Assistant Professor Ranjula Bali Swain
email: ranjula.bali@nek.uu.se

THE DEMAND AND SUPPLY OF CREDIT FOR HOUSEHOLDS

The demand and supply of credit in the rural credit markets is investigated in this paper using household data from India. The aim is to study the effects of household, farm productive characteristics and the policy variables on the demand and supply of credit. A type 3 Tobit model is estimated which corrects for sample selection and endogeniety bias. In addition, a generalised Double Hurdle model is estimated where the information on the household's access to credit is included to estimate the demand and supply of credit. The results suggest that the size of the operational holdings, net-wealth, dependency ratio, educational level of the household and the wages and output prices are important determinants of the demand and supply of credit for farm households. The Double Hurdle model confirms that the 'size of land owned' plays a crucial role in whether the household has access to a loan or not.

Introduction

Financial planning plays a crucial role in agricultural development in the developing economies. This leads to the need for a proper understanding of the working of the rural finance markets and the investigation into the factors affecting the demand for credit. There is a further need to study policy relevant issues like the relationship of ownership of land with the demand and supply of credit and the impact of government policies in other factor markets (for instance minimum wage policies) on the demand for credit. Using household level data from the Puri district, in India, this paper investigates the demand for and supply of credit for investment and consumption.

The quantitative research on the factors influencing rural loan demand is quite limited. 1 Many studies that try to estimate loan demand suffer from bias due to data truncation, resulting from the omission of the non-borrowers (Hesser and Schuh, 1962; Pani, 1966; Long 1968; Ghatak, 1976) and simultaneity bias arising from the endogeniety of interest rate. Moreover, the demand for credit of a household is often calculated from data that reports only a single loan transaction per household with the exception of a few studies (for instance, Nagarajan, Meyer and Hushak, 1995). Such estimates would be misleading in the presence of credit supply constraints and multiple loans. Furthermore, a majority of these studies are based on data that was collected over a decade ago. This paper accounts for most of these problems. Using recently collected data from Orissa, India, the demand and supply of credit for farm households is estimated using a type 3 Tobit 3 model, which deals with the problem of sample selectivity bias and the endogeniety of the interest rate and loan size. The estimates show that interest rate, net-wealth, area of operational holdings, primary activity of the head of the household and output price are factors that determine demand for credit. In addition, factors like family size and dependency ratio also influence the household's demand. Loan size, net wealth, operational holdings, distance from the bank and dependency ratio are the factors that are significant in determining the interest rate.

The Generalized Double Hurdle Model on the other hand does more than just estimate the demand and supply for credit. It goes a step further by taking the "access to loans" into account while estimating the demand and supply for the households. The econometric model is adapted to include the additional information on the household's access to loan, collected in the data. The empirical results in this paper are especially relevant for the current financial planning as the study uses recently collected data. The results from the Double Hurdle model indicate that the effective lending policies in the rural credit markets of Puri are asset based.

Size of land owned is an important determinant of households' access to loans. The interest rate and the wage of the household determine the demand for loans. Net wealth, land quality and education are important determinants on the supply side.

The paper is written in five compact parts with the following section reviewing some of the important features of the data. The theoretical framework is introduced in Section 3. The following section presents the econometric specification and the estimation issues of the type 3 Tobit and the Double Hurdle model. It also contains a description of the variables and the identification issues. A discussion on the results of the estimated models and the concluding remarks are presented in the final section of this paper.

Data

The data used for the analysis in this paper is collected by the author in the 'Rural Credit Market Survey of the Puri district in India' for the reference period 1996. The survey has information on 1052 households that were selected by a two stage stratified sample, from 66 villages, spread in the 11 administrative blocks of the Puri district, which is the coastal district of Orissa, in east India. After deleting the households with missing values we are left with information on 989 households. About 500 of these 989 households did not take any loan. Of the 489 households that borrowed, 430 had only single loans whereas 59 households took two loans during the reference period.

The majority of households are farm households, as 78% of the sample households, own land. 39% of the total sample households are marginal farmers whereas 21% are small farmers 2 .

The farms still use traditional forms of agriculture, though there is a slow change towards modern technology. Table 1, presents the sample means and standard deviations for some of the selected variables for different household category. Large landowners borrow about three times as much as the small landowners and about five times as much as the landless. On the average they pay a much lower interest rate as compared to the landless and small landowners.

Theoretical Framework

Theoretical Model

The theoretical framework for this paper is based on Iqbal (1981, 1983). The model is modified such that, the rate of interest is endogenously determined as a function of both the 2 Marginal farmers own less than 1 hectare while small farmers own between 1 and 2 hectares. This is a standard definition used in government and census reports. It takes the household as a basic unit of analysis and assumes that the household behaves as a single individual and maximises its utility over a time span of two periods. The utility function is well behaved, monotonic, twice continuously differentiable and strictly concave.

The household maximises its utility subject to the budget and time constraints. The model includes the labour-leisure choice with the consumption in the two periods. The two periods 'current' (period 1) and 'future' (period 2) capture the borrowing-investment-repayment cycle. The household has a given initial endowment of productive farm assets and socioeconomic household characteristics.

In the 'current' period the household produces some output using its household labour, initial endowment of productive farm assets and fixed farm characteristics. It also earns some income by supplying its labour to the market. The price of output and labour are exogenously given. The household borrows for both production and consumption purposes. 3 The loan has to be repaid in the 'future' period. In addition, no voluntary default by the household is assumed. Since there are no future periods, after period 2, it is assumed that the productive assets are consumed in the second period and the household does not leave any bequests for the subsequent period.

If the markets for products and factors were perfect, with exogenous prices and no transaction cost, there would be separability between the consumption and production decisions of the decide what profit level it should obtain. Given this profit level, the household would solve for its consumption and work problem. In the developing countries as also in Puri district, all markets do not work perfectly and the households are semi-commercialised. Thus, the separability between the production and consumption decisions does not necessarily work.

If the capital markets were functioning smoothly the rate of interest would have been given exogenously. However, in the credit markets of Puri, it is not unrealistic to assume that the rate of interest is household specific. The model assumes that the interest rate depends not just on the amount borrowed but also on the capability of the household to repay the loan and the fixed farm and household characteristics. We assume that the rate of interest charged on the loan is a function of both the amount of loan and initial endowment of productive farm assets. [START_REF] Nagaranjan | Demand for Agricultural Loans: A theoretical and econometric analysis of the Philippine credit market[END_REF] The formal model is explained in an earlier publication of the author [START_REF] Desai | Institutional Finance for Agricultural Development, An Analytical Survey of Critical Issues, Food Policy Review 1, International Food Policy Research Institute[END_REF] . The model implies an implicit demand function for borrowing, given as,

B B K z z p p p w w r h q K * * * ( , , , , , , , , ) = 1 1 2 1 2 (A)
Where B* is the amount borrowed, K 1 is the initial endowment of productive farm assets, z h are household characteristics, z q are fixed farm characteristics, p 1 and p 2 is the price of output in the period 1 and period 2 respectively. The depreciation function is denoted by p k, while w 1 and w 2 represent the market wage rates for period 1 and period 2. Therefore, the amount of

The Interest Rate Function

The supply side is represented by the interest rate function. The rate of interest is the price of credit and is therefore a function of the cost of lending the loan. Three kinds of costs are taken into consideration; the opportunity cost of funds (r O ), the administrative costs of servicing the loan (r A ) and the risk premium to be charged to the borrower (r R ). Therefore, the rate of interest function may be written as:

r f r r r O A R * ( , , ) = (B)
Where r* is the total rate of interest charged. The opportunity cost component of the rate of interest is the lender's unit cost in using the funds for lending rather than putting those funds to alternative use. Furthermore, the administrative cost would be the costs involved in 'servicing' the loan. The 'risk of default' on the loan, is reflected by a combination of the individual characteristics of the household and the nature of project for which the loan is taken. In the data, loans are broadly borrowed for two purposes: production and consumption purposes 6 . For obvious reasons, the risk associated with these two types of loans is different.

A part of the risk premium component of the interest rate function might also be influenced by the amount borrowed as the risk increases with bigger loan amounts.

The formal institutions like commercial banks, co-operatives and government programmes, give credit mostly for productive purposes. Their operating goal is a combination of profit maximisation and developmental assistance. For instance, profit maximisation is the driving Loans from friends and relatives are lent with some social or altruistic benefits in mind. On the other hand traders-merchants, landlords and employers lend to the people that they have interacted with in the labour or goods market. These kinds of loans are generally interlinked with the transaction in the other market and the gains and losses in one, can be adjusted in the other. Professional moneylenders are not much different from the banks in terms of their profit maximisation aims, but they have additional information about their clients due to former interactions, social relations or geographical proximity arising from staying in the same village. This is also true for almost all the informal lending institutions. Therefore, they could be characterised by competition between the lenders with relatively good information about the repayment probabilities. Although, all the three cost components of the interest rate function are active, the risk component will be taken as the one driving the interest rate function.

