonable the extrapolations are. In business planning, this may not be a problem because a business is likely to wish to be accurate. However, in an adversarial child support dispute, each party has the incentive to extrapolate using different methods to produce results that will favor their polar opposite positions. Hence, there is no way for a decision maker can objectively evaluate which method is more correct. Thus, in the context of s disputed child support case, non statistical extrapolation methods of essentially useless tools.

Statistical methods make assumptions about the randomness of the data and can therefore make statements regarding how reliable a given estimate is. Given the assumptions, non linear statistical methods generally approximate reliability while linear statistical methods can frequently employ exact tests of reliability. Consequently, linear statistical models are superior from a position of being able to validate its underlying assumptions.

A linear technique called an ordinary least squares (OLS) regression, is frequently used by researchers because of the objectivity in which the results of the model can be evaluated.


III. Statistical Model:

The optimal predictive model for Maryland Child Support Guidelines is:

In this model Y is defined as the basic child support obligation and X is defined as the parent's combined gross income. Hence, the model is predicting the basic level of child support from the parents combined gross income. The epsilon term (E) is a random error (i.e., disturbance) term. This term will be examined to reveal how well the underlying statistical assumptions of the model are being met. As a result, it will reveal how 'good' the model is. The beta terms (b0, b1, b2, b3, b4)are parameters that are being estimated. They are designed to model intention (2) and intention (3) accurately.

The model is nonlinear in the X variables (combined gross income) in order to accurately capture the behavior of intention (2) and intention (3). However, the model is linear in parameters and thus is consistent with OLS assumptions. As a result, standard statistical tests can be used to test the validity of the model. By design, the model has a limit on what Y (total child support) can be.

This is justified, intuitively, since there is only so much income that a child reasonably requires to be properly raised. In addition, analysis of the child support tables clearly indicates a child support limit.

The model defined here is in the class of reciprocal transformation models. Other models which were tested included linear models, constant elasticity models and semi log models. Objective statistical criteria revealed that the reciprocal transformation model far exceeded the other models and was, in fact, a near perfect predictor.

Generally, a scientist can not expect to achieve such a good model when analyzing socio-economic data. However, the guidelines were developed in a systematic manner and the model essentially captures the method which was used to construct the child support schedule.


IV. Estimated Model:

Statistical regression models are generally evaluated by the following criteria. This reciprocal model discussed here greatly surpassed all other models by the following, generally accepted, criteria for evaluating statistical regression models5. (Note that the child support schedule for each number of children was estimated independently and the results were virtually identical).

How well does the variation of combined gross income explain variations in basic child support?

The adjusted R-squared of the model is generally used to examine this criteria and ranges from 0 (the model explains none of the variation) to 1 (the model explains all of the variation). The adjusted R-squared of this model was .999 which can be interpreted as the model is virtually a perfect fit. Were the parameters being estimated (i.e b0, b1, b2, b3, b4) statistically significantly different than zero?

In other words, the test is asking whether each of the estimated parameters might actually be zero (i.e., have no impact on basic child support) and the estimate is just a random value with no real stability. At the 95% level of confidence, if the t statistics are above 2 in absolute value, the parameter is significantly different from zero. All parameters are greatly above 2 which means one can have confidence that the value of the parameter is stable.

Are there patterns in the estimated disturbance terms which are indicative of violation in the underlying statistical assumptions (see footnote regarding technical assumptions) ?

The estimated epsilon term (E ) should be completely random (i.e., white noise). When this is true, it confirms that the model meets the underlying assumptions.

Analysis of the disturbance term reveals that it meets the OLS assumptions and thereby validates this model. Examination of the extrapolated tables from this model successfully predicts what Maryland would award as the basic child support obligation within a couple of dollars for under $10,000 in combined gross income. Given this, it is extremely likely that, if one extrapolates past $10,000, it would be what the legislature had intended if they had decided continue the tables.

As a result, there is a strong argument to use extrapolated figures from this model as a starting point in evaluating basic child support obligation.

Finally, it must be emphasized that the results of the model are completely verifiable by a competent external source who uses sound statistical principles as a guide.

