WPS 3"'9
POLICY RESEARCH WORKING PAPER 3 004
Institutions, Trade, and Growth
Revisiting the Evidence
David Dollar
Aart Kraay
The World Bank
Development Research Group
Investment Climate
March 2003
POLICY RESEARCH WORKING PAPER 3004
Abstract
Several recent papers have attempted to identify the identified despite the apparently good performance of
partial effects of trade integration and institutional the instruments in first-stage regressions. Consequently,
quality on long-run growth using the geographical they argue that the cross-country variation in institutions,
determinants of trade and the historical determinants of trade, and their geographical and historical determinants
institutions as instruments. Dollar and Kraay show that is not very informative about the partial effects of these
many of the specifications in these papers are weakly variables on long-run growth.
This paper-a product of Investment Climate, Development Research Group-is part of a larger effort in the group to study
institutions and development. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington,
DC 20433. Please contact Anna Bonfield, room MC3-354, telephone 202-473-1248, fax 202-522-3518, email address
abonfield@worldbank.org. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The
authors may be contacted at ddollar@worldbank.org or akraay@worldbank.org. March 2003. (29 pages)
The Policy Research Working Paper Senes disseminates the findings of work in progress to encourage the exchange of ideas about
development issues. An obhective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The
papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the azuthors. They do not necessanly represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced bv the Research Advisorv Staff
Preliminary and incomplete
Comments welcome
Institutions, Trade, and Growth: Revisiting the Evidence
David Dollar and Aart Kraay
The World Bank
1818 H Street NW, Washington, DC 20433, ddollar(fworldbank.ora.
akraavAworldbank.org. We would like to thank Romain Wacziarg and Jeff Sachs for
helpful comments
1. Introduction
Two recent papers have proposed novel instruments and have used them to
separately identify strong causal effects of trade and institutions on economic
development. Frankel and Romer (1999, FR) show that the geographically determined
component of trade as a fraction of GDP exerts a strong positive effect on growth in the
very long run, while Acemoglu, Johnson and Robinson (2001, AJR) show that the
historically determined component of current institutional quality exerts strong effects on
development in a similar framework.
An open question, however, concerns the partial effects of institutions and trade
on growth in the long run. Several very recent papers have investigated this question,
but come to strikingly different conclusions. Alcala and Ciccone (2002, AC) estimate a
variety of regressions of GDP per worker on trade as a share of GDP and measures of
institutional quality. They instrument for these two variables using the FR instrument as
well as linguistic origins, and find that trade is quite significant, while institutional quality
is occasionally but not consistently significant. Dollar and Kraay (2002, DK) estimate a
specification very similar to that of AC. In contrast with AC, DK argue informally that the
cross-country variation in the data is uninformative about the relative contribution of
institutions and trade Finally, Rodrik, Subramanian and Trebbi (2002, RST) estimate a
variety specifications similar to those of AC and DK in an effort to sort out the
geographical, institutional, and trade-related determinants of development. In contrast
with AC and OK, RST conclude that institutions matter while trade does not.'
The objective of this paper is to show that empirical specifications which seek to
isolate the partial effects of institutions and trade can suffer from serious identification
problems. The issue, which we discussed informally in our previous paper, is
straightforward. In many of the specifications in these papers, the historical and
geographical instruments proposed in the previous literature tend to have good
1 In a related paper, Easterly and Levine (2002) attempt to disentangle the geographical and
institutional determinants of development. In a number of specifications they control for various
measures of policy, including trade policy. They generally find that institutions dominate
geography and trade. Since their paper considers trade policy rather than trade itself, we do not
consider it further here.
explanatory power for both endogenous variables, institutions and trade. Consequently,
the fitted values of institutions and trade from first-stage regressions are highly
correlated with each other, and these specifications are at best weakly identified, even
though first-stage regressions have apparently good explanatory power. In short,
although the historical and geographical instruments for institutions and trade proposed
by AJR and FR perform well in their respective univariate applications, they are not
strong enough to identify the partial effects of these variables.
We document the identification problem using the partial R-squared diagnostic
measures suggested by Shea (1997), and the minimum eigenvalue test of the null
hypothesis of weak instruments suggested by Stock and Yogo (2001). In most cases,
both diagnostic statistics as well as the formal tests verify the informal observation in DK
that these models are not very well identified. Consequently, inferences about the
structural parameters of interest, i.e. the causal effects of institutions and trade on long-
run growth, cannot reliably be based on conventional t-statistics.2 We therefore
compute confidence intervals for these structural coefficients of interest using three
methods suggested in the literature on inference with weak instruments: the AR statistic
proposed by Anderson and Rubin (1949), the conditional likelihood ratio statistic
proposed by Moreira (2002), and the S-statistic proposed by Startz, Zivot and Nelson
(2001). These methods which take into account the low strength of the instruments
produce substantially larger confidence intervals than those based on standard
asymptotic theory in the specifications we consider. In many cases, confidence intervals
for the parameters of interest cover (nearly) the entire real line. These results serve to
formalize the informal intuition in our previous paper that the cross-country variation in
trade, institutions, and their historical and geographical determinants is not very
informative about their relative importance for growth in the long run.
Finally, in our previous paper we also investigated the relative contributions of
institutions and trade over shorter horizons by looking at changes in decadal growth
rates over the past four decades. We apply the same weak instrument diagnostics to
these specifications. Although we find that dynamic regressions controlling only for
trade and initial income are well-identified, the regressions which add institutional quality
2 See Staiger and Stock (1997) for a seminal paper, and Stock, Wright, and Yogo (2002) for a
recent survey of weak instruments.
2
are poorly identified when institutional quality is taken as endogenous, but are
reasonably well-identified when institutional quality is treated as exogenous.
The empirical examples that we discuss in this paper are specific to the recent
debate on the relative importance of institutions and trade for long-run growth. We think
however that our results have broader implications for the cross-country empirical
growth literature, which has only in recent years begun to take seriously the endogeneity
of many of the key determinants of growth. Our results here highlight the more general
difficulty in finding exogenous and independent sources of variation required to identify
the partial effects of such determinants of growth.
The remainder of this paper proceeds as follows. In Section 2 we review some of
the main empirical specifications that have been advanced to show the effects of
institutions and trade on long-run growth. In Section 3 we describe and implement
diagnostic tests for the presence of weak instruments, and show that most of the
empirical specifications we consider in Section 2 are in fact weakly identified. In Section
4 we describe and implement three approaches to inference with weak instruments, and
show that existing estimates of the partial effects of institutions and trade are much less
precisely estimated than conventional t-statistics would suggest. In Section 5 we
examine the strength of the identification of the decadal regressions from our previous
paper. Section 6 concludes.
