constructing and using a multiplicative model of the impact of societal changes on violent crime

Quality & Quantity 30: 277-300, 1995. 0 1995 Kluwer Academic Publishers. Printed in the Netherlands.

277

Constructing and using a multiplicative model of the impact of societal changes on violent crime*

OLOF DAHLBACK Department of Sociology, Stockholm University, S-106 91 Stockholm, Sweden

Abstract. This study aims at exploring the possibilities of using a multiplicative model when explaining the impact of societal changes on violent crime in Swedish municipalities. A theory of criminality in municipalities is presented which is founded on an analysis of individual decision-making on the commission of crimes. According to this theory, the level of criminality in a given municipality is determined by two average properties for the individuals who stay there - the average amount of occasions when the circumstances are favorable to the commission of crimes and the average probability of committing a crime on such an occasion. On the basis of the theory, a model of the relationship between criminality and specified characteristics of the municipality has been constructed. Criminality is assumed to be the product of a range of factors, each of which is a linear function of current and earlier values of a municipality characteristic. Using this model, the relationship between changes in the level of criminality and variables measuring independent characteristics at different points in time has been empirically analyzed. The data used are of register type and refer primarily to the years 1970, 1975, and 1980. Model parameters are estimated by a least-square fit. It is found that the multiplicative model explains much more of the variance in changes in the level of criminality than does the linear model including the same municipality characteristics. In the multiplicative model, independent variables obtain weights that give a different picture of the causal processes that affect criminality as compared with the linear model.

1. Introduction

In the postwar period, violent crime seems to have increased dramatically in many Western industrial countries, for example in Sweden (see Yearbook of Judicial Statistics, 1985, p. 38; as to the Nordic countries, see pp. 146- 156; as to the USA, Canada, and England during the sixties and seventies, see Brantingham and Brantingham, 1984, pp. 119-139). One may ask how this increase in crime can be explained. This study aims at making an explanatory contribution by modelling the impact on criminality of societal changes in a manner that entails a new research approach.

The study presents and tests a theory of the relationship between violent crime and various societal factors. The theory is based on an analysis of the

* The research was financed by the Bank of Sweden Tercentenary Foundation and the Swedish Council for Research in the Humanities and Social Sciences. I thank Eero Carroll for valuable comments.

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decisions individuals make about whether or not to commit crimes. It explains on an abstract level the causes of the level of criminality at a given point in time. On the basis of the theory, a model of the relationship between the level of criminality and specified societal characteristics has been constructed. Based on this model, the relationship between the change in level of criminality and variables measuring the characteristics at different points in time has been analyzed using register data for Swedish municipalities. Thus, spa- tial as well as temporal variation in level of criminality is analyzed non- linearly - a type of analysis that is uncommon in the research.

The decision-making perspective used incorporates two other theoretical perspectives often used in the study of crime, the conflict and control perspectives, and it strongly resembles a third such perspective, the rational choice perspective.

Violent crime can of course be assumed to be the result of conflicts between individuals. These conflicts may be of different kinds - economic, political, racial, sexual, and others. For example, conflicts due to tensions in family life could perhaps be one explanation of the increase in violent crime in postwar Western societies. It seems that the family has been confronted with especially great strains in the postwar period - at least the increase in the rate of divorces would indicate so.

The control perspective on violent crime focuses on the factors in society that control this type of deviant behavior (Reiss, 1951; Hirschi, 1969; Samp- son and Laub, 1990). The adherence to law-abiding norms can be assumed to result to a great extent from the fact that individuals are affected in their social contacts by sanctions - their deviant behavior is punished, and their conforming behavior is rewarded. For the adherence to be solid, stable relations between individuals are advantageous to ensure that the sanctions may work. Relations within the family are presumably of particular importance in this regard. However, sanctions from authorities can be assumed to be an important factor as well.

Decreasing control and weaker adherence to norms as a result of changed social relations are often pointed out as causes of the increase in crime. Since the Second World War, social relations have changed considerably in most Western countries. The most striking development is perhaps the changed functions and the increased disintegration of the family. The family has to some degree been relieved of many of its previous functions - for example, educating and rearing children and nursing sick members. Probably as a result, individuals’ dependence on the family has diminished. Other social relations also seem to have declined in importance. These changes in social relations can be assumed to have made individuals less prone to control deviant behavior, as well as less susceptible to sanctions and therefore less

Model of societal changes 279

controllable. The assumed relationship between a society’s criminality and the extent of control is supported by the fact that strong relationships have been found between factors such as “broken home” rates and the rate of crime (Loftin and Hill, 1974). However, the idea that broken homes cause criminality has been questioned (for a short overview of research, see Bartol and Bartol, 1989, pp. 184-217).

According to the rational choice perspective, individuals commit crime after “rational” calculation. This perspective has probably been less used for violent crime than for property crime, due to the assumption that violent crimes are more expressive and therefore less calculated than property crimes. Rational choice research on individuals’ criminality has had difficulties producing conclusive results (for comments upon the research, see Pilia- vin et al., 1986, and Heinecke, 1988). Rational choice research on criminality in societies has mostly dealt with the significance of the average probability of being detected by the police when committing a crime and the average judicial punishment if detected that inhabitants may estimate on the basis of information about police activities and about the law. In this research, there have also been difficulties producing conclusive results (Gibbs, 1975).

