Saudi GDP II : Productivity & Capital Stock

In my last post I discussed Saudi’s simple GDP dynamics. Yet we did not discuss anything other than oil fluctuations and its relationship with growth rate of GDP and the importance of looking at growth rather than levels of GDP. Nor did we consider the important distinction between nominal and real GDP. Where real GDP is adjusted for inflation. In this post we do. We also make some adjustments to our GDP variable, looking closely at GDP per person to give us a clearer picture about the well-being of individuals. Below is the inflation adjusted gross domestic product for Saudi Arabia from 1970-2014.Rplot05.png

Factors of production

Playing around with more R and some data I provide some interesting visuals that asks important questions.  Before we do that, we need to refresh our memory about a certain element that constitutes the production process in a country. When talking about an economy’s output of goods and services, it is agreed that it depends on its quantity of inputs. These inputs are called the factors of production. An economy’s ability to turn these factors/inputs into output is represented by a production function.

The two most important inputs in production are capital and labor. Capital refers to the set of tools/machines/equipment that workers use, and Labor is the time people spend working. Another important element exists in the production process is the Total Factor Productivity (TFP). TFP is the portion of output that is not explained by the amount of input used in production. It determines how efficient inputs are utilized in production. The graphic below illustrates the process of converting inputs into outputs.


Consider three economies, that have the same level of inputs 100 Labor and 100 Capital, but they differ in productivity. The table below shows how TFP plays a role on output. Country A has a TFP of 1 and correspondingly its output is 10,000. Country B has a TFP of 1.2, suggesting it can convert its inputs more effectively and can produce 2,000 more output than country A. Country C has a TFP of 1.6 and therefore is the most efficient country that yields the highest output.


Total Factor Productivity (TFP)

Now that we have a solid introduction to these factors let us consider again the Saudi case. Using the Federal Reserve data of St. Louis that acquired the TFP data on Saudi Arabia from the “Next generation of the Penn World tables” .(TFP is indexed to USA =1). We plot the Productivity level on the left, and Productivity change on the right, of Saudi Arabia against time (1970-2014).TFP

Now, let’s plot the productivity change on top of Real GDP change. Consider the graph below, we can see below that Real GDP moves close with productivity. The rough estimated correlation is 0.6.Rplot03

Plotting the GDP per person against TFP (Below). We see that as productivity goes up we expect to see higher GDP per person. In other words, the more productive Saudis are, the more incomes they will earn.RGDP Per capita with TFP

Capital Stock 

Let us shift our focus to another aspect of the production function, Capital stock for Saudi Arabia. The capital stock is simply the amount of capital stock in Saudi Arabia across time. Consider the left graph that depicts capital stock levels and right graph capital stock change.

Capital stockCapital stock has been increasing since the 70s with the similar story of the dip in the 80’s, that followed a continuous rise. Now let us examine how changes in capital stock goes with output or Real GDP. Below we plot real GDP per person against change in capital stock. We see a somewhat linear relationship; the estimated correlation coefficient is

These visuals tells us that our production function story is relatively true, that is increases in capital and productivity are associated with higher incomes for people. We will refrain from discussing the labor input for another post.

To conclude

Let us see how it all adds up together. Below we plot real GDP per person on top of TFP (left graph).We see that there has been a close association from 1971-2000: the correlation between TFP and Real GDP per person is 0.95 (1971-2000).


This association departs in 2000, we see that after 2000 productivity did not catch up with the rise in GDP. This tells us something about the structure of Saudi’s economy, which is a natural resource dependent country. We also plot to the right the change in capital stock on top of TFP, we see that up to 90’s there was a close association between changes in capital stock and TFP: from (1971-1990) the correlation coefficient  is 0.95. The departure of the associations entails an interesting story. Despite the rapid increase in capital stock, Saudi’s productivity has remained within [1.0-1.5] range. Whether that is normal standards or not we can clearly see that dynamics of production have changed.




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