Accounting Exercise Books

[Melanie Wendelberger]

USGDP has grown by 8.2% since just before the pandemic, almost twice as fast as the next-best performer in the G7. The rise in the immigrant population since the end of 2019 accounts for at least a fifth (1.6 percentage points) of that US growth, accounting for direct labor supply, unemployment rate, and productivity effects. Absent immigration, the US labor supply would have shrunk by 1.2 million since 2019. Instead, it expanded by 2 million.

One driver of US economic growth over the last four years has been immigration. Immigration affects economic growth in multiple ways. One is just the direct mechanical increase in labor supply: more workers can produce more goods and services. Another is indirect spillover effects that can lead to greater innovation and more income and consumption among native-born workers over time.

This analysis partially quantifies how the rise in the foreign-born population since the end of 2019 has moved the US economy using a growth accounting identity framework. It cannot account for all channels, especially indirect ones, but it does roughly quantify how both lawful and unlawful immigration has directly affected labor supply, the unemployment rate, and the composition of productivity in the US.

where Y is real aggregate output (GDP), E is aggregate employment, and L is the labor force. Notice that Equation 1 is an identity because all of the non-Y terms cancel out. More importantly for interpretation, each of the ratios in Equation 1 has important independent meaning in labor and macroeconomic analysis. Recast in log differences, Equation 1 can be summarized as follows:

Equation 1 implies that, all else equal, a growing supply of labor helps drive economic growth. The mechanisms here are straightforward: a larger labor supply means more capacity for new businesses or firms to expand. It may also imply stronger aggregate demand.

The second piece of Equation 1 is labor force utilization, or (E/L). This measures the share of the workers who are employed among those who actively want and can take a job. Since the labor force is just equal to the number of employed plus the number of unemployed, (E/L) is equivalent to (1-U/L), which is (1-Unemployment Rate).

The final term in Equation 1 is productivity, which in the context of this analysis refers to output per worker or (Y/E). Immigrants affect both the level of productivity and productivity growth in different ways and at different time horizons. For example, immigrants have a simple, direct accounting effect on the level of productivity that depends on the compositional mix of the foreign-born population. More immigrants in high-wage industries such as H-1B visa holders likely raise average productivity levels, while more immigrants in lower-wage sectors likely lower it. It is important to recognize that in the short-run these are pure compositional effects on aggregate productivity, and do not identify effects of immigration on the productivity of the typical native-born worker. Immigration also has longer-term effects on productivity growth that accrue over time, raising it due to more efficient task specialization (Peri 2009), innovation measured for example by number of patents (Bernstein et al 2022), and higher rates of entrepreneurship (Kerr & Kerr 2019).

From the standpoint of the growth accounting identity, Figure 7 is the key measure. It shows that the ratio of the typical foreign-born hourly wage to the typical native-born wage ended 2023 at 87%, only slightly lower than the 88% where it ended 2019. Under our assumption that worker productivity growth is proportional to wage growth, that suggests that the relative productivity of foreign-born workers has largely kept pace with native-born workers over the last four years. Most of the productivity effect from immigration then has just been a pure compositional effect: a slightly greater employment share to lower-productivity employment.

Net net, the resulting estimate is that this compositional effect lowered cumulative total economy productivity growth by 0.2 percentage point over 2019 Q4 to 2023 Q4, though this estimate is uncertain in both directions.14

Immigration is of course not the sole purview of economics. It touches on a variety of social, moral, and humanitarian issues. But as even this admittedly-incomplete and limited analysis shows, the economics of immigration are consequential. While the short-run effects of immigration can be difficult to identity, economic evidence suggests its long-run effects are broadly and strongly positive, especially across subsequent generations (PWBM 2016). In fact, one compelling rationale for immigration policies viewed as fair, effective, and sustainable by both native- and foreign-born residents alike is to maintain ongoing support for this key ingredient in American prosperity.