In this study, there is no far-reaching assumption about the “rationality” of decision-making, but in practice this reflects no great difference in comparison with most rational choice studies, where the models of decision- making used are rather unsophisticated. However, this study differs from many rational choice studies by using different independent factors. The influence of the police and of the punishment meted out by authorities is not considered (it can be mentioned that the proportion of all violent crimes in the whole of Sweden that was cleared up by the police and the proportion of all legally processed perpetrators of these crimes that was sentenced to prison did not change much during the time period studied; see Knutsson, 1992).

2. Theory and general model construction

Individual criminal behavior as result of decision-making

In order to predict an individual’s choice of action at a certain point in time, one must know (1) which action alternatives he thinks there are, (2) which outcomes with utility values and probabilities he thinks there are for these alternatives (by the utility of an outcome is meant here a property that does not incorporate his attitude toward risk), and (3) the rules according to which he makes the choice. Aspects of the first two elements of special interest in

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the analysis of criminal behavior are: (1) the occurrence of occasions when crimes are possible action alternatives, and (2) the utility values and the probabilities for the outcomes of choices of criminal and non-criminal action alternatives. The occasions determine whether it is possible to commit crimes, while the utility values and probabilities of the outcomes, as well as the rules, determine whether possible crimes are committed.

The choice situation in which crime is one alternative will here be given a simplified description. Assume that the individual has two alternatives: to commit a crime or not to commit it. The alternative to commit the crime can lead to two outcomes: that the individual escapes detection by those who may punish him and obtains something advantageous, or that he is detected and punished and does not obtain the advantageous value. For him to consider committing the crime, the utility of committing it and remaining undetected must be greater than the utility of not committing it. The utility of commission and detection is generally lower than the utility of non- commission.

In many cases, the probability of detection and punishment is neither 0 nor 1. The decision to commit the crime then entails taking a risk - the individual may attain the gain that follows non-detection, but risks being detected and punished.

The probability of detection and punishment is influenced by several circumstances (such as how the crime is committed, the attentiveness of other actors, and the seriousness of the crime). The punishment can take various forms - for example, informal disapproval by the social environment or judicial sanctions imposed by authorities.

Even with knowledge of the utility values and probabilities which an individual assigns to the possible outcomes of a risk-filled action alternative, it is difficult in many cases to predict how he will determine the utility of this action alternative (Weber and Camerer, 1987; Slavic et al., 1988; Payne et al., 1992). Obviously, however, the relative utility of committing a crime compared with not committing it is affected in the following manner by utility values and probabilities of outcomes: the lesser the probability of detection, and the greater the utility of commission and non-detection as well as of commission and detection, the greater the relative utility. The individual is of course predicted to commit the crime if the utility of committing it is greater than the utility of not committing it.

Factors affecting the relative utility of committing a crime

Many factors may affect the utility of committing a violent crime compared with the utility of not committing it. Two types of factors which have such


an influence are the individuals’ social contacts on one hand, and their age and sex on the other. The influence of these factors, which can be assumed to vary between municipalities, is analyzed in this study.

The significance for the individual of his social contacts is affected by several factors - for example, conditions in working life, the residential environment, and cultural circumstances. Two factors of particular importance are family disintegration and change in place of residence. Disintegra- tion of a family naturally affects the contacts within that family (or household) and the relative amounts of contacts inside and outside the family. For example, children who spend much time outside of the home (such as in public leisure centers) presumably tend to form contacts with their families that are relatively less significant than are corresponding contacts formed by children who spend more time at home. Children in broken families tend to be especially ill-favored as to their contact with the parental generation. Changes in place of residence affect the contacts with people in the surroundings. For individuals who move often, the contacts with people in their surroundings tend to be less significant than for individuals who reside in the same place for a long time.

It is often claimed that many types of social contacts have become more superficial and less significant for the individual in modern Western society. There may be several reasons for this: individuals have become more mobile, work has become more specialized, the distance between the workplace and the residence has become greater, the contacts in newly built-up residential areas are relatively anonymous, and the household/family has lost important functions and has become more disintegrated. Differences of this kind, in addition to being evident in later as compared to earlier periods of time, can also be found between metropolitan and rural areas.

Social contacts influence the utility values and probabilities of outcomes as well as the utility values of action alternatives in crime decisions. First, individuals’social contacts - young individuals’ contacts with family members are crucial here - influence their adherence to law-abiding norms, and these norms influence their estimated value of committing crimes. A condition for the emergence of norms is that norm breakers can be punished and norm conformers can be rewarded. These sanctions are more effectively imposed among individuals with more significant contact with each other, because such individuals have more influence on their counterparts’ actions. The internalization of norms can also be assumed to be stronger when the contacts are more significant. Thus, individuals with more significant contacts will tend to conform to the norms of their contact counterparts more willingly. On the societal level, this means that norms held by the majority - that is, most law-abiding norms - will be more prevalent if the contacts people have

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are more significant for them. For young people, who are especially interesting for an analysis of criminality since they relatively often commit crimes, a decrease in the significance of their contacts with family members often greatly increases the significance of the contacts with peers. In most cases, the adult family members may be assumed to conform more strictly to law- abiding norms than do peers.

