Long-term Purchasing Power Parity - Essay Example

Finance and Accounting This version: This study investigates the relationship between the currency exchange rates, interest rates and prices of various products. It uses special models to determine the exchange rate of other currencies in relation to the contemporary position of US dollar rates. It also evaluates the determination of current account and international business co-movement. It does critical review of the operation of the international exchange rate systems. From the determination, it predicts and conducts critical assessment on the financial and macroeconomic impacts of exchange rate fluctuations and exchange rate policies. The study compares the currency exchange factors between US Dollars ($) and Euro (€). The first part of the paper is a design of a framework for testing for the absolute PPP and relative PPP following monetary approach. The second part is a brief summary of the interest rate parity conditions and their underlying logics and implications. This displays the application of the exchange rate used in forward contracts differ from the current spot rate. The emphasis is on the reasons for difference between the forward rates and the future spot rate expected by investors. Part 1: Empirical Study (Selected Question: Question 2) 1. Test for Long-term Purchasing Power Parity (PPP) 1.1. Introduction This study investigates the absolute and the relative PPP for international currencies including the US $ and the EURO in order to test the PPP hypothesis. The currencies support the PPP between the US and European Union with great emphasis considering that earlier studies refused to adopt the PPP hypothesis for the US and the EU countries (Mixon, 2005). Studies give evidence of the co-integration between the Euro and the US dollar rate as well as the prices of the two countries. The test for Long term PPP is conducted as an equilibrium connection using the multivariate co-integration method designed by Mixon (2005). This model allows various long-term links, short-term dynamics, and the adjustment certain regime shifts. If the short-term dynamics differ from the long-term links, the explicit measurement of the short-term dynamics is fundamental for a success in estimating the long-term relations of the time movement to the equilibrium (Mixon, 2005). Considering the possible shifts is vital because such shifts are able to change the statistical tests, which do not give their accounts. The Johansen method will allow for possible connections in determining the variables, such that no variable has an exaggerated priority. This technique will also allow for the testing of the alternatives measures of the PPP. 1.2. Framework Design Conventionally, the macroeconomic variations in the interest rates were subjected to empirical studies through well-established long-term symmetries in the framework data. These include regularities such as the ratio between consumption and income, the consumption or utility function and the currency demand functions. These functions are derivatives of an overall framework, which builds on the IS-LM model. The model explains the constant variations in the summative demand and the summative supply in the economy of the two countries involved. This model is a contemporarily substitute of the DSGE (Stochastic Dynamic General Equilibrium) method as the best way to do the experiential macroeconomics. The normal DSGE model operates with assumption of a utility maximizing factor, with balanced expectations. The argument is that because the macro-economy is the cumulative value of the micro units, the approach requires a macro-theory as a derivative of a micro-theory. However, in order to obtain a constant variable model to describe a number of structural variables, the model will have to depend on the impractical assumptions that majority of the outcomes are considered empirically inappropriate from the onset. Since the economic data is well described in the CVAR models, it is possible that there is need to formulate the empirically significant economic models as the active adjustment models (Mixon, 2005). This will work in consideration of the economic growth rates and the equilibrium errors, referred to as the equilibrium correcting models. These models will inherently be in line with the concept of unexpected shocks cumulating through a period to produce a stochastic trend among the parameters. The measure of the long-term purchasing power parity is done by considering the prices of products and the prevailing currency exchange rates during the trading period. The expectation of this model is to obtain the persistent stochastic trends based on the economy. The movements of the actual rates of exchange and interests form the fundamental positions during the trade period. We will thus conduct an econometric test in a CVAR available in the actual exchange rate, and will be empirically approaching the actual interest rate differential. From the discussion, the fundamental long-term relationships include the purchasing power parity, the actual rates of interest, the ration of capital to income, the UIP (uncovered interest-rate parity), the ratio of consumption to income, the term spread and the labour-income. In this situation, the computation can use the co-integration analysis to obtain the parameters and relations that show similar rewarding equilibriums and empirical stability errors. When variations in the equilibrium relations show evident determination, the computation logic behind the CVAR model communicates the fact that the compensating persistence will be available in the parameters that measure the regular growing rates (Mixon, 2005). This implies that for the economic and financial modelling, there is need to shift from a framework for the static equilibrium to the dynamic equilibrium relations. In this regard, the errors that were seen in the static equilibrium were unstable. This does not imply that the presence of the stable relationships facilitates the discussion of stability. In essence, the standard stationery long-run link can be tested as a special testable incident of more general relationship of a Dynamic Equilibrium. 