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NW_EntryModel.R
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NW_EntryModel.R
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# Nelson Winter Entry Model
# The model is based on the NW model discussed in Chapter 12 of
# Nelson, R.R., and Winter, S.G. (1982),
# "An Evolutionary Theory of Economic Change",
# Belknap Press, Cambridge, Mass. and London.
#
# Version 1.0 by
# Erol Taymaz
# Department of Economics
# Middle East Technical University
# Ankara Turkey
# www.metu.edu.tr/~etaymaz/nwm
# 18 September 2011
# R OPTIONS
# Enter recover option so that debugging will be easier
options(error=recover)
# Convert warnings to errors
options(warn=2)
# Run Simulations - nIter: number of iterations, nFirm: number of firms, setSeed: set the initial seed to 123 (TRUE) or not (FALSE)
run <- function(nIter=100, nFirm=8, setSeed=FALSE) {
# Set parameters
param <<- setPara(setSeed)
# Attach param list so that each paremeter will be used by its name
attach(param)
# Initialize firms
firms <<- setFirms(nFirm)
# Initialize markets
market <<- setMarket(nFirm)
# Data collection variables
outTech <<- list(c(max(firms$A),firms$A))
outMS <<- list(firms$q/sum(firms$q))
outID <<- list(c(1:nFirm))
# Simulate the model
for (time in c(2:nIter)) iterate(time)
# Detach parameter list
detach(param)
# Re-make outTech and outMS
outTech <<- remakeTech()
outMS <<- remakeMS()
# Plot results
pMarket()
# Plot market shares and technological level variables by using
# functions pMS() and pTech()
}
# Parameter setting function
setPara <- function(setSeed) {
# Set the seed for random number generator if setSeed parameter is TRUE
# Default is FALSE
if (setSeed==TRUE) set.seed(123)
parameters <- list(
rin = 0.0205, # Innovation expenditures, rin
rim = 0.00102, # Imitation expenditures, rim
cc = 0.160, # Cost of capital, c
an = 0.1250, # Innovation parameter, an
am = 1.250, # Imitation parameter, am
dep = 0.030, # Depreciation rate
dL = 67.000, # Demand level parameter
dG = 0.010, # Demand shift parameter
tL = 0.160, # Level
tG = 0.010, # Rate of change
tSd = 0.050, # Std dev
Bank = 1, # Bank
K = 390.8, # Initial total capital stock
nMax = 5, # Max number of new firms
nExo = 0.1, # Exogenous entry probability
nPro = 2.5, # Profit elasticity of entry rate
newS = 0.75, # Average entry size
newSd = 0.75, # Average std dev of entry size
newA = 0.75, # Average tech level of new firms
newAd = 2, # Ave std dev of tech level of new firms
minEntK = 1, # Min K stock of new firms
minEntA = 0.1, # Min tech level of new firms
maxNegProf = 5, # Max periods of negative profit before entry
minNFirm = 3
)
return(parameters)
}
# Firm initialization function
setFirms <- function(nFirm) {
# Set data frame for firms
firms <- data.frame(matrix(0, nrow=nFirm, ncol=7))
names(firms) <- c("id", "k", "A", "q", "profit", "I", "negP")
firms$id <- c(1:nFirm) # Firms' id number
firms$k <- K/nFirm # Capital stock
firms$A <- exp(tL) # Technology
firms$q <- firms$k*firms$A # Output
price <- dL/sum(firms$q) # Product price
firms$profit <- (price * firms$A) - cc - rin -rim
firms$negP <- rep(0, nFirm) # Performance counter
firms$I <- invest(price, firms$q, firms$A, firms$profit)
return(firms)
}
# Market initializaton function
setMarket <- function(nFirm) {
# Set data frame for the market
market <- data.frame(matrix(0, nrow=0, ncol=8))
names(market) <- c("Q", "P", "HI", "tF", "A", "Profit", "K", "invSh")
market[1,"Q"] <- sum(firms$q)
market[1,"P"] <- dL/sum(firms$q)
market[1,"HI"] <- 1/sum((firms$q/sum(firms$q))^2)
market[1,"tF"] <- max(exp(rnorm(1,tL,tSd)),market$tMax[1])
market[1,"A"] <- sum(firms$k*firms$A)/sum(firms$k)
market[1,"Profit"] <- sum(firms$k*firms$profit)/sum(firms$k)
market[1,"K"] <- sum(firms$k)
market[1,"invSh"] <- sum(firms$I)/sum(firms$k)
return(market)
}
# Investment function
invest <- function(P, q, A, profit) {
ms <- q/sum(q)
cash <- ifelse(profit<0, profit, profit*(1 + Bank))
desInv <- 1 + dep - (2-ms)/((P*A/cc)*(2-2*ms))
return((q/A)*pmax(0,pmin(cash,desInv)))
}
# Innovation function
innDraw <- function(K) {
return(rin*an*K > runif(length(K)))
}
# Imitation function
immDraw <- function(K) {
return(rim*am*K > runif(length(K)))
}
# New firm entry function
enterFirms <- function() {
nNew <-sum(runif(nMax) < (nExo + nPro*mean(firms$profit)))
