malmquist_index {deaR}

Malmquist index

Description

This function calculates the input/output oriented Malmquist productivity index under constant or variable returns-to-scale.

Usage

malmquist_index(datadealist,
                dmu_eval = NULL,
                dmu_ref = NULL,
                orientation = c("io", "oo"),
                rts = c("crs", "vrs"),
                type1 = c("cont", "seq", "glob"),
                type2 = c("fgnz", "rd", "gl", "bias"),
                tc_vrs = FALSE,
                vtrans_i = NULL,
                vtrans_o = NULL)

Arguments

datadealist

A list with the data (deadata objects) at different times, including DMUs, inputs and outputs.

dmu_eval

A numeric vector containing which DMUs have to be evaluated. If NULL (default), all DMUs are considered.

dmu_ref

A numeric vector containing which DMUs are the evaluation reference set. If NULL (default), all DMUs are considered.

orientation

A string, equal to "io" (input oriented) or "oo" (output oriented).

rts

A string, determining the type of returns to scale, equal to "crs" (constant) or "vrs" (variable).

type1

A string, equal to "cont" (contemporary), "seq" (sequential) or "glob" (global).

type2

A string, equal to "fgnz" (Fare et al. 1994), "rd" (Ray and Desli 1997), "gl" (generalized) or "bias" (biased).

tc_vrs

Logical. If it is FALSE, it computes the vrs bias malmquist index by using the technical change under crs (Fare and Grosskopf 1996). Otherwise, it uses the technical change under vrs.

vtrans_i

Numeric vector of translation for undesirable inputs in non-directional basic models. If vtrans_i[i] is NA, then it applies the "max + 1" translation to the i-th undesirable input. If vtrans_i is a constant, then it applies the same translation to all undesirable inputs. If vtrans_i is NULL, then it applies the "max + 1" translation to all undesirable inputs.

vtrans_o

Numeric vector of translation for undesirable outputs in non-directional basic models, analogous to vtrans_i, but applied to outputs.

Value

A numeric list with Malmquist index and other parameters.

Note

In the results: EC = Efficiency Change, PTEC = Pure Technical Efficiency Change, SEC = Scale Efficiency Change, TC = Technological Change, MI = Malmquist Index

Author(s)

Vicente Coll-Serrano ([e-mail]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([e-mail]). Department of Business Mathematics

Rafael Benitez ([e-mail]). Department of Business Mathematics

University of Valencia (Spain)

References

Caves, D.W.; Christensen, L. R.; Diewert, W.E. (1982). “The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity”. Econometrica, 50(6), 1393-1414.

Fare, R.; Grifell-Tatje, E.; Grosskopf, S.; Lovell, C.A.K. (1997). "Biased Technical Change and the Malmquist Productivity Index". Scandinavian Journal of Economics, 99(1), 119-127.

Fare, R.; Grosskopf, S.; Lindgren, B.; Roos, P. (1989). “Productivity Developments in Swedish Hospitals: A Malmquist Output Index Approach”. Discussion paper n. 89-3. Southern Illinois University. Illinois.

Fare, R.; Grosskopf, S.; Lindgren, B.; Roos, P. (1992). “Productivity changes in Swedish Pharmacies 1980-89: A nonparametric Malmquist Approach”. Journal of productivity Analysis, 3(3), 85-101.

Fare, R.; Grosskopf, S.; Norris, M.; Zhang, Z. (1994). “Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries”. American Economic Review, 84(1), 66-83.

Fare, R.; Grosskopf, S.; Roos, P. (1998), Malmquist Productivity Indexes: A Survey of Theory and Practice. In: Fare R., Grosskopf S., Russell R.R. (eds) Index Numbers: Essays in Honour of Sten Malmquist. Springer.

Grifell-Tatje, E.; Lovell, C.A.K. (1999). "A Generalized Malmquist productivity index". Top, 7(1), 81-101.

Pastor, J.T.; Lovell, C.A.k. (2005). "A global Malmquist productiviyt index". Economics Letters, 88, 266-271.

Ray, S.C.; Desli, E. (1997). "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries: Comment". The American Economic Review, 87(5), 1033-1039.

Shestalova, V. (2003). "Sequential Malmquist Indices of Productivity Growth: An Application to OECD Industrial Activities". Journal of Productivity Analysis, 19, 211-226.

Examples

# Example 1. With dataset in wide format.
# Replication of results in Wang and Lan (2011, p. 2768)
data("Economy")
data_example <- make_malmquist(datadea = Economy,
                               nper = 5, 
                               arrangement = "horizontal",
                               ni = 2, 
                               no = 1)
result <- malmquist_index(data_example, orientation = "io")
mi <- result$mi
effch <- result$ec
tech <- result$tc

# Example 2. With dataset in long format.
# Replication of results in Wang and Lan (2011, p. 2768)
data("EconomyLong")
data_example2 <- make_malmquist(EconomyLong,
                                percol = 2, 
                                arrangement = "vertical",
                                inputs = 3:4, 
                                outputs = 5)
result2 <- malmquist_index(data_example2, orientation = "io")
mi2 <- result2$mi
effch2 <- result2$ec
tech2 <- result2$tc

# Example 3. Replication of results in Grifell-Tatje and Lovell (1999, p. 100).
data("Grifell_Lovell_1999")
data_example <- make_malmquist(Grifell_Lovell_1999,
                               percol = 1,
                               dmus = 2,
                               inputs = 3,
                               outputs = 4,
                               arrangement = "vertical")
result_fgnz <- malmquist_index(data_example,
                               orientation = "oo",
                               rts = "vrs",
                               type1 = "cont",
                               type2 = "fgnz")
mi_fgnz <- result_fgnz$mi 

result_rd <- malmquist_index(data_example,
                             orientation = "oo",
                             rts = "vrs",
                             type1 = "cont",
                             type2 = "rd")
mi_rd <- result_rd$mi
 
result_gl <- malmquist_index(data_example,
                             orientation = "oo",
                             rts = "vrs",
                             type1 = "cont",
                             type2 = "gl")
mi_gl <- result_gl$mi