2012

19-Feb-12

Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Auto-Regression Technique (A Monetary

Model Approach)

IBS-2012

Submitted by:

Saurabh Trivedi –

10BSPHH011076

Vaibhav Joshi –

10BSPHH011052

Submitted to:

Prof. Trilochan Tripathy

Area Chair, Economics

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Table of Contents

List of Tables ............................................................................................................................. 3

1 Introduction ........................................................................................................................ 4

1.1 Objectives .................................................................................................................... 4

2 Theory and Literature Review ........................................................................................... 4

2.1 Types of Exchange Rate System ................................................................................. 4

Fixed Exchange Rate System: ..................................................................................... 4

Flexible Exchange rate System: .................................................................................. 5

Hybrid exchange rate systems: .................................................................................... 5

2.2 Theories of Exchange Rate Determination ................................................................. 5

Relative Purchasing Power Parity Model (RPPP) ............................................................. 5

International Fishers Effect(IFE) ....................................................................................... 7

Balance of Payment Model (BOP) .................................................................................... 7

Monetary Model................................................................................................................. 7

2.3 Theory: Forward Premia ............................................................................................. 8

2.4 Theory: Capital Flows ................................................................................................. 8

2.5 Theory: Central Bank Intervention ............................................................................. 9

2.6 Theory: Vector Auto regression Model ...................................................................... 9

3 Modeling and Forecasting the Exchange Rate................................................................... 9

3.1 Test of Non-Stationarity ............................................................................................ 11

3.2 Estimation of Model using VAR ............................................................................... 12

3.3 Forecasting Using the Above Developed Model ...................................................... 17

4 Concluding Observations ................................................................................................. 18

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4.1 Findings ..................................................................................................................... 18

4.2 Limitations ................................................................................................................ 18

5 Annexure .......................................................................................................................... 19

6 References ........................................................................................................................ 20

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List of Tables

Table 3-1: Expected Sign of Variables on Dependent Variable: lnex ..................................... 10

Table 3-2: Unit-Root Test (with constant and trend) ............................................................... 11

Table 3-3 VAR Lag Order Selection Criteria .......................................................................... 12

Table 3-4: VAR Estimation Output ......................................................................................... 15

Table 3-5: Estimation for System Equations of VAR ............................................................. 16

Table 3-6:Out of Sample Forecasting(Actual vs VAR) ........................................................... 17

Table 5-1: Data Definition and Sources................................................................................... 19

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1 Introduction

The exchange rate is that key financial variable which affects the decisions made by all the

parties involved in the exchange market which are importers, exporters, bankers, exchange

investors, businesses, financial institutions, policy makers, and tourists in all the markets.

The fluctuations in the exchange rate affect the value of international reserves, currency

value of debt payment, value of international investment portfolios, competitiveness of

exports and imports and cost of tourists in terms of their currency. Hence the movement in

exchange rates have important implications for the economic cycle of the economy as well

as capital flows and trade. Therefore, it demands timely forecasts which ultimately provide

valuable information to the decision makers as well as policy makers. The study covers

two main topics: first, various aspects of economic policy with respect to the exchange

rate, and second, modeling and forecasting the exchange rate.

1.1 Objectives

The project involves the development of an alternate model which will be used for

Exchange Rate forecasting. The model will follow the theory of monetary models while

incorporating some extra factors. The estimation technique used for the model

development in the project is Vector Auto regression (VAR).

This study concentrates on the post Jun’05 period and provides insights into forecasting

exchange rates for developing countries. The forecasting models are estimated using the

monthly data from June’05 to Dec’ 2010.

Then the out-of-sample forecasting will be done using the above developed model for the

period of next one year i.e. from Jan’2011 to Dec’2011.

2 Theory and Literature Review

2.1 Types of Exchange Rate System

Different countries follow different sets of exchange rate systems. A exchange rate system is

critical in determining the purchasing power of one currency with regard to the other

currency.

Some of the types of exchange rate systems are:

Fixed Exchange Rate System: Under this exchange rate system the government

intervenes and tries to keep the value of their currency constant to one another. This is

also known as pegged exchanged rate system. The country can peg its currency to a

precious metal such as gold, basket of other currency or to the value of some other stable

currency. To maintain the steady exchange rate, the central bank buys and sells currency

as the case may be. This buying and selling activity is performed using the foreign

exchange that a country has. When there is an excess demand of the foreign currency the

central bank would increase the supply by selling the foreign currency and buying the

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home currency in order to maintain the fixed rate and in the case of excess of supply the

case would be reversed.

Flexible Exchange rate System: As the name suggests under this type of exchange rate

system the exchange rates are not stable. The Exchange rates under this system are

defined by demand and supply factors pertaining to the currency that are prevailing in the

economy.

Hybrid exchange rate systems: This is known as a Hybrid system as it combines the

features of both fixed and floating exchange rate systems. This is done to allow the

currency to fluctuate to a certain extent and not beyond it. Some of the examples under

this system are:

a) Crawling pegs: Under this system the currency that follows a fixed exchange rate system

is allowed to fluctuate within a certain range referred to as bands. These bands are revised

depending upon market factors such as inflation, budget deficit. This gradual change in

the band helps in avoiding the shock of a sudden devaluation

b) Dollarization/Euroization: Under this system a group of countries give up their domestic

currency and take up either Dollar or Euro as their currency. All these countries share a

common currency and any new country joining this system would also follow the same

currency. Here although they are fixing their currency as USD/EURO is still a mixture of

fixed and floating as the value of USD/ EURO changes on a daily basis.

2.2 Theories of Exchange Rate Determination

In the international finance literature, various theoretical models are available to analyze

exchange rate determination and behavior. Most of the studies on exchange rate models prior

to the 1970s were based on the fixed price assumption. With the advent of the floating

exchange rate regime amongst major industrialized countries in the early 1970s, an important

advance was made with the development of the monetary approach to exchange rate

determination.

