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Productivity describes various measures of the efficiency of
production. A productivity measure is expressed as the ratio of output to inputs used in a production process, i.e. output per unit of input. Productivity is a crucial factor in production performance of firms and nations. Increasing national productivity can raise living standards because more
real income improves people's ability to purchase goods and services, enjoy leisure, improve housing and education and contribute to social and environmental programs. Productivity growth also helps businesses to be more profitable.
[1] There are many different definitions of productivity and the choice among them depends on the purpose of the productivity measurement and/or data availability.
Partial productivity[edit]
Productivity measures that use one class of inputs or
factors, but not multiple factors, are called partial productivities.
[2] In practice, measurement in production means measures of partial productivity. Interpreted correctly, these components are indicative of productivity development, and approximate the efficiency with which inputs are used in an economy to produce goods and services. However, productivity is only measured partially – or approximately. In a way, the measurements are defective because they do not measure everything, but it is possible to interpret correctly the results of partial productivity and to benefit from them in practical situations. At the company level, typical partial productivity measures are such things as worker hours, materials or energy used per unit of production.
[2]
Before widespread use of computer networks, partial productivity was tracked in tabular form and with hand-drawn graphs.
Tabulating machines for data processing began being widely used in the 1920s and 1930s and remained in use until mainframe computers became widespread in the late 1960s through the 1970s. By the late 1970s inexpensive computers allowed industrial operations to perform
process control and track productivity. Today data collection is largely computerized and almost any variable can be viewed graphically in real time or retrieved for selected time periods.
Labor productivity[edit]
Labour productivity levels in 2012 in Europe.
OECD
Comparison of average labor productivity levels between the
OECD member states. Productivity is measured as GDP per hour worked. Blue bars = higher than OECD-average productivity. Yellow bars = lower than average.
In macroeconomics, a common partial productivity measure is
labour productivity. Labour productivity is a revealing indicator of several economic indicators as it offers a dynamic measure of economic growth, competitiveness, and living standards within an economy. It is the measure of labour productivity (and all that this measure takes into account) which helps explain the principal economic foundations that are necessary for both economic growth and social development. In general labour productivity is equal to the ratio between a measure of output volume (gross domestic product or gross value added) and a measure of input use (the total number of hours worked or total employment).
The output measure is typically net output, more specifically the
value added by the process under consideration, i.e. the value of outputs minus the value of intermediate inputs. This is done in order to avoid double-counting when an output of one firm is used as an input by another in the same measurement.
[3] In macroeconomics the most well-known and used measure of value-added is the
Gross Domestic Product or GDP. It is widely used as a measure of the economic growth of nations and industries. GDP is the income available for paying capital costs, labor compensation, taxes and profits.(OECD 2008,11) Some economists instead use
gross value added (GVA); there is normally a strong correlation between GDP and GVA. (Freeman 2008,5)
The measure of input use reflects the time, effort and skills of the workforce. Denominator of the ratio of labour productivity, the input measure is the most important factor that influences the measure of labour productivity. Labour input is measured either by the total number of hours worked of all persons employed or total employment (head count). (Freeman 2008,5) There are both advantages and disadvantages associated with the different input measures that are used in the calculation of labour productivity. It is generally accepted that the total number of hours worked is the most appropriate measure of labour input because a simple headcount of employed persons can hide changes in average hours worked and has difficulties accounting for variations in work such as a
part-time contract,
leave of absence,
overtime, or shifts in normal hours. However, the quality of hours-worked estimates is not always clear. In particular, statistical establishment and household surveys are difficult to use because of their varying quality of hours-worked estimates and their varying degree of international comparability.
GDP per capita is a rough measure of average living standards or economic well-being and is one of the core indicators of economic performance. (OECD 2008, 14) GDP is, for this purpose, only a very rough measure. Maximizing GDP, in principle, also allows maximizing capital usage. For this reason GDP is systematically biased in favour of capital intensive production at the expense of knowledge and labour-intensive production. The use of capital in the GDP-measure is considered to be as valuable as the production’s ability to pay taxes, profits and labor compensation. The bias of the GDP is actually the difference between the GDP and the producer income. (Saari 2011,10,16)
Another labour productivity measure, output per worker, is often seen as a proper measure of labour productivity, as here: “Productivity isn't everything, but in the long run it is almost everything. A country's ability to improve its standard of living over time depends almost entirely on its ability to raise its output per worker.“
[4] This measure (output per worker) is, however, more problematic than the GDP or even invalid because this measure allows maximizing all supplied inputs, i.e. materials, services, energy and capital at the expense of producer income.
