New Directions

The format of this monograph is three essays, which we arrived at after spending a year writing over one hundred pages of what we even­ tually realized was a tedious reworking of old material. So we started over determined to write something new. At first we thought this approach might not work as a coherent mono­ graph, which is why we chose the essay format rather than chapters. As it turns out, there is a common thread-namely the directional distance function, which also gave us our title. As you shall see, the directional distance function includes traditional distance functions and efficiency measures as special cases providing a unifying framework for existing productivity and efficiency measures. It is also flexible enough to open up new areas in productivity and efficiency analysis such as environmen­ tal and aggregation issues. That we did not see this earlier is humbling; a student at a recent conference raised his hand and asked 'Why didn't you start with the directional distance function in the first place? In­ deed. This manuscript is intended to make up for our earlier oversights. This monograph contains papers coauthored with Wen-Fu Lee and Osman Zaim and one paper written by two former students, Hiroyuki Fukuyama and Bill Weber. We thank them for their contributions. An­ other former student, Jim Logan (Logi) read and critiqued the manu­ script for which we are grateful.

Efficiency Indicators And Indexes
. - The Nerlovian Profit Indicator. - The Revenue Efficiency Indicator. - Cost Efficiency Indicator. - Efficiency Indexes. - From Indicators to Indexes. - Hyperbolic Efficiency. - Remarks on the Literature. -
Environmental Performance
. - Good and Bad Outputs. - Productivity with Bads. - Environmental Quantity Index. - Shadow Pricing Undesirable Outputs. - Property Rights and Profitability. -
New Directions
. - Environmental Kuznets Curve. - Remarks on the Literature. -
Aggregation Issues
. - The Fox Paradox. - Koopmans Theorem. - Aggregating Indicators Across Firms. - Johansen Aggregation. - Aggregating Farrell Efficiency Indexes. - Luenberger Productivity Indicators. - Aggregation Across Inputs and Outputs. - Aggregation and Decompositions. - Performance in Japanese Banking. - Remarks on the Literature. -
Appendix: Axioms Of Production
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