Revisit Of Loomis'S Growth Predictions 10-Years Later

[Analytics]

Roger,

That’s kind of harsh, but you can phrase it however you want. We will have to just agree to disagree about this. The data are neither largely irrelevant nor misleading, they just didn’t agree with what you wanted to say. You admitted that your emphasis on changes in the growth rate only since 1979 was based on non-statistical considerations. There was no good data-based reason to restrict the training data to data post-1978. You gave some (unreferenced) reasons relating to the growth of other large organizations, and you hinted strongly but non-quantitatively about defection rates and unprecedented missionary efforts. But that is just unconvincing talk until you can back it up with a model, based on justifiable parameter values, that shows the growth rate can never stabilize again…

Hi Bruce,

Thanks for weighing in again.

I’ve tried to explain why in general, the continued exponential growth of anything is the exception, not the rule. If that’s generally true, then the null hypothesis of the future growth of anything should be a decreasing growth rate. Thus, those who believe in long-term continued exponential growth are the ones with the burden of proof. It appears we’re at an impasse on this basic point.

If I understand correctly, you and he-who-must-not-be-named believe that because he knows some people with 8 children, the birthrate among active Mormons has gone up. But you don’t know how much. So you then conclude that the decreasing crude birth-rate in the church is due solely to a high rate of defection….

The Church’s birth rate (defined as new members of record divided by total membership) has dropped to a level close to its mortality rate. That in-and-of-itself indicates an end of exponential growth, regardless of whether or not it has anything to do with inactivity rates.

Likewise, the Church’s conversion rate has dropped from 40 converts per-member to about 20 converts per-member, and appears to be continuing to decline. This is another indication of the end of exponential growth, regardless of whether or not it has anything to do with inactivity rates.

All of the data I can see is consistent with the null-hypothesis—the church isn’t growing exponentially.

10 years ago I made a crude forecast consistent with this observation. Just because the model was crude doesn't mean the reasoning was invalid. The forecast turned out to be slightly optimistic, with growth slowing down even more than I thought it would.

You’ve made vague insinuations that the lowering growth rate is a temporary phenomenon. Is it possible the growth rate will rebound? Yes, of course it is possible. But the null hypothesis is that it won’t. If you have a specific model that explains the slowdown and forecasts a rebound, I’d be interested in seeing it. Referring to previous rebounds in the growth rate proves that it’s possible for growth rates to rebound, but they don’t prove that in the future such rebounds are likely.

[zielkee]

Sure there are more missionaries now and sure there are more inactives on church membership rolls, but are there proportionately more of them? If so, how much more (proportionately)? My preliminary look at the missionary/member ratio actually shows a decrease.

I have heard the actual number of missionaries has not gone up, that maybe it has declined?

Evelyn

[zielkee]

I think an interesting correlation would be to overlay this graph with global economic trends. Maybe the stock market?

Evelyn

[zielkee]

This may be true that the internet has had a huge effect on people being converted.

I've heard that in Tennessee, referrals from the internet are 30 times what missionaries were getting from members and street proselytizing.

Evelyn.

[Bruce Schaalje]

Hi Bruce,

Thanks for weighing in again.

I’ve tried to explain why in general, the continued exponential growth of anything is the exception, not the rule. If that’s generally true, then the null hypothesis of the future growth of anything should be a decreasing growth rate. Thus, those who believe in long-term continued exponential growth are the ones with the burden of proof. It appears we’re at an impasse on this basic point.

Roger,

I don’t know if you have had a chance to play around with my difference equations. I want to show you the results of one simulation using this model. I seriously invite you (and the other unnamed guy also) to play around with it. Tell me if you think it misrepresents the situation in any way. I believe that it captures the essence of growth in church membership as represented by the numbers reported by the church in April conference every year. I used the model:

T_t = Y_t + X_t

Y_t = Y_t-1(a)(b +1-d1 + c)

X_t = Y_t-1(1-a)(1-d1) + X_t-1(1-d2)

where T_t is the total reported number of members in year t, Y_t is the number of active members on the rolls in year t, X_t is the number of inactive members on the rolls in year t, a is the yearly activity rate (and therefore 1 – a is the defection rate), b is the yearly birth rate for active members, d1 is the death rate for active members, d2 is the death rate/name removal rate/washout rate for inactive members on the rolls, and c is the per-active-member convert baptism rate. Note that none of the growth constants in this version of the model changes over time, so the underlying forces in this model are all strictly exponential.

I set the initial values of Y and X to 4000000 and 2000000. I set b=.02, a=.9, d1=.005, d2=.002, and c=.10. None of these values is out of line. I let the population grow for 50 years. Attached are the total population sizes and the crude (or resultant or apparent) growth rates. Note that even though the forces were all exponential, the resultant population growth curve looked linear, and the pattern of the apparent growth rates was decreasing.

This is the reason that I firmly believe that an apparent decline in crude growth rates in the church over the past 20 or 30 years says very little about the health of the underlying growth processes. There really is no warrant to claim that the proselyting effectiveness is decreasing, or that children are being taught the gospel less effectively than ever, or that the rate of defection is getting worse.

Please let me know if you find errors in anything I have done here. If you want, I can send you the R code for playing around with the model.

Bruce

[Analytics]

Hi Bruce,

Interesting model—thanks for taking the time to put these formulas together. You successfully make the point that the active membership of the church could be growing exponentially while the “crude” growth level does not. However, your formula doesn’t address your basic question: what changed? The nominal (i.e. “crude”) membership of the church was growing exponentially until about 30 years ago, and then the pattern switched to the declining growth rate that your model illustrates. What changed?