Second, the estimated value of detection and punishment is affected by the contacts in other ways than via the law-abiding norms, as is the estimated probability of detection. Often, a criminal with no significant contacts is not in such a bad situation when detected as is one with significant contacts. The latter may have valuable contacts destroyed and may have difficulty in replacing them. The former does not have any valuable contacts to jeopardize and therefore can more easily replace contacts that are destroyed. This affects the estimated value of detection and punishment. Further, the criminal with significant contacts tends to be the object of attention and to be less able to hide his criminal behavior than is the criminal with superficial contacts. This affects the estimated probability of detection.

Age and sex are factors that certainly can be assumed to affect the relative utility of committing crimes. Individuals of different ages and sexes commit crimes at different rates. Persons between 15 and 25 years of age tend to commit more crimes than do older or younger persons. Men tend to commit more crimes than women. The high rates of criminality among young people and males are well established (Nettler, 1974, pp. 98-105; Farrington, 1986). One explanation often given for the high criminality of young people is that their norms are not as established as those of older people. The high criminality among men is often explained by the influence of the male sex role.

Individual criminality

Here, violent crimes are defined as crimes characterized by violence or the threat of violence against persons (examples include assault, molestation, unlawful threat, violence or threat to a public official, violent resistance to arrest, robbery, rape, and sexual assault). Many of these crimes are the result of a conflict between the criminal and the victim; the criminal considers the victim to have treated him unfavorably in an unfair way. This type of crime is discussed below.

For the circumstances of an occasion to be favorable for an individual to commit crime, two conditions must be fulfilled: first, that the individual is in acute conflict with a person who is present or within reach, and, second, that violence or the threat of violence is a possible way of acting in the conflict. The number of occasions when the circumstances are favorable to


crime for the individual within a specific period of time (this number is denoted 4) can therefore be assumed to be the product of the quantity of his conflicts with persons in this period (k) and his propensity to react aggressively using violence or the threat of violence (a):

q = ka. (1)

The greater the quantity of conflicts and the stronger the propensity to react aggressively, the greater the number of occasions when the circumstances are conducive to crime. If the individual is not involved in conflicts with others or if he is totally disinclined to react aggressively, no such occasions arise.

The criminality of the individual is the result of his decisions to commit or not to commit crime on the occasions when the circumstances are conducive to crime. It can therefore be assumed to be the product of the number of such occasions and the probability that he will commit a crime on one such occasion. The probability is affected by his valuation of the relative utility of the commission of the crimes, compared with non-commission.

In the discussion which follows, no distinction will be made between different types of violent crimes. It is assumed that the individual generally has a propensity to value the relative utility of crime commission in a certain way. The probability of the individual committing a crime on a single occasion, denoted by p, is a non-diminishing function of this general utility value. The total number of crimes that the individual commits over a specific period of time can be expressed as:

9P (2)

or

kap . (3)

The number of crimes is thus the product of the individual’s quantity of conflicts, his propensity to react aggressively, and the probability that he will commit a crime on a single occasion.

A model of the criminality in a society

By a society is meant here a large geographical area with a collective of many interacting individuals that is organized in many respects. The criminality of a society during a certain period of time is the sum of all crimes committed during that period by individuals in that society. An expression for criminality

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which is formulated in terms of properties of the entire society will now be derived. A complication here is that individuals may be both inside and outside the society during the period for which criminality is assessed.

Consider the duration of individuals’ stays in the society (that is, the time spent there as resident, worker, temporary visitor or in any other capacity) over such a given period of time. Define a constant length of stay, denoted by 6, which is so small that the length of each individual’s stay approximates a multiple of 6. For an individual who spends all his time in the society, this multiple is denoted by t. Divide each individual’s stay into equal-sized units so that each unit has the length 6. Form the set of all units of stay duration created in this manner for all individuals in the society for the specific period of time; the index i (i = 1, , . . , W) denotes a unit of this set. Assume that the individual’s quantity of conflicts, propensity to react aggressively, and probability to commit a crime on a single occasion can, respectively, be described by using only one value for different units of stay duration; unit i’s value is denoted kl, ai, and pi, respectively. The values of ai and pi are not affected by the size of 6. The smaller 6 is, the lower the value of k:.

The total number of crimes in the society is

Instead of directly analyzing this total number, one can divide it by w/t, which is the size of the total actual population of the society, and analyze the resulting relative value. In this way, the comparison of different societies’ criminality is made easier. The relative level of criminality, which is denoted by V, is then

Increase the value of the quantity of conflicts of each unit of stay duration so that the resulting value corresponds to the full period. The resulting value for unit i of stay duration is denoted by ki. Since kj = kilt, (4) can be written as

v = xi”=, kaipi

0

It would be desirable to derive from (5) an expression of the societal crimi-


nality using only the mean values of the factors ki, ai, and pi. These mean values are measurable and therefore it would be possible to use the expression in empirical analysis. However, it is impossible to derive an exact expression of this kind, since the factors are probably correlated with one another. For the two variables x and y, which describe a number of o cases, it holds true that (2 xy)Io = M,M, + rxys,sy, where M, r, and s denote mean value, correlation, and standard deviation. By using this formula, the right- hand side of (5) can be transformed into an expression that is the sum of the product of the factors’ mean values and an expression in which the intercorrelations among the factors and factor products as well as the standard deviations of these factors and factor products are entered. The value of the latter expression is dependent upon the relationships among the factors and corrects the value of the product of the factors’ mean values for these relationships. Since the intercorrelations and the standard deviations are difficult or impossible to measure for most societies, the value of the correction is difficult to determine.

