Climate change and crop choice in Zambia: A mathematical programming approach

Figures & data

Fig. 1 Study sites.

Table 1 Characteristics of study sites, 2008.

	Site 1		Site 2
	Mean	SD	Mean	SD
District population density (persons/km^2)	44.78	(11.96)	12.19	(4.93)
Village distance to main road (km)	13.00	(11.73)	20.37	(20.80)
Household (HH) Size	5.55	(2.73)	5.49	(2.39)
1 = HH head completed primary school	0.25	(0.44)	0.53	(0.50)
1 = HH was poor (below $1 per capita per day)	0.92	(0.27)	0.82	(0.38)
Proportion income derived from off-farm sources	0.22	(0.26)	0.45	(0.42)
Tropical Livestock Units (excluding oxen)	3.10	(5.27)	0.55	(1.62)
Value of equipment/oxen (100s ZMK)	11.36	(21.50)	1.32	(8.11)
Obs.	1044		424
Of cropping households
1 = Smallholder HH (≤5 ha owned)	0.92	(0.27)	0.89	(0.32)
1 = Emergent farmer (5–20 ha owned)	0.06	(0.24)	0.08	(0.27)
Land cultivated (ha)	1.78	(1.43)	1.60	(1.37)
Number of field crops planted	2.66	(1.13)	2.62	(1.14)
1 = HH applied fertilizer	0.38	(0.49)	0.31	(0.46)
1 = HH owned water pump	0.00	(0.07)	0.00	0.00
Obs.	1032		395
No. cropping HHs	194,675		74,310

Source: SS 2008.

Table 2 Crop activities in farm household models.

	Crop	Seed Type	Tillage Method	Fertilizer	Time of Tillage	Code
Site 1	Maize	Local	Hand	No	Early	MZ1
	Maize	Hybrid	Hand	Yes	Late	MZ4
	Maize	Local	Ox	No	Late	MZ6
	Maize	Local	Hand	Yes	Early	MZ9
	Groundnuts	Local	Hand	No	Early	GR1
	Groundnuts	Local	Hand	No	Late	GR2
	Groundnuts	Local	Ox	No	Late	GR6
	Groundnuts	Improved	Hand	No	Late	GR12
	Sunflower	Local	Hand	No	Late	SUN2
	Sunflower	Improved	Ox	No	Late	SUN10
	Sweet potatoes	Local	Hand	No	Late	SP2
	Sweet potatoes	Improved	Hand	No	Late	SP12
	Cotton	Improved	Ox	No	Late	COT10
	Cotton	Improved	Hand	No	Late	COT12
Site 2	Maize	Local	Hand	No	Early	MZ1
	Maize	Local	Hand	No	Late	MZ2
	Maize	Hybrid	Hand	Yes	Early	MZ3
	Maize	Hybrid	Ox	Yes	Late	MZ4
	Groundnuts	Local	Hand	No	Early	GR1
	Groundnuts	Local	Hand	No	Late	GR2
	Groundnuts	Local	Ox	No	Late	GR6
	Groundnuts	Hybrid	Hand	Yes	Late	GR12
	Cassava	Local	–	–	–	CAS1
	Cassava	Improved	–	–	–	CAS2
	Sweet potatoes	Local	Hand	No	Late	SP2
	Sweet potatoes	Improved	Ox	No	Early	SP12
	Finger millet	Local	Hand	No	Early	MIL1
	Finger millet	Local	Hand	No	Late	MIL2
	Mixed Beans	Local	Hand	No	Early	MB1
	Mixed Beans	Local	Hand	No	Late	MB2
	Rice	Local	Hand	No	Early	RIC1
	Rice	Local	Hand	No	Late	RIC2

Table A1 Crop distributions by area (proportions).

Crop	Site 1		Site 2
	Smallholder	Emergent	Smallholder	Emergent
Maize	0.53	0.40	0.21	0.16
Groundnuts	0.13	0.08	0.07	0.04
Cassava			0.22	0.11
Sunflower	0.06	0.05
Sweet Potatoes	0.00	0.00	0.01	0.01
Finger Millet			0.05	0.03
Mixed Beans			0.12	0.08
Rice			0.05	0.01
Cotton	0.15	0.15
Fallow	0.13	0.32	0.25	0.56
Observations^a	3973	1054	1430	854
Total proportion of accessed land area that is covered by the above crops and fallow	0.97	0.97	0.98	0.99

Sources: SS 2008, CFS 2008–2010.

a ‘Observations’ refers to the total number of households captured in the pooled sample.

Table 3 Productivity of crop regimes.

