Chapter 5. Empirical estimation and predictions

In the analysis of poverty in Ecuador, the spatial autocorrelation of household consumption was calculated for the total sample (5 630 households), the rural households (2 264) and the urban households (3 366). Table 4 shows that there is a large and significant spatial autocorrelation in rural household consumption, whereas it is small but significant for the total sample and urban household consumption.

In order to account for the presence of significant spatial autocorrelation in the data, three spatial probit models were constructed: for the total sample and for the subsamples of the rural and urban households. The coefficient values, their z-value in all three models, were analysed and it was verified that there were no large differences. Hence, it was decided to use only one model: the total sample model.

Table 5 gives the estimated coefficients of the spatial probit regression that estimates the probability that the household is poor as a function of various households’ characteristics, various characteristics of the area in which the household resides and of a component (y*) standing for the spatial dimension. Table 5 reports the standard errors. Even if they do not have a theoretical meaning, they can have a descriptive value and provide some general information. However, some studies where the standard errors are computed both by standard statistical packages and bootstrap simulation techniques remark on the comparability of the results.

In both rural and urban areas, the household variables that have a significant relationship to a household’s probability of being poor are the adult literacy rates (if the components of the household have a diploma, the household’s probability of being poor decreases). The same effect is related to the adequacy of the house and to the presence of a waste collection truck (if the household lives in a house with solid walls and a toilet and there is the regular presence of a waste collection truck, the household’s probability of being poor decreases). Moreover, as the number of persons living in a single room of the house increases, the household’s probability of being poor also increases.

TABLE 4. Spatial autocorrelation

Spatial correlation estimate (total sample)

Statistic = “Moran”

Sampling = “free”

Correlation = 0.177

Null hypothesis: no spatial autocorrelation (rejection)

Spatial correlation estimate (rural sample)

Statistic = “Moran”

Sampling = “free”

Correlation = “0.651”

Null hypothesis: no spatial autocorrelation (rejection)

Spatial correlation estimate (urban sample)

Statistic = “Moran”

Sampling = “free”

Correlation = 0.0532

Null hypothesis: no spatial autocorrelation (rejection)

All the variables at the county level have a significant correlation with poverty. In particular, households living in counties with a high population density and high mortality rates have high probabilities of being poor.

Environmental factors also have a significant relationship to a household’s probability of being poor. In particular, households living close to roads, in large counties and with irrigation systems have a low probability of being poor.

TABLE 5. Coefficient estimates, standard error, z-value of the autologistic model
Coefficients	Estimate	Std. error	zvalue	Pr(>\|z\|)	Significance
Percentage adults illiterate in household	2.69E-02	1.02E-01	0.263	0.792368
Percentage persons with diploma	-2.12E+00	2.49E-01	-8.519	2.00E-16	***
Adequate home	-7.62E-02	6.33E-02	-1.204	0.228537
Home with drinking-water	-6.85E-03	5.01E-02	-0.137	0.891297
Home with adequate toilet	-1.07E-01	6.20E-02	-1.727	0.084099	.
Home with adequate wall	-1.83E-01	4.68E-02	-3.91	9.24E-05	***
Home with public electricity network	8.40E-02	7.28E-02	1.154	0.248359
Waste collection by truck	-3.13E-01	5.24E-02	-5.977	2.28E-09	***
Persons per room	3.75E-01	1.69E-02	22.142	2.00E-16	***
Population	7.98E-06	2.99E-06	2.67	0.007594	*
Mortality rate ()	5.81E-03	2.48E-03	2.347	0.018943	*
Number of babies	-2.80E-04	1.39E-04	-2.011	0.044284	*
Slippery and landslide	4.06E-01	2.05E-01	1.987	0.046905	*
Sulifluxion	3.61E-01	1.81E-01	1.997	0.045802	*
Temperate dry	4.93E-01	2.22E-01	2.221	0.026349	*
Temperate humid	2.88E-01	2.11E-01	1.363	0.173001
Hot and temperate	1.88E-01	2.22E-01	0.846	0.397364
Hot and temperate humid	8.46E-01	3.73E-01	2.264	0.023572	*
Flooding area	1.77E-01	1.48E-01	1.196	0.231526
Volcano area	6.42E-02	1.50E-01	0.428	0.668536
Spatial correlation variable (y*)	-1.35E-03	3.51E-04	-3.851	0.000118	***
Rural or urban	5.74E-02	6.01E-02	0.955	0.339784
People < 5 km from road	-2.34E-06	8.70E-07	-2.692	0.007101	*
People 5-15 km from road	1.95E-06	3.00E-06	0.651	0.515001
People > 15 km from road	-8.83E-07	1.20E-05	-0.074	0.941289
County surface (km²)	-3.15E-05	7.60E-06	-4.142	3.45E-05	***
Cereal production coefficient	3.83E-04	2.05E-04	1.871	0.061304	.
Protected area	1.01E-01	7.59E-02	1.332	0.18282
> 35% of irrigation area	-2.18E-01	7.44E-02	-2.925	0.00345	*
Closed forest	3.06E-02	6.90E-02	0.443	0.657655
Arable land (30-60%)	3.01E-02	7.61E-02	0.395	0.692683
Arable land (> 60%)	3.35E-01	2.15E-01	1.556	0.119686

