I've read articles recently which conclude that--adjusted for inflation--paychecks have roughly the same purchasing power that they had 40 years ago. As a layman, this suggests to me that although the average American standard of living hasn't improved in several decades, it hasn't worsened either. I am trying to reconcile this statistic with the "shrinking middle class" and the need for people to work multiple jobs to get by, trends which have emerged gradually over the same 40-year period. I suspect that the answer lies in the rising costs of housing, education, and healthcare, but aren't these variables included in the inflation adjustment calculation?
The challenge in describing a large economy with more than 300 million people in it is in finding helpful ways to simplify the data. Economists often measure economic performance by using one very simple statistic: income per capita, which is simply the total value of goods and services produced in an economy in a year divided by the population. This number shows how much each of us could consume if the total economic production was divided equally. By this measure the typical worker is doing fine. Real (adjusted for inflation) GDP per capita increased from around $24 thousand in 1970 to almost $57 thousand in 2018.
The problem arises because incomes and purchasing power are not equally divided. And, in fact, the inequality of this division has been increasing over time. In 1970 the top 1 percent of income earners took 10% of all incomes in the country. By 2015 they received more than 20% of total incomes. Looking at families at different points in the income distribution, the data show that families at the bottom of the income distribution (bottom 20%) experienced no growth in income since the 1970s, while the median family (the one for which 50% of households have lower incomes and 50% have higher incomes) experienced a growth of only 20%. In contrast to this relatively slow growth, incomes for families in the top 5% approximately doubled.
So, the explanation is not that costs have been rising. You are right that this effect is captured by measures of inflation. Rather it is that more and more of the riches produced by the economy wind up in the hands of the highest income earners, while the rest of the population has seen little or no growth in purchasing power.
If you want to read more, there is a good discussion of the various sources of income data produced by the Center on Budget and Policy Priorities here: https://www.cbpp.org/research/poverty-and-inequality/a-guide-to-statistics-on-historical-trends-in-income-inequality . Another useful article found Published by the Economic Policy Institute can be found here: https://www.epi.org/publication/top-1-percents-share-income-wealth-rising/ .