The relationships among the factors ki, ai, and pi can be assumed to be positive and rather strong. However, there are presumably significant unique components in the factors.

Introduce the following definitions:

w

(6)

The mean values K, A, and P will be called societal factors; ki, ai, and pi will be called individual factors. If all individuals spend the entire period of time in the society, K, A, and P are the means of their k, a, and p values.

The correction value that arises from a correlation between two individual factors has little significance. As mentioned, the mean value of the product of two factors is equal to the sum of the product of the factors’ mean values and a product of their intercorrelation and standard deviations. Since the factors have only positive values, their standard deviations are less than their means. If, for example, the standard deviations of two factors are one-third their means and the correlation between the factors is 0.50, the value of the correction is about 5.6% of the product of the means (for several societies

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and factors, the standard deviations and the correlation, as well as the correction, probably have even lower values). Moreover, for societies that are similar in structure, the variation is presumably greater in the means than in the standard deviations, and the variation in the intercorrelations is presumably rather small. This implies that the variation among the societies in the product of the means will be greater than the variation in the correction value.

If a correlation between two individual factors gives rise to an insignificant correction value, the same can be assumed to apply to the correlations between all three factors. If the variation in criminality among societies is to be analyzed, the correction can therefore be disregarded without introducing any large error, and use can be made of the multiplicative model

V=KAP. (7)

Registered and actual population

Formula (7) refers to the actual population of an area, not to the population registered for domicile (henceforth called registered population). However, the measures of criminality and independent factors that are used in this study refer to the registered population. This creates a problem since the registered population never or seldom is the same as the actual population. The difference between the populations may be more or less permanent and may have various causes (for example, moves for work, recreational moves, incorrect registration for domicile).

Formula (7) has been modified to refer to the registered population. Let unit i of stay duration now refer to this population. Assume that the factors k, a, and p have the same relative distribution in the area for the registered population as for the actual population. If Q is the quotient of the actual over the registered population, (5) can then be reformulated as

v = Q E?=I kaipi

w (8)

If the correction for the relationships among individual factors is disregarded, (8) can be written as

V = QKAP. (9)


Form of operationalized models

According to the general formula (9), a society’s criminality at a given point in time is a product of factors. The form of operationalized models for the relation between changes in independent characteristics and the resulting change in criminality will now be derived when the product consists of a number of m factors (in (9), m = 4). Assume that

where V, denotes criminality at time t and where Fit denotes factor j at t. Assume further that

(11)

that is, that factor j at t is a linear function of simultaneous and earlier values on independent characteristics xi (i = 1, . . . , n) - except, however, for the factor that corrects the estimated level of criminality for the discrepancy between the actual and the registered population (this factor is a function of only simultaneous values). The values, which form the independent variables, pertain to the points in time t, t - 1, t - 2, and so on. The distances between adjacent points in time are equally large. The variable Xit is weighted by a coefficient b,* for each factor j. Using (lo)-(ll), the change in criminality V, - V,-, can be given as a function of the independent variables.

If there is no information about the b and c coefficients in (ll), the model of criminality in (10) and (11) is unidentifiable. This is due to the fact that a unique coefficient enters in each term in each factor, which makes it possible to multiply all the coefficients in a factor by an arbitrary constant and divide the coefficients in another factor by this constant without changing the V, value.

In (lo), the factors assume only positive values. If the variables in each linear factor function described in (11) are defined so that their weighted sum can be negative and different from 0, the constants cj will therefore have positive values other than 0. Then the value of V, is not altered if each factor j is multiplied by l/ci and the total factor product by clc2 . * . cj * * . c,. After these multiplications, the model for criminality can be written as

V, = cOFIiltF2t . . . Fj, . . - F,,, (12)

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where co > 0 and equal to ~1~2 * * * cj * . * c, (for (9), equal to c1c2c3c4), and where

Fj, = 2 (bji,Xi, + bji,t-IXi,t-l + bji,t-zxi,t-z + * - .) + 1, i=l

(13)

if the b coefficients are redefined for the current version of the model. The constants in the factor expressions have thus been given the value 1. The model in (12) and (13) can be expected to be identifiable except for special cases. When the constants have the value 1, it is easy to find good initial values for the b coefficients in iterative parameter estimations, especially if the variables are standardized as described below.

In the empirical analysis presented in this paper, all independent variables that measure the same characteristic have been standardized so that they are metrically equivalent. This has been accomplished by taking the mean and the standard deviation of one of these variables in its original version as reference figures, subtracting the reference mean from each variable and dividing the result by the reference standard deviation. The standardization implies that the b coefficients show how a change by the same amount occurring at different points in time in a characteristic affects the factor in which this characteristic enters. Thus, the b coefficients for a characteristic can be compared. Such a comparison gives interesting information if one wishes to analyze the influences longitudinally.

It may be problematic to estimate the coefficients in (12) and (13) if information about the independent characteristics is not available for all points in time. Suppose that there is only information about xi for the late time points t and t - 1, but that Fj, is significantly influenced by earlier xi values. Then the values of bj, and bji,t-l must be estimated using a shortened version of (13) that does not include the terms in which x+2, x+3, . . . enter. These estimates may diverge from the true values of the coefficients. In many cases, the divergence will be greater for bji,f-l than for bjit, since X&--2, Xi,t--3, * * f are more similar to X~,?-~ than to xit, and the estimate of bji,,-, will to a significant degree describe influences from earlier points in time than t - 1.


