Stochastic Frontier Cost Function Model Specification and Estimation Results

Heshmati, Almas; Kim, Jungsuk

doi:10.1007/978-981-10-1017-0_5

Almas Heshmati³ &
Jungsuk Kim⁴

1384 Accesses
1 Citations

Abstract

This chapter compares the cost efficiency of the world’s 39 major airlines over the 1998–2012 period. We analyzed airlines’ cost efficiency using the stochastic frontier function methodology and investigated which factors account for differences in the level of efficiency. The mean and dispersion of cost efficiency amongst airlines differ according to geographical areas of operation, which may be a result of different market structures and deregulation processes; so the differences can be attributed to specific competitive conditions such as resource availability and strategic cooperation with competitors. The results confirmed that airlines are less successful in achieving cost efficiency over the period studied. Airline size showed a positive correlation with the level of cost efficiency, while larger airlines were not more efficient than their smaller counterparts in the case of the cost model. Our main findings show that carriers based in the Asia region are in general more cost efficient than carriers based in Europe and North America.

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Notes

1.
A number of strong assumptions are made prior to the estimation of a cost function. “In the stochastic frontier literature, the V _it are nothing but “statistical noise that is, the V _it are unexplainable error components which should not be systematically related with firms’ input or output decisions”. “Thus, a firm’s input decisions X _it should be strictly exogenous to the V _it; all leads and lags of X _it are uncorrelated with V _it. That is, X _i,t−1 and X _it should be uncorrelated with it, since it simply equals V _it” (Coelli 1996).
2.
“The measures of cost efficiency relative to the cost frontier is defined as: EFF_i = E(Y _i*|U _i, X _i)/E(Y _i*|U _i = 0, X _i), where Y _i* is the cost (or production) of the ith firm, which will be equal to Y _i when the dependent variable is in original units and will be equal to exp(Y _i) when the dependent variable is in logs” (Coelli 1996). In the case of a production frontier, EFF_i will take a value between zero and one—one indicating fully efficient, while it will take a value between one and higher than one in the cost function case, where values in excess of one indicate degree excess cost or cost inefficiency.
3.
It includes airport fees, landing fees, and ground handling charges.
4.
Annual inflation data was obtained from www.imf.org.
5.
Cargo output includes mail services.
6.
GDP per person employed is gross domestic product (GDP) divided by total employment in the economy; the purchasing power parity (PPP) index was use to convert the variable to 1990 constant international dollars using PPP rates (www.worldbank.org).
7.
Various studies used the HHI (Herfindahl-Hirschman Index) to proxy the market structure and competition. See also Chap. 2 for more details.
8.
These hypotheses are aimed to be tested on the basis of estimation results obtained from the Efficiency Effect model (EE).

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Authors and Affiliations

Jönköping International Business School, Jönköping, Sweden
Almas Heshmati
Sogang University, Seoul, Korea, Republic of (South Korea)
Jungsuk Kim

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Almas Heshmati
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Correspondence to Jungsuk Kim .

Appendices

Appendix 5.1: Development of Airline Cost Efficiency Over Time Based on the EC Model Specification