2. Empirical Background
All of the papers discussed above estimate variants on the following linear
instrumental variables regression:
*(1) In(GDP Per Capita), = j 0 +P, Institutions, +P2 .Trade, + 3'Controls1 +ui
Cross-country differences in GDP per capita today primarily reflect differences in growth
over the very long run since a date in the distant past when initial incomes were not very
different across counties. Consequently, this.specification can be thought of as
capturing the determinants of growth in the very long run. Institutions and trade are both
treated as endogenous, and are instrumented using their deep historical and
3
geographical determinants. Each of the papers discussed above differs somewhat in
the measures of institutions and trade used, the control variables included in the
regression, and the choice of instruments. Table 1 summarizes the key differences
across the main specifications of interest in each of these papers.
The top part of Tables 2 and 3 report some of the main results of these papers.
To conserve on space, we report only the coefficients on the main endogenous variables
of interest: institutions, trade, and their instruments in the first-stage regressions. Table
2 reports selected results from DK, while Table 3 reports selected results from RST. We
do not report results from AC as we were unable to obtain their dataset at the time of
writing. As a benchmark, the first two columns of Table 2 present regressions from DK
in the spirit of the original AJR and FR papers, estimating the effects of institutions and
trade separately, without controlling for the other variable. Specification 2.1 shows the
effects of institutions only, analogous to the basic specification of AJR. The main
differences with AJR is that DK use linguistic origins rather than settler mortality to
instrument for institutional quality, and use a different measure of institutional quality.
Nevertheless, the results are broadly similar to that of AJR. As the OLS regressions
show, institutional quality is strongly positively correlated with per capita incomes. The
IV regressions show a statistically and economically significant effect of institutions on
per capita income, with a slope coefficient larger than the corresponding OLS estimate.
Specification 2.2 shows the analog of the main FR specification. Here there are again
only two differences with the original paper: the trade/GDP ratio is measured at PPP,
and the only included exogenous variable is the logarithm of population. Again the
results are very similar to those of the original paper, with a large and significant effect of
trade on growth. In both specifications 2.1 and 2.2, the first-stage regressions of
institutions and trade on their respective instruments perform quite well, with comfortably
large F-statistics of 13.3 and 28.8.
Specification 2.3 reports the main DK result on the partial effects of institutions
and trade. Both institutions and trade enter positively in the OLS regression, with t-
statistics greater than 2. However, in the IV regression only institutional quality has a t-
statistic greater than 2, while the coefficient on trade falls to near zero and the t-statistic
falls to 0.3. In our other paper, we showed however that this apparent result on the
importance of institutions relative to trade was quite fragile, and that both variables were
4
insignificant once four influential observations were discarded. Here however we focus
on this main specification, and show more formally below that the apparent significance
of institutional quality vanishes once we take weak identification into account.
Table 3 presents the baseline RST specification, and three variants. RST
regress log per capita GDP on distance from the equator, the same institutional quality
variable as in DK, and trade as a fraction of GDP in local currency units.3 In their
preferred 80-country specification, they use settler mortality from AJR and distance from
FR as instruments. The first column of Table 3 replicates their basic specification. To
conserve on space, we again suppress the coefficient on distance from the equator (and
all other included exogenous variables). The IV estimate of the effect of institutions is
positive, large, and highly significant using a conventional t-test. In contrast, trade
enters negatively and insignificantly.
RST go on to provide a number of robustness checks on this basic variant. A
subset of these are reported in the remaining columns of Table 3. In specification 3.2,
they replace the local currency trade share with the PPP trade share in order to make
their results more comparable with DK and AC. In specification 3.3 they return to local
currency trade shares, but add measures of domestic market size (the logarithms of
area and population) in order to make their results more comparable with the original FR
paper which included these variables. In specification 3.4 we report one of several
specifications produced by RST including a variety of other variables capturing different
channels through which geography might matter for development. We focus on a cluster
of three variables they identify as jointly significant, consisting of land area in the tropics,
number of frost-days per year, and the incidence of malaria. In each of these
robustness checks, they find that institutions enter the IV specification positively and with
3In their paper, RST argue that this is preferable to using PPP-adjusted trade shares as do AC
and DK. The sketch a simple model in which an increase in productivity which raises the relative
price of non-tradeables relative to the benchmark country will also raise the PPP-adjusted trade
ratio. This is because the PPP-adjusted GDP will fall to reflect the higher price of non-tradeables.
Since the increase in productivity raises income, this can introduce a spurious correlation
between income and the PPP-trade share. While the choice of denominator for the trade ratio is
not the focus of this paper, we note in passing that we are not entirely convinced by this
argument. First, it as long as these other sources of productivity differences are uncorrelated with
the FR instrument, this potential bias will not matter for the IV coefficient estimates. Second, at a
more intuitive level, if we want to capture the size of the traded sector relative to overall economic
activity, it seems natural to use an internationally-comparable measure of overall economic
activity in constructing trade shares.
5
t-statistics in excess of two. In contrast, trade enters negatively in three of the four
specifications, and in all cases the t-statistics are well below 2. Based on these findings,
as well as the basic DK finding in specification 2.3, they conclude in the title of their
paper that "institutions rule". Below we aregue that these results could be interpreted
more cautiously once we take the strength of the identification into account.
3. Are the Partial Effects of Institutions and Trade Identified?
The key question in this paper is the extent to which the empirical strategy of the
papers discussed in the previous section is a good one for capturing the partial effects of
institutions and trade on growth in the very long run. Our focus here is on one
shortcoming of this approach - that existing instruments at best only weakly identify the
structural parameters of interest. In order to review the tools on which we base this
conclusion, some further notation is useful. The structural model in Equation (1) can be
written in the usual matrix notation as
(2) y = Xp + u
where y is an nxl vector of observations on the dependent variable, X is an nxk matrix of
endogenous regressors, 1 is a kxl vector of structural coefficients, and u is an nxl
vector of disturbances.4 Let Z represent an nxq matrix of instruments. Then the reduced
form consists of the following k+1 regressions of y and the columns of X on Z:
(3) y=Ze+v
X=ZX+e
where 0 is an qxl vector and r is a qxk matrix of reduced form coefficients, and v and e
are nxl and nxk matrices of reduced-form disturbances. Let a and E denote the variance
of vj and the covariance matrix of ej respectively, and let Q denote the covariance matrix
of (v, e,')'.
4 In what follows we suppress the additional exogenous control variables in the regression, by
interpreting y, X, and the instruments as the residuals from a regression of these variables on the
included exogenous control variables.
6
In order for the historical and geographical variables in Z to be valid instruments,
they need to be independent of u, which we assume to be the case, i.e. E[Z'u]=O. In
order for the structural parameters p to be identified, the two textbook order and rank
conditions must also be satisfied, i.e. the number of instruments is greater than the
number of endogenous variables (q>k), and the matrix r must be full rank (rank(r)=q).
Using this notation, the instrumental variables (IV) estimator of 3 is
= (X'Pz X)-' X'Pz y where Pz - Z(Z'Z)-'Z for any matrix Z.