With liberalization and development of foreign exchange and assets markets, variables such

as capital flows, and forward premium have also became important in determining exchange

rates. Furthermore, with the growing development of foreign exchange markets and a rise in

the trading volume in these markets, the micro level dynamics in foreign exchange markets

increasingly became important in determining exchange rates.

Relative Purchasing Power Parity Model (RPPP)

Purchasing power parity model indicates that the price levels in different countries determine

the exchange rates of these countries. This is based on the assumption of LAW of One Price.

According to this law the price of a commodity needs to be same across the world. If this was

not the case arbitrageurs would take advantage of this situation and drive the prices towards

equality. This states that arbitrage forces will lead to the equalization of goods prices

internationally once the prices are measured in the same currency. PPP theory provided a

point of reference for the long-run exchange rate in many of the modern exchange rate

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theories. It was observed initially that there were deviations from the PPP in short-run, but in

the long-run, PPP holds in equilibrium. However, many of the recent studies like Jacobson,

Lyhagen, Larssonand Nessen (2002) find deviations from PPP even in the long-run. The

reasons for the failure of the PPP have been attributed to heterogeneity in the baskets of

goods considered for construction of price indices in various countries, the presence of

transportation cost, the imperfect competition in the goods market, and the increase in the

volume of global capital flows during the last few decades which led to sharp deviation from

PPP.

Assumptions made by the Purchasing power parity model:

Free Movement of Goods

No Transportation Cost

No Transaction Cost

No Tariffs

There are two forms of Purchasing Power Parity (PPP):

a) Absolute Form Of PPP: This states that if law of one price were to hold good, the price of

the commodity would be determined by the following formula,

P (A) = S (A/B)*P (B)

Where P (A) and P (B) are price of a commodity in Country A and B

S (A/B) refers to the current exchange rate.

b) Relative Form of PPP: The relative purchasing power parity states that the currency’s

exchange rate depreciates over time at a rate equal to the difference in the inflation rates

prevailing in the two countries.

The formula determining the Relative Purchase power parity is

E = S*(1+P (D))/ (1+P (F))

Where S is the exchange rate

P (D) is the inflation in the home country

P (F) is the inflation in foreign currency

Reasons for PPP not holding Good:

1. Constraints on movement of commodities: The assumption that free movement of goods

is possible is not the case in reality. There involves certain costs such as transportation

which effect the prices. Also PPP cannot be used for non – traded goods.

2. Price Index: Different countries use different price basket of goods to compute their price

index as the usage and taste of both the countries are different. Also the base years used to

compute two different indexes will not be the same.

3. Two way of effect: One of the factors that affect the exchange rates is Inflation, but it is

also noticed that at times the inflation rate is affected by the exchange rate. One should

consider this two way effect. Also part from the inflation rate there are other factors that

affect the economy.

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International Fishers Effect(IFE)

The International Fisher Effect states that the real interest rates are equal across countries.

Using this, it states a hypothesis that at the difference in the nominal interest rates between

two countries determines the nominal exchange rate between the two countries. Lower the

nominal rate the better as it would indicate lesser inflation in the economy.

(1+Rf) / (1+Pf) = (1+Rd) / (1+Pd)

It means the 1+Nominal interest rate / 1+ inflation rate = real Interest rate.

Reason for failure of International Fishers Effect

Transaction Cost

Political Risk

Taxes

Liquidity Preferences

Capital control

Balance of Payment Model (BOP)

According to this theory, when there is free market situation, the exchange rates are

determined by the market forces i.e. demand for and supply of the foreign exchange. This

theory is based on simple market mechanism in which the price of any commodity is

determined.

Under this theory the external values of domestic currency depends on the demand for and

the supply of the currency. The Nation's overall Balance of Payments (BOP) can either be in

surplus or in deficits. When the nation's BOP is in deficits, the exchange rate depreciates, and

when BOP is in surplus, there will be healthy foreign exchange reserves, leading to the

appreciation of the home currency. Under deficits in the BOP, residents of a country in

question demands foreign currency, excessively leading to excess demand for foreign

currency in terms of home currency. However, under surplus BOP situation there is an excess

demand for home currency from foreigners than the actual supply of home currency. Due to

this price of home currency in terms of concerned foreign currency rises, i.e. exchange rate

improves or appreciates. Thus according to this theory the exchange rate is basically

determined by the demand for and the supply of foreign currency in concerned nations.

In our project we have taken four factors that determine exchange rate in BOP model:

Real National Income

Inflation

Exports

Current Account Deficit

Monetary Model

The failure of PPP models gave way to Monetary Models which took into account the

possibility of capital/bond market arbitrage apart from goods market arbitrage assumed in the

PPP theory. In the monetary models, it is the money supply in relation to money demand in

both home and foreign country, which determine the exchange rate. Model assume stable

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domestic and foreign money demand functions, perfect capital mobility, and uncovered

interest parity. In addition to flexible prices, the model also assumes uncovered interest

parity, continuous purchasing power parity and the existence of stable money demand

functions for the domestic and foreign economies. While the assumptions of the monetary

model rarely hold in the real world (especially in the short run), this model shows

theoretically well-grounded relationship between exchange rate, prices, money, real incomes,

and interest rates.

The basic monetary model can be represented the following way:

s = (m - m*) + α1(y - y *) + α2 (i - i*) + error (1)

Where, all small letters denote logarithms. Here‘s’ is nominal exchange rate, m is money

supply, y denotes real income (or industrial production, or real output), i is nominal interest

rate. Asterisk denotes a foreign country.

