**Source:**Amegashie, J. Atsu

J. Atsu Amegashie*

March 28, 2015

In his lecture on March 24, 2015, Dr. Mahamudu Bawumia, vice-presidential candidate of the NPP, asked "How can agriculture grow at 7.2%, industry at 4.5% and services at 5.6%, but then overall GDP at basic prices grows at 2.2%?"

At a press conference on March 26, 2015, Dr. Philomena Nyarko, head of the Ghana Statistical Service, gave the following response:

"On the issue of GDP Growth rates for 2009, Dr. Bawumia queried why the overall 2009 non-oil GDP growth rate was 2.2 percent, whereas agriculture sector grew by 7.2 percent, industry by 4.5 percent and services by 5.6 percent.

GSS wishes to state that there was an error during the transmission of the data unto its website". The correct figure is 4.8 percent and not the 2.2 percent which has subsequently been identified and corrected.": http://business.peacefmonline.com/pages/news/201503/236897.php

Two days later (March 28) on Joyfm's Newslife program, Mr. Kweku Baako jnr, editor-in-chief of the New Crusading Guide, asked:

"How is it possible that the sectoral figures remain the same yet the GDP figures are different? Don't they have a relationship? Don't they have an impact on the GDP? When it was 2.2% the figures were the same ... when it was 4.8% now the figures were the same.....there is something fishy out there " http://www.myjoyonline.com/politics/2015/March-28th/kweku-baako-predicts-explosive-expos-on-ghana-statistical-service-coming-soon.php#sthash.gJcrhRgr.dpuf

In 2009, we were not producing oil. Therefore, non-oil GDP in 2009 is the same as GDP in 2009. In what follows, I will make no distinction between GDP and non-oil GDP.

The GDP is the sum of output from three sectors: Agriculture, Industry, and Services. The growth of GDP is a weighted average of the growth rates in these sectors. It is important to note that when the average of a set of numbers is computed, the average must fall between the smallest number in the set and the largest number. So given that the growth rates of industry, services, and agriculture were 4.5%, 5.6%, and 7.2% respectively in 2009, the growth rate of total output (GDP) in 2009 had to lie between 4.5% (the smallest number) and 7.2% (the largest number). This was why Dr. Bawumia found it curious that the growth of GDP was 2.2%, a number that is not between 4.5% and 7.2%. If the oldest SHS 3 student is 20 years old and the youngest is 17 years old, the average age of SHS 3 students must fall between 17 and 20. This is a very trite point. The knowledge required to spot the anomaly pointed by Dr. Bawumia can be gained in any elementary course in statistics, economics, and other disciplines. In fact, a JHS student should be able to follow this logic. But someone had to look at the data to detect this anomaly. Thanks to Dr. Bawumia.

The GSS says that the correct number should have been 4.8%, a number that is between 4.5% and 7.2%. So far, so good. Dr. Bawumia posed a very basic question. The GSS' revised figure is a satisfactory answer to this basic question. However, it is not necessarily a satisfactory answer to a more stringent question. To pose this question requires more precision. To this end, let's define the following variables:

g is the growth rate of GDP in 2009

Ar is the growth rate of agriculture in 2009

Ir is the growth rate of industry in 2009

Sr is the growth rate of services in 2009

Ap is the proportion of GDP accounted for by agriculture in 2008 (i.e., agricultural output as a percentage of GDP)

Ip is the proportion of GDP accounted for by industry in 2008 (i.e., industrial output as a percentage of GDP)

Sp s the proportion of GDP accounted for by services in 2008 (i.e., output of services as a percentage of GDP)

Then the growth rate of GDP in 2009 is:

g = Ar times Ap + Ir times Ip + Sr times Sp. ------------------------------------- (1)

Necessarily the weights Ap, Ip, and Sp must add up to 100% because the sum of the output of the three sectors is GDP. Formally, Ap + Ip + Sp = 1 (100%). The derivation of the formula in (1) is available in an appendix to this article at: http://www.uoguelph.ca/~jamegash/GDPWeightedAverage.pdf

The formula in (1) says that the growth rate of GDP is a weighted average of the growth rates of agriculture, industry, and services in 2009, where the weights are the outputs of these sectors in 2008 as a proportion of GDP in 2008.

The answer to Kweku Baako's question is "the sectoral growth rates do not have to change". What the GSS meant was that given the numbers for Ar, Ap, Ir, Ip, Sr, and Sp, the figure for g obtained after applying the formula in (1) above was inadvertently not shown on its website. However, there appears to be a problem and so Kweku Baako's concern may be legitimate.

I have taken a look at a document by the GSS titled "Revised Gross Domestic Product 2014" (dated January 2015): http://www.statsghana.gov.gh/docfiles/GDP/GDP2015/2014%20Q3%20Annual%20GDP.pdf

According to column 4 of Table 1.2 of this document, Ap = 31% (0.31), Ip = 20.4% (0.204), and Sp = 48.6% (0.486). See also Table 1.6. When I put these figures in formula (1) above together with Ar = 7.2% (0.072), Ir = 4.5% (0.045), and Sr = 5.6% (0.056) in Table 1.8, I did not get 0.048 (4.8%) as claimed by the GSS in its press statement. I got 5.87%. The point is simple: the 4.8% figure for the growth rate of GDP is very close to the 4.5% figure for the growth rate of industry. Since industrial growth was the smallest, this would only make sense if the weight of industrial output (i.e., industrial output as a proportion of GDP) was high in 2008. This is was not the case. Its weight was only 20.4%. Or as Kweku Baako suspects, are the sectoral growth rates wrong?

I also note that the growth rates for the three sectors in Table 1.8 correspond to the rates at 2006 constant prices while the 4.8% growth rate is for GDP in the same table is at basic prices, although in its response to Dr. Bawumia, the GSS did not say that this was the source of the discrepancy. Therefore, my question to the GSS is "why is it that I don't get a GDP growth rate of 4.8% when I apply the formula in (1)?".

This is a serious matter because GDP figures are one of the bedrocks of national planning and governance. I do not wish to impugn the integrity of the GSS. It is my hope that the GSS will respond to my question.

*J. Atsu Amegashie teaches Economics at the University of Guelph.

**Columnist:**Amegashie, J. Atsu