A rapidly-growing recent literature on weak instruments has pointed out that the
validity of the usual approximation that ,IV is normally distributed in finite samples
depends crucially on the strength of the instruments. In the case of only one
endogenous variable, the instruments are weak if they jointly have poor explanatory
power for the endogenous variable in the reduced-form equation for X. Nelson and
Startz (1990), Staiger and Stock (1997) show that when the instruments are weak in this
sense, the IV estimator is biased towards the mean of the OLS estimator, and is not
normally distributed. Thus inferences about the structural parameters based on usual t-
tests can be highly misleading.
When there are multiple endogenous variables, and so more than one first-stage
regression, it is less obvious how to gauge the strength of the instruments and the
quality of the normal approximation. An important point, however, is that it is not
sufficient for the F-statistics in the individual first-stage regressions to be large.5
Shea (1997) has proposed a simple diagnostic statistic for determining the
strength of instruments when there are multiple endogenous variables. If X, and X2 are
two endogenous variables, then the instruments are strong if the component of the fitted
value of X, from the first-stage regressions that is orthogonal to the fitted value of X2 is
highly correlated with the component of X, that is orthogonal to X2 . In the case of a
single endogenous variable, this criterion is simply the R-squared from the first-stage
5 Shea (1997) gives a simple example. In the case of two instruments Z, and Z2 for the two
endogenous variables, X, and X2, if ZI is is a good predictor of X, and of X2, but Z2 iS
uncorrelated with both endogenous variables, then the first-stage F-statistics will be large but the
model will not be identified since there is in effect only one instrument for the two endogenous
variables.
7
regression. While this statistic is intuitive and easily calculated, results on its distribution
are not provided in Shea (1997) and so this statistic does not lend itself well to formal
tests of the null hypothesis of weak instruments.
More generally, Stock, Wright and Yogo (2002) point out that the validity of the
1 1
normal approximation depends on the concentration matrix ^1 = y 2']F'Z'Zr 2 being
large in the sense of the smallest eigenvalue of this matrix being large. Note that the
concentration matrix can be small for a variety of reasons. All instruments could be
nearly uncorrelated with the endogenous variables, i.e. all the elements of F are small
relative to the variances of the errorterms in the first-stage regressions. The
instruments could also be very highly correlated with each other so that Z'Z is not full
rank, i.e. there are essentially fewer instruments than endogenous variables. Finally
concentration matrix could also be small if the rank condition for identification fails, i.e. F.
is not full rank. This can occur if, as is the case in some of the applications considered
here, each of the instruments has strong explanatory power for both endogenous
variables.
Stock and Yogo (2001) develop a test of the null hypothesis that the instruments
are weak based on this idea. In particular, they provide critical values for a test of the
null hypothesis of weak instruments based on the minimum eigenvalue of
F = 71/2vXvPz,71/2, where i = X'(l - Pz )X/(n - q) is a consistent estimate of the
covariance matrix of errors from the first-stage regressions.6 In the version of the test
we implement below, the researcher specifies a null hypothesis that the instruments are
weak if the maximum size distortion of Wald tests about parameters of interest under the
null of weak instruments is equal to some pre-specified value. Stock and Yogo (2001)
then tabulate the critical values of the minimum eigenvalue of G for which the null of
weak instruments should be rejected.
6 When the instruments are weak, they show that E[G] = 2 / q + I. One drawback of this test in
our current application is that it is derived under the assumption of iid homoskedastic error terms
in the structural equation. The same is true for the approaches to inference discussed below.
We are unaware of tests for weak instruments which relax this assumption, and it is difficult to say
how important deviations from this assumption are for the results we obtain.
8
With these tools in hand we can investigate the strength of the instruments in the
specifications in Tables 2 and 3. Consider first the core DK specification in regression
2.3. In the first-stage regressions, we see that the linguistic origin variables and the FR
instrument are highly significant predictors of both endogenous variables. In our
previous paper we noted that this implied a very high correlation between the fitted
values of institutions and trade in the second-stage regression, which made the IV
estimates highly sensitive to a few influential observations. Table 2 reports that this
correlation of fitted values from the first-stage regression is 0.74, indicating strong
collinearity in the second-stage regression. From this we concluded informally that the
cross-sectional variation in institutions, trade and incomes was not very informative
about the partial effects of the former two on the latter.
The weak instrument diagnostics discussed in the previous subjection help us to
make this point more precisely. Consider first the Shea (1997) partial R-squared
statistics. We find in our specification that these statistics are very small at only 0.02
and 0.04 respectively. In contrast, the R-squareds from the first-stage regressions in the
first two univariate specifications in Table 2 were 0.14 and 0.29. This provides a first
indication of the idea that while linguistic origin and distance are reasonable instruments
when the effects of institutions and trade are estimated separately, they are quite poor
instruments when the effects of the two are considered jointly.
The middle panel of Table 2 also reports the eigenvalues of the matrix of
estimated coefficients in the first-stage regression, F, as well as the eigenvalues of G.
The first observation here is that the ratio of the largest to the smallest eigenvalues of r,
i.e. the condition number of r, is nearly 100 and the smallest eigenvalue is small at
0.025. This indicates that the matrix of estimated coefficients in the first-stage
regression is very close to not being of full rank, contributing to weak identification of the
parameters of interest. The smallest eigenvalue of G is 1.36. To interpret this value,
suppose we were to define the set of weak instruments very narrowly as only those
instruments that would lead to size distortions of 25% or more (i.e. the size of a nominal
5% test about a parameter of interest were actually 25%), we would not reject the null
hypothesis that the instruments in this application are weak according to this stringent
criterion, since the critical value provided by Stock and Yogo is 5.75.
9
The middle panel of Table 3 also reports the same diagnostic statistics for
selected specifications from RST. In all of these specifications, the first-stage
regressions perform well: seven of the eight first-stage F-statistics are larger than 10,
and even the smallest is still respectable at 8. However, these F-statistics are not
sufficient to diagnose the strength of the instruments. Closer inspection of the first-stage
regressions shows the same tell-tale signs of potential problems as in the DK
specification in Table 2. In seven of the eight first-stage regressions in Table 3, the
instrument for institutions (settler mortality) has strong explanatory power for both
institutions and trade, while the instrument for trade (the FR constructed trade share) is a
significant predictor of both institutions and trade at the 5% level in seven of the eight
specifications as well.
Table 3 also presents the same diagnostic statistics on instrument quality as in
Table 2. The Shea partial R-squared statistics are small in most cases, although not as
extremely so as in the basic DK specification. In four of the eight first-stage regressions,
the partial R-squareds are less than 0.1, and in seven out of eight they are less than 0.2.
