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Name of Journal: Journal of Policy Models

Article Title: A FORECASTING AND POLICY SIMULATION ORIENTED SMALL MACRO-MODEL FOR THE INDIAN ECONOMY

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Name of first author as on manuscript: Balwant Singh

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A FORECASTING AND POLICY SIMULATION ORIENTED SMALL MACRO-MODEL FOR THE INDIAN ECONOMY

Balwant Singh*

Abstract: The design of macro-models for the purposes of derivation of macroeconomic stabilization policies and obtaining forecasts is an important area of theoretical and empirical economic research. This is because such a stance presents an ideal blend of skillfully interweaving the essential theoretical ingredients of the contemporary macroeconomic paradigms with specific structural features of the country under reference. The use of macro-models enables the policy makers to build alternative policy evidences and thus this approach proves to be far superior to the alternative approaches based on intuitive or judgmental criteria. It is against this background that a macro-model for the Indian economy is estimated in an error-correction framework. Based on it, some policy simulation experiments are conducted. ECM and Time Varying Parameter based forecasts are obtained for inflation and growth for the Indian economy for the year 2003-04.

Key words: Macro-model; error-correction mechanism; policy simulations; time varying parameters.

JEL classification: C300; E 600.

Introduction There have been a wide range of changes in the design and implementation of the

macroeconomic policy in India in line with the economic reform process initiated since

the early 90s. The government has substantially deregulated private investment, eased

restrictions on the inflow of foreign capital, divested a part in the ownership of the

public sector enterprises and reduced custom and excise duties. The Bank rate has

been re-activated as a major monetary policy instrument. These shifts in the macro-

economic policy framework are likely to cause changes in the macro-economic

* Adviser in the Department of Statistical Analysis and Computer Services, Reserve Bank of India. This research work was conducted at the Centre for Central Bank Studies (CCBS), Bank of England, London, from June 9 to August 29, 2003, as a follow-up of the research workshop on ‘ Forecasting in Central Banks’ held at CCBS from June 2 to 6, 2003. I am highly grateful to Paul Robinson, Adviser, Monetary Policy, CCBS, for his advice and comments for the preparation of this paper. Errors and omissions if any is the sole responsibility of mine. Views expressed in this paper are purely my personal and are not reflections of the Reserve Bank of India.

This research work is dedicated to the memories of (late) Prof. M.J.Manohar Rao (architect of the applications of control method in India) my teacher, guide, and friend who always ‘ushered’ me through the difficult moments of my life.

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linkages. Thus, in order to design appropriate stabilisation policies, these changes

need to be evaluated using macro-economic system of the Indian economy.

With this backdrop, this paper attempts to develop a small macro model

incorporating some of the recent features of the Indian economy. The model tries to

represent the structure of the Indian economy in the post-reform period so that its

results are more relevant for policy design purposes. The development of the model

aims at: (a) deriving insight into the Indian economy especially covering relationships

relating to money, prices and output; (b) becoming a tool by which alternative policy

scenarios on the Indian economy could be assessed and (c) obtaining forecasts on

growth and inflation. The paper as such is divided into nine Sections. In Section 1, we

provide a gist of the economic reforms undertaken in various sectors of the Indian

economy, with special reference to the changes in monetary policy areas. In Section 2,

we provide a brief discussion on growth rates in the macro-aggregates, in 80s and 90s,

almost coincident with pre and post reform periods. In Section 3, we present

discussion on the specification and empirical results of the individual equations of the

model. Section 4 is devoted to evaluate collective performance of the model. Results of

some policy simulation experiments, based on this model, are discussed in Section 5.

In Section 6, we provide model-based forecasts on growth and inflation. In Section 7,

we provide forecasts on growth and inflation, using time varying parameters retrieved

using the Kalman filter method. In Section 8, we enumerate certain limitations of the

model and a summary and brief conclusions of the study are given in Section 9. A

select reference list is given at the end.

1 Recent Economic Reform in India with Special Reference to Monetary Policy

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The twin objectives of the economic reforms in India were (a) to improve

productivity and (b) to attain fiscal and external balances1. Though reforms started in

the mid-eighties, the event, which accelerated the reform process, was the external

payment crisis of 1991, which was largely a reflection of the deteriorating fiscal

situation. The 1980s, especially, the second half was marked by high fiscal deficits. In

order to finance the fiscal deficit, the government pre-empted borrowings from the

commercial banks, raising the statutory liquidity ratio. Banks were forced to invest in

government securities at below market-clearing interest rates. Increased financing of

the government deficit through automatic monetisation led to weaknesses in the

monetary policy operations. With this backdrop, the primary objectives of the fiscal

sector reforms in India in the 90s were focused on reducing the fiscal deficit through

both increased revenue generation and reduced current expenditure. Measures were

also initiated to curb pre-emption of the institutional resources by the government in

order to provide more resources to the private sector. Fiscal reforms were initiated in

three areas, (i) restoration of fiscal balances, (ii) restructuring of the public sector and

(iii) strengthening of the fiscal–monetary coordination (RBI, 2003). This involved

reforms in tax and non-tax revenue receipts, expenditure management, disinvestments

of Government ownership and initiating steps for improving the coordination of fiscal

and monetary policy. Tax rates in India have been significantly rationalized and brought

down to the levels comparable to some of the developed countries. Tax base was

widened, by bringing a number of services sector activities under the purview of tax-

regime. Corporate tax has been reduced. Similarly, custom duty has been reduced

substantially. An important area of fiscal reforms during the 90s has been in favour of

reducing the size of public sector and improving the participation of private sector.

In the 90s, the external sector has also undergone a spectrum of changes. They

were carried out to improve the exchange rate mechanism, by aligning it with market

forces. Other areas of reforms included dismantling trade restrictions, moving towards

1 A part of the discussion presented in this Section is based on the ‘Report on Currency and Finance’, RBI. 2001-02.

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current account convertibility and also gradual liberalizations of certain restrictions on

outflows. The tariff rates have been rationalised and reduced substantially. Over a

period of ten years, the weighted average import duty rate in India was reduced from

72.5 % in 1991-92 to 35.1 % in 2001.02 (RBI, 2003).

There has also been a wide range of changes in design of monetary policy. In the

pre-reform period, monetary policy operations were primarily carried out using direct

instruments, viz., through the cash reserve ratio (CRR), the statutory liquidity ratio

(SLR), selective credit control, refinance facilities, etc. The broad objective of these

policy measures was facilitating monetary expansion and its sectoral allocation,

compatible with overall demand, of real sector performance and social sector

objectives. The Bank rate (Br) was selectively used and had little policy bearing. RBI

accommodated a large part of the fiscal deficit, resulting in a high monetisation. To

offset the monetary impact of such an accommodation, the CRR had to be raised or

kept at a high level to dampen the process of credit creation.

In the post reform period, the operational focus of monetary policy has shifted

towards greater reliance on indirect instruments through open market operations

(OMO) and through adjustme in repo and reverse repo rates to maintain the desired

level of liquidity in the market. The interest structure in India, which was largely

regulated before the 90s, has undergone a radical change. During the pre-reform

period, the financial markets in India were highly segmented and lacked depth. The

interest rates were administered and had multiple layers. On the lending rate side, the

deregulation began in 1994 with emphasis on the development of money, government

securities and foreign exchange markets. Banks were given freedom to set their own

prime lending rates. Similarly, on the liability side, the entire gamut of deposit rates-

except on saving deposits– was deregulated and banks were given freedom to offer

different interest rates for different maturities. During 1997, another overriding

development with far reaching implications was, the reactivation of the Bank rate,

which was linked to other interest rates including the Reserve Bank’s refinance rate.

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The effectiveness of the Bank rate to cause changes in aggregate demand would,

however, crucially depend on the extent and speed of the official rate affecting the

lending rate. In Table-1, we provide a brief summary of the instruments of monetary

policy and their objectives, as used in the pre- and post -reform periods.

Table -1Instruments of Monetary Policy- Pre and Post Reform Comparison

Instrument Monetary control

Captive market for Govt. borrowings

Payment and settlement system

Signaling mechanism for interest rate

Short-term interest rate

Control of prices of essential commodities

Pre-reform

Crr

SLR

Selective credit control

Refinance facility

Bank rate

Post –reform

CRR

SLR

Selective credit controlRefinance facility

Bank rate

Repo rate

2 Macro Economic Trends in India- A Pre and Post-reform

Log-linear growth rates of important macro-aggregates, separately for the pre-

and post-reform periods, are presented in Table–2. The average growth in output

during 1990s, at 6.2 percent, was 0.8 percentages point higher than that during the

1980s, suggesting that performance of the Indian economy has improved in the post-

reform period.2 Private investment rose with a corresponding fall in the public sector

investment. Fiscal consolidation, if any, was due to a reduction in government

2 There has been a deceleration in the growth performance of the Indian economy in the recent years and the view that in the post reform period there has been gains in the productivity, is being contested by many.

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development expenditure rather than any curtailment of non-development expenditure.

On the monetary side, broad money supply growth was more or less of similar

magnitude during both the periods. However, in the post reform period, there has been

a substantial shift in the money creation process, through an increase in the money

multiplier on one side and a steep rise in the foreign assets of the RBI on the other. In

the 80s, reserve money expansion was primarily caused through the expansion in the

RBI credit to the government whereas in 90s, it was driven by a rise (its) in its foreign

assets. The post-reform period also reflects a marked improvement in external trade.