In this paper, apart from the above three factors in the monetary model, some more factors

like inflation differential have also been considered which are mentioned as below:

2.3 Theory: Forward Premia1

The forward premium is measured by the difference between forward and spot exchange rate

and can provide about future exchange rates. As per covered interest parity, the interest

differential between two countries is equal to the premium on the forward contracts. Hence, if

domestic interest rates rise, the forward premium on foreign currency will rise and ultimately

the foreign currency is expected to appreciate. The exchange rate defined as the price of

foreign currency in domestic currency and therefore, the forward premium is expected to be

related positively.

2.4 Theory: Capital Flows

Capital flows have become an important factor in determining exchange rate behavior with

the increase in liberalization and opening up of capital accounts at the world level. The

relationship between exchange rate and capital flows said to be negative (when exchange rate

is defined as the price of foreign currency in domestic currency). The reason for this is that

capital inflows imply purchase of domestic assets by foreigners and capital outflows as

purchase of foreign assets by residents. Since the exchange rate is determined by thee

demand and supply for domestic and foreign assets, the purchase of foreign assets drives up

the price of foreign currency. In the same way purchase of domestic assets drives up the price

of domestic currency. Thus, an increase in capital inflows will appreciate the domestic

currency when there is no government intervention in the foreign exchange market or if there

1Mathematically, forward rate equation can be expressed as:

( ) ( )

( ) ; where F is forward rate at time t; i is

domestic interest rate; i* stands for interestrates on foreign currency; and S is the spot rate, i.e. foreign currencies per unit of

domestic currency

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is persistent sterilized intervention. Where there is unsterilized government intervention the

potential of capital inflows to influence exchange rates decreases to a great extent.

2.5 Theory: Central Bank Intervention

Intervention by the central bank in the foreign exchange market also plays an important role

in influencing exchange rates in countries that have managed floating regime. With the

growing importance of capital flows in determining exchange rate movements in most

emerging market economies, intervention in foreign exchange markets by central banks has

become necessary from time to time to contain volatility in foreign exchange markets. The

motive of central bank intervention may be to align the current movement of exchange rates

with the long-run equilibrium value of exchange rates; to maintain export competitiveness; to

reduce volatility and to protect the currency from speculative attacks.

2.6 Theory: Vector Auto regression Model

In this study, multivariate forecasting models i.e., Vector Autoregressive (VAR) have been

used. A Vector Autoregressive (VAR) model does not require specification of the projected

values of the exogenous variables as in a simultaneous equations model. It uses regularities in

the historical data on the forecasted variables. Economic theory only selects the economic

variables to include in the model. An unrestricted VAR model (Sims 1980) is written as

follows:

,

Where y: (nx1) vector of variables being forecast; A (L): (nxn) polynomialmatrix in the back-

shift operator L with lag length p, i.e. A (L) = A1L +A2L2+...........+ApL

p; C: (nx1) vector of

constant terms; and ε: (nx1) vector of white noise error terms.

The model uses the same lag length for all variables. A serious drawback of the VAR model,

however, is that over-parameterization produces multicollinearity and loss of degrees of

freedom that can lead to inefficient estimates and large out-of-sample forecasting errors. A

possible solution is to exclude insignificant variables and/or lags based on statistical tests.

3 Modeling and Forecasting the Exchange Rate

The models discussed earlier will be estimated and evaluated in this section. The alternative

models are estimated from Jun’ 2005 through Dec’2010. The out-of-sample forecasting

performance of the alternative model is evaluated over January 2011 to Dec’ 2011.Figure 1

shows the movements in the Re/$ rate in the period under study:

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Figure 3-1 Exchange Rate - Re/$

MODEL:Monetary Model+ other variables (inflation differential + trade balance

differential + forward premium + capital inflows + Intervention);

As discussed earlier, monetary model consists of 3 factors namely Interest Rate differential,

Real Output differential between India and USA and Difference between Money Supply in

India (M3) and that in USA (M2).

Variables Expected Signs

infldiff +

intdiff +/-

lnMsupp +

fwdprm +

cap

TrdDiff -

Intrv +

Table 3-1: Expected Sign of Variables on Dependent Variable: lnex

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The notation is as follows:

lnex : Log of exchange rate of India (Rs./$)

infldiff : Difference between inflation rate of India and US

intdiff : Difference between Indian (domestic) and US (foreign)Treasury bill

Rate

lnMsupp : Difference between log of Indian and US money supply

fwdprm : 3-month forward premia

cap : Capital inflow in India (in USD)

TrdDiff : Difference between trade balance of India and US

Intrv : Government intervention in open market

Data definitions and sources are given in Annexure 1.

3.1 Test of Non-Stationarity The first step in the estimation of the alternative models is to test for non-stationarity. For the

test of non-stationarity 2 tests namely Augmented Dickey-Fuller (ADF) test and Phillips-

Perron (PP) Test have been used. Both these test have the null-hypothesis as:

H0 : The Series has a unit root.

Variables ADF Pr(t) PP Pr(t)

Lnex -1.72634 0.7301 -1.4975 0.8223

infldiff -2.2068 0.4774 -1.796402 0.6957

intdiff -2.503550 0.3258 -2.557650 0.3006

lnMsupp -1.282109 0.8849 -1.360923 0.8647

fwdprm -3.365770 0.0636 -3.491901 0.0473

Cap -9.737583 0.0000 -9.755744 0.0000

TrdDiff -1.059050 0.9287 -1.461773 0.8342

Intrv -6.235444 0.0000 -6.151841 0.0000

Table 3-2: Unit-Root Test (with constant and trend)

Table 3.2 reports the 2 tests with constant and trend. From the table, it is clear that apart from

Capital flow (Cap) and intervention (Intrv), all other variables are non-stationary. Testing for

differences of each variable confirms that all the variables are integrated of order one or two.

