Introduction to Modern Economic Growth (2) Even if Xi,t ’s were econometrically exogenous, a negative coefficient estimate for b1 could be caused by other econometric problems, such as measurement error or other transitory shocks to yi,t For example, because national accounts data are always measured with error, suppose that our available data on log yi,t contains measurement error In particular, suppose that we only observe estimates of output per capita y˜i,t = yi,t exp (ui,t ), where yi,t is the true output per capita and ui,t is a random and serially uncorrelated error term When we use the variable log y˜i,t measured with error in our regressions, the error term ui,t−1 will appear both on the left-hand side and the right hand side of (3.11) In particular, note that log y˜i,t − log y˜i,t−1 = log yi,t − log yi,t−1 + ui,t − ui,t−1 Since the measured growth is g˜i,t,t−1 ≈ log y˜i,t − log y˜i,t−1 = log yi,t − log yi,t−1 + ui,t − ui,t−1 , when we look at the growth regression g˜i,t,t−1 = X0i,t β + b1 log y˜i,t−1 + εi,t , the measurement error ui,t−1 will be part of both the error term εi,t and log y˜i,t−1 = log yi,t−1 + ui,t−1 , leading to a negative bias in the estimation of b1 Therefore, we can end up with a negative estimate of b1 , even when there is no conditional convergence (3) The interpretation of regression equations like (3.11) is not always straightforward either Many of the regressions used in the literature include the investment rate as part of the vector Xi,t (and all of them include the schooling rate) However, in the Solow model, differences in investment rates are the channel via which convergence will take place–in the sense that economies below their steady state will grow faster by having higher investment rates Therefore, strictly speaking, conditional on the investment rate, there should be no further effect of the gap between the current level of output and the steady-state level of output The same concern applies to interpreting the effect of the variables in the vector Xi,t (such as institutions or openness), which are typically included as potential determinants of economic growth However, many of these variables would affect growth 114