MARRIAGE, DIVORCE, AND LEGAL CHANGE: NEW EVIDENCE FROM ENGLAND AND WALES.

BINNER, JANE M. ; DNES, ANTONY W.

In this article, we explain the evolution of divorce rates in England and Wales over the post-war period. Following the approach of the predominantly North American literature in this area, we focus on the liberalization of divorce law and socioeconomic factors as determinants of the divorce rate. In line with the development of the literature, we find that the introduction of liberalized, no-fault divorce law had a significant effect on the divorce rate in England and Wales. The finding that the law affects the divorce rate is consistent with the view that marriage is characterized by indivisibilities that inhibit Coasian bargaining. (JEL C32, J12, K19)

I. INTRODUCTION

Our study of divorce rates in England and Wales is based on time-series analysis. An advantage of examining the English branch of Anglo-American law is that econometric analysis may be applied to a sizable, homogeneous base with a long run of consistently collated data. In particular, there is no problem of divorce law--induced migration because we are considering a single jurisdiction. Clearly, however, a disadvantage is the loss of the cross-sectional variation in data drawn across states, of which the U.S. literature has made considerable use (Peters, 1986; Allen, 1992; Brinig and Crafton, 1994; Friedberg, 1998). On balance, we are confident that our results add useful insights by extending the North American approach to English data.

We test for the existence of a long-run linear relationship between the divorce rate and the socioeconomic determinants of divorce, incorporating intervention variables to take account of structural shifts in the data caused by legal innovations in divorce legislation. [1] We explain short-run movements in both the divorce and marriage rates and also investigate the bivariate causal relationships between marriage and divorce variables. It is important to model both marriage and divorce as long-run effects from changes in divorce law could (but as it happens do not in this article) affect marriage.

We begin with a description of the data used in this analysis and its evolution over time. We then carry out the time-series analysis before summarizing our conclusions.

II. DATA AND GRAPHICAL ANALYSIS

In this section we describe the variables chosen to explain divorce rates in the U.K. and present graphs of the data. Annual data are used from 1948 to 1996, as 1948 is the first consistent observation for the data series used. In particular, 1948 marks the beginning of Supplementary Benefit/National Assistance (welfare) payments and the formal construction of a measure of GNP.

Data definitions and sources are presented in Appendix A. Data selection was guided by theory and existing work (see Friedberg, [1998]). We also incorporate the total number of marriages as an additional explanatory factor and examine the effect of sociolegal change on marriage. Both divorce and marriage series were measured as total counts and transformed to a measure of rate per thousand of population. We analyzed both the count and the rate data for comparative purposes, although our reported results focus on the rate data because there was little to distinguish between results obtained either way. We also tried both first-marriage and all-marriage data but found both series to exhibit similar properties over time (see Fig. 1). Therefore, in the interests of brevity, we report only results obtained using total marriages, although equivalent results for first marriage data and total count data for both marriage and divorce are available from the authors on request.

We restricted explanatory factors to three main areas: male and female earnings, transactions costs, and postdivorce welfare, as these capture the range of influences discussed in the literature. We hope at a future stage to extend the analysis to include a measure of fertility control as a factor influencing the likelihood of divorce. Unfortunately, a suitable measure, such as the rate of diffusion of the oral contraceptive pill, has thus far eluded us as a continuous time-series.

Rising real and relative wages have been much in evidence in England and Wales in the postwar period. Real wages for women are considered influential in this analysis because women who perceive themselves to be at risk from divorce can be assumed to insure themselves through greater participation in paid employment. Ultimately this may itself increase the likelihood of divorce as traditional home life is disrupted (Johnson and Skinner, 1986). In fact, this effect could also operate in the other direction, as women's bargaining power within marriage is increased owing to their better independent financial position and divorce is possibly avoided as male partners accommodate marital restructuring (consistent with Gray, [1998]).

The average real hourly wages of women, [W.sub.f], compared with those of men, [W.sub.m], is measured as the real wage ratio, ([W.sub.f]/[W.sub.m]). A rising ratio captures the improvement in postdivorce economic status for women. In view of the lack of a consistent unemployment series over the period, we included a business cycle variable. The United Kingdom's Central Statistical Office leading-indicator methodology for the derivation of cycles, used in Binner et al. (1999) and described in Appendix B, was employed here to capture the general level of economic conditions.