Multiple Loans

Some sample households in the data reported multiple loans. In the presence of supply constraints from a particular lender, the household tries to satisfy its demand from other

F o r P e e r R e v i e w
sources. As a result multiple loans are observed which may be indicative of the households that were loan size rationed by one lender and forced to fulfil their demand by borrowing from another lender. On the other hand households that borrow just one loan satisfy their entire loan demand from one lender. The treatment of multiple loans in this paper is similar to Nagarajan, Meyer and Hushak (1995). The amount borrowed by the household is the sum of all the loans taken by the household in the reference period. For households with more than one loan, the contract with the highest interest rate is chosen as the marginal contract, and is considered the interest rate charged to the household.

Econometric Framework

Estimating Demand and Supply with a Type 3 Tobit

The econometric framework is based on the theoretical model described in the previous section. In order to deal with the problems of sample selectivity bias and the endogeneity of the rate of interest and the size of the loan, the type 3 Tobit model is used to estimate the demand and supply of credit. The model is specified as follows:

B X r u a r X B u b B B if B if B c r r if B if B d * * * * * * * * * * ( ) ( ) ( ) ( )
= + + = + + = > = > 1 1 2 1 2 3 4 2 0 0 0 0 0 0 (1)
Where { } The econometric analysis starts by estimating the reduced form of the model by Heckman's two-step procedure and then predicting the endogenous explanatory variables using the estimated reduced form. Finally, the structural form is estimated with observed endogenous explanatory variables being replaced by the predicted endogenous explanatory variables and with Heckman's lambda added to each equation. These estimates are consistent but not efficient.

Description of the variables

The theoretical framework suggests that the demand for credit is affected by the interest rate, farm production characteristics, socio-economic characteristics of the households, current and expected output prices and wages. The dependent variable is taken as the total amount borrowed by the household in the reference period. In the case of the multiple loan households, the sum of all the loans is used to indicate the amount of loan demanded by the household.

Net wealth is the proxy for the initial endowment of the household and is calculated as the total wealth less the standing sum of all the loans that have to be repaid by the household in the reference period. 'Wealth' is calculated as the sum of the value of land 10 , house, tractor, water 9 Loan size rationing occurs when the loan amount received by the borrower is smaller than the one they demanded. 10 This is calculated by using the village specific prices on irrigated and unirrigated land. The information on prices prevailing in the village was collected simultaneously during the survey. . 11 In addition, the value of livestock, coconut and fruit trees and brass utensils was also added. 12 The size of the operational holdings and the proportion of irrigated land describe the farm production characteristics. The age of the head of the household, family size, dependency ratio and the primary activity of the household head are the variables used to describe the household's characteristics. The dummy takes the value one if the household's head is engaged in agriculture as a primary activity, and zero otherwise.

Output prices and wages are important variables suggested by the model. In the absence of data on expected output price and wage rate, the future price might be considered as a multiple of the current price. The 'average price of paddy' 13 , which was collected in the village level round of the survey 14 is used as a proxy for the output price. The data on the 'average daily male agricultural wage rate' is used for the wage variable. This would result in interpreting the sum of the coefficient of the current wage as the sum of the effects of both current and expected wages.

The interest rate function has three components, the opportunity costs of the funds, the administrative cost of the loan and the risk premium attached to each loan. Since these are not directly observed in the data, suitable proxies are identified and used. The administration cost might not be that important in this model because we do not distinguish between different lenders here. In addition, it is assumed that the opportunity cost, is the same through Puri for different lenders, due to similar and limited opportunity available in the regional economy for 11 Financial assets, which were mainly in the form of savings for the surveyed households, were not included due to under-reporting resulting in a lot of missing values.

12 In the pilot study the respondents were also asked to report on the value of gold and jewellery that they have. This question was later dropped, as the respondents were reluctant to answer it and became suspicious of the surveyors. This was considered necessary in order to preserve the quality of the data and the trust between the surveyor and the respondent. This trade off resulted in an under-estimation of the value of assets.

13 Paddy is the main crop and a majority of the households engaged in agricultural production produce it. The 'loan demand' is identified by the proportion of irrigated area, agriculture as the primary activity of the head of household, wages and the price of output. Agricultural activity in Puri is substantially dependent on weather, due to the use of traditional methods of cultivation and lack of proper irrigation facilities in the region. The proportion of irrigated land holding17 that a household affects its production capacity. However, this detailed information is not available to the lenders. Similarly, if the head of household has agriculture as his primary activity, the household has a higher production capacity given his experience. The output prices and the wages are factors that influence the household's level of demand for credit through the amount of consumption and leisure that it chooses.

The supply side is identified by distance from the bank, distance from the cooperative and the number of matriculates (level of education) in the households. Proximity to the formal The standard Cragg (1971) Double Hurdle model uses no information, which identifies those who are rationed from those who have no demand. In our survey there are responses to a question, which contribute useful information. The respondents were asked the question, 'did you try to take a loan in the reference period but did not get it?' 18 The households answering 'yes' constitute nearly 47.4 percent of the sample households. Using this information jointly with the data on the loans actually taken, three subgroups of households are identified and defined by the following events and the corresponding probabilities: The households with positive demand and access are empirically identified as the households, who have taken a loan independently of their response to the supplementary survey question (group 1). The group of households with a positive demand and no access to credit consists of 18 Additional information is needed on: whether the household did not borrow because it expected that it would be turned down. In addition, one should also have information on whether the household was loan size rationed.

Nevertheless, in this model we progress with the restricted amount of information available in the data. Land is the most preferred form of collateral by all lenders. Therefore households with larger land ownership would be expected to have a greater access to credit. Similar relationship is expected for the quality of land and the proportion of irrigated area, as they enhance the productive capacity of the farm. The increase in the number of working or earning male members of the household is perceived as favourable and should increase the accessibility of loan for the household. The non-land wealth of the household would also be expected to increase the chances for the household to get a loan.

The access function is identified by the size of land owned, the amount of net non-land wealth and the proportion of the irrigated area. The size of land owned and the amount of net nonland wealth signal the credit worthiness of the household. Whereas the amount of loan demanded and supplied to the household are based on the size of the operational holding. The supply function is identified by the distance from the banks and the education variable. While the demand equation is identified by the wages and the output price. The demand is identified from the supply through the number of male members working or earning in the household.

The banks are officially required to evaluate the loan on the basis of the incremental income expected from the project that is financed. Evaluation studies of some banks show that family labour was not included while making these calculations 19 and therefore this variable should not affect the supply to the formal sector.

19 For instance, refer to UCO Bank (1999), Manager's Handbook, fourth edition.

20 11.26% of the household's lease-in half or less than half of their operational holdings. Whereas 15.32% of the households lease in more than half or all of their operational holdings from others.

Results and Concluding Remarks

Type 3 Tobit Results

The results from the estimation of type 3 Tobit are presented in two tables. Table 2, shows the results from the probit and the reduced form interest rate and loan demand equations. Table 3, gives the results for the structural form of the interest rate and the loan demand equation.

We begin by inspecting the sample selection bias in the data (see Table 3). For the structural form of the interest rate equation the inverse of the Mill's ratio (lambdahat) is significant, thereby indicating the existence of a sample selection bias. The results for the structural form of the loan demand equation however do not show any significant sample selection bias.

Analysing the results from the structural form of the loan demand equation (Table 3), it is observed that the coefficients of interest rate and net wealth are significant. As expected, the demand for loan increases as the rate of interest decreases. Similarly, the increase in the net wealth of the household implies a decrease in the loan demanded, because a household with a higher initial endowment of productive farm assets has the capability to satisfy its needs without borrowing. The amount of loan demanded increases significantly with the size of the operational holding. This is probably due to the increase in the need for working capital for agricultural purposes. The coefficient of the dependency ratio is both positive and significant.

As one would expect, a higher ratio of non-earning members to the earning members implies more expenditure and less income. However, it has been difficult to reconcile this with the result that the increase in the family size actually decreases the demand for loans. One possible explanation could be that increased family size might actually reflect increased number of earning members in the family. The coefficient for the output price is negative and significant, which implies an increase in the income with the increase in the output price, resulting in a decline for the need to borrow.

The primary activity of the household's head is also significant. The variables proportion of irrigated area, as a percentage of the operational holdings, the age of the household's head and the wage rate are insignificant in the structural form of the loan demand equation.

