My favorite study on this question is work by Dan Goldhaber, Malcolm Wolff, and Tim Daly. They investigated how accurate early measures of achievement are in predicting later high school outcomes using data from three states, North Carolina, Massachusetts and Washington State. Here’s their conclusion (emphasis added):
A large literature shows that early academic performance, measured primarily by test scores, is predictive of later academic success, and that there are significant gaps in student achievement by student disadvantaged status. Our findings reaffirm these findings. Indeed, across three states we find consistent and very strong relationships between 3rd grade test scores and high school tests, advanced course-taking, and graduation. For instance, all else equal, a student at the lowest percentile of the 3rd grade math test distribution rather than the highest percentile is expected to be 48-54 (depending on state) percentile points lower in the high school math test distribution, is expected to be 45 to 50 percent less likely to take an advance course in high school, and 11 to 21 percent less likely to graduate. We conclude that early student struggles on state tests are a credible warning signal for schools and systems that make the case for additional academic support in the near term, as opposed to assuming that additional years of instruction are likely to change a student’s trajectory. Educators and families should take 3rd grade test results seriously and respond accordingly; while they may not be determinative, they provide a strong indication of the path a student is on.
State tests are not perfect. For example, my personal hobby horse is that states are too slow to release the results, which in turn makes them less usable by parents and educators.