Silver in Gray Divorces

"Marriage is among other things 'a shared enterprise or joint undertaking in the nature of a

partnership to which both spouses contribute—directly and indirectly, financially and non-

financially—the fruits of which are distributable at divorce.'"i

Abstract

The term ‘Gray divorce’ was coined by AARP in 2004ii to describe the phenomenon of

increasing rate of divorce among older couples in long lasting marriages, often involving very

substantial marital estates. Gray divorces are trending upwards. While the overall divorce rate in

the United States has decreased since 1990, it has doubled for those over age 50iii. Aging,

affluent, divorcing couples present unique challenges to the courts dealing with equitable

distribution issues. These marital estates are more likely to contain business interests that were

acquired prior to the marriage or inherited by one of the spouses. A core issue in such cases is the

appropriation of the growth in business value during the marriage among active (spousal effort),

and passive (economic environment) components. This paper presents an empirical estimation

method for identifying significant economic environmental factors and their relative contribution

to growth in revenues for selected product categories. The application of this method is

illustrated over the period 1992-2014 for which quarterly data were available as of the date of

publication.

Gray divorces occur at the confluence of three factors, age, wealth, and likelihood of divorce.

Age displays a significant positive relationship with amount of wealth in the household as well

as with the likelihood of divorce. Households acquire wealth primarily from two sources: they

save part of their earned income, and they receive intergenerational transfers through by lifetime

gifts or inheritance. Wealth accumulation from accumulated savings is also called lifecycle

saving. Lifecycle savings accumulate during working age and are at least partially consumed

during retirement. Household wealth data indicate that individuals save at an increasing rate

during their working lives, accumulating wealth which increases with age, reaching a hump

between 55 to 65 years of age. Median wealth increases rapidly during the later earning years

(54-64 years of age), and then stabilizes. A wealth draw down ensues, and while the accumulated

earnings increase slowly with investment returns, consumption increases modestly with inflation.

Any unspent part of this accumulated wealth passes to next generation as inheritance.

Table 1. Household Wealth and Age

A strong positive relationship between wealth accumulation and business ownership has also

been observed in economic data. For example, SBA data show that between 1998 and 2007,

median wealth for households owning a business more than tripled, growing by 214 percent

while the mean wealth for these households increased by 63.4 percent. Over the same time

wealth gains for households not owning a business were much smaller, with a median gain of

19.6 percent and a mean of 39.9 percent.iv

Table 2. Household Wealth and Business Ownership

HOUSEHOLD NET WORTH

Percentage of

households owning

a business

Mean

Business

Equity

Mean Net

Worth

$25,000 to $49,999 11.0 14,215 36,878

$50,000 to $99,999 11.2 22,899 73,099

$100,000 to $249,999 15.1 39,577 164,345

$250,000 to $499,999 18.5 87,024 354,668

$500,000 and over 28.7 548,404 1,920,956

Married Couple Households

Ages

Less than 35

years 35 to 54 years 55 to 64 years

65 years and

over

Median Household Net Worth 19,526 116,170 239,847 284,790

Wealth growth 495% 1128% 1359%

The second significant source of wealth accumulation is by bequest from one generation to the

next, by lifetime gifts or by inheritance at demise. Wealthier households tend to accumulate

larger quantity of wealth in their lifetime, and also inherit larger endowments of wealth by

bequest. This creates a dynamic relationship where the amount of household wealth increase

with age, and further, the proportion of household wealth comprising substantially of inherited

wealth, increases with the size of the household wealth. Intergenerational transfers and

accumulation of wealth have been studied extensively in economic literature. It has been

estimated that a substantial portion of accumulated household net worth, upwards of 30%, can be

attributed to inherited wealth. v

The third and critical factor is the likelihood of divorce. Demographic data suggest that by the

25th anniversary of marriage slightly more than half of the first marriages survive intact. More

than half of total divorces occur before the 10th anniversary, before substantial wealth

accumulation from earnings starts. However, as marriages mature, substantial assets are

accumulated from spousal earnings and/or by appreciation of the inheritance and assets owned

before marriage. As marital estates get larger, they are more likely to contain inherited wealth

and business interests acquired before marriage.