Site 1				Site 2
Crop regime	Obs.^a	Mean yield (kgs/ha)	Calories/ha (1000 s)	Crop regime	Obs.	Mean yield (kgs/ha)	Calories/ha (1000 s)
MZ1	1769	1,104.86	3944.34	MZ1	499	1597.64	5703.57
MZ4	1374	2,322.20	8290.25	MZ2	1074	1491.18	5323.52
MZ6	1456	1,196.34	4270.93	MZ3	495	3249.41	11,600.38
MZ9	1012	1,558.06	5562.26	MZ4	994	3337.59	11,915.21
GR1	710	551.40	3027.17	GR1	596	822.41	4515.02
GR2	2422	483.67	2655.35	GR2	1990	636.05	3491.89
GR6	1670	491.28	2697.10	GR6	136	541.99	2975.52
GR12	1030	454.83	2497.04	GR12	84	556.75	3056.55
SUN2	987	470.05	2284.45	CAS1	529	4776.48	7116.96
SUN10	715	502.38	2441.58	CAS2	232	7173.12	10,687.95
SP2	188	3,385.78	4096.79	SP2	440	3636.86	4400.60
SP12	138	4,591.56	5555.79	SP12	293	4234.55	5123.81
COT10	1237	909.91	6343.09^b	MIL1	711	1008.54	3439.10
COT12	2405	897.94	6259.68	MIL2	901	983.59	3354.04
				MB1	356	604.76	2219.47
				MB2	2298	595.37	2185.01
				RIC1	248	1505.20	5177.90
				RIC2	150	1079.08	3712.04

Sources: Yields: CFS 2008–2010 (cassava), CFS 2003–12 (all other crops); Calories: Wu Leung et al. (1968); Prices: SS 2004 and 2008, RALS 2012.

a When fewer than 30 observations are found within a study site, the geographic range is expanded to the province.

b Cotton harvest is translated into calories through the site-specific median cotton sales price and retail price of maize meal.

Table A2 Labor requirements (workdays per ha) for selected crop regimes (site 1).

Month	Half of month	MZ4	MZ6	SUN10	COT10	COT12
October	1
	2				4.50
November	1				5.50	15.00
	2		7.41		1.00	15.00
December	1	5.71	13.05		3.20	1.00
	2	15.00	25.44	8.00	3.20	1.00
January	1	15.24	19.80	10.60	3.20	7.50
	2	13.84	14.80	2.60		7.50
February	1	11.28		11.99	3.20
	2	2.75		11.99	3.20	7.50
March	1	2.75		11.99		7.50
	2	2.75
April	1
	2			6.80
May	1	5.87		9.80
	2	5.87	12.35	3.00	14.15	16.65
June	1	5.87	20.10		15.22	18.25
	2	7.92	7.75		15.22	18.25
July	1	7.92	7.75		1.07	1.60
	2	7.92

Sources: CFS 2011 and 2012 (maize, cassava, and rice), Siegel and Alwang (2005) (other crops), focus groups (timeline of agricultural tasks).

Table A3 Variable costs of crop activities (site 1).

Crop regime	Basal fertilizer (Kg/Ha)	Top fertilizer (Kg/Ha)	Seed/planting material (Kg/Ha)	Basal fertilizer (ZMK/Kg)	Top fertilizer (ZMK/Kg)	Seed/planting material (ZMK/Kg)	Plough (ZMK/Ha)	Total Variable Costs (ZMK/Ha)
MZ1			30.80			0.08		2.43
MZ4	132.07	140.43	25.65	2.46	2.62	6.80		867.69
MZ6			29.77			0.08	40.81	43.16
MZ9	103.69	134.19	29.39	2.46	2.62	0.08		609.34
GR1			51.83			0.32		16.43
GR2			39.87			0.32		12.64
GR6			46.84			0.32	40.81	55.66
GR12			46.09			2.73		125.63
SUN2			14.13			0.58		8.22
SUN10			13.53			8.04	40.81	149.62
SP2			631.08			0.03		17.68
SP12			695.15			0.10		67.67
COT10			26.95			3.91	40.81	146.07
COT12			26.68			3.91		104.19

Sources: SS 2004 and 2008, and RALS 2012 (fertilizer prices); CFS 2012 (seed and plough prices); CFS 2003–2012 (fertilizer/ha); RALS 2012 (seed/ha).

Note: Expenditures on herbicides and pesticides are omitted, as they are used by only a small proportion of Zambian households (4.36% and 12.22%, respectively) (source: RALS 2012).

Note: All figures are mean values, specific to the study site. When fewer than 30 observations are found, the geographic range is expanded to province. Seed that was free or saved from an earlier harvest is included in these estimates as having a cost of zero.

Table 4 Household endowments and crop productivity (mean values).

