The ghosts of frontiers past: Non homogeneity of inefficiency measures (input-biased inefficiency effects)

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The ghosts of frontiers past: Non homogeneity of inefficiency measures (input-biased inefficiency effects) Daniel Gregg Contributed presentation at the 60th AARES Annual Conference, Canberra, ACT,

1 The ghosts of frontiers past: Non homogeneity of inefficiency measures (input-biased inefficiency effects) Daniel Gregg Contributed presentation at the 60th AARES Annual Conference, Canberra, ACT, 2-5 February 2016 Copyright 2016 by Author(s). All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.

2 The ghosts of frontiers past: Non homogeneity of inefficiency measures (input-biased inefficiency effects) Daniel Gregg

3 Background

4 Background Inefficiency measured almost ubiquitously in terms of neutral shifts of the frontier However there may be important components of inefficiency which are not associated with homogenous contractions of inputs (or expansions of outputs). i.e. there may be input-bias effects in technical inefficiency

5 Empirical evidence Bernini et al. (2004) strongly hint at the non-neutral nature of efficiency effects in a study of hotel efficiency using quantile methods Behr (2010) explores some considerable differences in elasticities between frontier and nonfrontier firms using QR approaches My own paper (with John Rolfe) also explores scale and elasticity effects across efficiency quantiles

6 Conceptual aspects Without a conceptual reasoning for input-biased effects, empirical observations remain simply anomalies in the view of the extant 40 plus years of literature considering homogenous efficiency measures. One way to motivate the possibility of inputbiased efficiency effects is to consider inefficient firms production possibilities being characterised as the ghosts of frontiers past

7 Conceptual aspects It is quite widely accepted now that neutral technical change rarely holds at the economywide level let alone at industry or enterprise scales of analysis (Färe et al. 2004; Managi and Karemera 2004). Over time, particular inputs are being saved in production relative to other inputs which are being used more intensively.

8 Conceptual aspects x1 y0,t y0,t+1 x2

9 Conceptual aspects As time progresses, some firms may fail to move to the higher frontier. Likewise, some firms may move slowly in general and slowly become more inefficient. If technological progress is consistently inputbiased in a particular direction, these inefficient firms will be consistently input-biased, in efficiency terms, relative to the frontier

10 Conceptual aspects x1 y0,t1 y0,t2 y0,t3 y0,t4 x2

11 Conceptual aspects Rate = 80% Rate = 70% Rate = 50% Rate = 30%

12 Regression and efficiency quantiles Conditional quantile regression methods are increasingly being used for consideration of the measurement of productive efficiency.

13 Regression and efficiency quantiles A quantile regression function provides a measure of the technology: Q(Y τ) = {y is in R N : y is the τ th quantile of Y y, x } From which an efficiency measure can be calculated using: Q Y i τ = y i δ i τ δ i τ = y i Q(Y i τ)

14 Measures of Bias No measures of input biased inefficiency currently exist (that I m aware of) that do not rely on an underlying homogenous translation of the frontier. However a good deal of work has been done on considering bias in technological progress.

15 Measures of Bias Binswanger (1974) ran into this issue in considering many input biases in technological change. As a result he developed a simple measure based on the ratio of elasticities to scale elasticity (Antle 1984): B i = ln ε i ε ln t Where: ε i = Output elasticity for input i ε = scale elasticity t = time

16 Case study I use a case study on an unbalanced panel for rangelands grazing in northern Australia incorporating environmental inputs : GC, RAIN And human inputs LANDVAL, HEALTH, SUPP, LABOUR Land-type dummies are also specified. (see Gregg and Rolfe 2011 and Gregg and Rolfe under review for more details)

17 Case study The conditional regression quantiles approach of Koenker and Basset (1978) is used. Trans-log and various restrictions were tested using likelihood ratio and AIC, BIC scores resulting in selection of a Cobb-Douglas functional form with no time effects. Endogeneity was considered in a parametric framework with tests indicating no significant endogeneity. However it would be nice to formulate a quantile regression approach for this problem.

18 Case study Conditional quantile regressions were estimated for each percentile between the 20 th and 90 th deciles inclusive. The lower percentiles are generally more noisy in quantile regression and interpretation of regression functions around the 10 th percentile was unclear. OLS and the Aigner, Lovell and Schmidt (ALS) stochastic frontier model were estimated for comparison.

