Poverty projection using a small area estimation method: Evidence from Vietnam

Journal of Comparative Economics 39 (2011) 368–382

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Poverty projection using a small area estimation method: Evidence from Vietnam Nguyen Viet Cuong ⇑ Indochina Research; Consulting, Suite 1701, C’land Tower, Xa Dan, Dong Da, Hanoi, Vietnam

a r t i c l e

i n f o

Article history: Received 12 July 2009 Revised 21 April 2011 Available online 6 May 2011 JEL classification: I31 I32 C53 Keywords: Poverty measurement Poverty projection Poverty mapping Vietnam

a b s t r a c t Cuong, Nguyen Viet—Poverty projection using a small area estimation method: Evidence from Vietnam For poverty monitoring and evaluation, one needs poverty estimates at the different disaggregation levels. The prediction of poverty trend is also of interest for policy makers as well as researchers. This paper presents a method – that is based on a small area estimation method of Elbers et al. (2003) – to project a map of disaggregated poverty measures in the future. This method is applied to project a poverty map in rural Vietnam for the year 2008 using the 2006 Rural, Agricultural and Fishery Census and the 2004 and 2006 Vietnam Household Living Standard Surveys. Journal of Comparative Economics 39 (3) (2011) 368–382. Indochina Research; Consulting, Suite 1701, C’land Tower, Xa Dan, Dong Da, Hanoi, Vietnam. Ó 2011 Association for Comparative Economic Studies Published by Elsevier Inc. All rights reserved.

1. Introduction Poverty alleviation is a major policy goal in developing countries. Numerous poverty reduction programs have been implemented throughout the world, and the impact of these programs on poverty depends heavily on their poverty targeting. Poverty maps – a geographical visualization of poverty estimates – are an important tool for poverty targeting of antipoverty programs. Elbers et al. (2007) found that the impact of budget transferring on poverty is larger when geographic targeting units are smaller. Other studies such as Baker and Grosh (1994), Bigman and Fofack (2000) also highlight the role of geographic targeting in poverty reduction. Other positive impacts and applications of poverty maps can be found in Bedi et al. (2007). Yet, estimation of poverty measures at different disaggregation levels is not simple. Data on expenditure (or income) which are used for poverty estimation are available in household surveys. However, household surveys often have small sample sizes that are not representative for small areas. Population censuses, on the other hand, cover all households but do not contain information on expenditure and income. Fortunately, a so-called small area estimation method proposed by Elbers et al. (2002, 2003) can overcome the problem of data shortage in estimating disaggregated poverty measures by combining a household survey and a census. According to this method, a relation between household expenditure (or income) and household characteristics is modeled using data from a household survey. Then, this modeled relation is applied into a census to estimate expenditure for all households covered in this census, and these estimated expenditure data are used to compute poverty measures for small areas.

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N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382

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Poverty trends are also of interest for policy makers as well as researchers. Regular construction of poverty maps cannot be done by straightforward application of the method of Elbers et al. (2002, 2003), since censuses are not carried out on a regular basis. In most countries, censuses are often carried out every 10 years. Several studies produce poverty maps for non-census years by combining an old census and new household surveys (e.g., Emwanu et al., 2006; Nguyen, 2009). However, there have been no attempts to project a poverty map for the years to come. Information on poverty forecast can be useful for not only monitoring poverty changes but also planning poverty reduction programs in the next periods. In this paper, we propose a simple way to project poverty measures at the small area level and discuss several assumptions required by this estimation way. The poverty map projection uses the same estimation method of Elbers et al. (2002, 2003). However, its idea is different. In the poverty map projection, we use panel data from household surveys to estimate the relation between expenditure in the second period and household characteristics in the first period. Then this estimate relation is applied to a census in the second period to predict expenditure and poverty measures in the third period (a future period). Using the same estimation strategy, we can also predict the poverty estimate for a past period. Thus the main objective of the project method is to predict poverty estimates in a period when both a household survey and a census are not available. Vietnam has committed itself to a ‘‘growth with equity’’ strategy of development. The country has achieved high economic growth, with annual GDP growth rates of around 7% over the past 10 years. Poverty rates have declined remarkably from 58% to 16% between 1993 and 2006. The government of Vietnam has implemented an extensive public safety net with a large number of poverty alleviation programs. Accurate maps of poverty estimates can be helpful for the government in improving the poverty targeting of the antipoverty programs. Poverty maps have been receiving attention from policy makers and researchers in Vietnam. Up to now, several poverty maps have been constructed in Vietnam using the small area estimation method. Most studies rely on similar estimation methods but using different data sets. Minot (2000) combined the 1993 Vietnam Living Standard Survey (VLSS) and the 1994 Agricultural Census to estimate rural poverty maps in 1994. Minot et al. (2003) and Gian and van der Weide (2007) combined the 1998 VLSS and the 1999 Population and Housing Census to construct maps of poverty and inequality at the province and district levels in 1999. Nguyen (2009a, 2009b) used the 2002 and 2004 Vietnam Household Living Standard Surveys (VHLSS) and the 1999 Population and Housing Census to estimate the disaggregated poverty measures for the years 2002 and 2004. Recently, Nguyen et al. (2009) construct rural poverty maps using the 2006 VHLSS and a 50% sample of the 2006 Rural, Agricultural and Fishery Census. This paper aims to project a poverty map for rural Vietnam in the year 2008 using a 50% sample of the 2006 Rural, Agricultural and Fishery Census and the 2004 and 2006 Vietnam Household Living Standard Surveys (VHLSS). Since the 2008 VHLSS is also available, we can also construct a poverty map for 2008 using panel data of VHLSSs 2006 and 2008, and data from the 2006 Rural, Agricultural and Fishery Census (using a similar method of Emwanu et al., 2006). The poverty estimates from the updating method can be used for validation of the poverty estimates from the projection method. This study focuses on the rural population, since there are only data on rural households in the 2006 Rural, Agricultural and Fishery Census. In addition, poverty in Vietnam is mostly a rural phenomenon, with 95% of all poor living in rural areas. The paper is structured in five sections. Section 2 introduces the data sets used for poverty mapping in Vietnam. Section 3 presents the methods of small area estimation and poverty map projection. Next, empirical findings are presented in Section 4. Finally, Section 5 concludes.

2. Data set This study relies on two data sets. The first is the Vietnam Household Living Standard Surveys (VHLSS) in 2002, 2004, 2006 and 2008. These surveys were conducted by General Statistics Office of Vietnam (GSO) with technical supports from the World Bank. The 2002 covered around 29,530 households, while the 2002, 2004 and 2006 VHLSSs each covered around 9189 households. The number of rural households in the 2002, 2004, 2006 and 2008 VHLSSs is 22,621, 6938, 6882 and 6837, respectively. The collected information on household characteristics includes income, expenditure, employment status, education level, housing, fixed assets, credit and households’ participation in poverty alleviation programs. The surveys are designed to be representative at the regional level. It is interesting that two consecutive surveys set up panel data. More specifically, the 2002 and 2004 VHLSSs contain a panel data set consisting of 4008 households. The 2004 and 2006 VHLSSs have panel data of 4126 households, and the 2006 and 2008 VHLSSs have panel data of 4090 households. These surveys are not designed for panel data from more than two rounds. Thus there are few households who were covered by three as well as four surveys. The second data set is a 50% sample of the Rural, Agricultural and Fishery Census (RAFC) for 2006. The 2006 RAFC was also carried out by GSO.1 The 2006 RAFC covers all households in rural areas, and is conducted every 5 years. The 2006 RAFC contains information on household demography, education, dwelling unit characteristics and asset ownership, farming characteristics of households such as rice cultivation, aquatic cultivation, household ownership of farming tools and machinery.