Table-2

Growth Rates in the Important Macro-aggregates (Log-linear growth rates)

(Percent)Variable 1980-81 to1989-

901990-91 to 1999-2000

1980-81 to 1999-2000

Real output 5.4 6.2 5.7

Inflation rate 6.6 7.8 8.0Real investment 6.1 7.3 6.6Private investment(real)

7.4 9.5 8.1

Public sector investment (real) 4.5 3.4 3.2Broad money supply 17.3 17.4 17.4Net foreign exchange assets of banking sector 12.0 37.3 30.3Banks’ credit to the commercial sector 16.8 15.0 15.5

Non-development expenditure of the Central government

16.0 15.5 15.8

Development expenditure of the Central government 17.3(10.1)

10.5(2.4)

12.9(4.5)

Imports of goods (USA $) 4.8 11.4 7.4

Exports of good (USA$) 7.1 10.0 9.3

¤ Nominal values of private investment and public sector investment are deflated by the overall investment deflator

and, therefore, may not be exactly comparable with the growth rates of real private investment and real public sector

investment as reported in various official publications.

* Values in brackets represent real government development expenditure obtained by deflating nominal government

development expenditure with the wholesale price index.

3 Equations of the Model

3.1 Basics and Modeling Strategy

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The basic premises of the model are that monetary sector changes are the

reflections of the changes in fiscal and external sectors. Fiscal sector changes itself

occur due to the developments in real sector and price level. Changes in external

sector, in the exports and imports of goods, occur due to developments in the

domestic and to a certain extent in the world economy. Changes in the real sector and

price level, takes place due to a combination of factors, including monetary and fiscal

impacts. Thus, the model captures inter-linkages of the economy in a simultaneous

framework. With such a macro-economic system as background, Reserve Bank of India

maintains desired liquidity in the economy, in line with the set objectives of inflation

control and to meet credit needs of the economy, by making adjustments in credit

supply (through adjustments in cash reserve ratio) and the Bank rate. From the fiscal

side, model includes government development expenditure as one of the policy

variable.

The model is a very aggregated representation of the Indian economy. There are

five blocks of equations relating to output and investment; government revenue and

expenditure; money; prices and external trade. The model has a single production

function for the whole economy, implicitly assuming similar production functions for

the different sectors of the Indian economy. The assumption of homogenous

production function with respect to different sectors of the Indian economy

(agriculture, industry and services sector) may not be very realistic. Agriculture is

essentially supply driven whereas non-agriculture has now become considerably

sensitive to aggregate demand as well (Sastry and Singh, etl, 2003). Similarly, the

model does not have separate investment functions for agriculture and non-agriculture

sectors (as in Pani’s model of 1984) and thus investment functions, as assumed in this

model may not capture inter-sectoral sensitivity of investment, especially of the public

sector investment on the macro variables. Relaxing theses assumptions is an area for

future work.

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The model covers two distinct phases of the Indian economy–highly regulated

and deregulated and, therefore, some of coefficients, especially those, which have

gained prominence in the post-reform period, are unlikely to turn statistically

significant. However, considering their importance in the emerging Indian economy,

they have been retained in the model. The model consists of 17 equations, of which 10

are stochastic and 7 are identities. The parameters are estimated using annual time

series data for the fiscal years from 1985-86 to 2001-02.

Modeling strategy involves an application of a more rigorous approach rather

estimating equation either in levels or in a growth rate form. At the first stage, a long-

run relationship is estimated. While estimating a long run relationship, in some

equations, coefficients of some of the variables were restricted (to 1) to obtain

theoretically appropriate results. The appropriateness of the long-run relationship is

judged on the basis of the signs of the regression coefficients and whether the residual

series of the long-run relationship is stationary or not, evaluated using Dicky-Fuller

(DF) test as indicated in Annex-3. In addition, exogeneity tests have been conducted to

ensure the ‘exogeneity’ of the independent variables and these results are given in

Annex-2. The final relationship is estimated in an ECM framework, including both long

run and short-run information. Like-wise long run relationship, in some ECM equations

as well, coefficient of the residual terms, which was less than minus 1, was restricted to

minus 1. These problems prominently occurred in those variables which were

substantially affected by the reform process and whose modeling otherwise are also

inherently difficult, as in case of the private investment. The choice of variables of the

equations, long run as well short-run, is made on the basis of theoretical and statistical

criteria. Needless to say, several alternative specifications were tried (not reported for

lack of space) to arrive at the best fit of the equations. In many cases dummy variables

have been incorporated to neutralize the effects of outliers and irregular changes.

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Dummy variables are also used to cover two different policy regimes, wherever felt

essential. The list of endogenous and exogenous variables used in the model is given

in Annex-1.

3.2 Real Sector

3.2.1 Output

The long run relationship of real output could be specified as a conventional

production function in which output is determined by fixed capital (K), labour (L) and

total factor productivity. However, in respect of a country like India, the lack of quality

data on employment, especially relating to the unorganized sector, means that

including labour in the production function may not be realistic. Perhaps, in view of

such considerations, earlier modeling exercises in India (Rangarajan and Arif (1990),

Bhattachraya, Barman and Nag (1994)) and others) have not included labour in the

production functions specified in their studies. Therefore, real output is postulated as a

function of capital stock alone. However, a dummy variable representing the pre-reform

period is considered to take account of the impact of the policy regime on the

production function. In the short-run, however, output in India could be affected by

variety of demand- and supply-oriented factors. One of the most important factors is

rainfall. Rainfall affects the overall growth prospects, primarily through its impact on

agricultural sector which in turn affects industry as a supply factor in agro-based

industries, and through demand (Sastry, Singh, etl. 2003). Another factor, which

continues to affect the performance of the Indian economy, is the availability of bank

credit, essential for working capital needs. Earlier, Rangarajan and Arif (1990) used real

(broad) money balances as one of the variable in their output function. We used real

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bank credit rather than real money balances in the output equation. Bank credit

appears to be more appropriate for many reasons. In the Indian set-up, there is a vast

unorganised sector, which relies on bank credit to meet its working capital and

investment needs as this sectors lack its own resources. Another explanation is that

bank credit could be considered as a proxy for the potential utilization as well. An

increase in the (growth rate of real) bank credit (especially if caused because of

demand factors) generally reflects higher use of the existing resources (capital stock,

etc.). Given this, real output is postulated to be a function of changes in capital stock,

lagged by one year (log Kr-1), changes in (real) bank credit to the commercial sector (

log (Bccs/Wpi)) and rainfall (Rif3)and one lagged residual series of the long-run

equation.4

Long-run equation:

Log Yr =2.2712+0.76609 Log Kr + 0.04358 Der

t (8.35) (42.20) (2.82)

ECM equation:

LogYR=0.0140+0.2936ΔLogKr-1 +0.1696 Log (Bccs/Wpi) +0.07793 Rif –0.6612 Resyr(-1)

t (0.42) (0.72) (2.99) (2.58) (4.11)

R2(adj.) =0.78 DW=2.17 SEE=0.00892

The above equation was also estimated using a credit demand function discussed in

the monetary sector as an instrument because of the endogeneity of bank credit. That

is, by replacing actual values of bank credit by their estimates, as obtained through a

credit demand function.

3 There was a doubt whether excessive rainfall would adversely affect output performance and so whether there is a need to include quadratic form of the rainfall index as one of the explanatory variable, which should bear negative sign. However, data did not support this hypothesis.4 Other factors, which also could be considered, are the export performance and government expenditure affecting through the external and domestic demand, respectively (Bhattacharya, Barman and Nag (1994)).

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ECM equation using instrument variable for Log (Bccs/Wpi):

LogYr=0.0088+0.2942ΔLogKr-1 +0.2705 Log (Bccs/Wpi)ˆ +0. 0599 Rif –0.6280 Resyr(-1)

t (0.31) (0.85) (3.99) (2.26) (4.50)

R2(adj.)=0.84 DW=2.28 SEE=0.0076

3.2.2 Investment Equations

Investment data in India are available for the household, corporate and public

sectors. For the purpose of this study, data for corporate and household sectors is

clubbed together and is treated as capital formation in the private sector, also

occasionally referred to as investment in the private sector. Initially, regression

equations in nominal terms for capital formation in the private (Ipn) and public sectors

(Ign) are estimated separately and then are added-up and converted into real terms (Ir)

by using deflator for the capital formation deflator (Idf).

3.2.2.1 Capital Formation in the Private Sector

Long-run nominal capital formation in the private sector (Ipn) could be postulated

as a function of (nominal) output (Yn) and certain other factors, e.g. foreign resources.

Since the data for the other factors, especially foreign resources in India is not readily

available, they have been proxied by a time trend. Private investment is thus estimated

as function of (nominal) output and a time trend. The regression coefficient of Yn

turned out to be greater than one, which is theoretically impossible.5 Therefore, the

equation was re-estimated by restricting the coefficient of Yn to one. This is still

unattractive from a theoretical point of view because it implies that investment output

5 Long-run coefficient of Yn greater than one will imply that in the long-run entire Yn is used for investment and thus there will be no consumption.

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ratio (IPN/YN) grows over time. Though this is impossible in the long run, however, it

might be possible in the medium -term.