The estimates of structural form of the interest rate equation (Table 3) show that the amount borrowed and the net wealth, both have negative and significant coefficients. A higher level of net wealth of the household implies both a better capacity to repay the loan and/or ability of the household to offer better collateral for the loan. These imply a lower risk to the lender, a lower risk premium charged to the borrower and hence a lower interest rate. The loan amount has a negative coefficient probably because 60.5% of the loans by value come from the formal sector, which lends bigger average size loans (as compared to the informal sector), at a subsidised interest rate.

The coefficient of the operational holding is positive and significant. This might initially seem surprising but if we investigate the share of the leased-in land to the operational holding for each household, it is observed that 25% of the households do actually lease in land. 21 Similarly, 10% of the households actually lease out their land, whereas 5% of the households lease out more than half or all of the land that they own to others. This implies, that the size of operational holdings reflect a substantial number of households that are engaged in cultivation, but do not own a substantial amount of land that they are cultivating. We may recollect here that land is the most acceptable form of collateral. Therefore, the increase in the 21 11.26% of the household's lease-in half or less than half of their operational holdings. Whereas 15.32% of the households lease in more than half or all of their operational holdings from others. 19 interest rate with an increase in the size of the operational holdings is probably due to such households that are charged a higher risk premium by the lender.

The dependency ratio has a positive and significant coefficient. This is expected due to the higher number of dependants implying a higher consumption need of the household and a lower per capita availability of income. The negative coefficient of the distance of the household from the co-operative is also as expected. However, variables like the distance from the bank, education, family size, the age of the head of the household are not significant.

The usefulness of these results depends on the model's ability to replicate observed data. A Chi-square goodness of fit reveals that the simulated distribution and the observed distribution are dissimilar. The type 3 Tobit predicts rather well the loan amount distribution, but less well the interest rate distribution (see Figure 1 and 2). It is not able to replicate the spike at around 13 percent but puts it much close to zero.

The Double Hurdle Results

The amount of land owned is an important factor for accessibility to a loan (see Table 4). This confirms the widely held view in literature that ownership of land is an important factor in deciding whether a household gets a loan or not. However, the effect of nonland wealth23 of the household is not as expected. One reason for this anomaly could be the treatment of the lenders as a homogenous category. As stated before in the paper, the lenders are a diverse mix

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with co-operative societies, development and commercial banks on one hand and professional moneylenders, employers, landowners and friends and relatives on the other. Furthermore, some constituents of the non-land wealth can be very difficult to liquidate for the lender in case of default or by the borrower for repayment of a loan in case of imminent default. 24 The factors affecting the access function are the determinants of the credit worthiness of the household. Whereas those determining the supply are the ones affecting the cost of loan. The creditworthiness of the household in the eyes of the lender is not effected by how far or near he stays though it does affect the transaction cost of the borrower or the lender. Land quality and the size of the operational area are factors that affect the productive capacity of the farm and imply an increase in the income generated. Although it seems that these factors affect credit worthiness positively, many formal and some informal lenders make their judgement of the creditworthiness of households primarily on the basis of the amount of land that they own. This is supported by the fact that the quality of land and the proportion of irrigated area are statistically insignificant.

The supply side results show that the interest rate is not significantly affected by the amount of loan. 25 The net-wealth of the household, the quality of land and education are the factors that significantly affect the interest rate. As expected the net-wealth of the household is inversely related to the interest rate. A richer household implies a lower risk and hence a lower interest rate. Higher quality of land increases the productive capacity of land and its In order to test the importance of the extension of the Type 3 Tobit model to the Double Hurdle, a check was made to test if the two models are nested. Testing for the nesting of the models will therefore require that the = / 1 in equation 2, which would require that the explanatory variables going into the demand and the access equations are the same. However, this is not possible in our case, since the access equation captures the creditworthiness of the borrower in the eyes of the lender and is very different from the decision of the household to take a loan. The models cannot be tested for nesting and are therefore not the same. There remains a need for further research where a clear distinction is made between the formal and informal lender in the credit market.

Concluding Remarks

The estimations from the type 3 Tobit model. 26 and the Double Hurdle model provide a comprehensive view of the demand and supply situation of the credit market. The type 3

Tobit results show that apart from the interest rate the household characteristics like the net wealth owned, family size, dependency ratio and the primary activity of the household's head were important determinants of demand. In addition, the price of output and the area of operational holdings were also significant determinants on the demand side. Furthermore, in the Tobit model net wealth, loan size, operational holding and the dependency ratio were important determinants of the interest rate function. The Double Hurdle model, uses the additional data information on access to confirm the continuing importance of the role played by the amount of land owned, in determining whether the borrower gets the loan or not. If this is true then the landless, the agricultural labourers and the marginal and small farmers may continue to face difficulty to get a loan because of the lack of access to credit. It is precisely this group that the government wants to target, with its subsidised credit programs through the formal institutions. The futility of the current lending policies (for instance, provision of cheap credit) in benefiting the disadvantaged rural households has been well recorded in literature not just for India but also for other countries in Asia, Africa and Latin America.

Recognising that the lending approach, especially by the formal lending institutions is not suitable to the needs of the rural poor, some steps have been taken by the National Bank for Agriculture and Rural Development (NABARD). This involves the promotion of Self Help Groups (SHGs), which is a type of group lending schemes. However, this is only one step in this direction and lending in the rural credit markets need to be made more accessible to the landless and poor households. The asymptotic standard errors are reported in the parentheses; a , b and c represent the significance level at 1, 5 and 10% respectively. 29 Dependent variable takes value 'one' for borrowers and 'zero' for non-borrowers; the probit is estimated using all the exogenous variables affecting the loan demand and supply. 30 The reduced form interest rate and loan demand equations are estimated by the exogenous variables affecting both the demand for and supply of loans. 31 The dependent variable is the aggregate loan size of the household. The estimation is done using the variables that affect the loan demand. 32 The primary activity of the head of household takes value 'one' if the head of the household works as a 'self employed farmer'; it takes value zero otherwise. 33 These are the Daily Male Agricultural Wages, reported village-wise, in the data. 34 Average price of paddy, reported village wise in the data. 35 There are 500 non-borrowers. 36 The asymptotic standard errors are reported in the parentheses; a , b and c represent the significance level at 1, 5 and 10% respectively. The Huber-White standard errors have been used. 37 The structural form of the loan demand equation, when the rate of interest is taken as an endogenous variable.

F
The predicted values of the interest rate, $ r , are used in this regression. 38 The structural form of the interest rate equation, when the loan amount is an endogenous variable, which is predicted by the reduced form rate of interest equation as $ B . 39 The proportion of the irrigated area as a percentage of the operational holding. -8.3995 40 The asymptotic standard errors are reported in the parentheses; a , b and c represent the significance level at 1, 5 and 10% respectively. The Huber-White standard errors have been used. 21 observations were not used because the information was not available to decide whether the household was rationed or not. The above estimation is done using information on 966 households. 41 The proportion of irrigated area as a percentage of the operational holdings.

  and the quality of the borrower. This is in lieu with the semi-commercialised and highly personal atmosphere of the credit markets in developing economies, where the capital markets do not function smoothly.

  implies that the household would first solve its production problem and

  a function of both the exogenous variables in the model and the endogenous rate of interest, r*.

  and co-operatives decreases the administrative and transaction costs for the lenders. The number of matriculates indicates the household members with over 10 to 11 years of formal education. Households that have a high component of human capital constitute relatively lower risk.4.3 Integrating Access Using a Double Hurdle ModelFor a loan to be observed as a market outcome, the borrowing household has to pass two hurdles. It should have a positive demand for credit and access to it. The household's access to the loan and hence its ability to participate in the credit market depends on factors determining how credible the borrowing household is in the eyes of the lender. This decision is distinct from the 'decision of the household on the amount that it decides to borrow', which follows from the utility maximisation exercise of the household. In the Double Hurdle model the lender provides credit to only those households that he finds 'creditworthy' as he is concerned with maximising his profit and minimising his risk of default. The access to a loan is therefore defined as a function of the creditworthiness of the household in the eyes of the lender. However, at a given interest rate there may still be credit rationing because the adjustment of the interest rate to equate the ex ante supply is not the sense in which the rate is endogenous. In estimating the model the information collected in the survey about the respondents having access to the loan has been used. Adding an access function to the reduced form of 1(a) and 1(b) model becomes is the latent variable for loan, r* is the latent interest rate and D* is the latent access variable which reflects whether the household has access to the loan or not.

  Pr (household demands and has access to credit)= Pr[y*>0 and D* >0] Pr (household demands but has no access to credit)= Pr[ y*>0 and D* 0 ] (3) Pr(household did not ask for a loan)= Pr[y* 0]

  the lender are therefore considered to effect access to credit for a household.

