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#
# Author
# Jian-Cheng Li
# Sun Yat-Sen University.  Business School
# Address: No. 135, Xingang Xi Road, Guangzhou, 510275, P. R. China
# Tel: +86-17816876142
# E-mail:[email protected]; [email protected]
#
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#
#region为地区个数（省份、城市），period为年份数，marketclass 为商品种类数，firstyear为样本期的第一个年份
#region=a,period=b,marketclass=c,firstyear=y
#
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MarketIntergation <- function(data,a,b,c,y)
{
  regionpair<- data.frame(Province1=rep(unique(data$province),each=a),Province2=rep(unique(data$province),a))
  Matrix <- matrix(nr=a*a*b,nc=c)
  for(x in 1:c)
    {for(k in 1:(b-1))
      {for(i in 1:a)
        {for(j in 1:a)
          {Matrix[a*a*k+a*(i-1)+j,x] <- abs(log(data[data$year==(y+k),][i,x+2]/data[data$year==(y+k),][j,x+2])-
                                           log(data[data$year==(y-1+k),][i,x+2]/data[data$year==(y-1+k),][j,x+2]))
          }}}}
  
  year <- unique(data$year)
  Name <- paste(regionpair$Province1,regionpair$Province2,sep=".")
  Marketpair <- data.frame(rep(Name,b),Year=rep(year,each=a*a))
  Marketpair <- cbind(Marketpair,Matrix)

  for(x in 1:c)
    {for(i in year)
      {Marketpair[Marketpair$year==i,][,x+2] <- Marketpair[Marketpair$year==i,][,x+2]-mean(Marketpair[Marketpair$year==i,][,x+2],na.rm=TRUE)
    }}
  
  for(i in 1:length(Marketpair[,1]))    
     {Marketpair$Goodsvar[i] <- var(t(Marketpair[i,-c(1,2)]),na.rm = TRUE)}
  
  provincename <- unique(data$province)
  Market <- data.frame(Province=rep(provincename,each=b),Year=rep(year,a))
  Marketpair <- cbind(Marketpair,regionpair)
  Marketpair <- Marketpair [!(Marketpair$Province1==Marketpair$Province2),]
  
  Mindex <- vector()
  s <- 0
  for(i in provincename)
    {for(j in year)
      {s <- mean(Marketpair[ which((Marketpair$Province1==i) & (Marketpair$Year==j)),]$Goodsvar,na.rm=TRUE)
       Mindex=c(Mindex,s)}}
  
  Market$MarktINDEX <- Mindex
  Market$MarktINDEX <- sqrt(1/Market$MarktINDEX)
  return(Market)
}

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#Reference:
#毛其淋, 盛斌. 对外经济开放、区域市场整合与全要素生产率[J]. 经济学(季刊), 2012(01):185-214.
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