12. Informal definitions: production frontier The production frontier represents the maximum output attainable from each input level Hence, it reflects the current state of technology in the industry The dual relationship between production and cost functions means that it is also possible to specify and measure the cost frontier ECON377/477 Topic 1.1 5
13. Feasible production set A feasible production set is the set of all input-output combinations that are feasible This set consists of all points between the production frontier and the input (x) axis, inclusive of these bounds The points along the production frontier define the efficient subset of this feasible production set Note that this definition of the production set assumes free disposability of inputs and outputs 6 ECON377/477 Topic 1.1
14. Informal definitions: productivity The productivity of a firm is the ratio of the output(s) that it produces to the input(s) that it uses: productivity = outputs/inputs When the production process involves a single input and a single output, this calculation is a trivial matter However, when there is more than one input, a method for aggregating these inputs into a single index of inputs must be used to obtain a ratio measure of productivity 7 ECON377/477 Topic 1.1
15. Informal definitions: TFP Total factor productivity (TFP) is a productivity measure involving all factors of production TFP also includes all outputs in a multiple-output setting Other traditional measures of productivity, such as labour productivity in a factory, fuel productivity in power stations and land productivity (yield) in farming, are often called partial measures of productivity These partial productivity measures can provide a misleading indication of overall productivity when considered in isolation 8 ECON377/477 Topic 1.1
16. Informal definitions: technical efficiency Firms operate either on the production frontier, if they are technically efficient, or beneath the frontier, if they are not technically efficient Point A in the next slide represents an inefficient firm whereas points B and C represent efficient firms A firm operating at point A is inefficient because technically it could increase output to the level associated with the point B without requiring more input (output orientation) Or it could reduce input use to point C without reducing output (input orientation) 9 ECON377/477 Topic 1.1
19. Informal definitions: technical efficiency Point A in the next slide represents an inefficient point above the cost frontier, measured by an isoquant (assuming input prices are given), whereas point B represents an efficient point on the cost frontier A firm operating at point A is inefficient because technically it could reduce input use to the level associated with the point B without being required to alter its output Labour input declines from L1 to L2 and capital input declines from K1 to K2 12 ECON377/477 Topic 1.1
20. Labour A L1 B L2 Frontier isoquant K1 K2 0 Capital 13 ECON377/477 Topic 1.1
21. Allocative efficiency To this point, all discussion has involved physical quantities and technical relationships We have not discussed concepts such as costs and profits If information on prices is available, and a behavioural assumption such as cost minimisation or profit maximisation is appropriate, then performance measures can be devised that incorporate this information 14 ECON377/477 Topic 1.1
22. Allocative efficiency Allocative efficiency in input selection involves selecting that mix of inputs (for example, labour and capital) that produces a given quantity of output at minimum cost (given input prices) Allocative and technical efficiency combine to provide an overall economic efficiency measure On the next slide, points B and C are both technically efficient but only point C is economically efficient (that is, both technically and allocatively efficient) 15 ECON377/477 Topic 1.1
23. technically and allocatively inefficient Labour technically efficient but allocatively inefficient A B technically and allocatively efficient C Frontier isoquant Isocost curve Capital 0 ECON377/477 Topic 1.1 16
24. Technical change When one considers productivity comparisons through time, an additional source of productivity change, called technological change, is possible This involves advances in technology that may be represented by an upward shift in the production frontier, depicted on the next slide by the movement from 0F0 in period 0 to 0F1 in period 1 In period 1, all firms can technically produce more output for each level of input, relative to what was possible in period 0 ECON377/477 Topic 1.1 17
26. Scale economies By moving to point C, the ray from the origin is at a tangent to the production frontier and hence defines the point of maximum possible productivity This movement is an example of exploiting scale economies as C is the point of (technically) optimal scale A firm may be technically efficient (for example, point B) but may still be able to improve its productivity by exploiting scale economies 19 ECON377/477 Topic 1.1
27. Output F B Optimal scale C A 0 Input 20 ECON377/477 Topic 1.1
32. Overview of methods The first two methods are most often applied to aggregate time-series data and provide measures of technical change and/or TFP Both of these methods assume all firms are technically efficient 22 ECON377/477 Topic 1.1