Log Ipn = -2.19762+ 1.0 Log Yn + 0.0156 Time In the short-run, capital formation in the private sector is likely to be affected by

growth in nominal income, the cost of capital, proxied by prime lending rate adjusted

for expected inflation (Plr-Pe). To test the competing hypotheses of ‘crowding in’ or

‘crowding out’ of private sector investment by the public sector investment, growth in

capital formation in the public sector (ΔLog Ign), is also included,6 as an additional

variable (Blejer and Khan, 1984). The estimated coefficient on the ECM was less than

minus one and, therefore, equation was re-estimated restricting its (error term)

coefficient to one, which is still inappropriate.

ECM equation:ΔLog Ipn=0.031- 1.491 (Plr-Pe) +1.603 Δ Log Yn(-1)+0.202Log Ign(-1)–1.00 Resipn(-1)

t (0.21) (1.47) (1.82) (0.61) - R2(adj)= 0.68 DW =2.63 SEE= 0.0811

3.2.2.2 Capital Formation in the Public Sector

Long-run capital formation in public sector is modelled as a function of

government development expenditure (Gde), where development expenditure used is

that of the Central government.7

Log Ign = -0.1311 + 1.00 Log Gde t (0.32) (27.88) ECM equation: ΔLog Ign = 0.0679 + 0.3311 Δ Log Gde –0.6168Resign(-1)

t (3.16) (1.90) (3.23)

6 The empirical result indicated that the public sector investment has the maximum ‘crowding in’ effect on the private sector investment with one year lag.7 States expenditures are not included. We assume their exclusion will not alter the results.

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R2(adj)= 0.40 DW =2.01 SEE=0.0521

3.3 Fiscal Sector

The fiscal sector of the model involves equations for non-development

expenditure and revenue receipts of the Central government. Non-development

expenditure was also initially estimated as a function of nominal output. However, the

empirical results were considered inappropriate, as the residual series obtained from

the long-run equation was not stationary. Accordingly, the equation was modified and

re-estimated as a function of real output (Yr) and wholesale price index (Wpi)8.

Log Nde = -16.2881 + 1.8544 Log Yr + 0.4957 Log Wpi t (7.29) (8.56) (3.12) ECM Equation: Δ Log Nde = 0.0597 + 0.7923 Δ LogYr +0.5058 Δ Log Wpi+ 0.021 Der -0.8151 Resnde(-1)

t (1.58) (1.96) (1.67) (1.35) (3.96) R2(adj.) =0.53 DW=2.47 SEE=0.0267

Revenue receipts is modeled as a function of nominal output. Log Rr = -1.3205 + 0.9304 Log Yn+0.0543 Der t (3.72) (36.52) (1.42)

ECM equation Δ Log Rr = 0.0489 + 0.5627 ΔLog Yn –1.00 Resrr(-1)

t (0.96) (1.50) - R2(adj.)= 0.57 DW=2.21 SEE= 0.040

Finally, the gap between total expenditure (non-development expenditure plus

development expenditure) and revenue receipts, represented as gross fiscal deficit, is

financed either by market borrowings, including borrowings from the commercial

8 The similar specification was attempted for revenue receipts as well which was considered inappropriate as the coefficient of the residual series of the long-run relationship in the ECM equation turned out to be much greater than one.

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banks and other market borrowings, or borrowings from the Reserve Bank of India. For

the purpose of this model, borrowings of the Central government from commercial

banks and RBI are clubbed together, represented as ΔBcg.

3.4 Monetary Sector

Monetary sector is modeled at the aggregate level (M3). By identity, M3,

M3= Bcg + Bccs + Nfea+Om3 Of these, Bcg and Nfea have been endogenised and Bccs and ‘Om3’ are treated as exogenous variables.

3.5.1 Bank Credit to the Government

Bank credit to the government (Bcg) equals the fiscal gap between revenue receipts,

other receipts and total expenditure by identity.

Bcg = Nde +Gde –Rr –Otrc

3.5.2 Bank Credit to the Commercial Sector and Prime Lending Rate

Bank credit to the commercial sector (Bccs) has been as a kept as an exogenous

variable. The credit demand function is estimated for its use in the output as an

instrument. This equation is also used while conducting a policy simulation experiment

of assessing the impact of changes in the Bank rate on the other macro variables.

Banks credit to the commercial sector could be assumed to be exogenous (policy

variable) since the RBI can influence the supply of bank credit to the commercial sector

(Bccs) by adjusting the cash reserve ratio (CRR) while keeping the reserve money

unchanged.9 In this framework, changes in Bccs would influence prime lending rate,

which in turn is likely to influence investment, especially in the private sector. Real

bank credit to the commercial sector, (i.e. Bccs/Wpi) is estimated as a function of real

9 Reduction in crr causes a rise in the money multiplier and thus the same reserve money causes more monetary expansion.

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output (Yr), the real prime lending rate (Plr-Pe) and a dummy variable for pre-reform

period.

Long-run equation:LogBccs/Wpi =-4.2277+1.2277Log Yr – 0.6189 (Pl-Pe)+0.1211Der t (5.14) (20.53) (1.27) (3.10)

ECM equation: LogBccs/Wpi =0.0372 +0.4844 Log Yr –0.7281Resbccs(-1)

t (1.39) (1.04) (2.98) R2(adj.)= 0.49 DW= 1.11 SEE=0.0305 The lending rate (Plr), in the long run, is estimated as a function of the Bank rate (and a dummy variable for the pre-reform period).

Plr = 0.0470 + 1.00 Br +0.0175 Der t (2.53) (5.62) (2.52) Plr in the short-run is estimated as a function of changes in Br and changes in the bank credit to the commercial sector, representing liquidity conditions in the market.

ECM equation:

Δ Plr = 0.0066 +0.8340 ΔBr -0.0577 Δ Log Bccs –0.7964 Resplr(-1)

t (0.49) (1.86) (0.62) (2.40) R2(adj)=0.18 DW=1.90 SEE=0.0126

Although the equation seems appropriate in itself, its impact on the collective

performance of the model was not satisfactory especially when the model was solved in a dynamic mode. In view of these limitations of this ECM equation, for policy simulation purposes, a long-run relationship has been considered.

3.5 External Sector

In this model, we estimated empirical relationships for exports of goods (Expg)

and imports of goods (Impg) whereas net invisible receipts (Ninvr) and capital account

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(Cap) are treated exogenously. Finally, the net effect of these changes in the external

sector components are linked with the monetary sector through an identity:

Nfea = Expg +Ninvr -Impg + Cap + Eom

Eom is the balancing factor between changes in Nfea on the monetary side and

changes in the reserves on the balance of payments side.

3.5.1 Exports of Goods

In India external trade is generally invoiced in foreign currency denominations and

then converted into rupees. Thus, changes in exchange rate leads to rupee value of

exports and imports with no change in fundamental factor. In order to eliminate this

problem, these two variables are estimated by measuring them in US $ terms (as in Rao

and Singh (1995)). Because India’s share of trade in the world trade is relatively small,

the long run relationship for exports of goods from India is postulated as a function of

its real output. The reforms to this sector, especially the opening of the Indian

economy, have also significantly affected the external trade. A number of proxy

variables were considered as potential indicator of ‘openness’ for the export equation.

The variables tried were the ratio of net foreign exchange assets to broad money

(Nfea/M3) and a time trend. However, these measures of ‘openness’ were found to be

empirically inappropriate. Another possible variable is the reduction in the restrictions

on imports. Since information on effective custom duty is readily available from 1993, it

was used as a proxy variable representing ‘openness’ in the external sector in India.

Thus, the long-run relationship for exports was estimated as a function of real output

and a dummy variable for the pre-reform period and a variable indicating effective

custom duty (Impord). In the short-run, exports of goods is considered to be affected

by the changes in the real output of industrial countries (dlgdpic) and changes in the

real exchange rate (Leavgr=Log (Wpi*(Eavg/Wpi)). A large part of exports, especially

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diamond related items, is re-exported. To capture such an effect, (changes in) imports

in the previous year, is included as an additional variable.

Long-run equation:Log Expg/ Eavg = -10.9303 +1.4166 Log Yr –0.1515 Log imord -0.0766 Der t (-4.60) (9.09) (1.72) (1.12) ECM equation:ΔLogExpg/Eavg=-0.0154+2.4496ΔLogGdpic+0.4649Δ(LogImpg/Eavg)-1 t (0.21) (1.07) (2.32) + 0.3414Δ Log Eavgr(-1) -0.5632Resexpg(-1)

(0.92) (2.20) R2(adj.) =0.32 DW=1.45 SEE=0.0722

3.5.2 Imports of Goods

Imports of goods, measured in USA $, are postulated as a function of real output

in the long run. To take into account of the shift in policy, a pre-reform dummy variable

is included. The reduction in custom duty (Imord), is also included in the relationship

for the same reasons as discussed above.

Long-run equation:

Log Impg/Eavg = -8.3926 + 1.2892 Log Yr+0.1432 Der- 0.2861 Log Imord

t (3.28) (7.72) (1.96) (3.04) Imports of goods in the short-run are modeled as a function of changes in real output and changes in the real exchange rate.

