deaR (version 1.2.5)

malmquist_index: Malmquist index

Description

This function calculates the conventional input/output oriented Malmquist index under variable return-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)

Value

A numeric list with Malmquist index and other parameters.

Arguments

datadealist

A list with the data 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.

Author

Vicente Coll-Serrano (). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos (). Department of Business Mathematics

Rafael Benitez (). 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 Malquist 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 <- read_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 <- read_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 <- read_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