{"id":199,"date":"2012-07-25T04:21:12","date_gmt":"2012-07-25T01:21:12","guid":{"rendered":"http:\/\/ekqvist.goeuropeinfo.com\/rbloggerqvist\/?p=199"},"modified":"2012-07-25T04:21:12","modified_gmt":"2012-07-25T01:21:12","slug":"linear-programming-for-the-malmquist-productivity-growth-index","status":"publish","type":"post","link":"https:\/\/science.ekqvist.fi\/blogi\/dea\/linear-programming-for-the-malmquist-productivity-growth-index\/","title":{"rendered":"Linear Programming for the Malmquist Productivity Growth Index"},"content":{"rendered":"

Data Envelopment Analysis<\/h1>\n

Within couple of days I have been testing DEA modelling (Data Envelopment Analysis) with different R-package. Finally,…. I have found such a comprehensive way to calculate Malmquist indices.<\/p>\n

\"\"<\/a>
Chart 1<\/figcaption><\/figure>\n

My primary purpose is to show how to use nonparametric methods for measuring efficiency and productivity by using R-programs nonparaeff<\/em> -package.<\/p>\n

\"\"<\/a><\/p>\n

At this same time I will show you how to present Malmquist indices within googleVis<\/em> -world map and finally I will introduse how to make forecast chart for productivity (Chart 1), effectiveness and technical effectiveness indices. In this work I used R-program forecast -library.<\/p>\n

Used R-library documentation:
\nnonparaeff<\/a>
\ngoogleVis<\/a>
\nforecast<\/a><\/p>\n

First of all I would like to thank Author Dong-hyun Oh for nice work with this nonparaeff-package.<\/p>\n

In this working paper I will use example of faremalm2<\/em>. Like nonpraeff -package documentation we calculate Malmquist productivity growth index of OECD countries
\n(productivity, technical efficiency and efficiency). As data source we have used Penn World Table (like original sources) with following version:
\nOECD Timeseries 1980-1990\u00a0 version pwt5.6
\nOECD Timeseries 1990-2009\u00a0 version pwt7.0
\nIn pwt7.0 I cannot find capital stock data, so I downloaded it from here (http:\/\/www.ifw-kiel.de\/forschung\/datenbanken\/netcap<\/a>)<\/p>\n

Productivity calculation 1980-1990 As output variables is used\u00a0 Total GDP of a country. This variables\u00a0 is calculated using GDP per capita (rgdpl)
\nand amount of total population (pop). As input variables is used Total labor force (gdp\/rgdpwok) and Total capital stock\u00a0 (kapw * labor)<\/p>\n

In second productivity computing calculation 1990-2009 I only use one input and one output variables (labor and gdp). This is because there is no
\ncapital stock data available in pwt7.0 (please correct this If I missed something). I will re-calculate this period asap when I get capital data from all countries.<\/p>\n

In third productivity computing 1992-2002 I use pwt7.0 and get capital stock data from different OECD datasource
\n(http:\/\/www.ifw-kiel.de\/forschung\/datenbanken\/netcap<\/a>). As input I used labor and capital variables and as output variables gdp.<\/p>\n

When use faremalm2<\/em> function you will get the following outputs:
\npc.c –> Productivity growth for each country
\npc.y\u00a0 –> A trend of productivity growth of SELECTED countries (in this work we use OECD)<\/p>\n

tc.c –> Technical efficiency\u00a0 for each country
\ntc.y –> A trend of technical efficiency growth of SELECTED countries<\/p>\n

ec.c –> Efficiency change for each country
\nec.y –> A trend of efficiency change of SELECTED countries<\/p>\n

Useage of faremalm2<\/h2>\n

faremalm2(dat = NULL, noutput = 1, id = “id”, year = “year”)
\ndat –> The format of this data frame is data.frame(id, year, outputs, inputs).
\nnoutput –> number of outputs
\nid –> column name for DMU:s
\nyear –> column name for the time index<\/p>\n

## Malmquist productivity growth index of OECD countries
\n#First install data from OECD
\ninstall.packages(\"pwt\")\u00a0 # (installing a package can take a couple of minutes)
\n<\/code><\/p>\n

#Setting the library into use
\nlibrary(pwt) ## Use Penn World Table
\nlibrary(nonparaeff) # DEA modelling
\n<\/code><\/p>\n

More information about pwt data you can find there (http:\/\/pwt.econ.upenn.edu\/php_site\/pwt_index.php)<\/p>\n

