Relationship between GDP and Total Factor Productivity

7945 words (32 pages) Business Assignment

20th Apr 2020 Business Assignment Reference this

Tags: Business AssignmentsFinanceEconomicsGDP

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Macroeconomic background

1. Find GNP/GDP data for the last 5 years. Plot the growth rate. Compute total factor productivity (TFP) and plot the results for that period. Show how the TFP numbers are calculated according to the formula derived in class. (You may use published TFP numbers, but you are still required to show how they are being derived.)

The Gross National Product (GNP)[1] and Gross Domestic Product (GDP)[2] are economic indicators of the strength and size of a given nation’s economy[3] by measuring the amount of goods and services produced – ‘output’ (Sussman, 2019). Thus, we want to focus on the value added, which is the “difference between the value of output sold and the cost of intermediate inputs and raw materials” (Miles et al., 2012, p. 17)[4].  The total market value of the final[5] goods and services produced in a country’s boarders within a certain time period[6] is known as GDP (WallStreetMojo, 2019)[7].

Q1 2019 UK GDP growth was 1.8%, year-on-year[8] (Figure 1).  This larger than expected growth has been due to a boost from companies in the UK and European Union building stocks ahead of recent Brexit[9] deadlines.  This is deemed a temporary effect, with growth expecting to slow to in Q2 (Bank of England, 2019).[10] Indeed, the overall pattern of growth over the past 5 years has been subdued[11].

Figure 1 – GDP Year-on-Year Quarterly Growth, CV[12] (Past 5 years)

Source: ONS

GDP is in essence produced by three factors: (1) capital; (2) labour; and (3) total factor productivity (TFP).[13]  TFP is the measure of the efficiency of all inputs to a production process that cannot be attributed to the accumulation of capital and labour (Investopedia, 2019) – it is, hence, calculated as a residual.  Increases in TFP result usually from technological innovations[14], institutional or government policies[15], education and skills in the workforce[16], to name a few[17] (Hulten, 2000).

It is derived by dividing output, GY, by the weighted average of labour, GL, and capital input, GK, with the standard weighting of 0.6 for labour, SL, and 0.4, SK, for capital (Sussman, 2019).  The rate of TFP growth is calculated by subtracting growth rates of labour and capital inputs from the growth rate of output:

TFP = GY – (SK x GK+ SL x GL)

For Q1 2019, TFP growth was -4.5% (Figure 2): 13.1% – (0.4 x 15.3% + 0.6 x 19.1%).   Over the past 12 months, input growth has been matched by output growth (Figure 3), with TFP flat-lining during the same period (ONS, 2019).  The negative TFP growth the UK is exhibiting is a concern as it is a “source of long-run growth” for the economy (Miles et al., 2012, p. 51).[18]

Figure 2 – Cumulative Quarterly TFP (Past 5 years)

Source: ONS.

Figure 3 – Decomposition of Cumulative Quarterly Output Growth (Past 5 years)

Source: ONS.  Output growth is the cumulative q-o-q logarithmic change in GVA (market sector gross value added).

Bar chart shows contributions of components, calculated by weighting logarithmic changes in each component by its factor income share.

2. What is the earnings yield (inverse of the price-to-earnings ratio) in the domestic stock market? Is this number compatible with the performance of the economy as analysed in the previous question?

The earnings yield[19] refers to the earnings per share of a company divided by the current market price per share (Investopedia, 2019).[20]  The Q1 2019 earnings yield of the UK’s broad domestic market index (FTSE 100) is currently 5.9%; this represents a 200% increase since Q1 2016 (Figure 4).  A comparison of the yield on long-term government debt and the average yield on an equity market benchmark, Bond Equity Earnings Ratio (BEER), can be used to determine whether to invest in stocks.[21] If the ratio is above 1.0 then the stock market is said to be overvalued[22].  The FTSE’s current ratio is 0.2, which illustrates that UK equities are an attractive investment (Figure 5).[23]


Figure 4 – FTSE 100 Earnings Yield vs. 10 Year Treasury Yield (Past 5 years)

Source: Bloomberg


Figure 5 – BEER (Past 5 years)

Source: Bloomberg

Figures 6 illustrates an incompatibility between the earnings yield of the FTSE 100 and the UK’s economic performance, or GDP.  Intuitively, at least, high GDP growth rates should translate into high stock market returns.[24]  However, investigation shows that, at least in China, GDP growth rate do not translate into stock price appreciation.  When China had growth rates between 9% to 15% from 2007 to 2011, its Shanghai Composite Index dived from 5,500 to below 2,500 (Wu, 2012).  Furthermore, Dimson et al. (2002) and Ritter (2005) in separate studies of 16 and 19 developed countries, respectively, found that stock market returns were negatively related to GDP growth rates.


