The economic performance of firms and the economic growth of countries have never been more important than in this historical epoch, both in terms of how labor services are being replaced with capital services and artificial intelligence algorithms and how the divergence in compensation to labor and capital services appears to be increasing. The outcome of such a dynamic has not only economic implications but also serious political repercussions, especially in our increasingly globalized and interconnected world.

If effective public policies can be formulated to address the many aspects of economic growth that impact individual welfare, they will be based on the methods and analyses we have detailed in this textbook as well as in the further developments of these methods and analyses as the science of productivity and efficiency measurement continues to advance. Public policies that address income growth and income inequality will need to be economically as well as politically sustainable. This means that they will need to take advantage of market mechanisms and the compatible incentives that drive the functioning and operation of competitive markets. Decision-makers will need to recognize that, for a variety of reasons, firms may not be forced by market mechanisms to make decisions on economic allocations that are optimal relative to standard economic definitions of optimizing behaviors. Whether this is due to long-standing market failures, protected market niches, institutional or other external constraints is not as important as the need for optimizing behaviors to be tested as the alternative hypothesis, not stated as the null hypothesis when conducting economic research. Researchers and scholars will need to understand how the economic well-being of individuals and the wealth of nations evolve and devolve. Practitioners will need to be able to implement methods that allow them to construct the economic measures that tell them if there is an improvement in economic well-being. As with any meaningful empirical measurement of an important public phenomenon such as growth in per capita income levels or growth in a country's income and the distribution of this growth among economic agents, public resources will need to be brought to bear to make accurate measurement possible and transparent.

In this chapter we briefly discuss some of the issues that arise when using standard index numbers as input quantity or price measures, as well as particular data sets that can be used in productivity research. In regard to the latter, we focus first on the World KLEMS project data and recent studies using it. These studies are based on modern approaches to productivity measurement using largely neoclassical approaches that assume perfectly competitive markets and frontier behaviors by firms, industries, and countries. We discuss in our summary of these papers how concepts we have put forth in our book speak to the topics and approaches used in these studies and how, in many ways, their frameworks and methods are closely aligned with modeling approaches and scenarios we have discussed in our earlier chapters. We then provide a short description of many other public use datasets and information on how to access them. Of course, it is important to be able to have accessible and easy to use software to analyze such data using methods we have discussed in this book. The software is detailed in the last section of this, our concluding chapter.

DATA MEASUREMENT ISSUES

The accurate modeling and measurement of the productivity growth determinants and their contributions in an aggregate economy, in its component industries, and in particular firms, has advanced considerably since the Jorgenson and Griliches (1967) seminal treatise on the measurement problems inherent in assessing productivity growth. However, the problems that Jorgenson and Griliches pointed out over 50 years ago are still with us, as noted in Chapter 4. Although major improvements in data collection and methodology have been incorporated in government and private-sector data collection protocols through the efforts of Jorgenson and Griliches and their many collaborators and colleagues, variations in the quality of data still affect the measurement and analysis of productivity growth. Such issues tend not to be discussed in applied work. Griliches (1994) summarized the potential measurement issues pertaining to productivity analysis, listing the following general problems and questions: 1. Coverage issues, definition of the borders of a sector, and the relevant concept of “output” for it. For example, is illegal activity included? Are pollution damages counted against the “output” of an industry?; 2. The difficulty in measuring “real” output over time as prices and the quality of output change; 3.

So far, we have focused on measuring the efficiency of an individualproduction or decision-making unit (firm, country, etc.) relative to a frontier consistent with a behavior of this unit. In practice, researchers are often also interested in measuring the efficiency of a groupof similar units (entire industry of firms, region of countries) or particular types of these units (e.g., public firms vs. private firms, etc.) within such groups. Even when the focus is on the efficiency of individual units, at the end of the day, researchers might want to have just one or several aggregate numbers that summarize the results. This is especially important when the number of individual units is large and each of them cannot be published or easily comprehended. But, how can we aggregate? Can we just take an average? Which one: arithmetic, geometric, harmonic? Shall it be a weighted or a non-weighted average? The goal of this chapter is to outline the recently obtained and practically useful results of previous studies to answer these imperative questions.

THE AGGREGATION PROBLEM

The problem of constructing a group measure or a group score from individual analogues is an aggregation question, which has been recently studied in a number of works. The most important question here is the choice of aggregation weights. To illustrate the point, consider a hypothetical example (adapted from Simar and Zelenyuk, 2007) of an industry consisting of four firms, two firms in each of two types, whose efficiency and “an economic weight” (whatever that might be) are summarized in Table 5.1. Here, if a researcher were to use the simple (equally weighted) arithmetic average then group A and group Z are, on average, equally efficient. Note however that the efficiency scores are “standardized” so that they are between 0 and 1 and so they disregard the relative weights of the firms that attained these scores. If another researcher wanted to use a weighted arithmetic average, then a dramatically different conclusion might be reached – depending on the weighting scheme. For the example, in Table 5.1, group A has a higher-weighted average efficiency than that of group Z, yet the industry average could still be closer to the score of group Z if its group weight dominates the weight of group A (e.g., if their weight in the industry is 90 percent as in the table).