Financial Econometrics, Vector Autoregressive Modeling, Theoretical Models like PPP, IFE and BOP Models...

1. 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
1
Mathematically, 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
+...........+ApLp
; 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]

15. I B S - 2 0 1 2 Page 14
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

16. I B S - 2 0 1 2 Page 15
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

17. I B S - 2 0 1 2 Page 16
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.

18. I B S - 2 0 1 2 Page 17
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/$

19. I B S - 2 0 1 2 Page 18
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.

20. I B S - 2 0 1 2 Page 19
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

21. I B S - 2 0 1 2 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