#my.dat <- pwt5.6\u00a0 #used in 1980-1990
\n#my.dat <- pwt6.3\u00a0 #
\nmy.dat <- pwt7.0\u00a0 #used in 1990-2009 and 1992-2002
\n#head(my.dat)
\nsummary(my.dat)
\n#my.dat$country
\n<\/code><\/p>\n

#capital stock data missing so we get it from there
\n# http:\/\/www.ifw-kiel.de\/forschung\/datenbanken\/netcap
\n#picking up OECD countries
\nmy.oecd.ctry <- c(\"AUS\", \"AUT\", \"BEL\", \"CAN\", \"CHE\", \"DNK\", \"ESP\", \"FIN\", \"FRA\", \"GBR\", \"GER\", \"GRC\", \"IRL\", \"ISL\", \"ITA\", \"JPN\", \"KOR\", \"LUX\", \"MEX\", \"NLD\", \"NOR\", \"NZL\", \"PRT\", \"SWE\", \"TUR\", \"USA\", \"DEU\")
\n<\/code>
\n#NOTE WPCODE USED IN OLDER DATASET
\n#adding country code
\n#my.dat <- my.dat[my.dat$wbcode %in% my.oecd.ctry,]\u00a0 #use this with pwt5.6
\nmy.dat <- my.dat[my.dat$isocode %in% my.oecd.ctry,] #use this with pwt7.0
\nsummary(my.dat)<\/code><\/p>\n

#selecting appropriate years
\n#my.dat <- my.dat[my.dat$year %in% 1980:1990,]
\n#my.dat <- my.dat[my.dat$year %in% 1950:1992,]
\nmy.dat <- my.dat[my.dat$year %in% 1990:2009,]
\n#my.dat <- my.dat[my.dat$year %in% 1992:2002,]
\nsummary(my.dat)
\nmy.dat<\/code><\/p>\n

Note! I encounter problem (NA or other reason) thats why I do this out of box. my.dat is transformed into data.frame and after
\nthat modified with Excel. This is only used in timeseries 1992-2002 productivity calculation.<\/p>\n

#uploading my.dat
\n#my.dat_df <- as.data.frame(my.dat)
\n#out
\n#write.table(my.dat_df, file = \"c:\/data\/my.dat_df.txt\", sep = \"\\t\", col.names = NA, qmethod = \"double\")<\/code><\/p>\n

Capital stock data inserted in this phase. source: http:\/\/www.ifw-kiel.de\/forschung\/datenbanken\/netcap<\/a><\/p>\n