  Similarly, a higher education level of the household signifies higher human capital content and increases the ability of the household to generate income. Both education and quality of land are inversely related to the interest rate.The demand side estimates clearly reflect the results of the separation of the 'access' to credit, from the decision of the household on how much to borrow. According to this model the interest rate and the wage rate significantly determine the amount of loan demanded. The signs of these variables are in accordance to theoretical expectations. The increase in wage rate would imply substitution of the household's farm labour by the market labour and would therefore imply a decrease in the household's factor of production and hence a decrease in the amount of credit demanded.

  X 1 is the vector of the exogenous variables affecting the demand for loans and X 2 is the vector of exogenous variables affecting the rate of interest.

	observed interest rate;
	u u 1 , variances 1 2 and 2 2 are the i.i.d drawings from a bivariate normal distribution with zero mean, o r P e e r R e v i 2 , and covariance F e w
	10

12 . B* is the amount of loan demanded and r* is the rate of interest related to the loan demand. B and r are the observed loan amount and the

  using these funds in alternative ways. Therefore, it is the risk premium component that is driving the interest rate function. The cost components of the interest rate function are proxied by the net-wealth, the amount borrowed, the distance from the bank and co-operative society, the size of operational holdings, household characteristics (like family size, the age of household's head and the dependency ratio) and education15 . The dependent variable is the interest rate recorded for the positive borrowings observed in the data. In the presence of multiple loans and heterogeneity in the terms and conditions of the loan contracts, the selection of the 'marginal contract' in this 16 paper is done on the basis of the highest interest rate.

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14

While conducting the household survey, questionnaires were filled simultaneously for village level variables, for each of the sixty-six sample villages

Table 1 . Sample mean and standard deviations of some variables 1 .

 1 Standard deviations are in the parenthesis. Figures for the following variables; village bank, fertiliser, seed and pesticide shop and Notified area council have a few missing values. 2 Some landless households might have leased in land and a part of their operational holding might consist of irrigated land.

	Tables
	Variables & units	All households	Large land-owners 27	owners Small land-	Landless	Borrowers
	Amount borrowed in ref. period per	3,496	9,596	3,440	1,914	6,663
	household (Rs.)	(12,802)	(35,018)	(10,686)	(3,680)	(17,074)
	Interest rate (%)	22.2	15.0	22.6	23.0	22.2
		(19.0)	(11.6)	(19.0)	(21.3)	(19.0)
	Value of security (Rs.)	6,396	19,023	6,997	743	12,189
		(22,276)	(56,376)	(19,729)	(3,088)	(29,593)
	wage rate (Rs. per day) *	31	33	31	32	30
		(8)	(11)	(8)	(7)	(7)
	o r distance from nearest main road (Kms.) *	3.0 (3.5)	4.3 (4.6)	3.1 (3.4)	2.7 (3)	3.1 (3.6)
	distance from bank (Kms.) * distance from credit-co-op society (Kms.) * P e 5.6 (6.6) 4.0 (5.0) household's net wealth (Rs.) 137,261 e (156,067)	9.0 (10.0) 7.0 (9.0) 487,423 (227,681)	5.4 (6.3) 3.7 (4.6) 144,605 (116,909)	5.0 (6.4) 3.5 (4.7) 11,484 (25,072)	5.3 (6.4) 3.4 (4) 128,528 (150,915)
	household's non farm income (Rs.)	r 8,521	17,418	9,195	3,704	6,909
	household's size Age of household's head (yrs.)	(16,471) 8.0 R (4.5) e (20,720) 13.4 (6.7) i 47 49 v (13) (13)	(16,746) 8.0 (4.3) 48 (13)	(12,256) 6.5 (3.3) 46 (13.4)	(13,909) 8.2 (4.9) 48 (13)
	Land owned (hectares per household) household's working members	1.0 (1.0) 5.0 (3.3)	4.2 e (1.3) 8.4 w (5.3)	1.1 (0.7) 5.0 (3.1)	0.0 3.8 (2.1)	1.0 (1.2) 5.0 (3.5)
	proportion of irrigated land as a % of gross operational holding	0.3 (0.5)	0.4 (0.5)	0.4 (0.6)	2 (0.3) 0.2	0.4 (0.6)

1 * Village level data was collected for these variables.

27

Households owning more than 3 hectares of land are defined as large landowners.

Table 2 . The Borrowing decision (Probit) and the reduced form rate of interest and loan demand equations. 28

 2

		Borrowing decision (Probit) 29	Reduced form Interest rate equation 30	Reduced form Loan demand equation 31
			2	3
	Constant	1 .106	56.588 b	-125718.1 c
	Net wealth (Rupees)	(.622) -1.3e-6 a	(23.269) .00001	(64983.61) -.14 b
	Distance from co-operative (kms.)	(4.08 e-7) -.065 a	(.00003) 1.722	(.07) -7061.05 c
	Distance from bank (kms)	(.016) .028 b	(1.252) -.817	(3944.7) 3219.79 c
	Operational Holding (in hectares)	(.012) .014	(.555) 1.218	(1662.33) 3788.56 b
	Proportion of irrigated area as a	(.065) .099	(1.064) -4.933 b	(1660.15) 20677.56 b
	percentage of the operational	(.094)	(2.111)	(8861.03)
	holding Education (no. of matriculates in	.060 b	-2.910 b	8224.03 b
	the household) Family size	(.029) .014	(1.180) -.546 a	(3626.14) 1264.80 c
	Age of the household's head (yrs.)	(.011) .002	(.329) -.0.058	(724.62) 388.12 c
	Dependency ratio	(.003) .408	(.083) -1.449	(180.05) 44224.39 c
	Primary activity of the 32	(.332) .367 a	(8.916) -13.103 c	(26401.01) 34476.44 c
	household's head is agriculture. Wages 33 (Rs.)	(.095) -.059 a	(6.827) 2.177 c	(19399.36) -6775.64 c
	Output price 34 (Rs. per kg)	(.011) .282 a	(1.149) -10.348 c	(3872.55) 30001.90 c
	Lambda hat	(.087)	(5.352) -49.988 c	(16049.08) 183333.7 c
			(29.269)	(99603.87)
	Log likelihood	-618.21
	Chi -square	131.67
	Adjusted R-Square		0.10	0.29
	Root Mean Square Error		18.4	16601
	Observation	987	487 35	487
	28

Table 3 . Structural form of the rate of interest and loan demand equations, with and without the rate of interest and the loan amount as exogenous variables. 36

 3

		Structural form of the loan demand	Structural form of the interest rate
		equation 'r' is endogenous 37	equation 'B' is endogenous 38
	Constant	45449.16 b	12.22 b
	Interest rate	(18464.54) -2187.739 a	(6.59) -
	Amount of loan	(770.94) -	-.0002 b
	Net wealth (Rupees)	-.056 b	(.0001) -.00004 a
	Distance from co-operative	(.027) -	(7.7 e-6) -.610 c
	(kms.)		(.356)
	Distance from bank (kms)	-	.205
	Operational holding (in	5337.39 a	(.214) 2.21 b
	hectares)	(1737.32)	(.985)
	Proportion of irrigated area 39	(4909.91) 6572.971	-
	Education (no. of	-	-.425
	matriculates in the		(.530)
	household) Family size	-542.97 c	-.111
		(283.532)	(.218)
	Age of the household's	133.282	.067
	head (yrs.) Dependency ratio	(67.46) 23316.69 b	(.066) 13.22 b
	Primary activity of the	(11481.76) -9881.665 b	(5.78) -
	household's head is	(3994.947)
	agriculture.
	Wages (Rs.)	691.63	-
	Output price (Rs. per kg)	(439.79) -4633.947 b	-
	Lambda hat	(2084.5) 3996.605	9.82 a
		(8982.324)	(3.64)
	Adjusted R-Square	0.27	0.10
	Root Mean Square Error	16738	18.33

Page 25 of 27 Editorial

	Submitted Manuscript
	F o
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	P e
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	R e
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Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 4 . Estimated Coefficients for the Double Hurdle Model. 40

 4

	Access function
	Intercept	0.8396 a
	Size of land owned (in hectares)	(0.1352) 0.1219 b
	Non land wealth (Rupees)	(0.0727) -0.0252 c
		(0.0156)
	Quality of land	-0.0069
	Proportion of irrigated area 41	(0.1564) 0.1679
		(0.1482)
	No. of male members working or earning	0.0041
	in the household	(0.0328)
	Structural equation	Structural form of the loan demand equation	Structural form of the interest rate equation
	Intercept	1.2953	0.6336 c
	interest rate	(1.3921) -1.9230 c	(0.3351) -
		(1.4241)
	amount of loan	-	0.0018
	Wages (Rs.)	-0.2373 c	(0.2851) -
		(0.1778)
	Output price (Rs. per kg)	-0.0284	-
		(0.1521)
	No. of male members working or earning	0.0141	-
	in the household	(0.0359)
	Operational holding (in hectares)	0.0225	0.0343
	Net wealth (Rupees)	(0.2141) -0.2848	(0.0756) -0.1663 b
	Land Quality	(0.3198) -0.2034	(0.0619) -0.2100 c
		(0.4508)	(0.1402)
	Dependency ratio	0.1856	0.4669
	Education (no. of matriculates in the	(1.3902) -	(0.4678) -0.0638 c
	household)		(0.0467)
	Distance from banks (kms.)	-	-0.0027
	Sigma	2.8427 b	(0.0047) 1.0331 a
	Rho	(1.3418) 0.8744 a	(0.1385)
		(0.2756)
	Log L

Though the formal credit institutions lend primarily for the productive purposes, the informal credit institutions lend for both the consumption and production purposes.

