A Course in Macroeconomics Introduction to Key Macroeconomic Variables David Prescott, University of Guelph, Ontario, Canada

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1 A Course in Macroeconomics Introduction to Key Macroeconomic Variables David Prescott, University of Guelph, Ontario, Canada An Introduction to Essential Macroeconomic Variables Macroeconomics is the study of the economy at the aggregate level whereas microeconomics is concerned with the economic behaviour of individual people, households (families) and individual firms. The main variables of interest in macroeconomics include: The level of aggregate income or production - Gross Domestic Product, GDP (Y) The labour force available for work (LF) Actual employment in the entire economy (L) Number of unemployed (U) and the unemployment rate (UR) Total capital available to the entire economy (K) The variables listed above are referred to as real variables because they refer to quantities rather than money values. For example, Y refers to the total quantity of goods and services produced in one year. If the economy produced only tons of steel, Y would refer to the total quantity of steel produced in one year. Over time the change in Y would measure how the quantity of steel produced each year changes from year to year. In practice, the economy produces many goods and services so Y is an aggregate or combined total of all the individual products and services. To combine the individual products into a total, each must be weighted (multiplied) by its price. Consider an example using two individual products (t represents the date or time):,,,, In the next time period (t + ), the quantities will most likely change. The prices could also change, but to measure the real output the new levels of production are valued at the prices in period t.,,,,

2 The value of total production V in period (t + ) uses both the quantities and prices observed at time (t + ).,,,, The current value of total production is referred to as Nominal GDP or NGDP. Over time, changes in NGDP reflect changes in both prices and quantities whereas changes in real GDP measure changes in the quantity of production holding prices constant. The measures of real GDP and nominal GDP can be used to calculate an aggregate price level which is of course an average of the individual prices. Since real and nominal GDP are calculated in the way described above, together they imply a measure of the level of prices in the economy as a whole. Hence, we can define an Implicit GDP Price Index (P). This means that the GDP Price Index is implied by or is implicit in the real and nominal GDP calculations: Notice that in the period t, real and nominal GDP are identical since they both use the individual prices observed in period t. Hence in period t (the base period) the implicit price index is equal to. : We are often interested in the growth of variables as well as their levels. Let s write nominal GDP (V) and the product of real GDP (Y) and the price index, P (for convenience, we are setting the level of the price index to. in the base period): The growth of V can be calculated as where: If we think of nominal GDP as changing continuously as time advances, V at time t can be written as the function V(t). In this case the growth rate of V at time t is:

3 The continuous time version of equation [] is which can be differentiated with respect to time to give: The growth rate of nominal GDP can therefore be written as: We conclude that the growth of nominal GDP can be expressed as the sum of the growth rate of real GDP and the growth of the price level: The growth of the price level is called the rate of price inflation In general terms, the growth rate of a product XY is the sum growth rates of X and Y. Real GDP can be written as nominal GDP divided by the price level: From [] we know that. The growth of real GDP (the growth of the quantity of production) equals the growth of nominal GDP (the growth of the current value of production) minus the growth of prices. In general, the growth rate of a ratio is the growth of the numerator minus the growth of the denominator. Consider another example of a ratio. Economists often refer to GDP per capita. This is GDP divided by the total population or GDP per person. Let s consider real GDP (Y) per worker (L), which we will write as y: The growth of real GDP per person is the growth of real GDP minus the growth of employment:. From this relationship we can see that the growth of real GDP per person is zero if real GDP and employment grow at the same rate. Real GDP per person can only increase if real GDP grows faster than the level of employment.

4 Some Empirical Examples: Canada.8E+ Real & Nominal GDP 5.6E+.4E+.E+ E+ 8E+ GDP RealGDP 6E+ 4E+ E+ 5 5

5 3 GDP Implicit Price Index GDP Price Index Calculation of Average Compound Growth In the first quarter of 5, Canada s GDP was $8 billion. Sixteen years later, in the first quarter of, GDP had risen to $7 billion. Question: What was the average compound growth rate of GDP over these 6 years? Suppose the answer is g. It must be that 7 8 To solve for the average annual growth rate g we use: ln Where ln is the natural logarithmic function and exp is the exponential function. This equation can be substituted into Excel to make the calculation. The result is g =.48 which means the average annual growth rate of nominal GDP was 4.8%. This is the sum of the growth of real GDP and the growth of the price level (inflation) over this 6 year period of time. The details appear in the following table:

6 Growth Rates 5Q Q GDP Real GDP P Index Product Sum Labour Market Variables The following quotation is from Statistics Canada: The Canadian Labour Force Survey was developed following the Second World War to satisfy a need for reliable and timely data on the labour market. Information was urgently required on the massive labour market changes involved in the transition from a war to a peace-time economy. The main objective of the LFS is to divide the working-age population into three mutually exclusive classifications - employed, unemployed, and not in the labour force - and to provide descriptive and explanatory data on each of these. The labour force (LF) is made up of two groups, the employed (L) and the unemployed (U): To be classified as unemployed, a person must be available for work (not in full time education or out of the country) and seeking work (applying for jobs for example). There are many people who are not in the labour force such as those in full time education and retired people not looking for work. An important group consists of discouraged workers who are of working age but have been unable to find work for so long that they no longer look for work. The number of unemployed persons is therefore a smaller number of people than all those who do not have jobs but might work if jobs were available. The unemployment rate is defined as: The Working Age Population (WAP) consists the population 5 years and older (with some exceptions). The Working Age Population consists of three groups: Where NILF = Not In the Labour Force