1

GSO has not released full household data of the 2006 RAFC.

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N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382

Table 1 Estimates of the poverty indexes using the projection method in 2006. Source: Poverty estimates in 2006 are from Nguyen et al. (2009), and poverty estimates in 2008 are estimated by the author. VHLSS 2006

Projection using small areas estimation

P0

P1

P2

P0

P1

P2

Red River Delta

11.0 [1.1]

0.0187 [0.0025]

0.0051 [0.0009]

9.4 [1.3]

0.0165 [0.0031]

0.0046 [0.0011]

North East

29.9 [1.8]

0.0670 [0.0060]

0.0222 [0.0028]

28.9 [1.6]

0.0675 [0.0055]

0.0230 [0.0025]

North West

56.4 [3.7]

0.1811 [0.0146]

0.0751 [0.0075]

53.7 [3.2]

0.1662 [0.0129]

0.0557 [0.0069]

North Central Coast

33.1 [2.4]

0.0881 [0.0093]

0.0335 [0.0050]

31.9 [2.0]

0.0764 [0.0069]

0.0276 [0.0033]

South Central Coast

17.1 [2.1]

0.0362 [0.0065]

0.0117 [0.0027]

20.0 [2.0]

0.0500 [0.0055]

0.0178 [0.0026]

Central Highlands

34.4 [3.7]

0.1097 [0.0156]

0.0476 [0.0093]

37.0 [2.3]

0.1179 [0.0091]

0.0489 [0.0053]

South East

9.9 [1.5]

0.0261 [0.0054]

0.0108 [0.0028]

7.1 [1.1]

0.0211 [0.0026]

0.0033 [0.0010]

Mekong River Delta

11.8 [1.0]

0.0206 [0.0022]

0.0055 [0.0007]

13.4 [1.3]

0.0245 [0.0034]

0.0086 [0.0014]

Standard errors in brackets.

3. Methodology 3.1. Small area estimation method The small area estimation method developed by Elbers et al. (2002, 2003) can be described by two main steps as follows. Firstly, a functional relation between expenditure (or income if the poverty indexes are calculated based on income) and household characteristics is estimated using a household survey.

lnðyh Þ ¼ X h b þ eh ;

ð1Þ

where yh is per capita expenditure of household h. X is a vector of explanatory variables including household and community characteristics which are available in both the survey and the census. It should be noted that in the full presentation of Elbers et al. (2002, 2003), the error terms are decomposed into a household idiosyncratic component, uch, and a cluster component, gc, which is used to capture correlation of the error terms within cluster c.2 If the intra-cluster correlation of the error terms is not accounted for, standard errors of poverty estimates will be underestimated. For illustration of ideas, in this section we write the total error terms eh.3 In the empirical section, when estimating poverty measures and their standard errors, we follow the same method of Elbers et al. (2002, 2003). In this step, model (1) is estimated by Generalized Least Squares regressions in which the error terms are allowed to have heterogeneous variances and a within cluster correction. The parameters of the distribution of coefficients and error terms are also estimated. Secondly, the estimated expenditure model is applied into the census and a series of Monte Carlo simulations are carried out to estimate the poverty and inequality indexes using the census data. In each simulation, specific values of regression ^s , ^es , denote the drawn values of coefficients and error terms are randomly drawn from their estimated distributions. Let b h the coefficients, idiosyncratic and cluster in the s-th simulation, respectively. Then, the predicted expenditure for a household in the census is given by:

^s þ ^es Þ: ^sh ¼ expðX h b y h

ð2Þ

Next, we can estimate the three Foster–Greer–Thorbecke poverty indexes (see Foster et al., 1984) for a small area as follows:

bs ¼ 1 P a n

2 3

 n  X ^s a zy h

h¼1

z

^sh < zÞ; 1ðy

A cluster can be defined by a district, a commune or a village. Detailed description of the method is presented in Elbers et al. (2002, 2003).

ð3Þ

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Table 2 Estimates of the poverty indexes in 2006 and 2008. Source: Poverty estimates in 2006 are from Nguyen et al. (2009), and poverty estimates in 2008 are estimated by the author. Region

Poverty estimates in 2006 using the 2006 VHLSS

Poverty estimates in 2008 using the 2008 VHLSS

Poverty estimates in 2008 using the projection method

Poverty estimates in 2008 using the updating method

P0 (%)

P1

P2

P0 (%)

P1

P2

P0 (%)

P1

P2

P0 (%)

P1

P2

Red River Delta

11.0 [1.1]

0.0187 [0.0025]

0.0051 [0.0009]

5.2 [0.9]

0.0088 [0.0022]

0.0025 [0.0009]

7.1 [0.9]

0.0107 [0.0018]

0.0026 [0.0005]

8.1 [0.6]

0.0155 [0.0016]

0.0049 [0.0006]

North East

29.9 [1.8]

0.067 [0.0060]

0.0222 [0.0028]

23.4 [2.7]

0.0577 [0.0081]

0.0200 [0.0033]

22.2 [1.4]

0.0502 [0.0047]

0.0165 [0.0020]

26.0 [1.2]

0.0654 [0.0044]

0.0231 [0.0021]

North West

56.4 [3.7]

0.1811 [0.0146]

0.0751 [0.0075]

51.3 [5.7]

0.1371 [0.0195]

0.0486 [0.0091]

40.1 [2.8]

0.0992 [0.0106]

0.0341 [0.0049]

45.1 [2.2]

0.1258 [0.0093]

0.0490 [0.0048]

North Central Coast

33.1 [2.4]

0.0881 [0.0093]

0.0335 [0.0050]

20.7 [3.0]

0.0552 [0.0122]

0.0213 [0.0066]

21.7 [1.7]

0.0486 [0.0048]

0.0163 [0.0020]

19.3 [1.1]

0.0453 [0.0030]

0.0161 [0.0013]

South Central Coast

17.1 [2.1]

0.0362 [0.0065]

0.0117 [0.0027]

13.6 [3.1]

0.0307 [0.0095]

0.0101 [0.0041]

14.5 [1.3]

0.0312 [0.0033]

0.0102 [0.0013]

12.5 [0.9]

0.0310 [0.0023]

0.0116 [0.0010]

Central Highlands

34.4 [3.7]

0.1097 [0.0156]

0.0476 [0.0093]

28.6 [5.1]

0.0855 [0.0178]

0.0364 [0.0100]

27.8 [1.5]

0.0722 [0.0059]

0.0266 [0.0029]

32.7 [1.3]

0.1012 [0.0055]

0.0401 [0.0029]

South East

9.9 [1.5]

0.0261 [0.0054]

0.0108 [0.0028]

7.0 [2.0]

0.0148 [0.0051]

0.0058 [0.0026]

6.4 [0.7]

0.0118 [0.0016]

0.0034 [0.0006]

4.9 [0.7]

0.0079 [0.0014]

0.0020 [0.0005]

Mekong River Delta

11.8 [1.0]

0.0206 [0.0022]

0.0055 [0.0007]

9.2 [1.4]

0.0186 [0.0034]

0.0049 [0.0011]

7.4 [0.7]

0.0123 [0.0016]

0.0032 [0.0005]

9.7 [1.0]

0.0158 [0.0023]

0.0041 [0.0008]

Standard errors in brackets.