The welfare payments available to unemployed divorcees are of prime concern in the dissolution of a marriage. The value of the public assistance variable is modeled crudely here as value of weekly Supplementary Benefit ordinary-scale rates for a single householder, which is a measure of maximum benefit, although a complex range of more sophisticated alternative rates exist according to each individual claimant's particular means and needs. The state welfare variable here is measured in real terms by deflating by the retail price index. Preliminary analysis revealed that the variable measuring a single person's welfare benefit was highly correlated with the real hourly wages of women, [W.sub.f] (a correlation coefficient of 0.93 was detected). Hence, women's real wages were dropped from the analysis as little added explanatory power could be gained over and above that already obtained in using the single person's welfare benefit and the ratio of female-to-male real wages. The positive correlation almost certa inly arises owing to the tendency of both wage costs and welfare benefits to follow the growth rate for the economy over long periods of time.

Logarithmic transformations were performed on all variables (to stabilize the variance) with the exception of the cycle (which already has a constant variance) following Trundle (1982). Visual inspection of the evolution of the (log-transformed) divorce rate reveals an upward trend and a dramatic increase since the mid-1950s (see Fig. 2). Sudden surges in divorce, which follow changes in legislation, are apparent. Specifically, peaks are noted in 1949/50, 1971/72, 1977/78, and 1984/85. The peaks appear to represent the Legal Aid and Advice Act of 1949, the Divorce Reform Act of 1969 (and associated acts altering financial provision for former spouses), [2] the extension of a "special procedure" simplifying divorce, and the Matrimonial and Family Proceedings Act of 1984, respectively. The Legal Aid and Advice Act extended state-funded financial support to litigants meeting tests of financial need and case worthiness and permitted poorer women to fund a divorce action for the first time. The Divorce Reform Act introduced unilateral no-fault divorce, whereas the Matrimonial and Family Proceedings Act introduced an emphasis on achieving a "clean-break" divorce within a framework (emphasizing the needs of children and vulnerable former spouses) of judicial discretion concerning financial settlements. [3] A detailed list of legislation in England and Wales is presented in Appendix C.

The changes in the divorce rate are displayed in Fig. 3, where there are 48 annual observations. Thus, data are fairly limited. Therefore, identification of intervention variables, which incorporate the effects of structural shifts in the data resulting from the impact of the new laws, were restricted to outliers more than two standard deviations on either side of the mean of the first-differenced series. Hence [I.sub.49] and [I.sub.71/2] are formally identified as intervention variables in order to capture the effects of the Legal Aid and Advice Act and the Divorce Reform Act in 1949 and 1971, respectively. Note the effects of the latter carry over into 1972, hence [I.sub.71/2] is a dummy variable which takes a value of 1 in 1971 and 1972 and 0 otherwise. The two intervention variables are defined as pulse variables in the first-differenced divorce-rate series and hence as step variables in the levels data. [4] Compare this with Smith (1997), who appears to overlook the fact that a pulse dummy (representing legal change) on differenced data is a step in levels. Examination of the evolution of the first differenced data in Fig. 3 demonstrates that the changes in divorce no longer display an upward drift, but rather fluctuate over time around a constant mean.

III. STATIONARITY AND COINTEGRATION ANALYSIS

We report the results of Dickey-Fuller and augmented Dickey-Fuller tests in Table 1, which shows that all series under consideration contain unit roots and require first differencing to render them stationary. Since each series is integrated of order one, it is possible that common trends exist within them as a group, so that they could be cointegrated (Engle and Granger, 1987; Engle and Yoo, 1987). If this is the case, estimating a multiple time-series model using the first differences could result in a serious misspecification (Mills, 1990, chap. 6 and 11).

