Heterogeneity in agricultural factor productivity across and within farm size groups in Brazil

MEINERS, PEDRO GABRIEL; TORRES, MARCELO DE OLIVEIRA

doi:10.5935/0034-7140.20220005

PEDRO GABRIEL MEINERS pg.meiners@gmail.com

Universidade de Brasília, Departamento de Economia. Campus Universitario Darcy Ribeiro, FACE, Asa Norte, Brasilia, DF, CEP CEP 70910-900, Brasil. iD 0000-0001-6395-8839

https://orcid.org/0000-0001-6395-8839

MARCELO DE OLIVEIRA TORRES motorres@hotmail.com.br

Universidade de Brasília, Departamento de Economia. Campus Universitario Darcy Ribeiro, FACE, Asa Norte, Brasilia, DF, CEP CEP 70910-900, Brasil. iD 0000-0003-4277-8497

https://orcid.org/0000-0003-4277-8497

pg.meiners@gmail.com

motorres@hotmail.com.br

LASG(ha)	Number of Farms	Land Area(ha)	Labor Force (persons)	Purchased Inputs (R$ 1000)	Stock Capital (indexed units	Total Production (R$ 1000)
0–5	1,735,615 (37%)	1,917,812 (3%)	4,659,860 (31%)	2,788,405 (3%)	2,672,774 (7%)	10,501,654(3%)
5–20	1,298,667 (27%)	5,103,019 (10%)	3,823,178 (25%)	7,376,760 (10%)	6,472,814 (17%)	21,576,151 (15%)
20–100	1,196,948 (25%)	10,804,917 (21%)	3,985,668 (26%)	12,480,511 (17%)	10,030,734 (27%)	34,180,602 (24%)
100–500	358,908 (7%)	12,797,311 (25%)	1,621,092 (10%)	16,084,866 (22%)	8,832,156 (23%)	30,583,036 (21%)
>500	90,295 (2%)	20,330,326 (39%)	859,363 (5%)	31,761,024 (45%)	8,852,299 (24%)	44,247,807 (31%)
Brazil	4,680,433	50,953,385	14,949,161	70,491,565	36,860,777	141,089,251

LASG(ha)	Labor Force (persons)	Purchased Purchased Inputs (R$ 1000)	Stock Capital (indexed units	Total Production (R$ 1000)
0–5	2.429	1.453	1.393	5.475
5–20	0.749	1.445	1.265	4.228
20–100	0.368	1.155	0.928	3.163
100–500	0.126	1.256	0.690	2.389
>500	0.042	1.562	0.435	2.176

LASG (ha)	Land Area (ha)	Labor Force (persons)	Purchased Inputs (R$ 1000)	Stock Capital (indexed units)	Total Production (R$ 1000)
0–5
Max	825	24878	28087	147484	235169
Min	0.03	10	0.12	0.012	0.27
Mean	440.97	1071.47	641.16	614.57	2414.72
SD	710.52	1777.32	1215.32	3830.64	6451.38
5–20
Max	27240	13833	353071	351304	291113
Min	1	11	0.07	0.05	6
Mean	1081.14	809.99	1562.87	1371.35	4571.21
SD	1476.03	948.56	7132.23	7230.08	9922.2
20–100
Max	68362	11891	67211	174688	319601
Min	3.5	6	0.37	0.10	9.25
Mean	2235.19	824.5	2581.81	2075.03	7070.87
SD	3003.98	954.64	4124.08	6184.18	12417.85
100–500
Max	157312	7870	1081276	91961.55	876303.2
Min	1.2	5	0.23	0.007	6.10
Mean	2839.43	359.68	3568.86	1959.65	6785.67
SD	5248.15	475.91	18984.7	5084.45	18458.83
>500
Max	478887	11141	1194391	134477	794353
Min	3.5	8	0.00	0.01	0.41
Mean	8629.17	364.75	13480.91	3757.34	18780.9
SD	27587.15	591.45	62589.98	8797.89	49524.76

Inputs	Aggregated	0–5 ha	5–20 ha	20–100 ha	100–500 ha	>500 ha
Land	1.7%	10.6%	5.3%	0.5%	1%	4.5%
Labor	16%	19.2%	33.8%	17.8%	20.2%	7.2%
Purchased	0%	0.3%	0%	0.2%	0%	0%
Capital	16.2%	6.2%	11.4%	10%	8.6%	5.6%