The interest rate function is subject of the discussion in section 3.2.

Reference to author's earlier publication removed for the double anonymous peer review process.

The RBI report of 'A Review of the Agricultural Credit System in India', 1990.

The current interest rate regulations are: For loans below Rs. 25,000 the rate of interest charged is 12% and for loans between Rs. 25,000 and 200,000, the interest rate is 13.5%. For loans over Rs. 200,000, the banks are free to fix their own rates. (Information from the RBI).

Education is proxied by the 'number of matriculates' in the household. Matriculates are individuals who have completed at least 10 years of education but need two or more years to complete their senior school.

The interest rate function shows spikes that are present around 13% rate of interest for loans taken from formal institution.

The proportion of the irrigated land is over the total amount of operational holding (includes the amount of land owned plus (minus) the amount of land leased-in (leased-out).

This definition does not completely capture rationing. Additional information is needed on: whether the household did not borrow because it expected that it would be turned down. In addition, one should also have information on whether the household was loan size rationed. Nevertheless, in this model we progress with the restricted amount of information available in the data.

Major components of non-land wealth include farming equipment, houses or buildings, livestock, fruits or coconut trees, brass utensils.

For example, banks and co-operatives have no use for small houses or huts. It is also difficult to sell these houses as the rural areas have close personal bonding and most of the people in the area know each other. People will generally not buy the house because it might be uncomfortable to live there when you know that the acquaintances that you displace might not have any other place to stay.

This is not surprising since the interest rates are administered by the commercial and the development banks.In addition, a large number of loans (more than 17 per cent in the sample) are taken from friends and relatives.

The diagnostics of the Double Hurdle model does not necessarily reveal better results than the type 3 Tobit model, which is probably a result of the rather strong assumptions of the model.

, O17 -Formal, Informal Sectors; Shadow Economy, etc. < O1 -Economic Development < O -Economic Development, Technological Change, and Growth, C51 -Model Construction and Estimation < C5 -Econometric Modeling < C -Mathematical and Quantitative Methods, G20 -General < G2 -Financial Institutions and Services < G -Financial Economics

those who have answered yes to the survey questions and have not taken any loan (group 2).

Finally, the group of households that did not ask for the loan was empirically identified as those households, which took no loans and responded negative to the survey question (group 3). The log likelihood of the model is therefore given by,

Where is the normal bivariate pdf, is the cdf and y 1 , y 2 and y 3 are dummy variables taking the value one when an observation belongs to groups 1, 2 or 3 respectively. Following Cragg (1971) to improve identification, D 1 and D 2 were assumed to equal zero. The third term of the likelihood expression (equation 4) then becomes the product of the two marginal distributions. Subject to the conventional identifying restrictions there is a corresponding likelihood expression for the structural model. The structural parameters were estimated by maximising this function. A potential weakness of this model is that the implicit assumption that all households with non-zero demand tried to get a loan. Some of those might have responded "no" to the survey question might have anticipated that they would have got no for an answer even if they tried for a loan and thus never attempted to get one.

The factors effecting access of households to credit are the amount of land owned, the nonland wealth of the household, the quality of land, the proportion of irrigated area as a percentage of the operational holding and the number of males working and earning. The credit worthiness of the household depends on the lender's perception about the household's capacity to repay. The factors that affect the capability of the household to repay and are


A Structural Bayesian VAR for Model-Based Fan Charts

Keywords: Inflation, Forecasts, Uncertainty JEL Classification: C32, C53, E47, E52 Inflation, Forecasts, Uncertainty

HAL is

Introduction

Inflation forecasts, and the uncertainty surrounding them, are of interest to a large number of economic agents, not least because unexpected inflation redistributes wealth between borrowers and lenders and affects profits when prices are not completely flexible. Estimates of inflation forecast uncertainty which receive most attention in economies for which they are published are so-called inflation fan charts produced by inflation-targeting central banks, such as the Bank of England and Sveriges Riksbank.

The present methods used to generate such inflation fan charts have, however, been criticised recently by a number of authors, among them [START_REF] Leeper | An Inflation Reports Report[END_REF] and [START_REF] Clements | Evaluating the Bank of England Density Forecasts of Inflation[END_REF], and the criticisms are several. The Bank of England's inflation fan charts express the subjective probability distribution for inflation held by the Monetary Policy Committee.

However, there appear to be several layers of informal judgement included in the analysis and the procedure by which the analysis is conducted is unclear, leading some to question the statistical foundation of this method. Similarly, Sveriges Riksbank's fan charts are built on a shaky foundation whose main shortcoming is that no mechanism exists to guarantee internal consistency. For example, the method exhibits the peculiar feature that both inflation and the factors determining it can always be more (or less) uncertain than usual. Given these shortcomings, there is value in aiming to develop fan chart methods that are less ad hoc and better grounded in statistical theory. [START_REF] Cogley | Bayesian Fan Charts for U.K. Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System[END_REF] made a substantive contribution to improving fan chart methodology by employing a reduced-form Bayesian VAR with parameter drift to generate fan charts for U.K. inflation. This paper extends previous work by generating fan charts for a number of macroeconomic variables from a structural VAR estimated with Bayesian methods. The fan charts, which are given by the posterior predictive density from the model, are thereby generated in a model-consistent manner with a solid foundation in statistical theory.

Compared to [START_REF] Cogley | Bayesian Fan Charts for U.K. Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System[END_REF], we take the analysis forward in two directions; first and foremost, the model used to conduct the analysis in this paper is a structural VAR. This allows structural interpretation of the shocks in the system, extending the use of the model from forecasting and fan charts to policy analysis. Second, the model is set in a small open economy, thereby addressing issues that a country such as Sweden faces. Overall, the suggested framework means that forecasting and policy analysis are brought closer together and fan charts integrated into the framework. As such, this paper is related to other parts of the central banking literature in which fan charts are addressed in a model-consistent way; see for example [START_REF] Svensson | Monetary Policy with Model Uncertainty: Distribution Forecast Targeting[END_REF].

The paper is organised as follows: Section two presents a structural VAR for the Swedish economy. Section three outlines the estimation of the model and the properties of the estimated model, such as impulse response functions and out-of-sample point forecasting ability. Section four presents the fan charts generated by the model, relates the inflation fan chart to the present method used by Sveriges Riksbank and addresses potential shortcomings. Finally, Section five concludes.

A structural VAR for the Swedish economy

Structural VAR models have become increasingly popular over the last two decades and are nowadays standard tools for economic analysis. Whilst these models can be specified and estimated in many different ways, the common feature of these models is that a number of identifying assumptions are made in order to be able to make statements regarding a number of structural shocks in the economy. The issue of identification has been dealt with in different ways in the literature; for a range of alternative approaches, see for example [START_REF] Sims | Macroeconomics and Reality[END_REF], [START_REF] Bernanke | Alternative Explanations of the Money-Income Correlation[END_REF], [START_REF] Shapiro | Sources of Business Cycle Fluctuations[END_REF], [START_REF] Blanchard | The Dynamic Effects of Aggregate Demand and Supply Disturbances[END_REF], [START_REF] Crowder | A Cointegrated Structural VAR of the Canadian Economy[END_REF], [START_REF] Groen | Corporate Credit, Stock Price Inflation and Economic Fluctuations[END_REF] and [START_REF] Uhlig | What are the Effects of Monetary Policy on Output? Results from an Agnostic Identification Procecure[END_REF].

The structural model that will be used in this paper belongs to the family of K-models, using the terminology of [START_REF] Amisano | Topics in Structural VAR Econometrics[END_REF]. This means that restrictions are put on the coefficients of contemporaneous variables in particular structural equations.1 Turning to the specification of the model that we aim to estimate in more detail, it is given by ( )

t t t L ! " D µ x G + + = , (1)
where ( )

=

, we use the expression

( ) = 1 0 1 0 G G + (3)
to recover 0 G . In order to achieve identification, we must impose at least ( ) 2 1 n n restrictions on the system; these restrictions are given in the 0 G matrix and will be discussed in more detail below.

