Disaggregate-level estimates of indebtedness in the state of Uttar Pradesh in India-an application of small area estimation technique

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1 University of Wollongong Research Online Centre for Statistical & Survey Methoology Working Paper Series Faculty of Engineering an Information Sciences 2010 Disaggregate-level estimates of inebteness in the state of Uttar Praesh in Inia-an application of small area estimation technique Hukum Chanra University of Wollongong, Nicola Salvati University of Pisa, Italy U. C. Su Inian Agricultural Statistics Research Institute, New Delhi, Inia Recommene Citation Chanra, Hukum; Salvati, Nicola; an Su, U. C., Disaggregate-level estimates of inebteness in the state of Uttar Praesh in Inia-an application of small area estimation technique, Centre for Statistical an Survey Methoology, University of Wollongong, Working Paper 19-10, 2010, 28p. Research Online is the open access institutional repository for the University of Wollongong. For further information contact the UOW Library:

2 Centre for Statistical an Survey Methoology The University of Wollongong Working Paper Disaggregate-level estimates of inebteness in the state of Uttar Praesh in Inia-an application of small area estimation technique Hukum Chanra, Nicola Salvati an U.C. Su Copyright 2008 by the Centre for Statistical & Survey Methoology, UOW. Work in progress, no part of this paper may be reprouce without permission from the Centre. Centre for Statistical & Survey Methoology, University of Wollongong, Wollongong NSW Phone , Fax anica@uow.eu.au

3 Disaggregate-level estimates of inebteness in the state of Uttar Praesh in Inia-an application of small area estimation technique Hukum Chanra Centre for Statistical an Survey Methoology, University of Wollongong, Wollongong, Australia. Nicola Salvati Dipartimento i Statistica e Matematica Applicata all'economia, University of Pisa, Italy, salvati@ec.unipi.it U. C. Su Inian Agricultural Statistics Research Institute, New Delhi, Inia Abstract The National Sample Survey Organisation (NSSO) surveys are the main source of official statistics in Inia an generate a range of invaluable ata at the macro level (e.g. state an national level). However, the NSSO ata cannot be use irectly to prouce reliable estimates at the micro level (e.g. istrict or further isaggregate level) ue to small sample sizes. There is a rapily growing eman of such micro level statistics in Inia as the country is moving from centralize to more ecentralize planning system. In this article we employ small area estimation (SAE) techniques to erive moel-base estimates of proportion of inebte househols at istrict or at other small area levels in the State of Uttar Praesh in Inia by linking ata from the Debt-Investment Survey of NSSO an the Population Census 2001 an the Agriculture Census Our results show that the moel-base estimates are precise an representative. For many small areas it is even not possible to prouce estimates using sample ata alone. The moel base estimates generate using SAE are still reliable for such areas. The estimates are expecte to provie invaluable information to policy-analysts an ecision-makers. Key wors: inebte househols, NSSO survey, census, small area estimation, proportion.

4 1. Introuction In recent years, the thrust of planning process has shifte from macro to micro level. There is eman by the aministrators an policy planners for reliable estimates of various parameters at the micro level. In view of the emans of moern time the thrust of research efforts has also shifte to evelopment of precise estimators for small areas. An offshoot of this evelopment is that various small area estimation techniques are being propose by the researchers for implementation. In Inia there is great emphasis on istrict level planning. For example, the efforts to evelop atabases require for planning an ecision-making at lower than the State level, were initiate quite some time back with the Planning Commission of Government of Inia setting up a Working Group on Districts planning in September, The Working Group in its report clearly highlighte the ata requirement for planning an ecision-making at the istrict level. However, it was foun that though a lot of ata are collecte, processe an publishe for the country as a whole or for iniviual states, not much isaggregation of the ata for sub-state level is one. Inia has been in an avantageous position ue to availability of regular ata through National Sample Survey Organisation (NSSO) surveys. The NSSO surveys are planne to generate statistics at state an national level. There is no regular flow of estimates at further below level, e.g., at the istricts level. Inee, the NSSO surveys provie reliable state an national level estimates; they can not be use to erive reliable irect estimates at the istrict level owing to small sample sizes which lea to high levels of sampling variability (see [7] an [8]). Due to the lack of statistics at this level, proper planning, fun allocation an also monitoring of various plans is likely to suffer. 1