Table3. Household Age and Divorce

Recently granted Billion dollar divorce of Susan and Harold Hamm (2014), provides a classic

case study of Grey divorce. Susan Hamm was awarded one of the largest divorce settlements in

Married Couple Households Ages

Less than 35

years

Between 35 to 54

years

Between 55 to 64

years 65 years and over

Marriage Anniversary Percentage Divorced

5th 10.4 12.3 9.4 11.8

10th X 24.6 25.7 26.6

15th X 33.4 34.8 36.3

20th X X 40 41.3

25th X X X 45.6

US history, valued at $995.5 Million. While large in absolute terms, this award amounted to a

small fraction of the marital estate. A core issue in this case as in other similar ‘Gray divorce’

cases is the appropriation of the growth in business value during the marriage among active

(spousal effort), and passive (economic environment) components.

By way of introduction, here are some facts regarding this case. Continental Resources, initially

incorporated as Shelly Dean Oil Company by Harold Hamm in 1967, was valued at $50 Million

at the time of marriage (1988), went public at $ four Billion in 2007, increased in value to $13

Billion by 2012, the year the divorce was filed, ballooned to $20 Billion in 2013, and deflated

back to $14 Billion in 2014, by the time the divorce was granted. The stock has continued its

downward spiral since then, in line with the global energy prices. The 68 percent stake in

Continental Resources, owned by Harold Hamm, appreciated from $34 Million to $ 9.5 Billion

between the time of marriage and the divorce. Susan Hamm was awarded $975 Million, roughly

10% of the appreciation, effectively ruling that 80% of the appreciation was passive. This case is

a perfect example of ‘Gray divorce’, and powerfully illustrates the importance of correctly and

supportably identifying the passive factors and their impact on the value of the business during

the time of the marriage.

Divorce laws and their interpretations differ substantially across the states with varying

degrees of emphasis on the separation of marital and non-marital portions of the value of

business interests. However, in states that allow equitable distribution, two important

valuation issues arise when the closely held business needs to be valued in the course of a

divorce action. First is to identify the separate property component of the business, and,

second, to estimate the passive increase in value of this separate property during marriage.

In general, there appears to be a broad agreement that separate property, not subject to

distribution in divorce is

(1) Property acquired by a person before marriage; or

(2) Property acquired by a person during marriage, but excluded from treatment as marital

property by a valid agreement of the parties entered into before or during the marriage; or

(3) Property acquired by a party during marriage by gift, bequest, devise, descent or

distribution; and

(4) Any increase in the value of separate property as defined in subdivision

(1), (2), or (3) above, which is due to inflation or to a change in market value resulting

from conditions outside the control of the parties.

Once the subject interest has been identified as separate property not subject to distribution in

divorce, the following five-step analysis is needed to make a determination of the passive

appreciation component:

(1) Establish a value of the non-marital property, before it became subject to the passive

appreciation analysis ( e.g. at the date of marriage or acquisition during marriage by

gift, bequest, devise, descent or distribution);

(2) Assess the property's value at the commencement of the action, and compare this value

with the value on the date (s) it became subject to the appreciation analysis. The

difference between the starting and ending value of the separate property is the total

amount of appreciation.

(3) Identify the causal factors impacting the change in value of the separate property

during the marriage that are outside the control of the parties

(4) Measure the partial and aggregate impact of the identified causal factors, individually

and collectively, on the change in value of the separate property during the period of

marriage.

(5) Identify the proportion of total appreciation attributable to passive factors.

The first three parts of this analysis are primarily an exercise in fact finding, and, valuation

theories used for valuing the business at different points in time are well developed. However,

the last two steps are relatively complex. One of the most troubling issues involving the active

and passive appreciation doctrine is finding a viable “method” or “formula” for determining

the portion of appreciation attributable to spousal efforts (active) and the portion attributable

to third-party or market forces (Passive)vi. This paper presents a viable method for identifying

the passive component of change in business value during the period of analysis.