33. Overview of methods Methods 3 and 4, on the other hand, are most often applied to data on a sample of firms (at one point in time) and provide measures of relative efficiency among those firms Hence, these latter two methods do not assume that all firms are technically efficient 23 ECON377/477 Topic 1.1
34. Overview of methods However, multilateral TFP indices can also be used to compare the relative productivity of a group of firms at one point in time Also, DEA and stochastic frontiers can be used to measure both technical change and technical efficiency change if panel data are available Thus, the methods can be grouped according to whether they recognise technical inefficiency or not 24 ECON377/477 Topic 1.1
35. Overview of methods An alternative way of grouping the methods is to note that methods 1 and 4 involve the econometric estimation of parametric functions, while methods 2 and 3 do not These two groups may therefore be termed ‘parametric’ and ‘non-parametric’ methods, respectively But note that recent estimation innovations such as bootstrapping have blurred the distinction between ‘parametric’ and ‘non-parametric’ methods 25 ECON377/477 Topic 1.1
36. Overview of methods These methods may also be distinguished in several other ways, such as by their data requirements, their behavioural assumptions and by whether or not they recognise random errors in the data (that is, noise) These differences are discussed in later chapters 26 ECON377/477 Topic 1.1
37. Chapter 2 Review of production economics Production economics is reviewed, including a discussion of the various ways in which one can provide a functional representation of a production technology Production, cost, revenue and profit functions are presented, and information is provided on their properties and dual relationships A variety of production economics concepts, such as elasticities of substitution and returns to scale, are reviewed 27 ECON377/477 Topic 1.1
38. Chapter 3 Productivity and efficiency measurement concepts Alternative uses of set constructs to define production technologies are described The concept of a distance function is introduced to help define a number of efficiency measurement concepts Formal definitions are given of concepts such as technical efficiency, allocative efficiency, scale efficiency, technical change and TFP change 28 ECON377/477 Topic 1.1
39. Chapter 4 Index numbers and productivity measurement A description is given of the Laspeyres, Paasche, Tornqvist and Fisher index numbers An explanation is given why they may be preferred when calculating indices of input and output quantities and TFP The economic theory underlying index number methods is discussed, and the various axioms that index numbers should ideally possess are outlined 29 ECON377/477 Topic 1.1
40. Chapter 5 Data and measurement issues A range of issues relating to the collection of data on inputs and outputs are discussed, covering topics such as quality variations, capital measurement, cross-sectional and time-series data, constructing implicit quantity measures using price-deflated value aggregates, aggregation issues, international comparisons, environmental differences and overheads allocation The index number concepts introduced in Chapter 4 are used regularly in this discussion 30 ECON377/477 Topic 1.1
41. Chapter 6 Data envelopment analysis Data envelopment analysis (DEA) is introduced in this chapter It is the mathematical programming approach to the estimation of frontier functions and the calculation of efficiency measures Forms of DEA models are discussed: input- and output-orientated models under the assumptions of constant returns to scale and variable returns to scale These methods are illustrated using simple numerical examples 31 ECON377/477 Topic 1.1
42. Chapter 7 Additional DEA topics Further discussion of DEA models is provided on the issues of allocative efficiency, short-run models, environmental variables, the treatment of slacks, super-efficiency measures and weights restrictions A detailed empirical application is undertaken 32 ECON377/477 Topic 1.1
43. Chapter 8 Econometric estimation of production technologies An overview is given of the main econometric methods used to estimate economic relationships, with an emphasis on production and cost functions Much of the discussion is useful background for the stochastic frontier methods discussed in the following two chapters Data on rice farmers in the Philippines are used to illustrate a number of models 33 ECON377/477 Topic 1.1
44. Chapter 9 Stochastic frontier analysis The basic stochastic frontier model is introduced and illustrated in this chapter, using a simple example Topics covered include maximum likelihood estimation, efficiency prediction and hypothesis testing The rice farmer data from Chapter 8 are used to illustrate a number of models 34 ECON377/477 Topic 1.1
45. Chapter 10 Additional topics on stochastic frontier analysis Discussion of stochastic frontiers is extended in this final chapter to cover topics such as allocative efficiency, panel data models, the inclusion of environmental and management variables, risk modelling and Bayesian methods The rice farmer data from Chapter 8 are used to illustrate a number of models 35 ECON377/477 Topic 1.1