3. Method

Causal analysis of panel data

In this study, the effect of societal changes on criminality will be analyzed using municipality-level panel data. The longitudinal approach makes it possible to distinguish in the analysis between effects on criminality that occur after varying lengths of time. Being able to do this offers an important advantage, since these effects may be of different strengths and specifying them may therefore contribute to the understanding of the causal processes. There are factors that can be assumed to have strong short-range effects - for example, factors that directly affect the amount of occasions when circumstances are favorable to crime. Other factors, however, can be assumed to have weak short-range effects, but strong long-range ones. One such factor is upbringing. Its effects on criminality do not become strong until the young persons have reached a crime-active age.

In the study, simultaneous values of criminality and assumed independent factors are used. In many studies, the causal interpretation of the relationship between simultaneous values of societal factors is severely complicated by the fact that there is uncertainty about the chronological order between the factors. However, this is not the case in this study. Here, a relationship between simultaneous values of criminality and the assumed independent factors may not depend on the fact that criminality has affected the factors, but may well depend on the fact that the factors have affected criminality.

Moves of individuals in or out of the municipalities may of course compli- cate the interpretation of the longitudinal relationship between criminality and independent factors, especially if this migration is unevenly distributed over time. In an analysis of register data, it is difficult to take these complica- tions into account and this has not been done in this study.

In the analysis made using a multiplicative model, the influence of earlier changes on later changes in criminality is not considered. It is assumed that this influence is weak (for a simple test indicating that this assumption is correct, see Dahlback, 1992).

The municipalities

The geographical areas used as cases in this study have been defined so that they can be described using data from official statistics for the years 1970, 197.5, and 1980, or contiguous years. Statistics that can be used for measuring factors other than crime appear as a rule by municipality. The police use another set of divisions for reported crimes, but since 1972 Statistics Sweden

290 Olaf Dahlbiick

(Statistiska centralbyran, “SC,“) has produced crime statistics reported by municipality.

The municipal division in Sweden was radically changed in the early 1970s. On the 31st of December, 1970, there were 848 municipalities; by the same date in 1975, the number of municipalities had been reduced to 278, and it remained virtually the same (279) by 1980. By combining municipalities, a set of 274 areas has been constructed which covers the whole country for the studied period of time. How these areas are defined is reported in detail elsewhere (Dahlback, 1991). For the sake of simplicity, they will be called municipalities.

The municipalities display great variation in the number of inhabitants, area1 size, and the proportion of the population living in urbanized areas (see Dahlback, 1992). Presumably, many municipalities were communities with structures similar in character and with relatively few individuals crossing their borders. However, there were also municipalities with a deviant structure and a substantial flow of individuals across their borders, especially in the metropolitan areas.

Unsurprisingly, the municipalities were quite dissimilar in regard to which proportion of all violent criminality in Sweden was committed within their borders. A great part of this criminality was registered in metropolitan municipalities. When relative criminality is analyzed using unweighted data, as is done in this study, urban - and especially metropolitan - crime is underrepresented.

Ojjicial statistics

The data are selected from a larger study (Dahlback, 1991). Originally, they were obtained from various sources of official statistics compiled by Statistics Sweden. Details about the sources are reported elsewhere (Dahlback, 1991). The data are complete. Their accuracy can be assumed to be very high.

The crime statistics used encompass practically all violent crimes registered by the police in 1974, 1975, and 1980 (the data for 1974 are used in an analysis of the reliability of the used measure of criminality). The statistics include all events that are registered by the police as completed crimes or as attempts at or preparations for crime. Of all reported crimes in 1974, 1975, and 1980, respectively, 4.8%) 4.2%) and 7.2% were not assigned by Statistics Sweden to any given municipality. A large proportion of these crimes were, however, assigned to a county. In this study, the municipalities have been assigned these crimes in proportion to their known criminality in order to enhance the comparability of the crime figures used.

The data have been used in constructing two types of variables. Some


variables describe characteristics of municipalities at certain points in time or for certain periods of time; others describe changes in the characteristics between these points or periods. The characteristics are accounted for below. They are constructed as proportions of the total registered population, as quantities per inhabitant, and the like - that is, as relative properties that can be compared between municipalities with populations of different sizes.

The periods of time (that is, the years) referred to by the crime data are given above. The periods that other data refer to are in most cases the years 1970, 1975, and 1980. The points in time that other data refer to are in most cases December 31 of the same years. This creates a problem when compar- ing relationships between the change in criminality 1975-80 and changes in other municipality characteristics from December 31, 1970 to December 31, 1975, and from December 31, 1975 to December 31, 1980. The changes in a characteristic during these two five-year periods have not had the same possibility to affect criminality, since the crime data on the average refer to the mid-year figures of 1975 and 1980. The change during the first five-year period has had a greater such possibility than the change during the second period. However, the difference in potential influence is rather small. If one compares for different characteristics the relation between the relationship for the first period and the relationship for the second period, the problem is avoided. The problem would not have emerged if the means of the crime figures for 1975 and 1976 and for 1980 and 1981 were used instead of the crime figures for 1975 and for 1980 as measures of criminality; however, it has not been possible to measure the level of criminality in 1976.