[citation needed]
Multi-factor productivity[edit]
Trends in U.S. productivity from labor, capital and multi-factor sources over the 1987-2014 period.
When multiple inputs are considered, the measure is called Multi Factor Productivity or MFP.
[3] Multifactor productivity is typically estimated using
growth accounting. If the inputs specifically are labor and capital, and the outputs are
value added intermediate outputs, the measure is called
total factor productivity or TFP. TFP measures the residual growth that cannot be explained by the rate of change in the services of labour, capital and intermediate outputs. MFP replaced the term TFP used in the earlier literature, and both terms continue in use (usually interchangeably) (Hulten 2009,7).
TFP is often interpreted as a rough average measure of productivity, more specifically the contribution to economic growth made by factors such as technical and organisational innovation. (OECD 2008,11). The most famous description is that of Solow’s (1957): ”I am using the phrase ’technical change’ as a shorthand expression for any kind of shift in the production function. Thus slowdowns, speed ups, improvements in the education of the labor force and all sorts of things will appear as ’technical change’ ”. The original MFP model (Solow 1957) involves several assumptions: that there is a stable functional relation between inputs and output at the economy-wide level of aggregation, that this function has neoclassical smoothness and curvature properties, that inputs are paid the value of their marginal product, that the function exhibits constant returns to scale, and that technical change has the Hicks’n neutral form (Hulten, 2009,5). In practice, TFP is "a measure of our ignorance", as Abramovitz (1956) put it, precisely because it is a residual. This ignorance covers many components, some wanted (like the effects of technical and organizational innovation), others unwanted (measurement error, omitted variables, aggregation bias, model misspecification) (Hulten 2000,11). Hence the relationship between TFP and productivity remains unclear.
Accounting procedure[edit]
Accounting procedure of MFP (Saari 2012)
The MFP measure can be compactly introduced with an accounting procedure in the following calculation. We can use the fixed price values of the real process in the
production model to show the accounting procedure. Fixed price values of the real process depict commensurate volumes of the outputs and inputs. When we subtract from the output the intermediate inputs we obtain the value-added. Value-added is used as an output in MFP measure. The principle is to compare the growth of the value-added to the growth of labour and capital input. The formula of the MFP growth is as follows (Schreyer 2005,7):
- change of MFP = change of output (1.119)
- minus change of labour input x cost share of labour (1.150 x 0.475 = 0.546)
- minus change of capital input x cost share of capital (1.030 x 0.525 = 0.541)
As an accounting result the MFP growth is 1.119-0.546-0.541=0.032 or 3.2%.
Total productivity[edit]
When all outputs and inputs are included in the productivity measure it is called total productivity. Total productivity is a measure of total efficiency of a production process and as such is often presented as the objective to be maximized in a production process such as a business.
[2] Compared to total productivity, the MFP model replaces real income with the capital usage by assuming they are equal. The reason of this modification is not known nor argued but it weakens the validity of the measure.
Davis has deliberated
[5] the phenomenon of productivity, measurement of productivity, distribution of productivity gains, and how to measure such gains. He refers to an article
[6] suggesting that the measurement of productivity shall be developed so that it ”will indicate increases or decreases in the productivity of the company and also the distribution of the ’fruits of production’ among all parties at interest”. According to Davis, the price system is a mechanism through which productivity gains are distributed, and besides the business enterprise, receiving parties may consist of its customers, staff and the suppliers of production inputs.
Benefits of productivity growth[edit]
Labour productivity growth in Australia since 1978, measured by GDP per hour worked (indexed)
Productivity growth is a crucial source of growth in living standards. Productivity growth means more value is added in production and this means more income is available to be distributed.
At a firm or industry level, the benefits of productivity growth can be distributed in a number of different ways:
- to the workforce through better wages and conditions;
- to shareholders and superannuation funds through increased profits and dividend distributions;
- to customers through lower prices;
- to the environment through more stringent environmental protection; and
- to governments through increases in tax payments (which can be used to fund social and environmental programs).
Productivity growth is important to the firm because it means that it can meet its (perhaps growing) obligations to workers, shareholders, and governments (taxes and regulation), and still remain competitive or even improve its competitiveness in the market place. Adding more inputs will not increase the income earned per unit of input (unless there are increasing returns to scale). In fact, it is likely to mean lower average wages and lower rates of profit. But, when there is productivity growth, even the existing commitment of resources generates more output and income. Income generated per unit of input increases. Additional resources are also attracted into production and can be profitably employed.
