Paul Johnson, Steven Durlauf and Jonathan Temple 1161Sometimes partial identification is possible, in the sense that bounds on the
extent of measurement error can be used to derive consistent estimates of bounds
on the slope parameters. Although it can be difficult for researchers to agree on
sensible bounds on the measurement error variances, there are easier ways of for-
mulating the necessary restrictions, as discussed by Klepper and Leamer (1984).
Their reverse regression approach was implemented by Persson and Tabellini (1994)
and Temple (1998), but has rarely been used by other researchers. Another strat-
egy is to investigate sensitivity to varying degrees of measurement error, based on
method of moments corrections. Again, this is easy to implement in linear models,
and should be applied more routinely than it is at present. Temple (1998) provides
a discussion of both approaches in the context of the Mankiwet al.(1992) model.
24.7.3 Missing data
Some countries rarely appear in growth datasets, partly by design: it is com-
mon to leave out countries with small populations, oil producers, and transition
economies. These are countries that seem especially unlikely to lie on a regression
surface common to the majority of the OECD member countries or the developing
world. Other countries are left out for different reasons. When a nation experiences
political chaos, or lacks economic resources, the collection of national accounts
statistics will be a low priority. In other cases, countries appear in some studies but
not in others, depending on the availability of particular variables of interest.
Missing data can be a serious problem. If a researcher started from a represen-
tative dataset and then deleted countries at random, this would typically increase
the standard errors but not lead to biased estimates. More serious difficulties arise if
countries are missing in a non-random or systematic way, because then parameter
estimates are likely to be biased. This problem is given relatively little attention in
mainstream econometrics textbooks, despite a large body of research in the statis-
tics literature. A variety of solutions are possible, with the simplest being one form
or another of imputation, with an appropriate adjustment to the standard errors.
Hall and Jones (1999) and Hoover and Perez (2004) are among the few empirical
growth studies to implement this. It may be especially useful when countries are
missing from a dataset because a few variables are not observed for their partic-
ular cases. It is then easy to justify using other available information to predict
the missing data, and thereby exploit the additional information contained in the
variables that are observed. Alternative approaches to missing data are also avail-
able, based on likelihood or Bayesian methods, which can be extended to handle
missing observations.
24.7.4 Heteroskedasticity
It is common in cross-section regressions for the underlying disturbances to have
a non-constant variance. As is well known, the coefficient estimates remain unbi-
ased, but OLS is inefficient and the estimates of the standard errors are biased. Most
empirical growth research simply uses the heteroskedasticity-consistent standard
errors developed by Eicker (1967) and White (1980). These estimates of the standard