Unit 1: Macroeconomic Variables
Unit 1.1: Introduction to Macroeconomics
Macroeconomics is the study of aggregate economic activity – of the performance of the economy as a whole. Macroeconomics is about how aggregate economic variables are determined, how they are related to each other, and what policymakers can do about them. Macroeconomic variables are things like GDP, inflation, unemployment rates, interest rates, exchange rates, etc… that characterize features of the economy as a whole.
A Brief History of Macroeconomics
The classical distinction between macroeconomics and microeconomics is that microeconomics is about individual and firm decisions, and about individual markets, whereas macroeconomics is the study of aggregate economic activity. But the two are increasingly interconnected. Understanding macroeconomic patterns (e.g. consumption or investment) requires understanding how individuals and firms make decisions. And understanding financial markets or labor markets requires a good understanding of the fundamental microeconomics of how markets work. At the same time, many microeconomic questions may have macro-level implications, like taxes in commodity markets or changes to wage rules. Overall, the line between macroeconomics and microeconomics is not as clear as it once was.
Macroeconomics is very new. While even the ancient Greeks understood some basics of what we would today call microeconomics, systematic study of aggregate economic activity and reliable collection of macroeconomic data really did not begin until the 1930’s. John Maynard Keynes was the first true macroeconomist, and the Great Depression was the historical context for his work. The simultaneous economic collapse in worldwide markets led economists to start thinking seriously about economic activity as an aggregate unit, not just as a collection of markets.
Macroeconomic Trends
The most basic measure of the size of the economy is the Gross Domestic Product (GDP). We will cover its measurement in detail later, but informally you can think of it either as the total output of goods and services in the economy or as the total incomes generated by the economy.
US GDP is currently around $19 trillion a year. Here is a graph showing GDP since 1947.
In the most basic sense, the graph shows us the two key empirical regularities about how the economy moves over time that we will try to explain: (1) It grows, and (2) It fluctuates.
There are two basic flavors of macroeconomic models – Keynesian models and classical models – that offer contradictory answers on the fundamental drivers of economic performance. As a result, the models also offer different policy advice. While the differences are hotly debated and answers are elusive to some extent, broadly Keynesian models do a better job of explaining short-run fluctuations and deviations from the trend, while classical models do a better job of explaining economic growth and long-run trends. Throughout the class, we will use “fluctuations models” as a broad umbrella for Keynesian-style models and “growth models” as a broad umbrella for Classical-type models.
A second basic macroeconomic indicator is employment. Good employment outcomes basically fluctuate together with GDP. In other words, unemployment is low when GDP is high and unemployment is high when GDP is low.
A third key macroeconomic indicator is prices. The percentage change in price level from year to year is the inflation rate. The diagram below shows the inflation rate since 1960. After a period of high inflation in the 1970’s and early 1980’s, inflation since then has been quite low.
A key variable that may link the financial side of the economy with the real side of the economy is interest rates – the return you earn from investing the money, or the interest rate you pay in order to borrow money. There are many different interest rates, but a good place to start is the interest paid on US treasury bills; interest rates tend to go up and down together, so this is a good baseline. The diagram below shows interest rates since 1947. After a period of high interest rates, interest rates have been quite low for the last couple of decades and in fact have been practically zero since the financial crisis of 2008. That’s good news if you’re trying to buy a house, but the era of low returns is creating a pinch for investors. We’ll talk a lot about this issue later in the course.
The relationship between government spending and economic performance is a deep and fundamental question that we will address at length. In brief, Keynesian models imply that increases in government spending can drive increases in GDP. Classical models imply that government spending is neutral or harmful for GDP growth. The short-run and long-run answers to this question may differ, as well.
Turning to the foreign sector, the US is deeply involved in the global economy. US firms earn substantial revenues from exports of US goods and services abroad; about 12% of GDP is currently made up of exports. But we import far more than we export, leading to large trade deficits.
The diagram below shows the US trade deficit (exports – imports) since 1947. Our trade position was close to balanced for a long time, but the trade deficit exploded in the 1990’s and early 2000’s. The causes and consequences of these large trade deficits are the subject of substantial controversy that frequently spills over into the political arena.
Plan for the Class
The class is basically divided into five sections.
First, we will talk about measurement of key macroeconomic variables – how to interpret what they mean and why we care about them.
Second, we will talk about fluctuations models – the Keynesian model, the IS/LM model and the AD/AS model. These are a series of increasingly rich models that relate output, interest rates and price levels, which have had great empirical success in explaining short-run fluctuations.
Third, we will talk about microfoundations – the behavior underlying fundamental macroeconomic forces and how these microeconomic choices relate back to aggregate economic activity. Specifically, we will study the underlying determinants of consumption behavior, firm investment, government policy, the foreign sector, money supply and demand, price rigidity (or flexibility) and unemployment.