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3.2 Estimation of Model using VAR

The estimation period is taken from Jun’2005 to Dec’2010 (monthly).

Step 1: The first step in the VAR estimation is to select the lag order for the model. The VAR

lag order selection criteria are shown as below:

VAR Lag Order Selection Criteria Endogenous variables: LNEX CAP FWDPRM INFLDIFF INTDIFF INTRV LNMSUPP TRDDIFF

Exogenous variables: C

Date: 02/19/12 Time: 06:20

Sample: 2005M06 2010M12

Included observations: 50 Lag LogL LR FPE AIC SC HQ 0 -3382.733 NA 1.10e+49 135.6293 135.9353 135.7458

1 -3048.055 548.8720 2.26e+44 124.8022 127.5555* 125.8507

2 -2950.857 128.3020 7.28e+43 123.4743 128.6750 125.4547

3 -2858.099 92.75843 4.05e+43 122.3239 129.9720 125.2364

4 -2699.351 107.9485* 3.48e+42* 118.5340* 128.6295 122.3784* * indicates lag order selected by the criterion

LR: sequential modified LR test statistic (each test at 5% level)

FPE: Final prediction error

AIC: Akaike information criterion

SC: Schwarz information criterion

HQ: Hannan-Quinn information criterion

Table 3-3 VAR Lag Order Selection Criteria

As clear from the above table 3-3, the majority of the statistics (4 out of 5) are favoring the

lag order of 4. Hence, our lag order will be 4 for the VAR estimation.

Step 2: Now, with the lag order of 4, the Vector Autoregression will be estimated. The result

is shown as below:

Vector Autoregression Estimates

Date: 02/19/12 Time: 06:34

Sample (adjusted): 2005M10 2010M12

Included observations: 50 after adjustments

Standard errors in ( ) & t-statistics in [ ] LNEX CAP FWDPRM INFLDIFF INTDIFF INTRV LNMSUPP TRDDIFF LNEX(-1) 1.061484 -2.39E+11 0.260510 6.881240 -0.805317 7.95E+10 -0.568095 4.42E+10

(0.36880) (1.0E+11) (0.18681) (5.26909) (3.42793) (2.8E+10) (0.36258) (6.8E+10)

[ 2.87819] [-2.38180] [ 1.39450] [ 1.30596] [-0.23493] [ 2.86091] [-1.56680] [ 0.65413]

LNEX(-2) 0.120278 1.59E+11 -0.270281 1.476281 7.448523 -2.83E+10 -0.328848 -5.25E+10

(0.50614) (1.4E+11) (0.25638) (7.23120) (4.70443) (3.8E+10) (0.49760) (9.3E+10)

[ 0.23764] [ 1.15415] [-1.05423] [ 0.20415] [ 1.58330] [-0.74178] [-0.66086] [-0.56630]

LNEX(-3) -0.846649 8.52E+09 -0.083699 -0.233765 -7.167314 -7.52E+10 0.688912 1.75E+10

(0.51443) (1.4E+11) (0.26058) (7.34963) (4.78148) (3.9E+10) (0.50575) (9.4E+10)

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[-1.64581] [ 0.06090] [-0.32121] [-0.03181] [-1.49897] [-1.94026] [ 1.36216] [ 0.18576]

LNEX(-4) 0.649526 1.11E+09 -0.001095 1.140408 4.262848 2.97E+10 0.057423 -7.69E+09

(0.38883) (1.1E+11) (0.19696) (5.55520) (3.61407) (2.9E+10) (0.38227) (7.1E+10)

[ 1.67047] [ 0.01053] [-0.00556] [ 0.20529] [ 1.17952] [ 1.01252] [ 0.15022] [-0.10794]

CAP(-1) 2.77E-13 -0.557463 -2.22E-13 -6.10E-12 -7.62E-12 -0.076635 -2.80E-13 0.004118

(8.1E-13) (0.22101) (4.1E-13) (1.2E-11) (7.6E-12) (0.06120) (8.0E-13) (0.14894)

[ 0.34135] [-2.52230] [-0.53909] [-0.52530] [-1.00944] [-1.25219] [-0.35093] [ 0.02765]

CAP(-2) 1.09E-12 -1.054084 3.41E-13 -1.09E-11 7.76E-12 0.075095 -2.14E-12 0.123298

(9.9E-13) (0.26985) (5.0E-13) (1.4E-11) (9.2E-12) (0.07472) (9.8E-13) (0.18185)

[ 1.09899] [-3.90616] [ 0.67869] [-0.76762] [ 0.84147] [ 1.00497] [-2.19284] [ 0.67803]

CAP(-3) -3.38E-12 0.412189 9.55E-13 -2.11E-11 6.13E-12 -0.153197 4.54E-12 0.098225

(1.4E-12) (0.37103) (6.9E-13) (1.9E-11) (1.3E-11) (0.10274) (1.3E-12) (0.25003)

[-2.47608] [ 1.11093] [ 1.38186] [-1.08363] [ 0.48350] [-1.49109] [ 3.38777] [ 0.39285]

CAP(-4) 1.79E-13 0.265411 5.79E-13 -6.36E-11 5.86E-12 -0.205617 8.25E-13 0.271187

(1.6E-12) (0.44394) (8.3E-13) (2.3E-11) (1.5E-11) (0.12293) (1.6E-12) (0.29916)

[ 0.10941] [ 0.59786] [ 0.70001] [-2.72903] [ 0.38640] [-1.67264] [ 0.51426] [ 0.90650]

FWDPRM(-1) -0.019583 -3.04E+11 0.602767 -5.236294 -9.238421 9.33E+10 -0.350114 9.74E+10

(0.46602) (1.3E+11) (0.23605) (6.65798) (4.33151) (3.5E+10) (0.45816) (8.5E+10)