ECM equation: ΔLog Impg/Eavg =- 0.0827+ 3.0243 Δ Log Yr -0.3874ΔLog Eavgr –0.8084 Resimpg(-1)

t (1.54) (3.68) (1.32) (2.88)

19

R2(adj.)= 0.76 DW=1.97 SEE=0.0630

3.6 Prices

3.6.1 Investment & GDP Deflators The GDP deflator is obtained as a function of Wpi and unit value index of imports (Mp).

Log Ydf = -0.5159 +0.9951 Log Wpi + 0.0929Log Mp +0.03597 Der

t (3.20) (20.20) (1.62) (1.66) ECM Equation: Δ Log Ydf =0.0207 +0.7202 Δ Log Wpi+0.0566 Δ Log Mp –0.4260 Resydf(-1)

t (2.27) (6.05) (1.42) (2.06) R2(adj.)=0.73 DW=1.49 SEE=0.0125

The above equation suggests that in the short-run a 1 percent rise in the price

level raises the income deflator by 0.72 percent. In long run, however, this impact works

out to be around 1 percent.

Similarly, investment deflator is modelled as a function of Wpi and the unit value

index of imports.

Long-run relationship

Log Idf = -0.0705 + 0.7453 Log Wpi + 0.2134 Log Mp t (-1.01) (16.43) (4.86)

ECM equation: Δ Log Idf = 0.0022 + 0.7616 Δ Log Wpi +0.2033 Δ Log Mp - 1.00 Residf(-1) t (0.21) (5.98) (4.09) (3.71) R2(adj.) =0.77 DW=1.30 SEE=0.0130

A 1 percent rise in the price level, increase the income deflator by 0.76 percent in

the short-run and by a similar magnitude in the long- run.

3.6.2 Price Level

20

In the long run, inflation in India is assumed to be a monetary phenomenon and

the long-run link between money and price is assumed to be in the quantity theory

framework. Though, some studies suggest that the link between narrow money and

prices is stronger (Bhattacharya, Barman and Nag, 1994), we use broad money (M3)

since in India monetary policy is primarily concerned with it. The definition of narrow

money also varies across time.10 Thus, the long run relationship for WPI is postulated

as a function of broad money (M3) and real output (Yr). Two dummy variables, for the

years 1999-2000 and 2001-20002, when inflation in India was moderate despite strong

monetary expansion, and another for the period from 1985-86 to 1989-90, have also

been included in the equation. The Long run impact of the money on the prices is

assumed to be unity.

Log Wpi = 11.4565 +1.00 Log M3 – 1.4602 Log Yr –0.0525 Der –0.0559 dwp20 t (1.54) - (24.36) (1.64) (1.62)

The elasticity of money demand at 1.46 is very close to 1.50 used by the RBI while

following monetary targeting approach till very recent period. In the short-run,

however, wholesale prices in India are likely to be affected by changes in the prices of

food articles, energy prices as well money and output. Accordingly, short-run changes

in WPI are postulated as a function of both demand and supply factors. Changes in

food articles and energy prices are included as supply shock variables whereas

changes in broad money represent the demand side factor.

ΔLogWpi = 0.0272 +0.2764 Δ Log M3 – 0.2677Δ Log Yr +0.1836ΔLogWpifa +0.0463dwpi20+0.0828 Log Wpie t (0.58) (1.16) (1.05) (1.63) (2.64) (0.95) -0.4554 Reswpi(-1) (2.94) R2(adj.) = 0.64 DW=1.43 SEE=0.0167

10 For analytical purposes of monetary management in India, reference may be made to Vasudevan (1991).

21

3.7 Discussion

Real output turned out to be a satisfactory function of the capital sock in the long

run. In the short-run, however, bank credit and rainfall have major influence on the

output performance. Private investment is determined as a function of (nominal)

output and to a certain extent by real prime lending rate also. Impact of public sector

investment on the private investment turned out to be positive but comparatively low.

Incidentally, public sector investment turned to be an exact function of the government

development expenditure. Revenue receipts can be successfully modeled as a function

of nominal output, implying identical impact of real output and prices, whereas in case

of non-development expenditure, real output and prices show differential effect. Prime

lending rate responds to the Bank rate satisfactorily in the long run whereas in the

short-run their relationship is week. Export equation turned out to be poor as compared

to import equation. In both the equations, factor affecting them indicated desired

impact. But statistically, many were insignificant in the export equation. GDP and

investment deflators turned out to be satisfactory function of price level and unit value

index of imports. A long run relationship for prices could be determined in the quantity

theory framework, though the use of two dummy variables became essential to

satisfy stationarity properties of the residuals of the (long-run) relationship. In the

short-run, impact of food articles turned out to be stronger as compared to energy

prices, both in terms of ‘size’ and ‘t’ values of the coefficients.

4 Collective Performance of the Mode

Before conducting policy simulations or making use of the model for policy design

purposes or obtaining forecasts, it is essential to evaluate the collective performance

of the model. In other words, though the estimates of the individual equations of the

model may be satisfactory, it is necessary to test their collective performance and

22

goodness of fit as a whole by obtaining a simultaneous solution. The technique of

simulation has been used for this purpose. In simulation, an iterative procedure is used

to solve the simultaneous equation system for the set of endogenous variables. Both

static and dynamic simulation solutions are obtained. In static simulation, the actual

lagged values of the endogenous variables are used in obtaining the solution whereas

in dynamic simulation only the initial values of the data are used. Simulated values are

used for the subsequent periods. Thus, in static simulation the results represent a step-

ahead solution, without any inter-period linkages through the values of endogenous

variables generated by the model in the previous periods. In the dynamic simulation,

estimates of the various endogenous variables are linked over the period and,

therefore, the solution reflects a dynamic time-path of the endogenous variables. Both

simulations were conducted for a period of 17 years, from 1985-86 to 2001-02. The

simulation has been conducted at levels, by suitable transformation of the growth

rates.

In assessing the goodness of fit of the model, two measures of collective

performance have been considered:(i) mean absolute percentage error (MAPE) and (ii)

root mean square percentage error (RMSPE). MAPE and RMSPE of the important

endogenous variables are given in Table-3.

Table- 3

Mean Absolute Percentage Error and Root Mean Square Percentage Error of the Important Endogenous Variables- Static and Dynamic Simulation

Smpl: 1985-86- 2001-02 (Percent)

Variable Static Simulation- MAPE

Static Simulation- RMSPE

Dynamic Simulation-MAPE

Dynamic Simulation-RMSPE

Yr 0.82 1.04 1.29 1.53

Wpi 1.17 1.40 2.46 2.96

Kr 0.37 0.46 1.04 1.18

Ir 4.71 5.91 4.82 5.71

23

Ipn 4.64 6.46 6.92 8.53

Ign 7.87 9.71 6.40 7.66

Nde 2.48 3.58 2.76 3.72

Rr 3.43 3.97 3.79 4.46

M3 1.30 1.70 1.72 1.96

Expg 6.40 7.94 6.94 9.00

Impg 3.64 4.91 4.78 5.69

Idf 4.72 1.93 2.54 2.96

Ydf 2.50 1.20 1.90 2.33

These results are reasonably encouraging. Though the model is small but the

structure of the Indian economy changed markedly over the same period, the errors are

not too large. They are relatively big for investment & trade data, partly because of the

issues discussed in Section 3 but also partly because that these variables seem to be

inherently difficult to model. The result suggests that the model could be used for

simulation exercises and forecasting. They are discussed in the next three Sections.

5 Policy Simulations

Though the model has been validated in terms of MAPE and RMSPE, the same has

not been examined in terms of properties like stability, sensitivity to parametric

variations and exogenous shocks11 and, therefore, policy simulation results needs to be

interpreted with caution. To begin with model is allowed to work through its dynamic

path from 1985-86 to 2001-02 to provide estimates of the endogenous variables, known

as control or base run. In order to examine the effect of any policy (say change in the

Bank rate or government development expenditure), it is necessary to increase

(decrease) the policy variable above its original (control) level and to stimulate its

impact on the economy keeping all other exogenous conditions unaltered. Having,

11 The stability of the model could be evaluated by way of deriving properties of multipliers and determining their eigen vector and eigen values( Chow,1974). Sensitivity of parametric variations could be evaluated applying stochastic simulation. Any model complying with these norms is considered to be more robust.

24

altered only the exogenous policy variable, under ceteris paribus conditions, the model

is once again allowed to run through the same temporal path to yield a new set of

estimates (policy solution). The difference between the Base and Policy solution is

attributed to the policy under investigation

Two types of simulation techniques were attempted. Under these two techniques,

all the variables in the base run take their historical values over the sample period. The

policy simulation in the first case is a single exogenous shock administered once in a

year (in 1985-86). The effects of this policy are then allowed to work through the system

for the period from 1985-86 to 2001-02. The second alternative involves an increase in

the policy variable above its historical level – that is, repeated shock during each year

of the simulation period. In this study both type of policy experiments were conducted,

and except magnitudes, both the experiments yielded similar results. The simulations

those are discussed in this analysis are of the first kind. That is, dynamic runs over the

historical time path, with changes in policy variables (by 1 percentage point reduction

in the Bank rate and 5 percent rise in bank credit to the commercial sector and

government development expenditure) at one time point only in the beginning of policy

simulation.