Drivers of productivity growth[edit]
In the most immediate sense, productivity is determined by the available technology or know-how for converting resources into outputs, and the way in which resources are organized to produce goods and services. Historically, productivity has improved through
evolution as processes with poor productivity performance are abandoned and newer forms are exploited. Process improvements may include organizational structures (e.g. core functions and supplier relationships), management systems, work arrangements, manufacturing techniques, and changing market structure. A famous example is the
assembly line and the process of
mass production that appeared in the decade following commercial introduction of the automobile.
[7]
Mass production dramatically reduced the labor in producing parts for and assembling the automobile, but after its widespread adoption productivity gains in automobile production were much lower. A similar pattern was observed with
electrification, which saw the highest productivity gains in the early decades after introduction. Many other industries show similar patterns. The pattern was again followed by the computer, information and communications industries in the late 1990s when much of the national productivity gains occurred in these industries.
[8]
There is a general understanding of the main determinants or drivers of productivity growth. Certain factors are critical for determining productivity growth.
The Office for National Statistics (UK) identifies five drivers that interact to underlie long-term productivity performance: investment, innovation, skills, enterprise and competition. (ONS 3, 20)
- Investment is in physical capital — machinery, equipment and buildings. The more capital workers have at their disposal, generally the better they are able to do their jobs, producing more and better quality output.
- Innovation is the successful exploitation of new ideas. New ideas can take the form of new technologies, new products or new corporate structures and ways of working. Speeding up the diffusion of innovations can boost productivity.
- Skills are defined as the quantity and quality of labour of different types available in an economy. Skills complement physical capital, and are needed to take advantage of investment in new technologies and organisational structures.
- Enterprise is defined as the seizing of new business opportunities by both start-ups and existing firms. New enterprises compete with existing firms by new ideas and technologies increasing competition. Entrepreneurs are able to combine factors of production and new technologies forcing existing firms to adapt or exit the market.
- Competition improves productivity by creating incentives to innovate and ensures that resources are allocated to the most efficient firms. It also forces existing firms to organise work more effectively through imitations of organisational structures and technology.
Individual and team productivity[edit]
Technology has enabled massive personal productivity gains — computers, spreadsheets, email, and other advances have made it possible for a knowledge worker to seemingly produce more in a day then was previously possible in a year.
[9] Environmental factors such as
sleep and
leisure play a significant role in work productivity and received wage.
[10] Drivers of productivity growth for creative and knowledge workers include improved or intensified exchange with peers or co-workers, as more productive peers have a stimulating effect on one's own productivity.
[11] [12] Productivity is influenced by effective supervision and job satisfaction. Having an effective or knowledgeable supervisor (for example a supervisor who uses the
Management by objectives method) has an easier time motivating their employees to produce more in quantity and quality. An employee who has an effective supervisor, motivating them to be more productive is likely to experience a new level of job satisfaction thereby becoming a driver of productivity itself.
[13]
Detrimental impact of bullying, incivility, toxicity and psychopathy[edit]
Workplace bullying results in a loss of productivity, as meaured by self-rated
job performance.
[14] Over time, targets of bullying will spend more time protecting themselves against harassment by bullies and less time fulfilling their duties.
[15] Workplace incivility has also been associated with diminished productivity in terms of quality and quantity of work.
[16]
A
toxic workplace is a workplace that is marked by significant drama and infighting, where personal battles often harm productivity.
[17] While employees are
distracted by this, they cannot devote time and attention to the achievement of business goals.
[18] When toxic employees leave the workplace, it can improve the
culture overall because the remaining staff become more engaged and productive.
[19] The presence of a
workplace psychopath may have a serious detrimental impact on productivity in an organisation.
[20]
In companies in where the
traditional hierarchy has been removed in favor of an egalitarian, team-based setup, the employees are often happier, and individual productivity is improved (as they themselves are better placed to
increase the efficiency of the workfloor). Companies that have these hierarchy removed and have their employees work more in teams are called
Liberated companies or "Freedom inc.'s".