^sh < zÞ denotes an indicator function that where n is the number of household in a small area, z is the poverty line, and 1ðy s ^ equals 1 if yh < z, and 0 otherwise. a can be interpreted as a measure of inequality aversion. When a = 0, we have the poverty incidence (P0), which measures the proportion of people below the poverty line. When a = 1 and a = 2, we obtain the poverty gap index (P1), which measures the depth of poverty, and the squared poverty gap (P2), which measures the severity of poverty, respectively. After S simulations, say 500, we can obtain the estimates of the poverty indexes by computing the mean of simulated values:

ba ¼ 1 P S

S X

bs : P a

ð4Þ

s¼1

b a is calculated directly from the sample of S simulated values. Finally, the variance of P It is worth noting that Tarozzi and Deaton (2007) state explicitly two assumptions for validity of the small area estimation method. This first is called the ‘‘measurement of predictors’’ assumption, which requires that the explanatory variables in the expenditure equation are the same for households in the census and the survey. The second is referred as an assumption on ‘‘area homogeneity’’ (conditional independence), which states that the conditional distribution of expenditure given the explanatory variables in small areas and large regions is the same. The second assumption means that the expenditure function should be the same for small and large areas so that expenditure models of large areas such as regions that are estimated from the household survey can be applied validly to small areas in the census to estimate welfare measures for these small areas. 3.2. Projection of poverty indexes For poverty projection, in addition to census data, we need panel data from household surveys. Suppose that we have a census at time t2, and two household surveys at time t1 and t2 which set up two-period panel data. Our objective is to construct a poverty map at time t3 that equals [t2 + (t2  t1)]. For example, in this study, we aim to estimate a poverty map in 2008 using panel data of VHLSS 2004–2006 and the 2006 RAFC. Suppose there is a functional relationship between household expenditure in the current period and household characteristics in a previous period as follows:

lnðyh2 Þ ¼ X h1 b12 þ eh2

ð5Þ

where subscript ‘‘2’’ refers to time t2. Subscript ‘‘12’’ in the regression coefficients indicates the relation between expenditure in the second period and the independent variables in the first period. Similarly, we can assume a functional relation between the dependent variable in time t3 and the independent variables in time t2 as follows:

lnðyh3 Þ ¼ X h2 b23 þ eh3

ð6Þ

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N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382

Table 3 Estimates of the poverty incidence in 2006 and 2008. Source: Poverty estimates in 2006 are from Nguyen et al. (2009), and poverty estimates in 2008 are estimated by the author. Province

2006

2008

Poverty mapping

The projection method

Estimate

Std. Err.

Red River Delta Ha Noi Vinh Phuc Bac Ninh Ha Tay Hai Duong Hai Phong Hung Yen Thai Binh Ha Nam Nam Dinh Ninh Binh

4.8 13.6 9.4 11.7 10.9 12.0 12.0 11.5 14.6 10.9 15.6

1.5 2.4 1.6 1.8 1.9 2.2 2.0 2.2 2.9 2.0 3.0

North East Ha Giang Cao Bang Bac Kan Tuyen Quang Lao Cai Yen Bai Thai Nguyen Lang Son Quang Ninh Bac Giang Phu Tho

62.7 48.2 36.9 28.6 53.9 38.8 21.9 40.4 20.3 17.6 20.9

North West Dien Bien Lai Chau Son La Hoa Binh

Std. Err.

Estimate

Std. Err.

3.8 9.4 6.4 7.8 5.9 7.6 6.5 6.3 7.4 7.1 9.8

1.6 2.3 1.7 1.5 1.3 2.4 1.6 1.7 2.3 1.9 2.5

2.6 7.7 6.1 10.4 8.0 7.8 8.4 9.2 11.7 6.6 8.4

0.5 0.9 0.8 1.0 0.9 1.2 1.0 1.0 1.4 0.8 1.0

3.9 3.2 4.2 4.8 3.9 4.4 3.3 3.8 2.9 2.7 3.2

55.7 35.0 24.0 21.6 45.7 29.2 13.7 28.2 11.3 12.3 12.1

4.5 3.9 4.0 4.8 4.6 4.4 3.0 3.6 2.0 2.4 2.7

57.0 41.2 30.8 22.7 48.7 33.3 18.3 32.2 16.2 14.6 16.1

3.8 2.7 3.5 4.3 3.9 4.1 2.9 3.3 2.0 2.6 2.5

69.9 84.6 52.8 44.1

3.8 2.9 3.8 4.3

53.9 74.3 35.7 22.2

5.8 5.8 4.5 4.5

60.7 73.3 43.0 25.6

4.5 4.3 3.7 3.5

North Central Coast Thanh Hoa Nghe An Ha Tinh Quang Binh Quang Tri Thua Thien Hue

35.7 32.5 30.7 30.7 35.7 24.5

2.4 2.4 3.3 3.7 3.8 2.5

23.3 23.0 19.2 20.7 24.3 14.4

2.6 2.8 3.3 4.2 3.7 3.1

22.8 21.7 14.5 14.3 18.2 9.0

1.8 2.0 2.4 3.0 2.1 1.8

South Central Coast Da Nang Quang Nam Quang Ngai Binh Dinh Phu Yen Khanh Hoa

8.0 18.0 20.6 15.2 19.1 18.5

3.0 1.6 1.8 1.9 2.2 2.0

5.4 16.6 17.3 11.7 14.0 13.6

3.5 2.2 2.4 2.7 2.9 2.8

2.8 12.0 16.3 8.6 14.4 13.6

2.2 1.3 1.4 1.6 2.2 2.3

Central Highland Kon Tum Gia Lai Dak Lak Dak Nong Lam Dong

58.7 50.0 33.9 37.9 31.3

3.9 2.8 3.5 4.6 3.3

45.3 43.6 25.1 27.4 17.2

4.0 2.8 2.6 4.3 2.6

52.5 51.0 30.0 31.7 18.7

3.4 2.1 2.2 3.1 2.0

South East Ninh Thuan Binh Thuan Binh Phuoc Tay Ninh Binh Duong Dong Nai Vung Tau Ho Chi Minh

39.0 16.9 16.1 6.2 1.3 8.3 5.9 2.3

5.4 2.9 2.8 1.6 0.5 1.6 1.9 0.9

24.7 11.9 8.0 3.2 1.2 6.1 3.6 1.4

4.7 2.2 2.0 0.9 0.4 1.2 1.2 0.5

17.3 9.3 2.9 3.2 0.9 5.1 4.0 1.7

3.8 1.9 1.1 0.9 0.4 1.2 1.3 0.8

4.9 6.2

1.3 1.8

3.5 4.6

0.8 1.3

5.2 4.8

1.1 1.4

Mekong River Delta Long An Tien Giang

Estimate

The updating method

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N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382 Table 3 (continued) 2008 The projection method Std. Err.

Estimate

Std. Err.

Estimate

Std. Err.

8.8 16.7 8.7 11.7 15.4 18.6 11.1 10.8 20.8 13.3 17.0

2.3 3.9 2.7 2.3 3.4 3.5 3.4 3.3 3.4 2.8 3.1

5.2 11.4 5.5 5.9 7.3 10.5 7.3 7.7 12.4 7.2 10.1

1.5 2.5 1.5 1.2 1.3 1.9 2.2 2.2 2.4 2.1 2.0

7.9 11.6 8.5 9.9 12.5 13.8 8.1 9.7 13.5 9.7 11.4

1.8 2.5 2.0 1.8 2.2 2.5 2.6 2.6 3.0 2.2 2.4

20

40

60

80

100

20

40

60

80

100

The poverty incidence of districts (%)

0

20

40

60

80

100

The poverty incidence of provinces (%)

0

The updating method

Estimate

0

Estimates from the updating method

Ben Tre Tra Vinh Vinh Long §ong Thap An Giang Kien Giang Can Tho Hau Giang Soc Trang Bac Lieu Ca Mau

2006 Poverty mapping

Estimates from the updating method

Province

0

Estimates from the projection method

20

40

60

80

100

Estimates from the projection method

Fig. 1. Estimates of the poverty rate using projection and updating methods. Source: Author’s estimation.