Fourth, we will talk about growth models, focusing on the Solow model and its variants. In doing so, we will emphasize the contrast between the short-run and the long-run and between Keynesian demand-driven models of economic performance and classical supply-driven models. The unit will include a detailed discussion of cross-country differences in growth performance.
Unit 1.2: GDP
GDP Defined
Gross Domestic Product (GDP) is the total value of all final goods and services that an economy produces over a year. It is the flow of output over the course of a year. A few points:
• GDP counts only final goods and services, not intermediate goods that are sold to firms and used up in the production of other goods and services.
• GDP counts all output produced within the borders of the United States, no matter whether the company is owned by Americans or not.
• GDP counts only output that is designed for sale on the market place. Home production is not included.
US GDP in 2016 was $18.6 trillion.
Alternative Approaches to Measuring GDP
There are three approaches to measuring GDP, and the equivalency between them teaches us something important about the macroeconomy.
1. GDP measures expenditures on goods and services by different groups. 2. GDP measures production of goods and services by firms.
3. GDP measures income earned by producers of goods and services.
In a simple sense, you can see why these are equal.
Suppose a firm produces $1,000,000 of cars. It sells $900,000 of them but doesn’t sell the other $100,000. An economist would count the other $100,000 as an expenditure on inventory accumulation by the firm. Production and expenditure are equal as long as we count inventory accumulation as a firm expenditure.
The equality of expenditures, production and income represents an accounting identity – it holds by definition. They do not by themselves embody any theory about how the economy works or propose any testable hypotheses. They simply hold in an accounting sense because of how expenditures, production and income are defined.
Expenditure Approach
Using the expenditure approach, we count up GDP by looking at total expenditures on goods and services by different sectors in the economy. The basic identity is:
𝐺𝐺𝐺𝐺𝐺𝐺 =𝐶𝐶+𝐼𝐼+𝐺𝐺+𝑁𝑁𝑁𝑁
• 𝐶𝐶 is consumption spending, which represents about 70% of GDP
• 𝐼𝐼 is investment spending, which represents about 15% of GDP
• 𝐺𝐺 is government spending, which represents about 20% of GDP
• 𝑁𝑁𝑁𝑁 is net exports, which represents about −5% of GDP (imports > exports)
It is important in this definition to include only production of final goods and services. Resale of used goods does not count in GDP. And intermediate goods do not count in GDP. If a chef buys lettuce for $2 and buys tomatoes for $2 that he uses to produce a salad that he sells for $7, only the final $7 salad counts in GDP. Counting the lettuce and the tomatoes separately would be “double counting” since their value is already included in the final sale of the salad.
Let’s go through each sector.
Consumption
Consumption is spending by households on goods and services. It includes three components.
• Durable goods like washing machines, furniture and cars.
• Nondurable goods like food and gasoline.
• Services like medical care, haircuts and college tuition.
Investment
• Fixed investment consists of new plant machinery and equipment and new home construction.
• Nonresidential fixed investment consist of structures, equipment and intellectual property
• Residential fixed investment is new home construction
• Inventory accumulation is the change in the stock of inventories held by firms.
Let’s give a numerical example to illustrate how to deal with inventory accumulation. Suppose that a firm produces $200,000 of televisions in 2016. It sells $150,000 of them in 2016 but the other $50,000 are not sold until 2017.
In 2016, we count the $150,000 of televisions sold as consumption spending and the other $50,000 as inventory accumulation by firms.
2016
Consumption + $150,000
Investment (Inventories) + $50,000
GDP + $200,000
In 2017, we count the $50,000 of televisions sold to consumers as consumption spending. But we have to deduct the $50,000 of televisions that were decumulated from the firm’s inventories.
2017
Consumption + $50,000
Investment (Inventories) −$50,000
GDP No change
Government Purchases
Government purchases is the sum of all federal, state and local government purchases of goods and services. Spending on highways, fighter jets and schools is government spending.
Importantly, government purchases as included in GDP does not count all outlays of money by the government.
• Government purchases do not include transfer payments – pure cash transfers like unemployment pay, social security or welfare payments that do not involve production of a good or service in exchange for the payment.
• Government purchases do not include interest on the debt, which again is not production.
Basically, we only count government outlays that are actually purchasing goods and services. Not cash transfers and not interest on the debt.
Net Exports
Net Exports are exports minus imports.
Exports are goods and services produced in the US but sold overseas. We need to include these in GDP. Exports represent US production, but they are not counted in C, I or G because they are not sold domestically.
Imports are goods and services that are produced overseas but sold in the US. Purchases of imports are included in C, I or G (depending upon the purchaser), but we subtract them back out again because imports do not represent domestic production. The net contribution to GDP is zero.
Current Numbers
GDP in the United States for 2016 was $18.6 trillion. Here is a breakdown.