#...and in both source\n my.dat\u00a0 <- read.table(\"...\/mydat1990_2009.csv\",\u00a0 header=TRUE, \nsep=\";\", na.strings=\"NA\", dec=\",\", strip.white=TRUE)\nmy.dat <- read.table(\"http:\/\/ekqvist.goeuropeinfo.com\/rbloggerqvist\/\ndata\/oecd\/mydat1990_2009.csv\", header=TRUE, sep=\";\", na.strings=\"NA\", \ndec=\",\", strip.white=TRUE)<\/pre>\n
#INSERTING some variables\u00a0 to my.dat (ie. INPUT and OUTPUT -variables calculation)
\nmy.dat$rgdpl <- as.numeric(my.dat$rgdpl) ## GDP per capita
\nmy.dat$pop <- as.numeric(my.dat$pop) ## total population (1000)
\nmy.dat$rgdpwok <- as.numeric(my.dat$rgdpwok) ## GDP per labor<\/code><\/p>\n
my.dat$gdp <- my.dat$rgdpl * my.dat$pop ## Total GDP of a country
\nmy.dat$labor <- with(my.dat, gdp\/rgdpwok) ## Total labor force<\/code><\/p>\n
my.dat$capital <- with(my.dat, kapw * labor) ## Total capital stock\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 MISSING pwt7 note: this is used in pwt5.6\n #my.dat$capital <- as.numeric(my.dat$capital)\u00a0 \n## Total capital stock\u00a0 ADDED FROM DIFF. SOURCE now used in time \nseries 1993-2002<\/pre>\n
my.dat$kapw <- as.numeric(my.dat$kapw) ## Capital stock per labor\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 MISSING pwt7 note: this is used in pwt5.6\n #my.dat$kapw <- with(my.dat, my.dat$capital\/my.dat$labor) ## \nCapital stock per labor now used in time series 1993-2002<\/pre>\n
#variable used in 1990-2009 Malmquist productivity calculation<\/pre>\n
#1980-1990
\n#1990-2009
\n#1992-2002<\/p>\n
#these variables used in timeseries 1980-1990 and 1992-2002
\n#oecd <- my.dat[, c(\"country\", \"wbcode\", \"year\", \"gdp\", \"labor\", \"capital\")] #used in time series 1980-1990
\noecd <- my.dat[, c(\"country\", \"isocode\", \"year\", \"gdp\", \"labor\")] # 1990-2009
\n#oecd <- my.dat[, c(\"country\", \"isocode\", \"year\", \"gdp\", \"labor\", \"capital\")] #used in time series 1992-2002<\/code><\/p>\n
summary(oecd)
\nhead(oecd)
\n<\/code>
\n#removing\u00a0 NA-rows
\noecd <- oecd[!is.na(oecd$capital),]
\nsummary(oecd)<\/code><\/p>\n
#Now calcuatel productivity (pc), effiency (ec) and technical efficiency (tc)
\n#huom. t\u00e4m\u00e4 on tehty eri aikasarjoille ja hyv\u00e4 niin koska mahdollistaa eri aikajaksojen tarkastelun
\nlibrary(nonparaeff) # DEA modelling
\nre.oecd <- faremalm2(dat = oecd, noutput = 1, id = \"isocode\", year = \"year\")
\n#re.oecd <- faremalm2(dat = oecd, noutput = 1, id = \"wbcode\", year = \"year\")<\/code><\/p>\n
