Open knowledge and wealth (part 1)

Is there a relationship between open knowledge and wealth? Data from the Open Economics group show that there is a positive relationship between their open knowledge index and GDP per capita [see our previous post on this index]. So, richer countries have higher scores in the open knowledge index, as shown in this plot produced using their data.

Relationship between (log) GDP/capita and Open Knowledge Index

In effect, we can see that countries with lower GDP per capita such as India, China, Turkey, Mexico, Brazil, Chile and Russia (bottom-left part of the graphic) present also lower scores in the Open Knowledge Index compared to richer countries like Germany, South Korea, Norway or Luxembourg (upper-right part).

The linear relationship is represented by a regression coefficient of 0.28, which means that, for example, a 10 percent increase in GDP per capita would imply, on average, a 0.028 increase in the open knowledge index. This is not bad at all, considering that the index has been rescaled to have a value range of 0 and 1. Moreover, the model explains 55 percent of the variation between both variables (through the adjusted R-squared).

But, is the relationship between wealth and open knowledge really linear? Does a 10 percent increase in GDP per capita produce always, at all levels of wealth, a 0.028 increase in the open knowledge index? Or rather the open knowledge index will present different levels of increase at different levels of wealth?

A simple and eye-catching way to attack this problem is to fit a local regression model (LOESS) to the data and plot a LOESS curve against the data. I’ve done it using the loess.smooth R function, and the results can be seen in the figure below.

LOESS curve representing the relationship between GDP/capita and OKI

The curve in the figure shows that, indeed, the relationship between wealth and open knowledge is not linear—i.e., that we cannot expect that a similar increase in GDP per capita (say, a 10 percent) will produce the same increase of the open knowledge index, say, for India as for the Netherlands.

Although this analysis should be reproduced using a larger sample of countries, the figure suggests that relatively small increases in GDP per capita really make a difference in the open knowledge index, but only among the richer countries. In contrast, the poorer countries should experience relatively large increases in their GDP per capita in order to have decent increases in the open knowledge index.

Does this mean that the open knowledge question is just a matter of wealth? Do rich countries spend money in open knowledge because they are rich? Is the open knowledge culture some kind of post-materialist phenomenon and therefore just a matter of rich countries that have other needs (health, education, money) covered?

Finally, considering that our simple model using just the GDP per capita explains only 55 percent of the variation, can other factors be found that help explain better the relationship between wealth and open knowledge?

We will try to tackle some of these questions in our next post.

Below is the R code to freely reproduce the analyses and graphics of this post:

##################################################
#AUTHOR: JOAN-JOSEP VALLBE
#THEME: OPEN KNOWLEDGE AND WEALTH
#DATA SOURCE: <http://openeconomics.net/open-knowledge-indicator/>
#SOFTWARE: R version 2.13.2 (2011-09-30)
#MACHINE OS: LINUX UBUNTU 11.10 (Oneiric Ocelot)
##################################################

#################################
#LOAD THE DATA
#################################

data <- read.csv("data/open_knowledge_indicator_0.1.csv",
                 header=TRUE,
                 sep=",")
#This is to order the countries according to GDP per capita
ord.gdp <- order(data$GDP)
data <- data[ord.gdp,]

#####################
#RESCALE the open knowledge index to range [0,1]
####################

oki.res <- scale(data$Open_Knowledge_Index,center=FALSE)

require(plotrix)#You should have this R package installed

oki.res <- rescale(data$Open_Knowledge_Index,c(0,1))

data <- data.frame(data,oki.res)

######################
#LINEAR MODEL
######################
mod.1 <- lm(oki.res~log(GDP),data=data)

########################
#GENERATE FITTED VALUES
########################

a <- predict(mod.1,interval="confidence")

######################################
#PLOTTING THE DATA AND FITTING VALUES (linear model)
######################################

plot(data$GDP,data$oki.res,
     pch=20,
     type="p",
     col="black",
     log="x",
     xlab="Log GDP per capita (PWT 7.0)",
     ylab="Open Knowledge Index 2009-10 (normalized)")
text(data$GDP,data$oki.res,
     as.character(data$iso),
     cex=0.6,
     pos=1)
lines(data$GDP,a[,1],col="black",lty=2)

######################################
#PLOTTING THE LOESS CURVE AGAINST THE DATA
######################################

plot(data$GDP,data$oki.res,
     pch=20,
     type="p",
     col="black",
     log="x",
     xlab="Log GDP per capita (PWT 7.0)",
     ylab="Open Knowledge Index 2009-10 (normalized)")
text(data$GDP,data$oki.res,
     as.character(data$iso),
     cex=0.6,
     pos=1)
lines(loess.smooth(data$GDP,data$oki.res,
                   span=0.75))
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