Significance codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1.

Finally, it is important to underline the significant effect of the spatial correlation variable (y*) that denotes the presence of clusters in the spatial distribution of poverty and the influence between neighbour households on the probability of being poor.

The estimated parameters of the autol ogistic model (Equation 12) were applied to the data in the county database (INFOPLAN) in order to predict the distribution of poverty across all the counties in Ecuador. The percentage of poor households in each county was obtained from Equation 15.

In order to count the number of poor individuals, the average households’components in each county were multiplied by the number of poor families in each county (Figure 1).

Table 6. Poverty level comparison (in ascending order): econometric estimation and ECV data
County	% poor persons	County	Probit model (%)	County	Spatial probit model (%)
Milagro	16.7	Quito	7.6	Quito	10.8
Rumiñahui	17.0	Guayaquil	21.5	Rumiñahui	23.2
Quito	29.2	Rumiñahui	21.7	Cuenca	29.5
Zamora	31.5	Cuenca	29.6	Guayaquil	31.7
Quevedo	32.1	Machala	31.4	Machala	32.0
S. Dom. Colorados	32.7	Portoviejo	33.2	Portoviejo	33.5
Tena	33.3	Ambato	34.6	Ambato	35.2
Guayaquil	33.9	Manta	35.4	S. Dom. Colorados	36.5
Santa Rosa	34.0	S. Dom. Colorados	36.8	Manta	37.5
Machala	35.8	Quevedo	40.6	Quevedo	42.8
Pastaza	36.9	Esmeraldas	42.6	Pastaza	44.8
Ambato	38.2	Pastaza	43.6	Baños	45.6
Manta	40.7	Riobamba	44.6	Riobamba	45.8
Cuenca	42.3	Baños	45.3	Esmeraldas	45.8
Portoviejo	43.1	Loja	46.5	Loja	47.5
Baños	45.5	Milagro	47.8	Milagro	49.4
Playas	45.5	Santa Rosa	51.0	Santa Rosa	52.2
Morona	47.1	Cayambe	53.2	Cayambe	52.3
Cayambe	48.1	Piñas	53.5	Piñas	53.7
Santa Elena	49.6	Sucre	54.2	Sucre	55.9
S. Miguel De Los Bancos	50.0	Ibarra	56.8	Zamora	57.7
Gualaquiza	50.8	Zamora	57.7	Ibarra	58.9
Sucua	50.9	Playas	58.0	Playas	60.0
Esmeraldas	51.7	Tulcan	59.6	Urdaneta	60.1
Ventanas	51.9	Urdaneta	60.6	Junin	60.9
Urdaneta	52.1	Junin	61.3	Tulcan	61.1
Montecristi	54.5	Chimbo	62.2	Chimbo	62.2
Ibarra	54.7	Montecristi	64.1	Sucua	64.0
Quero	56.9	Morona	64.2	S. Miguel De Los Bancos	64.2
Sucre	57.6	S. Miguel De Los Bancos	64.4	Gualaquiza	64.2
Tulcan	58.8	El Empalme	65.5	Morona	64.3
Santa Lucia	59.3	Sucua	65.8	Montecristi	66.8
Chimbo	60.0	Gualaquiza	65.9	Tena	67.1
Loja	60.4	Tena	67.2	El Empalme	67.2
Junin	61.1	La Troncal	68.0	Quero	67.6
Lago Agrio	61.1	Ventanas	68.3	La Troncal	68.9
Catamayo	63.6	Quero	69.3	Ventanas	70.0
Riobamba	64.3	Catamayo	70.3	San Juan Bosco	71.3
Piñas	65.3	Jipijapa	70.8	Jipijapa	71.5
San Juan Bosco	67.8	Santa Elena	70.9	Catamayo	72.2
Santa Isabel	69.1	Calvas	71.4	Calvas	72.7
La Troncal	71.2	San Juan Bosco	71.9	Santa Elena	72.9
El Empalme	72.2	Montufar	72.3	Lago Agrio	73.1
Saraguro	72.4	Lago Agrio	72.7	Montufar	73.6
Calvas	72.5	Gualaceo	74.9	Gualaceo	75.8
Montufar	73.4	Zapotillo	76.5	Zapotillo	77.5
Quininde	76.4	Quininde	79.5	Quininde	78.6
Cotacachi	80.6	Santa Lucia	80.5	Santa Lucia	80.2
Zapotillo	80.9	Cotacachi	80.9	Cotacachi	80.8
Jipijapa	81.9	Santa Isabel	83.0	Santa Isabel	82.6
Gualaceo	82.2	Saraguro	85.6	Saraguro	85.7
Urbina Jado	84.1	Urbina Jado	87.8	Urbina Jado	88.8
Guamote	87.5	Guamote	95.9	Guamote	96.3
Total	47.7		45.6		48.2