5 Although in the Inian context, istrict is a very important omain for the planning process, we o not have surveys to prouce estimates at these levels. At the same time, it is also true that conucting any such surveys aime at this level is going to be very costly an time consuming job. Using the state level survey (e.g., NSSO surveys) ata to erive the irect estimates at istrict or smaller omain level, we may en up with very small sample sizes in these omains which may result in very unstable estimates for these omains. A solution to this problem is to consier small area estimation (SAE) techniques. The SAE techniques aim at proucing reliable estimates for such omains with small sample sizes by borrowing strength from ata of other omains. The SAE techniques are generally base on moel-base methos. The iea is to use statistical moels to link the variable of interest with auxiliary information, e.g. Census an Aministrative ata, for the small areas to efine moel-base estimators for these areas. Such small area moels can be classifie into two broa types: (i) Area level ranom effect moels, which are use when auxiliary information is available only at area level. They relate small area irect estimates to area-specific covariates (Fay an Herriot [4]) an (ii) Neste error unit level regression moels, propose originally by Battese, Harter an Fuller [2]. These moels relate the unit values of a stuy variable to unit-specific covariates. We aopt the area level moel since covariates are available only at the area level. In this article we employ small area estimation techniques to erive moel-base estimates of proportion of inebte househols at small area levels in the State of Uttar Praesh in Inia by linking ata from the Debt-Investment Survey of NSSO an the Population 2

6 Census 2001 an the Agriculture Census Small areas are efine as the ifferent istricts an istrict by lan holing classes of State of Uttar Praesh in Inia. The article illustrates how the NSSO an Census ata can be combine to erive reliable estimates for the proportion of inebte househol at the istrict level. The rest of the paper is organise as follows. In Section 2 we escribe the ata use for the analysis an in Section 3 we present an overview of the methoology use for the analysis. Section 4 iscusses the iagnostic proceures for examining the moel assumptions an valiating the small area estimates an escribes the results. Section 5 finally sets out the main conclusions. 2. Data In this article we aopt an area level small area moel to erive the small area level estimates (see [4]). Two types of variables are require for this analysis. (i) The variable of interest for which small area estimates are require is rawn from the Debt-Investment Survey of NSSO. We use 59 th roun ata of NSSO for rural areas on Debt an Investment survey conucte for the calenar year in the State of Uttar Praesh in Inia. The target variable use for the stuy was inebte househols. A househol is efine to be inebte if it has outstaning loan as on The parameter of interest is the proportion of inebte househol at the istrict an istrict by holing size level. (ii) The auxiliary (covariates) variables known for the population are rawn from the Population Census 2001 an the Agriculture Census It is noteworthy that use of covariates from the 2001 Population Census an the 2003 Agriculture Census to moel inebte househol from the NSSO survey may raise issues of comparability. 3

7 However, the covariates use in this stuy are not expecte to change significantly over a short perio of time. There were 158 covariates available from the Population Census 2001 an the Agriculture Census 2003 to consier for the moelling. Out of these, suitable covariates were selecte for the analysis as follows. We first examine the correlation of all these covariates with the target variable an then selecte the covariates with reasonably goo correlation with the target variable. This was followe by step-wise regression analysis. Finally, two variables the Crop loan istribute (Inian Rupees in lakhs) in Rabi season (Rabi) an Female Agricultural Labor (AL_F) were ientifie for the further analysis which significantly explaine the moel. The sampling esign use in the NSSO ata is stratifie multi-stage ranom sampling with istricts as strata, villages as first stage units an househols as the secon stage units. There are total of 11,814 househols (i.e. number of surveye househols which inclues both inebte an non-inebte househols) from the 69 istricts of the Uttar Praesh. The average lan holing size is 1.41 hectare. The istrict specific sample size varies from 55 to 340 with average sample size of 171. The istrict specific sample size becomes very small if we consier further sub-grouping of the istricts (e.g., istrict by lan holing classes). Base on lan holing size in hectare (hereafter ha) the househols are classifie into five ifferent holing classes as set out in Table 1. These are the stanar classification of lan holing classes in Inia. Our aim is to estimate proportion of inebte househols at istrict level for ifferent lan holing classes as well as for all classes combine together. Therefore, we efine ifferent istricts (Cat0) an istricts by lan holing classes (Cat1-Cat5) of the State of Uttar Praesh as the small areas of interest, see Table 1 for the efinition. The istrict an 4