Consumption $12.8 trillion (69%) Government $3.3 trillion (18%)
Durable goods 0.11 of consumption Federal defense 0.22 of government
Nondurable goods 0.21 of consumption Federal nondefense 0.16 of government
Services 0.68 of consumption State & Local 0.62 of government
Investment $3.0 trillion (16%) Net Exports −$501 billion (−3%)
Structures 0.16 of investment Exports $2.2 trillion
Equipment 0.35 of investment Goods 0.65 of exports
IP 0.25 of investment Services 0.35 of exports
New home construction 0.23 of investment Imports $2.7 trillion
Inventory accumulation 0.01 of investment Goods 0.81 of imports
One final caution – The GDP identity 𝐺𝐺𝐺𝐺𝐺𝐺= 𝐶𝐶+𝐼𝐼+𝐺𝐺+𝑁𝑁𝑁𝑁 is an accounting statement of how GDP is defined. It is not an economic model. For example, the identity does not mean that increasing government spending by $1 will cause GDP to rise by $1. Maybe higher government spending makes other things go up. Maybe it makes other things go down.1 That requires a model of how the economy works. Not simply an accounting definition.
Value Added Approach
Instead of looking at expenditures, we might think about looking to businesses directly. If we do it this way, it’s important to avoid double counting of output that is produced by one firm but sold as an intermediate good (input) to another firm. The value added for a firm is the difference between the revenue that it earns from selling its products and the amount that it pays for intermediate goods that it uses up in producing its products.
Here is an example. A lumberjack chops down a tree from his backyard and sells the wood for $100 to a paper mill. The paper mill produces paper and sells it to a wholesaler for $250. The wholesaler boxes the paper and sells it to an office supply store for $300. The office supply store sells the paper to customers for $600.
Using the expenditure approach, the addition to GDP is $600: the final paper sale to the consumer.
Alternatively, we could use the value added approach to add up the value added at each stage of production.
Lumberjack + $100
Mill + $150
Wholesaler + $50
Office Supply Store + $300
GDP + $600
The point is that adding up each stage of production produces the same answer as counting only expenditures on final goods and services, as long as we include only the value added at each stage.
It can be useful to think about where value is added across the economy by industry. See below for a broad overview. I would encourage you to look at the Value Added Tables produced by the Bureau of Economic Analysis for a more detailed breakdown by industry.
1 Here’s a good example. Total revenue is defined in an accounting sense as Price×Quantity. Does that mean that, if
Industry / Sector Value Added (%)
Agriculture, forestry, fishing, hunting 1.2%
Mining 2.6%
Utilities 1.6%
Construction 3.8%
Manufacturing 12.1%
Wholesale trade 6.0%
Retail trade 5.0%
Transportation and warehousing 2.9%
Information 4.8%
Finance and insurance 7.0%
Real estate, rental, leasing 13.0%
Professional, scientific and technical services 6.9%
Management 4.9%
Educational services 1.1%
Health care and social services 7.1%
Arts, entertainment and recreation 1.0%
Accommodation and food services 2.8%
Miscellaneous services 2.2%
Federal government 4.1%
State and local government 9.0%
Income Approach
A final way to measure GDP is to sum up how the money earned from sales of goods and services is paid out. This is the income approach to measuring GDP.
Some of our income is “used up” as depreciation of existing capital, so in essence this piece does not represent new income created. Firms can also pay out incomes as wages and salaries, profits, rental income, interest payments and production taxes. Here is a breakdown of 2016 GDP using the income approach. This basically tells us where the money from production of goods and services is paid out.
Compensation $10.1 trillion (53%) Corporate Profits $1.7 trillion (9%)
Wages and Salaries 0.81 of compensation Profits Taxes 0.32 of profits
Benefits 0.19 of compensation Dividends 0.49 of profits
Retained Profits 0.19 of profits
Proprietor Incomes $1.4 trillion (7%) Rental Income $705 billion (4%)
Interest $676 billion (4%) Production Taxes $1.3 trillion (7%)
Alternative Measures of Income
Starting from the income approach to measuring GDP, there are some alternative measures of total income earned in an economy that might be more appropriate, depending upon the question.
National Income (NI) is income that is actually available to be earned. As discussed earlier, part of our income every year is “used up” as depreciation, so this part is excluded from national income.
𝑁𝑁𝐼𝐼= 𝐺𝐺𝐺𝐺𝐺𝐺 −depreciation
Personal Income (PI) is income received by the public before taxes. Out of national income, some is retained as corporate profits, some is lost to production taxes, some is paid out by firms to social security and Medicare, and some is lost as interest on debt. These are subtracted out of national income, because these funds are never received by the public. At the same time, the public earns income on their financial assets and collects transfers from the government. These are added into national income to obtain personal income.
𝐺𝐺𝐼𝐼 =𝑁𝑁𝐼𝐼 −retanied profits−production taxes−social welfare taxes−interest + asset income + government trasnfers
Disposable Income (DI) is after-tax income received by the public. This is basically what is available to spend.
𝐺𝐺𝐼𝐼= 𝐺𝐺𝐼𝐼 −personal income taxes
For 2016, GDP was $18.6 trillion. National income was $16.1 trillion. Personal income was $16.0 trillion and disposable income was $14.0 trillion.