Airline	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	AVG
AA	0.512	0.501	0.491	0.480	0.469	0.459	0.448	0.437	0.426	0.415	0.404	0.393	0.382	0.371	0.360	0.436
AC	0.556	0.546	0.536	0.526	0.516	0.505	0.495	0.484	0.473	0.463	0.452	0.441	0.430	0.419	0.408	0.483
AF	0.447	0.436	0.426	0.415	0.404	0.392	0.381	0.370	0.359	0.348	0.337	0.326	0.315	0.304	0.293	0.370
AI	0.540	0.530	0.520	0.510	0.499	0.489	0.478	0.468	0.457	0.446	0.435	0.424	0.413	0.402	0.391	0.467
AV	0.706	0.698	0.691	0.683	0.675	0.667	0.658	0.650	0.641	0.633	0.624	0.615	0.606	0.597	0.587	0.649
AY	0.673	0.665	0.657	0.649	0.640	0.631	0.622	0.613	0.604	0.595	0.585	0.576	0.566	0.556	0.547	0.612
AZ	0.531	0.520	0.510	0.500	0.489	0.478	0.468	0.457	0.446	0.435	0.424	0.413	0.402	0.391	0.380	0.456
BA	0.522	0.511	0.501	0.490	0.480	0.469	0.458	0.447	0.436	0.426	0.415	0.404	0.392	0.381	0.370	0.447
CA	0.473	0.462	0.452	0.441	0.430	0.419	0.408	0.397	0.386	0.375	0.364	0.352	0.341	0.330	0.319	0.397
CX	0.627	0.618	0.609	0.600	0.590	0.581	0.571	0.562	0.552	0.542	0.532	0.522	0.511	0.501	0.490	0.561
CZ	0.444	0.433	0.422	0.411	0.400	0.389	0.378	0.367	0.356	0.345	0.334	0.323	0.312	0.301	0.290	0.367
DL	0.512	0.502	0.491	0.481	0.470	0.459	0.448	0.438	0.427	0.416	0.405	0.394	0.382	0.371	0.360	0.437
EI	0.788	0.782	0.776	0.770	0.765	0.758	0.752	0.745	0.739	0.732	0.725	0.717	0.710	0.703	0.695	0.744
GA	0.835	0.831	0.826	0.821	0.816	0.811	0.806	0.800	0.795	0.789	0.784	0.778	0.772	0.766	0.759	0.799
IB	0.576	0.566	0.556	0.547	0.537	0.527	0.516	0.506	0.496	0.485	0.474	0.464	0.453	0.442	0.431	0.505
JJ	0.686	0.678	0.670	0.662	0.654	0.646	0.637	0.628	0.619	0.610	0.601	0.592	0.582	0.573	0.563	0.627
JL	0.432	0.421	0.410	0.399	0.388	0.377	0.366	0.355	0.344	0.332	0.321	0.310	0.299	0.289	0.278	0.355
KE	0.627	0.618	0.609	0.600	0.591	0.581	0.571	0.562	0.552	0.542	0.532	0.522	0.512	0.501	0.490	0.561
LA	0.647	0.638	0.629	0.621	0.612	0.602	0.593	0.584	0.574	0.565	0.555	0.545	0.535	0.525	0.514	0.583
LH	0.419	0.408	0.397	0.386	0.375	0.364	0.353	0.342	0.331	0.320	0.309	0.298	0.287	0.276	0.265	0.342
LX	0.598	0.589	0.579	0.569	0.560	0.550	0.540	0.530	0.519	0.509	0.499	0.488	0.478	0.467	0.456	0.529
LY	0.765	0.758	0.752	0.745	0.739	0.732	0.725	0.717	0.710	0.703	0.695	0.688	0.680	0.672	0.664	0.716
MH	0.639	0.630	0.621	0.612	0.603	0.594	0.584	0.575	0.565	0.556	0.546	0.535	0.525	0.515	0.505	0.574
MU	0.482	0.471	0.460	0.449	0.439	0.428	0.417	0.406	0.395	0.384	0.372	0.361	0.350	0.339	0.328	0.405
NH	0.453	0.442	0.431	0.420	0.409	0.398	0.387	0.376	0.365	0.354	0.343	0.332	0.321	0.310	0.299	0.376
NZ	0.695	0.688	0.680	0.672	0.664	0.655	0.647	0.639	0.630	0.621	0.612	0.603	0.593	0.584	0.574	0.637
OS	0.635	0.626	0.617	0.608	0.599	0.590	0.580	0.571	0.561	0.551	0.541	0.531	0.521	0.510	0.500	0.569
PR	0.643	0.634	0.625	0.616	0.607	0.598	0.589	0.579	0.569	0.560	0.550	0.540	0.530	0.519	0.509	0.578
QF	0.585	0.575	0.566	0.556	0.546	0.536	0.526	0.515	0.505	0.495	0.484	0.473	0.463	0.452	0.441	0.514
QR	0.708	0.701	0.693	0.685	0.678	0.669	0.661	0.653	0.644	0.636	0.627	0.618	0.609	0.600	0.591	0.652
SK	0.518	0.507	0.497	0.486	0.476	0.465	0.454	0.443	0.433	0.422	0.411	0.399	0.388	0.377	0.366	0.443
SQ	0.613	0.604	0.594	0.585	0.575	0.566	0.556	0.546	0.536	0.526	0.515	0.505	0.495	0.484	0.473	0.545
SU	0.952	0.951	0.950	0.948	0.946	0.944	0.943	0.942	0.940	0.938	0.935	0.934	0.932	0.930	0.928	0.941
SV	0.568	0.558	0.548	0.538	0.528	0.517	0.507	0.497	0.486	0.476	0.465	0.454	0.443	0.432	0.421	0.496
TG	0.561	0.552	0.542	0.532	0.521	0.511	0.501	0.490	0.480	0.469	0.458	0.447	0.436	0.425	0.414	0.489
TK	0.980	0.980	0.980	0.980	0.980	0.980	0.980	0.980	0.980	0.980	0.980	0.980	0.980	0.980	0.980	0.980
TP	0.635	0.626	0.617	0.608	0.599	0.589	0.580	0.570	0.561	0.551	0.541	0.531	0.521	0.510	0.500	0.569
UA	0.514	0.503	0.493	0.482	0.471	0.461	0.450	0.439	0.428	0.417	0.406	0.395	0.384	0.373	0.362	0.439
US	0.519	0.509	0.499	0.488	0.477	0.467	0.456	0.445	0.434	0.423	0.412	0.401	0.390	0.379	0.368	0.444
AVG	0.606	0.597	0.588	0.579	0.570	0.560	0.551	0.542	0.532	0.523	0.513	0.503	0.493	0.484	0.474	0.541