summary(re.oecd)<\/code><\/p>\n
######################################################
\n#ISOCODE USED IN #1990-2009 and 1992-2002
\n#note:<\/code><\/p>\n
## productivity growth for each country
\npc.c <- tapply(re.oecd$pc, re.oecd$isocode, geometric.mean)
\n#pc.c <- tapply(re.oecd$pc, re.oecd$wbcode, geometric.mean)
\n## a trend of productivity growth of SELECTED countries
\npc.y <- tapply(re.oecd$pc, re.oecd$year, geometric.mean)<\/code><\/p>\n
## technical efficiency\u00a0 for each country
\ntc.c <- tapply(re.oecd$tc, re.oecd$isocode, geometric.mean)
\n#tc.c <- tapply(re.oecd$tc, re.oecd$wbcode, geometric.mean)<\/p>\n
## a trend of technical efficiency growth of SELECTED\u00a0 countries
\ntc.y <- tapply(re.oecd$tc, re.oecd$year, geometric.mean)<\/p>\n
## efficiency change for each country
\nec.c <- tapply(re.oecd$ec, re.oecd$isocode, geometric.mean)
\n#ec.c <- tapply(re.oecd$ec, re.oecd$wbcode, geometric.mean)
\n## a trend of efficiency change of SELECTED\u00a0 countries
\nec.y <- tapply(re.oecd$ec, re.oecd$year, geometric.mean)
\n######################################################
\npc.c<\/p>\n
#1980-1990, 1990-2009
\n#country -variable(we use it in google vis plotting)
\n## productivity growth for each country
\npc.c <- tapply(re.oecd$pc, re.oecd$country, geometric.mean)<\/code><\/p>\n
## technical efficiency\u00a0 for each country
\ntc.c <- tapply(re.oecd$tc, re.oecd$country, geometric.mean)<\/p>\n
## efficiency change for each country
\nec.c <- tapply(re.oecd$ec, re.oecd$country, geometric.mean)<\/p>\n

\n#missing time series 1992-2002 TURKEY, KOREA, LUXEMBOURG AND MEKSIKO capital stock data
\n#VUOSITTAINEN startyear-endyear KESKIARVO TEHOKKUUSKERTOIMESSA (MALMQUIST - FARREL)
\n#ec: efficiency change\u00a0 #TEHOKKUUSMUUTOS
\nec.c_df <- as.data.frame(ec.c)
\nsummary(ec.c_df)
\nec.c_df
\n#tc: technical change\u00a0 #TEKNISEN TEHOKKUUDEN MUUTOS
\ntc.c_df <- as.data.frame(tc.c)<\/code><\/p>\n
 <\/p>\n
#pc: productivity change\u00a0 #TUOTTAVUUDEN MUUTOS
\npc.c_df <- as.data.frame(pc.c)<\/p>\n
#LITTLE TRICK
\n#ec: efficiency change\u00a0 #TEHOKKUUSMUUTOS
\nwrite.table(ec.c_df, file = \"c:\/data\/ec.c_df.txt\", sep = \"\\t\", col.names = NA, qmethod = \"double\")
\nec.c_df2\u00a0 <- read.table(\"c:\/data\/ec.c_df.txt\",\u00a0 header=TRUE, sep=\"\\t\", na.strings=\"NA\", dec=\".\", strip.white=TRUE)
\nnames(ec.c_df2)<- c(\"Country\", \"Effiency\")<\/code><\/p>\n