[21][22][23][24][25] See also:
The Toyota Way
Business productivity[edit]
Productivity is one of the main concerns of business management and engineering. Many companies have formal programs for continuously improving productivity, such as a
production assurance program. Whether they have a formal program or not, companies are constantly looking for ways to improve quality, reduce downtime and inputs of labor, materials, energy and purchased services. Often simple changes to operating methods or processes increase productivity, but the biggest gains are normally from adopting new technologies, which may require capital expenditures for new equipment, computers or software. Modern productivity science owes much to formal investigations that are associated with
scientific management.
[26] Although from an individual management perspective, employees may be doing their jobs well and with high levels of individual productivity, from an organizational perspective their productivity may in fact be zero or effectively negative if they are dedicated to redundant or value destroying activities.
[9]
Productivity paradox[edit]
Overall productivity growth was relatively slow from the 1970s through the early 1990s.
[27] Although several possible causes for the slowdown have been proposed there is no consensus. The matter is subject to a continuing debate that has grown beyond questioning whether just computers can significantly increase productivity to whether the potential to increase productivity is becoming exhausted.
[28]
National productivity[edit]
In order to measure productivity of a nation or an industry, it is necessary to
operationalize the same concept of productivity as in a production unit or a company, yet, the object of modelling is substantially wider and the information more aggregate. The calculations of productivity of a nation or an industry are based on the time series of the SNA,
System of National Accounts. National accounting is a system based on the recommendations of the UN (SNA 93) to measure total production and total income of a nation and how they are used. (Saari 2006, 9)
International or national productivity growth stems from a complex interaction of factors. Some of the most important immediate factors include technological change, organizational change, industry restructuring and resource reallocation, as well as economies of scale and scope. A nation's average productivity level can also be affected by the movement of resources from low-productivity to high-productivity industries and activities. Over time, other factors such as research and development and innovative effort, the development of human capital through education, and incentives from stronger competition promote the search for productivity improvements and the ability to achieve them. Ultimately, many policy, institutional and cultural factors determine a nation's success in improving productivity.
At the national level, productivity growth raises living standards because more real income improves people's ability to purchase goods and services (whether they are necessities or luxuries), enjoy leisure, improve housing and education and contribute to social and environmental programs. Some have suggested that the UK's 'productivity puzzle' is an urgent issue for policy makers and businesses to address in order to sustain growth.
[citation needed] Over long periods of time, small differences in rates of productivity growth compound, like interest in a bank account, and can make an enormous difference to a society's prosperity. Nothing contributes more to reduction of poverty, to increases in leisure, and to the country's ability to finance education, public health, environment and the arts’.
[29]
Productivity is considered basic statistical information for many international comparisons and country performance assessments and there is strong interest in comparing them internationally. The OECD
[30] publishes an annual Compendium of Productivity Indicators
[31] that includes both labor and multi-factor measures of productivity. Several statistical offices publish productivity accounting handbooks and manuals with detailed accounting instructions and definitions. For example, the following:
Validity[edit]
Validity is a characteristic of the measure which is used in measuring. Validity implies how exact information the used measure can generate from the phenomenon. We need to understand the phenomenon, the measure and the possible difference between them. Often when we aim at simplicity and understandability in measuring, we have to lower the requirements for validity. For this reason it is important to evaluate the validity of the measurements used, case by case. Good measuring presupposes that those responsible for measuring are familiar with the validity of the measurements and also keep users informed of the validity. In order to evaluate validity of any measure we need to understand the phenomenon, the measure and the possible difference between them. In the case of productivity we cannot make this evaluation in a traditional way because the phenomenon intended to be measured is somewhat unclear. Instead we can identify the differences between models.
[citation needed]
See also[edit]
- Jump up ^ Courbois & Temple 1975, Gollop 1979, Kurosawa 1975, Pineda 1990, Saari 2006
- ^ Jump up to: a b c Sumanth, David J. Total Productivity Management (TPmgt): A Systemic and Quantitative Approach to Compete in Quality, Price and Time. CRC Press. p. 5. ISBN 9781574440577. Retrieved 11 March 2017.
- ^ Jump up to: a b "Multifactor Productivity - Overview". Bureau of Labor Statistics. U.S. Department of Labor. Retrieved 11 March 2017.
- Jump up ^ Paul Krugman (1994). The Age of Diminishing Expectations. MIT Press.
- Jump up ^ Davis, 1955
- Jump up ^ 1947, Journal of Accountancy, Feb. p. 94
- Jump up ^ Field, Alexander (2004). "Technological Change and Economic Growth the Interwar Years and the 1990s" (PDF).