Figure 6 – FTSE 100 Earnings Yield vs. UK GDP Growth (Past 5 years)

The Earnings Yield has been rising since 2016, although GDP growth has been on the decline over the past 5 years.

I submit that a robust linkage between earnings yield and GDP does not exist due to three principal reasons.  Firstly, the stock market does not full represent the whole economy.  GDP includes all public, private, government-owned and newly founded companies, whilst stock market returns only account for public companies (Jain & Krason, 2009).  Secondly, a company’s profits may come from overseas, especially where economies are becoming more interdependent.  For instance, the FTSE 100 is dominated by resource companies[25], who predominantly conduct their operations outside of the UK.   Thirdly, the value of current investors’ shares may be diluted if a company issues additional shares to raise capital (Wu, 2012).[26]  Thus, when making equity investment decisions, a micro-level, bottom-up, approach, is advisable.  In conclusion, one should consider the company and industry prior to investment at a country-level.


3. Find data for the price level and calculate the rate of inflation for the last 5 years. What was the nominal interest rate? What was the real interest rate?

“A price level is the average of current prices across the entire spectrum of goods and services produced in the economy” (Investopedia, 2019). It, hence, denotes the buying power of money (Sussman, 2019).[27] “The rate of inflation is the change in prices for goods and services over time” (ONS, 2019).[28] The Consumer Price Index including owner occupiers’ housing costs (CPIH)[29] is the UK’s leading inflation index[30].  As of May 2019, CPIH stood at 1.9% (Figure 6).  This Represents the 12-month inflation rate, down from 2% in April, due to falling fares for transport services and car prices (Figure 7). [31]

CPIH measures the cost to the consumer of purchasing a basket of commodities, in which a collection of prices for goods and services[32] are “weighted together based on how much the average consumer spends on each item” (Miles et al., 2012, p. 287).[33]


Figure 6 – CPIH Annual Time Series (Past 5 years)

Source: ONS

Figure 7 – Contributions to Change in CPIH Annual Rate (April to May 2019)

Source: ONS

A nominal interest rate refers to the interest rate before taking inflation into account.[34] Short-term nominal interest rates are set by the Bank of England and is currently set at 0.75% (Figure 8).[35] The Bank of England has evidently kept nominal rates at low levels in order to spur economic activity following the global financial crisis of 2008 (Figure 9).  In general, as interest rates are lowered, more people are able to borrow more money. The result is that consumers have more money to spend, causing the economy to grow and inflation to increase.[36]  This relationship is indeed evident in Figure 10.

Figure 8 – Nominal Interest Rate (Past 5 years)

Source: Bank of England

Figure 9 – Nominal Interest Rates (Historical Time Series)

Global Financial Crisis 2008

Source: Bank of England

Figure 10 – Nominal Interest Rates vs. Inflation (Historical Time Series)

A reduction in interest rates in 2009 has increased consumer spending, CPIH, in the UK

Source: Bank of England, ONS.

However, the disadvantage of using the nominal interest rate is that it does not adjust for the inflation rate.  Fisher (1930) postulates that the real interest rate – that takes inflation into account – is independent of monetary measures, especially the nominal interest rate (Investopedia, 2019).

The Fisher Effect is an economic theory that describes the relationship between inflation and both nominal and real interest rates (Investopedia, 2019):

r = i – π

Where the real interest rate (r) equals the nominal interest rate (i) minus the rate of inflation (π).[37]  Hence, “real interest rates fall as inflation increases, unless nominal rates increase at the same rate as inflation” (Investopedia, 2019).  The real interest rate as of Q1 209 is -1.2%.  Indeed, as illustrated by Figure 11, real interest rates have been consistently negative since 2015 due to the fact that the nominal rate has been set lower than the inflation rate in recent years.[38]


Figure 11 – Real Interest Rate (Past 5 years)

Source: Bank of England, ONS.