We used a full-information maximum-likelihood procedure (Johansen 1988; Johansen and Juselius 1990) to test for cointegration between the series, in preference to a two-step Engle-Granger procedure, [5] which has been criticized owing to small-sample bias present in the ordinary least squares estimation of the cointegrating equation (Banerjee et al., 1986). This bias carries over into the estimates of the disequilibrium errors and hence into the second-stage estimates of the short-run parameters. [6]

Because Johansen cointegration results can be sensitive to the lag specification in the vector autoregression (Hall, 1991) we ran the procedure on the log-levels data of all the endogenous and exogenous variables, that is,

(1) F = Divorce, Marriage, Cycle, Rwageratio, Rsingben, [I.sub.49], [I.sub.71/72])

over lags i to 3. The two legal intervention variables, [I.sub.49] and [I.sub.7l/72], were included in the vector autoregressive model as exogenous stationary, (I(0)), variables. One unique cointegrating vector was present in all cases, indicating the robustness of the finding. The results obtained for a lag length of order one were used for the further analysis, for reasons of parsimony. [7] The Johansen cointegration results for the vector autoregression of order one are shown in Table 2. The coefficients, which have been normalized to allow the log of divorce to be the dependent variable, appear in brackets. The long-run structural model provides sensible parameter estimates. A rising ratio of female to male real wages causes the largest positive impact on divorce; increases in marriage rates per thousand of population lead to corresponding increases in divorce rates; and increases in the single person's ordinary welfare benefit has a slight positive effect on divorce rates. A downturn in the business cycle creates a slight negative impact on divorce.

Having established the existence of one unique cointegrating vector for divorce rates, we now capture short-run dynamics in the form of dynamic error-correction models.

IV. SHORT-RUN DYNAMIC ERROR-CORRECTION MODELS AND CAUSALITY TESTING

Short-run dynamic error-correction models were estimated separately for both marriage and divorce to avoid the problems of simultaneous-equation bias. A general to specific strategy was used over the current and two past lags of each explanatory variable plus the lagged residual from the cointegrating relationship estimated previously. Insignificant parameters were sequentially deleted until we arrived at the parsimoniously preferred models detailed in Table 3. [8]

Only contemporaneous terms entered into the final divorce equation. All parameter estimates are significant at the 95% level, with the exception of the marriage variable in the divorce equation, which is significant at the 90% level. Divorce and marriage rates each exert a significant, positive, contemporaneous effect in the short run on each other (i.e., in the complementing equation). Thus an increase in the number of marriages yields some increase in divorce and vice versa, over the 1948-1996 sample period. Clearly, one simple observation is that an increased level of marriage will generate more divorces if the proportion of marriages ending in divorce remained the same. In fact, the proportion has increased from around 10% to over 35% of new marriages over the 1948-1996 period. In addition, although divorce tends to generate remarriage in the United Kingdom, just as it does in the United States, it actually generates rather more cohabitation in later years over the 1948-1996 period compared with the Unit ed States (Hoggett et al., 1996).

The evolving relationship between divorce and marriage over time is clearly visible in Figs. 1 and 2 and reflects a change in attitude toward these institutions. An examination of the statistical relationship between divorce and marriage reveals positive correlation over the subperiod 1948-1978 that becomes negative over the 1979-1996 subperiod. [9] The negative relationship between changes in divorce and marriage over recent years in England and Wales corresponds with findings for the United States (Brinig and Crafton, 1994). There are several possible influences at work, but we think that the main impetus comes from the different impacts of legislation and economic variables on the incentives to divorce and marry.

The marriage equation detailed in Table 3 is more strongly dominated by the macroeconomic explanatory variables, in the absence of large legislative impacts, which turned out not to be significant for marriage, and is again broadly comparable to the results for the United States. All three measures of economic well-being are found to enter the marriage equation: the wage ratio, business cycle, and the single person's benefit payments with a one-year delay. Interestingly, the propensity to get married is found to fall as female real wages rise relative to male real wages, which supports the idea that assortative mating occurs and females can now afford to be more selective in finding a suitable mate (Posner, 1992, 243). The lack of impact on marriage of the legislative variables may well reflect the canceling out of two trends. First, making divorce easier reduces the irreversibility of marriage and possibly makes it more attractive to some people. Second, observing a rising divorce rate may make others cynic ally aware that marriage may not last and cause them to avoid it (e.g., by cohabitation, which has no legal status in England and Wales, a different situation from U.S. states).

The impact of the move to no-fault divorce ([I.sub.71/72], the Divorce Reform Act of 1969) is significant at the 95% level in the divorce equation (with a t-statistic of 6.19). The elasticity [10] of divorce per head of population with respect to the Divorce Reform Act 1969 is 0.851. This means that unilateral divorce raised the divorce rate by more than 0.8 divorces per thousand people, a substantial impact relative to the average divorce rate of 1.84 over the period. Therefore, our result for England and Wales supports the findings of Allen (1992), Brinig and Buckley (1998), and Friedberg (1998), and, to a limited extent, Ellman and Lohr (1998). These American studies also find that relaxing the divorce law results in significant positive impacts on the level of divorce.