\n#tc: technical change\u00a0 #TEKNISEN TEHOKKUUDEN MUUTOS
\nwrite.table(tc.c_df, file = \"c:\/data\/tc.c_df.txt\", sep = \"\\t\", col.names = NA, qmethod = \"double\")
\ntc.c_df2\u00a0 <- read.table(\"c:\/data\/tc.c_df.txt\",\u00a0 header=TRUE, sep=\"\\t\", na.strings=\"NA\", dec=\".\", strip.white=TRUE)
\nnames(tc.c_df2)<- c(\"Country\", \"Effiency\")<\/code><\/p>\n
#pc: productivity change\u00a0 #TUOTTAVUUDEN MUUTOS
\nwrite.table(pc.c_df, file = “c:\/data\/pc.c_df.txt”, sep = “\\t”, col.names = NA, qmethod = “double”)
\npc.c_df2\u00a0 <- read.table(“c:\/data\/pc.c_df.txt”,\u00a0 header=TRUE, sep=”\\t”, na.strings=”NA”, dec=”.”, strip.white=TRUE)
\nnames(pc.c_df2)<- c(“Country”, “Effiency”)<\/p>\n
#REMOVING NA-VALUES
\nec.c_df2 <- ec.c_df2[!is.na(ec.c_df2$Effiency),]
\ntc.c_df2 <- tc.c_df2[!is.na(tc.c_df2$Effiency),]
\npc.c_df2 <- pc.c_df2[!is.na(pc.c_df2$Effiency),]
\nsummary(ec.c_df2)<\/code><\/p>\n
#just cecking country names
\nec.c_df2$Country<\/code><\/p>\n
#replace some country name with new one…
\nec.c_df3 <- gsub(“United States of America”, “United States”, ec.c_df2$Country)
\nec.c_df3 <- gsub(“Germany, West”, “Germany”, ec.c_df3)
\nec.c_df3 <- gsub(“Korea, Republic”, “South Korea”, ec.c_df3)<\/p>\n
tc.c_df3 <- gsub(“United States of America”, “United States”, tc.c_df2$Country)
\ntc.c_df3 <- gsub(“Germany, West”, “Germany”, tc.c_df3)
\ntc.c_df3 <- gsub(“Korea, Republic”, “South Korea”, tc.c_df3)<\/p>\n
pc.c_df3 <- gsub(“United States of America”, “United States”, pc.c_df2$Country)
\npc.c_df3 <- gsub(“Germany, West”, “Germany”, pc.c_df3)
\npc.c_df3 <- gsub(“Korea, Republic”, “South Korea”, pc.c_df3)<\/p>\n
#as a dataframe MUUNNETAAN DATA FRAMEKSI
\nec.c_df3 <- as.data.frame(ec.c_df3)
\ntc.c_df3 <- as.data.frame(tc.c_df3)
\npc.c_df3 <- as.data.frame(pc.c_df3)<\/p>\n
#check total number of rows KATSOTAAN RIVINUMEROINNIT MERGELLE
\nsummary(ec.c_df2)
\nnrow(ec.c_df2)
\nnrow(ec.c_df3)<\/p>\n
summary(tc.c_df2)
\nnrow(tc.c_df2)
\nnrow(tc.c_df3)<\/p>\n
summary(pc.c_df2)
\nnrow(pc.c_df2)
\nnrow(pc.c_df3)<\/p>\n
#used in time series
\n#1980-1990
\n#1990-2009
\n#giving row id ...NUMEROIDDAAN ID MERGE\u00c4 VARTEN
\nec.c_df2$id1=c(1:26)
\nec.c_df3$id1=c(1:26)
\ntc.c_df2$id1=c(1:26)
\ntc.c_df3$id1=c(1:26)
\npc.c_df2$id1=c(1:26)
\npc.c_df3$id1=c(1:26)
\n<\/code>
\n#...and for time series
\n#1991-2002
\n#giving row id ...NUMEROIDDAAN ID MERGE\u00c4 VARTEN
\nec.c_df2$id1=c(1:22)
\nec.c_df3$id1=c(1:22)
\ntc.c_df2$id1=c(1:22)
\ntc.c_df3$id1=c(1:22)
\npc.c_df2$id1=c(1:22)
\npc.c_df3$id1=c(1:22)
\n<\/code>
\n#merge data table and renamed country\u00a0 by id\u00a0 .....
\nec.c_df4 <-merge(ec.c_df2, ec.c_df3,\u00a0 by.x=\"id1\", by.y=\"id1\", all = TRUE)
\ntc.c_df4 <-merge(tc.c_df2, tc.c_df3,\u00a0 by.x=\"id1\", by.y=\"id1\", all = TRUE)
\npc.c_df4 <-merge(pc.c_df2, pc.c_df3,\u00a0 by.x=\"id1\", by.y=\"id1\", all = TRUE)<\/code><\/p>\n
#check the data
\nhead(ec.c_df4)
\nhead(tc.c_df4)
\nhead(pc.c_df4)
\nsummary(ec.c_df4)<\/code><\/p>\n
#selecting columns to the gvisGeoMapping\u00a0 .....
\nec.c_df5 <- data.frame(ec.c_df4$ec.c_df3, ec.c_df4$Effiency )
\ntc.c_df5 <- data.frame(tc.c_df4$tc.c_df3, tc.c_df4$Effiency )
\npc.c_df5 <- data.frame(pc.c_df4$pc.c_df3, pc.c_df4$Effiency )<\/code><\/p>\n
#check the data
\nhead(ec.c_df5)
\nhead(tc.c_df5)
\nhead(pc.c_df5)<\/code><\/p>\n
summary(ec.c_df5)
\nsummary(tc.c_df5)
