Unit 1 The supply side of the macroeconomy: Unemployment and real wages

1.4 Measuring the macroeconomy: Nominal wages, prices, and real wages

The nominal wage

nominal wage
The actual amount received in payment for work, per unit of time, expressed in a particular currency. Also known as: money wage. See also: real wage.

The nominal wage can be defined as the actual amount of money per unit of time such as per hour or per year, in a given currency, received in payment for work.

As well as having a job, people care about the wage and more precisely what it can purchase. The person in charge of a household’s budget will often have a sense of the family’s nominal wage income and prices, and therefore also a sense of what can be purchased. Reflecting these concerns, three of the statistics often reported for the performance of an economy are the growth of nominal wages, prices, and real wages. These statistics refer to averages across the economy. The average for wages is often median weekly or monthly earnings, and for prices, the price of a representative basket of goods and services.

A useful device for comparing trends is to use index numbers. In this case, we are interested in comparing the evolution of nominal wages and prices over time to understand what is implied for real wages. By setting the value of each series equal to 100 in a base year, the relative growth over subsequent years can be easily compared.

Nominal wages are expressed in the currency of the country such as pesos, dollars, or rupees. They vary widely by occupation and industry. For this reason, wage statistics are aggregated to provide a macroeconomic indicator of average nominal wages. For example, the US Bureau of Labor Statistics reports the median weekly earnings for workers in the US aged 16 and older.

To construct the nominal wage index, we start by choosing a year as the baseline (in our case, 2010), and assigning it a value of 100. We then allow the index to measure changes to the nominal wage by converting the figures expressed in a given currency to index values relative to the baseline. For example, in 2010 the weekly nominal wage in the United States was $746—this is our baseline. In 2011, the nominal wage increased from $746 to $756 per week, a 1.3% rise. Therefore, if the nominal wage index is 100 in 2010, it will increase by 1.3% and reach \(\text{Nominal Wage Index} = 100 \times 1.013 = 101.3\) in 2011. The following year, wages increased to $768, a 1.6% increase from 2011. As such, the nominal wage index in 2012 will be \(101.3 \times 1.016 = 102.9\).

Figure 1.6 shows the nominal wage index for the US from 2010 to 2022.

This is a line chart plotting the US’s nominal wage index. The horizontal axis shows the year, ranging from 2010-2022. The vertical axis shows the nominal wage index, where 2010 = 100 is the base year. It ranges from 90-140. The US’s nominal wage index is increasing throughout this period, and in 2022 is around 142.
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https://www.core-econ.org/macroeconomics/01-supply-side-macroeconomy-04-prices-wages.html#figure-1-6

Figure 1.6 Nominal wage index for the US (2010–2022), using 2010 as the base year.

The consumer price index

consumer price index (CPI)
A measure of the general level of prices that consumers have to pay for goods and services, including consumption taxes.

The consumer price index (CPI) is a metric that tracks the total price of a ‘shopping basket’ of goods and services commonly purchased by households, such as food, beverages, utilities, rent, healthcare, education, and financial services. An increase in the CPI represents an increase in the overall prices in the economy.

The consumer price index can be constructed in a similar way to the nominal wage index, by taking a baseline year and tracking the changes in the price level. Figure 1.7 shows the consumer price index for the US from 2010 to 2022.

This is a line chart that plots the US’s Consumer Price Index (CPI). The horizontal axis shows the year, ranging from 2010-2022. The vertical axis displays the CPI, where 2010 = 100 is the base year. It ranges from 90-140. The CPI increases steadily from 2010-2020, and from 2020 it sees a sharper increase. In 2022, the CPI is around 134.
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https://www.core-econ.org/macroeconomics/01-supply-side-macroeconomy-04-prices-wages.html#figure-1-7

Figure 1.7 Consumer price index for the US, using 2010 as the base year.

The real wage

The real wage differs from the nominal wage by taking into account changes in prices across time. It measures the actual purchasing power that workers have from their earnings.

real wage
The wage expressed in terms of the amount of goods and services the worker can buy with it. It is calculated by dividing the nominal wage by the current price level in the same currency. See also: nominal wage.

We can now define the real wage more precisely. If your nominal wage (measured in pesos, euros, rupees, or the relevant local currency) is W per week, and the price of one unit of output measured in the same currency is P, then you can use your wage to buy W/P units of output each week. Your nominal wage depends on the currency used in the economy, whereas your real wage does not.

For a given year, a real wage index can be constructed by dividing the nominal wage index by the consumer price index and multiplying by 100:

\[\displaystyle\mbox{real wage index} = \displaystyle\left(\frac{\mbox{nominal wage index}}{\mbox{consumer price index}}\right)\times 100\]

Figure 1.8 shows the real wage index for the US between 2010 and 2022.

This is a line chart that plots the US’s real wage index. The horizontal axis shows the year, ranging from 2010-2022. The vertical axis shows the real wage index, where 2010 = 100 is the base year. It ranges from 90-140. The real wage index decreases slightly but remains relatively flat from 2010 to 2014, and from 2014-2019 it increases steadily. From 2019-2020, the real wage index increases sharply where it peaks at around 111, and then declines steadily 2020 onwards. In 2022, the real wage index is around 106.
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https://www.core-econ.org/macroeconomics/01-supply-side-macroeconomy-04-prices-wages.html#figure-1-8

Figure 1.8 Real wage index for the US, using 2010 as the base year.