GDP and GNP
There is a subtle difference between domestic output and national output.
As mentioned earlier, Gross Domestic Product incorporates all output produced within the borders of the United States. By contrast, Gross National Product (GNP) incorporates all output produced by American firms, no matter where they are located. But Gross National Product excludes output produced by foreign firms in the United States. In brief, GDP is output produced in America. GNP is output produced by Americans.
Real GDP and Nominal GDP
GDP is the value of the output that an economy produces. But how should we value that output? In other words, what prices should we use? Consider an economy whose output consists of apples and oranges. The table below shows output and prices for 2011, 2012 and 2013.
2011 Price Quantity
Apples $1 100
Oranges $5 60
2012 Price Quantity
Apples $2 110
Oranges $8 80
2013 Price Quantity
Apples $5 120
Oranges $30 85
Nominal GDP gives each year’s output valued at that current year’s prices.
• 2011: Nominal GDP = 100 apples × $1 + 60 oranges × $5 = $400
• 2012: Nominal GDP = 110 apples × $2 + 80 oranges × $8 = $860
• 2013: Nominal GDP = 120 apples × $5 + 85 oranges × $30 = $3150
Look at the growth in nominal GDP between 2011 and 2012. This seems unreasonably high. The actual production of apples and oranges only went up a bit, but the size of the economy as measured by nominal GDP more than doubled. The problem is that most of this growth in nominal GDP is due to changes in prices and not to changes in output. When nominal GDP rises, we don’t know whether it’s because the economy is producing more output or just because prices are higher.
Real GDP – Traditional Method
Real GDP is designed to look only at changes in output. The traditional approach to calculate real GDP is to fix prices in some base year, and then to value all output from all years at the prices from the base year.
• 2011: Real GDP = 100 apples × $1 + 60 oranges × $5 = $400
• 2012: Real GDP = 110 apples × $1 + 80 oranges × $5 = $510
• 2013: Real GDP = 120 apples × $1 + 85 oranges × $5 = $545
These numbers actually represent growth in output only, since prices are fixed, and therefore provide a more accurate measure of growth of the economy. When looking at GDP over time, it’s important to use real figures rather than nominal figures.
Chain-Weighting
That was the older, traditional method of calculating real GDP. One drawback of this method is that using old prices can sometimes be misleading. For example, it would be ridiculous to value computers today at the same price as a computer in 1980. Computers then were very expensive and we only produced a few. The government now uses a newer method called chain-weighting, which in effect calculates an average growth rate year-on-year to continuously update prices.
Let us take 2011 as the base year. To calculate real GDP for 2012, we need to compare the value of 2011 and 2012 output. The basic approach for chain-weighted GDP is to do this comparison both at 2011 prices and at 2012 prices, and then average the two growth rates together.
First, we compute the value of 2011 and 2012 output using 2011 prices.
• 2011 output at 2011 prices: 100 apples × $1 + 60 oranges × $5 = $400
• 2012 output at 2011 prices: 110 apples × $1 + 80 oranges × $5 = $510
Using 2011 prices, the growth in real output from 2011 to 2012 is:
𝑔𝑔1 =510400 = 1.275
In words, using 2011 prices to value production, output grew 27.5% between 2011 and 2012.
Second, we compute the value of 2011 and 2012 output using 2012 prices.
• 2011 output at 2012 prices: 100 apples × $2 + 60 oranges × $8 = $680
• 2012 output at 2012 prices: 110 apples × $2 + 80 oranges × $8 = $860
Using 2012 prices, the growth in real output from 2011 to 2012 is:
Using 2012 prices to value production, output grew 26.4% between 2011 and 2012.
Now we take the geometric average of these two growth rates to obtain the growth rate we will use for our calculations.
𝑔𝑔̅ =√1.275 × 1.264 = 1.269
Using this average growth rate, 2012 GDP is 26.9% higher than 2011 GDP. We thus take 2011 GDP and increase it by 26.9% to obtain 2012 real GDP using the chain-weighting method.
2012 Real GDP = 400(1 + 0.269) = $507.60
For 2013 chain-weighted GDP, we do the same calculations to compare 2012 and 2013. First compute 2012 and 2013 output valued at 2012 prices.
• 2012 output at 2012 prices: 110 apples × $2 + 80 oranges × $8 = $860
• 2013 output at 2012 prices: 120 apples × $2 + 85 oranges × $8 = $920
For a growth rate:
𝑔𝑔1 =920860 = 1.070
Now compute 2012 and 2013 output using 2013 prices.
• 2012 output at 2013 prices: 110 apples × $5 + 80 oranges × $30 = $2950
• 2013 output at 2013 prices: 120 apples × $5 + 85 oranges × $30 = $3150
For a growth rate:
𝑔𝑔2 = 31502950 = 1.068
We then average these two approaches to calculating the growth rate.