Notes:

1 Hans Dutt is an economist with the Office of the Actuary of the Health Care Financing Administration who has conducted this research in his private capacity as a citizen. This work was conducted outside the scope of Mr. Dutt's employment. The opinions expressed within are Mr. Dutt's alone and in no way reflect that of the Health Care Financing Administration, the Department of Health and Human Services or any other part of the U.S. Government. Send any comments to: Hans R. Dutt, 7578 Rainflower Way, Columbia, MD 21046. 2 For the purposes of this study, the general term 'total support' and Maryland's term 'basic child support obligation' will be used interchangeably. In the same manner, the general term ' combined gross income' and Maryland's term 'combined adjusted actual income' will be used interchangeably as well. 3 For a more in-depth discussion on this topic, see Econometric Models and Economic Forecasts, 4th Edition, by Robert S. Pindyck and Daniel L. Rubield (Irwin-Mcgraw Hill, 1998)

4 For a discussion of efficacy of alternative model specifications, see Basic Econometrics, 2nd Edition, by Damodar N. Gujarati (McGraw-Hill(1988)).

5 Technically the standard (classical) OLS assumptions are a follows:(1) the dependent variable can be calculated as a linear function of a specific set of independent variables plus a disturbance term; (2) the expected value of the disturbance term is zero; (3) the disturbance terms have the same variance (homoskedasticity) and are uncorrelated; (4) there are more observations than the number of independent variables and there is no linear relationship between the independent variables; and (5) observations on independent variables are fixed in repeated samples. If these assumptions are violated, it is generally apparent upon examination of the disturbance term.





Extrapolated Mary1and Chi1d Support Tables

Maryland child support Guidelines
Statistical Model: Reciprocal OLS Regression Extrapolation
Schedule for 1 child


































































































































































































































































































OBS
Combined Gross Monthly Income
Maryland Basic Support Obligation
Modeled Basic Support Obligation
Percent Of Model Basic CS To Comb. Gross
Percent Of MD Basic CS To Comb. Gross

1
1000
198
198.00
19.8
19.8

2
1500
267
266.80
17.8
17.8

3
2000
332
333.96
16.7
16.6

4
2500
386
383.09
15.3
15.4

5
3000
441
438.46
14.6
14.7

6
3500
497
498.50
14.2
14.2

7
4000
557
559.23
14.0
13.9

8
4500
616
618.01
13.7
13.7

9
5000
670
673.48
13.5
13.4

10
5500
722
725.13
13.2
13.1

11
6000
774
772.86
12.9
12.9

12
6500
823
816.82
12.6
12.7

13
7000
861
857.26
12.2
12.3

14
7500
899
894.47
11.9
12.0

15
8000
929
928.74
11.6
11.6

16
8500
958
960.34
11.3
11.3

17
9000
989
989.55
11.0
11.0

18
9500
1014
1016.60
10.7
10.7

19
10000
1040
1041.69
10.4
10.4

20
10500
.
1065.02
10.1
.

21
11000
.
1086.76
9.9
.

22
11500
.
1107.05
9.6
.

23
12000
.
1126.04
9.4
.

24
12500
.
1143.82
9.2
.

25
13000
.
1160.52
8.9
.

26
13500
.
1176.22
8.7
.

27
14000
.
1191.02
8.5
.

28
14500
.
1204.97
8.3
.

29
15000
.
1218.16
8.1
.

30
16000
.
1242.46
7.8
.

31
17000
.
1264.34
7.4
.

32
18000
.
1284.14
7.1
.

33
19000
.
1302.13
6.9
.

34
20000
.
1318.56
6.6
.

35
25000
.
1382.97
5.5
.

36
3000Q
.
1427.73
4.8
.

37
40000
.
1485.77
3.7
.

38
50000
.
1521.73
3.0
.

39
75000
.
1571.05
2.1
.

40
100000
.
1596.30
1.6
.