Note in particular (and as mentioned above) that because it arises in a differenced model, the significant pulse change resulting from the dummy variable representing the introduction of no-fault divorce is equivalent to a step change in the underlying levels. We therefore find a permanent impact from the easing of divorce law in the 1970s. The step change is highly visible around 1969-72 in any graph of either the level of divorce or the divorce rate per thousand population. The change occurs over too short a time period to be explained by secular changes in female economic conditions. It is important to remember that the 1969 no-fault legislation became effective from 1971 onward.

Our result showing a permanent impact from introducing no-fault contrasts with earlier authors (e.g., Smith [1997], Ellman and Lohr [1998]). It is an article of faith among British sociolegal scholars in family law that the 1969 act released a bottleneck and had only a temporary effect (Hoggett et al., 1996). Our result fails to support this belief. Furthermore, bottlenecks have origins that give a permanent impetus to traffic; this piece of common sense also supports our findings.

The signs of the parameter estimates are all in accordance with economic priors with the exception of the sign on [I.sub.49] (which is highly significant with a t-statistic of -5.28) indicating that the introduction of Legal Aid had an instantaneous negative impact on the propensity to divorce. However, this is really only true at the beginning of our data run. An additional pulse intervention variable fitted at I = 1 in 1952 and 0 otherwise is significant at the 95% level and improves the overall fit of the model. The [R.sup.2] term increases to 71% and the standard error of the divorce equation reduces to 0.066 when the after-effects of the Legal Aid and Advice Act experienced in 1952 are incorporated explicitly, although no other changes are in evidence. [11] There are no comparable U.S. studies of the impact of legal aid, as there is no legal aid of the British kind in the United States.

A possible explanation for the pattern of signs associated with the legal-aid intervention is that it may have initially deterred men from divorcing, given the greater ease with which women could defend a petition, but that subsequently the lower cost of divorce for them encouraged more women to initiate divorce. Such a pattern is consistent with observations that can be made on the rate of female-initiated divorce ("wife, petitioning"), which begins its rise in the early 1950s from a negligible level to its present level of some 70% of all divorces in England and Wales. (This increase is the subject of a separate study that we are currently completing.) An alternative explanation for the pattern of signs associated with the legal-aid intervention is the often-noted increase in fertility experienced in the late 1940s. A fertility-based explanation is unfortunately not testable owing to the absence of a suitable time-series covering fertility.

The error-correction term appears in the marriage equation only, failing to meet the required level of significance for entry into the divorce equation. This implies that marriage is endogenously determined within this particular system, whereas divorce is exogenously determined. The coefficient of -0.302 on the error-correction term indicates that following a disturbance to the equilibrium level of divorce, the steady state is restored within three years or so. The negative sign on the error-correction term is further confirmation that a cointegrating relationship does exist and that marriage is indeed endogenously determined within this system. [12]

Bivariate Granger causality tests were conducted between divorce and each explanatory variable identified above using standard F-tests. The lag length in the current work was set at 2 for reasons of parsimony. In no case was causality detected, in the Granger sense, from the explanatory variables to divorce (or vice versa). Lagged relationships appear to play no role in the determination of divorce and we can say that the change in divorce does not Granger cause the legal changes, an important result given the priors of the sociolegal community (Hoggett et al., 1996). The lack of temporal (Granger) causality between explanatory variables and the divorce rate provides some evidence against feedback effects, such as a linkage between female labor-force participation, female wages, and divorce.

V. CONCLUDING REMARKS

The results presented above, based on the Johansen full-information maximum-likelihood estimation, yield some interesting insights into the evolution of divorce rates in England and Wales over the 1948-96 period. The factors that are influential in explaining the growth in divorce rates are female relative wages, the marriage rate, the introduction of legal aid in 1949, and the move to unilateral no-fault divorce in the early 1970s.