2006

2008: projection method

2008: updating method

Fig. 2. Estimates of the provincial poverty incidence. Source: Poverty estimates in 2006 are from Nguyen et al. (2009), and poverty estimates in 2008 are estimated by the author.

374

N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382

2006

2008: projection method

2008: updating method

Fig. 3. Estimates of the district poverty incidence. Source: Poverty estimates in 2006 are from Nguyen et al. (2009), and poverty estimates in 2008 are estimated by the author.

The forecast of poverty depends on the following functions:

b23 ¼ b12

ð7Þ

Varðeh3 Þ ¼ Varðeh2 Þ:

ð8Þ

Condition (7) means that the correlation between current expenditure and past characteristics is unchanged over time. It is more likely to be satisfied if the duration t1  t2 is equal to the duration t2  t3, i.e., t3 = [t2 + (t2  t1)]. Condition (8) is required so that a simulated value of the error terms at time t3 can be randomly drawn from the distribution of the error terms at time t2. To project a poverty map at time t3, we run regression of expenditure model (5) using panel data from household surveys, then apply this estimated model to a census to predict household expenditure and poverty indexes at small areas (the poverty map). More specifically, in this paper, we will estimate the following model using the panel data from VHLSSs 2004 and 2006:

lnðy2006 Þ ¼ X 2004 b2004

2006

þ e2006 ;

ð9Þ

Next, we estimate expenditure in 2008 for all households covered in the 2006 RAFC:

^2004 ^2008 ¼ expðX 2006 b y

2006

þ ^e2008 Þ;

ð10Þ

and we use the predicted expenditure and the simulation method to estimate the poverty indexes of a small area for the year 2008 and their standard errors. It should be noted that the condition specified in Eq. (7) is more likely to be satisfied if the economic growth rate between 2004 and 2006 is similar to that between 2006 and 2008. The economic growth pace in Vietnam is rather stable during the period 2004–2008. The annual growth rate of GDP in the years 2004, 2005, 2006, 2007 and 2008 is 7.8, 8.4, 8.2, 8.5 and 6.3, respectively. The economic slowdown only happened in Vietnam in final months of 2008 year. In addition, expenditure data in the 2004 and 2006 VHLSSs refers to expenditure for past 12 months before the interview date, thus expenditure data in the 2004 and 2006 VHLSSs can be interpreted as the 2003/2004 expenditure and the 2005/2006 expenditure. As a result, the poverty map is projected for the 2007/2008 time which was before the economic slowdown in Vietnam. In addition to the three assumptions mentioned above, we need a so-called ‘‘population growth independent of poverty’’ assumption to project a poverty map (see Nguyen, 2009b), since the census at time t2 cannot capture population changes related to poverty during t2 and t3. This assumption requires that the population growth (including natural growth and net immigration growth) of small areas between time t2 and time t3 is independent of the areas’ poverty. This assumption means that the population growth of a small area should be exogenous to poverty. For example, this assumption does not hold for an area in which poor households are more likely to migrate to other areas than the non-poor, and we can overestimate poverty for this area. This assumption is more plausible for a not long time period such as the period 2006–2008 in this study. The 2004 and 2006 VHLSSs show that the proportion of rural population is almost the same during the 2004–2006 period, at 73%.

N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382

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In this paper, we will illustrate the project method by projecting a poverty map for rural Vietnam in the year 2008 using a 50% sample of the 2006 RAFC and the 2004 and the 2006 VHLSS. Since the 2008 VHLSS is also available, we can also construct a poverty map for 2008 using panel data of VHLSSs 2006 and 2008, and data from the same census using a similar method of Emwanu et al. (2006). Then, the poverty estimates from the updating method can be used to validate of the poverty estimates from the projection method. A reason why the updating method can be used as a benchmark for the projection method in this paper can be explained as follows. In this updating method, expenditure in time t3 is observed, and we can run a regression of expenditure in time t3 on explanatory variable in time t2. In other words, the expenditure model in Eq. (6) (i.e., ln (yh3) = Xh2b23 + eh3) can be estimated directly. Assumptions (7) and (8) are not needed in the updating methods. If our objective is to estimate the poverty map in time t3 and a household survey is available in time t3, the updating method is always preferred to the projection method. The main objective of the project method is to predict the poverty map to the time when both a household survey and a census are not available. We can predict the poverty estimate for not only the future period but also a past period using the same estimation strategy. 3.3. Idea illustration and validation method We can use VHLSSs to illustrate the idea of the projection method and examine its validation. More specifically, we use the panel data from VHLSSs in 2002 and 2004 to project the poverty indexes in 2006 and compare these projected values to the actual estimates based on the 2006 VHLSS. Firstly, we run the GLS regression of logarithm of per capita expenditure in 2004 on the explanatory variables in 2002.4 Secondly, we use this estimated expenditure model and the explanatory variables from the 2004 VHLSS to project the poverty measures for 2006. Table 1 compares the poverty indexes estimated by the projection method with the poverty indexes calculated directly from the 2006 VHLSS. The results are very encouraging. The difference in the estimates of the poverty incidence between the 2006 VHLSS and the projection method is just around 2% points. For all the regions, we cannot reject the hypothesis that the poverty estimates from the projection method are equal to the poverty estimates based on the 2006 VHLSS. To test the projection method at the smaller areas such as provinces and districts, we will compare the poverty estimates, which are obtained from the projection method using data from the panel of VHLSSs 2004 and 2006, and the 2006 RAFC, to those which are estimated by the updating method using the panel of VHLSSs 2006 and 2008, and the 2006 RAFC. According to the updating method proposed by Emwanu et al. (2006), we will estimate an equation in which logarithm of per capita expenditure in 2008 is a function of explanatory variables in 2006. Then, the estimated equation is applied into the 2006 RAFC to predict the poverty rates of small areas in 2008. 4. Empirical results 4.1. Consumption models 4.1.1. Consumption models in the poverty projection The first step in the projection of a poverty map is to construct a model of per capita expenditure using household survey data. A main problem in the model construction is to select explanatory variables. Data on these variables must be also available in a census, and data on the explanatory variables should be comparable between the household survey and the census. To select the explanatory variables, we compare not only summary statistics on these variables but also the questionnaires between the 2006 VHLSS and the 2006 RAFC. After checking the comparison, we select 29 household variables for the expenditure model and six geographical variables. The list of the explanatory variables used for estimation of the expenditure model is presented in Table A1 in Appendix A. The consumption models are estimated using panel data of the VHLSSs in 2004 and 2006. The dependent variable is logarithm of per capita expenditure in 2006, and the explanatory variables are household variables in 2004. There are eight geographical regions in Vietnam, and ideally there should be a separate expenditure regression for each region. However, since some regions have a small number of observations, some similar regions are combined together. More specifically, we estimate an expenditure regression with a regional dummy variable for North East and North West, and a regression for North Central Coast, South Central Coast and Central Highlands, and a regression for South East and Mekong River Delta. Thus, there are four expenditure regressions in total. The GLS regressions of logarithm of per capita expenditure are presented in Tables A2 and A3. It shows that all the significant explanatory variables have expected signs.5 The value of adjusted-R2 ranges from 0.32 to 0.57. The highest R2 is for North West and North East, whereas it is lowest for Red River Delta. Given that there is a time difference between the dependent variable and the explanatory variables, these results of R2s are very encouraging. Tables A2 and A3 also report the model of heteroskedasticity of error terms in the expenditure models. 4 The regressions are not reported in this paper, since similar estimation strategy and regressions will be presented in details in Section 4. Readers who are interested in the regressions in this section can contact the author to have the regression results. 5 We use the PovMap program to estimate poverty. Districts are specified as clusters in modeling location effect. We do not use communes as clusters since in many communes there are only 1 or 2 observations.