8 istrict by lan holing class-wise sample sizes for the NSSO ata use in this analysis are presente in Table 2. The most striking point in Table 2 is that the sample size 0 an 1 can be seen in many istricts or small areas. For example, category 5 (Cat 5) has 9 istricts with sample of size 0. For these istricts it is not possible to generate the irect estimates using traition sample survey estimation approaches. Among the six categories efine above, the last three categories Cat3 to Cat 5 have very small average sample sizes (average over the ifferent istricts) of 18, 9 an 3 respectively. Further, there are many other istricts in Cat 4 an Cat 5 with sample of size 1. It is again ifficult to erive reliable estimates an their stanar errors for such istricts. Inee, SAE is an obvious answer to these problems. The SAE techniques provie reliable estimates for the istricts having small or even no sample ata ([8]). The unerlining theory of SAE has been illustrate in next Section. 3. An overview of the methoology We now set out the small area estimation techniques use to prouce the moel-base estimates an their measure of precision. To start, we first fix our notation. Throughout, we use a subscript to inex the quantities belonging to small area ( = 1,..., D), where D is the number of small areas (or areas) in the population. The subscript s an r are use for enoting the quantities relate to the sample an non-sample parts of the population. So that n an N represent the sample an population sizes in small area, respectively. The value of variable of interest y (which is the number of inebte househol) in the area is efine by y an we enote by y s an y r the sample an non-sample counts of inebte househols in area. Inee, the variable of interest y s has a Binomial istribution with parameters n an π, enote by ys ~ Bin( n, π ), where π is the 5

9 probability of an inebt househol in area, often terme as the probability of a success. Similarly, yr ~ Bin( N n, π ). Further, y s an y r are assume to be inepenent Binomial variables with π being a common success probabilities. Recall that in moelbase small area estimation the survey ata is supplemente by the availability of auxiliary information from various sources, e.g., Census an Aministrative recors. Let x be the k-vector of the covariates for area from the previous sources. The moel linking the probabilities of success π with the covariates x is the logistic linear mixe moel (see [3], [6] an [9]) given by π logit( π) = ln = η = x β + u, ( = 1,..., D), (1) 1 π where β is the k-vector of regression coefficient often known as fixe effect parameters an u is the area-specific ranom effect that accounts for between area issimilarity beyon that explaine by the auxiliary variables inclue in the fixe part of the moel. We assume that u s are inepenent an normally istribute with mean zero an variance ϕ. Uner moel (1), we get { exp( } x u ){ exp( x u } 1 1 π = exp( η ) 1 + η ) = exp( β β + ). It is evient that moel (1) relates the area level proportions to area level covariates. This type of moel is often referre to as area-level moel in SAE terminology, see for example [8]. Such type of moel was originally use by Fay an Herriot [4] for the preiction of mean per-capita income (PCI) in small geographical areas (less than 500 persons) within counties in the Unite States. The Fay an Herriot (FH) metho for SAE is base on area level linear mixe moel an their approach is applicable to a continuous 6

10 variable. In contrast, moel (1) is a special case of a generalize linear mixe moel (GLMM) with logit link function (see [3]) an suitable for iscrete, particularly binary variable. It is noteworthy that the FH moel is not applicable in such cases. Saei an Chambers[9] an Manteiga et al.[6] escribe this moel in the context of SAE. By efinition, the means of y s an y r given u uner moel (1) are: Let T ( ) = π = exp( x + )( 1+ exp( x + )) 1 E ys u n n β u β u (2) ( ) = ( ) π = ( ) exp( x + )( 1+ exp( x + )) 1 E yr u N n N n β u β u. (3) enotes the total number of inebt househols in small area. We can write T = ys + y r, where the first term y s, the sample count is known whereas the secon term y r, the non-sample count, is unknown. Therefore, an estimate Tˆ of the total number of inebte househols in area is obtaine by replacing y r by its preicte value uner the moel (1). That is, Tˆ ˆ ( ) exp( ˆ ˆ )( 1 exp( ˆ )) 1 = ys + yr = ys + N n x β + u + xβ + uˆ. (4) Often we come across the situations when small areas o not have sample ata at all (Table 1 an 2). That is n = 0 an y = 0. For example, in the NSSO ata for Cat5 there are 9 s istricts with n = 0. Eventually traitional survey estimation approaches o not provie solution to this problem. In contrast, SAE can be use to erive estimates for such areas. In particular, for the small areas with n = 0, we use synthetic-type estimator for computing T efine as 1 { x ˆ β ( x ˆ ) } ˆ Syn T = N exp( ) 1+ exp( β ). (5) 7