[-0.04202] [-2.39686] [ 2.55351] [-0.78647] [-2.13284] [ 2.65719] [-0.76418] [ 1.13993]

FWDPRM(-2) 0.728143 -1.20E+10 0.144353 0.194391 13.72395 1.05E+11 -0.654209 -6.85E+10

(0.65149) (1.8E+11) (0.33000) (9.30785) (6.05544) (4.9E+10) (0.64050) (1.2E+11)

[ 1.11766] [-0.06779] [ 0.43743] [ 0.02088] [ 2.26638] [ 2.13149] [-1.02140] [-0.57362]

FWDPRM(-3) -0.912584 8.68E+10 -0.007981 -1.531841 -5.754637 -6.50E+10 0.483617 8.10E+10

(0.62466) (1.7E+11) (0.31641) (8.92447) (5.80603) (4.7E+10) (0.61412) (1.1E+11)

[-1.46094] [ 0.51095] [-0.02522] [-0.17165] [-0.99115] [-1.38213] [ 0.78750] [ 0.70770]

FWDPRM(-4) 0.280324 -6.70E+10 -0.155990 4.968926 -0.620142 -1.06E+10 -0.238529 -7.40E+10

(0.39714) (1.1E+11) (0.20116) (5.67389) (3.69129) (3.0E+10) (0.39044) (7.3E+10)

[ 0.70586] [-0.62035] [-0.77544] [ 0.87575] [-0.16800] [-0.35452] [-0.61093] [-1.01664]

INFLDIFF(-1) -0.018828 -4.28E+09 0.006051 0.851241 -0.262604 -1.00E+09 0.003233 -4.40E+09

(0.01465) (4.0E+09) (0.00742) (0.20926) (0.13614) (1.1E+09) (0.01440) (2.7E+09)

[-1.28547] [-1.07417] [ 0.81555] [ 4.06784] [-1.92892] [-0.90677] [ 0.22448] [-1.64029]

INFLDIFF(-2) -0.010941 7.63E+09 0.003949 -0.721960 -0.034240 -2.84E+09 0.053541 2.67E+09

(0.02615) (7.1E+09) (0.01325) (0.37360) (0.24305) (2.0E+09) (0.02571) (4.8E+09)

[-0.41839] [ 1.07281] [ 0.29810] [-1.93246] [-0.14087] [-1.43993] [ 2.08265] [ 0.55741]

INFLDIFF(-3) 0.001772 -4.08E+09 0.019868 0.276315 0.087016 1.74E+08 -0.015028 -3.09E+09

(0.02140) (5.8E+09) (0.01084) (0.30576) (0.19892) (1.6E+09) (0.02104) (3.9E+09)

[ 0.08281] [-0.70116] [ 1.83277] [ 0.90370] [ 0.43744] [ 0.10820] [-0.71425] [-0.78766]

INFLDIFF(-4) 0.002494 2.06E+10 -0.004858 -0.452235 -0.134233 -1.06E+09 0.021070 -1.81E+09

(0.02168) (5.9E+09) (0.01098) (0.30970) (0.20148) (1.6E+09) (0.02131) (4.0E+09)

[ 0.11508] [ 3.48614] [-0.44246] [-1.46024] [-0.66623] [-0.64823] [ 0.98870] [-0.45577]

INTDIFF(-1) 0.007937 1.63E+09 0.015664 0.641589 1.480287 3.13E+09 0.006911 -3.14E+09

(0.02496) (6.8E+09) (0.01264) (0.35661) (0.23200) (1.9E+09) (0.02454) (4.6E+09)

[ 0.31798] [ 0.23992] [ 1.23892] [ 1.79914] [ 6.38052] [ 1.66407] [ 0.28163] [-0.68683]

INTDIFF(-2) -0.008392 1.96E+09 -0.018239 0.123185 -0.895375 -1.34E+10 -0.009695 2.57E+09

(0.03843) (1.0E+10) (0.01947) (0.54903) (0.35719) (2.9E+09) (0.03778) (7.0E+09)

[-0.21839] [ 0.18745] [-0.93700] [ 0.22437] [-2.50675] [-4.64215] [-0.25662] [ 0.36437]

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INTDIFF(-3) -0.026622 8.26E+09 0.008762 -0.486182 0.404362 6.09E+09 0.072023 -2.16E+08

(0.03725) (1.0E+10) (0.01887) (0.53218) (0.34623) (2.8E+09) (0.03662) (6.8E+09)

[-0.71470] [ 0.81554] [ 0.46437] [-0.91356] [ 1.16791] [ 2.17002] [ 1.96669] [-0.03158]

INTDIFF(-4) 0.035072 -2.94E+09 0.002055 -0.607591 -0.252452 4.46E+08 -0.050820 -3.93E+09

(0.02665) (7.3E+09) (0.01350) (0.38076) (0.24771) (2.0E+09) (0.02620) (4.9E+09)

[ 1.31601] [-0.40549] [ 0.15224] [-1.59575] [-1.01914] [ 0.22190] [-1.93962] [-0.80381]

INTRV(-1) -5.59E-12 0.249162 1.55E-12 5.79E-11 -4.91E-13 -0.657634 8.33E-12 -0.699318

(2.3E-12) (0.62057) (1.2E-12) (3.3E-11) (2.1E-11) (0.17184) (2.2E-12) (0.41819)

[-2.44878] [ 0.40151] [ 1.34326] [ 1.77803] [-0.02317] [-3.82699] [ 3.71549] [-1.67225]