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4.1.2. Consumption models in the poverty updating To update the poverty using panel data of VHLSSs 2006 and 2008, we run regressions of logarithm of per capita expenditure in 2008 on explanatory variables in 2006. In addition to the household and geographic variables, we can also construct commune level data from the 2006 ARFC and merge the commune data with household data. The list of commune variables is presented in Table A1 in Appendix A. Similar to the poverty projection method, there are four expenditure regressions for different regions. It should be noted that the 2008 expenditures are deflated in terms of the 2006 price using food and non-food CPIs. The GLS regressions of logarithm of per capita expenditure and the error term heteroskedasticity regressions are presented in Tables A4 and A5. All the significant explanatory variables have expected signs. The value of adjusted-R2 ranges from 0.33 for Red River Delta to 0.51 for North West and North East. 4.2. Poverty estimates In the projection method, the consumption models which are estimated from the panel data of VHLSSs 2004 and 2006 are applied into the 2006 RAFC to project poverty measures at different desegregation levels for the year 2008. In the updating method, the consumption models which are estimated from the panel data of VHLSSs 2006 and 2008 are also applied into the 2006 RAFC to estimate poverty measures for the year 2008. In this paper, a household is defined as poor if their per capita expenditure is below the expenditure poverty line constructed by World Bank and GSO. The poverty line is equivalent to the expenditure level that allows for nutritional needs, and some essential non-food consumption such as clothing and housing. The expenditure poverty line in 2006 is equal to 2560 thousand VND. Table 2 presents the regional estimates of the poverty rate, poverty gap index, and the poverty severity index in 2006 and 2008. The 2006 estimates are calculated from the 2006 VHLSS, while the 2008 estimates are obtained from three ways: directly from the 2008 VHLSS; the projection method; and the updating method. It shows that the poverty estimates in 2008 from there estimation ways are quite similar. For all regions, we cannot reject the hypothesis on equality of the poverty incidence from different estimation methods. The poverty indexes estimated directly from the 2008 VHLSSs have higher standard error than those which are estimated from the two poverty map methods. The Table 2 shows that all regions experienced reduction in poverty estimates during the period 2006–2008. North West remains the poorest region, followed by Central Highlands. The poverty rate of provinces in 2006 and 2008 are presented in Table 3. The poverty estimates for 2006 are obtained from Nguyen et al. (2009).6 The poverty estimates in 2006 are presented to examine the poverty reduction during 2006– 2008 at the district and province level. The comparison of poverty estimates between the projection method and the updating method at the province and district levels is examined in Fig. 1. The projection method yields the poverty incidence quite similar as the updating method. The estimates of the poverty gap and the poverty severity indexes at the provincial levels are presented in Table A6 in Appendix A. The comparison of the estimates of the poverty gap and severity indexes is examined in Fig. A1 in Appendix A. The spatial visualization of the province and district poverty incidences in 2006 and 2008 are presented in Figs. 2 and 3. Poverty in Vietnam still has a rather strong geographical dimension with high poverty in mountainous and highland areas. Within some regions and provinces, there exists a high variation in poverty across areas. Again, the poverty map projection method and the poverty map updating method give similar spatial patterns of poverty incidences in Vietnam. 5. Conclusions The small area estimation method proposed by Elbers et al. (2002, 2003) estimates disaggregated poverty measures by combining a household survey and a census. According to this method, a functional relation between household expenditure and household characteristics is modeled using data from a household survey. Then, this modeled relation is applied into a census to estimate expenditure for all households covered in this census and poverty measures of small areas. In this paper, we propose a simple method to project poverty measures at the small area level in a period when both a census and a household survey are not available. Although, the projection method uses the same estimation method of Elbers et al. (2002, 2003), its idea is different. More specifically, we use panel data from two household surveys to estimate expenditure in the second period as a function of household characteristics in the first period, then apply this estimated function into a census in the second period to predict expenditure and poverty measures in the third period. This projection method can be also used to predict a poverty map in a past period. In this paper, the small area estimation method is applied to project a poverty map in rural Vietnam for the year 2008 using a 50% sample of the 2006 Rural, Agricultural and Fishery Census and the 2004 and 2006 Vietnam Household Living 6

Nguyen et al. (2009) construct rural poverty maps using the 2006 VHLSS and a 50 percent sample of the 2006 Rural, Agricultural and Fishery Census.

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Standard Surveys (VHLSS). More specifically, the logarithm of per capita expenditure in 2006 is assumed to be a linear function of household characteristics in 2004, and this function is estimated by Generalized Least Squares using the panel data of the 2004 and 2006 VHLSSs. Then, this estimated function is inserted into the 2006 RAFC to project the poverty indexes of rural provinces and districts for the year 2008. To assess the poverty estimates from this projection method, we compare them to the poverty estimates which are estimated by the updating method using the panel of VHLSSs 2006 and 2008, and the 2006 RAFC. Since the updating method relies on the actual data on expenditure in 2008, it can produce more accurate poverty estimates in 2008. Thus in this study, the poverty estimates which are obtained from the updating method can be regarded as a benchmark to validate the poverty estimates from the projection method. It is found that the poverty estimates using the projection method are very encouraging. The poverty projection method and the poverty updating method produce quite similar estimates, especially the estimates of the poverty incidence at the regional and provincial level. The estimation results show that poverty in Vietnam remains to have a strongly geographical dimension with high poverty in mountainous and highland areas in 2008. Within some regions and provinces, there exists a high variation in poverty across areas. These findings on the poverty pattern are consistent to previous poverty map studies (e.g., Minot et al., 2003; Nguyen et al., 2009). Appendix A

0

.05

.1

.15

.2

.25

.1

.2

.3

.4

The poverty gap index of districts

0

Estimates from the updating method

0

.05

.1

.15

.2

.25

The poverty gap index of provinces

0

.1

.2

.3

The poverty severity index of districts

.02

.04

.06

.08

Estimates from the projection method

.1

.15 .1 .05 0

.08 .06 .04 .02 0

.4

.2

The poverty severity index of provinces

Estimates from the updating method

Estimates from the projection method

.1

Estimates from the projection method

0

Estimates from the updating method

Estimates from the updating method

Fig. A1 and Tables A1–A6.

0

.05

.1

.15

.2

Estimates from the projection method

Fig. A1. Estimates of the poverty indexes using projection and updating methods. Source: Author’s estimation.

