APPLICATION OF THE COUNTRY PRODUCT DUMMY METHOD TO CONSTRUCT SPATIAL AND TEMPORAL PRICE INDICES FOR SRI LANKA

Inadequate geographic coverage, inadequate population coverage, and short length of series make existing Sri Lankan price indices less than optimal to measure long-term trends inequality and poverty. Since they are based on binary methodologies they also do not satisfy the property of transitivity. In contrast, the multilateral Country Product Dummy (CPD) method satisfies the axiom of transitivity and ensures base region invariance. This paper applies the CPD method to construct spatial and temporal price indices that can be used for inequality and poverty analysis in Sri Lanka. It uses expenditure data from the Labor Force and Socio-Economic Surveys (LFSS) of 1980/81 and 1985/86 and the Household Income and Expenditure Surveys (HIES) of 1990/91, 1995/96, 2002, 2006/07 and 2009/10 conducted by the Department of Census and Statistics, Sri Lanka, to construct the indices. The former conflict-affected regions are excluded due to lack of data. The study reveals some recently emerging differences in rural and urban prices that are significant and cause for concern. These differences merit careful investigation to find out underlying factors using more appropriate and extensive data.


INTRODUCTION
This paper applies the Country Product Dummy method to construct spatial and temporal price indices that can be used for inequality and poverty analysis in Sri Lanka over the period 1980-2010.The former conflict-affected regions are excluded from the analysis due to lack of data from these regions for most of this period.
There are several reasons why currently available indices are not appropriate for the purpose of inequality measurement. Among them are the following: inadequate geographic coverage, inadequate population coverage and short length of series. For example, almost all existing price indices (indices constructed and used by Department of Census and Statistics, 2004, Datt and Gunewardena, 1997, Gunewardena, 2007have been computed for the specific purpose of measuring poverty, and use the consumption patterns of 40 per cent of households with the lowest consumption expenditure to construct the price indices. As a result, these price indices are not appropriate for the purpose of measuring inequality. Nor are they the most optimal to adjust consumption to measure poverty with. This is because existing indices are based on binary methodologies such as Paasche, Laspeyres and Fisher, which do not satisfy the property of transitivity. This means that the set of price comparisons that the binary methodologies yield are not inherently internally consistent between all possible direct and indirect comparisons (Kravis et al., 1982).
In contrast, multilateral methods such as the Elteto-Koves-Szulc (EKS) index, the Geary-Khamis (GK) method, and the Country-Product-Dummy (CPD) method, satisfy the property of transitivity. Nevertheless, the EKS and GK methodalso require a set of region or region-wise prices and quantities of items of uniform quality specifications, which is difficult to obtain. In contrast, the CPD methodology was originally developed as a specialized regression technique to deal with representative price lists of different countries that were not identical and to ensure base country invariance (Coondoo et al., 2004).
Hence this paper applies the CPD methodology to construct price indices for the analysis of inequality and poverty trends in Sri Lanka. We believe that the length of the series, covering a period of thirty years, and the fact that it covers the urban and rural (including estates) sectors in seven provinces, will be useful for researchers conducting trend analyses with household income and expenditure data, whether in inequality measurement, or in poverty measurement. Only the Colombo Consumers' Price Index (CCPI) covers a longer period. Besides, while the CCPI is a temporal series, it is not a spatial series, as it takes into account only the consumption patterns of consumers in Colombo.

METHODOLOGY AND DATA
The CPD methodology is really a bridge-region method that links two regions together on the basis of the relationship of each to a (base) region by taking into account all price comparisons with all other regions (Kravis et al., 1982). Consequently, the method regards each price as being dependent on the region in which it is observed, and on the item to which it refers.
The standard CPD formulation regresses the logarithm of observed prices on two sets of dummy variables, one relating to the various regions and the other to the various commodities. The model has no intercept. It includes the observations of unit prices for the base region in the base year in its vector of prices representing the dependent variable but does not include a dummy to represent the base as an explanatory variable.