INTRV(-2) 9.38E-13 0.656246 -1.09E-12 8.21E-12 4.23E-11 -0.993715 4.37E-12 -0.327457

(3.2E-12) (0.85734) (1.6E-12) (4.5E-11) (2.9E-11) (0.23740) (3.1E-12) (0.57774)

[ 0.29755] [ 0.76544] [-0.68592] [ 0.18236] [ 1.44452] [-4.18575] [ 1.40995] [-0.56679]

INTRV(-3) 2.52E-12 0.216463 -1.07E-12 -1.34E-11 -7.38E-11 0.071293 -7.57E-13 0.014377

(3.2E-12) (0.86216) (1.6E-12) (4.5E-11) (2.9E-11) (0.23874) (3.1E-12) (0.58099)

[ 0.79472] [ 0.25107] [-0.66634] [-0.29631] [-2.50609] [ 0.29863] [-0.24299] [ 0.02475]

INTRV(-4) 7.62E-12 -0.571436 -1.68E-12 -9.25E-11 5.99E-11 1.392135 -8.07E-12 -0.616823

(3.6E-12) (0.97283) (1.8E-12) (5.1E-11) (3.3E-11) (0.26939) (3.5E-12) (0.65557)

[ 2.13028] [-0.58739] [-0.92513] [-1.81059] [ 1.80318] [ 5.16782] [-2.29655] [-0.94089]

LNMSUPP(-1) -0.436797 -1.25E+11 0.110842 10.79248 -1.092345 1.59E+10 0.809159 -4.52E+10

(0.36160) (9.8E+10) (0.18316) (5.16620) (3.36099) (2.7E+10) (0.35550) (6.6E+10)

[-1.20795] [-1.26932] [ 0.60515] [ 2.08906] [-0.32501] [ 0.58525] [ 2.27610] [-0.68122]

LNMSUPP(-2) 0.306115 8.46E+10 -0.229849 -1.600320 0.696476 -8.51E+10 0.367198 1.35E+10

(0.47628) (1.3E+11) (0.24126) (6.80469) (4.42695) (3.6E+10) (0.46825) (8.7E+10)

[ 0.64272] [ 0.65267] [-0.95272] [-0.23518] [ 0.15733] [-2.37146] [ 0.78419] [ 0.15436]

LNMSUPP(-3) 0.039091 -3.39E+10 0.007192 -4.067877 0.604075 1.71E+10 -0.431027 -1.06E+10

(0.36772) (1.0E+11) (0.18627) (5.25369) (3.41791) (2.8E+10) (0.36152) (6.7E+10)

[ 0.10631] [-0.33841] [ 0.03861] [-0.77429] [ 0.17674] [ 0.61577] [-1.19225] [-0.15730]

LNMSUPP(-4) 0.119572 5.89E+10 0.075386 -3.064341 0.935643 5.74E+10 0.173287 1.97E+10

(0.30713) (8.4E+10) (0.15557) (4.38801) (2.85473) (2.3E+10) (0.30195) (5.6E+10)

[ 0.38932] [ 0.70488] [ 0.48456] [-0.69834] [ 0.32775] [ 2.48198] [ 0.57389] [ 0.34945]

TRDDIFF(-1) -1.07E-12 0.482022 -8.45E-14 -2.64E-11 -3.81E-11 -0.616094 3.13E-12 0.010674

(1.7E-12) (0.45150) (8.4E-13) (2.4E-11) (1.5E-11) (0.12502) (1.6E-12) (0.30425)

[-0.64510] [ 1.06761] [-0.10055] [-1.11453] [-2.47191] [-4.92784] [ 1.91884] [ 0.03508]

TRDDIFF(-2) -1.19E-13 -0.308527 1.40E-12 1.80E-12 2.31E-11 0.073152 1.12E-12 -0.318710

(1.5E-12) (0.39782) (7.4E-13) (2.1E-11) (1.4E-11) (0.11016) (1.4E-12) (0.26808)

[-0.08135] [-0.77554] [ 1.89537] [ 0.08597] [ 1.69595] [ 0.66405] [ 0.78164] [-1.18884]

TRDDIFF(-3) 5.98E-13 0.655008 -2.83E-13 -3.80E-11 -2.03E-11 -0.271511 1.32E-12 0.129157

(1.8E-12) (0.47677) (8.9E-13) (2.5E-11) (1.6E-11) (0.13202) (1.7E-12) (0.32128)

[ 0.34145] [ 1.37385] [-0.31868] [-1.51650] [-1.24740] [-2.05658] [ 0.76825] [ 0.40200]

TRDDIFF(-4) 6.00E-13 0.499294 4.71E-13 -1.28E-11 3.19E-12 0.234423 -1.36E-12 -0.206780

(1.2E-12) (0.32109) (6.0E-13) (1.7E-11) (1.1E-11) (0.08891) (1.2E-12) (0.21637)

[ 0.50846] [ 1.55502] [ 0.78793] [-0.75671] [ 0.29107] [ 2.63660] [-1.17509] [-0.95567]

C 0.144611 1.54E+11 0.175136 -25.15822 -9.244026 2.83E+10 0.116150 2.43E+10

(0.59841) (1.6E+11) (0.30311) (8.54942) (5.56204) (4.5E+10) (0.58831) (1.1E+11)

[ 0.24166] [ 0.94576] [ 0.57779] [-2.94268] [-1.66199] [ 0.62683] [ 0.19743] [ 0.22106] R-squared 0.975940 0.782544 0.920545 0.983783 0.995534 0.931549 0.997131 0.968898

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Adj. R-squared 0.930652 0.373215 0.770984 0.953256 0.987128 0.802699 0.991731 0.910354

Sum sq. resids 0.005179 3.83E+20 0.001329 1.057123 0.447424 2.94E+19 0.005006 1.74E+20