In order to further present the structural model, we first need to introduce the variables included in the system. Nine endogenous variables are modelled in the VAR. We define All variables except interest rates and the real exchange rate have been seasonally adjusted.

As we want the variables in the system to be stationary, we have taken the first difference of wages and foreign and Swedish GDP. The stationarity of the variables has been investigated using the Augmented Dickey-Fuller test [START_REF] Said | Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order[END_REF] and the results are presented in Table A1 in Appendix A. Clearly, not all of the variables which have been modelled in levels in the system are judged stationary by the unit root tests. We nevertheless choose to model these variables in levels based on theoretical arguments and previous empirical findings; see for example Österholm (2004). 3We have now presented the model's general form and the variables included. It should be noted that compared to previous work in this field, the model employed in this paper introduces both structure and a high dimension in the system. However, this adds a layer of complication relative to the analysis in for example [START_REF] Cogley | Bayesian Fan Charts for U.K. Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System[END_REF] where a three variable reduced form VAR was used. We therefore have to trade off something else in order to make estimation possible. As can be seen from equation (1), we choose to estimate the model using constant parameters over time. Given the problems of identifying drifting parameters in general, we consider it reasonable to leave this outside the model. In particular, since the number of parameters grows extremely fast with the dimension of the system we believe that this is a relevant trade off, despite the fact that parameter drift employed by [START_REF] Cogley | Bayesian Fan Charts for U.K. Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System[END_REF] is an appealing feature of a model. 4Turning to the identification of the model, it is most easily presented by the relation

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (4)
The chosen system could be described as an open economy model inspired by the model used by [START_REF] Blanchard | A Traditional Interpretation of Macroeconomic Fluctuations[END_REF] in a study on U.S. data. To Blanchard's model have three equations for the foreign economy and a real exchange rate equation been added. In specific, equations one to three give -in a highly reduced form -aggregate demand, Phillips curve and monetary policy reaction function for the foreign economy. The fifth equation in the system represents Swedish aggregate demand whereas equations four, six and seven describe the supply side of the Swedish economy in greater detail; these represent Okun's law, a wage setting equation and a price setting equation respectively. Equation eight represents a monetary policy reaction function and, finally, equation nine an "arbitrage condition" for the real exchange rate. 5In accordance with the above presented system, nine structural shocks are identified. Three of these are for the foreign economy, namely a foreign aggregate demand shock ( f d ), a foreign cost-push shock ( f c ) and a foreign monetary policy shock ( f ir ). For the Swedish economy, we identify an aggregate supply shock ( ), an aggregate demand shock ( d ), a wage setting shock ( ws ), a price setting shock ( ps ), a monetary policy shock and, finally, a real exchange rate shock ( q ). 6

Estimation and results

Quarterly data on the variables ranging from 1980Q2 to 2004Q4 were supplied by Sveriges Riksbank. Apart from the variables in t

x -which were defined above -we let t D be a dummy variable which takes on the value 1 between 1980Q1 and 1992Q4 and 0 otherwise. 7 Lag length in the model was set to 4 = p .

The model is estimated using Bayesian methods and priors on dynamics in the model follow the standard modelling approach, as they take their starting point in a Minnesota prior. 8 A minor modification is, however, introduced regarding the dynamics as block exogeneity of the foreign economy not is enforced in the model with probability one; instead, the exogeneity restriction is controlled using an additional hyperparameter. 9 Priors on the constant term, the dummy variable and 0 G all follow those in [START_REF] Villani | Monetary Policy Analysis in a Small Open Economy Using Bayesian Cointegrated Structural VARs[END_REF] with diffuse normal priors. 10

The numerical evaluation of the posterior distributions is conducted using the Gibbs sampler; see for example [START_REF] Tierny | Markov Chains for Exploring Posterior Distributions[END_REF]. Convergence of the chain appears to be fast and reliable, an issue which has been confirmed using CUSUM plots. 11 Given this, the burn-in sample is set to only 2 000 draws and the analysis is then performed on the 20 000 draws following these. As is well-known, the chain is serially dependent but there has been no thinning of it. Whilst 6 Most of the shocks are standard and straight forward to interpret. Regarding the shocks that could be less obvious to interpretate, the aggregate supply shock corresponds to changes in productivity and/or labour supply, the wage setting shock could for instance reflect changes in bargaining power on the labour market and the price setting shock can correspond to higher input prices or changes in mark-ups. 7 This might seem like an overly simplistic way to model the regime shift in Swedish monetary policy which occurred in the early 1990s. However, it appears to have worked well when used previously in the literature; see for example [START_REF] Jacobson | Monetary Policy Analysis and Inflation Targeting in a Small Open Economy: A VAR Approach[END_REF] and [START_REF] Villani | Monetary Policy Analysis in a Small Open Economy Using Bayesian Cointegrated Structural VARs[END_REF]. Moreover, since several of the countries that have large weights in the TCW index also experienced policy changes around the same period -for example Germany, Norway and the U.K. -we also let the dummy variable affect the foreign economy. Changing this assumption, thereby letting the dummy affect the Swedish economy alone, has negligible effects on the results. 8 See for example [START_REF] Litterman | Forecasting with Bayesian Vector Autoregressions -Five Years of Experience[END_REF] and Robertson and Tallman (1999). 9 See for example [START_REF] Villani | Monetary Policy Analysis in a Small Open Economy Using Bayesian Cointegrated Structural VARs[END_REF]. 10 As the model is invariant to sign switches in the equations in 0 G -see for example Sims and Zha (1999) - we must also employ some kind of normalisation to the system. In this paper we employ the [START_REF] Waggoner | Likelihood Preserving Normalization in Multiple Equation Models[END_REF] normalisation which has been shown to have good properties both theoretically and empirically. 11 Results not reported but available upon request. this could be done in order to increase efficiency, it is largely a matter of taste since at convergence the draws are identically distributed according to the posterior distribution; see for example Gelman et al. (2004). Based on this sampling we can conduct simulation-based inference for a range of functions from the model. This will next be the focus of our attention.

Impulse response functions

Whilst the purpose of the model primarily is to generate a model-based fan chart for inflation, it is initially of interest to establish whether the properties of the model are in line with our expectations based on economic theory. One important feature of this analysis is to investigate the properties of the impulse response functions from the model. In a model where monetary policy analysis is the primary objective, the effects of a domestic monetary policy shock are obviously of particular interest. This section will therefore focus on responses to this shock. Figure 1 presents the impulse response functions of a Swedish monetary policy shock to the variables of the system. Initially, we can note that the foreign economy is block exogenous in practice in line with our expectations; all effects of the Swedish shocks on the foreign economy are zero. Regarding the effects on Swedish variables, we can see that unemployment rises and GDP growth falls as one would expect.

The significance of the latter effect may be discussed though, as could the effect on wage growth which is a touch anomalous with the point estimate indicating an increase initially.

We can note that the cumulative effect of the median impulse response is correct though. This gives us the sum as the horizon goes to infinity and provides the effect of a permanent change to the interest rate. Turning to inflation we find what appears to be a traditional price puzzle -see for example [START_REF] Sims | Interpreting the Macroeconomic Time Series Facts: The Effects of Monetary Policy[END_REF] and [START_REF] Creel | The 'Price Puzzle' Once More[END_REF] -since inflation rises significantly before it falls. However, this is partly due to the fact that CPI is being used as the price measure. The way the CPI is constructed, there is a mechanical explanation to a part of this effect as housing expenses directly depend on the interest rates. This is confirmed by using exactly the same model except for the price measure. Apart from the price puzzle, many structural VAR models tend to suffer from what is known as an exchange rate puzzle; see for example [START_REF] Grilli | Liquidity Models in Open Economies: Theory and Empirical Evidence[END_REF]. The present model shows no sign of such a puzzle as the exchange rate significantly appreciates on impact when a monetary policy shock hits the system.

To further investigate the open economy aspects of the model, we also look at the response of a real exchange rate shock to the system. This is given in Figure 2 and as we can see the effects are all in line with our expectations. As before, there is no effect on the foreign economy but for the domestic variables we can see that unemployment decreases, whereas GDP growth, wage growth, CPI inflation and the interest rate all rise. Clearly, all of these effects are in line with a traditional exchange rate channel. Summing up the effects of monetary policy and real exchange rate shocks, we find that the model generates impulse responses that largely are in line with expectations. As the model seems reasonably wellbehaved, we think that the model seems fit for policy analysis.

