To provide a comparison between binary recursive trees and more standard multivariate analysis, vve begin by reporting the probit estimates (where the dependent variable equals unity for fast growth observations):







The probit (which predicts 68 percent of the observations correctly) identifies investment, inflation, population growth, human capital, and black market exchange rate premia (as well as the “catch-up” term, and drought or war conditions) as “significant” determinants of rapid economic growth. But it does not reveal whether, for example, the effects on inflation on growth depend upon the level of investment, or whether investment has any positive effect on growth in countries engaged at war. To address that type of question, we turn next to binary recursive trees.

The first tree, based on a classification of observations into the top-third versus the bottom-third growth rates, is depicted in figure 1. The overall quality of the rules embodied in the tree can be evaluated by their ability to divide the test sample into high and low growth observations. Seventy-five percent of the low growth observations and almost seventy percent of the high growth observations were correctly classified.’ Continue reading »


THRESHOLDS AND CONTEXT DEPENDENCE IN GROWTH: DataWe use an annual data set covering all IMF member countries for which data are available over the period 1960-1996. The data are taken from the IMF’s World Economic Outlook and International Finance Statistics databases. The starting sample comprises 2,181 growth observations for 107 countries. We first sort this data set, according to the per capita GDP growth rates, into three equal-sized groups. Observations in the top one-third are classified as “high growth” (corresponding to average per capita growth rates of 6 percent per year), and observations in the bottom third are classified as low growth (corresponding to average per capita growth rates of -2.5 percent per year); the middle one-third observations are dropped, yielding 1,454 observations in the data, set used for the analysis.

Growth can arise from the accumulation of inputs and from disembodied productivity improvements. On the accumulation side, we follow the usual practice of measuring the growth in physical capital by the investment to GDP ratio (I/\r). Human capital accumulation has been proxied by a variety of different variables in the empirical growth literature, including school enrollment rates, average years of primary and secondary education, life expectancy and student/teacher ratios. Continue reading »


For each sub-branch, the algorithm is then repeated. In principle, this process could continue until every observation has been placed into its own branch. This would be akin to including as many explanatory variables as observations in a regression and thus getting a “perfect,” if meaningless, fit. A termination rule is thus required. The rule used resembles, loosely speaking, an adjusted R2 criterion. After each split, the improvement in the overall fit (which, just like the change in the raw R2 upon adding an additional explanatory variable is always non-negative) is combined with a penalty on the number of branches which promotes parsimony. If the penalty exceeds the improvement, the branch is terminated at the prior node, if not, the algorithm continues. Continue reading »


THRESHOLDS AND CONTEXT DEPENDENCE IN GROWTH: Binary Recursive Trees continueTo illustrate, suppose we sort all growth observation by size, and define the top third of observations as “high growth”, coded as 1, and the bottom third as “low growth”, coded as 0. The sample is then randomly separated into a core sample and a smaller test sample used for robustness checks. For the core sample, the algorithm searches for sequential splits, each consisting of the explanatory variable, and its associated threshold value, which best discriminates between the two groups. In most cases, the fit will not be perfect. Suppose, for example, that investment is correlated with growth, and is thus a potentially useful discriminant. There will, however, be some countries that have high investment rates but (nonetheless) belong to the low growth sample (a type I error), and others that have low investment rates but belong to the high growth sample (a type II error). The algorithm searches over all observed values of the investment rate until it finds the threshold value £j which minimizes the sum of the type I and type II errors. Continue reading »


He empirical growth literature seeks to identify factors which are important in determining output growth. In the familiar cross-country regression framework (and likewise in limited dependent variables regressions if the dependent variable is “high” growth versus “low” growth), a variable is considered “important” if, controlling for the other regressors, it can explain a large fraction of the variation in the dependent variable. To be sure, this is a relevant gauge of the universal importance of a variable. Yet, even if a factor is not robustly linked to growth for the entire sample, it may well be of key importance for a subgroup of observations. This is more difficult to unearth within a regression framework, which implicitly assumes that the same functional form to apply to all countries.

For instance, human capital may be robustly associated with growth, but for the subgroup of countries suffering from military conflict, devoting more resources to education will arguably have a very limited effect. Standard regression analysis in effect computes an average of the effect over the two subsamples (war/no war), impeding identification of the link. If the type of non-linearity is known, controls can of course be included, in the above case, adding a dummy for civil conflict as well as the product of the dummy and the human capital accumulation variable would suffice to capture the effect. Continue reading »