Setting region j = 1 as base and introducing the dynamic of time t ( 1, 2,..., ) tT  , the regression version of the model is: (1) In equation (1) the base year and the subscripted region at the subscripted time. e  is the purchasing power parity for that particular region relative to the base of region 1 when 1 t  . Rao (1995)generalised the estimation procedure of the model by making use of quantity and value data and extending the model to allow for the use of weights. The extension had its roots in weighted least squares with weights being equivalent to the square root of expenditure shares, jit v , as in equation (2) The analysis in this paper uses expenditure data (value and quantity) from the Labour Force and Socio-Economic Surveys (LFSS) of 1980/81 and 1985/86 and the Household Income and Expenditure Surveys (HIES) of 1990/91, 1995/96, 2002, 2006/07 and 2009/10 conducted by the Department of Census and Statistics, Sri Lanka. The surveys are broadly comparable in design and methodology, particularly in the schedules related to household expenditure. The surveys could not be carried out in the Northern and Eastern Provinces for twenty years after 1985, although with the ending of the conflict (from most of the East in 2007 and in the North in 2009), first the Eastern Province and then the Northern Province were covered. However, since the present paper aims to construct price indices that can be used to investigate inequality and poverty trends in Sri Lanka during the post-liberalization period, we are compelled to exclude the North and the East because of the lack of data. Nevertheless, in a companion paper we intend to construct spatial and temporal price indices for the analysis of inequality and poverty for all Sri Lankan provinces including the North and the East for the years 1985/86, 2009/10 and 2012/13,in order to enable the analysis of inequality and poverty trends in the entire island.
Equation 2 was estimated over two samples. To construct the price indices for inequality analysis, we estimated the model over data on the value and quantity of all non-durable consumption expenditure of all households in all the surveys other than those households in the North and the East. In contrast, the price indices for poverty analysis were constructed by estimating equation (2) only over the non-durable consumption expenditure data of households with per capita consumption expenditure that was in the lowest four deciles. Expenditure data that was used to select the poorest 40 per cent of households in this way, excluded expenditure on durables and nonconsumption expenditure such as provident fund contributions, social activities and litigation.
Household price and expenditure data from the two samples for seven survey years for seven provinces, each with urban and rural sectors, were used to construct both sets of indices. It should be noted that the rural sector includes the estates sector as well. The price index for the urban sector in region 1 (Western Province) in 1980/81, the first year for which data is available, was set as the base or numeraire. Consequently, the number of regional dummies in the basic model of equation (1) applied to seven survey years, seven provinces and two sectors amounted to a total of 97 for each estimation (7 regions*7 years*2 sectors -1 [for base] = 97). Aggregated food and non-food commodity dummies amounted to 43, and these related to those categories for which quantity data were available. The classification system for expenditure categories was based largely on Datt and Gunewardena's (1997)  (3) In this equation, ji v denotes average expenditure on commodity i consumed in region j, while ji q denotes the average quantity of commodity i consumed in region j.
Conventionally, the poverty line is expressed in national prices. Therefore, in order to express the national poverty line in terms of price levels prevailing in different regions at different times, it becomes necessary to construct national price indices that will permit temporal and spatial analyses. In this paper we have constructed two such indices, one national, and the other sectoral, so that researchers can select the price index most appropriate for their analysis. The analysis follows Datt and Gunewardena (1997) to construct the national price indices as weighted averages of the temporal and spatial price indices, where the weights are the population shares by sector, province and year.

RESULTS
Ordinary Least Squares estimation can be used to obtain the coefficients of the explanatory variables in equation (2), so long as the least squares assumptions hold. One such assumption is that the explanatory variables are independent from each other. If, however, there are one or more exact linear relationships among the explanatory variables, then the least squares estimator cannot be defined. Tests for multicollinearity ruled out the presence of exact collinearity between explanatory variables in both estimations of equation (2), although the two commodity dummy variables for rice and cereals and food-bought-out, reported high (>10) variance inflation factors. However, the solution for this problem, either dropping the correlated variables or instrumenting for them, was not practical as the first two commodities are staples and represent an important component of household consumption, while the third commodity is heavily based on the first two. In any case, in the absence of exact collinearity, the least squares estimator still remains the best linear unbiased estimator by the Gauss-Markov theorem (Hill et al., 2011). Besides, our interest here is on the coefficients of the regional dummies from which we derive our spatial and temporal price indices, rather than the coefficients of the commodity dummies, and tests for multicollinearity ruled out the presence of exact linear relationships between our variables of interest.