𝑔𝑔̅ =√1.070 × 1.068 = 1.069
Finally, we can calculate the 2013 chain-weighted GDP by raising 2012 GDP by 6.9%
Now you can see where the “chained” descriptor comes from. Starting with the base year, each successive year’s real GDP is calculated by “chaining” off of the previous year’s real GDP using the growth rate we calculate. Each year’s real GDP is “chained” to the previous year’s real GDP.
One important caveat in using chain-weighted GDP you should take note of – Let’s say you calculated chain-weighted GDP by including every item that’s in GDP. Then let’s say you calculated chain-weighted consumption by including every item in consumption spending, and you did the same thing with investment spending, government spending and net exports. If you add these four numbers, the answer would not be the same as what you obtained by you chain-weighted the entire GDP together. The basic issue is that the weighting itself across the four categories included in the total changes and so chain-weighted GDP is not additive across categories.
Weaknesses of GDP
Finally, we should take note of a few weaknesses in using GDP to measure to size of an economy. Understanding these limitations is critical to interpreting economic statistics properly.
• GDP does not incorporate quality improvements. A television is a television in calculating GDP, with no adjustment for improving quality over time.
• GDP does not include the underground economy. Various legal and illegal activities are part of economic output but are not measured. Legal activities include off-the-books and barter transactions. Illegal activities include the drug trade, prostitution, etc… By some estimates, the underground economy might be as high as 8% of measured GDP.
• GDP does not include nonmarket production. Even though growing your own food, taking care of your children and producing breastmilk all have value, they are not measured for GDP. This issue leads to significant undercounting of GDP in developing countries, where a substantial part of economic activity is off the grid and never goes through a market.
Unit 1.3: Inflation
Besides output, a second important economic variable is the price level, a measure of average prices. Inflation is an increase in the price level and deflation is a decline in the price level. How to measure price levels and inflation is the subject of this section.
Laspeyres and Paasche Price Indexes
The starting point for a price index is to construct a market basket with goods and services typical of what a household buys. For simplicity, we will consider households that buy apples and oranges. The example below shows the market basket of a typical household – number of apples and oranges purchased – for three years, along with the price of an apple and an orange in each year.
2011 Price Quantity
Apples $1 100
Oranges $2 50
2012 Price Quantity
Apples $1.10 120
Oranges $3 30
2013 Price Quantity
Apples $1.20 150
Oranges $5 10
The most commonly used price index in the United States is the Consumer Price Index (CPI), with a market basket containing goods and services typical of what a household purchases.2 The CPI is a Laspeyres index. A Laspeyres price index fixes the market basket in the base year and then measures the cost of this fixed basket in the base year and subsequent years. To calculate it:
Laspeyres Index =�Cost of base year basket in current yearCost of base year basket in base year �× 100
2 There is also the producer price index (PPI) which is calculated the same way. In this case, the basket is designed
Note that the CPI in the base year is always equal to 100. The current year and the base year are the same thing, so the ratio in the formula is equal to 1. This is a general feature of index numbers.
We can calculate the CPI / Laspeyres price index for each year, using the formula above. The
inflation rate is the percentage change in the price index from one year to the next.
Year Laspeyres Price Index (CPI) Inflation Rate
2011 �100 apples × $1 + 50 oranges × $2
100 apples × $1 + 50 oranges × $2�× 100 = 100
2012 �100 apples × $1.10 + 50 oranges × $3100 apples × $1 + 50 oranges × $2 �× 100 = 130 130−100
100 = 0.3 = 30%
2013 �100 apples × $1.20 + 50 oranges × $5100 apples × $1 + 50 oranges × $2 �× 100 = 185 185−130
130 = 0.42 = 42%
The essential feature of a Laspeyres index is that the quantities are fixed at the base year level, but the prices are updated each year. Basically, the approach is to fix the market basket in the base year and then continue to buy this basket and compare the cost in every subsequent year.
From this example, you can see a key criticism of Laspeyres indexes: Laspeyres price indexes overstate the rate of inflation experienced by consumers because they do not allow readjustment of the market basket. Oranges are going up in price much faster than apples are going up in price. Yet, the Laspeyres index continues to use 100 apples and 50 oranges for the calculation. In reality, the consumer adjusts for the price changes by buying fewer oranges and substituting apples, but the Laspeyres index never takes the readjustment of the basket into account. This is the well-known
substitution bias. The substitution bias implies that fixed-basket measures of inflation will overstate the true rate of inflation.