11 An estimate of proportion of inebte househols p in a small area is obtaine as 1 { ( ) exp( x ˆ )( 1 exp( x ˆ ) ) } Tˆ 1 pˆ ˆ ˆ = = ys + N n β + u + β + u. (6) N N Similarly, for areas with n = 0, proportion is estimate by p ˆ exp( ˆ) ( Syn = x 1+ exp( x ˆ )) 1 β β. (7) It is obvious that in orer to compute the estimates given by equation (4) to (7), we require estimates of the unknown parameters β an u. A major ifficulty in use of logistic linear mixe moel (LLMM) for SAE is the estimation of unknown moel parameters β an u since the likelihoo function for LLMM often involves high imensional integrals (compute by integrating a prouct of iscrete an normal ensities, which has no analytical solution) which are ifficult to evaluate numerically. We use an iterative proceure that combines the Penalize Quasi-Likelihoo (PQL) estimation of β an u = ( u,..., u ) 1 D with restricte maximum likelihoo (REML) estimation of φ to estimate these unknown parameters. Detaile escription of the approach can be followe from [6, 9]. We now turn to estimation of mean square error (MSE) for preictors given by equation (6) an (7). The MSE estimates are compute to assess the reliability of estimates an also to construct the confience interval (CI) for the estimates. The mean square error estimate of (6) uner moel (1) is (see [6, 9]) given by mse( pˆ ) = m ( ˆ φ) + m ( ˆ φ) + 2 m ( ˆ φ ). (8)

12 The first two components m 1 an m 2 constitute the largest part of the overall MSE estimates in (8). These are the MSE of the best linear unbiase preictor (BLUP)-type estimator when φ is known ([8]). The thir component m 3 is the variability ue to the estimate of φ. For simplicity, we use few notations to write the analytical expression of various components of the mean square error (8). We enote by ˆ = iag { n pˆ (1 pˆ )} {( ) (1 } r 1 A= { iag( N )} ˆ V r { V an s Vˆ = iag N n pˆ pˆ ), the iagonal matrices efine by the corresponing variances of the sample an non-sample part respectively. Similarly, we efine X s an B= X T X an ˆ 1 = ( φ I Vˆ ) 1 1, iag( N )} ˆ ˆ ˆ Vr r A svs s T +, where s D s X r are the sample an non-sample part of auxiliary information an I D is an ientity matrix of orer D. We further write ˆ { ˆ ˆ ˆ ˆ } 1 T = X V X X V TV X an (1) s s s s s s s s Tˆ =Tˆ + TˆVˆ X Tˆ X Vˆ T ˆ. With these notations, assuming moel (1) hols, the various (2) s s s s (1) s s s components of equation (8) are m ˆ ˆ 1( φ ) = AT sa, m ˆ ˆ 2 ( φ ) = BT ( 1) B, an 3 ( ˆ ˆ ˆ ˆ i j φ ) m ( ˆ φ) = trace Σ v( ) with Σ ˆ = Vˆ +φ ˆI Vˆ Vˆ. s D s s Here v( φ) ˆ is the asymptotic covariance matrix of the estimates of variance components ˆ φ, which can be evaluate as the inverse of the appropriate Fisher information matrix for ˆ φ. Note that this also epens upon whether we are using maximum likelihoo (ML) or restricte maximum likelihoo (REML) estimates for ˆ φ. We use REML estimates for ˆ φ, then ˆ ( ˆ ) 2 ˆ v( φ)= 2 φ ( D 2 t ) + φ t with t = ˆ φ t ce( Tˆ 2) ) an t = trace( Tˆ Tˆ ). Let ra ( 11 (2) (2) 9

