Diffusion analysis: Methods and variables

I followed a dyadic approach (Gilardi and Füglister 2008; Neumayer and Plümper 2010) to find out factors which facilitate convergence between the sample countries.

Dyadic analysis uses pairs of countries as the unit of analysis. A dyadic dataset hence consists of observations in which two individual countries (henceforth referred to as country A and country B) in a given year form a pair (dyad). Each row in the dataset lists a dyad-year (Neumayer and Plümper 2010: 150).

The outcome of interest is whether country A converges towards country B over time. In technical terms the outcome of interest is a reduction in the difference between two countries forming a dyad in regards to a measure they are compared by at two points in time (Gilardi and Füglister 2008: 422):

|measure_At− measure_Bt−1| < |measure_At−1− measure_Bt−1|

An example helps to illustrate the idea: country A converges towards country B if the difference between the imprisonment rate (= measure) of country A in a given year and the imprisonment rate of country B in the previous year is smaller than the difference between the imprisonment rates of both countries in the previous year. Let country A be Austria and country B be the Czech Republic. In 1996 the imprisonment rate of Austria is 88 and the imprisonment rate of the Czech Republic is 202. In the following year, 1997, the imprisonment rate of Austria is 91. The imprisonment rate of Austria hence converged towards that of the Czech Republic, as the difference between the rates of Austria in 1997 and Czech Republic in 1996 (111) was smaller than the difference between the two countries in 1996 (114).

Convergence can take place in two directions. Country A can move closer to country B, but country B can also move closer to country A. Therefore the analysis is based on a directed dyadic data set in which each combination of countries appears twice (e.g. Austria-Hungary and Hungary-Austria). Consequently each country takes the role of A in one dyad and the role of B in the other. All possible pairs between the 21 sample countries were considered, with the dataset for the upcoming analyses comprising 420 dyads, each of which is observed over a period of 15 years (1996-2010). This results in 6720 dyad-year observations.

The dependent variables, i.e. the variables for identifying convergence, are coded 1 if convergence of an indicator within a dyad takes place in a given year, i.e. if the above equation is true. The variables are coded 0 in cases where country A increases its difference on an indicator compared to country B in the previous year, or in cases where the difference between the two countries forming a dyad remains unchanged.

The variables whose convergence among the sample countries was assessed were selected according to their capacity to discriminate between clusters. In regards to the collective experience of crime the following sections only investigate conver-gence of homicide and imprisonment rates because both indicators significantly and consistently differed between clusters in the 1995-2000 as well as in the 2005-2010 data.

Only convergence of total social expenditure and expenditure for unemployment benefits are analysed for solidarity. Even though expenditure for unemployment benefits did not significantly differ between the clusters identified above, the factors which contribute to the convergence of this particular aspect of institutionalised solidarity are still of interest. Unemployment benefits represent one of the most outreaching forms of institutionalised solidarity as they do not target the middle classes, but are directed at vulnerable groups of the population. The risk of having to claim unemployment benefits is not distributed equally and is highest for people in the working class with low-income jobs and/or who suffer from chronic diseases (Heidenreich 2015; Karren and Sherman 2012). Furthermore, benefit cuts are often discussed with a special focus on the unemployed, arguing that cuts are necessary so that people are encouraged to work rather than ‘taking the easy way of claim-ing benefits’ (Marx and Schumacher 2016). Furthermore, figure 27 in section 5.4 showed that public concern for the wellbeing of unemployed fellow citizens is lowest compared to concern for the wellbeing of the elderly and the sick and disabled.

To identify convergence across time, for each of these four indicators a dichoto-mous variable was created, which is coded 1 if convergence took place in a given year, and 0 if the difference between two countries forming a dyad remained the same or increased. The dependent variables of the research are thus four dichoto-mous variables.