The analysis in this report relies on estimates of the civilian adult noninstitutional population from the Current Population Survey (CPS), a joint product of the Census Bureau and the Bureau of Labor Statistics. The analysis makes adjustments to the CPS microdata survey weights to account for annual population controls, but otherwise takes as given the foreign-born population shares implied by the CPS.

In the last two years, estimates of overall employment from the CPS have diverged from estimates from the Current Employment Statistics (CES), a survey of business establishments with a much larger sample than the CPS, even when the employment concepts are on an apples-to-apples basis (see Appendix Figure 1). Nonfarm payroll employment in the CES was 3.8 million, or 2.5%, higher in February 2024 than the CPS after harmonizing the employment definition in the latter. That 2.5% gap is the highest since the modern incarnation of the CPS began in 1994, other than a short-lived spike in the depths of the pandemic.

The cause of this wedge is an economic and statistical mystery. One possibility is that the CPS is more accurately reflecting recent employment dynamics, and that therefore the CES is overstating the strength of the labor market post-2022. In this scenario, the CES would eventually be adjusted down towards CPS estimates. The CES is revised every year to align it with administrative data from the unemployment insurance system about employment and firm counts. These annual benchmark revisions to the CES can be either positive or negative, and can sometimes be substantial. One issue with this hypothesis however is that CES data through March 2023 has already been re-benchmarked; the gap that month remains a still-large 1.7 million, or 1.1%.

Another possibility is that it is in fact the CPS that is off, understating employment gains, in part because it is undercounting recent immigration. This is a difficult hypothesis to test at the moment. The true size of the immigrant population can be difficult to ascertain. Census uses annual population controls to ensure that the CPS accurately represents the demography of the US, but foreign-born status is not a dimension that Census benchmarks in this process. More detailed data come from the decennial Census, but the next one is not until 2030. Note too that some economists have had the opposite interpretation of recent CPS data; Chicago Fed economists for example argue in a recent blog that the CPS has overcounted immigrants (Butcher et al 2024).

Note that an upweight to foreign-born workers in the CPS would change both the household employment counts and the payroll employment shares in this analysis. For example, if there were 7% more foreign-born workers in 2022 and 2023 than implied by the household survey, Figure 4 would show growth of 600,000 payroll jobs for native-born workers since 2019 Q4 (rather than 2.2 million) and 8 million more since 2020 Q4 (instead of 9.6 million.

The labor force statistics quoted in this piece are adjusted for annual Current Population Survey (CPS) population controls and therefore differ from official figures published by Census and the Bureau of Labor Statistics (BLS) from the CPS, which do not make such adjustments. We backcast annual population controls by age-sex categories in a similar vein to Bauer et al (2023): non-decennial Census controls (e.g. 2021 and 2023) are backcast 12 months, while the decennial controls implemented in 2022 are backcast 10 years. See the Appendix for a more speculative discussion about CPS counts of foreign-born residents.

Per capita economic growth is less affected by immigration in the short-run and may even be temporarily lower, depending on the types of immigrants arriving. It is important to recognize however that a negative effect on average per capita growth is almost entirely a compositional effect, not a reflection of actual changes to well-being for the typical native-born worker. This same caution extends to interpretations of average productivity, as discussed later in this piece.

The CPS asks respondents about their citizenship status, but not their legal status. Therefore the non-citizen category will include both foreign-born workers authorized to work in the United States (such as green card holders, H-1B visa holders, and temporary parolees authorized to work) and those without authorization.

This analysis uses household employment as the employment concept for the purposes of the growth decomposition since it is a broader, total economy concept, but this section also analyzes payroll employment since it is a closely-followed metric.

This rise is almost entirely due to a substantial expansion in their participation rates: the employment-to-population ratio for non-citizens was down slightly by 0.1 percentage point, but their labor force participation rate was up by 1.3 percentage points.

That said, healthy skepticism of this assumption is warranted. There are reasons why productivity may not strictly follow wage growth, especially over short periods of time. Changes in capital quality unrelated to labor may affect productivity. Certain factors may also drive a wedge between wages and productivity for immigrant workers specifically, such as discrimination and employer visa lock-in.

3a8082e126