Table A1 Common household variables between the 2006 VHLSS and the 2006 RAFC. Variables

Type

Household variables Ethnic minorities (yes = 1) Household size Permanent house

Binary Discrete Binary (continued on next page)

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N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382 Table A1 (continued) Variables

Type

Semi-permanent house Temporary house Tap water Clean water Other water Flush toilet Other toilets No toilet Have radio Have computer Have motorbike Have color television Have mobile Have telephone Have fridge Have fan Fraction of female members to working members Fraction of working member to household size Fraction of service members to working members Fraction of working members without vocational training Fraction of working members with vocational training Fraction of working members with college/university Log of per capita living area (log of m2) Use or own annual land (yes = 1) Area of annual crop land (1000 m2) Use or own water surface (yes = 1)

Binary Binary Binary Binary Binary Binary Binary Binary Binary Binary Binary Binary Binary Binary Binary Binary Continuous Continuous Continuous Continuous Continuous Continuous Binary Binary Continuous Binary

Geographic variables at the district level Percentage of area elevation lower than 250 m in total area Percentage of area slope lower 4 degree in total area Mean elevation (m) Mean sunshine (annual hours) Mean temperature (degree Celsius) Mean rainfall (mms)

Continuous Continuous Continuous Continuous Continuous Continuous

Commune variables (from the 2006 RAFC) Commune have national electricity system cover all villages The road to this commune center is concrete and always available in year Fraction of concrete road in commune Numbers of primary schools per 1000 households Numbers of secondary schools per 1000 households Number of irrigation per 1000 households Number of extension staff per 1000 households Number of markets per 1000 households Number of concrete markets per 1000 households Have bank branch

Binary Binary Continuous Discrete Discrete Discrete Discrete Discrete Discrete Binary

Table A2 Poverty map projection: GLS regression on per capita expenditure for Red River Delta and North Central Coast, South Central Coast and Central Highlands. Source: Author’s estimation. Explanatory variables

Expenditure model (Beta model) Intercept Having clack television Having color television Household size squared Living in permanent house Log of living area per capita (m2) Having motorbike Fraction of household members without education degree Fraction of female household members Fraction of working household members Having telephone Have flush toilet

Red River delta

North East and North West

Coef.

Std. Err.

|Prob|>t

Coef.

Std. Err.

|Prob|>t

7.9425 0.1520 0.2250 0.0051 0.0741 0.0779 0.0884 0.2029 0.1275 0.2978 0.2459 0.2010

0.1139 0.0654 0.0416 0.0016 0.0346 0.0351 0.0354 0.0537 0.0643 0.0664 0.0523 0.0534

0.0000 0.0204 0.0000 0.0018 0.0328 0.0268 0.0128 0.0002 0.0479 0.0000 0.0000 0.0002

7.7975

0.1046

0.0000

0.2891

0.0342

0.0000

0.1762 0.1863 0.3292

0.0284 0.0318 0.0557

0.0000 0.0000 0.0000

0.2671

0.0723

0.0002

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N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382 Table A2 (continued) Explanatory variables

Red River delta Coef.

Std. Err.

Have no toilet Ethnic minorities Having electric fan Having mobile phones Percentage of area elevation lower than 250 m in total area Mean elevation (m) Number of obs. Number of cluster Adjusted R squared Rhoa Heteroskedasticity model (Alpha model) Intercept Fraction of service members to working members ⁄ yhat Other toilet Harvester⁄yhat⁄yhat Household size⁄yhat⁄yhat_ Mean temperature Fraction of working members with vocational training Adjusted R squared

North East and North West |Prob|>t

Coef.

Std. Err.

|Prob|>t

0.1652 0.1311 0.0914 0.4313 0.0000 0.0002

0.0468 0.0380 0.0394 0.1183 0.0000 0.0001

0.0004 0.0006 0.0206 0.0003 0.0229 0.0013 604 103 0.5667 0.1069

9.301

1.4889

6.2467

0.0095 0.002 0.2044 1.7209

0.0034 0.0008 0.0622 0.6873

2.774 2.439 3.2842 2.5039 0.0328

676 82 0.3271 0.1066 3.0984 0.1012 0.7383

0.2276 0.0347 0.2316

13.6120 2.9186 3.1882

0.0182

Note: what is the predicted value of the dependent variable in Beta model (i.e., predicted logarithm of per capita expenditure). a ^ 2g =r ^ 2u , which measures the relative component of location errors in the total errors in the model. Rho is the ratio of r

Table A3 Poverty map projection: GLS regression on per capita expenditure for North Central Coast, South Central Coast and Central Highlands, and South East and Mekong River Delta. Source: Author’s estimation. Explanatory variables

Expenditure model (Beta model) Intercept Having color television Having annual crop land (yes = 1) Ethnic minorities Having electric fan Household size squared Living in temporary house Log of living area per capita (m2) Having motorbike Fraction of household members without education degree Fraction of working household members Having telephone Have flush toilet Tap water Other clean water sources Having fridge Mean elevation (m) Percentage of area elevation lower than 250 m in total area Number of obs. Number of cluster Adjusted R squared Rho Heteroskedasticity model (Alpha model) Intercept Log of living area per capita (m2) Tap water⁄yhat⁄yhat Permanent house Tap water⁄yhat Adjusted R squared

North Central Coast, South Central Coast and Central Highlands

South East and Mekong River Delta

Coef.

Std. Err.

|Prob|>t

Coef.

Std. Err.

|Prob|>t

7.5080 0.2223

0.1189 0.0317

0.0000 0.0000

8.0136

0.0959

0.0000

0.2344 0.1603 0.0028 0.0920 0.1458 0.1786 0.2497 0.4024 0.3028 0.1279 0.3125 0.1020

0.0544 0.0415 0.0008 0.0375 0.0307 0.0328 0.0532 0.0701 0.0622 0.0510 0.0805 0.0432

0.0000 0.0001 0.0006 0.0142 0.0000 0.0000 0.0000 0.0000 0.0000 0.0123 0.0001 0.0186

0.0000 0.1925

0.0000 0.0603

0.0094 0.0014

0.1561 0.2096 0.2402 0.2523 0.2430

0.0310 0.0255 0.0300 0.0531 0.0607

0.0000 0.0000 0.0000 0.0000 0.0001

0.1267

0.0390

0.0012

0.0003 0.0000

0.0001 0.0000

0.0007 0.0252 825 134 0.5399 0.1109

0.0687 0.2771 0.0008

0.0312 0.0483 0.0003

0.0277 0.0000 0.0056

4.5541 0.5311 0.0072

0.5139 0.1435 0.0027

8.8623 3.7021 2.6414

0.0201

941 128 0.4389 0.1061 2.8888

0.2885

10.0118

0.7016 0.0468

0.2633 0.0158

2.6645 2.9611 0.0135

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N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382

Table A4 Poverty map updating: GLS regression on per capita expenditure for Red River Delta and North Central Coast, South Central Coast and Central Highlands. Source: Author’s estimation. Explanatory variables

Red River Delta

Expenditure model (Beta model) Intercept Having electric fan Household size Household size squared Log of living area per capita (m2) Having motorbike Fraction of household members without education degree Fraction of working household members Having fridge Having telephone Having toilet (not flush) Not using clean water (Other water) Semi-permanent house Temporary house Having mobile phone Numbers of secondary schools per 1000 households Fraction of service members to working members Fraction of households living in semipermanent house in communes Fraction of households having fridge in communes Fraction of households using clean water in communes Fraction of people without education degree in communes Mean temperature (degree Celsius) Mean temperature Number of observations Number of clusters Adjusted R squared Rho Heteroskedasticity model (Alpha model) Intercept Log of living area per capita (m2) Motorbike Computer Television ⁄yhat⁄yhat_ Flush toilet Proportion of female members Adjusted R squared

North East and North West

Coef.

Std. Err.

|Prob|>t

Coef.

