Chapter Background

Measurement of efficiency in HE has been well explored in the literature for more than 20 years. The growing public concern regarding performance and efficiency measures in the HE sector can be explained by the massive expansion of the HE systems worldwide. Additionally, the financial constraints stemming from the current economic challenges associated with tight government budgets and increasing pressure for greater autonomy of HEIs have contribute to this end (Cunha and Rocha, 2012).

HE financial policy commonly goes hand in hand with numerous subsidies and grants supported by political authorities. The main aim of HEIs is to obtain at least some of their income from public funds; therefore, it is essential, in the interests of accountability, to measure inter- and intra-institutional efficiency (Johnes, 2005). The HE sector, however, has characteristics that make it difficult to assess efficiency: it is non-profit making; there is an absence of output and input prices; and HEIs produce multiple outputs from multiple inputs (Johnes, 2006).

Economic efficiency (EE) is concerned with the optimal production and distribution of scarce resources and measures, and whether those resources (i.e. agricultural research and extension, tertiary healthcare, and HE, etc.) are being used to get the best value for money. Both productivity and efficiency measures have been defined as the ratio between output and input (Sengupta, 1995; Cooper et al., 2000). However, instead of defining efficiency as the ratio between outputs and inputs, it can be seen as a distance between the quantity of input and output. In particular, the quantity of input and output defines a frontier, the optimal frontier for a DMU relative to other units of its cluster (Daraio and Simar, 2007).

More than 60 years ago, Key (1940) laid down a challenge for economists to resolve the ‘basic budgeting problem’, namely, the scarcity of public funds and public expenditure management (Fozzard, 2001). Such considerations feature efficiency as a methodological tool to explore the relation between resource inputs35 (i.e. costs, in the form of labour, non-labour expenditures in capital stock, buildings, equipment, and student services) and either intermediate36 _{outputs (average attainment scores at the end}

35 _{Intermediate or not.}

36 _{Economic evaluations should focus on final educational outcomes rather than intermediate outputs as a measure of efficiency,}

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of each key stage,37 _{university instruction hours, etc.) or final educational outcomes}

(degrees gained, number of credit hours, etc.). Solutions for the basic budgeting problem adopting the criterion of EE implies that resource allocation decisions are the result of technical analysis and political processes (Fozzard, 2001). Policymakers make choices that maximise the educational outcomes gained from the resources allocated to HE, stressing the importance of transparency in the process itself. Inefficiency exists when resources could be reallocated in a way that would further increase the educational outcomes attained.

Economic efficiency can be further discerned into different types, which are not exactly equivalent depending on the assumptions made for the optimal production, consumption, and distribution of scarce resources. The mutual assumption made in all these definitions of efficiency is the idea that a system is efficient if nothing more can be achieved given the available resources. The principal definition of productive efficiency encompasses the production of goods and services with the optimal combination of inputs38 to produce the maximum output for the minimum cost. To be productively efficient means that a firm must be producing on its production possibility frontier (i.e. it is impossible to produce more of one good without producing less of another). Thus, productive efficiency is concerned with producing at the lowest point on the short-run average cost curve.

Productive efficiency is closely related to the concept of technical efficiency, since productive efficiency requires technical efficiency. According to Farell (1957), technical efficiency (TE) reflects the ability of a firm to produce the maximum output from the minimum quantity of inputs, such as labour, capital, and technology. TE requires the input-output combinations be on the isoquant. Production cost efficiency requires TE, and the level of inputs used depends on the prices paid for the inputs (Wagner, 2012). However, a firm is said to be totally economically efficient only if it is technically efficient and, at the same time, allocatively efficient. This means that, apart from using the optimal proportions of inputs, a firm should also distribute the goods and services according to consumer preferences. A firm could be productively efficient but produce goods people do not need; this would be allocative inefficient. Therefore, the firm should reallocate production with strict boundaries on the respective prices and the production technology so that the price of the good should be equal to the marginal cost (MC) of production.39 _{In a formal representation, allocative efficiency}

(AE) is achieved when a firm employs factors of production up to the point at which the marginal rate of technical substitution between any two of its inputs equals the ratio of corresponding input prices (Huang and Wang, 2002).

A considerable body of literature exists on the measurement of TE in the HE sector (Worthington, 2001; Johnes, 2004; De Witte and López-Torres, 2015; Johnes, 2015;

37 _{For further details follow Garniss (2006): www.oecd.org/std/na/37562338.ppt} 38 _{Given amount of inputs.}

39 _{A more precise definition of AE is at an output level, where the price equals the MC of production. This is because the price}

that consumers are willing to pay is equivalent to the marginal utility that they get. Therefore, the optimal distribution is achieved when the marginal utility of the good equals the MC. Firms in perfect competition are said to produce at an allocatively efficient level, while monopolies can increase the price above the MC of production and are allocatively inefficient.

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Thanassoulis et al., 2016). Efficiency and productivity measures, as well as the Malmquist index, are concepts that have been analysed radically in the past decades in an attempt to assess the performance of universities. Early studies of TE in UK HE focused on individual departments such as accounting (Tomkins and Green, 1988), chemistry and physics (Beasley, 1990, 1995), economics (Johnes and Johnes 1993), and business schools (Doyleet al., 1996), or departments within a university (Sinuany-Stern et al., 1994).

Broadly speaking, two main camps have emerged for assessing efficiency among the proposed approaches. These are classified into parametric or econometric approaches and non-parametric techniques or programming approaches. Those that estimate maximal output and attribute all departures from this as inefficient are known as DEA,40

and those that allow for both unobserved variation in output due to shocks and measurement error as well as inefficiency are known as SFA (Parmeter and Kumbhakar, 2014).

Both methods seek to characterise and quantify notions of efficiency; however, they are fundamentally different in their construction and underlying assumptions. Given that each possesses its own strengths and limitations, neither is generally regarded to be superior to the other (Salerno, 2003). Lovell (1993) demonstrates a taxonomy of parametric and non-parametric methods, making the assumption that, when using statistical approaches, the functional form of the production possibility set is the link between inputs and outputs, while, in non-parametric techniques, the input and output data themselves are used to compute the production possibility frontier, by using linear programming methods.

More recently, DEA has been applied at the HEI level to produce measures of efficiency for all HEIs in the sector (Athanassopulos and Shale, 1997; Flegget al., 2004; Glasset al., 2006; Johnes, 2006; Flegg and Allen, 2007a, 2007b; Johnes, 2008; Flegg and Allen, 2009; Johnes, 2014). These studies differ in terms of the time period covered, model specification (i.e. inputs and outputs), returns to scale (RTS) assumed, and the HEIs included in the analysis. Early studies concentrate on a particular sub-sector (such as pre-1992 universities or post-1992 HEIs) and find that, on average, efficiency is remarkably high with average TE levels between around 80 percent and 95 percent (Athanassopulos and Shale, 1997; Flegget al., 2004; Glasset al., 2006; Johnes, 2006; Flegg and Allen 2007a, 2007b, 2009; Johnes, 2014). Later studies that extend the dataset to include the complete HE sector that we observe in the UK today find a much wider range in mean TE at around 0.75 to 0.95.

The objective of this chapter is not to develop a formal theory or definition of production methodology. Rather, the aim is to detail the important econometric area of efficiency estimation in both HE past approaches as well as new methodologies. Beginning with the seminal work of Farrell (1957), various approaches to discerning output shortfall have been developed.

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