More formally, in each of the four specifications, we cannot reject the null hypothesis that
the instruments are weak. However, the size of the set of weak instruments under the
null is different in the four specifications. In specifications 2 and 4, the minimum
eigenvalues of G are 1.95 and 3.24, and we cannot reject even the most conservative
set of weak instruments tabulated in Stock and Yogo (2001). In specifications 1 and 3,
the minimum eigenvalues of G are 6.2 and 6.8, and we cannot reject the null that the
instruments fall in the larger set of weak instruments that would lead to size distortions of
at least 5 percent, i.e. a test with nominal size of 5% would in fact have a true size of
10%.
These results suggest that there are reasons to question inferences about the
importance of trade and institutions based on conventional t-statistics in the main
specifications considered by RST as well. In the next section of the paper we discuss
approaches to inference that are valid even when the instruments are weak, and show
that the confidence intervals for the parameters of interest are much larger than simple t-
statistics would suggest.
10
4 How Large are the Partial Effects of Institutions and Trade?
In this section we briefly describe three approaches to constructing valid
confidence intervals when instruments are weak. The first is based on the Anderson-
Rubin statistic:
(4) AR(Po )- (y - X0 )'Pz (y - Xp0)/ q
(y - XPO )'(1 - PZ )(y - Xpo )/(n - q)
which was first proposed by Anderson and Rubin (1949). Under very general conditions,
including for any arbitrary concentration matrix ,u, Staiger and Stock (1997) show that q
times the AR statistic converges in distribution to a %2(q) random variable. Since the
asymptotic distribution of the AR statistic does not depend on any nuisance parameters
even when the instruments are arbitrarily weak, it is pivotal and can be used for
inference. Wang and Zivot (1998) suggest the use of this result to form valid (1-a).100%
confidence sets for the elements of 3 by 'inverting" this statistic, i.e. by finding the set of
values of Po such that AR(po3) s ¸ ) where x2 (q) denotes the (1-ca).100 percentile of
qa
a x2(q) distribution. In the case of two endogenous variables, the joint confidence sets
for the two elements of ,B can take a variety of shapes. Confidence intervals for the
individual elements of 1 can be obtained by projecting these joint confidence sets on the
appropriate axes.7
Figure 1 shows an example of two such 95% confidence sets, and the
associated confidence intervals. The top panel shows the case where the 95%
confidence set is the area inside an ellipse, corresponding to the coefficients on
institutions and trade in RST specification 3.1. The confidence intervals for the
coefficients on trade and institutions are obtained by projecting the height and the width
of the ellipse on the corresponding axes. The bottom panel shows a case where the
95% confidence set is the area inside a hyperbola, corresponding to the DK specification
7Kleibergen (2002) develops an altemative test which corrects the deficiency of the AR statistic
which is that it has low power when the number of instruments is large. In our applications with at
most three instruments this is not a concern, and inferences based on Kleibergen's K-statistic are
almost identical to those based on the AR statistic.
11
2.3. Projecting this on the two axes shows that the 95% confidence intervals-for the
coefficients on institutions and trade are the entire real line. That is, the data is so
uninformative due to weak identification that it is consistent with any value of these
parameters. We will discuss the specific cases to which these confidence sets apply
below when we present the empirical results in more detail.
Moreira (2002) has proposed a conditional likelihood ratio statistic as the basis
for inference when instruments are weak. Moreira observes that it is possible to write
the usual likelihood ratio statistic for the linear IV model as a function of two orthogonal
sufficient statistics: S = Z'Ybo and T = Z'YQ-'Ao where Y -(y,X), bo (1, -Po')', and
AO = (Po, Ik). His key observation is that since S is a function only of data and the
parameters of interest, the likelihood ratio statistic conditional on the value of T observed
in the data can be used to make inferences about the parameters of interest. In
particular, Moreira shows that the likelihood ratio statistic can be written as:
(5) LR = S'S Xmin
where S = (Z'Z)-'S(bo'Qbo)-112 and T (Z'ZY1T(AO'Q-1Aoy)'2 are the standardized
versions of S and T, and Xmin denotes the smallest eigenvalue of (S,T)' (s, T).
Confidence intervals for ,B can be constructed by inverting this statistic in the same way
as the AR statistic. The LR statistic does not have a known distribution on which to base
critical values. However, Moreira (2002) suggests a strategy for simulating this
distribution empirically to obtain the necessary critical values, which we adopt here.8
The final approach to inference with weak instruments is based on the S-statistic
proposed by Startz, Nelson and Zivot (2001). This statistic is defined as:
(6) S2 = Tj(X)2 /( aT'(X) V[XJ aT8'PG)
ax ax
8 In particular, since S follows a standard normal distribution, the distribution of LR conditional on
the value of T observed in the data can be simulated by repeatedly taking draws from the
distribution of S and evaluating LR at the observed value of T.
12
where X is a vector containing all of the reduced-form coefficient estimates,
,f() pi Iv /V,IV is the IV estimate of the ij element of 13; and p1 o is its value
under the null hypothesis. The S-statistic is the square of the standardized value of
T,(X), and rejects the null when it is large. To provide an intuition for this statistic,
Startz, Nelson and Zivot (2001 ) note that the numerator of , (x) is the distance between
the IV estimate and its hypothesized value. The denominator is the middle part of the
concentration matrix, and is small when identification is weak. Thus the S-statistic will
reject the null if the coefficient estimate is far from the null, or if identification is weak.
Startz, Nelson and Zivot (2001) show that the S statistic converges to a X2(1)
random variable when the instruments are good, and is bounded above by a
x2 (q - k + 1) random variable when the instruments are weak. To construct confidence
intervals for the ith element of 13, we need only find the set of hypothesized null values
for which the S-statistic is less than the appropriate critical value. Figure 2 illustrates
one such confidence set, for the coefficient on institutions in the RST specification 2.1.
Note that the confidence set need not be the usual closed interval, but can consist of two
disconnected intervals. A further convenient property of this approach to inference is
that it is possible to construct confidence intervals for a single parameter directly, and -
that projection methods needed for the AR and LR statistic are not required in this case.
The bottom panels of Tables 2 and 3 present confidence intervals constructed
using these three approaches to inference that are robust to weak instruments. For
reference purposes, we first report 95% confidence intervals for the coefficients on
institutions and trade based on the usual Wald statistics, i.e. the estimated coefficient
plus or minus two estimated standard errors. In the remaining rows we report the 95%
confidence intervals based on the AR, LR, and S-statistics, respectively.
Consider first the main DK specification in the third column of Table 1.
Conventional confidence intervals for the coefficients on institutions and trade are (0.57,
1.95) and (-1.00, 1.35) respectively, suggesting a positive and significant effect of
institutions and an insignificant effect of trade. Confidence intervals that are robust to
13
weak instruments lead to quite different conclusions. All three statistics give confidence
intervals that consist of the entire real line for both the coefficients on institutions and on
trade. This finding formalizes the informal observation in our previous paper that the
cross-country variation in institutions, trade, and their geographical and historical
determinants is not sufficiently informative to pin down the partial effects on growth of
either of these endogenous variables.
