they cannot be directly compared with the annualized stream). (The curves actually represent the averages of impacts for immigrants of different ages at arrival and education level, rather than representing any single age at arrival and education level; in all cases, length of time in the United States is taken into account, along with all descendants.) The state and local impact is substantially negative initially, at about -$2,270, and the federal impact is initially close to zero (-$120), for a total impact of about -$2,400. This is very different from the annualized total impact of +$2,430. Indeed, the total impact does not turn positive until 22 years after the arrival of this composite immigrant, and the state/ local impact does eventually turns positive, but only after about 40 years. (Note that the impact turns positive just after 2016 when, according to baseline assumptions, taxes are raised and benefits cut in order to control the debt/GDP ratio.) Evidently, even if immigrants have positive NPVs, they nonetheless impose substantial costs in their initial years in the United States.
The immigrants themselves more quickly have a positive fiscal impact at the state and local level; for example, by the 25th year, immigrants have a positive impact of +$910. However, they have also borne children who themselves have had children, and these descendants impose costs of more than $1,660 at the state and local level in the 25th year, so the total impact is still negative, at more than $700. At the federal level, the immigrant has a strong positive effect that is only very slightly offset by the costs of children, at $1,570. After 50 years, both the immigrant and the second generation are making sufficiently positive impacts to offset the substantial costs of the third generation, yielding a positive impact at the state and local level. At the federal level, the composite immigrant is now elderly and has become costly. These costs, however, are more than offset by the second generation, resulting in a strong positive total impact of $1,520.
The NPV calculations are based on projections that reach 300 years into the future, and it would be absurd to claim that the projections into the 23rd century are very reliable. How much do our NPV calculations depend on such long-run outcomes? Since we are discounting at 3 percent, the future is heavily discounted. At 25 years, the discount factor is 0.5; at 50 years, 0.22; at 75 years, 0.1; and at 100 years, 0.05. Calculation of truncated NPVs for varying time horizons shows how much the distant future affects the results. Table 7.8 gives the fraction of the full NPV (based on 300 years) that is achieved with different time horizons.
The approach to the ultimate value is not rapid. Although the total flow turns positive after 23 years, it takes 40 years for the total NPV to turn positive. By 75 years, the planning horizon used for Social Security, more than half the long-run NPV has been reached. It may seem that 50 or 75 years are unacceptably long horizons for measuring the fiscal impacts of immigrants, but reasonable calculations over any shorter period are scarcely possible, since it is very important to include the later-life cycle stage of immigrants in the calculations. But doing that brings in the second generation as schoolchildren, as taxpayers, and as parents