5.1 Reduction in the Bank Rate

A fall in the Bank rate should have softening impact on the overall interest rate

structure and thereby bringing down prime lending rate, which in turn is likely to

improve growth prospects through higher demand for investment. In order to take into

account the inflationary effect of this policy, by way of expansion in money growth,

banks’ credit to the commercial sector (which otherwise is an exogenous variable in

the model), has been endogenised. The final impact of the policy shock will, however,

depend upon the sensitivity of interest rate on investment and demand for credit.

Results of this policy are presented in Figure-1. In view of space limitations, we have

confined our analysis on growth and inflation only.

25

Figure 1

Initially, reduction in the Bank rate invokes inflationary pressure in the economy

through higher monetary expansion, which, however, turns out to be temporary. In the

long run, the policy, in fact, indicates certain level of fall in the price level accompanied

by an improved growth performance.

5.2 Increase in Bank Credit to the Commercial Sector

In this experiment an attempt is made to verify the impact of sustained increase in

bank credit on real output and prices. For this purpose, a policy run is conducted by

raising bank credit to the commercial sector by 5 percent from its historical level for the

first time point of simulation period and obtaining the estimates of endogenous

variables. Results of this policy simulation are presented in Figure-2.

26

Figure 2

Results of this policy indicate that a rise in bank credit to the commercial sector initially

causes a steep rise in the output in the first time-point. However, this effect is

temporary, and in the long-run inflationary impact becomes stronger, neutralising

positive effect on the output. The long-run effect of the policy turns out to be almost

‘neutral’ to the output. This policy simulation experiment is conducted under the

assumption that a rise in banks’ credit to the commercial sector takes place through

the reduction in cash reserve ratio (which will raise money multiplier or alternatively

increase resources with the commercial banks) and not through the increase in reserve

money. In case, rise in bank credit is accommodated through an expansion in reserve

money, monetary expansion will be much larger invoking higher inflationary pressure

in the economy.

5.3 Increase in the Government Development Expenditure

Government development expenditure is an exogenous variable in the model. By

varying this policy variable, its impact on the economy was studied. A shock of 5

percent above its historical level for the first time period of simulation was

administered to this variable. All other exogenous variables were maintained at the

27

base level. A rise in government developmental expenditure will cause monetary

expansion and a rise in prices thereof. In this policy simulation experiment, it is

assumed higher credit demand by the government is accommodated through reduction

in cash reserve ratio and not through an expansion in reserve money. Results of this

policy are presented in Figure-3.

Figure 3 A rise in developmental expenditure of the government is likely to cause a rise in

inflation and fall in output in the initial years of this policy. However, after 3-4 years

output effect is likely to outperform the price effect. In the long run the economy is

likely to experience fall in price level whereas output will stabilise at a higher level.

6 Forecasts on Growth and Inflation

In this Section, we obtain forecasts on real output and inflation for the year 2003-

04. For obtaining these forecasts, there is a need to predict all the exogenous variables

for the year 2003-04, which appears to be difficult task due to the fact that information

regarding their prevailing trends in the year is not readily available. Under these

circumstances, forecasts on inflation and growth are obtained using their individual

equations as well simultaneous framework, requiring predictions on a few exogenous

28

variables only. Use of full model for forecasting, is a part of the further work on this

area. Accordingly, at the outset of this Section, a detailed analysis is made to assess

the within sample performance of the single and simultaneous equations.

6.1 Within Sample -Simulated Values on Growth and Inflation

6.1.1 Simulated Values Based on Individual Equations Dynamically simulated values on growth (g) and inflation (Π) for within the sample

are given in Table-4 and Table-5, respectively.

Table - 4 (Percent)

Year Actual(ga)

Estimated (ge)

Simulated (gs)

1986-87 4.24 4.02 4.751987-88 3.75 4.33 4.361988-89 9.96 9.24 9.101989-90 6.48 6.48 6.971990-91 5.41 6.03 2.201991-92 1.28 1.35 2.251992-93 4.99 5.74 7.121993-94 5.73 6.00 4.871994-95 7.00 7.52 8.151995-96 7.08 7.63 6.571996-97 7.54 6.48 5.241997-98 4.68 5.52 6.681998-99 6.30 5.87 5.621999-2000 5.89 5.22 6.722000-01 4.28 4.45 5.692001-02 5.41 4.18 4.50

Table -5

(Percent)Year Actual

(Πa)Estimated(Πe)

Simulated(Πs)

1986-87 5.75 7.66 7.471987-88 7.71 8.23 8.071988-89 7.16 8.52 7.741989-90 7.28 5.91 4.681990-91 9.68 9.34 8.07

29

1991-92 12.96 12.00 13.201992-93 9.54 9.03 11.111993-94 8.01 7.14 8.551994-95 11.77 9.25 9.931995-96 7.77 5.12 6.861996-97 4.50 5.75 6.391997-98 4.30 5.11 5.121998-99 5.77 8.24 7.951999-2000 3.21 2.49 1.512000-01 6.91 7.80 7.542001-02 3.53 4.25 3.88

To obtain an quantitative measure of the closeness between simulated and actual

values of growth and inflation, we estimated a simple regression equation between

them (actual and simulated growth rates).

ga = 1.60 + 0.71 gs R2(adj.)=0.45 SEE=1.42 Mean =5.62 t (1.37) (3.63) Πa =0.92 +0.85 Πs R2(adj) =0.73 SEE=1.45 Mean =7.24 t (0.88) (6.39)

6.1.2 Simulated Values Based on Simultaneous System

Table-6 presents the simulated values of growth and inflation obtained through

the simultaneous system of these two variables.

Table- 6 Simulated values of growth and inflation rate based on both equations.

(Percent)Year Growth (gs) Inflation (Πs)1986-87 4.11 7.571987-88 4.54 7.961988-89 9.12 7.581989-90 7.83 4.561990-91 2.15 8.351991-92 1.42 14.641992-93 6.76 11.411993-94 5.21 8.121994-95 8.96 9.381995-96 6.74 5.881996-97 4.14 6.901997-98 6.38 6.291998-99 5.40 8.15

30

1999-2000 7.76 1.482000-01 5.76 6.382001-02 4.55 2.90

ga = 2.30 +0.57 gs R2(adj)=0.41 SEE=1.47 Mean =5.62t (2.20) (3.39)

Πa =1.79 + 0.74 Πs R2( adj) =0.65 SEE=1.64 Mean =7.24 t (1.65) (5.40)

The simulated values of growth and inflation, as obtained through single equation

and simultaneous system, are close to their actual values, except at a few time points.

Further, in case of extreme values of growth and inflation, performance of these

equations is reasonable. Thus, under the assumption that parameters of these

equations do not change and exogenous variables are predicted accurately, these

equations appears suitable for forecasting growth and inflation outside the sample

period. Accordingly, outside sample performance of these equation is judged by

predicting growth and inflation for 2002-03 for which full information is available.

6.1.3 Prediction on Growth and Inflation for 2002-03

2002-03 was an abnormal year in the Indian economy especially in terms of

performance of the real sector. A near draught severely affected agricultural sector

performance. Advance estimates by the Central Statistical Organisation (CSO)

estimates agricultural output fall by about 3 percent during 2002-03. However, the

industrial and services sectors are likely to have a growth by 5.8 percent and 7 percent,

respectively. Overall GDP during 2002-03 is predicted to have a growth by about 4.4

percent. Despite the draught, price rises were moderate at 3.5 percent. Thus, predicting

growth and inflation for an abnormal year like 2002-03 is likely to face problems.

Information on all the exogenous variables, except monetary aggregates, is readily

available in useable form and is presented in Table-7. Mergers of financial institutions,

however, complicates interpretation of monetary data available inclusive and exclusive

31

of merger effect. To circumvent this problem, we have obtained separate predictions

using monetary aggregates, which are inclusive and exclusive of merger effects and

took their average. Separate predictions were also obtained using single equation and

simultaneous equation because earlier analysis showed that some time single equation

shows better performance (than simultaneous equations) and vice versa. Thus, for

output growth, four values of forecasts (based on single equation and simultaneous

equation- with and without merger) were obtained and their average, assumed to be its

representative value in 2002-03, is given in Table-8. Like-wise, forecast of inflation are

also obtained and is given in Table-8.

Table –7 Values of the Exogenous Variables for the Year 2002-03

Variable ActualM3 17,24,578

(16,94,907)Bccs 9,01,440

(8,75,769) Wpifa 179.18Wpie 239.18Rif 75.0Kr(estimated) 38,38,634

Values in bracket are exclusive of merger effect

Table-8 Actual and Model Based Predicted Values-2002-03

(Percent)Variable Actual PredictedGrowth in output (g) 4.4 6.1Inflation rate (Π) 3.4 1.9

The differences between the predicted and actual values, as given in Table-8, may

be due to the fact that year 2002-03 was abnormal year and thus such a divergence was

not unwarranted. Or, it may be a reflection of some changes in the parameters of the

regression equations used. Assuming that these divergences were on account of

abnormal year, we obtain forecasts for 2003-04. The issue of changes in parameters is

examined in the next the Section.

32

6.1.4 Predictions on Growth and Inflation for 2003-04

Price rise in food articles and energy prices is assumed to be around 5 percent

during 2003-04. Growth in monetary aggregates viz. in M3 and Bccs is assumed to be

around 15 percent for 2003-04. Growth rate in investment is assumed to be similar to

the previous year. Based on these assumptions, predictions on inflation rate and

growth rate for the year 2003-04 are placed at around 4 percent and 6.2 percent,

respectively. These predictions are based on the assumption that during the year 2003-

04, rainfall would be normal and well spread throughout the country and overall index

would be around 102.