Economists have been studying determinants of consumer demand extensively since Marshall’s

seminal work on elasticity of demandvii. A very rich theoretical and empirical body of literature,

describing rational consumer behavior in allocating current and anticipated income to

consumption choices has evolved over time. We can apply this prior framework to model the

impact of economic factors impacting the demand for a business’ product/service in the market

place. Managers of a business, under most circumstances, have to take the economic

environment as a given and are unlikely to be able to significantly change these variables

impacting the demand for their products. Therefore, the impact of these economic variables can

be used to measure the passive component of the change in business revenues attributable to the

changes in economic environment over the period of estimation. Revenues are the lifeblood of

any business and depend on consumer demand for the product / service offered by the business.

The underlying logical nexus relating the economic factors to value of the business can be

summarized as follows.

Table 4. Logical Nexus formulation

1. Consumption follows consumers.

2. Consumption is funded by current and anticipated income (including consumer credit).

3. Desired Consumption creates demand.

4. Demand generates revenues.

5. Revenues generate value.

Correlation and Causality

A core issue in empirical analysis is identifying causal relationships before their impact can be

evaluated. It is important to make a clear distinction between correlation and causality as we

start our empirical analysis. The adage ‘correlation is not causation’ is often tossed as a Hail

Mary pass, obscuring the fact that correlation is a necessary (but not sufficient) condition for

causation. Correlation suggests causation, but any claim of causation relies on one or more

premise(s) that flow from the underlying logical nexus. While correlation may exist without a

causal relationship, it is highly unlikely that causation would exist without correlation.

Empirically confirmed correlation is a necessary but not sufficient condition for causality.

However, once correlation is confirmed, we can empirically test for causality based on the

underlying logical nexus.

Correlation can be formally defined as an observed co-movement between phenomena that tend

to vary, to occur together in a way not expected on the basis of chance alone. While correlation

can provide powerful evidence for a cause-and-effect relationship between an economic factor

and various outcomes, further analysis is needed before concluding that one factor causes a

particular outcome. Causal pathway needs to be established theoretically and tested empirically.

Correlation, by definition, is bi-directional. If x and y are positively correlated higher values of y

are observed with higher values of x. Conversely if x and y are negatively correlated higher

values of y are observed with lower values of x. Observation of a statistically significant

correlation between x and y may suggest three potential causal pathways.

1. Changes in x may be causing changes in y

2. Changes in y may be causing changes in x

3. Changes in a third factor z may be causing changes in both x and

Causation can be formally defined as a relationship between two events or states such that one

produces or brings about the other; where one is the cause and the other its effect. Causality is

unidirectional while correlation is bidirectional. Changes in the causal factor result in changes in

the impacted factor. For example, an observed increase in shoe sales and population in an area

indicates a positive correlation between population and shoe sales. It is unlikely that availability

of more shoes results in grater fertility, a more plausible explanation is that more individuals

need more shoes. Causality cannot be defined in terms of statistical associations alone but needs

to be supported by an underlying logical nexus. Causality can be inferred theoretically and

confirmed empirically using a statistical test of causality. Hill (1965)viii identified a set of

criteria, listed below, that must be met for a reliable finding of causation. While these criteria

were initially suggested for use in epidemiological study, they provide valuable guidance and

have been adopted in a broad range of disciplines, such as economics, social, and behavioral

sciences.

Table 5. Hill’s Criteria for Causation

1. Temporal: Cause always precedes the outcome

2. Strength: The stronger the association, the more likely it is that the relation of "A" to "B" is

causal.

3. Consistency: if a relationship is causal, we would expect to find it consistently among

different populations and different time periods.

4. Plausibility: There needs to be some theoretical basis for positing an association between one

phenomenon and another.

5. Coherence: The association should be compatible with existing theory and knowledge.

The first two criteria, temporal order, in cause preceding the impact, and the statistical strength

of the causation can be empirically tested using a Causality Test proposed by Granger (1969). ix

The Granger causality test confirms that the cause happens prior to its effect, and the causal

factor provides unique information about the future values of its effect. The underlying logical

nexus provides the needed validation for plausibility and coherence criteria. Testing across time

periods and population groups/products allows us to validate the consistency criterion.

