Heed the Weakest Link : A Model of Interdependent Institutions
Furthermore , we introduce a multiplicative nature for the interactions of institutions , instead of an additive nature , because failure in any one dimension could have serious consequences for the entire system ( in analogy to the chain snapping at its weakest link ). Interestingly enough , this implies that while success is a collective action , failure is more easily seen to be due to certain specific factors .
Proposition 2 : Since each institution has a proportional influence on the overall outcome , we adopt a multiplicative ( rather than additive ) specification to account for the high degree of interdependence .
The overall economic output Y , measured in terms of GDP per capita , can therefore be represented by the product of each individual institutional dimension , and can be written as follows :
Hence we obtain a lognormal distribution of GDP per capita :
( Incidentally , Equation ( 2 ) resembles the usual regression specification adopted by empirical investigations into the determinants of economic growth .)
Since the log ( xi ) are i . i . d . distributed , Central Limit Theorem implies that Log ( Y ) is normally distributed , and hence that GDP per capita is lognormally distributed .
3.2 A Numerical Example
Table 2 helps to further illustrate the multiplicative specification .
Consider the case where an economy has three high-performance institutions ( scoring 0.9 ) and one low-performing institution ( scoring 0.1 ). In this model , this economy will perform worse than an economy with medium-performance institutions ( scoring 0.6 in each dimension ) even if the sum of resources in the first economy ( 0.9 + 0.9 + 0.9 + 0.1 = 2.8 ) is higher than the sum of resources available in the second economy ( 0.6 + 0.6 + 0.6 + 0.6 = 2.4 ).
To summarize Table 1 : if all relevant dimensions score highly , the business will succeed . If all but one relative dimension scores highly , but one dimension performs very poorly , the business will have great difficulties . If , however , each dimension has an intermediate score , the business will do better than in the previous scenario .
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