	Site 1		Site 2
	Smallholders	Emergent farmers	Smallholders	Emergent farmers
Land owned (ha)	1.92	7.33	1.49	8.46
Prime-age members	2.54	3.16	2.66	2.56
Adult equivalents	4.11	5.05	4.04	4.74
Fertilizer expenditure (ZMK)	267.94	1,105.70	206.80	615.31
Crop calories produced (1,000 s)	6482	21,905	5963	19,826
Gross value crop production (ZMK)	2756	9253	2927	10,736
Observations	1952	400	598	231

Sources: SS 2008 and RALS 2012 (pooled).

Table 5 Climate predictions of HadCM3 and CCSM.

		Baseline		Year 2050
		Meteorological station data		Expected% change (GCM projections)
Site	Climate variable^a	Mean	SD	HadCM3	CCSM
1	Rainfall (mm)	989.70	(286.25)	−8.34	3.84
	Average temperature (°C)	24.20	(0.46)	9.76	9.26
	CV rain within season	0.48	(0.16)	1.89	−0.23
2	Rainfall (mm)	1,039.47	(214.82)	−0.75	6.93
	Average temperature (°C)	20.46	(0.66)	10.52	9.43
	CV rain within season	0.37	(0.19)	9.32	3.67

a All variables refer to the November–March growing season.

Table A4 Derivation of expected yield changes for selected crop regimes (site 1).

	Coefficients								Estimated% change
	Year	Rain	Rain^2	Temp	Temp^2	CVrain	Obs.	Adj. R^2	HadCM3	CCSM
MZ4	0.04	1.41E-03	−5.83E-07	−0.02		−0.52	627	0.46	−8.22%	−4.02%
	(0.00)	(0.00)	(0.00)	(0.20)		(0.00)
MZ6	0.02	1.49E-03	−6.62E-07	−0.01		−0.56	642	0.39	−5.48%	−2.24%
	(0.00)	(0.00)	(0.00)	(0.41)		(0.00)
SUN10	0.06			0.02		−0.45	313	0.27	+5.37%	+5.53%
	(0.00)			(0.40)		(0.01)
COT10	0.03	−2.51E-04		2.42	−0.05	−0.82	245	0.36	+5.05%	+3.98%
	(0.01)	(0.05)		(0.00)	(0.01)	(0.00)
COT12	0.03	−2.51E-04		2.42	−0.05	−0.82	245	0.36	+5.05%	+3.98%
	(0.01)	(0.05)		(0.00)	(0.01)	(0.00)

Sources: ZMD and IPCC (2013b).

P-values in parentheses. Coefficients of district dummies selected as regressors are not shown.

Table 6 Estimated yield changes under climate change scenarios.

Site 1			Site 2
	Expected% change			Expected% change
Crop regime	HadCM3	CCSM	Crop regime	HadCM3	CCSM
MZ1	−5.48	−2.24	MZ1	−4.79	−2.77
MZ4	−8.22	−4.02	MZ2	−4.79	−2.77
MZ6	−5.48	−2.24	MZ3	−6.72	−3.86
MZ9	−12.55	−11.42	MZ4	−6.72	−3.86
GR1	−41.25	−37.05	GR1	+4.00	+5.68
GR2	−41.25	−37.05	GR2	+4.00	+5.68
GR6	−41.25	−37.05	GR6	+4.00	+5.68
GR12	−15.18	−12.06	GR12	−15.10	−11.07
SUN2	+3.98	−2.05	CAS1	+5.61	+8.68
SUN10	+5.37	+5.53	CAS2	+5.82	+6.10
SP2	−0.15	−0.24	SP2	−1.06	−1.40
SP12	−14.03	−13.67	SP12	−11.79	−11.23
COT10	+5.05	+3.98	MIL1	−22.41	−21.74
COT12	+5.05	+3.98	MIL2	−22.41	−21.74
			MB1	−10.32	−7.97
			MB2	−10.32	−7.97
			RIC1	−18.92	−17.72
			RIC2	−18.92	−17.72

Source: Authors’ calculation based on CFS (2003–2011) and the climate predictions of Table 5.

Table 7 Baseline results.

	Site 1			Site 2
	Crop regime	Smallholder	Emergent	Crop regime	Smallholder	Emergent
Budget constraint (ZMK)		100	650		100	650
Budget constraint binding?		Yes	Yes		Yes	Yes
Land binding?^a		Yes	No		Yes	No
Land cultivated (ha)		1.82	4.31		1.49	3.52
Labor binding (months)		Dec, Jan, June	Jan, Feb, May, June		Oct–Dec	Oct–Dec, June, July
Net returns per AE per day (ZMK)		1.37	3.20		1.90	4.45
Calories per AE per day		4999.95	10,131.01		5498.42	9084.99
Ha per crop regime	MZ1	1.66	0.14	MZ1	0.35	0.00
	MZ4	0.02	0.00	MZ2	0.34	0.12
	SUN10	0.00	2.13	MZ3	0.04	0.36
	SP2	0.03	0.00	GR1	0.16	0.18
	COT10	0.10	2.03	GR6	0.00	1.33
	Fallow	0.10	3.02	CAS2	0.00	0.29
				SP2	0.00	0.00
				SP12	0.36	0.25
				MIL2	0.00	1.00
				RIC1	0.23	0.00
				Fallow	0.00	4.94
Validation tests
Total% difference in land use		36.08	46.03		65.00	26.97
% deviation (gross value production)		21.83	29.18		0.65	22.29
% deviation (calories produced, excluding cotton)		5.46	73.64		35.97	20.72