\nsummary(pc.c_df5)<\/p>\n
#naming trick
\nnames(ec.c_df5)<- c(\"Country\", \"Effiency change in OECD 1980-1990\")
\nnames(tc.c_df5)<- c(\"Country\", \"Technical Effiency change in OECD 1980-1990\")
\nnames(pc.c_df5)<- c(\"Country\", \"Productivity change in OECD 1980-1990\")
\n<\/code><\/p>\n
#naming time series 1991-2009
\nnames(ec.c_df5)<- c(\"Country\", \"Effiency change in OECD 1991-2009\")
\nnames(tc.c_df5)<- c(\"Country\", \"Technical Effiency change in OECD 1991-2009\")
\nnames(pc.c_df5)<- c(\"Country\", \"Productivity change in OECD 1991-2009\")
\n<\/code><\/p>\n
#1991-2002
\nnames(ec.c_df5)<- c(\"Country\", \"Effiency change in OECD 1991-2002\")
\nnames(tc.c_df5)<- c(\"Country\", \"Technical Effiency change in OECD 1991-2002\")
\nnames(pc.c_df5)<- c(\"Country\", \"Productivity change in OECD 1991-2002\")<\/code><\/p>\n
head(ec.c_df5)
\nhead(tc.c_df5)
\nhead(pc.c_df5)<\/code><\/p>\n
#set library
\nlibrary(googleVis)<\/p>\n
#1980-1990
\n#me\/230712
\n#1
\n#KMEAN VALUE OF MALMQUIST INDICES 1980-1990 Efficency change
\nGeo1=gvisGeoMap(ec.c_df5, locationvar=\"Country\", numvar=\"Effiency change in OECD 1980-1990\", options=list (height=450, width=800, dataMode='regions'))
\n#plot(Geo1)
\ncat(Geo1$html$chart, file=\"...\/oecd_mean_eff_1980_1990_malmquist2.html\")
\n<\/code><\/p>\n
#2
\n#KESKIARVO MEAN VALUE OF MALMQUIST INDICES 1980-1990 Efficency change
\nGeo2=gvisGeoMap(tc.c_df5, locationvar=\"Country\", numvar=\"Technical Effiency change in OECD 1980-1990\", options=list(height=450, width=800, dataMode='regions'))
\n#plot(Geo2)
\ncat(Geo2$html$chart, file=\"...\/oecd_mean_tech_eff_1980_1990_malmquist2.html\")<\/code><\/p>\n
#3
\n#KESKIARVO MEAN VALUE OF MALMQUIST INDICES 1980-1990 Efficency change
\nGeo3=gvisGeoMap(pc.c_df5, locationvar=\"Country\", numvar=\"Productivity change in OECD 1980-1990\", options=list(height=450, width=800, dataMode='regions'))
\n#plot(Geo3)
\ncat(Geo3$html$chart, file=\"...\/oecd_mean_prod_1980_1990_malmquist2.html\")
\n<\/code><\/p>\n
#1991-2009 (capital var dropped)
\n#me\/240712
\n#1
\n#KESKIARVO MEAN VALUE OF MALMQUIST INDICES
\nGeo1=gvisGeoMap(ec.c_df5, locationvar=\"Country\", numvar=\"Effiency change in OECD 1991-2009\", options=list (height=450, width=800, dataMode='regions'))
\nplot(Geo1)
\ncat(Geo1$html$chart, file=\"...\/oecd_mean_eff_1991_2009_malmquist2.html\")
\n<\/code><\/p>\n
#2
\n#VALUE OF MALMQUIST INDICES
\nGeo2=gvisGeoMap(tc.c_df5, locationvar=\"Country\", numvar=\"Technical Effiency change in OECD 1991-2009\", options=list(height=450, width=800, dataMode='regions'))
\nplot(Geo2)
\ncat(Geo2$html$chart, file=\"...\/oecd_mean_tech_eff_1991_2009_malmquist2.html\")
\n<\/code><\/p>\n
#3
\n#KESKIARVO MEAN VALUE OF MALMQUIST INDICES
\nGeo3=gvisGeoMap(pc.c_df5, locationvar=\"Country\", numvar=\"Productivity change in OECD 1991-2009\", options=list(height=450, width=800, dataMode='regions'))
\nplot(Geo3)
\ncat(Geo3$html$chart, file=\"...\/oecd_mean_prod_1991_2009_malmquist2.html\")<\/code><\/p>\n
#1991-2002 (capital as input)
\n#me\/240712
\n#1
\n#KESKIARVO MEAN VALUE OF MALMQUIST INDICES
\nGeo1=gvisGeoMap(ec.c_df5, locationvar=\"Country\", numvar=\"Effiency change in OECD 1991-2002\", options=list (height=450, width=800, dataMode='regions'))
\nplot(Geo1)
\ncat(Geo1$html$chart, file=\"...\/oecd_mean_eff_1991_2002_malmquist2.html\")
\n<\/code><\/p>\n