We first set out the results for the estimation of price indices for inequality analysis using the CPD method in Tables 1 to 4. The results for the estimation of price indices for the analysis of poverty are set out in Tables 5 to 8. Consider the outcomes of the estimation of price indices for inequality first. Table 1 presents the regression results for the spatial dummy variables for the urban sector, while Table 2 sets out the results for the rural sector, based on expenditure data from the full sample. Regression results for the commodity dummies are not presented as they are not required for the construction of regional price indices other than in the specification of the CPD model, but are available from the authors on request. The full set of urban and rural price indices is set out in in Table 3, which is derived from the exponentials of the coefficients of the regional dummies in Tables 1 and 2. The regression results appear sensible. For example, all proved significant at the 1 per cent or 5 per cent critical level other than for the coefficients representing first year (1980/81) variables for all regions and both sectors. With Western Province's urban sector of the first survey year, 1980/81, taken as the base, the data suggests a twelve (urban)to sixteen (rural) fold increase in prices between 1980/81 and 2009/10. This is in keeping with the movement of the Colombo Consumer's Price Index(CCPI) over the same period(Central Bank of Sri Lanka, various years). Moreover, the twelve to fifteen-fold increase in urban prices since 1980/81 is broadly consistent across regions.
However, rural prices have been generally lower than urban prices until 2002. They appear to have caught up in 2006/07, and by 2009/10, rural prices in Western and Southern Provinces appear to exceed urban prices in the same provinces. To test whether the coefficients for the regional dummies both urban and rural, were equal to each other, we conducted Wald tests and Table 4 sets out the results. It can be seen that other than for rural prices of 2006/07 and 2009/10, the hypothesis that regional prices are different from each other in any year was rejected at the 5 per cent level of significance. It is likely that variations in commodity prices across regions averaged out to produce regional price indices that are close to each other during most of this period. The relatively higher rural prices of 2006/07 and 2009/10, however, merit further investigation in future research.
We turn next to the estimation of spatial and temporal price indices for poverty analysis. Table 5 presents the regression results for the spatial dummy variables for the urban sector, while Table 6 sets out the results for the rural sector, based on expenditure data from the poorest 40 per cent of the survey sample. The full set of urban and rural price indices is set out in in Table 7, which is derived from the exponentials of the coefficients of the regional dummies in Tables 5 and 6. The series for Sri Lanka as a whole, and for urban and rural Sri Lanka are the provincial and sectoral averages weighted with relevant population shares. The regression results in Tables 5 and 6 also appear sensible and the price index for Sri Lanka as a whole has recorded a 13-fold increase during the reference period. However, while the price index for urban Sri Lanka records an 11-fold increase, that for rural Sri Lanka records a 14-fold increase. Here, rural price indices for Western, North Western and Uva in 2009/10 exceeding urban prices in the same provinces have caused rural prices to exceed urban prices. Table 8 reports the results of the Wald tests of whether the coefficients for the regional dummies, both urban and rural, were equal to each other. Other than for rural prices of 2006/07, the hypothesis that regional prices are different from each other in any year was rejected at the 5 per cent level of significance. Again, underlying reasons merit further investigation in future research.
We can compare the price indices for poverty analysis for 1985/86 and 1990/91 generated by this study, with those derived by Datt and Gunewardena (1997). While their study configured some of the regions somewhat differently, they also reported price indices for the combined urban and rural sectors. Their results show that rural prices were 5 per cent and 6.25 per cent less than urban prices for 1985/86 and 1990/91 respectively. In contrast, as Table 7 shows, the price indices for the rural sector generated by the CPD method were 12 per cent and 9.7 per cent less than the urban sector's price indices in1985/86 and 1990/91. The larger rural-urban price differentials in the present series clearly arise from the CPD methodology used to generate the price indices. We are unable to carry out a similar comparison between the price indices for later years in this study with the series generated by the Department of Census and Statistics, as their series is constructed at district level and does not differentiate between the urban and rural sectors (see Department of Census and Statistics 2004).
The empirical research revealed some recently emerging differences in rural and urban prices that are significant and cause for concern. These differences merit careful investigation to find out underlying factors, using more appropriate and extensive data. For example, multivariate time series analysis using the spatial consumer and producer price data series maintained by the Central Bank of Sri Lanka, may throw further light on the extent to which commodity markets are spatially integrated, and help identify the commodities and district markets that are lagging behind. As importantly, such an analysis will show whether differentials between the prices that consumers pay for products, and the prices that producers receive, have decreased over the years with better transport and connectivity, or whether these differentials have remained the same, or even increased, due to other reasons such as anti-market practices. Research on these lines can better inform policies aimed at controlling inflation even while making sure that producers get better prices for their products.
A major limitation of the present study is that the price indices produced cannot be used to analyze the progress of inequality and poverty in the North and the East, and, in fact, in the country as a whole. However, in a companion paper, we intend constructing a spatial and temporal price index for all Sri Lankan provinces including the North and the East for the years 1985/86, 2009/10 and 2012/13 that will enable the analysis of poverty and inequality in those regions as well.