19 Quantile Regression Model Conditional mean models Q20 Q30 Q40 Q50 Q60 Q70 Q80 Q90 OLS ALS Case Parameter study estimates: Intercept * ** ** (1.238) (1.4249) (0.9893) (0.8287) (0.9747) (0.6097) (0.7015) (0.6997) (1.0279) (0.7982) DESERT landtype ** ** ** (0.1509) (0.1291) (0.0909) (0.0837) (0.099) (0.1069) (0.0957) (0.0828) (0.1113) (0.0866) IRONBARK landtype *** (0.0928) (0.1048) (0.0814) (0.0667) (0.0595) (0.0416) (0.0613) (0.0654) (0.0838) (0.0632) MITCHELL landtype * (0.1755) (0.1484) (0.1342) (0.1458) (0.174) (0.1156) (0.0716) (0.0814) (0.1288) (0.0952) LANDVAL *** ** *** *** 0.121*** *** *** * *** *** (0.0573) (0.0567) (0.0402) (0.038) (0.0401) (0.0263) (0.0352) (0.0367) (0.0465) (0.034) HEALTH *** *** *** *** *** 0.166*** *** *** *** 0.153*** (0.0274) (0.0297) (0.0222) (0.0249) (0.0326) (0.0197) (0.0261) (0.029) (0.0305) (0.0206) SUPPLEMENTS *** * * (0.0101) (0.0217) (0.018) (0.0168) (0.0178) (0.0133) (0.0113) (0.0171) (0.0171) (0.012) LABOUR *** *** *** *** *** *** *** *** *** 0.32*** (0.0733) (0.0755) (0.0585) (0.0537) (0.0554) (0.0409) (0.0411) (0.0497) (0.0634) (0.0512) RAINFALL 0.391*** *** 0.264*** *** ** *** *** (0.1011) (0.115) (0.0866) (0.0815) (0.0847) (0.0442) (0.0718) (0.073) (0.0866) (0.0712) GROUNDCOVER *** ** ** 0.58*** ** *** *** *** 0.689*** ** (0.2874) (0.3269) (0.2277) (0.1913) (0.2256) (0.1427) (0.1627) (0.1641) (0.2379) (0.1846) Error components (OLS & ALS): Sigma *** (0.6099) Lambda (ALS only) *** (0.0404) Model stats: AIC BIC loglik n k

20 Case study efficiency ranks 10th percentile model Pearson Rho= th percentile model Pearson Rho= th percentile model 90th percentile model 50th percentile model Pearson Rho= th percentile model Pearson Rho= th percentile model 90th percentile model

21 Case study efficiency ranks Ranks from ALS model Pearson Rho= Ranks from quantile frontier (90th percentile) model

22 Overall effects (Gregg and Rolfe, under review) Returns To Scale (output elasticity) Returns To Scale (output elasticity) Total RTS Total RTS RTS(x) RTS(x) RTS(RAIN) RTS(RAIN) RTS(ENVM) RTS(ENVM) Q10 Q10 Q20 Q20 Q30 Q30 Q40 Q40 Q50 Q50 Q60 Q60 Q70 Q70 Q80 Q80 Q90 Q90 Quantile Quantile

23 Case study neutral technical efficiency change Cumulative Sum of Quantile-differenced neutral TC Brigalow Desert Ironbark Mitchell Efficiency quantile

24 Case study scale efficiency change Cum. Sum of Quantile-differenced Scale change Efficiency quantile

25 Case study input-biased change Cum. Sum of Quantile-differenced input-biased TC LANDVAL Cum. Sum of Quantile-differenced input-biased TC HEALTH Efficiency quantile Efficiency quantile

26 Case study input-biased change Cum. Sum of Quantile-differenced input-biased TC SUPP Cum. Sum of Quantile-differenced input-biased TC LABOUR Efficiency quantile Efficiency quantile

27 Case study input-biased change RAINFALL GROUNDCOVER Cum. Sum of Quantile-differenced input-biased TC Cum. Sum of Quantile-differenced input-biased TC Efficiency quantile Efficiency quantile

28 Case study - conclusions Technical efficiency has a large homogenous component but also substantial scale and inputbiased components. The most inefficient producers appear to be largely failing to invest in consistent levels of end-of-dry season ground cover (environmental health). More broadly across the efficiency distribution more efficient producers are substantially labour-saving and supplement and fodder using More efficient producers are also rainfall using.

29 Considerations on inputbiased efficiency Efficiency is clearly not homogenous in many cases. Both conceptually and empirically there is no reason to believe that the homogeneity imposed by most measures of technical efficiency is true. Whilst in practice homogenous measures are still correct (in terms of the frontier) they potentially leave out important information regarding the structure of inefficient production practices key information needed to derive strategies to facilitate efficiency improvements

30 Considerations on measurement Quantile regression functions are robust econometric methods and useful in considering non-frontier production technologies. Nonparametric conditional quantile methods are of interest and will be considered for the full version of this paper in addition to constrained NP approaches. In the primal context conditional quantile regression functions are potentially affected by endogeneity. So we should use the dual right?

31 Considerations on inputbiased efficiency Does it make any sense to think of inner locations of dual (minimum cost functions) as mapping to a related production function? To do this we require that producers are cost minimisers subject to their inefficient technologies. This only makes sense if input-bias is due to a strict type of Morroni (1992) inefficiency as suggested by Asche (2009) empirically. If inefficient production is due to a lack of knowledge of the efficient points of a given production technology a dual mapping in a conditional quantile sense may not be able to rely on conditional cost minimisation.

32 Considerations on inputbiased efficiency Thank you for listening Any questions

Applying regression quantiles to farm efficiency estimation

Applying regression quantiles to farm efficiency estimation Eleni A. Kaditi and Elisavet I. Nitsi Centre of Planning and Economic Research (KEPE Amerikis 11, 106 72 Athens, Greece kaditi@kepe.gr ; nitsi@kepe.gr