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Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)
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Modeling and forecasting the Indian Re/US dollar exchange rate using Vector Autoregression technique (A Monetary Model Approach)

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

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

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  • 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
  • 2. I B S - 2 0 1 2 Page 1 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
  • 3. I B S - 2 0 1 2 Page 2 4.1 Findings.....................................................................................................................18 4.2 Limitations ................................................................................................................18 5 Annexure..........................................................................................................................19 6 References........................................................................................................................20
  • 4. I B S - 2 0 1 2 Page 3 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
  • 5. I B S - 2 0 1 2 Page 4 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
  • 6. I B S - 2 0 1 2 Page 5 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
  • 7. I B S - 2 0 1 2 Page 6 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.
  • 8. I B S - 2 0 1 2 Page 7 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
  • 9. I B S - 2 0 1 2 Page 8 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
  • 10. I B S - 2 0 1 2 Page 9 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:
  • 11. I B S - 2 0 1 2 Page 10 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
  • 12. I B S - 2 0 1 2 Page 11 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.
  • 13. I B S - 2 0 1 2 Page 12 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)
  • 14. I B S - 2 0 1 2 Page 13 [-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

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