Notes: Spearman coefficients: ECV and probit model = 0.781; ECV and spatial probit model = 0.791; probit model and spatial probit model = 0.995.

The first validation test draws its conclusion about the reliability of the incidence of poverty from the counties’ranking. The higher the coefficient of rank correlation for the counties, the higher the likelihood that the ranking of counties established by these estimates will also be highly correlated with the ranking established by the ECVdata. Table 6 compares the results using the probit model and the spatial probit model with the estimates obtained directly from the ECVdata.

Figure 2 shows the aggregate poverty situation at the province level. Table 7 compares these results with those obtained by applying a probit regression without the spatial component.

Figure 1. Percentage of poor people in each county

Figure 2. Percentage of poor people in each province

Table 7. Comparison between probit and spatial probit in the headcount index and in the percentage of poor people in the provinces of Ecuador, total sample
Province	Total poor Bigman (a)	Total poor spatial p. (b)	Total pop.	% poor Bigman (a)	% poor spatial p. (b)	*Differences [((b-a)/b)100]**
Azuay	235 579	235 692	506 090	46.5	46.6	0.048
Bolivar	107 848	108 660	155 088	69.5	70.1	0.747
Ca_ar	138 804	140 292	185 927	74.7	75.5	1.061
Carchi	97 513	98 698	141 482	68.9	69.8	1.200
Chimborazo	242 872	245 923	362 430	67.0	67.9	1.240
Cotopaxi	196 531	197 070	276 324	71.1	71.3	0.273
El Oro	199 160	201 868	412 725	48.3	48.9	1.342
Esmeraldas	205 404	209 311	315 449	65.1	66.4	1.867
Guayas	941 136	1 115 349	2517 398	37.4	44.3	15.620
Imbabura	178 447	181 566	265 499	67.2	68.4	1.718
Loja	254 383	257 534	384 545	66.2	67.0	1.223
Los Rios	324 256	330 755	527 559	61.5	62.7	1.965
Manabi	570 799	576 256	1 031 927	55.3	55.8	0.947
Morona Santiago	58 653	57 962	84 216	69.6	68.8	-1.193
Napo	40 434	40 063	57 316	70.5	69.9	-0.926
Orellana	34 845	34 930	46 328	75.2	75.4	0.243
Pastaza	21 227	21 448	41 554	51.1	51.6	1.029
Pichincha	264 323	306 122	1 756 228	15.1	17.4	13.654
Sucumbios	58 287	57 895	76 952	75.7	75.2	-0.677
Tungurahua	157 685	157 312	361 980	43.6	43.5	-0.237
Zamora Chinchipe	44 769	44 517	66 167	67.7	67.3	-0.567
Total	4 372 957	4 619 221	9 573 184	45.6	48.2	5.394