Source: Authors’ calculations.

a The land constraint can be binding even when some land is left fallow, as the models require that land be left fallow when cotton or cassava are selected.

Table A5 Validation tests of baseline LP models.

Site 1	Smallholder			Emergent
	Prediction	Selection	% Difference^a	Prediction	Selection	% Difference
Crops (ha)
Maize	1.02	1.68	34.47	2.93	0.14	−38.03
Cotton	0.29	0.10	−9.54	1.10	2.03	12.75
Groundnuts	0.25	0.00	−13.00	0.59	0.00	−8.00
Sweet Potatoes	0.00	0.03	1.61	0.00	0.00	0.00
Sunflower	0.12	0.00	−6.00	0.37	2.13	24.07
Fallow	0.25	0.10	−7.54	2.35	3.02	9.21
Total	1.92	1.92		7.33	7.33
Total% difference in land use			36.08			46.03
Gross value production (ZMK)	2756.26	2154.42	21.83	9253.29	6553.29	29.18
Calories produced, excluding cotton (1,000s)	6481.60	6835.72	5.46	21,905.13	5773.78	73.64
Site 2
Crops (ha)
Maize	0.31	0.74	28.36	1.35	0.48	−10.35
Cassava	0.33	0.00	−22.00	0.93	0.29	−7.61
Millet	0.07	0.00	−5.00	0.25	1.00	8.82
Groundnuts	0.10	0.16	4.01	0.34	1.51	13.89
Mixed beans	0.18	0.00	−12.00	0.68	0.00	−8.00
Sweet Potatoes	0.01	0.36	23.16	0.08	0.25	1.90
Rice	0.07	0.23	10.46	0.08	0.00	−1.00
Fallow	0.37	0.00	−25.00	4.74	4.94	2.35
Total	1.49	1.49		8.46	8.46
Total% difference in land use			65.00			26.97
Gross value production (ZMK)	2926.86	2908.08	0.65	10,736.03	8342.43	22.29
Calories produced, excluding cotton (1,000s)	5962.72	8107.97	35.97	19,825.95	15,717.94	20.72

Sources of predicted values: SS 2008, CFS 2008–2010, and RALS 2012.

a The% difference for a given crop is calculated as [(Prediction (ha) − Model selection (ha))/Total land (ha)]*100. The total% difference in land use, our validation test, is calculated as the sum of absolute values of the% land misplaced in the above rows, divided in half. The latter step is necessary because we would otherwise be double-counting each unit of ‘misallocated' land.

Fig. 2 Cropping choices under HadCM3 climate change scenario.

Source: Authors’ calculations

Table 8 Calories reclaimed or gained through adaptation.

	Site 1		Site 2
	Smallholder	Emergent	Smallholder	Emergent
Baseline
Calories/AE/day	5000	10,131	5498	9085
HadCM3
Calories − Without adaptation	4774	10,619	5071	8548
Calories − With adaptation	4842	10,633	5199	8724
% change in calories with adaptation	−3.16	4.95	−5.44	−3.97
% calories reclaimed/gained through adaptation	1.35	0.14	2.34	1.94
% calories reclaimed through adaptation (of what would be lost)	29.98	N/A	30.03	32.83
CCSM
Calories − Without adaptation	4915	10,559	5158	8690
Calories − With adaptation	4942	10,561	5297	8841
% change in calories with adaptation	−1.17	4.25	−3.67	−2.68
% calories reclaimed/gained through adaptation	0.53	0.03	2.53	1.66
% calories reclaimed through adaptation (of what would be lost)	31.08	N/A	40.81	38.26

Source: Authors’ calculations.

Table 9 Smallholder vulnerability to crop shortfalls.

	Mean calories produced or acquired/AE/day	Likelihood of falling below
		3000 cal/AE/day	Monte Carlo baseline mean calories/AE/day
Site 1
Baseline	4813.92	0.80%	45.60%
HadCM3	4606.56	1.20%	60.20%
CCSM	4726.78	0.60%	53.70%
Site 2
Baseline	5309.16	0.20%	41.80%
HadCM3	4934.79	0.70%	70.80%
CCSM	5001.58	0.40%	67.30%

Source: Authors’ calculations.