Point forecasts

Given that we think that the model has sensible properties in terms of its impulse response functions, our next step is to evaluate its forecasting ability. A reasonable performance with respect to the out-of-sample point forecast accuracy seems like a relevant requirement for the model to be taken seriously. The model's forecasts at horizons one, four and eight quarters for the key variables a t y , cpi t and t i are evaluated using rolling out-of-sample forecasts. 12

The out-of-sample forecasts are generated beginning in 2000Q1; the last forecasts being evaluated are based on the model estimated on data including 2004Q3. This implies that there will be seven (three) more forecasts to evaluate at the one-quarter horizon than at the eight-quarter (four-quarter) horizon. y is the growth rate in Swedish GDP over the last four quarters. As the VAR is specified in first and not fourth differences for Swedish GDP, the forecasts are therefore first summed up to fourth differences and then evaluated. The criterion used for evaluation is the root mean square error (RMSE) and results from this exercise are presented in Table 1. RMSEs for the VAR are given in column three of the table and RMSEs for a naïve forecast -which is optimal if the process being forecasted is a univariate random walk -are given in column four. For further comparison are the RMSEs based on Sveriges Riksbank's official forecasts in the Inflation Report shown in column five.

Strictly speaking, the RMSEs from Sveriges Riksbank's forecasts are not completely comparable to the other forecasts for several reasons. First, the inflation forecasts from the VAR are evaluated against actual inflation numbers based a seasonally adjusted CPI series. Sveriges Riksbank's inflation forecasts on the other hand are evaluated against actual inflation numbers based on the original CPI series. Second, it should be noted that despite the fact that equally many forecast errors are recorded at all horizons for all models, there is a small difference in the information set used. In particular, even though the difference generally is small, the timing of the forecasts in the Inflation Reports of Sveriges Riksbank does not perfectly correspond to the timing of the VAR and naïve forecasts. 13 Finally, Sveriges Riksbank did under the period analysed rely the assumption that the repo rate would remain constant during the forecast horizon. Such an assumption could clearly lead to suboptimal forecasts and would make us argue that better forecasts should have been generated without this assumption. However, whether this assumption has been properly used in practice has recently been questioned by for example [START_REF] Faust | Is Inflation Targeting Best Practice Monetary Policy?[END_REF] and [START_REF] Faust | Forecasts and Inflation Reports: An Evaluation[END_REF]. There is evidence that the assumption of a constant repo rate has not been used consistently and the forecasts of Sveriges Riksbank might therefore have less of a disadvantage in practice than in theory. However, despite the potential advantages and disadvantages that the forecasts of Sveriges Riksbank may have had relative to those from the VAR, we think that they still can provide at least a reference point for a comparison.

Looking at the results in Table 1, we find that they are not overly flattering for the VAR when evaluating the forecasts performance for a t y and t i . The VAR is actually outperformed by the naïve forecast at all horizons. For cpi t though, it appears that the VAR is doing reasonably well as its RMSEs are smaller than, or equal to, those of the naïve forecast. 13 The fact that Sveriges Riksbank also has to use real-time data -whereas the VAR relies on ex post data in the out-of-sample forecast exercise -is a related issue. For a discussion regarding issues on real-time data, see for example Croshoure and Stark (2002) and [START_REF] Orphanides | The Unreliability of Output-Gap Estimates in Real Time[END_REF]. Comparing the forecasts from the VAR to those of Sveriges Riksbank, it can be seen that the VAR outperforms Sveriges Riksbank at the eight quarter horizon but not at the two shorter horizons. A potential explanation for the good performance of Sveriges Riksbank's forecasts at the shorter horizons could be the use of judgement -a feature that the VAR lacks. Numerous forecasters argue that judgement should be included in the forecasting process as it typically is assumed to improve forecasts, in particular at the short horizons. 14

The differences are not large at any horizon though and should therefore not be overinterpreted. Rather, it seems promising that the VAR's inflation forecasts are approximately as good those of Sveriges Riksbank.

Whilst the out-of-sample forecast exercise here is reasonably short, the results regarding GDP growth and the interest rate indicate that there might be some minor problems with the VAR's forecasts. One potential problem which is common for both VARs and univariate processes is that they occasionally tend to converge to the "wrong" level. The forecasts will converge to the estimated unconditional means of the process and these are a function of the estimated parameters in µ , ( )

L G
and " . If the estimates of these parameters are "unfavourable", the estimated unconditional means can be far from what we expect it to be. For instance, we would expect the forecast of cpi t to level out at two percent since this is the target of Sveriges Riksbank.

One way to incorporate information about the unconditional means of the variables in the system is to use the framework in [START_REF] Villani | Inference in Vector Autoregressive Models with an Informative Prior on the Steady State[END_REF]. This recently developed method relies on estimation of a Bayesian VAR in mean-adjusted form and we accordingly specify the model as

( )( ) t t t L ! 7D 8 x G = (5)
which allows us to put informative normal priors on the unconditional means; see [START_REF] Villani | Inference in Vector Autoregressive Models with an Informative Prior on the Steady State[END_REF] for details. 15 Working in this mean-adjusted form and adding informative priors on the unconditional means -but keeping the model unchanged otherwise, including 14 For a discussion on this issue, see for example [START_REF] Lawrence | The Accuracy of Combining Judgemental and Statistical Forecasts[END_REF] and [START_REF] Mcnees | The Role of Judgment in Macroeconomic Forecasting Accuracy[END_REF] and [START_REF] Svensson | Monetary Policy with Judgement: Forecast Targeting[END_REF]. 15 For the model in equation ( 5) the unconditional means for the periods 1980Q2 to 1992Q4 and 1993Q1 to 2004Q4 are given by 7 8 + and 8 respectively. identification -we get the RMSEs in column six of Table 1. It can be seen that the VAR's forecasting ability generally improves and it tends to outperform the naïve forecast when it comes to cpi t and a t y . Regarding cpi t , we also see that the mean-adjusted VAR largely is on par with Sveriges Riksbank's forecasts. However, for t i it is still the case that the naïve forecast is better than that of the VAR. Given the slow mean reversion of the variables considered though, we know that the naïve forecast tends to be difficult to beat and therefore think that the above results favour the viewpoint that the model's forecasting ability is quite acceptable. 16

The inflation fan chart

Typically, the focus when it comes to forecasting has been on the point estimate from a particular model. Whilst we think that this is an important feature of any model that want to be taken seriously, this paper is mainly concerned with describing forecast uncertainty and thereby the distribution of forecasts.

The distribution of forecasts from the VAR model is generated in a simple way. For every draw from the posterior distribution, a sequence of shocks are drawn and used to generate future data. Based on this routine, we get as many paths for each variable as we have iterations in the Gibbs sampling algorithm. For each variable in the system, we can plot chosen percentiles from the marginalised distributions. We thereby get model generated fan charts which take both shock and parameter uncertainty into account in a straight forward way. Clearly, numerical analysis is not necessary in many models to achieve this. However, it offers a convenient approach since it basically always can be conducted.

The posterior predictive density gives us fan charts -not only for inflation, even though this is our main interest in this paper -but for all variables in the model. Figure 3 presents the fan charts generated by the model under investigation in this paper. 17 The median forecast (black line) is given together with 50 and 90 prediction intervals in order to be able to compare the inflation forecasts from the model with those presented in Sveriges Riksbank's Inflation 16 Persistence estimates for the different time series are given in Table A2 in Appendix B. Note though that a t y is more persistent than t y due to the overlapping nature of the former series. 17 Note that for variables specified in first differences, the numbers in Figure 3 all refer to growth rates over the last four quarters. As was the case for Swedish GDP in the out-of-sample forecast evaluation above, the forecasts are therefore summed up to fourth differences. Report. As can be seen from the figure, the model predicts that inflation will rise slowly during the forecast horizon and -judging by the median forecast -approach the target level of two percent by early 2008. Turning to the issue of forecast uncertainty though, we find that the inflation forecast is associated with a considerable amount of this. As a reference between the present modelwhich builds on a weighting of split-normal distributions [START_REF] Blix | Uncertainty Bands for Inflation Forecasts[END_REF] But does the method presently used by Sveriges Riksbank underestimate inflation forecast uncertainty or does the VAR overestimate it?