\n#2
\n#KESKIARVO MEAN VALUE OF MALMQUIST INDICES
\nGeo2=gvisGeoMap(tc.c_df5, locationvar=\"Country\", numvar=\"Technical Effiency change in OECD 1991-2002\", options=list(height=450, width=800, dataMode='regions'))
\nplot(Geo2)
\ncat(Geo2$html$chart, file=\"...\/oecd_mean_tech_eff_1991_2002_malmquist2.html\")
\n<\/code><\/p>\n
#3
\n#KESKIARVO MEAN VALUE OF MALMQUIST INDICES
\nGeo3=gvisGeoMap(pc.c_df5, locationvar=\"Country\", numvar=\"Productivity change in OECD 1991-2002\", options=list(height=450, width=800, dataMode='regions'))
\nplot(Geo3)
\ncat(Geo3$html$chart, file=\"...\/oecd_mean_prod_1991_2002_malmquist2.html\")<\/code><\/p>\n
World Map (producitivity, efficiency)<\/h1>\n
1980-1990<\/h4>\n
oecd_mean_eff_1980_1990_malmquist2<\/a><\/p>\n
oecd_mean_prod_1980_1990_malmquist2<\/a><\/p>\n
oecd_mean_tech_eff_1980_1990_malmquist2<\/a><\/p>\n
1991-2002<\/h3>\n
oecd_mean_eff_1991_2002_malmquist2<\/a><\/p>\n
oecd_mean_prod_1991_2002_malmquist2<\/a><\/p>\n
oecd_mean_tech_eff_1991_2002_malmquist2<\/a><\/p>\n
1991-2009<\/h4>\n
oecd_mean_eff_1991_2009_malmquist2<\/a><\/p>\n
oecd_mean_prod_1991_2009_malmquist2<\/a><\/p>\n
oecd_mean_tech_eff_1991_2009_malmquist2<\/a><\/p>\n
The cubic smoothing spline model<\/h1>\n
Now we plot productivity, effectiveness and technical effectiveness mean values historical trend and forecast by using
\nThe cubic smoothing spline model. It is equivalent to an ARIMA(0,2,2) model.<\/p>\n
###############################################################
\nlibrary(forecast)
\n#library(ggplot2)
\n#1980-1990
\n#1990-2009
\n#1991-2002
\n#####################################################################
\n#1
\n#1980-1990
\n#####################################################################
\n#PRODUCTIVITY
\npc.y
\nfcast_pc <- splinef(pc.y,h=10, fan=T) #NOTE confidence leve 50, 99
\nplot(fcast_pc,\u00a0 main=\"Productivity, forecast from Cubic Smoothing Spline\", ylab=\"Malmquist indices - Productivity\", xlab=\"Year(0=1980, 10=1990, 20=2000)\")<\/code><\/p>\n
# example – output graph to jpeg file
\njpeg(“…\/Productivity 1980_1990_Forecast Cubic_Smoothing_Spline10y2.jpg”)
\nplot(fcast_pc,\u00a0 main=”Productivity, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Productivity”, xlab=”Year(0=1980, 10=1990, 20=2000)”)
\ndev.off()
\n\"\"<\/a><\/p>\n
#TECHNICAL EFFICIENCY
\nfcast_tc <- splinef(tc.y,h=10, fan=T)
\nplot(fcast_tc,\u00a0 main=”Technical Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Technical Efficiency”, xlab=”Year(0=1980, 10=1990, 20=2000)”)<\/p>\n
# example – output graph to jpeg file
\njpeg(“…\/Technical efficiency 1980_1990_Forecast Cubic_Smoothing_Spline10y2.jpg”)
\nplot(fcast_tc,\u00a0 main=”Technical Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Technical Efficiency”, xlab=”Year(0=1980, 10=1990, 20=2000)”)
\ndev.off()<\/p>\n
\"\"<\/a><\/p>\n
#EFFICIENCY
\nfcast_ec <- splinef(ec.y,h=10, fan=T)
\nplot(fcast_ec,\u00a0 main=”Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Efficiency”, xlab=”Year(0=1980, 10=1990, 20=2000)”)<\/p>\n
# example – output graph to jpeg file
\njpeg(“G:\/data\/home\/2012\/marko\/blogi_rbloggerqvist\/tekstiaihiot\/40\/Efficiency 1980_1990_Forecast Cubic_Smoothing_Spline10y2.jpg”)
\nplot(fcast_ec,\u00a0 main=”Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Efficiency”, xlab=”Year(0=1980, 10=1990, 20=2000)”)
\ndev.off()<\/p>\n
\"\"<\/a><\/p>\n
summary(fcast_pc)
\nsummary(fcast_tc)
\nsummary(fcast_ec)<\/p>\n
#####################################################################
\n#2
\n#1991-2009
\n#####################################################################
\n#PRODUCTIVITY
\npc.y
\nfcast_pc <- splinef(pc.y,h=10, fan=T) #NOTE confidence leve 50, 99
\nplot(fcast_pc,\u00a0 main=”Productivity, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Productivity”, xlab=”Year(0=1990, 20=2010)”)<\/p>\n
# example – output graph to jpeg file
\njpeg(“…\/Productivity 1991_2009_Forecast Cubic_Smoothing_Spline10y2.jpg”)
\nplot(fcast_pc,\u00a0 main=”Productivity, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Productivity”, xlab=”Year(0=1990, 20=2010)”)
\ndev.off()<\/p>\n
\"\"<\/a><\/p>\n
#TECHNICAL EFFICIENCY
\nfcast_tc <- splinef(tc.y,h=10, fan=T)
\nplot(fcast_tc,\u00a0 main=”Technical Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Technical Efficiency”, xlab=”Year(0=1990, 20=2010)”)<\/p>\n