4. Find money supply data for your country. Can you find correlations between the money supply and the rate of inflation?


“The money supply is the entire stock of currency and other liquid instruments circulating in a country’s economy as of a particular time” (Investopedia, 2019).[39]  There are just two official UK measures of money supply pertaining to the spectrum of liquidity, or spendability of such financial assets[40]. M0 is referred to as the “wide monetary base” or “narrow money” and M4 is referred to as “broad money” or simply “the money supply”.

  • M0: equates to sterling notes and coin in circulation outside the Bank of England (Bank of England, 2019).[41]
  • M4: comprises of cash outside banks (i.e. in circulation with the public and non-bank firms); private-sector retail bank and building society deposits; private-sector wholesale bank and building society deposits; and certificates of deposit (Wikipedia, 2019).

M4 is a key economic indicator of the underlying strength of economic activity. For instance, when the global economy went into recession in 2008, we saw a sharp fall in UK M4 growth from 15% a year to negative growth (Figure 12).[42]   Conversely, narrow money growth has remained constant and was less impacted by the financial crisis (Figure 13).  That said, M0 is a relatively small percentage of the total money supply.[43]

Figure 12 – M4 Quarterly 12-month growth rate, seasonally adjusted (1989-2019)

Global Financial Crisis 2008

Source: Bank of England.

Figure 13 – Monthly Average Outstanding of Sterling Notes and Coins in Circulation, Seasonally Adjusted (1989-2019)

Source: Bank of England.

Monetarism[44], derived from the quantity theory of money, proposes that if the quantity of money increases, all prices increase proportionately, with no real effect on the economy (Sussman, 2019).  Hume (1752) eloquently states“… the price rises, first of one commodity, then of another; till the whole at last reaches a just proportion with the new quantity of specie which is in the kingdom”.  Thus, the percentage change in the money supply (M) plus the % change in velocity (V) equates to the % change in prices (P) plus the change in output (Y):

M x V = P x Y[45]

An increase in the supply of money typically lowers interest rates, which in turn, generates more investment and puts more money in the hands of consumers, thereby stimulating spending and thus increasing inflation.[46]  However, the UK economy does not support this monetarist view in the relevant period, at least, as illustrated by Figure 14.  Indeed, although the money supply has historically shown a correlation exists between it and inflation, since 2000, these relationships have become unstable, reducing their reliability as a guide for monetary policy (Sussman, 2019).[47]

Figure 14 – Money Supply (M4) and Inflation (1989 – 2019)

Source: Bank of England, ONS.


5. What was the exchange rate five years ago and what is it now? (By exchange rate we mean the price of the foreign currency in terms of domestic currency; be sure to state the units of the exchange rates that you post.) Has the domestic currency appreciated or depreciated during this period? What was the real appreciation/depreciation? Did interest rate parity hold during this period? If not, infer in what direction (above or below) did expectations deviate from actual changes in the exchange rate? (For those who are aware of the difference, the question is about the uncovered interest parity.)

The nominal exchange rate is the rate at which you can swap the currency of one country for another (Miles et al., 2012).   The UK’s sterling (GBP) bilateral exchange rate[48] against the United States Dollar (USD) currently stands at $1.30 (Figure 15).  Five years ago, it was $1.65.  Thus, the sterling has depreciated 27% during this period[49].

Figure 15 – GBPUSD Quarterly Average Exchange Rate (Past 5 Years)

Source: Bloomberg

In contrast, the real exchange rate (RER) represents the relative cheapness, or price level of all goods and services, of one country in comparison to another (Miles et. al, 2012):

RER = Nominal Exchange Rate x Domestic Price/Overseas Price

The purchasing power parity (PPP) applies the law of one price[50] to all goods and implies that real exchange rates should equate to 1, as all countries should have the same prices and, hence, the nominal exchange rate should equal the ratio of prices between countries (Miles et. al, 2012).  The Economist magazine has popularised a version of PPP with its Big Mac Index (Miles et al., 2019).[51]  Utilising this index, we can obtain the real exchange rate in an easily digestible form[52].  The UK price of a Big Mac is £3.19, with the U.S. price at $5.58, thus 1.30 x (3.19 ÷ 5.58) yields an RER of 0.74. Five years ago, the RER was 0.99.[53]  Hence, the real GBPUSD exchange rate has depreciated by 25% (Figure 16).  The sterling is, thus, said to be undervalued against the USD by 26% today, and the PPP did not hold over this period.[54]

Figure 16 – GBPUSD Real Exchange Rate (2019 vs. 2014)


Source: The Economist, Bloomberg.

