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International Encyclopedia of the

Social Sciences, 2nd edition

International Encyclopedia of the

Social Sciences, 2nd edition

VOLUME 2

COHABITATION–ETHICS IN EXPERIMENTATION

William A. Darity Jr.

EDITOR IN CHIEF

COGNITIVE

DISTORTIONS

SEE Psychotherapy.

problematic for female cohabitants. This compares to

500,000 cohabiting couples in 1970.

This growing popularity of cohabitation has resulted

in a concern among some observers that the practice pre-

sents a challenge to marriage as a method of coupling.

They argue that marriage is being redefined as one of sev-

eral choices. The literature suggests that for older cohabi-

tants and for African American couples this lifestyle

choice does represent an alternative to marriage. For most

Americans, however, marriage remains the primary choice

for coupling. Cohabitation is increasingly viewed as a

transitional stage between single life and marriage, rather

than as an alternative to marriage. Unlike in the United

States, however, cohabitation is a significant alternative to

marriage for young Scandinavian couples. In addition,

increasing economic inequality in the United States is

decreasing the opportunities for marriage among less-

affluent Americans.

The most commonly cited reasons for moving in

together are romance, convenience, the need for housing,

and the chance to save money. How well do cohabitants

get along with each other? Recent research has found that

cohabiting couples are significantly less satisfied in their

unions than those who are legally married. This is due, in

part, to the fact that cohabiting couples often have more

precarious economic circumstances than do married cou-

ples. In addition, the presence of children, which reduces

satisfaction levels for both married and cohabiting cou-

ples, has a more profound effect on nonmarital unions.

This is significant in that children are present for 40 per-

cent of cohabiting couples. Further, it is widely assumed

that the outcomes are worse for children raised by cohab-

COGNITIVE MATRIX

SEE Rituals.

COHABITATION

Cohabitation is defined as a situation in which opposite-

sex couples live together outside of marriage. Much of the

literature on cohabitation is derived from research find-

ings by sociologists and psychologists, which places this

literature in a central position within the social sciences.

This entry provides a brief discussion of who cohabits,

why people choose to cohabit, and the consequences of

cohabitation for couples, children, and society.

Cohabitation has become increasingly popular since

the 1960s, with the majority of young adults in the

United States experiencing cohabitation. For most cou-

ples, this is a relatively short-term experience, with only

one-third of American couples cohabiting for at least two

years and only 10 percent doing so for at least five years.

About 60 percent of these unions eventually result in mar-

riage. In 2007 nearly five million opposite-sex couples in

the United States were living together outside of marriage,

largely without legal protections, which is particularly

INTERNATIONAL ENCYCLOPEDIA OF THE SOCIAL SCIENCES, 2ND EDITION

Cohort Effects

iting couples, as opposed to children raised by married

parents.

Lastly, does living with one’s partner prior to marriage

increase the likelihood of success after marriage? Couples

who move in together before marriage have up to two

times the odds of divorce compared to those couples who

do not live together prior to marriage (Blackwell and

Lichter 2000). Some argue that living together creates

social pressure to get married, which can contribute to

poor mate selection.

SEE ALSO Family; Marriage

to be integrated of order one [denoted I(1)]. Growth rates

of these series do not tend to drift, which is consistent

with the growth rates being nonintegrated, I.E., inte-

grated of order zero [denoted I(0)]. Moreover, efficient-

market theories in economics and finance suggest that

asset and commodity prices follow a random walk, which

is the simplest I(1) process.

Cointegration occurs when a relationship ties

together nonstationary economic time series such that a

combination of those time series is I(0). The concepts of

integration and cointegration are intrinsically statistical in

nature. Cointegration formalizes, in statistical terms, the

property of a long-run relation between integrated eco-

nomic variables.

BIBLIOGRAPHY

Blackwell, Debra L., and Daniel T. Lichter. 2000. Mate

Selection among Married and Cohabiting Couples. Journal of

Family Issues 21 (3): 275–302.

Willetts, Marion C. 2006. Union Quality Comparisons Between

Long-Term Heterosexual Cohabitation and Legal Marriage.

Journal of Family Issues 27 (1): 110–127.

SOME ECONOMIC IMPLICATIONS

OF COINTEGRATION

While cointegration is a statistical concept, it has eco-

nomic implications. For example, it plays important roles

in five aspects of economics: (1) long-run relations, (2)

agent optimization, (3) the problem of nonsense regres-

sions, (4) equilibrium correction (or error correction)

models (ECMs), and (5) economic forecasting.

First, cointegration embeds the economic notion of a

long-run relationship between economic variables in a sta-

tistical model of those variables. If a long-run relation

exists, then the variables are cointegrated.

Second, market forces or optimizing behavior often

provide an economic rationale for cointegration. For

instance, consumers’ expenditure and income may be

cointegrated because of economic agents’ budget con-

straints or because of intertemporal optimization plans for

lifetime saving.

Third, the statistical theory of unit-root processes

aids inference about the empirical existence of cointegra-

tion. Econometric theory historically relied on the

assumption of stationary data even though many observed

economic time series were trending and nonstationary.

Cointegration explicitly allows for nonstationarity, thus

providing a sounder basis for empirical inference.

Cointegration also clarifies the problem of nonsense

regressions, in which intrinsically unrelated nonstationary

time series are highly correlated with each other.

Fourth, cointegration implies, and is implied by, the

existence of an equilibrium correction representation of

the relevant variables. Cointegration thus solidifies the

statistical and economic bases for the empirically success-

ful class of equilibrium correction models, in which past

disequilibria in levels have an effect on current changes in

the variables. Through ECMs, cointegration provides a

systematic framework for jointly analyzing short-run (e.g.,

cyclical) and long-run properties. This framework also

resolves the debate on whether to model data in levels or

Paul R. Newcomb

COHORT EFFECTS

SEE Period Effects.