# example – output graph to jpeg file
\njpeg(“G:\/data\/home\/2012\/marko\/blogi_rbloggerqvist\/tekstiaihiot\/40\/Technical efficiency 1991_2009_Forecast Cubic_Smoothing_Spline10y2.jpg”)
\nplot(fcast_tc,\u00a0 main=”Technical Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Technical Efficiency”, xlab=”Year(0=1990, 20=2010)”)
\ndev.off()<\/p>\n
\"\"<\/a><\/p>\n
 <\/p>\n
#EFFICIENCY
\nfcast_ec <- splinef(ec.y,h=10, fan=T)
\nplot(fcast_ec,\u00a0 main=”Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Efficiency”, xlab=”Year(0=1990, 20=2010)”)<\/p>\n
# example – output graph to jpeg file
\njpeg(“…\/Efficiency 1991_2009_Forecast Cubic_Smoothing_Spline10y2.jpg”)
\nplot(fcast_ec,\u00a0 main=”Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Efficiency”, xlab=”Year(0=1990, 20=2010)”)
\ndev.off()<\/p>\n
\"\"<\/a><\/p>\n
summary(fcast_pc)
\nsummary(fcast_tc)
\nsummary(fcast_ec)
\n######################################################################3
\n#1991-2002 (capital included)
\n#
\n#####################################################################
\n#PRODUCTIVITY
\nfcast_pc <- splinef(pc.y,h=10, fan=T) #NOTE confidence leve 50, 99
\nplot(fcast_pc,\u00a0 main=”Productivity, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Productivity”, xlab=”Year(1=1991, 10=2000, 20=2012)”)<\/p>\n
# example – output graph to jpeg file
\njpeg(“…\/Productivity 1991_2002_Forecast Cubic_Smoothing_Spline10y2.jpg”)
\nplot(fcast_pc,\u00a0 main=”Productivity, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Productivity”, xlab=”Year(1=1991, 10=2000, 20=2012)”)
\ndev.off()<\/p>\n
\"\"<\/a><\/p>\n
 <\/p>\n
#TECHNICAL EFFICIENCY
\nfcast_tc <- splinef(tc.y,h=10, fan=T)
\nplot(fcast_tc,\u00a0 main=”Technical Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Technical Efficiency”, xlab=”Year(1=1991, 10=2000, 20=2012)”)<\/p>\n
# example – output graph to jpeg file
\njpeg(“…\/Technical efficiency 1991_2002_Forecast Cubic_Smoothing_Spline10y2.jpg”)
\nplot(fcast_tc,\u00a0 main=”Technical Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Technical Efficiency”, xlab=”Year(1=1991, 10=2000, 20=2012)”)
\ndev.off()<\/p>\n
\"\"<\/a><\/p>\n
 <\/p>\n
#EFFICIENCY
\nfcast_ec <- splinef(ec.y,h=10, fan=T)
\nplot(fcast_ec,\u00a0 main=”Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Efficiency”, xlab=”Year(1=1991, 10=2000, 20=2012)”)<\/p>\n
# example – output graph to jpeg file
\njpeg(“…\/Efficiency 1991_2002_Forecast Cubic_Smoothing_Spline10y2.jpg”)
\nplot(fcast_ec,\u00a0 main=”Efficiency, forecast from Cubic Smoothing Spline”, ylab=”Malmquist indices – Efficiency”, xlab=”Year(1=1991, 10=2000, 20=2012)”)
\ndev.off()<\/p>\n
\"\"<\/a><\/p>\n
summary(fcast_pc)
\nsummary(fcast_tc)
\nsummary(fcast_ec)
\n#####################################################################<\/p>\n
Ok, that’s it,
\nHave fun with Linear Programming for the Malmquist Productivity Growth Index and its wide range of applications…<\/p>\n
Marko<\/p>\n
 <\/p>\n","protected":false},"excerpt":{"rendered":"
Data Envelopment Analysis Within couple of days I have been testing DEA modelling (Data Envelopment Analysis) with different R-package. Finally,…. I have found such a comprehensive way to calculate Malmquist indices. My primary purpose is to show how to use nonparametric methods for measuring efficiency and productivity by using R-programs nonparaeff -package. At this same […] Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"gallery","meta":[],"categories":[16,17,18,19,23],"tags":[31,40,48],"_links":{"self":[{"href":"https:\/\/science.ekqvist.fi\/blogi\/wp-json\/wp\/v2\/posts\/199"}],"collection":[{"href":"https:\/\/science.ekqvist.fi\/blogi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science.ekqvist.fi\/blogi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science.ekqvist.fi\/blogi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science.ekqvist.fi\/blogi\/wp-json\/wp\/v2\/comments?post=199"}],"version-history":[{"count":0,"href":"https:\/\/science.ekqvist.fi\/blogi\/wp-json\/wp\/v2\/posts\/199\/revisions"}],"wp:attachment":[{"href":"https:\/\/science.ekqvist.fi\/blogi\/wp-json\/wp\/v2\/media?parent=199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science.ekqvist.fi\/blogi\/wp-json\/wp\/v2\/categories?post=199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science.ekqvist.fi\/blogi\/wp-json\/wp\/v2\/tags?post=199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}