Finally, there is probably measurement error in the log entry wage. Any measurement error in this wage will impart a negative bias on its coefficient (towards minus one). The spurious negative correlation arises because the log entry wage appears on both sides of the equation, but with different signs. One can assess the sensitivity of the results to measurement error by using instrumental variables to eliminate the spurious correlation.
The construction of the Census data suggests two alternative instruments for the log entry wage. The regressions reported in the first panel of Table 4 use the rate of wage growth observed for the immigrant cohorts that arrived in 1960-64, 1965-69, 1970-74, or 1975-79. To eliminate the measurement error, we can use the log entry wage of the preceding immigrant cohort as an instrument for the entry wage of a particular cohort. Consider, for example, the Mexican immigrants who were 25-34 years old in 1980 and who entered the United States between 1975 and 1979. The proposed instrument would be the wage of Mexican immigrants who were 25-34 in 1980 but who entered the country between 1970 and 1974. The construction of this instrument, of course, implies that the immigrants who arrived between 1960 and 1964 do not contribute any observations to the regression (since no preceding cohort is observed for this group).
The top panel of Table 5 reports both the OLS and IV convergence coefficients in this subsample of the data. The OLS coefficients resemble those reported earlier: there is a positive correlation between the log entry wage and the rate of wage growth in the raw data, and this correlation turns negative once the regression controls for educational attainment. The IV procedure leads to a much stronger positive correlation between the log entry wage and the subsequent rate of wage growth when the regression does not control for initial educational attainment, and greatly weakens the negative correlation (in fact, it is essentially zero) when the education control is added. The IV estimation, therefore, raises questions about the robustness of the finding of conditional convergence.