Table-9 Model Based Predicted Values for 2003-04

(Percent)Variable ForecastGrowth in output 6.2Inflation rate 4.1

7 Forecasting Growth and Inflation using the Kalman Filter- Some Exploratory Results

Divergence between actual and predicted values of growth and inflation for the

year 2002-03, as obtained in the previous Section, may be on account of abnormal

developments in the real sector during the year or partly may be on account of changes

in the parameters. The problem of changes in parameters is likely to be encountered by

all the economies undergoing structural changes in their economic systems. In the

conventional regression analysis, if the point of structural change is known, generally a

suitable dummy variable is incorporated to neutralise the outlier effect of the structural

change. But as economy with many changes will require use of many dummy

variables. A more appropriate and parsimonious approach to the representation of an

economic system undergoing changes in the economic system, like in India, is to build

33

a model using a methodology, which takes account of the structural instability viz.

Time Varying Coefficient (TVC) (Brown, etl.1997)

Engle and Watson (1987) suggest three reasons for using TVC models in

economic modeling. Firstly, the Lucas (1976) critique provides a behavioral motivation

for parameter variation. According to Lucas, economic agents adjust not only their

behaviour in response to new policies, but also their estimates of the economic model

considered relevant to the previous policies. Secondly, changes in the unobservable

components of economic variable will cause structural change in the data generating

process (DGP). To the extent that these variables can’t be measured satisfactorily by

the inclusion of proxy variables in the model, the parameter changes caused by their

variation may be simulated by time series representation (AR, MA, ARMA) of the

parameters (Harvey, 1993). Finally, model mis-specification is another source of Time

Varying Coefficients since it is generally not possible to develop a perfect specification

of an economic DGP. The non-white noise residuals from the mis-specified model can

be partly explained by the changing coefficient values in the TVC models.

In this backdrop, in this Section an attempt is made to extend the coverage of

the study to obtain Time Varying Coefficients in respect of ECM representations of

growth and price equations. Later on, efforts would be made to obtain a more general

specification to obtain TVC, either estimating the coefficients of long run and short-run

factors through the same equation or initially estimating a TVC version for the long-run

equation and then estimating varying parameters for the ECM equation as well.

For deriving TVC in respect of ECM equations, we have made use of Kalman filter

algorithm, on almost similar lines as by Rao and Singh (1995). Strictly speaking, the

term Kalman filter refers to an estimation method commonly used to estimate state-

space models (Rao, 1987). The state-space models originated in engineering (Kalman,

1960, Kalman and Bucy, 1961) and were imported into economics by Rosenberg (1968),

Vishwakarma (1974), Chow (1975), Aoki (1975) and others.

34

The Kalman filter model (KFM) consists of two parts: the transition equation,

which describes the evolution of a set of state-space variables; and the measurement

equation, which describes how the data actually observed is generated from the state

variables. The KFM is an updating method that bases the regression estimates only on

data upto and including the current period. Its importance in economics is partly due to

its ability to model time-varying parameters (TVPs) and this makes it highly useful for

investigating structural changes or obtaining forecasts. The general form of KFM

comprise of two equations: the measurement and transition equations (Harvey, 1989).

The measurement equation is given by:

Yt = Xt ßt + ut, Var( ut) = R (6.1) The transition equation is given by:

ßt = λ ßt-1 + vt , V ar ( vt ) = Q (6.2)

In the formulation above, Yt is the dependent variable and there are n independent

variables Xt. The measurement equation, eq. (6.1), is an ordinary regression equation

with time-varying parameters, ßt, while the transition equation, eq. (6.2), defines the

evolution of the parameters over time. If we have an estimate of ßt-1 and its covariance

matrix Σ t-1,, then the updated estimate of ßt, given Yt and Xt, is given by the following

Kalman filter algorithm:

St = λ Σ t-1 λ' + Q (6.3a) Σ t = St – Kt Xt St (6.3b) ßt = λ ßt-1 + K t ( Yt - X t-1 ß t-1 ) (6.3c)

Thus, the calculations of the Kalman filter estimation proceed by forward

recursions. In eq. (6.3c), the one-step forecast, λ ßt-1, is a strict update of the previously

estimated value, whereas the best estimator involving current data, ßt, is weighted

35

average of the one-step forecast and the error that one makes in predicting y t. The

weighting matrix, Kt, referred to as the Kalman gain, is given by:

Kt = St Xt' (Xt St Xt' +R) –1 (6.4)

where the covariances are updated using eqs. (6.3a) and (6.3b) . If the estimator for ß t is

to be based on all the data, yt, t=1, T, we need the Kalman smoother estimators. These

smoothers, denoted by ßt* , can be developed by successively solving the following

back-ward recursions for t, t= T, T-1, …., 1:

ß*T-1

= ßT-1 + JT-1

(ßT-1 - λ ßT-1 ) ( 6.5 )

where = ßt’s are the original Kalman filter estimators and where the weighting matrix is given by:

Jt-1 = Σ t-1 λ'(S t-1)-1 ( 6.6)

The main problem that remains is to develop appropriate estimators for the five

unknown parameters of the model, i.e., ß0, Σ0, R, λ and Q, that are required to generate

the recursions.

In this context, the initial state vector, ß0, was set equal to the initial estimates of

the parameters obtained by using OLS over the sample period from 1985-86 to 1999-

2000; the initial covariance matrix of the states Σ0, was formed by using the

corresponding variances of the parameters along its principal diagonal; and the

variance of the measurement equation, R, was the square of the standard error of

regression (SER) of the OLS equation.

To obtain λ and Q, we initially estimated the concerned equation in recursive

manner, with allowing the coefficients ßt to evolve recursively, with ß0, being estimated

from the first m data observations where m was the number of coefficients in the

equation; ß1 from the first m+1 observations, and so on. We then regressed the

coefficients values ßt on their corresponding lagged values, ßt-1, and the state transition

36

matrix by using these estimated auto-regressive parameters along its diagonal12; while

the covariance matrix of the transition equation (Q) was formed by using the standard

errors of each of these estimated coefficients along its principal diagonal.

7.1 Modelling Inflation Using the Kalman Filter

For modelling inflation initially we have estimated a long run and ECM

equation for the inflation rate using a sample of 1985-86 to 1999-2000 on the same line as

described in 3.6.2. Thereafter, following the procedure as described above, we obtained

time-varying parameters for the ECM equation.

Long-run equationLog Wpi = 10.28 +1.00 Log M3 – 1.37 Log Yr –0.025 Der –0.068 Dwp20

The postulated relationship for retrieving TVPs for the price equation:

ΔLogWpi =α0+ α1 Δ Log M3 + α2 Δ Log Yr + α3 ΔlogWpifa+ α4 Dwpi20+ α5 Log Wpie+ α6 Reswpi(-1)

Where the TVPS of the equation, i.e. α0, α1, α2, α3, α4, α5 and α6, need to be estimated

using Kalman filter. The following estimators for the five unknown parameters were

used to model the TVPs of the ECM oriented price equation.

The initial state vector ß0 was given by:

ß0 = ( -0.015 0.429 -0.248 0.288 0.128 -0.330) '

The initial covariance matrix of the state vector was:

Σ0 (diagonal) = (0.0037 0.109 0.126 0.022 0.0298 0.0567)

12 Coefficients of the transition equation were restricted to 1 if they showed wide deviation from 1.

37

which were the variances of these parameter estimates.

The variance of the measurement equation, which was the square of the SER, worked

out to be R = 0.000434.

The coefficient matrix in the transition equation (T) was:

T (diagonal) = ( -0.12 0.89 0.85 0.85 0.60 0.86)

In view of wider deviation of the transition coefficients from 1, they were restricted to 1.

Thus the transition coefficient matrix used was:

T (diagonal) = ( 1 1 1 1 1 1)

The variance of the transition equation (Q) was given by:

Q(diagonal) = ( 0.1531 0.0160 0.0047 0.0554 0.0063 0.0065)

Based upon the above estimates, and using the Kalman filter, we obtained an evolving

set of parameters for the period 1987-88 to 2001-2002 which have been used to obtain

dynamically simulated values for inflation (and growth) . Again the above equation was

solved for the period 2000-01 to 2001-02 only and the Kalman filter estimators were

obtained for obtaining predictions on inflation (and growth) for the years 2002-03 and

2003-04.

7.2 Modelling Growth Using the Kalman Filter

For modeling growth, we followed the similar procedure as for inflation rate, and

initially we estimated a long-run relationship and thereby ECM equation (as described

in 3.2.1) and thereafter we obtained the time-varying parameters for the ECM equation.

Long-run equation Log Yr =2.19+0.77709 Log Kr + 0.045927 Der

The postulated relationship for ECM eq. was:

38

LogYr= α0 + α1 ΔLogKr-1 + α2 Rif + α3 Log (Bccs/Wpi + α4 Resyr(-1).

The initial state vector ß0 was given by:

ß0 = ( 0.023 0.158 0.099 0.168 -0.56 ) '

The initial covariance matrix of the state vector was:

Σ0 (diagonal) = (0.00109 0.1636 0.00099 0.00274 0.0263 )

which were the variances of these parameter estimates. The variance of the

measurement equation, which was the square of the SER, worked out to be

R = 0.0000668942.