Data and Methodology

In the following section we present an empirical analysis of the revenue impact of economic

environmental changes on product sales over the period 1992-2014 for which quarterly economic

data were available as of the date of publication. Economic data were obtained from the Bureau

of Economic Analysis, U.S. Census, and the Federal Reserve Bank of St. Louis.

This period is interesting as a combination of modest inflation and a steep drop in cost of

borrowing resulted in consumer spending outpacing the rise in personal income. The aggregate

debt service burden fell due to the fall in mortgage servicing costs even as the increased

consumer debt service burden increased. Consumer credit outstanding increased sharply in

absolute terms, and as share of the total economy. Total population increased and the level of

unemployment fell. These stimulating factors resulted in an increased level of consumption

fueled by cheap credit.

Table 6. Economic Environment 1992-2014

Per Capita Measures Growth

Changes in Economy Growth

Personal Income 126%

Total Population 25%

Disposable Personal Income 123%

Unemployment -23%

Personal Consumption

Expenditure 134%

Inflation (CPI) 71%

Personal Consumption Non-

Durables 106%

Inflation ( Personal

Consumption) 54%

Consumer Credit Outstanding 230%

Consumer Credit as % of GDP 50%

Consumer Debt Service as % of

Disposable Personal Income 8%

Bank Prime Rate -50%

Mortgage Debt Service as % of

Disposable Personal Income -23%

New car Loan 48 month Interest

rate -59%

Total Debt Service as % of

Disposable Personal Income -9%

Credit Card Interest rate -34%

We start our analysis by identifying the theoretical nexus for causal relationships between the

economic environmental variables and the product sales. This nexus can be based on factors

identified by prior studies, industry publications, management interviews, and other appropriate

sources. Once the likely causal factors are identified, we calculate Pearson correlation

coefficients between the level of reported quarterly sales for the product and the economic

variable(s) being investigated. These coefficients provide a starting point for our empirical

work. After establishing that a significant relationship exists between the product sales and an

economic variable, we have to ensure that there is a cause and effect relationship between our

variable of interest and the product sales. We then confirm theoretically valid causal

relationship empirically by using a series of Granger-Causality Wald Tests. This test allows us to

confirm that the economic factor A influences the sales of product B in a statistically significant

manner, while sales of product B do not impact the economic factor A in a significant manner. If

the economic factor A and sales of product B impact each other in a circular relationship, we

drop factor A from our list of causal variables. We also test the explanatory variable for cross

impact. For example, if economic factors A1 and A2 both influence sales of product B, and

factor A1 is influenced by A2, then A2 is used as a causal factor and A1 is dropped.

Once one or more factors have been confirmed as causal factors, we need to test for / deal with

the issue of multicollinearity. Economic data describe economic conditions at a point in time.

Economic environment is dynamic. As economic changes percolate through the economy,

economic measures exhibit significant correlation among themselves. This makes simultaneous

consideration of impact for multiple factors complicated. Correlated explanatory variables in a

regression can introduce multicollinearity. Presence of multicollinearity can cause individual

coefficients to change sign and become less significant as the same redundant economic

information may be showing up in two or more variables. For example, total personal income

can be decomposed in to per capita income and population. Total personal income and

population are correlated and therefore, including both in the same regression can result in

multicollinearity. In such cases, the impact of each variable, and variable combination should be

assessed separately and compared for explanatory power. The variable combination providing

the best explanatory power should be selected. Information criteria method is a measure of

goodness of fit or uncertainty for the range of values of the data. In the context of multiple linear

regression, information criteria measures the difference between a given model and the “true”

underlying model. The model providing the minimum value of this difference is ranked as the

best possible model for the given data. Akaike (1973)x introduced the concept of information

criteria as a tool for optimal model selection. We use a rigorous ranking Information criteria test

known as AIC (Akaike’s Information Criteria) test to compare possible models and pick the

model with the lowest AIC score as the true model.