Below, the used measures of criminality and independent factors are accounted for. If not otherwise indicated, they refer to the years 1970, 1975, and 1980.

Criminality

Criminality is measured as the number of violent crimes per 10,000 inhabitants (figures for various crime categories for different years are shown in Dahlback, 1992). The registered criminality in a municipality is probably a good measure of the criminality detected there, but one may well suspect that detected criminality differs a great deal from actual criminality. The undetected proportion of actual criminality can be assumed to be high. However, there seems to be no reason why the relative undetected proportion would differ much between municipalities. The comparability between municipalities can therefore be assumed to be rather good. Further, it seems to be rather unproblematic to compare the different years’ registered criminality. No important changes in the law or in the registration procedures

292 Olaf Dahlbdck

have occurred. The proportion of missing values varies between the years, but probably not enough to seriously impair the comparability.

The crime data are of high quality. However, this does not mean that the relative number of crimes, calculated on the basis of the data and used as a measure of a municipality’s normal criminality, has very high reliability since this number is affected by random factors. The reliability of a measure of relative criminality in a municipality is affected by the absolute number of crimes that the measure is based on. The more crimes, the higher the reliability tends to be - random influences on the measured level of criminality tend to be less important when the absolute number of crimes increases, since these influences then cancel each other out to a greater extent. The larger the population of the municipality, the more crimes there tend to be and therefore presumably the higher the reliability of the relative criminality. This can be tested in the data, using the correlation between the criminality values for 1974 and 1975 as an approximation of the reliability. However, the difference between these values of course does not only depend on random influences but also on non-random ones, and therefore the reliability of the cross-sectional measure of criminality can be assumed to be higher than the correlation. The data set has been split into two subsets made up of municipalities with more and municipalities with fewer than 16,061 registered inhabitants. Each subset consists of 137 cases. As expected, the correlation between the criminality values for 1974 and 1975 is much higher for the former than for the latter municipalities (the figures are 0.87 vs. 0.66).

The difference between the criminality values for 1980 and 1975, which will be used as the dependent variable, has a reliability that can be estimated on the basis of the correlation between these values (which is 0.79 and 0.56, respectively, for the two subsets of municipalities), the dispersions in criminality for the two years, and the reliability of the cross-sectional measure (formula according to Mosier, 1943). This has been done using the correlation between the values for 1974 and 1975 as an approximation of the reliability of the cross-sectional measure. However, since this correlation underestimates reliability, the estimated reliability of the difference is too low. It can be taken as a minimum value - a value that the true reliability cannot fall below. As expected, the estimated minimum value of the reliability of the difference between crime in 1980 and in 1975 is considerably higher for the municipalities with more than 16,061 inhabitants than for those with fewer inhabitants (0.42 vs. 0.23). Due to these facts, relationships between independent variables and the change in criminality will be analyzed only for the municipalities with more than 16,061 inhabitants. These municipalities have a higher


average level of criminality than the other municipalities (for 1975, the means are 37 and 31, respectively).

Independent characteristics

The effects that movements across the municipal boundaries have on the relation of the actual to the registered population are measured by the relative size of the agriculturalpopulation (the proportion of the total gainfully employed night-time population consisting of individuals who work in agricul- ture or forestry or who live by hunting). Municipalities with a relatively large agricultural population probably have a larger actual than registered population during the hot season of the year due to seasonal moves for work and recreation.

The average quantity of conflicts is measured by the proportion of divorced inhabitants (the number of divorced inhabitants in per cent of the total number of married and divorced inhabitants). This characteristic is also assumed to measure such contacts that affect the probability of committing a crime.

There is no measure of the average propensity to react aggressively. The average probability of committing a crime is measured by characteris-

tics that describe social contacts as well as the age and sex of inhabitants. The social contact aspects that are measured are family disintegration and changes in place of residence. Family disintegration is measured by the proportion of divorced inhabitants (mentioned above) and the proportion of children in public leisure centers. The proportion of children in public leisure centers is measured as the number of children per 1,000 (7-14 years of age) who use these centers (data refer to 1971, 1975, and 1980).

The changes in place of residence are measured by migration. For the first point in time, the measure is the number of all moves into and out of the municipality during 1968-70 divided by the sum of its population in 1970 and the number of all moves out during 1968-70 (the municipality characteristics refer to points or periods in time; however, for the sake of simplicity, “point in time” will now and below also be used to denote the periods). Corresponding measures are constructed for the second and the third points in time. The variable thus describes how common it is to move into or out of the municipality, regardless of the move’s direction. The migration is of course related to the size of the area of the municipality; for municipalities with larger areas, a greater part of all moves will tend to occur within their boundaries.

The relative frequency of male inhabitants in crime-active ages is measured

294 Olaf Dahlbiick

by the number of 15-24 year-old males as a proportion of the total population. These individuals can be assumed to be particularly inclined to commit crimes (see Yearbook of Judicial Statistics, 1976, Table 3.2.11 and p. 76).

Variables

The values at each point in time for each municipality characteristic have been standardized using the mean and the standard deviation of this characteristic at the middle point in the studied time period for all 137 municipalities. The change variables are constructed as the difference between the standardized values of the last and the middle point in time and of the middle and the first point in time, respectively. These variables thus describe how a municipality has changed with respect to a characteristic in relation to the dispersion in all municipalities’ values for this characteristic at the middle point in the studied time period.