Inputs	Aggregated	0–5 ha	5–20 ha	20–100 ha	100–500 ha	>500 ha
ψ̂ _A	0.1789	0.0677	0.1821	0.1711	0.1883	0.2312
ψ̂ _L	0.0640	0.1718	0.0563	0.0480	0.0792	0.1723
ψ̂ _I	0.5294	0.5585	0.5324	0.5648	0.5082	0.4282
ψ̂ _K	0.1963	0.1860	0.2089	0.1972	0.1987	0.2231
Σψ	0.9687	0.9840	0.9797	0.9811	0.9744	1.0549
N	4,913	4,349	4,720	4,834	4,507	2,356

\ln Y_{i} = α_{0} + \sum_{k = 1}^{4} β_{k} \ln X_{k i} + \frac{1}{2} \sum_{k = 1}^{4} \sum_{h = 1}^{4} γ_{k h} \ln X_{h i} + \sum_{w = 1}^{2} ω_{w} \ln W_{w i} + \frac{1}{2} \sum_{w = 1}^{2} \sum_{z = 1}^{2} ζ_{w z} \ln W_{w i} \ln W_{z i} + \sum_{w = 1}^{2} \sum_{k = 1}^{4} μ_{w k} \ln W_{w i} \ln X_{k i} + u_{i},

\ln Y_{c i} = α_{0} + \sum_{k = 1}^{4} β_{c k} \ln X_{c k i} + \frac{1}{2} \sum_{k = 1}^{4} \sum_{h = 1}^{4} γ_{c k h} \ln X_{c k i} \ln X_{c h i} + \sum_{w = 1}^{2} ω_{w} \ln W_{w i} + \frac{1}{2} \sum_{w = 1}^{2} \sum_{z = 1}^{2} ζ_{w z} \ln W_{w i} \ln W_{z i} + \sum_{w = 1}^{2} \sum_{k = 1}^{4} μ_{c w k} \ln W_{w i} \ln X_{c k i} + u_{c i} .

{\hat{ψ}}_{X_{k i}} = \frac{\partial \ln Y_{i}}{\partial \ln X_{k i}} = {\hat{β}}_{k} + {\hat{γ}}_{k k} \ln X_{k i} + \sum_{h = 1}^{3} {\hat{γ}}_{j h} \ln X_{h i} + \sum_{w = 1}^{2} {\hat{μ}}_{w k} \ln W_{w i}

{\hat{ψ}}_{X_{c k i}} = \frac{\partial \ln Y_{c i}}{\partial \ln X_{c k i}} = {\hat{β}}_{c k} + {\hat{γ}}_{c k k} \ln X_{c k i} + \sum_{h = 1}^{3} {\hat{γ}}_{c j h} \ln X_{c h i} + \sum_{w = 1}^{2} {\hat{μ}}_{c w k} \ln W_{w i}

{\hat{ψ}}_{X_{c k i}} (θ) = \frac{\partial Q_{\ln Y} (θ | X)}{\partial \ln X_{c k i}} = {\hat{β}}_{c k} (θ) + {\hat{γ}}_{c k k} (θ) \ln X_{c k i} + \sum_{h = 1}^{5} {\hat{γ}}_{c j h} (θ) \ln X_{c h i},

\min_{b_{c} \in ℝ} [\sum_{(i / \ln Y_{c i} > \ln X_{c i}^{T} b_{c})} | \ln Y_{c i} - \ln X_{c i}^{T} b_{c} | + \sum_{(i / \ln Y_{c i} < \ln X_{i}^{T} b_{c})} | \ln Y_{c i} - \ln X_{c i}^{T} b_{c} |] .

L V_{c b i} = L_{c b i} * \frac{S V_{c b i}}{S_{c b i}} or L V_{c b i} = L_{c b i} * \frac{\sum_{i} S V_{c b i}}{\sum_{i} S_{c b i}},

[1] pg.meiners@gmail.com

Brasil

Brasil

Heterogeneity in agricultural factor productivity across and within farm size groups in Brazil

Abstract