The most likely answer to this question is that the truth lies somewhere in between. Critique against the present method has been put forward in for example [START_REF] Leeper | An Inflation Reports Report[END_REF] where it is indicated that there might be systematic problems with it. One problem is that in the weighting of the split-normal distributions, the weights are taken as given. This implies that parameter uncertainty largely is ignored in the model, which clearly is a shortcoming. The consequence of this omitted parameter uncertainty is an underestimation of the forecast variance. However, it is highly unlikely that this fact alone can explain the discrepancy between the two models. Another potential reason why the method presently used by Sveriges Riksbank generates a narrower inflation fan chart is simply that the shock variance to inflation and/or its determinants could be underestimated. A potential problem with the VAR on the other hand is that shock uncertainty might be overestimated. If the high level of inflation in the 1980s also was associated with a large variance, averaging over these regimes could clearly generate too wide prediction intervals. To settle this issue an evaluation in which one evaluates the forecast densities is needed. This is, however, difficult to perform in practice since the number observations for such an analysis would be too small to be meaningful and therefore beyond the scope of this paper. 18 To sum up the discussion regarding the fan charts, it should be clear that even though the framework suggested in this paper has potential shortcomings -which could be due to the choice of using constant parameters over time -it still has several advantages over the methodologies presently used by the Bank of England and Sveriges Riksbank. First, we would like to argue that accounting for both shock and parameter uncertainty is an appealing feature of the method. Second, the usage of a structural VAR gives a general equilibrium perspective to the analysis. This should be compared to the present method employed by Sveriges Riksbank which is fundamentally partial in its analysis and thereby highly likely to be plagued by inconsistencies. Finally, we would like to point out the benefits of the joint predictive density for all the variables in the system generated in this framework. Faced with the joint predictive density it is easy to study joint probability questions of the type investigated by [START_REF] Leeper | A Theory of Modest Policy Interventions[END_REF]. Knowing for example what the probability of inflation above target and negative output growth at a particular horizon is should clearly be of interest to policy makers. This kind of analysis is excruciatingly difficult -or even impossible -in the frameworks presently used at the Bank of England or Sveriges Riksbank.

The fact that it is readily conducted in the framework suggested in this paper must therefore be seen as another major benefit of the method.

Conclusions

This paper has presented a structural Bayesian VAR for the Swedish economy with several appealing features. Fan charts can be generated in a straightforward manner for variables in the system, with a particular focus here upon inflation. the model can be employed for both forecasting and policy analysis. Whilst the latter has not been the focus of attention in this paper, it represents an advantage over analyses conducted with reduced-form VARs, such as that of [START_REF] Cogley | Bayesian Fan Charts for U.K. Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System[END_REF].

The analysis in this paper has all been carried out under the assumption that we rely solely upon the model's unconditional forecast. The framework, however, can be extended to allow variables to be conditioned upon, for instance in order to incorporate external information, take into account early data releases or evaluate how likely a certain scenario is given the history of data. 19 Evaluation exercises related to forecast densities, such as those in Adolfson x is the transformation of the variable appearing in Table A2 and t D is a dummy variable which takes on the value 1 between 1980Q1 and 1992Q4 and 0 otherwise. Lag length in the regressions is based on the Augmented Dickey-Fuller test and accordingly set to p when p-1 lagged differences were selected for the Augmented Dickey-Fuller test.

Following [START_REF] Murray | The Purchasing Power Parity Puzzle is Worse than You Think[END_REF], the half-life of a shock to a series is then calculated as

Figure 1 .

 1 Figure1. Impulse response functions of variables in the system with respect to Swedish monetary policy shock.

  If we instead turn to the UND1X index -which excludes this mechanical effect as the interest rate component has been removed from CPI -there is no significant price puzzle in the model anymore. The impulse response functions for the alternative model are shown in Figure A1 in Appendix C.

Figure 2 .

 2 Figure 2. Impulse response functions of variables in the system with respect to Swedish real exchange rate shock.

Figure 3 .

 3 Figure 3. Fan charts for variables in the system.

  -and the structural Bayesian VAR used in this paper, Figure 4 presents the inflation fan chart generated by Sveriges Riksbank in its Inflation Report 2005:1. It is obvious from Figures 3and 4that the VAR generates a wider inflation fan chart than the present method used by It should be noted though that, unlike the VAR used in this paper, the method used by Sveriges Riksbank allows for time-varying forecast uncertainty. To ensure that the fan chart presented in Figure4was not a particularly narrow (or wide) fan chart, we also investigated the width of the inflation fan charts in the other Inflation Reports. This showed us that the fan chart in Figure4is reasonably representative.

Figure 4 .

 4 Figure 4. Sveriges Riksbank's fan chart for inflation in Inflation Report 2005:1.

  et al.(2005) and[START_REF] Cogley | Bayesian Fan Charts for U.K. Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System[END_REF], are accordingly readily conducted within this framework. Given the flexibility of the methodology and its strong statistical foundations, it represents a potential improvement compared to methods currently used by Sveriges Riksbank and the Bank of England to generate fan charts.

Figure A1 .

 A1 Figure A1. Impulse response functions of variables in the system with respect to Swedish monetary policy shock.

Table 1 .

 1 RMSEs from out-of-sample forecast exercise.

	Variable	Horizon in quarters	VAR	Naïve	Riksbank VAR -mean adjusted
		cpi t	1	0.549	0.549	0.501	0.518
			4	1.221	1.246	0.939	0.690
			8	1.165	1.503	1.241	1.454
	y	a t	1	0.678	0.379	-	0.493
			4	2.804	1.972	-	1.810
			8	2.356	1.669	-	1.484
	t i		1	0.519	0.264	-	0.379
			4	1.604	0.746	-	1.972
			8	2.612	1.294	-	1.669
	12	a
		t

  The proposed framework serves as a formal and model-consistent methodology in contrast to methods presently used to generate fan charts at the Bank of England and Sveriges Riksbank. Another appealing feature is that

	F o r
	P
	e
	e r
	R e v
	i e
	w
	18

18

See for example

[START_REF] Diebold | Evaluating Density Forecasts with Application to Financial Risk Management[END_REF]

and

[START_REF] Diebold | Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters[END_REF]

for a discussion on how to evaluate density forecasts.

Table A2 .

 A2 Persistence measures for the individual time series.Persistence is measured as the sum of the AR coefficients from univariate regressions of the

																				Equation (A1)	Equation (A2)
															Persistence		Half-life in	Persistence	Half-life in
																						quarters	quarters
				y	t	f											0.458		1	0.456	1
				cpi t	,	f									0.947		13	0.904	7
	i	t	f													0.924		9	0.793	3
	t u													0.983		41	0.970	23
				y	t												0.449		1	0.448	1
				t w											0.338		1	0.178	0
				cpi t											0.948		13	0.860	5
	i	t															0.995		144	0.807	3
	q	t													0.945		12	0.854	4
	type
	x	t	=	+	1	x	t	1	+	K	+	p	x	t	p	+	t	(A1)
	and
	x	t	=	+	1	x	t	1	+	K	+	p	x	t	p	+	t D	+	t	.	(A2)

t

Studies using K-models include[START_REF] Bernanke | Alternative Explanations of the Money-Income Correlation[END_REF],[START_REF] Kim | Exchange Rate Anomalies in the Industrial Countries: A Solution with a Structural VAR Approach[END_REF],[START_REF] Camarero | Monetary Transmission in Spain: A Structural Cointegrated VAR Approach[END_REF] and[START_REF] Villani | Monetary Policy Analysis in a Small Open Economy Using Bayesian Cointegrated Structural VARs[END_REF].

We are also well aware of the low power of Dickey-Fuller type tests when the investigated series have roots close to -but less than -unity or when they are subject to structural breaks; see for example[START_REF] Froot | Perspectives on PPP and Long-Run Real Exchange Rates[END_REF] and[START_REF] Perron | The Great Crash, the Oil Price Shock and the Unit Root Hypothesis[END_REF].

Not allowing for time-varying parameters in the model implies -apart from the fact that the model could be mis-specified -that one potential source of uncertainty has been left out. This could clearly affect the fan charts from the model. As pointed out by[START_REF] Cogley | Bayesian Fan Charts for U.K. Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System[END_REF] though, constant parameters are a reasonable assumption from a forecasting point of view as long as the forecasting horizon is short -the reason for this being that parameter drift typically is very small. Support for usage of constant parameters can also be found in[START_REF] Doan | Forecasting and Conditional Projection Using Realistic Prior Distributions[END_REF] who argue that the improvement in forecast performance from using time-varying parameters typically is very small.

Note that both the foreign central bank and the Riksbank are assumed unable to react to innovations in GDP contemporaneously. This is justified by the substantial publication lag in GDP numbers; see for example[START_REF] Leeper | What Does Monetary Policy Do?[END_REF].

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Acknowledgements

I am grateful to Meredith Beechey, Per Jansson, Eric Leeper, Lars Svensson, Mattias Villani, Anders Vredin, seminar participants at Sveriges Riksbank and an anonymous referee for valuable comments and to Mattias Villani for providing Matlab code. A special thanks to Jack Lucchetti for clarifying instructions regarding the issue of identification. Financial support from Jan Wallander's and Tom Hedelius' foundation is gratefully acknowledged.

Appendix A -Unit root tests