- Jump up ^ Ayres, Robert U.; Warr, Benjamin (2006). "Economic growth, technological progress and energy use in the U.S. over the last century: Identifying common trends and structural change in macroeconomic time series, INSEAD" (PDF).
- ^ Jump up to: a b Fuller, Ryan (19 April 2016). "The Paradox of Workplace Productivity".
- Jump up ^ Gibson, Matthew; Shrader, Jeffrey (14 July 2014). "Time Use and Productivity: The Wage Returns to Sleep". eScholarship. Retrieved 11 March 2017.
- Jump up ^ Borowiecki, Karol J. "Geographic clustering and productivity: An instrumental variable approach for classical composers" "Journal of Urban Economics", 2013, 73: 94-110
- Jump up ^ Borowiecki, Karol J. "Agglomeration Economies in Classical Music" "Papers in Regional Science", 2015, 94(3): 443-68
- Jump up ^ Thompson, K.R., & And., 0. "The Effects of MBO on Performance and Satisfaction in a Public Sector Organization" "Journal of Management", 1981
- Jump up ^ Helge H, Sheehan MJ, Cooper CL, Einarsen S "Organisational Effects of Workplace Bullying" in Bullying and Harassment in the Workplace: Developments in Theory, Research, and Practice (2010)
- Jump up ^ Fisher-Blando, J. L. (2008). Workplace bullying: Aggressive behavior and its effect on job satisfaction and productivity (Unpublished doctoral dissertation). University of Phoenix
- Jump up ^ "9 signs your work place needs civility, 6 steps to achieve it - TechJournal". Retrieved 25 September 2014.
- Jump up ^ Benoit, Suzanne (2011) "Toxic Employees: great companies resolve this problem, you can too!" Falmouth, Maine: BCSPublishing
- Jump up ^ Bitting, Robert. "Using Effective Leadership Strategies in the Workplace". http://www.robertbitting.com/files/articles/Toxic-Employees-in-the-Work-Place.pdf. Retrieved May 13, 2011.
- Jump up ^ Mayhew, Ruth "Is employee turnover always bad?" accessed at: http://smallbusiness.chron.com/employee-turnover-always-bad-11089.html
- Jump up ^ Boddy, C. R. (2010) ‘Corporate Psychopaths and Productivity', Management Services Spring, 26–30.
- Jump up ^ Free Inc. terminology and list of companies
- Jump up ^ L'entreprise liberée
- Jump up ^ Holacracy
- Jump up ^ Poult system
- Jump up ^ SEMCO
- Jump up ^ Nelson, Daniel (1980). Frederick W. Taylor and the Rise of Scientific Management. University of Wisconsin Press. ISBN 978-0299081607.
- Jump up ^ Brynjolfsson, Erik (1993). "The productivity paradox of information technology". Communications of the ACM. 36 (12): 66–77. ISSN 0001-0782. doi:10.1145/163298.163309.
- Jump up ^ Zelenyuk (2014) "Testing Significance of Contributions in Growth Accounting, with Application to Testing ICT Impact on Labor Productivity of Developed Countries" International Journal of Business and Economics 13:2, pp. 115-126.
- Jump up ^ Alan Blinder and William Baumol 1993, Economics: Principles and Policy, Harcourt Brace Jovanovich, San Diego, p. 778.
- Jump up ^ http://stats.oecd.org/Index.aspx?DataSetCode=LEVEL
- Jump up ^ Compendium of Productivity Indicators, OECD
References[edit]
- Abramovitz, M (May 1956). "Resource and Output Trends in the United States since 1870" (PDF). American Economic Review. NATIONAL BUREAU OF ECONOMIC RESEARCH. 46 (2): 5–23.
- Bechler, J.G (1984). "The Productivity Management Process". American Productivity Center.
- Courbois, R.; Temple, P. (1975). La methode des "Comptes de surplus" et ses applications macroeconomiques. 160 des Collect,INSEE,Serie C (35). p. 100.
- Craig, C.; Harris, R. (1973). "Total Productivity Measurement at the Firm Level". Sloan Management Review (Spring 1973): 13–28.
- Davis, H.S. (1955). Productivity Accounting. University of Pennsylvania.
- Freeman, R. (2008). Labour productivity indicators (PDF). OECD.
- Genesca, G.E.; Grifell, T. E. (1992). "Profits and Total Factor Productivity: A Comparative Analysis". Omega. the International Journal of Management Science. 20 (5/6): 553–568. doi:10.1016/0305-0483(92)90002-O.