Std. Err.

|Prob|>t

10.1484 0.2056 0.1112 0.0171 0.1764 0.1389 0.1129 0.3193 0.0992 0.1611 0.0826 0.3003 0.0760

0.9667 0.0744 0.0579 0.0062 0.0440 0.0426 0.0564 0.0738 0.0522 0.0475 0.0435 0.1442 0.0403

0.0000 0.0059 0.0552 0.0061 0.0001 0.0012 0.0458 0.0000 0.0578 0.0007 0.0579 0.0377 0.0599

9.3132 0.1654 0.0567

0.2498 0.0438 0.0119

0.0000 0.0002 0.0000

0.2446 0.3511 0.2321 0.1764 0.1255 0.1529

0.0403 0.0735 0.0842 0.0836 0.0767 0.0487

0.0000 0.0000 0.0060 0.0352 0.1022 0.0018

0.1428 0.1972 0.2094 0.2477

0.0452 0.0992 0.0891 0.0814

0.0017 0.0473 0.0191 0.0025

1.2270

0.2632

0.0000

0.2895 1.1231 0.2521

0.1186 0.2165 0.1277

0.0149 0.0000 0.0488

0.0001 0.1004

0.0000 0.0421

0.0094 0.0173 677 86 0.3332 0.0269

4.4038 0.0037 0.4402

0.3545 0.0018 0.1643

12.4229 2.0719 2.6796

586 112 0.5126 0.1015 4.2724

0.3604

11.8545

2.9063 0.0243 4.0078 1.1553

0.8773 0.0069 1.8044 0.4773

3.3129 3.4991 2.2211 2.4204 0.0066

0.0129

Table A5 Poverty map updating: GLS regression on per capita expenditure for North Central Coast, South Central Coast and Central Highlands, and South East and Mekong River Delta. Source: Author’s estimation. Explanatory variables

Expenditure model (Beta model) Intercept Ethnic minorities Log of living area per capita (m2) Having mobile phone Having motorbike Fraction of working members without vocational training Fraction of working members with vocational training Fraction of working members with college/university Fraction of working member to household size Having fridge Having telephone Not having toilet Having annual crop land (yes = 1) Having electric fan Household size Number of markets per 1000 households Fraction of households having mobile phone in communes

North Central Coast, South Central Coast and Central Highlands

South East and Mekong River Delta

Coef.

Std. Err.

|Prob|>t

Coef.

Std. Err.

|Prob|>t

7.0990 0.4761 0.2059 0.1274 0.2024

0.1399 0.0585 0.0302 0.0709 0.0324

0.0000 0.0000 0.0000 0.0725 0.0000

7.5992

0.1473

0.0000

0.1953 0.1365 0.2148 0.1432

0.0359 0.0504 0.0367 0.0729

0.0000 0.0069 0.0000 0.0498

0.3883 0.3754 0.3268 0.1833 0.1579 0.1058

0.0889 0.1828 0.0663 0.0707 0.0553 0.0406

0.0000 0.0403 0.0000 0.0097 0.0044 0.0093

0.4888 0.2478 0.1819 0.1574

0.1600 0.0740 0.0509 0.0464

0.0023 0.0008 0.0004 0.0007

0.0580 0.1253 0.0217 0.1146 0.6222

0.0343 0.0376 0.0114 0.0584 0.2490

0.0916 0.0009 0.0580 0.0501 0.0127

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N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382 Table A5 (continued) Explanatory variables

Fraction of households having color television in communes Percentage of area slope lower 4 degree in total area Percentage of area elevation lower than 250 m in total area Mean temperature (degree Celsius) Number of observations Number of clusters Adjusted R squared Rho Heteroskedasticity model (Alpha model) Intercept Fraction of working members without vocational training Telephone⁄yhat⁄yhat Adjusted R squared

North Central Coast, South Central Coast and Central Highlands

South East and Mekong River Delta

Coef.

Std. Err.

|Prob|>t

Coef.

Std. Err.

|Prob|>t

0.4655

0.1264

0.0002

0.0000 0.0001

0.0000 0.0000

0.0572 0.0060 807 143 0.4996 0.0932

0.0000 0.0000

0.0000 0.0000

0.0176 0.0505

3.6896 0.8602

0.2333 0.2554

895 150 0.4257 0.0840

15.8116 3.3676

4.8979

0.0896

54.6558

0.0065

0.0022

2.8998 0.0082

0.0127

Table A6 Estimates of the poverty gap and severity indexes in 2006 and 2008. Source: Author’s estimation. Province

Estimates in 2006 using the standard method

Estimates in 2008 using the projection method

Estimates in 2008 using the updating method

P1

Std. Err. of P1

P2

Std. Err. of P2

P1

Std. Err. of P1

P2

Std. Err. of P2

P1

Std. Err. of P1

P2

Std. Err. of P2

Red River Delta Ha Noi Vinh Phuc Bac Ninh Ha Tay Hai Duong Hai Phong Hung Yen Thai Binh Ha Nam Nam Dinh Ninh Binh

0.0080 0.0242 0.0160 0.0208 0.0185 0.0214 0.0210 0.0195 0.0262 0.0187 0.0287

0.0031 0.0053 0.0032 0.0040 0.0039 0.0050 0.0045 0.0047 0.0065 0.0042 0.0072

0.0022 0.0068 0.0043 0.0058 0.0050 0.0059 0.0058 0.0052 0.0073 0.0051 0.0082

0.0010 0.0017 0.0010 0.0013 0.0012 0.0016 0.0015 0.0015 0.0021 0.0014 0.0025

0.0057 0.0152 0.0096 0.0123 0.0085 0.0116 0.0094 0.0090 0.0109 0.0106 0.0158

0.0029 0.0045 0.0031 0.0029 0.0023 0.0046 0.0029 0.0031 0.0042 0.0035 0.0051

0.0014 0.0040 0.0023 0.0031 0.0020 0.0029 0.0022 0.0021 0.0026 0.0026 0.0041

0.0008 0.0013 0.0009 0.0009 0.0006 0.0013 0.0008 0.0008 0.0012 0.0010 0.0016

0.0049 0.0162 0.0111 0.0215 0.0145 0.0147 0.0154 0.0168 0.0222 0.0119 0.0165

0.0011 0.0021 0.0017 0.0025 0.0021 0.0027 0.0023 0.0025 0.0036 0.0019 0.0023

0.0016 0.0058 0.0033 0.0072 0.0043 0.0045 0.0045 0.0049 0.0067 0.0035 0.0053

0.0004 0.0008 0.0006 0.0010 0.0007 0.0010 0.0008 0.0009 0.0013 0.0007 0.0009

North East Ha Giang Cao Bang Bac Kan Tuyen Quang Lao Cai Yen Bai Thai Nguyen Lang Son Quang Ninh Bac Giang Phu Tho

0.1765 0.1279 0.0886 0.0628 0.1480 0.0969 0.0438 0.0956 0.0425 0.0341 0.0405

0.0197 0.0152 0.0142 0.0138 0.0180 0.0156 0.0085 0.0132 0.0072 0.0067 0.0087

0.0655 0.0464 0.0305 0.0204 0.0549 0.0341 0.0132 0.0323 0.0134 0.0102 0.0119

0.0100 0.0077 0.0061 0.0053 0.0088 0.0069 0.0030 0.0056 0.0026 0.0024 0.0032

0.1499 0.0826 0.0500 0.0455 0.1134 0.0707 0.0257 0.0489 0.0215 0.0172 0.0229

0.0213 0.0148 0.0117 0.0130 0.0192 0.0145 0.0073 0.0101 0.0046 0.0058 0.0073

0.0544 0.0276 0.0154 0.0142 0.0384 0.0244 0.0074 0.0147 0.0063 0.0050 0.0067

0.0106 0.0067 0.0045 0.0048 0.0091 0.0063 0.0025 0.0038 0.0016 0.0021 0.0028

0.1692 0.1159 0.0732 0.0480 0.1374 0.0826 0.0361 0.0726 0.0340 0.0332 0.0318

0.0189 0.0128 0.0114 0.0119 0.0176 0.0135 0.0075 0.0103 0.0056 0.0072 0.0068

0.0675 0.0450 0.0254 0.0152 0.0530 0.0296 0.0108 0.0239 0.0108 0.0102 0.0096

0.0101 0.0070 0.0049 0.0045 0.0090 0.0059 0.0027 0.0042 0.0021 0.0028 0.0026

North West Dien Bien Lai Chau Son La Hoa Binh

0.2559 0.3551 0.1562 0.1132

0.0245 0.0292 0.0181 0.0174

0.1191 0.1789 0.0634 0.0410

0.0154 0.0211 0.0095 0.0082

0.1429 0.2142 0.0816 0.0448

0.0247 0.0339 0.0148 0.0120

0.0510 0.0787 0.0268 0.0135

0.0119 0.0175 0.0062 0.0044

0.1917 0.2417 0.1106 0.0542

0.0230 0.0281 0.0135 0.0106

0.0802 0.1032 0.0405 0.0170

0.0127 0.0165 0.0062 0.0042

North Central Coast Thanh Hoa 0.0847 Nghe An 0.0802 Ha Tinh 0.0676 Quang Binh 0.0716 Quang Tri 0.0983 Thua Thien 0.0582 Hue