13 us write Δ=AT ˆs an ˆ i = ( Δi) φ ˆ = ( AT ˆ i s) φ, where A φ φ ˆ i is the = φ = φ th i row of the matrix A. The MSE estimates of (7) is a special case of (8) when n = 0, given as Syn mse( pˆ { ˆ (1 ˆ )} ˆ { ˆ ) = iag p p φ D iag p(1 pˆ ) I } (9) The numerical results reporte in Sections 4 are obtaine using R version Empirical results 4.1 Diagnostic proceures Generally two types of iagnostics proceures are teste in small area estimation, the moel iagnostics an the iagnostics for the small area estimates, see for example[1]. The first iagnostics are use to verify the assumptions of unerlying moel an the secon iagnostics are applie to valiate the reliability of the moel-base small area estimates. The ranom area effects u ( = 1,..., D) in moel (1) are assume to have a normal istribution with mean zero an variance ϕ. If the moel assumptions are satisfie then the istrict level resiuals are expecte to be ranomly istribute an not significantly ifferent from the regression line y=0, where uner moel (1), the area level resiuals are efine as r = ˆ η ˆ x β. The istribution of the istrict level resiuals (left sie plots) an q-q plots (right sie plots) for Cat0 to Cat5 ata are shown in Figure 1. The Figure 1 clearly reveals that the ranomly istribute istrict level resiuals an the line of fit oes not significantly iffer from the line y=0 as expecte in all the plots. The q-q plots also confirm the normality assumption. Therefore the moel iagnostics are fully satisfie for the ata. To valiate the reliability of the moel-base small area estimates we use the bias iagnostics, coefficient of variation (CV) an compute the 95 percent confience 10

14 intervals. The bias iagnostics are use to investigate if the moel-base estimates are less extreme when compare to the irect survey estimates, when it is available [5]. In aition, if irect estimates are unbiase, their regression on the true values shoul be linear an correspon to the ientity line. If moel-base estimates are close to the true values the regression of the irect estimates on the moel-base estimates shoul be similar [1]. We plot irect estimates on Y-axis an moel-base estimates on X-axis an we look for ivergence of regression line from Y = X an test for intercept = 0 an slope = 1 (see for example [1]). The bias scatter plots of the irect estimates against the moel-base estimates for Cat0 to Cat5 ata are set out in Figure 2. The results for bias test are given in Table 3. It is noteworthy that the moel base estimates use in bias tests are base on synthetic moel. It is meaningful because it overcomes the shrinkage effect an shows that the eterministic part of the moel gives unbiase preictions as o the irect estimates. The bias iagnostic results in Table 3 clearly show that only the slope for cat4 fails this iagnostic. The plots show that the moel-base estimates are less extreme when compare to the irect estimates, emonstrating the typical SAE outcome of shrinking more extreme values towars the average. It has to be note that istricts with extreme irect estimates are mainly those with small sample sizes. Such cases were observe more in the plots belonging to Cat3 to Cat 5. We compute the coefficient of variation (CV) to assess the improve precision of the moel-base estimates compare to the irect estimates. The CVs show the sampling variability as a percentage of the estimate. Estimates with large CVs are consiere unreliable (i.e. smaller is better). There are no internationally accepte tables available that allow us to juge what is "too large" ([1] an [5]). Figure 3 presents the istrict-wise 11

15 istribution of the percentage CV of moel base estimates an irect estimates for all six categories (Cat0-Cat5) consiere in the analysis. The estimate CVs show that moelbase estimates have a higher egree of reliability when compare to the (non-zero) irect estimates. We note that the average sample size for the istricts become smaller as we move from Cat 0 to Cat 5. As expecte, relative performance of moel base estimates are better as sample size ecreases (see Figure 3). Particularly, for Cat 5 irect estimates have very high CV. The moel base estimates still perform well. It is interesting to note that for Cat 5 out of 69 istricts there are 9 istricts with no sample ata. For these 9 istricts we cannot prouce the irect estimates, however, moel base estimates generate for these istricts have reasonably goo CV values an that to within the acceptable limit (Table 4). In Table 5 we present the istricts-wise 95% confience intervals of the moel-base an the irect estimates. The 95% confience intervals (CIs) for the irect estimates are calculate assuming a simple ranom sample generate the weighte proportions. Obviously, this ignores the effects of ifferential weighting an clustering within istricts that woul further inflate the true stanar errors of the irect estimates. The stanar errors of the irect estimates are too large an therefore the estimates are unreliable. Note that for many istricts we can even not prouce the confience intervals ue to unavailability of stanar errors. 4.2 Discussions The small area estimates iagnostic measures clearly epict that the moel-base estimates (i.e. the estimates generate by the SAE approach) are reliable an more stable than the corresponing irect estimates (Figure 3). Table 5 presents the irect estimates an moel- 12