Maryland child support Guidelines
Statistical Model: Reciprocal OLS Regression Extrapolation
Schedule for 2 children
































































































































































































































































































OBS

 Combined Gross Monthly Income Maryland Basic Support Obligation Modeled Basic Support Obligation
Percent Of Model Basic CS To Comb. Gross

Percent Of MD Basic CS To Comb. Gross

1
1000
307
307.01
30.7
30.7

2
1500
413
412.55
27.5
27.5

3
2000
515
517.66
25.9
25.8

4
2500
598
594.77
23.8
23.9

5
3000
684
681.26
22.7
22.8

6
3500
773
774.80
22.1
22.1

7
4000
867
869.25
21.7
21.7

8
4500
960
960.57
21.3
21.3

9
5000
1043
1046.71
20.9
20.9

10
5500
1123
1126.88
20.5
20.4

11
6000
1203
1200.94
20.0
20.1

12
6500
1277
1269.14
19.5
19.6

13
7000
1334
1331.86
19.0
19.1

14
7500
1391
1389.55
18.5
18.5

15
8000
1441
1442.69
18.0
18.0

16
8500
1490
1491.69
17.5
17.5

17
9000
1539
1536.98
17.1
17.1

18
9500
1577
1578.90
16.6
16.6

19
10000
1616
1617.80
16.2
16.2

20
10500
.
1653.97
15.8
.

21
11000
.
1687.66
15.3
.

22
11500
.
1719.11
14.9
.

23
12000
.
1748.52
14.6
.

24
12500
.
1776.09
14.2
.

25
13000
.
1801.97
13.9
.

26
13500
.
1826.30
13.5
.

27
14000
.
1849.22
13.2
.

28
14500
.
1870.85
12.9
.

29
15000
.
1891.28
12.6
.

30
16000
.
1928.94
12.1
.

31
17000
.
1962.85
11.5
.

32
18000
.
1993.52
11.1
.

33
19000
.
2021.40
10.6
.

34
20000
.
2046.84
10.2
.

35
25000
.
2146.64
8.6
.

36
3000Q
.
2215.97
7.4
.

37
40000
.
2305.87
5.8
.

38
50000
.
2361.58
4.7
.

39
75000
2437.97
3.3
.

40
100000
.
2477.08
2.5
.






Maryland child support Guidelines
Statistical Model: Reciprocal OLS Regression Extrapolation
Schedule for 3 children
































































































































































































































































































OBS Combined Gross Monthly Income Maryland Basic Support Obligation Modeled Basic Support Obligation Percent Of Model Basic CS To Comb. Gross

Percent Of
MD Basic CS To Comb. Gross

1
1000
332
332.07
33.2
33.2

2
1500
517
515.61
34.4
34.5

3
2000
645
650.56
32.5
32.3

4
2500
750
745.68
29.8
30.0

5
3000
857
852.62
28.4
28.6

6
3500
968
968.93
27.7
27.7

7
4000
1085
1086.83
27.2
27.1

8
4500
1201
1201.09
26.7
26.7

9
5000
1304
1309.05
26.2
26.1

10
5500
1404
1409.63
25.6
25.5

11
6000
1504
1502.63
25.0
24.6

12
6500
1597
1588.32
24.4
23.8

13
7000
1669
1667.17
23.8
23.2

14
7500
1741
1739.73
23.2
22.6

15
8000
1804
1806.58
22.6
22.0

16
8500
1866
1868.25
22.0
21.4

17
9000
1928
1925.24
21.4
20.8

18
9500
1977
1978.02
20.8
20.3

19
10000
2026
2027.00
20.3
.

20
10500
.
2072.54
19.7
.

21
11000
.
2114.98
19.2
.

22
11500
.
2154.59
18.7
.

23
12000
.
2191.65
18.3
.

24
12500
.
2226.38
17.8
.

25
13000
.
2258.99
17.4
.

26
13500
.
2289.65
17.0
.

27
14000
.
2318.54
16.6
.

28
14500
.
2345.79
16.2
.

29
15000
.
2371.54
15.8
.

30
16000
.
2419.01
15.1
.

31
17000
.
2461.74
14.5
.

32
18000
.
2500.41
13.9
.

33
19000
.
2535.56
13.3
.

34
20000
.
2567.63
12.8
.

35
25000
.
2693.47
10.8
.

36
3000Q
.
2780.91
9.3
.

37
40000
.
2894.31
7.2
.

38
50000
.
2964.59
5.9
.

39
75000
.
3060.96
4.1
.

40
100000
.
3110.31
3.1
.


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