S.E. equation 0.017454 4.75E+09 0.008841 0.249367 0.162232 1.31E+09 0.017160 3.20E+09

F-statistic 21.54935 1.911771 6.154952 32.22679 118.4277 7.229726 184.6516 16.54983

Log likelihood 158.4324 -1158.030 192.4404 25.46487 46.95986 -1093.827 159.2829 -1138.295

Akaike AIC -5.017297 47.64121 -6.377614 0.301405 -0.558394 45.07307 -5.051316 46.85180

Schwarz SC -3.755362 48.90315 -5.115679 1.563340 0.703541 46.33501 -3.789380 48.11374

Mean dependent 3.786580 2.93E+09 0.029320 1.183669 1.566263 6.41E+08 -2.180109 4.85E+10

S.D. dependent 0.066279 6.00E+09 0.018475 1.153385 1.429917 2.96E+09 0.188707 1.07E+10

Determinant resid

covariance (dof adj.) 6.04E+40

Determinant resid covariance 1.08E+37

Log likelihood -2699.351

Akaike information criterion 118.5340

Schwarz criterion 128.6295

Table 3-4: VAR Estimation Output

Step 3: In this step the system equation is generated for VAR to get the value of the required

coefficients. The estimation technique used for generating the system equation is OLS. The

coefficients along with their significance level are shown as below. Due to very huge output,

only the coefficients related to the equation in which the exchange rate is the dependent

variable is being shown:

System: UNTITLED

Estimation Method: Least Squares

Date: 02/19/12 Time: 06:41

Sample: 2005M10 2010M12

Included observations: 51

Total system (unbalanced) observations 407 Coefficient Std. Error t-Statistic Prob. C(1) 0.968287 0.371521 2.606280 0.0101

C(2) 0.021554 0.513438 0.041979 0.9666

C(3) -0.906033 0.525297 -1.724800 0.0867

C(4) 0.743504 0.392274 1.895369 0.0601

C(5) 3.29E-13 8.32E-13 0.396100 0.6926

C(6) 7.11E-13 9.77E-13 0.728262 0.4676

C(7) -3.24E-12 1.39E-12 -2.326828 0.0214

C(8) 1.25E-12 1.47E-12 0.848302 0.3977

C(9) -0.254041 0.444615 -0.571372 0.5686

C(10) 0.641382 0.664478 0.965241 0.3361

C(11) -1.051627 0.631706 -1.664742 0.0982

C(12) 0.456869 0.385226 1.185978 0.2376

C(13) -0.028315 0.013250 -2.136926 0.0343

C(14) 0.013874 0.019440 0.713650 0.4766

C(15) 0.003414 0.021896 0.155897 0.8763

C(16) 0.015268 0.020082 0.760269 0.4483

C(17) 0.015379 0.024972 0.615828 0.5390

C(18) -0.024372 0.037545 -0.649139 0.5173

C(19) 0.009755 0.026946 0.362006 0.7179

C(20) 0.027122 0.026663 1.017219 0.3108

C(21) -4.63E-12 2.23E-12 -2.078735 0.0394

C(22) 3.49E-12 2.61E-12 1.334664 0.1841

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C(23) 4.81E-12 2.77E-12 1.737379 0.0845

C(24) 7.55E-12 3.66E-12 2.060808 0.0411

C(25) -0.630158 0.341542 -1.845037 0.0671

C(26) 0.556732 0.451125 1.234098 0.2192

C(27) -0.015313 0.374642 -0.040873 0.9675

C(28) 0.066523 0.312248 0.213045 0.8316

C(29) 3.88E-14 1.49E-12 0.026100 0.9792

C(30) 8.21E-13 1.33E-12 0.619738 0.5364

C(31) 1.75E-12 1.58E-12 1.108291 0.2696

C(32) 5.14E-13 1.21E-12 0.425844 0.6709

C(33) 0.424840 0.576753 0.736608 0.4626

Observations: 51

R-squared 0.976077 Mean dependent var 3.789739

Adjusted R-squared 0.933546 S.D. dependent var 0.069382

S.E. of regression 0.017886 Sum squared resid 0.005758 Durbin-Watson stat 2.287630

Table 3-5: Estimation for System Equations of VAR

Model Equation:

LNEX = 0.96*LNEX(-1) + 0.021*LNEX(-2) - 0.90*LNEX(-3) + 0.74*LNEX(-4) + 3.29e-13*CAP(-1) + 7.11e-13*CAP(-2) - 3.24e-12*CAP(-3) + 1.25e-12*CAP(-4) - 0.25*FWDPRM(-1) + 0.64*FWDPRM(-2) - 1.05*FWDPRM(-3) + 0.46*FWDPRM(-4) - 0.028*INFLDIFF(-1) + 0.015*INFLDIFF(-2) + 0.0034*INFLDIFF(-3) + 0.015*INFLDIFF(-4) + 0.015*INTDIFF(-1) - 0.024*INTDIFF(-2) + 0.0098*INTDIFF(-3) + 0.027*INTDIFF(-4) - 4.63e-12*INTRV(-1) + 3.49e-12*INTRV(-2) + 4.81e-12*INTRV(-3) + 7.55e-12*INTRV(-4) - 0.63*LNMSUPP(-1) + 0.56*LNMSUPP(-2) - 0.015*LNMSUPP(-3) + 0.07*LNMSUPP(-4) + 3.88e-14*TRDDIFF(-1) + 8.21e-13*TRDDIFF(-2) + 1.75e-12*TRDDIFF(-3) + 5.14e-13*TRDDIFF(-4) + 0.42

As clear from table 3.5 the correlation of the estimated system equation for VAR model is

significantly high i.e. 97.6. Also standard error of the regression is quite low i.e. .0178. The

only problem is Durbin-Watson stat which is 2.28 indicating some sort of negative serial

correlation.