16 base estimates along with 95% confience intervals for the State of Uttar Praesh for five ifferent lan-holing classes as well as combine. These results show the egree of inequality with respect to istribution of inebte househols in ifferent istricts as well as between various lan-holing classes. The most interesting point is the moel base estimates for istricts where there is very small (e.g. n = 1 or 2) or no sample information. So it is not feasible to have irect estimates an their CI for such cases. In Table 5 there are many istricts where there is no irect estimate an their 95% confience interval. This leaves us with no way except SAE. Table 4 presents the moel-base estimates for 9 istricts of Cat 5 with n =0. These estimates are reliable with CVs below 5%. Note that these estimates can be biase if synthetic assumption is violate. A critical review of Table 5 shows that in many istricts the lower boun (Lower) of 95% confience interval is negative an upper boun (Upper) is greater than 1.0 which results in practically impossible an inamissible values of CI for irect estimates. For example, the CI of irect estimates for Chitrakut in Cat 2 an Mathura in Cat 3 excees 1.0. In contrast, the moel estimate of Chitrakut an Mathura with precise CI an reasonable CV percent are still reliable. A similar problem, but in other situation was observe when there was no variability in the sample ata of istrict. For example see Lalitpur in Cat 2 where all y values in sample were 1 an estimate irect proportion was 1.0 an estimate SE was 0. That is CI with extreme sample value provies very little information. These abnormalities with irect estimation were seen in many istricts when we observe Cat 4 an 5. In Cat 4 there are 31 out of 69 istricts where irect estimation can not even efine proper CI. We note that in Cat 5 more than half istricts have sample of size 0, 1 or 2 an therefore the problem with irect estimates is worst. Out of 69 istricts there are only 3 13

17 istricts where CI for irect estimates is even efine. In such circumstance, SAE plays an important role in generating micro level statistics. The results clearly show the avantage of using SAE technique to cope up the small sample size problem in proucing the estimates or reliable confience intervals. These estimates can efinitely be useful for resource allocation an policy ecisionmaking relating the inebteness. The lan holing class specific estimates have ae avantages for policy planning an resource allocation base on farm category wise. These estimates are also helpful in ientifying the istricts/regions or farm categories with higher level of inebteness. For example, in the buget year , Govt of Inia announce the creation of a farmers ebt relief fun. This scheme waives the ebts of farmers in general an small an marginal farmers in particular. The implementation of this scheme will efinitely nee the estimates generate in this stuy. The concerne Govt epartment can use these estimates to allocate the fun to various istricts accoring to the proportion of inebte farmers. 5. Conclusions A great eal of theoretical research has been one for the SAE. This is the time for their real life applications an implementation. The metho for estimation of proportions for small areas is well evelope ([6 an 9]), however, there is limite application in the area of agricultural or social sciences. Further, there is rarely any application to the Inian ata. In this article we emonstrate the application of SAE techniques to estimate the istrict level statistics of inebteness for ifferent lan holing classes as well as all classes combine together using survey an census ata. The iagnostic proceures clearly 14

18 confirm that the moel-base istrict level estimates for ifferent lan holing classes as well as all classes combine together have reasonably goo precision. The SAE metho has also generate reliable estimates for the istricts with no or very small sample sizes such as 1 or 2. This application of small area analysis is the first of its kin with most popular NSSO ata in Inia to estimate the proportions at isaggregate levels. In Inia, Censuses are usually limite as they ten to focus mainly on the basic socio-emographic an economic ata an not available for every time perio. The NSSO survey, on the other han, contributes to proviing estimates at the State an National level. They o not provie sub-state level statistics. However, it is known that regional an national estimates usually mask variations (heterogeneity) at the sub-state or istrict level an rener little information for micro level planning an allocation of resources. These ays a lot of emphasis is being given to micro level planning in Inia. District is an important omain for planning process in the country an therefore availability of istrict level statistics is vital for monitoring of policy an planning. For example, Govt of Inia UNDP project on Capacity Development for District Planning. It expects ecentralise planning to improve effectiveness of evelopment programmes. This stuy prouces reliable statistics at micro level using existing surveys an other alreay available seconary ata an can be seen as an inicative example for further applications. Such micro level statistics can be generate without conucting separate survey for this purpose an unlike Census regular estimates can be prouce from regular existing surveys. Govt of Inia currently has number of schemes (for example, Inira Awaas Yojana, Prahan Mantri Gram Saak Yojana, Mahatma Ganhi National Rural Employment Guarantee Scheme etc.) for rural areas since the rural evelopment in Inia is one of the most important factors for the growth of the Inian economy. These isaggregate level estimates are useful for implementation of these schemes. 15

