Paul Johnson, Steven Durlauf and Jonathan Temple 1171- Here we are being imprecise in referring to within-model priors for Sala-i-Martinet al.
(2004), but note that, following Ley and Steel (2008), their analysis is interpretable in
this way. - A detailed discussion of regression tree methods appears in Breimanet al. (1984). The
technical appendix of Durlauf and Johnson (1995) presents a treatment tailored to the
specific question of identifying multiple regimes in growth models. - Motivated by the debate over trade openness and growth, Papageorgiou (2002) applies
Hansen’s (2000) methods to the Durlauf and Johnson (1995) data, with the trade share
added to the set of variables on which sample splits may occur. - Projection pursuit methods are developed in Friedman and Tukey (1974) and Friedman
(1987). Appendix A of Desdoigts (1999) provides a useful primer. - The assumed rarity of large shocks implies that movements between basins of attraction
of each of the steady-states are sufficiently infrequent that they can be ignored in estima-
tion. This assumption is consistent with, for example, the Bianchi (1997) and Paap and
van Dijk (1998) findings that there is relatively little mobility within the cross-country
income distribution. - See Temple (2003) for more discussion of this point and the long-run implications of
different growth models. - This is true of the many published studies that have used version 5.6 of the Penn World
Tables. Now that more recent data are available, there is more scope for estimating panels
with a longer time dimension. - See Arellano (2003, pp. 47–51) for a more formal treatment of this issue.
- Note that the long-run values of log output are evolving over time when time-specific
effects are included in the model. - An alternative approach would be to use small-sample bias adjustments for GMM panel
data estimators, such as those described in Hahn, Hausman and Kuersteiner (2001). - This connection with the treatment effect literature is sometimes explicitly made, as
in Giavazzi and Tabellini (2005), Papaioannou and Siourounis (2007) and Persson and
Tabellini (2003). The connection helps to understand the limitations of the evidence,
but the scope for resolving the associated identification problems may be limited in
cross-country datasets. - Although this “reverse causality” interpretation of endogeneity is popular and important,
it should be remembered that a correlation between an explanatory variable and the error
term can arise for other reasons, including omitted variables and measurement error. As
we discuss, it is important to bear a general interpretation of the error term in mind when
judging the plausibility of exclusion restrictions in instrumental variable procedures. - Put differently, one does not require a precise definition of what makes an instrument
valid in order to debate whether a given instrument is valid or not. To take an example
due to Taylor (1998), the absence of a precise definition of money does not weaken my
belief that the currency in my wallet is a form of money, whereas the computer on which
this paper is written is not. To claim such arguments cannot be made is known as the
Socratic fallacy. - This estimator should not be confused with trimmed least squares and other methods
based on deleting observations with large residuals in the OLS estimates. A residual-based
approach is inadequate for obvious reasons. - This and the following discussion assume classical measurement error. Under more gen-
eral assumptions, it is usually even harder to identify the consequences of measurement
error for parameter estimates. - To give a specific example, the macroeconomic literature on international technol-
ogy differences only rarely acknowledges relevant work by trade economists, including
estimates of the Heckscher–Ohlin–Vanek model that suggest an important role for
technology differences. See Acemoglu (2008) and Klenow and Rodriguez-Clare (1997)
for more discussion.