The coefficient matrix in the transition equation (T) was: T (diagonal) = ( 0.862 0.89 0.998 0.998 0.986)

In view of wider deviation of the first two elements from 1, these two coefficients were

restricted to 1. Thus, the transition coefficient matrix used was:

T (diagonal) = ( 1 1 0.998 0.998 0.986 )

The variance of the transition equation (Q) was given by:

Q(diagonal) = (0.0252 0.01011 0.000245 0.002523 0.0003022 )

Based upon the above estimates, and using the Kalman filter, we obtained an

evolving set of parameters for the period 1987-88 to 2001-2002 which have been used to

obtain dynamically simulated values for growth (and inflation). Again the above

equation was solved for the period 2000-01 to 2001-02 and the Kalman filter estimators

were obtained.

39

7.3 Simulated Values for Inflation and Growth Based on the Time-Varying Parameters

Dynamically simulated values for inflation and growth for the sample period from

1987-88 to 2001-02, using Time Varying Parameters, are as reported in Table-10.

Table-10 Kalman Filter Based Simulated Values on Growth and Inflation Rate

(Percent)

Year Growth(gs) Inflatin(Πs)

1987-88 5.40 7.32

1988-89 9.82 9.38

1989-90 7.68 5.25

1990-91 3.72 7.49

1991-92 2.51 12.59

1992-93 5.32 10.01

1993-94 5.42 8.20

1994-95 7.45 12.00

1995-96 6.83 6.87

1996-97 5.32 6.93

1997-98 6.12 5.43

1998-99 6.15 6.68

1999-00 5.99 3.87

2000-01 6.50 6.06

2001-02 4.44 3.04

To evaluate the overall performance of the above procedure, we have obtained

simple regression equations in respect of actual and simulated growth values and like-

wise of actual and simulated values of inflation rate.

ga = 0.52 +0.88 gs R2(adj)=0.58 SEE=1.26 Mean =5.72t (0.43) (4.50)

40

Πa =0.42 +0.93 Πs R2( adj) =0.77 SEE=1.36 Mean =7.34 t (0.39) (6.92)

The performance of the above equations is an improvement over the corresponding equations for ECM.

7.4 Kalman Filter Based Prediction on Growth and Inflation for 2002-03

Before using the above procedure for obtaining forecasts for 2003-04, we obtained

the predicted values for the year 2002-03 in order to validate the model. For this

purpose, we obtained the time varying parameters for the year 2001-02 and using those

parameters we obtained the predicted values of growth and inflation for the year 2002-

03 as given in Table-11.

Table-11

Actual and Kalman Filter Based Predicted Values (Percent)Variable Actual PredictedGrowth in output(g) 4.4 4.8Inflation rate (Π) 3.4 3.9

Results of Table-11 reflect that the Kalman filter based predicted values for growth and

inflation rate for the year 2002-03 are much closer to their actual values.

7.5 Kalman Filter Based Predictions on Growth and Inflation for 2003-04

Time-varying parameters obtained for the year 2001-02 have been used to obtain

the forecasts for the year 2003-04 as given in Table-12.

Table-12 Kalman Filter Based Predicted Values for 2003-04

(Percent)Variable ForecastGrowth in output 7.3

Inflation rate 5.6

41

As per above the forecasts for inflation and growth for the year 2003-04 are placed

much above than as obtained using ECM based system of equations.

7.6 ECM Versus the Kalman Filter- Concluding Remarks

ECM based predictions for growth and inflation for the year 2002-03 were

underestimate. As against this, their Kalman filter based predictions were very close to

the actual values. However, for the year 2003-04, forecasts appears to be reasonable as

per ECM but a little overestimated as per the Kalman filter. Accordingly, forecasts for

more time points would be worked out to make some judgment about the comparative

performance of these procedures for the Indian economy. Assuming that actual values

of inflation and growth in 2003-04 would be a mid-way of these two, their forecasts are

placed around 4.9 percent and 6.8 percent, respectively.

8 Limitations of the Model and Agenda for Further Research

The model is very aggregative in nature and needs to be further expanded to take

into account other aspects of the economy. Real sector, in terms of output and

investment functions, at the sectoral level, need to be incorporated in the model.

Similarly, monetary sector should include other important variables viz., reserve money,

aggregate deposits and cash reserve ratio. Fiscal sector covers only fiscal operations of

the Central government, which could be enlarged to cover fiscal operations of the

Central and state government together. Coverage of the external sector also needs to be

expanded in order to cover capital account and other components of the current account

as endogenous variables. Equations relating to investment and price level are not

theoretically fully appropriate and therefore need further empirical work. Similarly,

forecasts presented are based on a part of the model and therefore forecasts for all the

endogenous variables based on full model needs to be attempted.

42

In respect of technical aspects, there appears to two major limitations, which need

to be addressed before model is used for policy or forecasting purpose. Firstly, to test

the stationarity of the residual series of the long-run relationships, DF test has been

used, results of which may not always be fully robust. There may be a need to employ

other tests as well. Similarly, for verifying the exogeneity of the independent variables,

more rigorous test like vector error correction model (VECM) needs to be employed.

9 Summary and Broad Conclusions of the Study

In this paper, a small model for the Indian economy has been developed with a

view to conduct certain policy simulation experiments and also to obtain predictions on

growth and inflation using it. Individual equations of the model were estimated in error

correction mechanism. Collective performance of the model was evaluated using static

and dynamic simulations. Based on two equations of output and prices, as estimated

in the model, their forecasts for 2003-04 were obtained. Their (real output and inflation)

forecasts were obtained using Time Varying Parameters also estimated using the

Kalman filter method.

Estimates of the individual equations, as obtained in this model, reflect that

availability of (real) bank credit is important factor affecting output performance. Impact

of rainfall is also important and asymmetric - a shortage of rainfall is more detrimental

to growth than excessive rainfall. Impact of price rise in food articles, on the overall

prices, turned out to be stronger than energy prices. Investment is sensitive to (real)

interest rate, however, its impact is mild as reflected through its ‘t’ value in the

investment equation.

43

A rise in government development expenditure, provided entirely used for capital

formation in the public sector, is likely to improve growth prospects without any ‘add-

up’ of inflationary pressure. As against this, any monetary expansionary policy by way

of increasing bank credit, autonomously by the RBI, is likely to invoke inflationary

pressure without any ‘add-up’ in the real output. A fall in the Bank rate is likely to

stimulate growth and may even cause decline in inflation rate.

Assuming normal rainfall during 2003-04, ECM based predictions for growth and

inflation are placed around 6.2 percent and 4.1 percent, respectively. As against this,

their (growth and inflation) Kalman filter based predictions are placed around 7.3 and

5.6, respectively. Assuming that actual growth and inflation would be a mid-way of

these two forecasts, growth in real output and inflation rate for the year 2003-04 are

likely to be around 6.8 percent and 4.9 percent, respectively

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Annex-1List of Endogenous Variables

Sr.No. Variable Description Unit

1 Yr Gross domestic product at factor cost Amount in Rs at 1993-94 prices

2 Yn Gross domestic product at factor cost Amount in Rs at current prices

3 Kr Capital stock(cumulated investment from 1970-71 onwards)

Amount in Rs at 1993-94 prices

4 Ir Investment during the year Amount in Rs at 1993-94 prices

5 In Investment during the year Amount in Rs at current prices

6 Ipn Private investment during the year Amount in Rs at current prices

45

7 Ign Public sector investment during the year Amount in Rs at current prices

8 Rr Revenue receipts of the Central government Amount in Rs at current prices

9 Nde Non-development expenditure of the Central government

Amount in Rs at current prices

10 Bcg Banks’ credit to the government Amount in Rs at current prices

11 M3 Broad money Amount in Rs at current prices

12 Wpi Whole sale price index Index, 1993-94=100

13 Ydf Deflator for nominal income Index, 1993-94=100

14 Idf Deflator for nominal investment Index, 1993-94=100

15 Impg Imports of goods Amount in Rs at current prices

16 Expg Exports of goods Amount in Rs at current prices

17Nfea Net foreign exchange assets of the banking sector Amount in Rs at

current prices

18 Plr Prime lending rate(advance rate of the State Bank of India)

Rate

List of Exogenous VariablesSr. No Variable Description Unit1 Br Bank rate Rate2 Pe Expected inflation Rate3 Gde Government development expenditure Amount in Rs at

current prices 4 Rif Rainfall index Index5 Bccs Banks’ credit to the commercial sector Amount in Rs at current

prices6 OM3 Other components of broad money suplly(=M3—Bcg-

Bccs-Nfea)Amount in Rs at current price

7 Eavg Exchange rate Rs per USA $8 Wpic Price index for industrial countries Index. 1997=100 9 Gdpic Output index for industrial countries Index, 1997=10010 Cap Capital account balances Amount in Rs at current

prices11 Eom Balancing factor between BOP and monetary identity Amount in Rs at current

prices12 Imord Effective custom duty rate Rate13 Ninvr Net invisible receipts Amount in Rs at current

price14 Wpie Wholesale price index for energy price Index, 1993-94=10015 Wpifa Wholesale price index for food articles Index, 1993-94=10016 Mp Unit value index of imports Index,17 Otrc Other receipts of the Central government Amount in Rs at current

prices18 Der Dummy for pre-reform period ‘1’ for the period 1985-

86 to 1989-90 and ‘0’ for rest of the period.