Playing with your model, I thought I’d use all of the parameters you suggest, except setting the initial values of Y and X to 7,596,348 and 3,798,174 respectively. This gives a T of 11,394,522 for 12/31/2001. On the graph below, this model is called “Bruce”. This model forecasts the size of the church for 12/31/2011 to be 19,200,000 (when it was really 14,400,000), so the values are a little off. I did two things to calibrate it. First, I changed c from 0.1 to 0.037273. This value gives the correct number of conversions for 2002. This caused 2011 to come in at about 14,000,000 members. To further fine-tune it, I changed a (the activity rate) from 0.9 to 0.921438, so that the membership as-of 2011 comes in at 14,441,000. This is the model I’m called “Bruce Calibrated”.

That doesn’t look right to me either—adjusting the conversion rate and activity rate to match recent experience causes the growth rate of the actives to be negative—not the point you were trying to make. And with the growth of units, it’s clear the actives are in fact growing.

I decided to try the initial Y and X as 3,418,357 and 7,976,165, corresponding to only 30% of the members active. The calibrated active conversion rate to jump up to 0.082829, and the active rate at 0.921438 still fit. This model projects 47,364,012 members as-of 2080 (less than nine million of which are active).

In any case, your model illustrates my basic point—the assertion that the nominal membership will grow exponentially for 100 years is unlikely. My two attempts to calibrate your model both produce results that are very close to my original model for several decades, and establish that my original 30-million estimate, plus or minus 10-million, is a much more likely range for the size of the 2080 church than Stark’s 80-280 million range.

Edited April 13, 2012 by Analytics

[Bruce Schaalje]

Hi Bruce,

Interesting model—thanks for taking the time to put these formulas together. You successfully make the point that the active membership of the church could be growing exponentially while the “crude” growth level does not.

Roger,

I guess we’re at a good point then.

I agree with you that nominal church growth over the past 30 years has been approaching a linear pattern, and nominal growth rate has been decreasing. If birth, death, conversion, and defection rates remain constant (i.e. the underlying growth processes are exponential), exponential nominal church growth will not happen again although something like linear nominal growth will continue.

I do not agree that the presumption (or null hypothesis), for a church of 14 million nominal members out of a world population of 7 billion (0.2%), is necessarily for an intrinsically slowing growth rate. At some point, of course, growth must intrinsically slow.

Most importantly, I do not agree that nominal linear growth implies anything negative about the church or its missionary program or its families. In your original paper you discussed external and internal forces and limits that might account for the linear growth, but the difference equation model illustrates that the decrease in nominal growth rate can happen even when nothing sinister is going on. The Tribune’s take your article was predictably more negative, and Xander even more predictably took the opportunity early in this thread to gloat about the inevitable dark implications:

The Church's growth rate is dropping substantially. It is becoming more and more difficult to obtain the level of success it once enjoyed in the past. The biggest enemy of the Church is information, and in our age of information, it is just an uphill battle for them.

The number of missions is actually dropping, and the number of converts per missionary has dropped substantially since the early 90's. The number of missionaries in the mission field has dropped since the mid-90's and has since leveled off (despite claimed increases in overall membership) because of the increasing levels of inactivity among Mormon teens. . . .

All evidence points to the fact that the more people know about the Church, the less likely they are to join it.

These are conclusions that are not justified by the membership data reported by the church.

However, your formula doesn’t address your basic question: what changed? The nominal (i.e. “crude”) membership of the church was growing exponentially until about 30 years ago, and then the pattern switched to the declining growth rate that your model illustrates. What changed?

I have played around with some parameter values in the difference equation model that result in an increase followed by a decrease in the nominal growth rate. That kind of thing might play a role, but I don’t think it fully explains the changes. Lots of other things were going on: the age structure of the church changed (especially due to aging of the baby boomer generation), the revelation on the priesthood occurred, the Soviet empire collapsed, other major international economic and political events occurred, other randomness occurred and was propagated by the complex dynamics of church growth. I really don’t believe that intrinsic growth forces have ever been constant. I think there is room for both Stark-like euphoria about the growth of the church and Loomis-like caution.

One final thing: I think the membership numbers as reported by the church are honest good-faith values. A call has to be made about how to count non-active members; I think the church statistical department has made a sensible choice, and has been consistent in their counting and reporting. The church membership numbers are not like Soviet production statistics. They are not perfect, but they are consistent. Knowing that they are honest, we can have useful discussions like this.

[Analytics]

Hi Bruce,

As a concluding remark about my church growth analysis, the line “Bruce Calibrated 2” and “Loomis” are essentially the same until 2040. That is clearly the path the church is on. Of course something might change at any time, but the growth has been essentially linear on that slope for 30 years and I don’t see anything happening that will cause that pattern to change in the short term.

Around 2040, the two lines finally diverge. That’s because of the moderate exponential growth entailed within Calibrated-2 two finally starts to pick up momentum at that point. It wouldn’t be extraordinary if the church follows that path; exponential growth often continues. However, more often it does not. That’s why I wouldn’t predict the exponential growth of anything in the real world to last 70 years unless I had specific positive reasons to believe so.

I don’t think any of this says anything negative about the church either; there is nothing wrong with not growing exponentially. Quite the opposite in fact--

.

I am sure that there is nothing explicitly dishonest about the numbers that are reported. However, the church is selective with what it reports. Doing so is certainly its prerogative, but it’s misleading to cite 14.4 million adherents when the true number of people who even acknowledge their membership is at least a few million fewer. By not being more forthright with things like the number of active members and the number of temple-recommend holders, the church is inviting speculation and suspicion.

Thanks again for weighing in on this thread. I’m going to put it out of its misery now and focus on other things. I hope we can talk about this more in 2022.

-Roger