1094 The Econometrics of Convergence
(GMM) estimator to analyze a panel variant of the standard cross-country growth
regression. The variation in the outcomes of these responses to endogeneity sug-
gests that the effects of endogeneity onβ-convergence tests remain an open
question.
A distinct third source of correlation between errors and regressors is measure-
ment error. This is a particular concern in growth contexts since, despite the best
efforts of those compiling the data, it is inevitable that output per capita will be
mismeasured, particularly in developing economies. Measurement errors in ini-
tial levels of per capita income will tend to bias estimates ofβin favor of the
β-convergence hypothesis, through the effects of the standard attenuation bias.
One way to see this is to consider convergence in terms of the association (or cor-
relation) between final output and initial conditions. When convergence is rapid,
final output will be only weakly associated with initial conditions; when conver-
gence is slow, the two will be strongly associated. The standard attenuation bias
implies that when initial output is measured with temporary error, this weakens
the partial correlation between initial and final output, and so biases the regression
finding towards a rate of convergence that is too fast. Exactly the same logic carries
over when the dependent variable is the growth rate, since a model relating growth
to initial log income can alternatively be reparameterized as a model that relates
the log of final output to the log of initial output.^14
However, as Temple (1998) notes, in more general settings the actual direction of
the bias will depend on the stochastic properties of the measurement error itself, as
well as the possibility of measurement errors in several of theZicontrol variables.
He investigates the effects of allowing for measurement error in the models esti-
mated by Mankiwet al.(1992), using the measurement error diagnostics developed
by Klepper and Leamer (1984) and Klepper (1988), together with classical method
of moments adjustments. The possibility of small errors in the measurement of
initial income implies a lower bound on the estimated rate of convergence that,
while positive, is too close to zero to give conditional convergence the status of a
stylized fact.
Mindful of the possible effects of measurement error, Romer (1990) estimates a
growth equation by both OLS and IV using the number of radios per 1,000 inhab-
itants and (the log of) per capita newsprint consumption as instruments for initial
income and the literacy rate. In the OLS case, he finds a negative and significant
coefficient on initial income, but in the IV case the coefficient is insignificant,
perhaps suggesting that the significance in the OLS case is attributable to measure-
ment error. Using lagged income as instruments for initial income, Barro (1991)
and Barro and Sala-i-Martin (2004) find little change in the estimated convergence
rates compared to OLS, and conclude that measurement error is not an important
factor behind their findings supportingβ-convergence.
Another important criticism ofβ-convergence regressions concerns the power
of the test against non-convergent alternatives, such as models with endogenous
growth or poverty traps. As shown above,β<0 is an implication of the neoclas-
sical growth model, butβ<0 is also potentially consistent with economically
interesting alternatives. To see this, assume that there is no technical change or