After identifying and confirming a set of causal factors, we test for economic significance of the

relationship between the causal economic factors and the product sales. Partial elasticity of

impact for each of the variables included in estimation is calculated by regressing log of the

dependent variable (product sales) on the log(s) of the explanatory causal factor(s). Statistically

significant elasticity estimates can be used to measure individual and aggregate impact of

percentage changes in the economic variables on the percentage of change in sales of the

product. One of the criteria we used to establish causation was temporal order, in that the change

in causal variable precedes the change in the target variable. For example, change in income is

followed by change in consumption. Since we are dealing with data across time, we need to test

for serial correlation as the impact of a change in the causal variable percolates through across

time. Ordinary regression analysis is based on several statistical assumptions. One of these

assumption is that the residual errors are independent of each other. However, with time series

data, the ordinary regression residuals usually are correlated over time. Since the ordinary

regression residuals are not independent, they contain information that can be used to improve

the prediction of future values. We can, therefore, increase the accuracy of the estimated

elasticity by augmenting the regression model with an autoregressive model. This procedure is

often called autoregressive error correction or serial correlation correction. The elasticities

estimated after correcting for the autoregressive error are used to measure the individual and

aggregate impact of the causal economic factors on the product sales.

The last step in this analysis is to compare the aggregate change in the value of the product sales

over the period of analysis with the indicated change as a result of the changes in the causal

factors over the same period. We tabulate the changes in individual causal factor values over the

period, multiply each factor change with the estimated partial elasticity for the factor, to get the

individual impact of each of the factors. We sum these impacts to get the overall change in

product sales attributable to the changes in the causal factors. The proportion of the total change

in product sales attributable to the causal economic factors which are outside the control of the

managers of the business represents the passive component of the change in product sales.

Empirical Results

We use three products to illustrate the use of this methodology. The first product is a staple

necessity, Groceries, the second is a luxury, Jewelry, and the third is a hybrid, footwear. In each

case we find that a very substantial part of the growth in product sales is attributable to the

change in economic conditions. We would expect the passive component to be highest for

Groceries and lowest for Jewelry, with shoes falling in between. Our results follow theoretical

expectations and indicate that a substantial part of the change in revenues comes from

environmental factors.

Groceries

We find that a very significant relationship exists between the level of growth in population and

the level of inflation, and sales of Groceries. Income, interest, and debt service levels do not

appear to have a significant impact on Groceries consumption.

The regression parameters show a strong relationship. Elasticities are positive and significant,

indicating that a one percent change in population leads to a 1.2477% change in Grocery sales.

Similarly a one percent change in the level of inflation leads to a change of 0.5533% in Grocery sales.

For the period 1992-2014, we know that the population growth was 25.27%, and the level of inflation grew

by 70.87%. Multiplying each growth level by corresponding elasticity, the aggregate impact of changes in

population and inflation level is 70.74%, which accounts for 88.38% of the change in Grocery sales as

shown below.

Total Change in Grocery Sales 80.04%

Factor Elasticity Estimate

Factor Change Factor Impact

% of Total change due to Factor

(Passive Component)

% change Total Population 1.2477 25.27% 31.53% 39.39%

% Change CPI 0.5533 70.87% 39.21% 48.99%

Total 70.74% 88.38%

Autoregressive parameters assumed given

Variable DF Estimate

Standard

t Value

Approx.

Error Pr > |t|

Intercept 1 -6.9517 4.0627 -1.71 0.0906

% change Total

Population

1 1.2477 0.3743 3.33 0.0013

% Change CPI 1 0.5533 0.1409 3.93 0.0002

Grocery Sales Elasticity Estimates

Variable DF Estimate

Standard

t Value

Approx.

Error Pr > |t|

Intercept 1 -6.9517 4.0627 -1.71 0.0906

% change Total

Population

1 1.2477 0.3743 3.33 0.0013

% Change CPI 1 0.5533 0.1409 3.93 0.0002

Jewelry

We find that a very significant relationship exists between the changes in sales of Jewelry and

level of changes in disposable personal income and unemployment levels. Population, interest,

and debt service levels do not appear to have a significant impact on Jewelry purchases. The

regression parameters show a strong relationship. Elasticities are positive for disposable income

and negative for unemployment and significant, indicating that a one percent increase in

disposable income leads to a 0.6882% change in Jewelry sales. Similarly a one percent change in the

level of unemployment reduces Jewelry sales by almost 4%.

