Farm-heterogeneity and persistent and transient productive efficiencies in Ethiopia’s smallholder cereal farming

Figure 1

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Figure 3

Mean efficiency measures by AEZs

Components	Persistent		Transient
AEZs\Model	FE and KH	KLH	TFE	KH	KLH
Lowland	0.220	0.763	0.897	0.151	0.525
Midland	0.311	0.794	0.794	0.215	0.548
Highland	0.387	0.813	0.960	0.267	0.560

Frequency distribution of persistent and transient TEs

TE-Interval (%)	Persistent TE		Transient TE
	FE and KH models	KLH model	TFE model	KH model	KLH model
0−10	2.91	0	0	13.41	0
11−20	25.34	0	0	42.72	0.36
21−30	29.15	0	0	25.55	0.91
31−40	19.28	0	0	12.50	4.13
41−50	10.76	0	0.12	3.58	19.54
51−60	6.50	0.22	0.00	1.40	50.24
61−70	3.36	5.38	0.18	0.67	23.97
71−80	1.12	47.09	7.40	0.12	0.85
81−90	1.35	47.31	2.61	0.06	0
91−100	0.22	0	89.68	0	0
Mean	0.304	0.791	0.944	0.210	0.545
Std. Dev.	0.155	0.053	0.065	0.111	0.082
Minimum	0.054	0.567	0.427	0.020	0.105
Maximum	1.000	0.889	1.000	0.840	0.783
Yearly mean of the transient efficiency
1999	0.964	0.213	0.550
2004	0.958	0.195	0.523
2009	0.941	0.215	0.559
2015	0.918	0.210	0.541

Estimates of the Parameters, Elasticities, TC, and RTS across Models (NT=1,648)

Variables	TFE model			FE, KH, and KLH models
	Estimate	SE	Elasticity	Estimate	SE	Elasticity
Constant	4.144***	0.457		4.678***	0.396
Fertilizer	0.089	0.067	0.012	0.064	0.080	0.004
Agrochemicals	0.096**	0.050	0.066	0.108*	0.059	0.071
Labor	0.344***	0.095	−0.115	0.351***	0.114	−0.116
Machinery	−0.295***	0.064	−0.324	−0.290***	0.076	−0.304
Livestock	0.225**	0.106	0.275	0.197	0.126	0.247
Oxen	0.386	0.244	0.471	0.380	0.292	0.495
Area	0.013	0.113	0.276	0.067	0.132	0.322
Fertilizer*Fertilizer	−0.003	0.015		−0.002	0.018
Agrochemicals*Agrochemicals	−0.001	0.012		−0.005	0.014
Labor*Labor	−0.031	0.019		−0.035	0.023
Machinery*Machinery	0.062***	0.013		0.059***	0.016
Livestock*Livestock	0.125***	0.024		0.122***	0.028
Oxen*Oxen	−0.217	0.185		−0.218	0.222
Area*Area	−0.124***	0.022		−0.118***	0.026
Fertilizer*Agrochemicals	−0.008	0.011		−0.004	0.013
Fertilizer*Labor	0.013	0.021		0.019	0.025
Fertilizer*Machinery	−0.003	0.012		−0.002	0.014
Fertilizer*Livestock	−0.099***	0.025		−0.093***	0.029
Fertilizer*Oxen	0.112**	0.056		0.103	0.066
Fertilizer*Area	0.126***	0.030		0.111***	0.035
Agrochemicals*Labor	−0.007	0.016		−0.012	0.020
Agrochemicals*Machinery	0.001	0.011		0.001	0.013
Agrochemicals*Livestock	0.070***	0.024		0.067***	0.028
Agrochemicals*Oxen	−0.107**	0.044		−0.104**	0.053
Agrochemicals*Area	−0.002	0.023		−0.007	0.028
Labor*Machinery	0.071***	0.016		0.069***	0.019
Labor*Livestock	0.045	0.038		0.051	0.046
Labor*Oxen	−0.098	0.080		−0.104	0.096
Labor*Area	−0.036	0.036		−0.043	0.043
Machinery*Livestock	0.006	0.021		0.002	0.025
Machinery*Oxen	0.018	0.450		0.021	0.054
Machinery*Area	−0.042*	0.230		−0.042	0.027
Livestock*Oxen	−0.208**	0.107		−0.195	0.128
Livestock*Area	−0.195***	0.058		−0.193**	0.070
Oxen*Area	0.326***	0.120		0.332**	0.143
Time (1=1999,...,4=2015)	0.666***	0.139		0.686***	0.162
Time*Time	0.392***	0.048		0.356***	0.052
Time*Fertilizer	−0.026**	0.012		−0.024*	0.014
Time*Agrochemicals	−0.011	0.009		−0.010	0.011
Time*Labor	−0.119***	0.018		−0.114***	0.022
Time*Machinery	−0.036**	0.015		−0.029*	0.017
Time*Livestock	−0.052**	0.022		−0.050**	0.026
Time*Oxen	0.078*	0.043		0.090*	0.052
Time*Area	0.118***	0.026		0.114***	0.031
RTS			0.660			0.710
Rate of TC			0.901			0.880

Kendall’s rank order correlation between different models

Components	Persistent			Transient
Model	FE	KH	KLH	TFE	KH	KLH
PTE_FE	0.998
PTE _KH	0.998	0.998
PTE _KLH	0.998	0.998	0.998
TTE_TFE	−0.024	−0.024	−0.024	1.000
TTE_KH	0.845	0.845	0.845	−0.013	1.000
TTE_KLH	0.322	0.322	0.322	0.043	0.477	1.000

Summary statistics of the data (NT=1,648 observations)

Variable	1999		2004		2009		2015		All-waves
	Mean	SD	Mean	SD	Mean	SD	Mean	SD	Mean	SD	CV
Cereal output	1,260	1,320	1,253	1,300	2,065	2,390	3,020	4,000	1,952	2,682	1.37
Fertilizers	107.8	115.1	88.0	140.9	81.0	104.3	179.0	166.2	116.1	139.0	1.19
Agrochemicals	26.9	71.5	23.7	77.0	114.7	461.5	336.7	675.5	133.9	447.0	3.34
Labor	316.3	423.9	266.2	290.7	170.8	241.4	593.9	1,222.2	342.6	714.0	2.08
Machinery	0.6	4.6	41.3	301.4	836.8	3,216.4	376.4	915.5	336.3	1,776.0	5.28
Livestock	5.7	4.3	4.5	4.0	7.2	6.3	7.9	7.4	6.5	5.9	0.91
Land area	1.5	1.1	4.9	22.6	2.8	14.2	1.8	1.4	2.6	12.4	4.77
Oxen	1.8	1.2	1.4	1.3	1.9	1.5	1.9	1.4	1.8	1.4	0.78