THRESHOLDS AND CONTEXT DEPENDENCE IN GROWTH: Introduction endIn this paper we adapt an alternative approach, abandoning the regression framework in favor of binary recursive tree estimation, a technique potentially well suited to identifying both threshold effects and cross-dependencies in a wide range of potential explanatory variables. Based on a sorting of countries into a fast- and a slow-growing group, the tree analysis searches across a set of potential explanatory variables to produce a sequence of criteria (in essence, a decision tree) which help determine the likelihood that a country will fall into each group. Since the sequence of criteria can depend upon previous branchings of the tree, the algorithm can readily accommodate cross-dependencies between the explanatory variables. The technique also establishes a hierarchy among the explanatory variables, based on their ability to discriminate between groups, thus providing a natural criterion for deciding which determinants belong in the ‘”core” and which are of secondary importance. Finally, because the algorithm uses interior thresholds, it is by construction extremely robust to outliers, unlike regression analysis. Continue reading »


More recent work covering thresholds, path dependence and cross-dependence includes Clark, Murphy, Shleifer and Vishny, David, Arthur, Azariadis and Drazen, Jones and Manuelli, Kre-mer, Aghion and Howitt, Matsuyama, Easterly and Ciccone and Matsuyama, among others. Ex ante, the existence of such threshold effects is not implausible. For instance, it is hard to believe that raising the primary school enrollment rate from 90 to 95 percent has much effect on GDP growth. Yet arguably there is some threshold level of human capital below which GDP growth begins to suffer. Similarly, the effects of inflation on growth may be highly nonlinear, with a positive effect at very low inflation rates (as inflation “greases” the economy), and a negative effect at higher inflation rates (as inflation confuses relative price signals in the economy) [Bruno and Easterly ].

More complex non-linearities enter to the extent that the effect of one growth determinant depends on the level, or presence, of another determinant. Thus, trivially, accumulation of human capital is unlikely to do much for a country ravaged by civil war. Similar, if less extreme, complementarities are likely to arise for many growth determinants. Continue reading »


THRESHOLDS AND CONTEXT DEPENDENCE IN GROWTH: IntroductionWhat separates winners from losers in the great growth game? A decade of intensive research has identified a range of determinants influencing both rates of factor accumulation and disembodied technological progress. Yet to day no universal growth “recipe” has emerged from this literature: cross-sectional regressions continue to suffer from severe robustness problems [Levine and Renelt ]. At the same time, the set of potential determinants found to be significant in some context or other continues to grow. Indeed, the empirical growth literature now arguably sufFers from an embarrassment of riches, with proposed determinants of growth spanning a wide field including learning by doing [Arrow ], education [Barro and Lee (1993a)], openness [Edwards ], policy distortions [Easterly ], inflation [Bruno and Easterly ], fiscal policy [Barro ], financial sector development [Greenwood and Jovanovic ], income distribution [Perotti ], R&D policies [Grossman and Helpman ], natural resource endowments [Sachs and Warner ], culture [Carroll, Rhee and Rhee ], ethnic divisions [Easterly and Levine ], democracy [Helliwell ], equipment investment [DeLong and Summers ], macro policies [Fischer ], institutions [Knack and Keefer ] and stock markets (Levine ], among others. Continue reading »

Followership: An Important Partner of Leadership: A Path to Effective Followership, Final Remarks

It is clear that without strong motivation, people cannot effectively operate the tasks. A number of studies have demonstrated the importance of intrinsic motivation for workers to commit to their jobs and in turn uplift the organizational development (Amabile, Conti, Coon, Lazenby, & Herron, 1996; Oldham & Cummings, 1996). Motivation is the driving force that pushes individuals toward excellence. Therefore, good followers should have higher motivation to perform the required tasks and to successfully get the job done while providing high quality work in order to meet or exceed the organization’s expectations.

Followership should be credited as leadership. As Rosenau (2004) pointed out, “leadership requires a voluntary followership” (p. 15). Therefore, more attention, recognition, and possible investment should be given to follower development either in an organizational or educational level (Dixon & Westbrook, 2003; Neal, 2010). Continue reading »

Followership: An Important Partner of Leadership: A Path to Effective Followership continue

Followership: An Important Partner of Leadership: A Path to Effective FollowershipApart from an organizational level, Hertig (2010) provided several suggestions for practitioners to follow in order to become an effective follower. First, redefine followership and leadership. Second, maximize one’s strengths and improve one’s weaknesses. Third, engage in continuous performance evaluations and provide honest feedback. Fourth, seek opportunities. Fifth, find a mentor. Sixth, always ask why. And finally always present solutions to problems (p. 1431). Moreover, Whitlock (2013) held a positive view for applying good followership and stated that potential effects of good followership “could make a significant contribution towards establishing high performing, safety-conscious organizational teams with the will and conditions for continuous quality improvement” (p. 23).
After a survey of related literature, it is proposed that there are three key elements to being an effective follower in organizational environments. The first is work-related knowledge, especially creative and critical thinking skills. The major role of a follower is to assist a leader to make informed decisions. Continue reading »

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