0.0082 0.0082 0.0104 0.0115 0.0136 0.0082

0.0291 0.0288 0.0220 0.0245 0.0385 0.0203

0.0035 0.0036 0.0042 0.0047 0.0064 0.0036

0.0529 0.0526 0.0373 0.0447 0.0609 0.0296

0.0075 0.0076 0.0086 0.0113 0.0109 0.0081

0.0180 0.0180 0.0110 0.0148 0.0225 0.0092

0.0031 0.0030 0.0031 0.0043 0.0049 0.0031

0.0541 0.0558 0.0241 0.0287 0.0510 0.0167

0.0052 0.0054 0.0054 0.0063 0.0069 0.0039

0.0190 0.0212 0.0063 0.0096 0.0204 0.0049

0.0023 0.0024 0.0017 0.0021 0.0038 0.0013

(continued on next page)

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N.V. Cuong / Journal of Comparative Economics 39 (2011) 368–382

Table A6 (continued) Province

Estimates in 2006 using the standard method P1

Estimates in 2008 using the projection method

Estimates in 2008 using the updating method

Std. Err. of P1

P2

Std. Err. of P2

P1

Std. Err. of P1

P2

Std. Err. of P2

P1

Std. Err. of P1

P2

Std. Err. of P2

South Central Coast Da Nang 0.0131 Quang Nam 0.0411 Quang Ngai 0.0495 Binh Dinh 0.0284 Phu Yen 0.0410 Khanh Hoa 0.0427

0.0058 0.0040 0.0053 0.0045 0.0055 0.0052

0.0035 0.0143 0.0175 0.0084 0.0134 0.0148

0.0017 0.0016 0.0023 0.0015 0.0020 0.0020

0.0089 0.0379 0.0407 0.0211 0.0273 0.0298

0.0069 0.0056 0.0067 0.0060 0.0067 0.0073

0.0024 0.0130 0.0142 0.0060 0.0083 0.0100

0.0021 0.0023 0.0029 0.0020 0.0023 0.0028

0.0044 0.0314 0.0470 0.0164 0.0327 0.0330

0.0041 0.0034 0.0047 0.0030 0.0053 0.0055

0.0011 0.0122 0.0189 0.0052 0.0115 0.0121

0.0012 0.0016 0.0025 0.0009 0.0021 0.0023

Central Highlands Kon Tum 0.1979 Gia Lai 0.1670 Dak Lak 0.0962 Dak Nong 0.1054 Lam Dong 0.0881

0.0229 0.0168 0.0141 0.0188 0.0125

0.0857 0.0727 0.0378 0.0409 0.0346

0.0134 0.0100 0.0070 0.0094 0.0060

0.0849 0.1126 0.0636 0.0658 0.0374

0.0142 0.0131 0.0088 0.0140 0.0074

0.0289 0.0450 0.0230 0.0228 0.0120

0.0061 0.0070 0.0040 0.0060 0.0029

0.1538 0.1712 0.0802 0.0844 0.0439

0.0162 0.0131 0.0081 0.0120 0.0065

0.0598 0.0738 0.0299 0.0312 0.0148

0.0083 0.0079 0.0038 0.0057 0.0028

South East Ninh Thuan Binh Thuan Binh Phuoc Tay Ninh Binh Duong Dong Nai Vung Tau Ho Chi Minh

0.1061 0.0353 0.0341 0.0094 0.0017 0.0156 0.0095 0.0035

0.0202 0.0081 0.0077 0.0032 0.0009 0.0037 0.0037 0.0017

0.0404 0.0112 0.0110 0.0023 0.0004 0.0046 0.0025 0.0009

0.0094 0.0032 0.0031 0.0010 0.0002 0.0013 0.0011 0.0005

0.0563 0.0223 0.0137 0.0047 0.0016 0.0103 0.0056 0.0019

0.0137 0.0053 0.0043 0.0016 0.0006 0.0026 0.0022 0.0008

0.0190 0.0065 0.0037 0.0011 0.0004 0.0028 0.0014 0.0004

0.0055 0.0018 0.0014 0.0004 0.0002 0.0008 0.0006 0.0002

0.0330 0.0156 0.0041 0.0044 0.0011 0.0080 0.0059 0.0023

0.0093 0.0042 0.0019 0.0016 0.0005 0.0025 0.0023 0.0014

0.0096 0.0041 0.0010 0.0010 0.0002 0.0020 0.0014 0.0005

0.0032 0.0013 0.0005 0.0004 0.0001 0.0008 0.0006 0.0004

Mekong River Delta Long An 0.0077 Tien Giang 0.0104 Ben Tre 0.0155 Tra Vinh 0.0321 Vinh Long 0.0144 Dong Thap 0.0205 An Giang 0.0291 Kien Giang 0.0365 Can Tho 0.0190 Hau Giang 0.0179 Soc Trang 0.0431 Bac Lieu 0.0251 Ca Mau 0.0351

0.0025 0.0037 0.0050 0.0096 0.0056 0.0050 0.0083 0.0089 0.0074 0.0068 0.0094 0.0067 0.0081

0.0020 0.0028 0.0043 0.0095 0.0038 0.0057 0.0084 0.0109 0.0051 0.0047 0.0135 0.0074 0.0111

0.0007 0.0011 0.0016 0.0034 0.0018 0.0016 0.0029 0.0032 0.0023 0.0021 0.0036 0.0023 0.0030

0.0052 0.0079 0.0079 0.0201 0.0085 0.0091 0.0121 0.0179 0.0117 0.0123 0.0220 0.0114 0.0166

0.0013 0.0029 0.0028 0.0057 0.0028 0.0023 0.0027 0.0041 0.0044 0.0043 0.0054 0.0041 0.0042

0.0012 0.0023 0.0020 0.0055 0.0021 0.0023 0.0031 0.0048 0.0030 0.0031 0.0061 0.0029 0.0043

0.0004 0.0011 0.0008 0.0018 0.0008 0.0007 0.0008 0.0013 0.0013 0.0013 0.0018 0.0012 0.0013

0.0078 0.0070 0.0122 0.0193 0.0134 0.0162 0.0212 0.0233 0.0125 0.0151 0.0228 0.0157 0.0183

0.0020 0.0026 0.0036 0.0055 0.0041 0.0040 0.0048 0.0056 0.0053 0.0052 0.0068 0.0044 0.0049

0.0019 0.0016 0.0030 0.0050 0.0033 0.0042 0.0056 0.0062 0.0031 0.0037 0.0060 0.0040 0.0046

0.0006 0.0007 0.0011 0.0018 0.0012 0.0013 0.0016 0.0018 0.0017 0.0015 0.0022 0.0013 0.0015

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