We have identified a well-behaved long-run equilibrium relationship. The short-run error-correction models are well specified and pass standard diagnostic tests. Both socioeconomic and sociolegal factors explain divorce levels. The calculated elasticities are 0.861 for the wage ratio, -0.728 for legal aid, and 0.851 for the move to no fault. This shows that proportionate increases in divorce levels resulting from legal change (both the move to no fault and the introduction of legal aid) are similar in magnitude to those resulting from increasing female wages relative to male wages. We can conclude that the law increased divorce by making it easier to divorce. Furthermore, the pulse dummy for the move to unilateral no-fault divorce reflects a step change in underlying levels, which gives a permanent shift in the divorce rate consistent with the change observed in England and Wales.

The general level of economic prosperity, measured here by the business cycle, has only a minor effect on divorce in the long run, although it has a greater influence on marriage. Further work in this area would permit additional explanatory factors to be identified and incorporated into the model to increase its power. Such factors would, for example, include a measure of fertility control, such as the diffusion of contraception.

Interesting new evidence has been revealed on the interrelationship between divorce and marriage. This research presents the first available evidence from England and Wales on the long-run structural model that links the two. First, it seems that legislative effects are important for divorce but not for marriage. Second, the divorce rate does affect marriage positively, which suggests that modern couples may in fact desire less commitment. Awareness of a greater divorce rate (perhaps indicating the enhanced social acceptability of divorce) appears to encourage marriage.

Binner: Senior Lecturer in Finance, Nottingham Business School, The Nottingham Trent University, Burton St., Nottingham, NG1 4BU, UK. Phone +44 115 848 2429, Fax +44 115 948 6512, E-mail jane.binner@ntu.ac.uk

Dnes: Associate Dean (Development) and Research Professor, The Business School, University of Hertfordshire, Hertford Campus, Mangrove Road, Hertford, Herts, SG13 8QF, UK. Phone +44 1707 285464, Fax +44 1707 285409, E-mail a.w.dnes@herts.ac.uk

(1.) We apply the Johansen maximum-likelihood estimation technique (Johansen, 1988; Johansen and Juselius, 1990) and construct a vector autoregressive(VAR) system to explain short-run movements in both the divorce and marriage rates. We also investigate the bivariate causal relationships between marriage and divorce variables.

(2.) The Divorce Reform Act of 1969 became effective in 1971.

(3.) Which is to say that the English system does not follow a system of community property, although it may do so before long.

(4.) A pulse variable models an intervention lasting for one period only, while a step variable models a step change in the series.

(5.) The Engle-Granger procedure was used by Smith (1997).

(6.) A further problem with the two-stage Engle-Granger procedure in the multivariate ease is that estimation of long-run relationships is seriously complicated by the possibility that variables integrated of order one may be linked by more than one cointegrating vector.

(7.) A maximum eigenvalue of 45.9679 was significant at the 95% level compared with the critical value of 37.07. This result was further confirmed by the accompanying trace test statistic of 87.57, which is significant compared with the 95% critical value of 82.23.

(8.) Construction of a vector autoregressive system was initially thought to be appropriate to allow feedback in the determination of the relationship between marriage ratios and divorce. However, owing to the largely contemporaneous relationships that exist between marriage and divorce variables, it is better to estimate the relationship using separate equations to avoid the problem of simultaneous-equation bias.

(9.) A positive correlation coefficient of 0.42 over the subperiod 1948-1978 reverses in sign to -0.13 over the 1979-1996 subperiod.

(10.) The magnitude of the elasticity is the effect of a percentage change of the independent variable on the dependent variable. The estimated coefficients on the socioeconomic variables have been logarithmically transformed and thus may be interpreted directly as elasticities. The estimated coefficients on the zero-one dummy variables fitted to the two legal interventions need to be scaled first because the elasticity is calculated at the point of the means of each variable.

(11.) Further univariate analysis in the form of a multiple input transfer function noise model incorporating the legal-aid intervention variable, as described in Box and Jenkins (1976, 26), would allow the length of time for the impact to take place and the length of time to decay to be measured and built into the model. Constraints on degrees of freedom imposed by the multivariate approach adopted here do not allow such detailed analysis.

(12.) It is clear that the dynamic error-correction models are well specified and that the residuals from both the divorce and marriage equations are indeed white noise (Ljung and Box, 1978). Q-statistics of 26.43 and 21.72 are less than the 95% tabulated Chi-squared statistic of 31.41, indicating there is no serial correlation present in the residuals and the models are adequately determined.