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3.3 Forecasting Using the Above Developed Model

The out-of-sample forecasting has been done for the period from Jan ’2011 till Dec’2011.

The final graph and values (antilog values) are shown as below:

Date Actual Forecast

01-01-11 45.87156 41.45233

01-02-11 45.6621 43.64711

01-03-11 45.45455 49.10776

01-04-11 44.84305 44.27752

01-05-11 45.04505 42.64432

01-06-11 45.45455 49.85142

01-07-11 44.84305 47.78816

01-08-11 45.45455 40.17814

01-09-11 47.84689 49.78611

01-10-11 49.75124 53.77115

01-11-11 51.02041 40.25624

01-12-11 53.19149 49.09833

Table 3-6:Out of Sample Forecasting(Actual vs VAR)

Figure 3-2: Out of Sample Forecast for Re/$

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4 Concluding Observations

The study covers three main topics: First, various theoretical models for modeling and

forecasting exchange rates have been studied. Second, an alternative model has been

developed by incorporating some extra factors like- forward premium, capital inflow,

government intervention and inflation differential in the theoretical monetary model. Third,

the Out of sample forecasting for the exchange rate has been done using this model for thee

period from Jan’11 to Dec’11.

4.1 Findings

Information on certain variables like- forward premium, capital inflow and inflation

differential in timely manner can drastically improve the accuracy of the forecasting from

significantly high correlation of the model developed above. It is thus possible to beat the

previous theoretical models for predicting exchange rates.

Including data on central bank intervention helps to improve forecast accuracy further.

The possibility of beating the naive model and other theoretical models may be due to the

fact that the intervention by the central bank (RBI) may help to curb the volatility arising

due to the demand-supply mismatch and stabilize the exchange rate. The exchange rate

policy of the RBI is guided by the need to reduce excess volatility.

Though the science of the sum of the coefficients in the model developed are not

consistent but if we see the overall forecasting done with the help of the model and

system correlation then the model developed seems to be quite satisfactory.

Since this model has been developed for the Indian forex market, it can be used for other

similar developing countries where there is floating exchange rate system like that of in

India provided the data is available on time.

4.2 Limitations

The model suffers from the limitations of VAR which are- over parameterization, loss of

degree of freedom due to large number of variables incorporated.

The signs of the lags of the exogenous variables in the system equation are not consistent.

The lag order or length is four due to which number of variables generated (233)

estimated in the system equation is very high.

The forecasting accuracy has not been compared with the other theoretical models.

To overcome the mentioned problems of VAR, Bayesian VAR (B-VAR) could have been

used.

Johansen Co-integration and Granger Causality test has not been included in the paper.

Some more factors like Order flow and volatility of Capital Inflows could have been

considered.

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5 Annexure

Variable Definition Source Ex

Int

Int*

Msup

Msup*

Trd

Trd*

Fwdprm

Cap

Infl

Infl*

Intrv

Rupee/ US Dollar Spot Exchange Rate

Auctions of 91-day Government of India

3-Month Treasury Bill of US, Secondary Market

Rate

Money supply(M3) for India

M2 for US, seasonally adjusted

Trade Balance of India in US $

Trade Balance of US in US $

Three-month forward premium ( % per annum)

Capital flows measured by Foreign Direct

Investment plus Foreign Private Investment

Inflows in India in US $

Year-on-year Inflation Rate

Year-on-year Inflation Rate calculated: from

Consumer Price Index for All Labor Statistics

Urban Consumers; All Items for US (Purchase

minus Sale) of US Dollars

by RBI

Handbook of Statistics on the

Indian Economy and RBI

Bulletin

Handbook of Statistics on the

Indian Treasury Bills

Economy and RBI Bulletin

Board of Governors of the

Federal Reserve System

Handbook of Statistics on the

Indian Economy and RBI

Bulletin

Board of Governors of the

Federal Reserve System

RBI Bulletin

US Census Bureau of

Economic Analysis

Handbook of Statistics on the

Indian Economy and Weekly

Statistical Supplement

Handbook of Statistics on the

Indian Economy and RBI

Bulletin

Inflation.eu,worldwide

inflation data

Inflation.eu,worldwide

inflation data

Handbook of Statistics on the

Indian

Table 5-1: Data Definition and Sources

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Page 20

6 References

RBI Database for Indian Economy (http://dbie.rbi.org.in)

Modelling and forecasting the Indian Re/US dollar exchange rate – Pami Dua and Rajiv

Ranjan

http://www.inflation.eu/

http://www.census.gov/compendia/statab/

http://www.oanda.com/currency/historical-rates/

Brooks C., 2nd Edition, 2008. Introductory Econometrics for Finance. New York:

Cambridge University Press

Gujarati Damodar N., Sangeetha., 4th Edition, 2007. Basic Econometrics: Tata McGraw-

Hill Publishing Co.Ltd.

An Introduction to Applied Econometrics (A Time-Series Approach) – Kerry Patterson

The Canadian-US Exchange Rate: Evidence from a Vector Autoregression - David

Backus - The Review of Economics and Statistics, Vol. 68, No. 4 (Nov., 1986), pp. 628-

637

Empirical Exchange Rate Models For Developing Economies: A Study On Pakistan,

China And India - Syed Mohammad Abdullah Khalid

The Monetary Approach to the Exchange Rate: Rational Expectations, Long-Run

Equilibrium, and Forecasting: Ronald Macdonald and Mark P. Taylor- Staff Papers -

International Monetary Fund, Vol. 40, No. 1 (Mar., 1993), pp. 89-107

http://mospi.nic.in/Mospi_New/site/India_Statistics.aspx

http://elibrary-data.imf.org