The RST results are less stark, but still show that inferences based on the usual
t-statistics can be misleading. In the basic RST specification 3.1, the 95% confidence
intervals for institutions based on the AR and LR statistics are much wider than those
based on the usual Wald statistic, but still contain only positive values.The confidence
interval for institutions based on the S-statistic consists of two disjoint intervals, (-0, -
1.77) and (1.67, o). The former two tests suggest that the partial effect of institutions is
positive, but much less tightly estimated than a conventional t-test would suggest. The
third statistic indicates that the coefficient on institutions is in fact very imprecisely
estimated, in that the data are consistent with a wide range of both positive and negative
values for this coefficient. The intervals for the coefficient on trade based on the AR, LR
and S-statistics are also much larger that those based on conventional t-statistics, but
mostly tend to include negative values. Overall, the substantially-larger confidence
intervals based on weak instrument asymptotics suggest that the partial effects of
institutions and trade are not very tightly estimated.
The remaining specifications consider some of the robustness checks in RST.
First, RST argue that their finding on the relative importance of trade is robust to using
PPP trade shares to measure trade. The results in specification 3.2 suggest that this
equation is also weakly identified. In the bottom panel of Table 3 we see that the AR, LR
and S-statistics all produce very large confidence intervals in the form of two disjoint sets
which exclude only what might be thought of as a priori reasonable values for these
parameters in the general vicinity of the OLS estimates. The results of this specification
are therefore more similar to those in the basic DK finding, in which the partial effects of
institutions and trade are essentially unidentified. The same is true in specification 3.4
with additional geographical control variables. The correct 95% confidence intervals
span nearly the entire real line, indicating that the data are consistent with virtually any
partial effect of institutions and trade. In specification 2.3 the AR and LR statistics give
14
confidence intervals that are similar (but substantially wider) to conventional ones, while
those based on the S-statistic encompass a very large range of parameter values.
To sum up, we have seen that the basic DK conclusion that the cross-sectional
data in their specification is uninformative about the partial effects of institutions and
trade is supported by the more formal weak instrument asymptotic approximations used
here. The same techniques also suggest that the RST findings on the relative
importance of institutions may be less robust than meets the eye. In their specifications
using PPP trade shares and adding additional geographical controls, the data appears
consistent with virtually any values of the parameters of interest, due to the weak
identification of these equations. In their basic specification, the different approaches to
inference lead to different precise conclusions. Qualitatively however they all lead to
much larger confidence intervals than those based on t-statistics, especially in the case
of the S-statistic.
5. Decadal Regression Results
How might we proceed from the negative findings above that the partial effects of
institutions and trade are not identified in cross-country regressions of levels of per
capita GDP on instrumented institutions and trade? One possibility which we explored in
our previous paper was to instead look at decadal changes in growth, trade and
institutional quality in the hopes that the partial effects of the latter two variables would
be better identified in this framework relying on internal instruments. Of course, a
drawback of this approach is that by construction it cannot pick up the very long-run
effects of institutions and trade emphasized in the levels regressions above. Moreover,
while we showed that there is non-trivial variation in measures of trade and institutional
quality even at decadal frequencies, we are less sure how informative this variation is
about true unobserved changes in these variables. In our previous paper we found that
changes in trade volumes were a significant predictor of changes in decadal growth
rates. However, the effects of changes in five measures of institutional quality on
changes in growth were very imprecisely estimated and rarely statistically significant
across specifications.
15
In this section we deploy the tools descriped above to verify the strength of the
instruments in the decadal regressions of our previous paper. We began with the
following standard cross-country growth regression:
(7) YCt =Po + P1 YC,t-k + P2'Xct +C + Yt + VCt
where Yct is log-level of per capita GDP in country c at time t, YC,t-k iS its lag k years ago
(k=1 0 years in our application using decadal data) and Xc, is a set of control variables
which are measured as averages over the decade between t-k and t. We will consider
trade volumes and measures of institutional quality among the variables in X.
Subtracting lagged income from both sides of the equation gives the more conventional
formulation in which the dependent variable is growth, regressed on initial income and a
set of control variables. The disturbance term in the regression consists of an
unobserved country effect that is constant over time, jc, an unobserved period effect
that is common across countries, -yt, and a component that varies across both countries
and years which we assume to be uncorrelated over time, vct.
We adopted the approach of Caselli, Esquivel and Lefort (1996), which is to
estimate equation (7) in differences, using appropriate lags of the right-hand side
variables as instruments. In particular, we estimate the following regression:
(8) yct yc,t = (Yc,t-k Yc,t-2k)+p2(Xct -Xc,t-k)+(Yt Yt-*)+(Vct VC,t-k)
This is nothing more than a regression of growth on lagged growth, and on changes in
the set of explanatory variables. Or, subtracting lagged growth from both sides of the
equation, we have changes in growth from one decade to the next as a function of initial
growth and changes in the explanatory variables. Our identifying assumption is that
while trade volumes and institutional quality may be correlated with the
contemporaneous and lagged shocks to GDP growth (E[Xdtvc,..t-]#0 for s2O), they are
uncorrelated with future shocks to GDP growth, (E[(XYdv,,t+]=O for s>0). We therefore
instrument for lagged growth using the log-level of per capita income at the beginning of
decade t-2k, and we instrument for the changes in trade and institutional quality using
their levels at the beginning of decade t-k.
16
The first column of Table 4 reports the results of this specification when X
contains only the share of trade in GDP. The OLS and IV estimates replicate those in
our previous paper. We find a positive effect of trade on growth at this decadal
frequency, with a coefficient that is economically sensible and has a t-statistic greater
than 2. In the first-stage regressions, we find that while only initial income is a significant
predictor of growth, both initial income and initial trade are significant predictors of trade.
This suggests some concerns about the strength of the identification. The diagnostic
statistics for the presence of weak instruments paint a somewhat mixed picture as well.
The Shea partial R-squared for growth is very small, while the partial R-squared for trade
is a respectable 0.25. On the other hand, the Stock-Yogo test statistic for the null of
weak instruments is large enough that we can reject the null. The bottom panel reports
conventional Wald-based confidence intervals as well as intervals based on the S-
statistic.9 While the confidence interval for the coefficient on initial income is very large,
the confidence interval for the coefficient on trade is essentially the same as that based
on the usual Wald statistic. This gives us some confidence in the robustness of this
basic finding on the effects of trade on growth at decadal frequencies, even though the
coefficient on initial income appears to be less well identified.