if (nNew>0) {
aveK <- mean(log(firms$k))
sdK <- sd(log(firms$k))
aveA <- mean(log(firms$A))
sdA <- sd(log(firms$A))
newId<- max(firms$id)+c(1:nNew)
newk <- max(minEntK, exp(rnorm(nNew, newS*aveK, newSd*sdK)))
newA <- max(minEntA, exp(rnorm(nNew, newA*aveA, newAd*sdA)))
newq <- newProfit <- newI <- newNP <- rep(0, nNew)
newFirms <- data.frame(newId, newk, newA, newq, newProfit, newI, newNP)
names(newFirms) <- c("id", "k", "A", "q", "profit", "I", "negP")
firms <<- rbind(firms, newFirms)
}
}
# Exit function
exitFirms <- function(){
survive <- maxNegProf > firms$negP
if (sum(survive) > minNFirm) firms <<- firms[survive,]
}
# Iteration function
iterate <- function(time) {
id <- firms$id
innDr <- innDraw(firms$k)
immDr <- immDraw(firms$k)
k <- pmax(0,firms$I+((1-dep)*firms$k))
tMax <- max(firms$A)
tF <- max(exp(rnorm(1,tL+((time-1)*tG),tSd)), market$tF[time-1], tMax)
A <- pmax(firms$A,
innDr*(firms$A + runif(length(firms$A))*(tF-firms$A)),
immDr*(firms$A + runif(length(firms$A))*(tMax-firms$A)))
q <- k*A
Q <- sum(q)
P <- (dL*(1+dG)^(time-1))/Q
HI <- 1/sum((q/sum(q))^2)
profit<- (P * A) - cc - rin - rim
I <- invest(P, q, A, profit)
negP <- pmax(0, firms$negP + ifelse(profit>0, -1, 1))
avePr <- sum(k*profit)/sum(k)
aveA <- sum(k*A)/sum(k)
sumK <- sum(k)
aveISh<- sum(I)/sum(k)
# Change/append global variables
firms <<- data.frame(id, k, A, q, profit, I, negP)
market[time,] <<- c(Q, P, HI, tF, aveA, avePr, sumK, aveISh)
# Append data collection variables
outTech[[time]] <<- c(tF, A)
outMS[[time]] <<- q/Q
outID[[time]] <<- id
# Exit firms
exitFirms()
# Enter new firms
enterFirms()
# Print iteration number
# if ((time%%10)==0) cat("Iteration : ", time, "\n")
}
# Graphics functions
pMarket <- function() {
# Create a layout for plots
# Four charts will be plotted on the same page
layout(matrix(c(1,2,3,4), 2, 2, byrow = TRUE))
plot(market$P, type="l", ylim=c(0, max(market$P)), main="Product price", xlab="Time", ylab="Price")
plot(market$HI, type="l", ylim=c(0, max(market$HI)),main="Concentration level", xlab="Time", ylab="1/HI")
plot(log(market$tF), type="l", main="Technology frontier", xlab="Time", ylab="Frontier level (log)")
plot(log(market$A), type="l", main="Average productivity", xlab="Time", ylab="Average productivity (log)")
}
pAccum <- function() {
# Create a layout for plots
# Four charts will be plotted on the same page
layout(matrix(c(1,2,3,4), 2, 2, byrow = TRUE))
plot(ma(growth(market$Q), 5), type="l", main="Output growth rate", xlab="Time", ylab="Growth rate, 5-year MA (%)")
plot(ma(growth(market$K), 5), type="l", main="Capital stock growth rate", xlab="Time", ylab="Growth rate, 5-year MA (%)")
plot(ma(100*(market$Profit), 5), type="l", main="Average rofit rate", xlab="Time", ylab="Profit rate (%)")
plot(ma(100*market$invSh, 5), type="l", main="Average investment rate", xlab="Time", ylab="Investment rate (%)")
}
pTech <- function() {
x <- c(1:nrow(outTech))
n <- ncol(outTech)
layout(matrix(c(1), 1, 1))
plot(x,log(outTech[,1]), type="n", main="Technological level", xlab="Time", ylab="Technological level (log)")
for (i in c(1:n)) lines(x, log(outTech[,i]), type="l", col=palette()[1+i%%8])
}
pMS <- function() {
x <- c(1:nrow(outMS))
n <- ncol(outMS)
layout(matrix(c(1), 1, 1))
y1 <- floor(100*min(apply(outMS, 1, minNA)))
y2 <- ceiling(100*max(apply(outMS, 1, maxNA)))
plot(x,100*outMS[,1], type="n", main="Market shares", ylim=c(y1, y2), xlab="Time", ylab="Market share (%)")
for (i in c(1:n)) lines(x, 100*outMS[,i], type="l", col=palette()[2+i%%8])
}
# Additional auxiliary functions
growth <- function(a) {
n <- length(a)
g <- 100*log(a[c(2:n)]/a[1:(n-1)])
return(g)
}
remakeTech <- function() {
iter <- length(outID)
maxID <- 1
for (i in c(1:iter)) maxID <- max(c(maxID, 1+outID[[i]]))
Tech <- matrix(NA, nrow=iter, ncol=maxID)
for (i in c(1:iter)) Tech[i,c(1,1+outID[[i]])] <- outTech[[i]]
return(Tech)
}
remakeMS <- function() {
iter <- length(outID)
maxID <- 1
for (i in c(1:iter)) maxID <- max(c(maxID, outID[[i]]))
MS <- matrix(NA, nrow=iter, ncol=maxID)
for (i in c(1:iter)) MS[i,outID[[i]]] <- outMS[[i]]
return(MS)
}
minNA <- function(x) {
return(min(x, na.rm=TRUE))
}
maxNA <- function(x) {
return(max(x, na.rm=TRUE))
}
ma <- function(x, n) {
r <- x
if (n > 0) {
s <- length(x)
r <- rep(0, s+1-n)
for (i in c(1:n)) r <- r + x[c(i:(s+i-n))]
r <- r/n
}
return(r)
}