Only two independent characteristics used changed much during the two periods - the proportion of divorced inhabitants and the proportion of children in public leisure centers. On the average, the proportion of divorced inhabitants almost doubled from 1970 to 1980. The proportion of children in public leisure centers was about six times as high in 1980 as in 1971.

Each variable has been given a compound notation which consists of a stem that describes the characteristic and an ending that describes the type of the variable. The following stem denotations are used: CRIM = criminality, AGRI = relative size of agricultural population, DIVOR = proportion of divorced inhabitants, PUBL = proportion of children in public leisure centers, MIGR = migration, YOUNG = proportion of 15-24 year-old males. If a variable describes the difference in a characteristic during the first period, the ending “Pl” is used; if it describes the difference during the second period, the ending “22” is used; and if it describes the value of the characteristic in year 19NN, the ending “NN” is used.

4. Results

As a basis for the empirical analysis, the following assumptions about the influences on criminality can be made. The proportion of divorced inhabitants has a positive effect on criminality in the short run via the conflict factor, but the corresponding effect that occurs after a period of time has elapsed may well be negative due to the fact that old conflicts have decreased. The proportions of divorced inhabitants and children in public leisure centers have no important effects in the short run on criminality via the probability


factor, but have strongly positive effects via this factor after a period of time. However, migration and the proportion of young men have effects in the short run via the probability factor. Finally, the greater the size of the agricultural population, the more the value of criminality should be corrected upwards. These assumptions are in accordance with ideas presented above.

Based on the assumptions, analyses that are not reported here have been made of the municipality data. The results of these analyses indicate that there are strong interactions between the characteristics that measure the probability factor, making it reasonable to divide this factor into subfactors according to (12) and (13). Therefore, the following model of the change in level of criminality will be used:

CRIMP2 = c,&AGRI80 + l)&,DIVOR80 + b2,,_,DIVOR75 + 1) (b,PUBL80 + b3,,-1PUBL75 + l)(b,,DIVOR80 +b+rDIVOR75 + l)(&MIGR80 + bg,t--1MIGR75 + 1) (&YOUNG80 + b6,,-1YOUNG75 + 1) -c,,(b,,AGRI75 + l)(&,DIVOR75 + b2,,-rDIVOR70 + 1) (14)

(b,,PUBL75 + b3Z,-1PUBL71 + l)(&DIVOR75 + b+rDIVOR70 + l)(bS,MIGR75 + b+rMIGR70 + 1) (&YOUNG75 + b,,,-rYOUNG70 + 1).

In this model, the correction factor (factor 1) is assumed to be a function of the value of the agricultural population at time t when the crimes have occurred. The average quantity of conflicts (factor 2) is assumed to be a linear function of the proportions of divorced inhabitants at times t and t - 1. The average probability is assumed to be the product of four subfactors (factors 3-6). Each subfactor is a linear function of values at t and t - 1 of only one characteristic. The characteristics used are the proportion of children in public leisure centers (factor 3), the proportion of divorced inhabitants (factor 4), migration (factor 5), and the proportion of young men (factor 6). The subfactors thus describe conditions of four kinds that can be assumed to influence the probability of crime commission: poor contacts between the generations, family conflicts, changes in residence, and the presence of men in crime-active ages. These conditions may reinforce each other’s positive influence on the probability. The inclusion of the subfactor that is a linear function of earlier and later values of the proportion of divorced inhabitants means that this proportion appears in two factors (but it is assumed that the coefficients in these factors will be different).

The model has been fitted to data by Gauss-Newton iterations. Two sets of initial coefficient values have been used. No proof is given that any of the

296 Olaf Dahlbdck

Table 1. Coefficients for the relationship between independent variables and the change in level of criminality according to model (14)

Coefficient Characteristic Solution I Solution II

Initial Obtained Initial Obtained value value value value

CO

b If b 2f h,r-1 b b: f,- 1 b b::c-1 b b:ft-, b b::t-1

AGRI DIVOR DIVOR PUBL PUBL DIVOR DIVOR MIGR MIGR YOUNG YOUNG

1.0 0.17 1.0 3.81 0.1 0.52 0.1 0.35 0.3 2.56 0.3 0.19

-0.3 -2.50 -0.3 -0.21 0.0 -0.10 0.0 -0.02 0.3 1.36 0.3 0.16 0.0 0.13 0.0 -0.06 0.3 0.71 0.3 0.26 0.2 0.51 0.3 0.23 0.0 -0.15 0.0 -0.00 0.1 0.03 0.3 0.03 0.0 0.09 0.0 -0.00

