This quantity index satisfies some of Fishers 1922 important tests like

This quantity index satisfies some of fishers 1922

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This quantity index satisfies some of Fisher's (1922) important tests like homogeneity,time reversal, transitivity, and dimensionality.5
The index of bad outputs is constructed using an "input" distance function approach. Theargument is obvious, it is desirable to reduce such outputs. Thus the input based distancefunction is defined as})/,,(:sup{),,(TbyxbyxDb.This distance function is homogeneous of degree +1 in bad outputs, and it is defined byfinding the maximal contraction in these outputs. Given ),(00yx, the quantity index ofbad outputs compares kband lbagain using the ratios of distance functions i.e.,),,(),,(),,,(000000lbkblkbbyxDbyxDbbyxQ.Like the good index ),,,(00lkbbbyxQsatisfies the above mentioned Fisher tests.Next, following Färe, Grosskopf and Hernandez-Sancho (1999) we define theenvironmental performance index as the ratio of two quantity indexes, i.e.,),,,(),,,(),,,,,,(0000000.lkblkylklklkbbyxQyybxQbbyybyxE.This performance index follows the tradition of Hicks-Moorsteen4by evaluating howmuch good output is produced per bad output.In the simple case of one good and one bad output, the index takes the following simpleform due to homogeneity of the component distance functionsllkklkbybyE..This one bad one good index shows that the index is the ratio of average good per badoutput for kand l.6
3. Data and ResultsIn computing the environmental performance indicators for each of the OECD countriesin our sample, we chose aggregate output measured by Gross Domestic Product (GDP)expressed in international prices (1985 U.S. dollars) as the desirable output and carbondioxide emissions (in metric tons) and solid particulate matter (in kilograms) as the twoundesirable outputs. The two inputs considered are aggregate labor input as measured bytotal employment and total capital stock. The input and the desirable output data arecompiled from the Penn World Tables (PWT 5,6) initially derived from the InternationalComparison Program benchmark where cross-country and over time comparisons arepossible in real values5. Pollution related data are obtained from MonitoringEnvironmental Progress6. In developing the environmental performance index, we used time series data for theyears 1971-1990 for each of the OECD countries and constructed our index so that itcompares each year in the sample with the initial year 1971 which then takes a value ofunity.In computing the distance functions, we chose the data envelopment analysis (DEA) (oractivity analysis) methodology among competing alternatives, so as to take advantage ofthe fact that the distance functions are reciprocals of Farrell efficiency measures.In this particular application, we chose the initial year 1971 as our reference. Thus we areassuming that 0lwhich then refers to the associated quantities for 1971. We letKk,....,1index the years in the sample. Thus for each year Kk,......,1', we maycompute for each country7
KkzNnxzJjbbzMmyyzstbyxDkKkknkKkjkjkKkkmkmkky,......,10,....,1x,....,

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• Spring '14
• DanielKevles
• Environmental Economics, Per capita income, Random effects model, environmental performance, Environmental Performance Index