The middle panel of Table 4 reports results adding one of the five time-varying
measures of institutional quality we considered in our previous paper. Following Clague,
Keefer, Knack and Olson (1999) we proxy for the strength of property rights protection
using what they refer to as "contract-intensive money", i.e. the share of currency in
circulation held inside the banking system. In the middle panel of Table 4, we enter this
variable and treat it as endogenous. The top part of the table again replicates the results
of our previous paper. We find that the coefficient on trade does not change very much
relative to the previous case, while the measure of institutional quality enters negatively
with a very large standard error. However, the diagnostic statistics for the presence of
weak instruments strongly point to identification problems in this specification. The Shea
partial R-squared statistics are tiny, as is the minimum eigenvalue of the concentration
matrix. Not surprisingly, in this case confidence intervals based on the S-statistic cover
9 In this section we report only the confidence intervals based on the S-statistic because of its
convenient property that projection methods are not required. This is most useful in the middle
specification of Table 4 where we have three endogenous variables, and ensures that the results
are comparable across these three specifications.
17
the entire real line, suggesting that this specification is entirely uninformative about all of
the parameters of interest.
The reason for the poor performance of the IV estimator is however somewhat
different from the levels regressions discussed before. In the levels regressions the
problem was that the instruments for trade also explained institutional quality while the
instruments for institutional quality also predicted trade well. This is not the case here.
In our previous paper we noted that initial levels of trade predict subsequent changes in
trade but not changes in institutions. Conversely initial levels of institutions predict
changes in institutions but not changes in trade. However, the problem here is that initial
institutions also predicts the endogenous change in initial income, while initial levels of
per capita income that are supposed to instrument for the change in initial income also
explain changes in trade and changes in institutions. This is why the identification of this
specification breaks down.'°
We obtain rather more encouraging results when we treat institutions as
exogenous. In our previous paper we noted that the large estimated standard errors on
the coefficient on institutional quality in the dynamic regressions might be due to weak
instruments. We then also discussed results in which we treated institutions as
exogenous, which if anything were likely to exaggerate the effects of institutions on
growth. In these specifications we continued to fail to find a significant impact of
institutions on growth, while trade continued to enter positively and significantly. In the
final panel of Table 4 we revisit this altemative specification. The results are quite
similar to those in the first panel where institutional quality was omitted entirely. The
main difference now however is that the Stock-Yogo test favours the null hypothesis of
weak instruments. Closer inspection of the first-stage regressions suggests that this
may be because initial levels of income are predicting both lagged growth and changes
in trade. When we compute appropriate confidence intervals using the S-statistic, we
1' RST argue that the significance of trade in the decadal regressions in DK is not robust to the
inclusion of selected regional dummies and their interactions with decadal dummies. For
example, for the specification using contract-intensive money as a proxy for institutional quality,
when these variables are estimated, nothing is significant in the IV regression. In light of the
results above, this is perhaps not very surprising. Since these additional exogenous variables are
likely to be good predictors of all three endogenous variables, this is likely to further weaken the
performance of the instruments. Moreover, given that these additional dummy variables are not
significant in this specification, we are not sure that it is a good strategy to include them and
undermine any hopes of identification.
18
find once.again that the coefficient on initial income is not very precisely estimated.
Nevertheless we do find that the coefficient on trade is fairly precisely estimated, with a
confidence interval very similar to that based on a conventional Wald test.
Overall these results suggest that it is also difficult to identify the partial causal
effects of institutions on growth in this shorter-run framework. We do not appear to have
sufficiently informative variation in the decadal data to identify the partial effects of
institutions and trade treating both as endogenous. However, the specification which
includes institutions but treats this variable as exogenous still serves a useful purpose,
since it helps to control for a spurious correlation of changes in trade with changes in
institutional quality, even if we cannot properly identify the partial effects of the latter.
6. Conclusions
In this paper we have argued that existing attempts to isolate the partial effects of
institutions and trade on growth in the long run suffer from serious identification
problems. The reason for this is simple -- existing historical and geographical
instruments in the literature tend to have strong predictive power for both institutions and
trade. As a result, these specifications are only weakly identified, despite the apparent
good performance of first-stage regressions.
How do we move forward from such a negative result? One possibility is to rely
more on the time-series variation in institutions, trade and growth, in the hopes that
internal instruments will be less weak than in the cross-sectional applications we have
described. This is the approach we followed in our previous paper. However, this
approach appears to yield mixed results regarding the strength of the instruments. If we
treat institutions as exogenous, we are at least able to uncover a significant partial
association between trade and growth which survives the inclusion of a variety of proxies
for institutional quality. However, if we allow institutions to be endogenous, we find that
the model is too weakly identified to be able to sharply estimate any of the parameters of
interest.
Clearly simple cross-country linear instrumental variables regressions, either in
levels or in decadal differences, cannot provide definitive answers about questions as
19
complex as the interacting roles of institutions and trade for growth. At best this
approach can summarize interesting partial correlations in the data while at least
partially controlling for obvious endogeneity problems. Combining this approach with
more microeconometric evidence, case studies, and descriptions of historical episodes
is likely to constitute fruifful research agenda. In the meantime, the empirical examples
we provide here illustrate a broader problem in the cross-country empirical growth
literature, which only in recent years has begun to take serious the problem of
endogeneity of many of the key determinants of growth. Finding compelling instruments
for these endogenous variables is difficult to begin with. If in addition we are interested
in sorting out the partial effects of multiple endogenous determinants of growth, the
search for instruments is further complicated by the need to find exogenous and
independent sources of variation in order to identify partial effects of interest.
20
References
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Alcala, Francisco and Antonio Ciccone (2001). "Trade and Productivity". CEPR
Discussion Paper No. 3095.
Anderson, T.W. and H. Rubin (1949). "Estimation of the Parameters of a Single
Equation in a Complete System of Stochastic Equations". Annals of
Mathematical Statistics. 20:46-63.
Caselli, Francesco, Gerardo Esquivel and Fernando Lefort (1996). "Reopening the
Convergence Debate: A New Look at Cross-Country Growth Empirics." Journal
of Economic Growth, 1: 363-389.
Clague, Christopher, Philip Keefer, Stephen Knack, and Mancur Olson (1999).
"Contract-Intensive Money: Contract Enforcement, Property Rights, and
Economic Performance." Joumal of Economic Growth, 4:185-211.
Dollar, David and Aart Kraay (2002). "Institutions, Trade and Growth". Paper Prepared
for the Carnegie Rochester Conference on Public Policy.
Frankel, Jeffrey A. and David Romer (1999). "Does Trade Cause Growth?" The
American Economic Review, (June) 379-399.
Easterly, William and Ross Levine (2002). "Tropics, Germs, and Crops: How
Endowments Influence Economic Development". Paper Prepared for the
Carnegie Rochester Conference on Public Policy.
Kleibergen, Frank (2002). "Pivotal Statistics for Testing Structural Parameters in
Instrumental Variables Regressions". Econometrica.
Moreira, Marcelo (2002). "A Conditional Likelihood Ratio Test for Structural Models".
Manuscript, Harvard University.
Rodrik, Dani, Arvind Subramanian, and Francesco Trebbi (2002). "Institutions Rule:
The Primacy of Institutions over Geography and Integration in Economic
Development". NBER Working Paper No. 9305.
Shea, John (1997). "Instrument Relevance in Multivariate Linear Models: A Simple
Measure". Review of Economics and Statistics. 79:348-352.