A different approach is a Paasche index. A Paasche index also compares the cost of a market basket in the current year and the base year. The difference is that it uses the current year’s market basket for the comparison, rather than fixing the market basket permanently in the base year. Precisely, the Paasche index is:
Paasche Index = �Cost of current year basket in current yearCost of current year basket in base year �× 100
Year Paasche Price Index Inflation Rate
2011 �100 apples × $1 + 50 oranges × $2
100 apples × $1 + 50 oranges × $2�× 100 = 100
2012 �120 apples × $1.10 + 30 oranges × $3
120 apples × $1 + 30 oranges × $2 �× 100 = 123 123100−100= 0.23 = 23%
2013 �150 apples × $1.20 + 10 oranges × $5150 apples × $1 + 10 oranges × $2 �× 100 = 135 135−123
123 = 0.098 = 9.8%
Notice that Paasche inflation is significantly lower than Laspeyres inflation. This is true in general. When some things go up in price more than other things, consumers will readjust their spending towards the relatively cheaper items. Laspeyres fixes the market basket and continues to buy the same amount of these relatively expensive products. But Paasche uses the new, readjusted market basket, so it reflects less inflation.
While the Laspeyres index overstates the true impact of inflation, the Paasche index is generally understood to understate the true impact of inflation. If the consumer has to adjust and buy more apples and fewer oranges because of the price changes, this forced readjustment must negatively impact his welfare – otherwise he would have purchased fewer oranges to begin with. The Paasche index takes this new basket as a given, and does not in any way reflect the welfare loss associated with switching.
Since the Laspeyres index overstates inflation and the Paasche index understates inflation, an obvious strategy is to average them together. The Fisher Index is the geometric mean of the Laspeyres and the Paasche indexes.
Fisher Index =�𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿×𝐺𝐺𝐿𝐿𝐿𝐿𝐿𝐿𝑃𝑃ℎ𝐿𝐿
We calculate the Fisher price index and corresponding inflation rates using this formula.
Year Fisher Price Index Inflation Rate
2011 √100 × 100 = 100
2012 √130 × 123 = 126.5 126.5−100
100 = 0.265 = 26.5%
2012 √185 × 135 = 158.0 158−126.5
To extend even further, you could use this average to develop a chained CPI (with each year “chained” off of the previous year using measured growth rates) that will generally show a lower rate of inflation than the conventional Laspeyres-based CPI. This is a hot political issue because increases in social security and other public benefits are tied to the CPI. If these increases were tied to a chained CPI, people receiving these benefits would get lower cost-of-living increases.
Real and Nominal Values
An important use of price indexes is to create real-valued series from nominal values. For example, a graph showing nominal wages over time is useless because of inflation. Without some information about price changes, there’s no way to compare $10 an hour in 1960 to $30 an hour in 2014. Nothing expressed in nominal dollars – wages, government spending, national debt, or anything else – is comparable across time.
Precisely, nominal values are not adjusted for price changes and are not comparable over time. By contrast, real values are adjusted for price changes and are comparable over time. The conversion between real and nominal values is the following:
real = �nominalCPI �× 100
As an example, Donald Trump makes $400,000 a year, whereas Abraham Lincoln made only $25,000 a year. Is President Trump overpaid?
Using 1983 as the base year (i.e. the CPI is normalized to 100 in 1983), the CPI in 2017 when Trump was inaugurated was 242.84. The CPI when Lincoln was inaugurated in 1860 was 8.06. We can use these to calculate their real wages.
• Trump: �$400,000
242.84 �× 100 = $164,718
• Lincoln: �$25,000
8.06 �× 100 = $310,174
This adjustment converts their nominal salaries from the respective years into base year dollars. In other words, Trump earning $400,000 today is the same as if he had earned $164,718 in the base year. He has the same purchasing power today with his $400,000 that he would have had with $164,718 in 1983 (the base year).
To illustrate how easy it is for people to be misled by this kind of reasoning, the graphs below show the change in nominal wages and the change in real wages since 1965. Two very different pictures.
Besides the CPI and other price indexes, a second approach to measuring inflation uses deflators. The idea is that growth in nominal GDP reflects both price effects and the effect of growth in output. Real GDP reflects only output growth. Thus, the ratio of nominal GDP to real GDP “cancels out” the quantities and gives an indication of price changes. The formula is:
GDP Deflator =�nominal GDP
real GDP �× 100
The GDP deflator basically calculates inflation by taking into account the prices of all items included in GDP, whereas the CPI and the PPI are specifically designed to capture price changes of goods and services that consumers and producers purchase, respectively.
Real Interest Rates
Nominal interest rates can be misleading. If you invest in a bond that pays a 5% nominal interest rate, but inflation is 3% over the year that you hold the bond, then your real return is only 2%. The relationship between the nominal interest rate 𝑖𝑖, the inflation rate 𝜋𝜋 and the real interest rate 𝐿𝐿 is:
𝐿𝐿= 𝑖𝑖 − 𝜋𝜋
Weaknesses of Inflation Measures
Like with GDP, the reported inflation rate is not a perfect measure of the rate of inflation that consumers in the economy experience. Here are a few weaknesses.
• Substitution bias – As discussed earlier, Laspeyres-based measures of inflation like the CPI overstate inflation because they use a fixed market basket and do not incorporate readjustment based on differential price changes.
• New technologies – Obviously a fixed-market basket measure cannot incorporate new technologies that developed after the base year in which the market basket is set.