Table 8. Comparison between probit and spatial probit in the headcount index and in the percentage of poor people in the provinces of Ecuador, rural sample
Province	Total poor Bigman (a)	Total poor spatial p. (b)	Total pop.	% poor Bigman (a)	% poor spatial p. (b)	*Differences [((b-a)/b)100]**
Azuay	207 797	204 639	302 537	68.7	67.6	-1.543
Bolivar	103 282	103 631	139 358	74.1	74.4	0.337
Ca_ar	110 052	110 075	130 958	84.0	84.1	0.021
Carchi	75 624	75 176	92 440	81.8	81.3	-0.596
Chimborazo	217 438	217 950	255 942	85.0	85.2	0.235
Cotopaxi	176 080	175 486	214 655	82.0	81.8	-0.338
El Oro	89 114	87 217	123 728	72.0	70.5	-2.175
Esmeraldas	144 262	143 221	172 741	83.5	82.9	-0.727
Guayas	309 035	307 138	414 686	74.5	74.1	-0.618
Imbabura	123 950	123 367	142 879	86.8	86.3	-0.472
Loja	208 061	207 866	250 089	83.2	83.1	-0.094
Los Rios	227 863	227 714	294 834	77.3	77.2	-0.065
Manabi	391 569	386 384	542 961	72.1	71.2	-1.342
Morona Santiago	55 657	54 802	75 970	73.3	72.1	-1.560
Napo	38 381	37 838	49 443	77.6	76.5	-1.437
Orellana	31 294	31 148	38 523	81.2	80.9	-0.468
Pastaza	18 707	18 600	27 116	69.0	68.6	-0.575
Pichincha	119 782	112 367	367 646	32.6	30.6	-6.599
Sucumbios	50 358	49 597	63 787	78.9	77.8	-1.535
Tungurahua	134 471	131 623	217 213	61.9	60.6	-2.164
Zamora Chinchipe	42 364	41 937	58 119	72.9	72.2	-1.018
Total	2 875 141	2 847 776	3 975 625	72.3	71.6	-0.977

Table 9. Comparison between probit and spatial probit in the headcount index and in the percentage of poor people in the provinces of Ecuador, urban sample
Province	Total poor Bigman (a)	Total poor spatial p. (b)	Total pop.	% poor Bigman (a)	% poor spatial p. (b)	Differences *[((b-a)/b)100]**
Azuay	27 783	31 053	203 553	13.6	27.0	10.531
Bolivar	4 566	5 029	15 730	29.0	25.7	9.198
Ca_ar	28 752	30 216	54 969	52.3	52.6	4.847
Carchi	21 889	23 522	49 042	44.6	42.8	6.942
Chimborazo	25 434	27 973	106 488	23.9	28.3	9.075
Cotopaxi	20 452	21 585	61 669	33.2	36.3	5.249
El Oro	110 046	114 651	288 997	38.1	43.7	4.017
Esmeraldas	61 141	66 090	142 708	42.8	48.4	7.488
Guayas	632 101	808 211	2 102 712	30.1	39.6	21.790
Imbabura	54 497	58 199	122 620	44.4	46.3	6.361
Loja	46 323	49 667	134 456	34.5	33.9	6.734
Los Rios	96 394	103 040	232 725	41.4	46.3	6.451
Manabi	179 230	189 872	488 966	36.7	40.7	5.605
Morona Santiago	2 996	3 160	8 246	36.3	36.9	5.169
Napo	2 052	2 225	7 873	26.1	31.5	7.774
Orellana	3 551	3 781	7 805	45.5	49.4	6.098
Pastaza	2 520	2 848	14 438	17.5	31.7	11.505
Pichincha	144 542	193 756	1 388 582	10.4	19.6	25.400
Sucumbios	7 929	8 298	13 165	60.2	62.9	4.453
Tungurahua	23 214	25 689	144 767	16.0	23.2	9.636
Zamora Chinchipe	2 405	2 579	8 048	29.9	28.9	6.776
Total	1 497 815	1 771 445	5 597 559	26.7	31.6	15.506

With the spatial probit regression, the percentage of poor persons in the total population is 48 percent, compared with 45 percent for the probit regression. The difference (5.39 percent) is very significant. For the rural population, the corresponding figures for the spatial probit regression and the probit regression are 71 and 72 percent respectively (Table 8). The differences among the urban population are more evident (Table 9), even if the spatial autocorrelation is very small. These differences are very important if poverty distribution is analysed at the county level (Table A.1 in Annex A).

TABLE 10. Comparison of three methods for estimating poverty, percentage of poor people in Ecuador
Area	Method
Area	*Lanjouw et al.* (1995)**	Bigman et al.	Spatial probit
Costa	54	46	50
Urban	43	33	39
Rural	75	75	74
Sierra	58	42	44
Urban	42	17	20
Rural	78	69	69
Oriente	65	69	69
Urban	47	36	39
Rural	70	75	75
Ecuador	56	45	48
Urban	42	26	31
Rural	76	72	71

Figure 3. Comparison between the Lanjouw et al. method and spatial probit at regional level

Figure 4. Comparison between the Bigman et al. method and spatial probit at regional level

The method applied in this study for poverty mapping at the level of small geographical areas provides a more accurate specification of poverty by incorporating a spatial component into the classical model regression.

Recalling the comparison performed in Chapter 3, Table 10 and Figures 3 and 4 compare the percentage of poor individuals at the regional level as obtained with spatial probit regression with the percentage of poor persons using the Lanjouw et al. and Bigman et al. methods.