Simulation of how funding formula for UK universities creates disparities between institutions over time. See blogpost The Matthew Effect and REF2014 on http://deevybee.blogspot.co.uk/.

1. #------------------------------------------------------------------------------------# REFsim by D V M Bishop
# Simulates impact of REF on university income
# 13/10/13
#------------------------------------------------------------------------------------# Plots funding income for each university over each funding cycle
# Assumes greater funding allows higher-level academics are appointed
# You can vary the following:
# N universities (Nunis)
# Nstaff per university (Nstaff; currently constant for all unis)
# turnover ; proportion of staff changing over each cycle
# nrounds ; number of cycles of hiring/REF
# cutoff; mycut dimension: zscores corresponding to 1*,2*,3*,4* the higher cut[4] is, the fewer will
meet 4*
# starwt; dimension specifying weighting given to each star level
# budget; arbitrary - currently kept constant at each cycle
# plotdec; determines whether plot shows all unis or grouped into deciles
# results also depend on unipower, which is computed below
# unipower determines how spending power relates to calibre of new academics
# it's a weighted z-score of income
Nacads=10000; #total pool of academics
Nunis=100
Nstaff=50
# N universities
#Nstaff per uni
turnover=.1; #% staff change each run
turnstaff=round(turnover*Nstaff)
nrounds=6;
mycut=c(-1,0,1,2)

2. #zscorecutoffs for 1star, 2star,3star and 4star
#determines the percentage of cases meeting criteria for each star band
starwt=c(0,0,1,9)
#determines the weighting given to each star in funding formula band
budget=5000; #arbitrary number to keep total spend constant over time
plotdec=0; #set to one to plot decile ranges rather than all unis
uniall=matrix(rep(0,nrounds*Nunis),nrow=Nunis)#initialise matrix
#------------------------------------------------------------------------acadscore=rnorm(n=Nacads, m=0, sd=1) #random normal distribution of outputs
#assign academics to universities
acaduni = matrix(
sample(acadscore,Nstaff*Nunis), # the data elements
nrow=Nunis ,
# number of rows
ncol=Nstaff,
# number of columns
byrow = TRUE)
#--------------------------------------------------------------# initialise funds to zero for all
#--------------------------------------------------------------fundsuni=matrix(rep(0,Nstaff*Nunis),
nrow=Nunis, ncol=Nstaff)
#------------------------------------------------------------#
# loop start here
#-----------------------------------------------------------for (thisround in 1:nrounds){
fourstar=which(acaduni>mycut[4])
threestar=which(acaduni>mycut[3])

3. twostar=which(acaduni>mycut[2])
onestar=which(acaduni>mycut[1])
fundsuni[onestar]=starwt[1]
fundsuni[twostar]=starwt[2];
fundsuni[threestar]=starwt[3];
fundsuni[fourstar]=starwt[4];
unirawtotalincome=rowSums(fundsuni) #income per uni not adjusted for budget
unitotalincome=budget*unirawtotalincome/sum(unirawtotalincome) #adjusted for budget
#uncomment lines below to show histogram
# mytitle=c('round',thisround,'totalspend',sum(unitotalincome))
# hist(unitotalincome,main=mytitle,breaks=10)
#readline("Press <return> on console to continue")
incmean=mean(unitotalincome)
incsd=sd(unitotalincome)
unipower=(unitotalincome-incmean)/(incsd*.75) #formula that relates income to
# calibre of new staff
for (thisuni in 1:Nunis){
changestaff=sample(1:Nstaff,turnstaff)
acaduni[thisuni,changestaff]=acaduni[thisuni,changestaff]+unipower[thisuni]
}
uniall[,thisround]=unitotalincome

4. }
# for plotting sort the unis by income
unisorted=(uniall[order(uniall[,1]),] )
pickuni=seq(1,Nunis,by=10)#pick every 10th uni
uniall2=(unisorted[pickuni,]+unisorted[pickuni+1,]+unisorted[pickuni+2,]+unisorted[pickuni+3,]+unis
orted[pickuni+4,]+unisorted[pickuni+5,]+unisorted[pickuni+6,]+unisorted[pickuni+7,]+unisorted[pick
uni+8,]+unisorted[pickuni+9,])/10
mytitle=t(c('Weights: 1*=',starwt[1],"; 2*=",starwt[2],'; 3*=',starwt[3],'; 4*=',starwt[4]))
mydata=uniall #default plot all unis
if (plotdec==1){
mydata=uniall2 #otherwise plot decile bands
}
matplot(t(mydata),type='l',lwd=2,las=1,xlab='Cycle',ylab='Income',main=paste(mytitle,collapse=''),co
l=1,lty=2,ylim=c(0,300))