- Gollop, F.M. (1979). "Accounting for Intermediate Input: The Link Between Sectoral and Aggregate Measures of Productivity Growth". Measurement and Interpretation of Productivity. National Academy of Sciences.
- Hulten, C.R. (January 2000). "TOTAL FACTOR PRODUCTIVITY: A SHORT BIOGRAPHY" (PDF). NATIONAL BUREAU OF ECONOMIC RESEARCH. doi:10.3386/w7471.
- Hulten, C.R. (September 2009). "GROWTH ACCOUNTING" (PDF). NATIONAL BUREAU OF ECONOMIC RESEARCH. doi:10.3386/w15341.
- Jorgenson, D.W.; Griliches, Z. (1967). "The Explanation of Productivity Change". Review of Economic Studies. 34 (99): 249–283. JSTOR 2296675. doi:10.2307/2296675.
- Jorgenson, D.W.; Ho, M.S.; Samuels, J.D. (2014). Long-term Estimates of U.S. Productivity and Growth (PDF). Tokyo: Third World KLEMS Conference.
- Kendrick, J.; Creamer, D. (1965). "Measuring Company Productivity: A handbook with Case Studies" (89). The National Industry Productivity Board.
- Kendrick, J.W. (1984). Improving Company Productivity. The Johns Hopkins University Press.
- Kohli, U (2012). Productivity: National vs. Domestic (PDF). Sydney, Australia: EMG Workshop, University of New South Wales, November 21–23, 2012.
- Kurosawa, K (1975). "An aggregate index for the analysis of productivity". Omega. 3 (2): 157–168. doi:10.1016/0305-0483(75)90115-2.
- Loggerenberg van, B.; Cucchiaro, S. (1982). "Productivity Measurement and the Bottom Line". National Productivity Review. 1 (1): 87–99. doi:10.1002/npr.4040010111.
- Mundel, M.E. (1983). Improving Productivity and Effectiveness. Prentice-Hall, Inc.
- OECD (2008). Compendium of Productivity Indicators 2008. OECD.
- ONS 3 (Office for National Statistics, UK). Productivity Theory and Drivers.
- Pineda, A. (1990). A Multiple Case Study Research to Determine and respond to Management Information Need Using Total-Factor Productivity Measurement (TFPM). Virginia Polytechnic Institute and State University.
- Riistama, K.; Jyrkkiö E. (1971). Operatiivinen laskentatoimi (Operative accounting). Weilin + Göös. p. 335.
- Saari, S. (2006a). Productivity. Theory and Measurement in Business. Productivity Handbook (In Finnish). MIDO OY. p. 272.
- Saari, S. (2011). Production and Productivity as Sources of Well-being. MIDO OY. p. 25.
- Saari, S. (2006). Productivity. Theory and Measurement in Business (PDF). Espoo, Finland: European Productivity Conference.
- Schreyer, P. (2005). Measuring Productivity (PDF). Tokyo: OECD.
- Solow, R.N. (August 1957). "Technical Change and the Aggregate Production Function" (PDF). The Review of Economics and Statistics. NATIONAL BUREAU OF ECONOMIC RESEARCH. 39 (3): 312–320. doi:10.2307/1926047.
- Vygotsky, L. (1962). Thought and Language. MIT Press (original work 1934).
Further reading[edit]
- Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73–86, March.
- Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, vol. 50(6), pages 1393-1414, November.
- Alexandra Daskovska & Léopold Simar & Sébastien Bellegem, 2010. "Forecasting the Malmquist productivity index," Journal of Productivity Analysis, Springer, vol. 33(2), pages 97–107, April.
- Färe, R., Grosskopf, S., Norris, M., & Zhang, Z. 1994. Productivity growth, technical progress, and efficiency change in industrialized countries. The American Economic Review 84, pages 66–83.
- Simar, Leopold & Wilson, Paul W., 1999. "Estimating and bootstrapping Malmquist indices," European Journal of Operational Research, Elsevier, vol. 115(3), pages 459-471, June. ]
- Mayer, A. and Zelenyuk, V. 2014. "Aggregation of Malmquist productivity indexes allowing for reallocation of resources," European Journal of Operational Research, Elsevier, vol. 238(3), pages 774-785.
- Zelenyuk, V. 2006. "Aggregation of Malmquist productivity indexes," European Journal of Operational Research, vol. 174(2), pages 1076-1086.
External links[edit]