• Quality changes – Like GDP, the CPI does not include a mechanism to adjust price changes for changes in the quality of the item.
• Growth in discount shopping – Obviously the prices of goods and services can depend on where you buy them. Generally, more and more consumers are benefitting from low prices at discount shopping establishments like Walmart and Costco.
Why does inflation matter?
Inflation imposes two direct costs on society.
• Menu costs: Inflation forces firms to reprint signs, menus, price tags, etc…
• Search costs: When prices are stable, consumers know how much to expect to pay for things. When prices change a lot, consumers have to spend time and energy searching for prices.
But these are not the largest costs of inflation on society. The indirect costs of inflation are much larger and more serious.
First, inflation benefits borrowers and harms lenders. Suppose you borrow money from someone and repay it next year. If there has been a lot of inflation over the year, then the money you repay has less value. This is good for you but bad for the person who lent you money. This does not in and of itself destroy wealth, but high inflation generates a large redistribution of income in favor of borrowers at the expense of the lenders they are repaying. Inflation is especially costly for banks.
destructive to the economy because long-run growth relies on saving and investment. Inflation is sort of a “hidden tax” on people who save since the real value of their savings falls.
Unit 1.4: Unemployment
Calculating the Unemployment Rate
The labor force (L) consists of people who are employed (N) and people who are not employed (U).
𝐿𝐿= 𝑁𝑁+𝑈𝑈
The unemployment rate (u) is the fraction of people in the labor force who are not employed.
𝑢𝑢 = 𝑈𝑈𝐿𝐿
Seems simple, but the tricky part is defining the labor force. The unemployment rate is not the fraction of people in the population who are unemployed. It is the fraction of people in the labor force who are unemployed. Many people in the population are not part of the labor force and, even if they do not have jobs, are not counted in the unemployment rate.
In the United States, the Bureau of Labor Statistics (BLS) conducts the Current Population Survey every month. They phone tens of thousands of people every month who are members of the
civilian noninstitutional population – people who are over 18, are not institutionalized (in the hospital or in prison) and who are not active members of the armed forces.
The BLS sorts every person it surveys into three categories.
1. Employed – Worked one hour or more in the previous week (includes self-employment, unpaid work in family business or on vacation from regular job).
2. Unemployed – Did not work but looked for a job in the last four weeks.
3. Out of the labor force – Did not work and did not look for a job in the previous four weeks.
The labor force consists of people from the civilian noninstitutional population who are in (1) or (2). The unemployment rate is the percentage of people in the labor force who are unemployed.
calculation. Furthermore, anyone who has not looked for work in the previous four weeks is out of the labor force – stay-at-home moms, full-time students, sick people, discouraged workers, etc… They are not counted as unemployed. They are not part of the labor force, and do not show up anywhere in the calculation of the unemployment rate.
Some Statistics
The labor force participation rate (LFPR) is the percentage of the adult, civilian noninstitutional population that are in the labor force. The US labor force participation rate is currently around 63%. Here is a graph of the LFPR since 1948. Overall, it trended upwards until about 2000, mainly due to entry of women into the workforce. It has been trending down since then, which is mainly attributable to an aging population.
Here is a graph of male and female labor force participation since 1948.
Employment Flows
There are three sources of flows into unemployment.
1. Job destruction – Employer terminates worker and does not refill position. Manufacturing industries have featured a high level of job destruction recently, most of it due to outsourcing. There is typically a large burst of job destruction at the beginning of recessions.
2. Job loss without destruction – Employer terminates worker, but the discharged worker is replaced. There is no net loss in jobs. This kind of turnover is common in the US economy and hits about 5% of workers every month. The construction industry is especially prone to turnover coming from reorganization and replacement.
3. Personal transitions – Employees voluntarily leave. About 13% of unemployed people are unemployed because they quit their jobs.
As for flows out of unemployment, about 2/3 of flows out of unemployment result because workers find jobs and about 1/3 because workers leave the labor force. Workers who leave unemployment because they find jobs either enter new jobs or they replace existing workers. New jobs arrive at a rate of about 2% every month, approximately the same as the rate of job destruction, but job creation is more stable (even during recessions) than job destruction. This is why there is typically a “backlog” of unemployed people that takes awhile to clear, even after recessions end.
Interpreting the Unemployment Rate
The unemployment rate will never be zero. Capitalist economies feature a high degree of job turnover and, at its core, the unemployment rate depends on how quickly jobs are lost relative to how quickly people can find new jobs. Thus, the economy features a natural rate of unemployment that will exist even when an economy is operating at full employment. Most economists consider a 4-5% unemployment rate to represent normal flows in and out of jobs. Importantly, the way economists use the phrase, “full employment” does not mean everyone has a job.
The unemployment rate also depends on cyclical swings in the business cycle, and typically exceeds the natural rate of unemployment during recessions.
Weaknesses of the Unemployment Rate
Like our other economic statistics, the unemployment rate is not a perfect indicator of the impact of unemployment on the economy. Here are some big limitations.