Since the dependent variables are all dichotomous, irrespective of which indicator is compared over time, logistic regressions were calculated to determine factors which facilitate or hinder convergence. Separate logistic regressions were calculated for convergence of homicide and imprisonment rates, and for convergence of total social expenditure and expenditure for unemployment benefits.

Three independent variables shed light on whether convergence is more likely to happen within or across clusters, within or across families of nations, or within or across worlds of welfare. These three variables are dichotomous. The first variable indicates whether the two countries forming a dyad are within the same solidarity or collective experience of crime cluster during 1995-2000 respectively. The second variable indicates whether the two countries that form a dyad are within the same family of nations. The third variable indicates whether the two countries forming a

dyad are within the same world of welfare classification.

Convergence of policy outputs between countries, as well as convergence of social indicators like homicide, can result from those countries facing similar challenges and situations. In addition, policy convergence can also result from the spread of what is considered ‘best practice’ (Gilardi and Füglister 2008). The primary aim of this chapter is not to explain the exact mechanisms which underlie diffusion processes and which can thereby instigate convergence, but rather to identify the likelihood of convergence of policy outputs and social indicators within or across groupings of countries. Nevertheless, it is important to control for the existence of political and social factors which might instigate a diffusion process and thereby facilitate or hinder convergence.

Thus, the models include a number of control variables. On dyadic level the analyses control for a number of similarities between two countries forming a dyad that potentially influence convergence. The following variables assess the similarities between two countries forming a dyad for each year in the data.

First, analyses assess whether the two countries forming a dyad are both charac-terised by high levels of inequality. This variable is coded 1 if in a given year both countries that form a dyad are among the 25 percent of countries with the highest Gini coefficient (i.e. highest level of inequality) in the sample, and 0 otherwise.

Second, models control for whether the two countries that form a dyad experience the same economic development in a given year. This variable is coded 1 if both countries forming a dyad experienced GDP growth, or if both countries experienced a decline in GDP. If the GDP of country A grew while the GDP of country B de-clined, or vice versa, this variable is coded 0. Third, analyses assess whether the largest government parties of both countries that form a dyad have the same ideo-logical orientation. Government’s ideoideo-logical orientation can significantly influence policy output and therefore contribute to convergence (Hibbs 1977). This variable is coded 1 if both governments are either dominated by a left, both are dominated by a centre, or both are dominated by a right-wing party in a given year. The variable is 0 if two governments have different ideological orientations, i.e. one left while the other one is centre and so on. Fourth, analyses of convergence of imprisonment rates also control for whether crime is a salient issue on the political agendas of both countries in a given year. This variable is coded 1 if political parties’ manifestos in both countries are among the top 25 percent that give the greatest issue attention to support for law and order, and 0 if otherwise. Fifth, analyses of convergence of total social and unemployment expenditure control for whether both countries are troubled with high unemployment rates. This variable is coded 1 if both countries are among the 25 percent of countries with the highest unemployment rate within

the sample, and 0 if otherwise.

Analyses also include control variables at the country level. Even though these variables do not describe the pair of countries, it is still important to control for cer-tain country characteristics which can influence the measure by which the countries are compared. Therefore analyses control for income inequality (Gini coefficient), economic development (GDP growth) and the ideological orientation of the largest government party in country A, as previous research has shown these measures to be significantly associated with crime, imprisonment rates and social policy outputs by previous research (Adema, Fron, and Ladaique 2012; Downes and Hansen 2006;

Fajnzylber, Lederman, and Loayza 2002; Jennings, Farrall, and Bevan 2012; Sutton 2004). Analyses concerned with convergence of imprisonment rates also control for the issue attention given to law and order in manifestos of political parties in coun-try A, while analyses concerned with institutionalised solidarity control for councoun-try A’s unemployment rate.

Standard errors were clustered around dyads to account for the non-independence of observations over time within dyads. Time-fixed effects were included to account for temporal effects.

6.5.2 Convergence of violent crime, imprisonment, and welfare state