I submit that the interest parity did not hold during the period, as the expected sterling depreciation rate was well above the actual depreciation rate of 27%.  “Uncovered interest rate parity (UIP) theory states that the difference in interest rates between two countries will equal the relative change in currency foreign exchange rates over the same period” (Investopedia, 2019).  The expected exchange rate in the future is calculated is as follows:

F0 = S0 x [(1 + ic)/(1+ib)]n

Where F0=expected forward rate, S0=spot rate, ic= interest rate quoted currency, ib= interest rate in the base currency, and n is the number of years.  The expected 5 year forward rate in 2014, utilising the UIP, was 1.65 x (1+0.25%)/(1+0.5%)5 = 1.63 (equating to an expectation of a 1% depreciation in the sterling).


[1] The main difference is that GNP considers the income receipts by the country in question’s national citizens from abroad. GNP is usually calculated by taking the sum of individual consumption expenditures, private domestic investment, government expenditure, net exports and any income earned by residents from overseas investments, minus income earned within the domestic economy by foreign residents (Sussman, 2019).   Net exports represent the difference between what a country exports minus any imports of goods and services (WallStreetMojo, 2019). The GNP formula is: GNP= GDP + NR – NP. Where NR= Net Income Receipts, NP= Net outflow to foreign assets.

[2] Economics is the study of the allocation of scarce resources. Macroeconomics examines the economy in aggregate – it looks holistically at the outcomes of all decisions that governments, corporations and consumers make in an economy.  Long-term macroeconomic questions examine issues such as: the role of investment in machines and infrastructure to foster growth; the importance of skills and education to increase output; and the critical role of technological innovation (Miles et al., 2012).

[3] At the heart of economics is the concern with human welfare.  GNP and GDP attempts to measure this welfare on the following rationale: if an economy produces more output in terms of goods and services, then it can meet more of the demands of society.

[4] In her best-selling book, No Logo, Klein (1999) comments on the absurdity that a $1 shirt becomes a $100 fashion item if a logo is attached to it.  However, from a value-added perspective, consumers do place huge importance on marketing and design, but not on physical manufacturing of plain t-shirts – hence, the $1 price tag.

[5] For instance, the value of the vehicle engine that Ford manufactures is not directly included in GDP, however, their value is included in the final prices of the vehicles that have the Ford engine.  Similarly, a Picasso painting sold for £20 million at auction in Sotheby’s in London will not be included in the 2019 GDP figure, as it was not produced during this period.

[6] GDP is usually calculated on a quarterly and annual basis.

[7] It includes only purchases of newly produced goods and services and does not include the sale or resale of goods produced in previous periods.  Although goods and services provided by government are included in the GDP calculations, the transfer of payments made by the government such as unemployment, retirement, and welfare benefits are not economic output and are not included in the calculation of GDP (Miles et al., 2012).

[8] GDP is calculated as follows via the expenditure method:

GDP = C + I + G + (X – M)

Where, C= Total Private Consumption, I= Total Investment Amount, G= Government Spending, and, X – M= Difference between the export and Import of a country.  GDP can be measured either as value of output produced, the income earned in the economy (by labour and capital), or the expenditure of final products.

[9] A portmanteau of “British” and “exit” is the withdrawal of the United Kingdom (UK) from the European Union (EU).  The British public, following a referendum held on 23 June 2016, voted to leave the EU with a 51.9% majority.

[10] The subdued quarterly growth reflects the impact of the slowdown in global growth and ongoing Brexit uncertainties (Bank of England, 2019).

[11] Two sequential quarters of negative growth indicates that an economy is in technical recession.

[12] Chained Volume (CV) measures are used here, rather than current prices.  This is because economists are ultimately interested in welfare, and so we are interested in the real output, rather than the nominal output.  I have, therefore, calculated the GDP by using the same constant prices as weights for every year.