COINCIDENT

INDICATORS

SEE Lagging, Leading, and Coincident Indicators.

COINTEGRATION

Time-series data consist of multiple observations of firms,

households, persons, or other entities over several time

periods. Many economic time series have empirical distri-

butions that are nonconstant over time, with changing

means and variances, making these series nonstationary.

Stochastic trends occur when there are persistent long-

term movements in time series data; and such trends rep-

resent a major source of nonstationarity, causing variables

to drift over time. Series with stochastic trends are thus

called “integrated” or “unit-root” processes.

In 1982, Charles Nelson and Charles Plosser showed

that, empirically, many macroeconomic time series appear

INTERNATIONAL ENCYCLOPEDIA OF THE SOCIAL SCIENCES, 2ND EDITION

Cointegration

in differences, with classical econometric models and

George Box and Gwilym Jenkins’s time-series models

both being special cases of ECMs.

Fifth, optimal forecasts of cointegrated variables are

themselves cointegrated. Hence, the existence of cointe-

gration may improve the long-term forecasting of eco-

nomic time series.

unbalanced regressions involving variables of different

orders of integration.

Economic theory rarely specifies orders of integration

for variables, so a practitioner must analyze the data for

both integration and cointegration. While the presence of

unit roots complicates inference because some associated

limiting distributions are nonstandard, critical values have

been tabulated for many common cases. David Dickey

and Wayne Fuller calculated critical values of tests for unit

roots in univariate processes, and many robust unit-root

tests have subsequently been developed.

Numerous cointegration tests have also been

designed. In 1987, Engle and Granger proposed a single-

equation approach that is intuitive and easy to implement,

though it includes nuisance parameters in inference and

may lack power (see Hendry 1986). A test of cointegra-

tion is also feasible in the corresponding ECM (see Neil

Ericsson and James MacKinnon 2002).

Søren Johansen has provided a system-based approach

in which cointegration relations are estimated via maxi-

mum likelihood in a vector autoregression (VAR).

Johansen’s test statistics for cointegration generalize the

Dickey-Fuller statistic to the multivariate context. Several

authors have tabulated critical values, which are also

embodied in software such as Cats for Rats and PcGive. In

Johansen’s framework, hypotheses about cointegration

properties are also testable. For instance, testing the long-

run homogeneity of money with respect to prices is equiv-

alent to testing whether the logs of money and prices are

cointegrated with a unit coefficient. Other hypotheses,

such as weak exogeneity, can be tested in Johansen’s frame-

work as well. Weak exogeneity is satisfied if the cointegrat-

ing vector entering the conditional model does not appear

in the marginal model of the conditioning variables. Under

weak exogeneity, inference on those parameters from the

conditional model alone is without loss of information rel-

ative to inference in the complete system.

In summary, cointegration and equilibrium correc-

tion help us understand short-run and long-run proper-

ties of economic data, and they provide a framework for

testing economic hypotheses about growth and fluctua-

tions. At the outset of an empirical investigation, eco-

nomic time series should be analyzed for integration and

cointegration, and tests are readily available to do so. Such

analyses can aid in the interpretation of subsequent results

and may suggest possible modeling strategies and specifi-

cations that are consistent with the data, while also reduc-

ing the risk of spurious regressions.

HISTORY

The history of cointegration was examined by David

Hendry in “The Nobel Memorial Prize for Clive W. J.

Granger” (2004). Hendry and Mary Morgan, in The

Foundations of Econometric Analysis (1995), highlight the

following events in that history. In 1901, R. H. Hooker

illustrated and analyzed the difficulties attendant to non-

stationarity, which he viewed as “common trends.” In

1926, G. Udny Yule showed that I(1) and I(2) observa-

tions would generate “nonsense correlations”; for exam-

ple, high correlations lacking causal explanation, such as

between church marriages and mortality rates. In 1974,

Clive Granger and Paul Newbold reemphasized the dan-

gers of nonsense correlations, and Peter Phillips presented

a formal analysis in 1986, which he updated in 1998.

Klein’s great ratios of economics (e.g., of consumption to

income) suggested that variables’ levels can be closely

related. J. Denis Sargan established the link between

static-equilibrium economic theory and ECMs in 1964.

In the 1980s, Granger and Robert Engle developed coin-

tegration analysis as such.

MODEL SPECIFICATION

In 1987, Engle and Granger established an isomorphism

between cointegration and ECMs. Cointegration entails,

and is entailed by, an ECM, which explicitly embeds a

steady-state solution for its variables, while also allowing

them to deviate from that steady state in the short run.

In a nonstochastic steady state, an equilibrium relation

would typically be motivated by economic theory. Hence,

economic hypotheses are testable in a cointegration

framework. In empirical work, conditional ECMs have

been popular and may be interpretable as agents’ contin-

gent plans. Applications include wages and prices, con-

sumers’ expenditure, and money demand.

TESTING FOR INTEGRATION AND

COINTEGRATION

Cointegration makes the economic concept of equilib-

rium operational; that is, data allow tests of whether a

long-run relation holds. With suitable tests, asymptoti-

cally correct inferences can be obtained. In addition, spu-

rious regressions can be detected and avoided, as can

BIBLIOGRAPHY

Banerjee, Anindya, Juan J. Dolado, John W. Galbraith, and

David F. Hendry. 1993. Co-integration, Error Correction, and

INTERNATIONAL ENCYCLOPEDIA OF THE SOCIAL SCIENCES, 2ND EDITION

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