REFERENCES

Allen, D. "Marriage and Divorce: A Comment." American Economic Review, 82, 1992, 679-85.

Banerjee A., J. J. Dolado, D. F. Hendry, and G. W. Smith. "Exploring Equilibrium Relationships in Econometrics through Static Models: some Monte Carlo Evidence." Oxford Bulletin of Economics and Statistics, 48, 1986, 253-77.

Binner, J. M., A. Fielding, and A. W. Mullineux. "Divisia Money in a Composite Leading Indicator of Inflation." Applied Economics, 31, 1999, 1021-31.

Box, G. E. P., and G. M. Jenkins. Time Series Analysis: Forecasting and Control, rev. ed., San Francisco: Holden-Day, 1976.

Brinig, M. F., and F. Buckley. "No-Fault Laws and At-Fault People." International Review of Law and Economics, 18, 1998, 325-40.

Brinig, M. F., and S. M. Crafton. "Marriage and Opportunism." Journal of Legal Studies, 23, 1994, 869-94.

Ellman, I. M., and S. L. Lohr. "Dissolving the Relationship between Divorce Laws and Divorce." International Review of Law and Economics, 18, 1998, 341-59.

Engle, R. F., and C. W. J. Granger. "Cointegration and Error Correction: Representation, Estimation and Testing." Econometrica, 55, 1987, 251-76.

Engle, R. F., and B. S. Yoo. "Forecasting and Testing in Co-Integrated Systems." Journal of Econometrics, 35, 1987, 143-59.

Friedberg, L. "Did Unilateral Divorce Raise Divorce Rates?" American Economic Review, 88, 1998, 608-27.

Gray, J. S. "Divorce-Law Changes, Household Bargaining, and Married Women's Labor Supply." American Economic Review, 88, 1998, 628-43.

Hall, S. G. "The Effect of Varying Lag Length VAR Models on the Maximum Likelihood Estimates of Cointegrating Parameters." Scottish Journal of Political Economy, 38, 1991, 317-23.

Hoggett, B., D. Pearl, E. Cooke, and P. Bates, The Family, Law and Society: Cases and Materials. London: Butterworths, 1996.

Johansen, S. "Statistical Analysis of Cointegration Vectors." Journal of Economic Dynamics and Control, 12, 1988, 231-54.

Johansen, S., and K. Juselius. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money." Oxford Bulletin of Economics Statistics, 52(2), 1990, 169- 210.

Johnson, W. R., and J. J. Skinner. "Labor Supply and Marital Separation." American Economic Review, 76(3), 1986, 455-69.

Ljung, G. M., and G. E. P. Box. "On a Measure of Lack of Fit in Time Series Models." Biometrika, 65, 1978, 265-70.

Mackinnon, J. G. "Critical Values for Cointegration Tests," in Long Run Equilibrium Relationships, edited by R. F. Engle and C. W. J. Granger. Oxford: Oxford University Press, 1991, 267-76.

Mills, T. C. Time Series Techniques for Economists. Cambridge: Cambridge University Press, 1990.

Posner, R. A. Sex and Reason. Cambridge: Harvard, 1992.

Smith, I. "Explaining the Growth of Divorce in Great Britain." Scottish Journal of Political Economy, 44(5), 1997, 519-45.

Trundle, S. M. "The Demand for M1 in the UK." Bank of England Discussion Paper, 1982.

 Order of Integration Tests
Variable DF ADF (2)
LDIV per 1,000 pop -3.1861 -2.7969
LMARR per 1,000 pop 0.7855 -1.3087
CYCLE -1.9322 -2.5757
LRWF -1.9705 -2.2917
LRWAGERAT -2.0048 -1.7798
LSINBEN -0.7987 -1.3335
[delta]LDIV per 1,000 pop -9.0387 -7.7610
[delta]LMARR per 1,000 pop -6.9046 -3.8825
[delta]CYCLE -3.7333 -3.9875
[delta]LRWF -6.7538 -3.3467
[delta]LRWAGERAT -7.9576 -3.9669
[delta]LSINBEN -4.9030 -2.5684
95% critical values (-3.5066) (-3.5025)
 with trend [*]
95% critical values (-2.9241) (-2.9215)
 without trend [*]
(*.)Given in MacKinnon (1991, Table 1).
 Estimated Cointegrated Vector
 (Johansen Estimation)
 Vector 1 (Lag Length=1)
LDIVPOP 1.1364
 (-1.0000)
LMARRPOP -3.1638
 (2.7841)
CYCLE 0.01380
 (-0.0122)
LRSINBEN -1.0683
 (0.9401)
LWAGERAT -5.9589
 (5.2438)
Note: I(0) variables included in the
VAR = [I.sub.49], [I.sub.71/2]. Sample
period covers priod 1949 to 1996.
Normalized coefficients are in parentheses.