7 The labour force participation rate (PR) is the ratio of the labour force to the working age population: The following charts illustrate some aspects of the Canadian labour market. 85 Participation Rates Percent Males Females

8 5 Unemployment Rates, by Age 76 Percent

9 6 Unemployment Rates, by Sex 76 4 Percent Males Females 8

10 6 Participation Rates, Percent 3 Males Females 8

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12 8 UR by Region Percent Alberta BC NovaScotia Ontario 8 Financial Variables An important variable that can be controlled by a country s central bank is the stock of money (M). There are a number of definitions of the stock of money. Narrow definitions are limited to cash and chequable deposits. Broader definitions include savings deposits and other liquid assets that can easily be converted into cash or spendable deposits. The stock of money is a nominal variable. The real stock of money is equal to where P is the aggregate price level.

13 There is a vast range of interest rates. We will use the symbol R to represent the interest rate. Commonly quoted rates include: The Treasury bill rate of varying maturities Mortgage rates of varying maturities Prime lending rate The rates of return generated by financial assets such as these are nominal interest rates. They are nominal interest rates because the interest to be received in the future is expressed in dollars. If future prices are higher than current prices the real value of the future interest payments will be reduced. The real return on a bond, the real interest rate, which is represent by the symbol r, can be calculated by subtracting the increase in the price level (inflation) from the nominal interest rate. Hence, The previous formula applies after the fact that is to say we can calculate past real interest rates by subtracting actual past inflation from past nominal interest rates. Looking forward, we do not know what price inflation will be over the next year. While we can see the nominal interest rate that applies to one-year loans we cannot calculate the real interest rate over the next year because future inflation is unknown. But we can use expected inflation to calculate an expected real interest rate. The expected (future) real interest rate is referred to as the ex-ante real interest rate. The actual real interest rate that occurred in the past is called an ex post real interest rate. Economic decisions taken in the current period such as whether to borrow money to invest in new machinery depend on the ex-ante real interest rate one that cannot be calculated with certainty. Finally, consider two variables that are important in international trade. The first is the nominal exchange rate. This is the published exchange rate for which one currency can be exchanged for another. The following chart shows the recent exchange rate between the United States Dollar and the Euro

14 A related concept is the real exchange rate otherwise known as the terms of trade. The terms of trade describe the rate at whichh one country s goods exchange forr another country s goods. For example, Australia exports wheat while Saudi Arabiaa exports oil. The terms of trade between these countries can expressed as the rate at which a bushel of wheat exchanges for a barrel of oil. If fewer bushels of wheat are required to get a barrel of oil the terms of trade improve for Australia. Of course Australia exports more items than wheat and Saudi Arabiaa imports more than wheat. In aggregate the real exchange rate is calculated using the nominal exchange rate and the ratio of each country s price level. Suppose the price levels in two countriess are: The nominal exchange rate between the two currencies iss, which is the price of currency j in terms of currency i. A unit of output from country j has a price in local currency. In terms of currency i the unit price of country j s product is,. The real exchange rate is defined as:,, Suppose the price level in country i is unchanged while the price level in country j rises % %. Country j will find its exports will drop, the demand for its currency will declinee and its exchangee rate will fall. A % decline in the value of country j s currency is a % decline in

15 ,. This combination of a % increase in the price level and a % decline in the exchange rate leaves price of country j s output unchanged in terms of the other country s currency and as a result the real exchange rate is unchanged. Summary A number of essential macroeconomic variables have been described. They are either real or nominal variables. Nominal Variables Symbol V M P R, Name Nominal GDP Money stock or supply Aggregate price level Nominal interest rate Exchange rate (cost of currency j in country i s currency) Real Variables Symbol Y = V/P M/P r,, Name Real GDP Real Money stock or supply Real interest rate Real exchange rate

16 Exercises. Over a year period a country s real GDP increases from $5 billion to $685 billion. What is the average annual growth rate?. A country s real GDP grows at a rate of.% per year while employment grows at the rate of % per year. The price level grows at the rate of.5% per year. What is the growth of nominal GDP per person? 3. A farmer produces apples and pears. Total sales is the sum of the apple and pear sales: Show that the growth of total sales is a weighted average of the growth of apple and pear sales. What are the weights? 4. If a full time student decides to leave school and look for a job what happens to: the labour force; the number of unemployed, the unemployment rate and the participation rate? 5. If a person who was working in an economically depressed region loses his job and quickly decides it is a waste of time to look for a new job what happens to: the labour force; the number of unemployed, the unemployment rate and the participation rate? 6. In Canada, how have the male and female labour force participation rates behaved since the mid-7s 7. What might explain the behaviour of the participation rates of people over 55 in Canada? 8. On st January 6 the 3 month Treasury bill rate was.6% (annual rate). During the 3 months January to March an index of aggregate prices rose from to.56. What was the real rate of return? Is this an ex-ante or ex-post real return?. A bond pays 8% interest after one year. Suppose the interest rate is cut in half, but compounded twice what is the annual rate of return? Suppose the interest rate is reduced by a factor of 4 but compounded every 3 months (4 times per year) what is the annual rate of return? Suppose the interest rate is reduced by a factor n to (8/n)% but interest is compounded n times per year? What is the limiting annual rate of as n tends to infinity?