Application of the Limited Enthusiasm Model with Reversion, Written in 2022.

The Roman Catholic church in England and Wales is part of the worldwide Catholic Church, whose headquarters are in Rome. The Roman church came to England in the 6th century, gradually placing the existing Celtic churches. Most of the church became protestant at the reformation, with the remaining Catholic adherents going underground. They were only able to worship openly after 1791. The church grew partly through conversion and partly through immigration from Catholic countries. It has declined since 1960. This analysis investigates the likelihood of decline leading to denominational extinction.

Estimating Model Parameters

I will use the Roman Catholic Church’s Mass attendance data to estimate the parameters of the Limited Enthusiasm Model with Reversion. Using this cut-down version of the Demographics Model avoids estimating values for child retention among church members, hardening rates etc. There is no information about these values for the Catholics in England and Wales. The reversion model has only five parameters:

  1. Reproduction Potential
  2. Duration Enthusiastic
  3. Loss Rate
  4. Fraction of Converts who Become Enthusiasts
  5. Initial Fraction of Enthusiasts in the Church

The key parameter is the reproduction potential. If this potential is less than one, then the Roman Catholic’s decline is to extinction.

Calibration Strategy

The best fit between data and model is found using least squares. Avoiding systematic deviations from the data can help reduce the number of best fits. To help find the most suitable parameter values, I vary parameters 3-5 above and optimise for 1-2, the reproduction potential and duration enthusiastic. Out of this optimisation set, I count how many indicate the church will become extinct. Although these parameter values cannot be determined with certainty, the likelihood of extinction is more robust.

Mass Attendance 2000–2020

I took the Mass attendance data from Brierley (2008-2020).

Most optimisations indicate that the Roman Catholic Church in England and Wales will become extinct. However, some optimisations suggest it could survive at a lower level than the present.

A typical declining optimisation is given in figure 1. The reproduction potential chosen was an average figure of 0.91, just under the extinction threshold of 1.

Limited enthusiasm model and the Roman Catholic church
Figure 1: Data Fit for Roman Catholic Mass Attendance in England and Wales and the Limited Enthusiasm with Reversion Model

The decline of the church’s Mass attendance is accelerating, figure 1. This model forecasts that the decline will slow again in the future. However, with a reproduction potential of 0.91, it will eventually become extinct.

Range of Optimised Parameters

The optimisations indicate a range of possible parameter values:

Reproduction Potential0.26–1.01
Duration Enthusiastic0.1–4.0 years
Loss Rate
(Reversion and Deaths)		3%–7%
Fraction of Converts who Become Enthusiasts10%-50%
Initial Fraction of Enthusiasts in the Church0.5%–3%
Model Parameters for the Roman Catholic Church in England and Wales

The very wide range of the reproduction potential reflects the difficulty of estimating parameters from attendance data alone. Simulations for the smallest and largest reproduction potentials are compared with a “middle” value of 1 on the margins of survival in figure 2. Nevertheless, whereas most optimisations indicate that Catholicism in the England and Wales will become extinct, there is the intriguing possibility of an eventual bounce-back later in the century. I would need further data, for example, leaving and death rates, to narrow down the possibilities.

Figure 2: Possible future scenarios for the Roman Catholic Church in England and Wales

Possible Extinction Date

Although the model predicts extinction, it does not indicate an extinction date. This model contains exponential decline because it does not capture the effects of ageing. By 2050, it forecasts the Roman Catholic church’s Mass attendance will be between a quarter and half a million in England and Wales. This result may be too optimistic.

Fitting a straight line to the data gives a more realistic estimate of the extinction date, as decline through ageing is a linear process. In the worst-case scenario, the Roman Catholic church would be extinct by 2048, figure 3. Averaging the data from 2000 gives a later extinction date of 2062. The church’s future will likely lie somewhere between linear and exponential decline. By 2030 some slowing down of its decline may be seen, perhaps avoiding extinction altogether.

Figure 3: Linear Fit to Roman Catholic Mass Attendance Data (England & Wales)

Long–Term View

Mass attendance shows the general pattern of the institutional lifecycle, figure 4, though I doubt if institutionalism is the main cause of this behaviour. The Catholic church has been an institution for many centuries. Also, the church does not make a large number of converts in the UK compared to its size. Instead, it has had long-term loyalty from most of its members. Thus, I would think most of the rise to 1960 is due to immigration and a high Catholic birth rate.

Figure 4: Roman Catholic Mass Attendance in England and Wales 1900–2020.

The decline may have more to do with a loss of loyalty, particularly among younger Catholics. That loyalty loss could come about if attachment to the church were more out of culture than commitment. Nevertheless, there are many committed Catholics. If that commitment is passed on to subsequent generations, then the Catholic decline could slow later in the century.