Short-Run Dynamic Error-Correction Models for Divorce and Marriage

[delta][LDIVPOP.sub.t] = 0.468[delta][LMARPOP.sub.t] + 0.861[delta][LRWAGRAT.sub.t] + -0.272 [I.sub.49] + 0.318 [I.sub.71/72]

(1.85) (2.27) (-5.28) (6.19)

[R.sup.2] = 0.66 SE of regression = 0.070 DW statistic = 2.117 Q stat = 26.43

[delta][LMARCPOP.sub.t] = 0.106[delta][LDIVPOP.sub.t] + 0.006[delta][CYCLE.sub.t] + 0.185[delta][LRSINBEN.sub.t-1] +

(3.22) (2.06) (2.14)

-0.516[delta][LRWAGERAT.sub.t-1] + -0.302[ECT.sub.t-1]

(-3.94) (-3.68)

[R.sup.2] = 0.44 SE of regression = 0.024 DW statistic = 2.564 Q stat = 21.72

Notes: ECT comprises the lagged residuals from the cointegrating vector for a VAR lag = 1 (i.e., represents the error-correction term). T-ratios are in parentheses.

[Graph omitted]

[Graph omitted]

[Graph omitted]

APPENDIX A

 Data Definitions and Sources (England and Wales)
Variable Name Definition
Divorce Total on petition
Marriages Total marriages/first marriages
Population Population and
 vital statistics
Real wage rate Average gross hourly earnings
Supplementary Benefit National Assistance 1948-
 Supplementary Benefit 1966-
 Income Support 1988-1996
Cycle (See Appendix B)
Retail Price Index Annual (all items) index
Variable Name Source
Divorce Series FM2, no. 16, table 4.1.
 British Social Trends
Marriages Series FM2, no. 16, table 2.1.
 Office of Population Census
 and Surveys
Population Office for National Statistics
Real wage rate Dept. Employment Gazette/New
 Earnings Survey
Supplementary Benefit
 Dept. Social Security
Cycle Office for National Statistics
Retail Price Index Office for National Statistics

APPENDIX B

Derivation of Cyclical Growth Rates (following methods of the Central Statistical Office for the United Kingdom).

Construction of the CYCLE variable:

Annual GDP data from 1948--1996 obtained.

i. Calculate annual growth rates for the GDP series.

ii. Take natural logs.

iii. Take a 5-year moving average of the series. The 20 missing datapoints from the start and end of the series are replaced by estimates from a sinusoidal regression.

iv. Take the exponent of the resulting series as the trend.

v. Detrend the series (actual -- trend / trend) x 100. The result is the cycle.

vi. Take a three-period moving average of the cycle to smooth the resulting series.

APPENDIX C

 Major Legislative Changes
 (England and Wales)
Act of Parliament Notes
Legal Aid Act (1949) Introduced payment of legal fees
 (administration and attorneys)
 subject to test of applicant's
 means and public-interest test.
Divorce Reform Act (1969) Introduced no-fault divorce as an
 (effective 1971) option although retained
 fault-based routes.
Matrimonial Proceedings Introduced mainly needs-based
 and Property Act (1970) (discretionary) financial settlements.
Marital Causes Act (1973) Consolidates 1969 Divorce Reform
 Act and Matrimonial
 Proceedings and Property Act (1970).
Special Procedure (1977) Developed from Marital Causes Act
 of 1973 as a quick route for
 granting uncontested divorces
 by judge's action.
Matrimonial Causes Act Introduced clean-break financial
 (1984) settlements.
Family Law Act (1996) Introduces mediation and full
 no-fault divorce. Not yet
 operational and, moreover,
 temporarily halted in
 implementation.