[13] TFP, also known as the Solow residual, is a measure of economic efficiency within a country with which productive inputs are combined to produce output (Sussman, 2019).

[14] There is a strong linkage between technological innovation and TFP growth.  Comin et al. (2006) found cross country differences in technology are 4 times greater than cross-country differences in income per capita.

[15] Good governance, lack of corruption, and high social capital are all vital in growing TFP (Miles et al., 2012).

[16] Hanushek & Woessmann (2010) and Crafts (1991) illustrate there is a significant relationship between educational outcomes and economic growth amongst countries, and can explain why to some extent, even with the effects of diminishing marginal product of capital, investment still flows into capital-rich countries.

[17] Hulten identifies many factors that cause a shift in the production function, but highlights that it should not be equated with technological innovation, which it often is.

[18] Indeed, Hall & Jones (1999) empirically illustrated that the TFP has a greater influence in a nation’s productivity and GDP that human and physical capital.

[19] “Earnings yield as an investment valuation metric is not as widely used as the price-to-earnings ratio (P/E ratio). Earnings yield can be useful when concerned about the rate of return on an investment. For equity investors, however, earning periodic investment income may be secondary to growing their investments’ values over time. This is why investors may refer to value-based investment metrics such as P/E ratio more often than earnings yield when making stock investments” (Investopedia).

[20] Thus, “the earnings yield illustrates the percentage of how much a company earned per share and is an indicator utilised by investors by to determine whether certain assets, or regions, are attract investments” (Investopedia, 2019).

[21] The BEER formula is: BEER = Bond Yield/Earnings Yield.

[22] A reading of less than 1.0 indicates the stock market is undervalued.

[23] Economic theory suggests that investors in equities should demand an extra risk premium several percentage points above prevailing risk-free rates, such as rates on government bonds, in their earnings yield to compensate them for the higher risk of owning stocks over bonds (Sussman, 2019).

[24] Based on the following logic: (1) a high GDP rate leads to increased aggregate corporate profits; (2) growing corporate profits translate into increased earnings yield; and (3) increased earnings yield manifests a higher stock price (MSCI, 2010).  Indeed, Investopedia (2019) stated that although people are not able to predict stock market returns precisely based on GDP growth rate over shorter term, the relationship does hold loosely over the long haul.

[25] The core operations of Energy, gas and mining companies are generally conducted off-shore, or in locations outside the United Kingdom.

[26] Hence, “if the net income is increasing, earnings per share could be decreasing” (Wu, 2012, p. 22).  Another explanation for the lack of observable correlation between GDP growth and stock returns is that expected economic growth is already impounded into the prices (Siegel 1998), thus lowering future returns from the stock market perspective (MSCI, 2010).

[27] Economists usually describe the state of the economy by looking at how much people can buy with the same unit of currency (Sussman, 2019).

[28] A sharp increase in general price levels can cause economic harm.  High levels of inflation can result in people paying higher income taxes, thus, becoming worse off.  Furthermore, inflation exerts a cost by reducing the value of cash and, as a result, hampers long-run growth. Similarly, deflation, a sharp decrease in the general level of prices, can cause economic damage. Deflation may mean weaker consumption spending and weaker investment by companies (Miles et al., 2012).

[29] The Retail Price Index (RPI) is another price index in the UK where housing costs are included within the calculations.  Thus, mortgage interest costs and council taxes are utilised as a proxy for the cost of owner-occupied housing (Miles et al., 2012).

[30] The measure the Bank of England utilises to set monetary policy is the CPI, and stands at 2% (as of May 2019).  The government has set the Bank of England a target of maintaining inflation at 2%.  A 0% inflation target is unattractive for principally two reasons: (1) allowing a modest amount of inflation, the central bank can achieve some variation in real wages even if nominal wages are stocky downwards; and (2) a zero target increases the probability of the UK economy entering deflation (Miles et al., 2012).

[31] Partially offsetting upward contributions derived from rising games, toys and accommodation services.

[32] Includes commodities purchased in shops, through mail order or over the internet, and goods produced within the UK, domestically, or abroad (Miles et al., 2012).

[33] Rather than expressing the measure via a geometric mean approach.