19 Dwp20 Dummy for Wpi ‘1’ for 1999-00 and 20001-02 and ‘0’ for rest of the period

20 Time Time trend 1,2,…….,17

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Annex-2 Before estimating a long-run relationship it may be useful to verify the exogeneity of the independent

variables. The appropriate methodology involves an estimation of cointegrating vector at the first stage and

estimation of a vector autoregessive model including lagged values of the error term obtained from the long

run relationship as one of the explanatory variable. In brief, it involves estimation of a vector error correction

model (VECM). However, in this case a simple procedure has been adopted. Instead of estimating residuals

through the cointegrating vector, residuals as obtained form the long-run relationship, using OLS, have been

used and these results are discussed as hereafter.

Test for exogeneity:

Between Yr and Kr:

dlyr = 0.01+0.19 dlyr(-1)+0.13dlyr(-2)+1.36dlkr(-1)-1.04dlkr(-2)-1.02resyr(-1) t: ( 0.29) (1.03) (0.76) (1.27) (1.03) (4.73)

dlkrr = 0.004+0.04 dlyr(-1)+0.01dlyr(-2)+0.77dlkr(-1)+0.11dlkr(-2)-0.10resyr(-1) t: ( 0.31) (0.72) (0.35) (2.42) (0.35) (1.68)

Between Ign and Gde:

dlign = 0.13-0.34dlign(-1)-0.21dlign(-2)+0.19dlgde(-1)+0.04dlgde(-2) –0.98resign(-1) t (2.64) (0.96) (0.68) (0.64) (0.18) (1.48)

dlgde = 0.20-0.62dlign(-1)-0.58dlign(-2)+0.22dlgde(-1)+0.004dlgde(-2) +0.48resign(-1) t (3.43) (1.48) (1.57) (0.62) (0.01) (1.16)

Between Ipn and Yn In this case two equations have been estimated, firstly without any restrictions on the coefficient of Yn and in second case its (yn) coefficient is restricted to one.

Without Restriction: dlip =-0.28+0.44dipn(-1)+0.07dlipn(-2)+1.55dyn(-1)+1.34dlyn(-2) –2.09resipn(-1) t (1.57) (1.08) (0.32) (1.45) (0.90) (3.29)

dlyn= 0.03+0.04dlip(-1)-0.05dlipn(-2)+0.60dlyn-1)+0.164dlyn(-2) -0.088resipn(-1) t (0.55) (0.32) (0.70) (1.78) (0.41) (.41)

With restriction on Lyn (lipn=f(lyn,Time)

dlip =-0.32+0.43dipn(-1)-0.002dlipn(-2)+1.64dlyn(-1)+1.34dlyn(-2) –2.09resipn(-1) t ( 0.10) ( 2.10 ) (1.77) (1.71) (0.12) (3.45)

dlyn= 0.02+0.06dlip(-1)-0.04dlipn(-2)+0.0.58dlyn-1)+0.21dlyn(-2) -0.12resipn(-1) t (0.40) (0.48) (0.61) (1.76) (0.53) (0.59)

Between Rr and Yn

drr =-0.11-0.06dlrr(-1)-0.207dlrr(-2)+1.23dlyn(-1)-0.99dlyn(-2) –0.88resrr(-1) t (1.52) ( 0.34) ( 1.10) (2.79) (1.94) (1.59)

dlyn= 0.03-0.08dlrr(-1)+0.05dlrr(-2)+0.63dlyn-1)+0.12dlyn(-2) +0.073resrr(-1) t (0.61) (0.63) (0.37) (1.85) (0.31) (0.17)

Between NDE and Yr and WPI:

dlnde=0.16+0.10dlnde(-1)+0.06dlnde(-2)-0.16dlyr(-1)-0.66dlyr(-2)+0.13dlwpi(-1)-0.02dlwpi(-2) t (1.83) (0.25) (0.17) (0.23) (1.12) (0.26) (0.06)-0.78resnde(-1)

47

(1.70)

dlyr=0.06-0.11dlnde(-1)+0.12dlnde(-2)+0.15dlyr(-1)-0.16dlyr(-2)-0.15dlwpi(-1)+0.15dlwpi(-2) t (1.00) (0.41) (0.52) (0.34) (0.44) (0.43) (0.47)+0.08resnde(-1) (0.31)

dlwpi=0.01+0.14dlnde(-1)-0.25dlnde(-2)+0.066dlyr(-1)+0.40dlyr(-2)+0.57dlwpi(-1)+0.06dlwpi(-2) t (0.24) (0.51) (1.03) (0.13) (0.98) (1.55) (0.18)+0.328resnde(-1)(1.00)

Between Bccsr and Yrdlbccsr=0.10+0.15dlbccsr(-1)+0.36dlbccsr(-2)-0.47dlyr(-1)-0.87dlyr(-2)-1.07resbcscr(-1) t (3.36) (0.82) (1.96) (1.05) (2.04) ( 4.78) dlyr=0.07+0.03dlbccsr(-1)-0.05dlbccsr(-2)-0.11dlyr(-1)-0.18dlyr(-2)-0.27resbccsr(-1) t (3.37) (0.26) (0.40) (0.34) (0.61) ( 1.75)

Between exports and output:dlexpgr=0.06+0.56dlexpgr(-1)-0.096dlexpgr(-2)+1.79dlyr(-1)-1.95dlyr(-2)-0.67resexpgr(-1) t ( 0.74) (1.58) (0.23) (1.56) (1.81) ( 0.96) dlyr=0.07-0.67dlexpgr(-1)+0.06dlexpgr(-2)+0.06dlyr(-1)-0.48dlyr(-2)+0.13resexpgr(-1) t (2.80) (0.48) (0.23) (0.17) (1.36) ( 0.55) Between imports and output:dlimpgr=0.02+0.52dlimpgr(-1)+0.306dlimpgr(-2)-0.27lyr(-1)+0.12dlyr(-2)-1.77resimpgr(-1) t ( 0.27) (2.71) (1.76) (0.24) (0.10) ( 6.84) dlyr=0.07+0.09dlimpgr(-1)+0.08dlimpgr(-2)-0.186dlyr(-1)-0.22dlyr(-2)-0.14resexpgr(-1) t (2.73) (1.59) (1.52) (0.53) (0.63) ( 1.84) Between Idf and Wpi and Mp:dlidf= 0.01+0.57dlidf(-1)+0.19dlidf(-2)+0.37dlwpi(-1)-0.41dlwpi(-2)+0.10dlmp(-1)-0.07dlmp(-2) t (0.70) (1.63) (0.65) (1.43) (1.57) (1.58) (0.96) -0.05 residf(-1) (0.14) dlwpf= 0.01-0.32dlidf(-1)+0.64dlidf(-2)+0.55dlwpi(-1)-0.23dlwpi(-2)+0.05dlmp(-1)+0.07dlmp(-2) t (0.57) (0.76) (1.84) (1.77) (0.75) (0.61) (0.79) +0.29 residf(-1) (0.68)

dlmp= 0.01+2.44dlidf(-1)-1.05dlidf(-2)+004dlwpi(-1)-1.50dlwpi(-2)+0.32dlmp(-1)-0.50dlmp(-2) t (2.83) (4.34) (2.22) (0.08) (3.54) (2.94) (4.49) + 3.59residf(-1) (6.0)

Between Ydf and Wpi and Mp:

dlydf= 0.001+0.62lydf(-1)+0.57dlydf(-2)+0.01dlwpi(-1)-0.34dlwpi(-2)+00048dlmp(-1)-0.04dlmp(-2) t (0.04) (1.15) (0.76) (0.04) (0.55) (0.06) (0.54) - 0.13resydf(-1) (0.26)

dlwpi= 0.006+0.18dlydf(-1)+0.012dlydf(-2)+0.41dlwpi(-1)-0.21dlwpi(-2)-0.01dlmp(-1)+0.07dlmp(-2) t (0.17) (0.28) (0.014) (0.87) (0.29) (0.17) (0.89) + 0.68resydf(-1) (1.10)

dlmp=-0.013+0.44lydf(-1)+1.22dlydf(-2)+0.65dlwpi(-1)-1.30dlwpi(-2)+0.44dlmp(-1)-0.44dlmp(-2) t (0.11) (0.24 (0.47) (0.46) (0.61) (1.67) (1.90) + 0.89resydf(-1) (0.50)

Annex-3

48

DF test for the residuals of the long-run relationshipRelationship is estimated in the following form:

Δet =a + b et(-1)

‘ t ’ values of the coefficient of a and b of the various equations

Variable Value of ‘t’ for a( intercept term)

Value of ‘t’ for coefficient( b)

DW

Resyr -0.41 -3.57 1.88Reswpi -0.28 -2.88 1.75Resipn 0.01 -4.99 2.03Resign 0.10 -2.98 1.81Resrr 0.35 -3.77 1.89Resnde 0.74 -4.47 1.63Resydf 0.15 -2.48 1.55Residf 0.89 -5.36 1.26Resimpg 0.07 -3.88 1.99Resexpg 0.42 -3.11 1.98Resplr -0.25 -3.24 2.03Resbccs 0.16 -2.30 1.98

49