US Bureau of Labour Statistics. 2023. Note: constructed from the nominal wage and price indices.

Figure 1.9 shows the three indices on the same plot.

This is a line chart that plots three indices for the US: the nominal wage index, the Consumer Price Index (CPI), and the real wage index. The horizontal axis shows the year, ranging from 2010-2022. The vertical axis shows the index, where 2010 = 100 is the base year. It ranges from 90-140. Nominal wages begin below CPI and they both rise steadily from 2010-2014, during which time real wages decrease slightly. In 2015 nominal wages overtake CPI, and real wages start to increase. In 2020 CPI begins rising faster than nominal wages, and real wages begin to decline.
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https://www.core-econ.org/macroeconomics/01-supply-side-macroeconomy-04-prices-wages.html#figure-1-9

Figure 1.9 Indices for nominal wages, consumer prices, and real wages in the US (2010–2022), with 2010 as the base year.

US Bureau of Labour Statistics. 2023. Note: the real wage index is constructed from the nominal wage and price indices.

Note that when the general increase in prices over time is larger than the nominal wage rise (as in the period between 2010 and 2014), workers will have a lower real wage than the baseline year. Conversely, as the nominal wage grows faster than prices, workers’ real wages will increase.

When the price level and the nominal wage have increased by the same amount after a period of time (as in 2015 in Figure 1.9), the real wage is at the same level as in the base year: the median worker earned approximately 8% more in 2015 than they did in 2010, but prices are also about 8% higher, so the purchasing power of their nominal wages is effectively the same.

The indices for nominal and real wages and consumer prices for the UK and Italy are shown in Figure 1.10.

This figure shows two line charts for the UK and Italy for their nominal wage index, Consumer Price Index (CPI), and Real Wage Index. The horizontal axis shows the year, ranging from 2010-2022. The vertical axis shows the index, where 2010 = 100 is the base year. For both countries, the nominal wage index and CPI see an increasing trend from 2010, while in Italy, following the pandemic in 2020, the CPI sees a sharper increase while the nominal wage index plateaus. Italy’s real wage index remains around the its 2010 levels at 100 until 2020, when it sees a sharp decline to around 95. The UK’s real wage index is on a slight decline from 2010 to 2014, after which it is on an upward trend, and remains around its 2010 level of 100 in 2022.
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https://www.core-econ.org/macroeconomics/01-supply-side-macroeconomy-04-prices-wages.html#figure-1-10

Figure 1.10 Indices for nominal wages, consumer prices, and real wages in the UK and Italy (2010–2022), with 2010 as the base year.

Median weekly real wages fluctuated over the decade 2010–2019 in all three countries. The US ended the decade with a higher real wage than at the start of the decade, but in Italy and the UK in 2019, real wages were roughly the same level as in 2010. Italy experienced a particularly sharp decline in real wages following the pandemic.

Question 1.2 Choose the correct answer(s)

The table shows quarterly CPI data for Brazil in 2021–2022, taken from the World Bank’s inflation database. Based on this data, read the following statements and choose the correct option(s).

Year and quarter CPI value
2021 Q1 130.5
2021 Q2 133.0
2021 Q3 136.5
2021 Q4 140.9
2022 Q1 144.5
2022 Q2 148.9
2022 Q3 148.3
2022 Q4 149.4
  • With 2021 Q1 as the base period, the 2022 Q1 CPI value would be 112.
  • With 2021 Q1 as the base period, the 2022 Q4 CPI value would be 114.
  • With 2022 Q1 as the base period, the 2021 Q1 CPI value would be 90.
  • The purchasing power of people in Brazil has generally decreased over the period shown.
  • With 2021 Q1 as the base period, the 2022 Q1 CPI value would be (144.5/130.5) \(\times\) 100 = 111.
  • With 2021 Q1 as the base period, the 2022 Q4 CPI value would be (149.4/130.5) \(\times\) 100 = 114.
  • With 2022 Q1 as the base period, the 2021 Q1 CPI value would be (130.5/144.5) \(\times\) 100 = 90.
  • The price level has generally increased, but to determine whether purchasing power has changed, we need information about how nominal wages have changed over the same period. Purchasing power would not decrease if nominal wages were rising at the same rate as inflation.

Exercise 1.2 Rebasing indices

Download US data for the consumer price index (CPI) and real wages (measured as weekly earnings) from the St Louis Federal Reserve website.

For this exercise, only use the data from 2010 (or January 2010) to the latest available year (or month).

  1. The monthly CPI data currently has the months in 1982–1984 as the base. Rebase the CPI data so that January 2015 is the base (the CPI for January 2015 should equal 100).
  2. Create an index for real wages with 2015 as the base year (the real wage for 2015 should equal 100).
  3. Use statistical software of your choice (such as Excel or Google Sheets) to make a line chart similar to Figure 1.9 for your rebased data from Questions 1 and 2. Discuss the similarities and differences between the charts.
  4. Discuss some criteria that you think would be important for choosing the base year for a data series.