Staiger, D. and J.H. Stock (1997). "Instrumental Variables Regression With Weak
Instruments". Econometrica. 65:557-586.
Startz, Richard, Charles R. Nelson and Eric Zivot (2001). "Improved Inference for the
Instrumental Variable Estimator". Manuscript, University of Washington.
21
Stock, James H. and Motohiro Yogo (2001). "Testing for Weak Instruments in Linear IV
Regression". Paper Prepared for Festschrift in Honour of Thomas Rothenberg.
Stock, James H, Jonathan H. Wright, and Motohiro Yogo (2002). 'A Survey of Weak
Instrument and Weak Identification in Generalized Method of Moments". Journal
of Business and Economic Statistics. 20(4):528-529.
Wang, Jiahui and Eric Zivot (1998). "Inference on Structural Parameters in Instrumental
Variables Regression with Weak Instruments". Econometrica. 66(6):1389-1404.
22
Table I -- Summary of Estimates of Effects of Institutions and Trade on Growth
Paper Dependent Varable Institutions Variable Trade Variable Instruments Induded Exogenous Vanables
Frankel and Romer (1999), Table Real GDP Per Capita Excluded Trade/GDP in current Trade predicted by gravity Area, Population
3, Column 2 at PPP, 1985 local currency units model
Acemoglu, Johnson and Robinson Real GDP Per Capita Intemational Country Excluded Settler mortality None, but several other
(2001), Table 4, Column 1 at PPP, 1995 Risk Guide specifications indude a number
of other exogenous control
vanables
Alcala and Ciccone (2002), Table Real GDP Per Intemational Country Trade/GDP at PPP Population, log(Population), log(Area), regional dummies,
6, Column 3 Worker at PPP, 1985 Risk Guide Area, Trade predicted by distance from equator
gravity model, log(Trade
predicted by gravity model),
fraction of population
speaking English, fraction of
population speaking major
European language
Dollar and Kraay (2002), Table 1, Real GDP Per Capita Rule of Law from Trade/GDP at PPP Trade predicted by gravity log(Population)
Column 6 at PPP, 1995 Kaufmann, Kraay model, fraction of population
and Zoido-Lobaton speaking English, fraction of
(2002) population speaking major
European language
Rodrik, Subramanian and Trebbi Real GDP Per Capita Rule of Law from Trade/GDP in current Trade predicted by gravity Distance from equator
(2002), Table 2, middle panel at PPP, 1995 Kaufmann, Kraay local currency units model, Settler mortality
and Zoido-Lobaton
23
Table 2 - DolGar-Kraay (2002) Specification
2.1 -- Institutions Only i 2.2 -- Trade Only 23 - Institutions and Trade
fEndogenoius RHS Vanables Institutions rad ! nstrti&oni F Tr-_ Insti ution J7rd
O0Ls and- iV Estimates
'OLS l 0 985 I g 1 1077 0 792 0 405
(0044) 1 0(B8) (0.075) (D.102)
,-. I
IIV 1 310 1.258 0 178
(0.141) 95
'Included Exogenous Variables Inpop Inpop
'First-Stage Regressions I
Ln(FrankelRomer) 0386 0.643 468
i~~~~~~~~~~~~~~~~~~~~~~0 I | @9) |(0.122) O (.J0
Engfrac 0 86. 0 944 0 368
(0.356) Ii0348) )292)
Eurfrac 0.500 0.691 0 363
E -~~~~~~ ~~~~ i ~~~ (0.247) I I @ '2i) | @1681)
F-Statistic 13.350 2800 13.540 1i770
R-Squared 0.139 0285 0d6 1 0 342
~~~~~~~ I f j i
I #Observations 134 134 134
iWeak Instrument Diagnositics j
1shea Partiai R-Squared i 0 139 i .285 0039 02
ICorr(Fitted Values) 0.740
iEigqnvalues of r l 0 025, 2 239
1Eigenvaluesof' 27191
195% Confidence Intervals
Wald (D5 7.1.9 51); (-1.00,1.35)
AR ; I (.w!Z) , (~.wi)
'LR E:| (.) ¢ sXm
Note: Dependent variable in all specifications is In(Real GDP per capita at PPP) in 1995.
Heteroskedasticity-consistent standard errors in parentheses.
24
Table 3 - Rodrik, Subramanian and Trebbi (2002) Specifications
3.1 - Institutions and Trade 3.2 - Institutions and Trade
LC Trade Share PPP Trade Share
Endogenaus RHS Variables Institutions Institutlons Trde
OLS and IV Estimates
'OLS 0 745 0 259 0 548 0 474
'(109) (O 161) (0115) (0101)
IV 2 126 -0 513 2 880 -0 909
([1.S89) (0.420) (1 261) (0 972)
Included Exogenous bISTEO OISTEQ
Vana bles
;First-Stage Regressions
Ln(FrankelRomer) 0222 b 86 0222 0 491
( 0104) (0057) (0104) (0110)
Engfrac
',Eurfrac
| LnSetMor -0 264 -0.133 -0 264 -0 212
t -Stat;stic 17D00FO 3b 130 17.000 8 030
' R-Squared b 413 0594 0 413 0 284
# Observations E0 72
,Weak Instrument Diagnostics
,Shea Partial P-Squared 0110 b 324 0 052 0 083
fCarr(Frtted Values) 0 202 0 667
IEigenvalues of I 0035s 447 0015,0380
|Eigenvalues of r 6273, 40 834 1 792,13 210
i95Y Confidence Intervais
Wald (0 95, 3 3) (-1 35, 0 33)3 ( 34, 5.33) (-2 E51 03)
} AR (1 44, 7 86 (-3 81. 0 15) , -7 2b)Uti U 9.-) (,012)9U(5 83,-)
t LR (1.44, 7 36) (-4 14, 0 15) ,-,-7.26) U (1 79,-) (-@, 0 28) U (J83,)
S &-@ -i 7i) U (1 67,) & (-, -0 i8) (-,0 20) U t2 32,1m) ( (,2 - 11) U (1 07,
Note: Dependent variable in all specifications is In(Real GDP per capita at PPP) in 1995.
Heteroskedasticity-consistent standard errors in parentheses.