Appendix 5.2: Development of Airline Cost Efficiency Over Time Based on the EE Model Specification

Airline	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	AVG
AA	0.505	0.504	0.503	0.509	0.504	0.534	0.543	0.551	0.558	0.563	0.568	0.585	0.589	0.591	0.597	0.547
AC	0.715	0.720	0.699	0.676	0.698	0.713	0.729	0.747	0.751	0.747	0.766	0.774	0.744	0.751	0.755	0.732
AF	0.631	0.632	0.618	0.614	0.620	0.612	0.590	0.587	0.585	0.580	0.587	0.598	0.607	0.608	0.551	0.601
AI	0.792	0.814	0.818	0.822	0.828	0.821	0.682	0.803	0.809	0.655	0.669	0.692	0.702	0.712	0.730	0.757
AV	0.976	0.982	0.982	0.983	0.985	0.989	0.987	0.986	0.976	0.974	0.972	0.972	0.964	0.887	0.522	0.942
AY	0.831	0.850	0.858	0.866	0.880	0.882	0.886	0.891	0.894	0.904	0.915	0.941	0.959	0.970	0.973	0.900
AZ	0.729	0.729	0.751	0.738	0.734	0.753	0.765	0.746	0.756	0.760	0.742	0.818	0.230	0.119	0.833	0.680
BA	0.588	0.594	0.597	0.604	0.611	0.615	0.620	0.620	0.629	0.636	0.664	0.676	0.686	0.704	0.702	0.636
CA	0.719	0.744	0.735	0.728	0.704	0.631	0.615	0.609	0.600	0.592	0.590	0.575	0.574	0.550	0.552	0.634
CX	0.744	0.752	0.734	0.741	0.739	0.747	0.731	0.725	0.720	0.718	0.688	0.710	0.700	0.693	0.695	0.723
CZ	0.626	0.615	0.607	0.614	0.616	0.584	0.556	0.537	0.530	0.524	0.601	0.602	0.574	0.558	0.510	0.577
DL	0.541	0.541	0.540	0.561	0.570	0.582	0.582	0.599	0.606	0.615	0.623	0.636	0.580	0.582	0.587	0.583
EI	0.980	0.982	0.984	0.988	0.990	0.991	0.991	0.992	0.991	0.991	0.991	0.991	0.991	0.991	0.992	0.989
GA	0.955	0.965	0.970	0.970	0.968	0.972	0.967	0.976	0.978	0.978	0.978	0.980	0.978	0.970	0.963	0.971
IB	0.672	0.674	0.687	0.690	0.697	0.702	0.691	0.702	0.712	0.717	0.725	0.756	0.758	0.750	0.765	0.713
JJ	0.941	0.949	0.953	0.879	0.826	0.877	0.886	0.945	0.803	0.764	0.766	0.769	0.755	0.751	0.762	0.842
JL	0.613	0.613	0.630	0.642	0.595	0.587	0.563	0.570	0.576	0.581	0.580	0.598	0.617	0.615	0.631	0.601
KE	0.738	0.740	0.728	0.737	0.734	0.742	0.742	0.745	0.740	0.735	0.738	0.750	0.749	0.751	0.750	0.741
LA	0.972	0.948	0.954	0.938	0.937	0.940	0.921	0.904	0.898	0.887	0.867	0.878	0.861	0.839	0.818	0.904
LH	0.625	0.602	0.605	0.599	0.601	0.600	0.558	0.552	0.554	0.543	0.523	0.530	0.533	0.527	0.536	0.566
LX	0.763	0.755	0.773	0.868	0.815	0.841	0.863	0.887	0.883	0.899	0.871	0.892	0.892	0.876	0.882	0.851
LY	0.991	0.991	0.991	0.992	0.992	0.992	0.992	0.991	0.992	0.992	0.991	0.992	0.992	0.992	0.992	0.992
MH	0.658	0.693	0.693	0.697	0.702	0.703	0.693	0.702	0.712	0.730	0.736	0.762	0.755	0.754	0.781	0.718
MU	0.781	0.745	0.745	0.735	0.721	0.723	0.689	0.664	0.629	0.625	0.623	0.617	0.596	0.597	0.603	0.673
NH	0.575	0.565	0.565	0.574	0.575	0.567	0.558	0.558	0.558	0.562	0.556	0.559	0.561	0.552	0.564	0.563
NZ	0.765	0.765	0.758	0.762	0.750	0.754	0.756	0.751	0.766	0.754	0.738	0.760	0.780	0.785	0.786	0.762
OS	0.898	0.922	0.927	0.924	0.864	0.865	0.855	0.857	0.855	0.852	0.847	0.883	0.917	0.929	0.939	0.889
PR	0.952	0.978	0.978	0.981	0.980	0.981	0.982	0.980	0.979	0.980	0.979	0.977	0.978	0.981	0.986	0.978
QF	0.630	0.632	0.632	0.631	0.619	0.613	0.615	0.622	0.627	0.624	0.576	0.597	0.599	0.595	0.622	0.615
QR	0.745	0.971	0.976	0.994	0.994	0.993	0.992	0.990	0.987	0.985	0.983	0.982	0.976	0.969	0.963	0.967
SK	0.638	0.644	0.654	0.664	0.646	0.660	0.651	0.654	0.776	0.767	0.768	0.749	0.774	0.766	0.775	0.706
SQ	0.716	0.714	0.711	0.720	0.713	0.728	0.722	0.714	0.712	0.711	0.706	0.735	0.734	0.730	0.733	0.720
SU	0.871	0.894	0.907	0.900	0.920	0.925	0.923	0.921	0.919	0.910	0.900	0.930	0.923	0.907	0.889	0.909
SV	0.770	0.769	0.763	0.760	0.767	0.773	0.767	0.768	0.778	0.786	0.794	0.802	0.812	0.819	0.828	0.784
TG	0.697	0.699	0.696	0.699	0.706	0.709	0.704	0.708	0.707	0.699	0.699	0.717	0.723	0.719	0.728	0.707
TK	0.845	0.871	0.897	0.907	0.927	0.938	0.935	0.927	0.919	0.915	0.901	0.892	0.877	0.865	0.856	0.898
TP	0.876	0.881	0.904	0.906	0.908	0.908	0.904	0.932	0.929	0.899	0.879	0.897	0.912	0.916	0.923	0.905
UA	0.512	0.511	0.514	0.534	0.549	0.581	0.581	0.595	0.595	0.603	0.611	0.635	0.596	0.643	0.563	0.575
US	0.535	0.560	0.587	0.633	0.676	0.697	0.705	0.719	0.713	0.662	0.614	0.635	0.640	0.640	0.644	0.644
AVG	0.747	0.757	0.760	0.764	0.761	0.765	0.756	0.762	0.762	0.754	0.752	0.765	0.748	0.742	0.751	0.756