19 References [1] R. Ambler, D. Caplan, R. Chambers, M. Kovacevic, an S. Wang, Combining unemployment benefits ata an LFS ata to estimate ILO unemployment for small areas: an application of a moifie Fay-Herriot metho. Proceeings of the Int. Assoc. of Survey Stat., Meeting of the ISI, Seoul, August [2] G. E. Battese, R. M. Harter, an W. A. Fuller, An error component moel for preiction of county crop areas using survey an satellite ata, J. of the Amer. Stat. Assoc. 83 (1988), pp [3] N. E. Breslow an D. G. Clayton, Approximate inference in generalize linear mixe moels, J. of the Amer. Stat. Assoc. 88(1993), pp [4] R. E. Fay an R. A. Herriot, Estimation of income from small places: an application of james-stein proceures to census ata, J. of the Amer. Stat. Assoc. 74(1979), pp [5] F.A. Johnson, H. Chanra, J. J. Brown, an S. Pamaas, District-level estimates of institutional births in ghana: application of small area estimation technique using census an DHS ata, J. of Off. Stat. 26 (2010), pp [6] G.W. Manteiga, M.J. Lombarìa, I. Molina, D. Morales, an L. Santamarìa, Estimation of the mean square error of preictors of small area linear parameters uner a logistic mixe moel, Comput. Stat. & Data Anal. 51(2007), pp [7] D. Pfeffermann, Small area estimation: new evelopments an irections. Int. Stat. Rev. 70(2002), pp [8] J.N.K. Rao, Small Area Estimation. Wiley Series in Survey Methoology, John Wiley an Sons Inc, [9] A. Saei an R. Chambers, Small area estimation uner linear an generalize linear mixe moels with time an area effects, Meth. W.P. No. M03/15(2003), Southampton Statistical Sciences Research Institute, University of Southampton, UK. 16

20 Table 1. Definition of lan holing classes Sample size Category Descriptions Lan holing size (ha) Min Max Average Total Cato All All lan holing size Cat1 Marginal less than 1 ha Cat2 Small l an < 2 ha Cat3 Semi-meium 2 ha an < 4 ha Cat4 Meium 4 ha an < 10 ha Cat5 Large l0 ha

21 Table 2. Distribution of istricts-wise sample size. District Cat0 Cat 1 Cat2 Cat3 Cat4 Cat5 Saharanpur Muzaffar Nr Bijnor Moraaba Rampur J.B.P. Nagar Meerut Baghpat Ghaziaba Bula Shahar Aligarh Hathras Mathura Agra Firozaba Etah Mainpuri Baaun Bareilly Pilibhit Shahjahanpur Kheri Sitapur Haroi Unnao Lucknow Raibarely Farukhaba Kannauj Etawah Auraya Kanpur Dehat Kanpur Nr Jalaun Jhanshi Lalitpur Hamirpur Mahoba Bana Chitrakut Fatehpur Pratapgarh Kaushambi Allahaba Barabanki Faizaba Ambeker Nr Sultanpur Bahraich Srawasti Balrampur Gona Siharth Nr Basti S.Kabir Nr Maharajganj Gorakhpur Kushi Nr Deoria Azamgarh Mau Ballia Jaunpur Ghazipur Chanauli Varanasi St. Ravias Nagar Mizapur Shanbhara Total Nr= Nagar 18

22 Table 3. Bias iagnostics test for Cat0- Cat5. Category Parameters Estimate St error t Prob> t Cat0 Intercept Moel base estimate Cat1 Intercept Moel base estimate Cat2 Intercept Moel base estimate Cat3 Intercept Moel base estimate Cat4 Intercept Moel base estimate Cat5 Intercept Moel base estimate