Determinants of Changes in Jewelry Sales

Variable DF Estimate Standard t Value Approx.

Error Pr > |t|

Intercept 1 3.6815 0.2399 15.35 <.0001

% Change Unemployment 1 -3.9295 0.6264 -6.27 <.0001

% Change Disposable Personal Income

1 0.6882 0.0322 21.4 <.0001

For the period 1992-2014, we know that the level of unemployment declined by 22.62%, and disposable

income grew by 178.99%. Multiplying each growth level by corresponding elasticity, the aggregate

impact of changes in unemployment and disposable income population and inflation level is 212.09%

which accounts for 56.59% of the change in Jewelry sales as shown below.

Total Change in Jewelry Sales 374.75%

Factor Elasticity Estimate

Factor Change

Factor Impact % of Total change due to

Factor

(Passive Component)

% Change Unemployment -3.9295 -22.62% 88.90% 23.72%

% Change Disposable Personal Income 0.6882 178.998% 123.19% 32.87%

Total 212.09%

56.59%

Footwear

We find that a very significant relationship exists between the changes in sales of footwear and

population, level of changes in consumer debt service burden as% of disposable personal

income, and unemployment levels. Interest rates were not found to be significant The regression

parameters show a strong relationship. Elasticities are positive for population, and negative for

debt service as % of disposable income and unemployment. All are significant, indicating that a

one percent increase in population leads to a 2.6% increase in shoe sales, an increase of 1% in

debt service burden as % of disposable personal income leads to a larger 8.4% decrease, and a

one percent increase in the level of unemployment reduces footwear sales by almost 2.4

Determinants of Footwear sales

Variable DF Estimate Standard t Value Approx.

Error Pr > |t|

Intercept 1 -23.1832 1.3778 -16.83 <.0001

Population 1 2.5847 0.1126 22.95 <.0001

Unemployment 1 -2.4147 0.5926 -4.07 0.0001

Consumer Debt Service Burden as % of Disposable Personal Income

1 -8.3968 1.5857 -5.3 <.0001

Total Change in Footwear Sales 76.70%

Factor Elasticity Estimate

Factor Change Factor Impact

% of Total change due to Factor

(Passive Component)

% change Total Population 2.5847 25% 65.31% 85.16%

% Change Unemployment -2.4147 -22.62% 54.63% 71.23%

% Change Consumer Debt Service Burden as part of Disposable Personal Income

-8.3968 8.28% -69.51% -90.64%

Total 50.43% 65.75%

Conclusion and suggestions for future research

This paper presents an initial exploration of economic environment determinants of business

performance. We illustrate that passive component of business performance is very significant

and needs to be accounted for when attributing any growth in business value between active and

passive components. The accelerating trend in Gray divorces, which are highly likely to involve

marital estates containing separate property and its appreciation and need to be assessed for

division, makes this a very important issue for valuation and legal communities.

i J. Gregory, The Law of Equitable Distribution (1989) § 1.03 pp. 1-6.

ii The Divorce Experience: A Study of Divorce at Midlife and Beyond, AARP, May 2004

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2010 Susan L. Brown and I-Fen Lin Journal of Gerontology B Psychology Sci Soc Sci. 2012

Nov; 67(6): 731–741.

iv Income and Wealth: How Did Households Owning Small Businesses Fare from 1998 to 2007

by George W. Haynes, Ph.D. Montana State University Bozeman, MT 59717 Small Business

Administration, Office of Advocacy, Release Date: January 2010

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Kotlikoff Yale University Lawrence H. Summers Massachusetts Institute of Technology,

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vi Deborah H. Bell, "Equitable Distribution: Implementing the Marital Partnership Theory

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vii Marshall, Alfred BOOK III, CHAPTER VI, Principles of Economics, 8th edition 1920

viii Austin Bradford Hill, “The Environment and Disease: Association or Causation?,”

Proceedings of the Royal Society of Medicine, 58 (1965): 295-300.

ix Granger, C. W. J. (1969). "Investigating Causal Relations by Econometric Models and Cross-

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