Appendix 5.3: Correlation Matrix of the Determinants of Cost Efficiency Effects

Parameters	ATK_TTL	LF	WAGE	ENG_INDX	INT_CS	EMP	FREQ	PRICE	MS
ATK_TTL	1.000
LF	0.147	1.000
(sig)	(0.000)
WAGE	0.401	0.218	1.000
(sig)	(0.000)	(0.000)
ENG_INDX	0.215	0.221	0.129	1.000
(sig)	(0.000)	(0.000)	(0.002)
INT_CS	−0.272	0.357	0.192	−0.004	1.000
(sig)	(0.000)	(0.000)	(0.000)	(0.921)
EMP	0.795	0.143	0.269	0.040	−0.326	1.000
(sig)	(0.000)	(0.001)	(0.000)	(0.331)	(0.000)
FHRS	0.880	0.130	0.426	0.228	−0.429	0.795	1.000
(sig)	(0.000)	(0.002)	(0.000)	(0.000)	(0.000)	(0.000)
PRICE	−0.198	0.019	0.172	0.058	0.006	0.041	−0.128	1.000
(sig)	(0.000)	(0.646)	(0.000)	(0.161)	(0.880)	(0.318)	(0.002)
MS	0.745	0.355	0.423	−0.066	0.228	0.610	0.588	−0.064	1.000
(sig)	(0.000)	(0.000)	(0.000)	(0.111)	(0.000)	(0.000)	(0.000)	(0.123)

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Heshmati, A., Kim, J. (2016). Stochastic Frontier Cost Function Model Specification and Estimation Results. In: Efficiency and Competitiveness of International Airlines. Springer, Singapore. https://doi.org/10.1007/978-981-10-1017-0_5

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DOI: https://doi.org/10.1007/978-981-10-1017-0_5
Published: 19 May 2016
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-1015-6
Online ISBN: 978-981-10-1017-0
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