• The unemployment rate does not capture the problem of involuntary part time work. Anyone in the civilian noninstitutional population who works even one hour is counted as employed, even if he wanted to work full time.
• The unemployment rate does not capture the problem of underemployment. Anyone in the civilian noninstitutional population who works is counted as employed, even if the job is at an inappropriately low skill level.
• The unemployment rate does not capture the discouraged worker effect. Many people without jobs and who want to work are not counted as unemployed because they get discouraged and give up looking. Anyone who has not looked for a job in the last four weeks is out of the labor force, even if the person wants to work.
The discouraged worker problem is particularly serious, and accounts for the perverse observation that the unemployment rate often falls during the worst part of a recession. It doesn’t fall because unemployed people are finding jobs; it falls because many of them give up and leave the labor force altogether.
Why do we care about unemployment?
the economy’s GDP will be below its potential, which creates an output gap and means that society is missing out on some economic growth in output as a result of unemployment.
While economists do tend to agree that too much unemployment is destructive because of the lost output that it represents, don’t take this to the extreme. Some unemployment can be good for the economy, for example if a worker is seeking a job where he will be more productive. The high turnover that characterizes the US labor market may be good for the economy – the fluid rematch between workers and jobs contributes to keeping people productively employed and keeping jobs filled with the most productive employees for the job. Another basic economic point is that we really don’t care all that much about employment per se, but about productivity. We can pay people to dig holes and then fill them up again and, while that’s a job, it’s not a productive activity. People need to do a job, not just to have a job.
Two Relationships
Phillips Curve
Traditional thinking is that, when the economy is overheated – high GDP growth and low unemployment – prices will tend to rise more rapidly. This leads to the Phillips Curve, which can alternately be expressed either as:
• An inverse relationship between inflation and unemployment
• A direct relationship between inflation and GDP growth
The relationship is supposed to be inverse (higher unemployment associated with lower inflation), but it obviously features a lot of noise. Let’s try to be more precise.
Regression analysis is a useful tool for describing the relationship between two variables and for assessing the strength of that relationship. The regression line is plotted for the data above and running the regression of the inflation rate (dependent variable) on the unemployment rate (independent variable) in Excel produces the following results.3
Reading the coefficient estimates for the intercept and for the slope on unemployment, the estimated regression line is:
𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐿𝐿𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼� = 2.42 + 0.20⋅ 𝑈𝑈𝐼𝐼𝐿𝐿𝑈𝑈𝐿𝐿𝐼𝐼𝐼𝐼𝐿𝐿𝑈𝑈𝐿𝐿𝐼𝐼𝐼𝐼
In words, each unit increase in the unemployment rate is associated with a 0.2-unit increase in the rate of inflation. This is exactly the opposite of what the Phillips curve postulates!
3 In Excel, under the Data tab, click Data Analysis and then select Regression. Enter the data range for the dependent
The relationship is very noisy. The p-value on the unemployment coefficient is 0.37, which means that the coefficient is not significant at conventional levels. Remember that a coefficient is significantly different from zero when its p-value is lower than the desired significance level. For example, for testing the significance of a regression coefficient at a 5% level, the p-value would need to be lower than 0.05 to indicate statistical significance. Also, The 𝑅𝑅2 of the regression is only 0.01, meaning that the independent variable explains only 1% of variation in the dependent variable.
All in all, the estimated relationship between inflation rates and unemployment rates using US data is very noisy and the regression coefficient is not significant. And the estimated coefficient actually has a positive sign, whereas the Phillips curve suggests an inverse relationship.
Okun’s Law
We noted in the first section that employment and GDP outcomes tend to move together. Faster growth in GDP is associated with more jobs and with a decline in the unemployment rate. Specifically, each 1% increase in GDP growth tends to be associated with an approximately 0.4% reduction in unemployment. This empirical relationship is known as Okun’s Law. It is more of an observation or “rule of thumb” than a law, but the descriptor has stuck.4 The key lessons are
that unemployment rises during recessions and falls during expansions, and that economic growth can reduce unemployment.
The diagram below plots the change in unemployment rate and the growth rate in real GDP in the US each year from 1948 to the present. At first glance, the relationship seems to be strong and fairly close to what theory would predict.
4 Why isn’t the relationship one-for one? The firm-level explanation is that a firm that reduces its output is unlikely to
Doing the regression analysis in Excel gives an estimated coefficient of −0.38, which is negative, as expected – higher output growth is associated with reductions in the unemployment rate. Furthermore, the magnitude is quite close to Okun’s predicted value of −0.4.
And the relationship is strong. The p-value on the coefficient is almost zero, which shows statistical significance at any conventional level. Furthermore, the 𝑅𝑅2 of the regression is 0.67, which indicates a relatively tight relationship.
One interesting thing to note on the graph – zero change in unemployment rate occurs at about 3% GDP growth. In other words, we need 3% growth in GDP to keep unemployment steady. Higher growth in GDP reduces unemployment.