[34] It is the interest rate quoted on bonds and loans.  For example, you borrow £100 at a 2% interest rate, you can expect to pay £2 in interest without taking inflation into account.

[35] These rates are the basis for other interest rates that are charged by banks and other institutions to consumers.

[36] The opposite holds true for rising interest rates.  As interest rates are increased, consumers tend to have less money to spend. With less spending, the economy slows and inflation decreases.

[37] For instance, if your bank pays 3% per annum in interest on your deposits, but inflation over the next year increases the price level by 1%, then although you have 3% more sterling a year from now, you only have 2% greater purchasing power.

[38] From the Fisher equation, you can see that if the real interest rate is held constant, an increase in the inflation rate must be accompanied by an equal increase in the nominal interest rate. The Fisher Effect is an evidence that purely monetary developments will have no effect on the country’s relative prices in the long run. In the short run, however, the Fisher Effect does not necessarily hold since the nominal rate might need time to adjust if the inflation was unexpected.

[39] “The money supply can include cash, coins, and balances held in checking and savings accounts, and other near money substitutes” (Investopedia, 2019).

[40] For example, financial assets such as notes and coins are readily available to utilise to purchase goods and services, whilst stocks and shares are less liquid and thus cannot be labelled a money in the strict sense.

[41] Including those held in banks’ and building societies’ tills, and banks’ operational deposits with the Bank of England.  When the Bank introduced Money Market Reform in May 2006, the Bank ceased publication of M0 and instead began publishing series for Reserve Balances at the Bank of England to accompany Notes and Coin in circulation (Bank of England, 2018).

[42] Furthermore, negative M4 growth during 2011-2012 was a sign that economic activity was falling.  As expected, the UK economy went into a double-dip recession.

[43] Indeed, in 2010 the total money supply (M4) measure in the UK was £2.2 trillion while the actual notes and coins in circulation totalled only £47 billion: 2.1% of the actual money supply.

[44] Nobel Laureate Milton Friedman is one of the most prominent advocates of monetarism.

[45] Hence, assuming that the velocity of money is constant and the that value-added is not influenced by the money supply, money supply directly increases inflation (Miles et al., 2012):

M – Y = P

[46] The opposite can occur if the money supply falls or when its growth rate declines.

[47] Inflation can be caused by several factors other than the money supply.

[48] The effective exchange rate is the domestic currency against a trade weighted average basket of all currencies.

[49] Since 1992, the UK has a free-floating exchange rate, meaning the external value of the sterling has been left to market forces, i.e. supply and demand in the foreign exchange global markets (Tutor2u, 2019).  The UK’s Conservative party under John Major was forced to withdraw from the European Exchange rate mechanism (ERM) after the events of Black Wednesday, which resulted in a loss of £3.4 billion and the UK being unable to keep the pound above its agreed lower limit.  There are four common alternative exchange rate systems countries operate: (1) managed-floating system; (2) semi-fixed exchange rate system; (3) fully-fixed exchange rate system; and (4) a Monetary Union, e.g. the Eurozone.

[50] The law of one price dictates that the same commodity should sell for the same price in all countries due to the result of price arbitrage (Miles et al., 2012).  However, in reality there is a deviation for this hypothesis due to transportation costs, tariffs, and border effects, not to mention pricing to market.

[51] It has since become a global standard for price comparison, where one can measure the RER between two countries in terms of a single representative good – the Big Mac.

[52] The limitations of the Big Max index as three-fold.  First, it pertains more to the law of one price than PPP as it refers to one commodity, not a basket of goods (Miles et al., 2012).  Second, the Big Mac represents a commodity is not tradeable between countries.  Finally, the variations in rental space, indirect taxes and local labour across countries is reflected in the cost of a Big Mac and hence makes it a different commodity in Lagos in comparison to London.

[53] In January 2014, the UK price was £2.79 and the U.S. price is $4.63, then (1.65) x (2.79) ÷ 4.63 yields an RER of 0.99.

[54] One can conclude that over the 5-year period, the UK and US currencies are not in equilibrium.  Indeed, Miles et al. (2012) postulates that as the PPP holds to some degree in the long-run (greater than 10 years), the consensus view is that that the short-run fluctuations in the real exchange rate reflect variations in the nominal exchange rate.

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