It depends on how you measure it. According to a recent NBER paper by Dartmouth economist Bruce Sacerdote, most estimates use the CPI-U as a price deflator. Sacerdote instead
calculate[s] real wages using either the Fed’s preferred inflation measure of PCE (Personal Consumption Expenditures) or using simple adjustments to CPI using magnitudes suggested by the Boskin commission (Boskin et al 1996) and Costa (2001). This adjustment reverses the finding of wage stagnation. Using the PCE to deflate nominal wages suggests real wage growth of 24 percent from 1975-2015 or about .54% growth in real wages per year. Importantly that growth is significantly less than the 1.18% annual growth in real wages (using PCE inflation) seen in the earlier decade 1964-1975 and is significantly less than GDP per capita growth of 1.8 percent over the 1975-2015 period. But 24 percent growth over the 1975-2015 is substantially better than zero growth and the PCE inflation could itself still contain upward bias. Adjusting for the Hamilton (1998) and Costa (2001) estimates of CPI bias implies real wage growth of 1 percent per year during 1975-2015 and GDP per capita growth of 2.7 percent per year.
In short, “PCE adjusted wages appear to have grown at .5% per year during 1975-2015 while the de-biased CPI adjusted wages grew at 1% per year over the same time period.”
So why do so many Americans feel worse off? Sacerdote hypothesizes,
First, I am only examining consumption within very large sections of the income distribution and there may be specific groups (for example less than high school educated men) for whom consumption is actually falling. Second, it’s possible that the quality of some services such as public education or health care could be falling for some groups. Third, the rise in income inequality coupled with increased information flow about other people’s consumption may be making Americans feel worse off in a relative sense even if their material goods consumption is rising. Fourth, changes in family structure (e.g. the rise of single parent households) , increases in the prison population, or increases in substance addiction could make people worse off even in the face of rising material wealth. A deep future research agenda would be to understand how America has lost its sense of optimism about living standards and whether the problem is one of consumption, relative consumption (relative to other people) or something entirely different.
On top of this, Harvard’s Martin Feldstein points out that innovation and new products are often ignored when measuring economic growth and the state of living standards:
Ignoring the introduction of new products is therefore a serious further source of understating the real growth of output, incomes, and productivity. New products and services are potentially valuable in themselves and are also valued by consumers because they add to the variety of available options. In an economy in which new goods and services are continually created, their omission in the current method of valuing aggregate real output makes the existing measure of real output even more deficient and more of a continually increasing underestimate of true output. Hulten (2015) summarizes decades of research on dealing with new products done by the Conference on Research in Income and Wealth with the conclusion that “the current practice for incorporating new goods are complicated but may miss much of the value of these innovations.” …[T]he official statistics ignore the very substantial direct benefit to consumers when new products and services become available, causing an underestimate of the rate of increase in real output and an overestimate of the corresponding price index…The failure to take new products into account in a way that reflects their value to consumers may be an even greater distortion in the estimate of real growth than the failure to reflect changes in the quality of goods and services. There is no way to know (pgs. 11-12, 14).
Feldstein has made this argument before in more popular writing. A good number of economists agree. While growth in real wages could be better, it seems to be inaccurate to say that they have stagnated.