23 Table 4. District-wise moel-base estimates for the istricts of Cat 5 with no sample ata. 95% Confience Interval District Estimate CV,% Lower Upper Hathras Agra Firozaba Etah Farukhaba Kanpur Nr Srawasti S.Kabir Nr Kushi Nr

24 Table 5. District-wise moel-base an irect estimates of proportion of inebte househols. Cat0 Cat1 Direct Moel-base Direct Moel-base Region District Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper Western Saharanpur Muzaffarnagar Bijnor Moraaba Rampur J.B.P.Nr Meerut Baghpat Ghaziaba Bula Shahar Aligarh Mathura Hathras Agra Firozaba Etah Farukhaba Mainpuri Baaun Bareilly Pilibhit Shahjahanpur Kannauj Etawah Auraya Central Kheri Sitapur Haroi Unnao Lucknow Raibarely Kanpur Dehat Kanpur Nr Fatehpur Southern Jalaun Jhanshi Lalitpur Hamirpur Mahoba Bana Chitrakut Eastern Pratapgarh Kaushambi Allahaba Barabanki Faizaba Ambeker Nr Sultanpur Bahraich Srawasti S.Kabir Nr Kushi Nagar Balrampur Gona Siharth Nr Basti Maharajganj Gorakhpur Deoria Azamgarh Mau Ballia Jaunpur Ghazipur Chanauli Varanasi St. Ravias Nr Mizapur Shanbhara

25 Table 5. District-wise moel-base an irect estimates of proportion of inebte househols(cont.). Cat2 Cat3 Direct Moel-base Direct Moel-base Region District Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper Western Saharanpur Muzaffarnagar Bijnor Moraaba Rampur J.B.P.Nr Meerut Baghpat Ghaziaba Bula Shahar Aligarh Mathura Hathras Agra Firozaba Etah Farukhaba Mainpuri Baaun Bareilly Pilibhit Shahjahanpur Kannauj Etawah Auraya Central Kheri Sitapur Haroi Unnao Lucknow Raibarely Kanpur Dehat Kanpur Nr Fatehpur Southern Jalaun Jhanshi Lalitpur Hamirpur Mahoba Bana Chitrakut Eastern Pratapgarh Kaushambi Allahaba Barabanki Faizaba Ambeker Nr Sultanpur Bahraich Srawasti S.Kabir Nr Kushi Nagar Balrampur Gona Siharth Nr Basti Maharajganj Gorakhpur Deoria Azamgarh Mau Ballia Jaunpur Ghazipur Chanauli Varanasi St. Ravias Nr Mizapur Shanbhara

26 Table 5. District-wise moel-base an irect estimates of proportion of inebte househols(cont.). Cat4 Cat5 Direct Moel-base Direct Moel-base Region District Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper Western Saharanpur Muzaffarnagar Bijnor Moraaba Rampur J.B.P.Nr Meerut Baghpat Ghaziaba Bula Shahar Aligarh Mathura Hathras Agra Firozaba Etah Farukhaba Mainpuri Baaun Bareilly Pilibhit Shahjahanpur Kannauj Etawah Auraya Central Kheri Sitapur Haroi Unnao Lucknow Raibarely Kanpur Dehat Kanpur Nr Fatehpur Southern Jalaun Jhanshi Lalitpur Hamirpur Mahoba Bana Chitrakut Eastern Pratapgarh Kaushambi Allahaba Barabanki Faizaba Ambeker Nr Sultanpur Bahraich Srawasti S.Kabir Nr Kushi Nagar Balrampur Gona Siharth Nr Basti Maharajganj Gorakhpur Deoria Azamgarh Mau Ballia Jaunpur Ghazipur Chanauli Varanasi St. Ravias Nr Mizapur Shanbhara

27 Figure 1. Distribution of the istrict level resiuals (left han sie plots) an normal q-q plot of the istrict level resiuals (right han sie plots) for Cat0 (up) to Cat 5(own). 24

28 Figure 2. Bias iagnostics plots with Y = X line (soli) an regression line (otte) for Cat0- Cat5. Cat0 Cat1 Cat2 Cat3 Cat4 Cat5 25

29 Figure 3. District-wise coefficient of variation for irect (soli line) an moel-base estimate (ash line) for Cat0- Cat5. Cat0 Cat1 Cat2 Cat3 Cat4 Cat5 26