solutions is global. In the first set of initial values c = 1, bI, = 0.1, bzt = 0.3, bz,f--l = -0.3, b3t = 0, b3,t--1 = 0.3, b4r = 0, b+1 = 0.3, bst = 0.2, b.+l = 0, bet = 0.1, b6,tpl = 0. The obtained solution, called Solution I, explains 45% of the variance in the changes in level of criminality (uncorrected for lost degrees of freedom, as is also the case for the two models reported below). The obtained coefficient values are shown in Table 1. Of these coefficients, co has a low positive value. The coefficients for the independent variables have values that to a large degree accord with what could be expected considering the previous discussion. The value of bzt is positive and numerically very high and the value of b2,t-1 numerically about as high but negative - that is, the factor that is used to describe the quantity of conflicts has a strong positive relationship with the later proportion of divorced inhabitants, but a strong negative relationship with the earlier proportion. The value of b,,,-I is positive and numerically high and the value of bqt positive but low. The factor that is assumed to describe the influence of family conflicts on the probability thus has a positive relationship with the earlier proportion of divorced inhabitants, and this relationship is more important than the relationship with the later proportion. There is a similar difference in relationship for the earlier and the later proportion of children in public leisure centers (see coefficients b3t and b3,t--1). The coefficient b,, for later migration has a positive value that is higher than the value of the coefficient bs,,-I for earlier migration, which is negative and numerically low. The coefficient bI, for the agricultural population has a positive value. For the proportion of young men, both coefficients have numerically very low,


positive values. The coefficient b6,t-1 for the earlier proportion has a higher value than the coefficient bet for the later proportion, which is unexpected.

Thus, the main features in the obtained picture of the influences on criminality are the following. New problems in couples’ relationships lead quickly to a great increase in the quantity of conflicts and thereby also quickly to an increase in criminality. However, the effect of these problems tends to be short-lived - after a period of time, the increase in the quantity of conflicts they have caused is almost cancelled out by a later decrease. On the other hand, an increase in family disintegration leads after a period of time to an increase in criminality, due to the fact that the probability of committing a crime increases. The effect in the short run is insignificant here. Migration has also a positive effect in the short run on the probability of crime commission and the level of criminality.

The explained proportion of the variance in the changes in criminality is insensitive to changes in the coefficient values. This can be exemplified by a comparison of the solution just presented with another solution, called Solu- tion II (see Table l), that is obtained if the mentioned set of initial values is used again except for the values of bw and bgt which are changed to 0.3. Solution II differs much from Solution I, but explains only 1.5% less of the variance in the changes in criminality. Most of the coefficients have much lower numerical values in Solution II than in Solution I, due to the fact that the value of co is much higher in Solution II. The relations between the absolute values of the coefficients of different factors are also very different in the two solutions. Especially, the coefficients of the proportions of divorced inhabitants and of children in public leisure centers have lower relative such values. However, it can be seen from the table that the trend of the coefficients in the factors (with the exception of factor 6) is the same.

The multiplicative model can be compared with a corresponding linear model. In a linear model, criminality at a certain point in time is a linear function of values of independent characteristics at the same point in time and one period earlier (however, for characteristics measuring the correction factor only simultaneous values enter the function). This means that the change in criminality is a linear function of changes in the characteristics during the two periods. Table 2 shows the obtained regression coefficients for such a linear model corresponding to model (14). The linear model explains 33% of the variance in the changes in criminality - that is, considerably less than both solutions of the multiplicative model. The multiplicative model includes two more coefficients than the linear model, but this difference in lost degrees of freedom cannot explain much of the great difference in explained proportion of variance. In the linear model, the highest coefficient is found for the change in the agricultural population. The next

298 Olaf Dahlbiick

Table 2. Coefficient values for the relationship between independent variables and the change in the level of criminality in a linear model

Independent variable Coefficient value

AGRIPZ 0.74 DIVORP2 0.32 DIVORPl 0.30 PUBLP2 0.01 PUBLPl 0.40 MIGRP2 0.41 MIGRPl 0.17 YOUNGP2 0.16 YOUNGPl -0.02 Intercent -0.26

highest coefficients are found for the change in migration during the second period and for the change in the proportion of children in public leisure centers during the first period. The coefficient for the change in the proportion of divorced inhabitants in the second period has about the same positive, rather high value as the coefficient for the change in the same proportion in the first period, which should be interpreted to mean that these changes have about the same influence on the change in criminality. Further, for the changes in migration during the first period and the proportion of young men during the second period there are coefficient values of substantial magnitude. Obviously, then, the obtained coefficient values in the two solutions for the multiplicative model give a picture of the influences on criminality that differs considerably from the picture that is given by the coefficients in the linear model.

5. Concluding remarks

Using the multiplicative model presented in this study has advantages over using the corresponding linear model. This model allows for an analysis of complicated non-linear relationships. Using the model, it has been possible to explain much more of the variance in the changes in criminality than has been the case using the linear model.

Admittedly, however, there are also disadvantages. Using the multiplicative model, greater demands must probably be made upon the validity of the independent variables, since multiplication of measurement errors with measurement errors may create greater deviations from the true theoretical values of criminality than when such errors are linearly combined. There is


of course also the problem of finding a global minimum of the sum of squares. In this study, the explained proportion has been shown to be insensitive to changes in the coefficient values. Moreover, a multiplicative model is especially problematic to use in statistical induction. In the study presented here, such induction is irrelevant. It is not possible to generalize statistically in a strict sense beyond the 137 analyzed municipalities. Obviously, these municipalities are not a random sample drawn from all 274 municipalities. Neither can they reasonably be seen as a random sample from a hypothetical population of units obtained by various divisions of the total area they occupy or obtained by using various points in time. Further, measurement errors do not seem to create induction problems. The independent variables can be assumed to have perfect or nearly perfect reliability, and the possibly low reliability of the difference in criminality is not very troubling since an ordinary least-square fit is used. However, in studies other than the one presented here, statistical induction may of course be seriously problematic.

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constructing and using a multiplicative model of the impact of societal changes on violent crime

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