25
Table 3, cont'd - Rodrik, Subramanian and Trebbi (2002) Specifications
3.3 - Institutions and Trade 3.4 - Institutions and Trade
-~ LC Trade Share LC Trade Share, Add Area
Adddogenoi~s Area,/anabIes Poe) Pop. Tropics Frost, Malaria
*Endbqenovs RHS Vanabbes Ins1d4tions ICd nst utiDns
iOLS and IV Estimates
IOLS 0.737 0 304 o.i79 0232
(0 i1) O184)i pi33) (170
dIv 105o 0.351 15859 -0502
(0421 i(0 98) (O 822) ( 601)
oIncluded Exogenous DiSTEG LNAEA, LNPOP DISTEQ, LNAREA, LNPOP
IVanabIrs TROPICS, FROST. MALARIA
Flist-Stage Regressions
Ln(FrankelRomer) - b 2 bi
-0 471 0 288 0 330 0 605
Engfrac (0 249) 0:124) t° 142) t°088)
Eurfrac
LnSetMor -0 lid -- 104 -0202 -0063
(0 075) ( 049) (0 102) 0 065i)
F-Statistic 12.120 24 690 19.920 10 320
R-Squarad 0.481 0B62S 0.525 056
# Observations 80 7n
'Weak Instrument Diagnostics
1Shea Partial R-Squared 0 169 0.089 006i2 0 196
Corr(Fitted Values) 0 042 o 0oi
Eigenvalues of il 01032, 0 315 0 021, 0 499
Eigevalues of r 3.035, 9 708 3 148, 21 222
i95% Confidence !nteFvals
Wald 98, 83) (-1 62,2 32) .0,3.30) (1 70, 0.70)
AR (i 04,4 31) 4l57 9 337) (-= -7 4) U (80,=) (-., 0.10) U (451,
LR (1 04, 4 49) (-4 57,11 02) (--,-745)Ut080,-) (--6 010)U(4 51,-)
S (1 39, i (-c,e) (m.) (-=, 1.74) U (3.66, -)
Note: Dependent variable in all specifications is ln(Real GDP per capita at PPP) in 1995.
Heteroskedasticity-consistent standard errors in parentheses.
26
Table 4 - Decadal Regressions from Dollar and Kraay (200?)
4.1 Trade Only - 4.2 Institutions and Trade, 4.3 Institutions and Trade,
.EndoqenousR-PHS Vanable are - institutionks; Endogen-o-us Institutions Ex-ogenous;-
Decade-verageGro~thin -~Initial Income Trade Initial Income Trade Institutions Initial Income Trade~
O0LS and IV Estimates _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _
-- ~~~~~~ ~ ~~(00567) _(00 148)_ _(OSS§) _(0_048)_ (02?23) _(0_SS)__ (00P48)-
-0-732 -- -0249-- - -0649---- -02------06 -00632 ~ 0 209_-
Uncluded - - (0246) ___ J1 108) ~~~~~~~~~~~~~90 Li~LA 7 (366) (0107)p
Fn-uddExogenous Variables Decadal dummies Decadal dummies Decadal dummies, Institutions
_ag_Rgressiorks
decade of-
-nPeCpia0.004 0 1 010 01 0.002 - - 0.036 _ 0.012
001 g 2 _ __ -0__ 01 0__ _ _ _ ___ _2 __
IntTrade/GOP) ~~~~~0.002 -0.014 0.001 .0 019 -0 001 0.0013 -0 018
-- ~~~~~~ ~~(0_00) ~ (0_02) _ ) (0002) (0001) (02) -- (002)
nsi-4tutio-n's- 0034 0 021 -002___
-- - (0010) ~~~~~~~~~~~~~~_(001) (005)
F-Statistic 19 74 20.16 _ 14 56 _17 79 12.39 12 94 _ 19.04
R-Sa uared 0.215 0.272 0 252 0 347 0 273 0.238 0.344
#bservations 27 __ ___ 93 193
Wea fIstrument D a gn _ __ __ __ __ __cs__ -- -- - -- - - _ _-- _
Se a_-P-a-r,t!a- PR--S-q u-a-re-d _0_ 0053 42 7 -------- -0-0-0-5 0- 01 03
--- -- r12-025, r13~~~~~~~~~~~~~~~~~~~~Ll 006, r23~:-0 12 -- -0.29
~E-ienvlues oal 00M,002.003 1 xlDE-6, 0.0004, 0002 0 00002, 0.0005
7718.43934 ~~~~-- -- 0.169-. 18759.5-.-527 36,3.7
45~( Confidencie iinteivals - ----- ----
Wia-ld- -(0.2-5-,1-22) 0040) 4(-1243)0 0.45) ---3 47 6)1 55) 0, 042?)
- S - (fl2~~~~~~~~~~3.) (.4. 046) i~~ 4
Note: Dependent variable is decadal average annual growth. Heteroskedasticity-consistent standard errors in parentheses.
Figure 1: Confidence Sets Based on AR Statistic
C13~~....... ...... 13.1
. . . . . ~~~~~~~11.53
. . - 'tr W .t N r. 32 NO
. . . . . = =|i =~~~~~~~~~6.71 co
. . < a 5 . 1 1 '~~~~~5.1
3.50
1.90
31.35 e
| | = 1 E -~~~~~~~6.13
. | | - 7 . 73~~~~~-.7
> l . l ~ . .............. !1iUl!!lil|lUll!llii -9.34
'7 CR '11~ ~ ~ 9 C
Coefficient on Trade
9.07
7.71~~~~~~~~~~~77
6.35~~~~~~~~~~63
gg gg49~~~~499
0
3.63 .2
2 28 c
0.92 °
~~~~~~0 ~~~~~~~044 i
- 1 . 80 t~~~~~~~~~-18
g g gWt ~~~~~~~~~3.15
-5.87~~~~~~~~~~~58
¢ ' N G N B , ~~~~~~~-7.23
c 0 CD 04 NO) 0) c Djt CN 0C °N
ON~ In C4 o~ (p on Trade
Coefficient on Trade
Figure 2: Confidence Intervals Based on S Statistic
Coefficient on Institutions
10
9
8
7-
6-
X-squared(1 ,0.95)
3-
2 -S-Sttstic
i-0-
-15 -10 -5 0 5 10 15
29
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and Firm Size Asl1 Demirguq-Kunt 31001
Vojislav Maksimovic
WPS2998 Does Micro-Credit Empower Women? Mark M. Pitt March 2003 P. Kokila
Evidence from Bangladesh Shahidur R. Khandker 31001
Jennifer Cartwright
WPS2999 Explaining Liberalization Philipp Harms March 2003 P. Flewitt
Commitments in Financial Aaditya Mattoo 32724
Services Trade Ludger Schuknecht
WPS3000 International Climate Regime beyond Franck Lecocq March 2003 V Soukhanov
2012: Are Quota Allocations Rules Renaud Crassous 35721
Robust to Uncertainty?
WPS3001 An Introduction to Financial and Antonio Estache March 2003 G. Chenet-Smith
Economic Modeling for Utility Martin Rodriguez Pardina 36370
Regulators Jose Mar[a Rodriguez
German Sember
WPS3002 Information-Based Instruments for Uwe Deichmann March 2003 Y D'Souza
Improved Urban Management Somik V Lall 31449
Ajay Sun
Pragya Rajoria
WPS3003 The Investment Climate and the Mary Hallward-Driemeier March 2003 P. Sintim-Aboagye
Firm: Firm-Level Evidence from China Scott Wallsten 37644
Lixin Colin Xu