1.3. Theoretical Justification of the Framework 1.3.1. Economic Background Recent studies on PPP have focused on applying the idea of co-integration in form of an equation as: et = γ0 + γ1 * pat + γ2 pa*t + SWt {4} Here pat is an indicator of the logs of the levels of price setting in the domicile market whereas pa*t is an indicator of the pricing level for the foreign country. The variable et represents the log of currency exchange in the economy of the domicile country and SWt is the parity error term. Strong PPP is displayed by the proportionality constraint γ1=1.0 and γ2 = -1.0. et = γ0+pt-pt*+SWt {5} This demonstrates that every moment the monetary or imbalances occur in the country economy, the concept of instantaneous cost free arbitrage makes the prices the US and the European Union Countries weighed in the different currencies to be similar. Regardless of the absence of objection against the conceptual statement of strong PPP, it cannot be constantly hold as an experiential suggestion. The product price of commodities may not always be the same in different countries. There are various variables differentiating the exchange market between the US and the EU countries such as the cost of transportation, the cost of information access and the possible tariff barriers between the international boundaries. Furthermore, the measurement error challenges originating from the published indices of product prices do not correspond with the conceptual prices. This has to be considered when testing the PPP empirically (Mixon, 2005). This relationship will most likely degenerate into a weak PPP form produced by the constraints γ1=- γ2, being the restriction of symmetry. The model is as shown below: et = γ0+γ1 * (pt - pt*) + SWt {6} with γ1 being a constant factor which accounts for assumed constant transportation, information costs and measurement errors. γ1 is allowed to differ from unity, implying that long-term proportionality between the exchange rate and relative prices may not be exactly one-to-one, for the derivation of a model allowing for transportation costs and measurement errors. Nonetheless, even when the PPP is weak, it will not necessarily hold be able to hold. Differences in consumer tastes cause the variation in exports demand, relevant significance of the business sectors and the variation in the influential factors like the productivity, statutory expenditure and the decisions on the pricing strategy by various companies. These cause the exchange rates to move beyond the expected PPP level. 1.3.2. Econometric Technique The empirical analysis, equation gives the definition of the long-term equilibrium correlations in the commodity market. From the theoretical concept of this technique, when the equation 5 is applies as an empirical model, it will have to undergo modification to accommodate the stochastic features of the data. Additionally, there possibly exist other unspecified factors such as the changes in policy and structural breaks. To consider these factors, the methodology backs the principle step of constructing a congruent unobstructed vector auto-regressionon (VAR). This is viewed as an ample depiction of the mutual distribution of the available factors facilitating the modification and application of the empirical model. In the framework for VAR, the co-integration links between the various factors can be defined using the procedure suggesting the representation of the principal VAR in form of the vector error correction model (VEC). Empirical studies provide statistical tests that define the rank of the matrix as r. It demonstrates that indeed the test for linear constraints on the co-integrating vector variable or permits their loading as the related vectors are common to all model. In the current analysis of the PPP, variables in model 1, 2 and 3 test the conceptual hypothesis on the long-term properties of the hypothesis about proportionality and symmetry. On the hand, variables on model 4, 5 and 6 apply in the test to for the hypothesis on the long-term variables (Mixon, 2005). 1.4. Summary Statistics of the Dataset The empirical data contains the rate of exchange for two different countries, US and the European Union with the comparison of the US Dollars and the EURO behaviours in the exchange market. The EURO is rated against the US Dollar ($). The data was extracted from the statistical data from the UNCTAD repository (http://unctad.org/en/pages/Statistics.aspx.). It covers a period of years from 1950 to 2013. Figure 1: Measure of the Mean and Standard Error Figure 2: Results for Mean and Standard Deviation  Currency Skewness Eur / Usd 0.27 Usd / Eur -0.17 Table 2: Measure of Skewness of the distribution Table 2, Figure 1 and Figure 2 shows the statistical descriptive summary of the data extracted. The mean for each of the series is greater than zero while the standard deviation gives suitable values. The mean was lower in the cases of exchange rates, which traders saw to be important. The rates of exchange rates are moving this indicator downwards. Additionally, the skewness of the series does not indicate asymmetrical distributions of the prices. Autocorrelation pUS AR 1 - 10 F( 10, 82) = 0.9644 [0.47682] PEUR AR 1 - 10 F( 10, 83) = 1.391 [0.26405] Normality pUS χ2 (2) = 1.664 [0.37933] PEUR χ2 (2) = 7.745 [0.02938] Table 3: VAR Tests Table 1 shows the residual statistical features of the last VAR tests. From the diagnostic tests, the VAR is the congruent statistical form of the dataset. The VAR test confirms the statistical hypothesis needed in the Johansen method; hence, the co-integration analysis can move on. Investigation on the graphical representation of the product prices series demonstrates the presence of a linear pattern in the price series. As a result, the model estimation can be done with constraints of the constant factors to include during the co-integration. Eigenvalues Max Eigen (Using T_nm) Trace (Using T_nm) 0.315338 34.8 114.7 0.2892131 32.17 78.58 0.226837 24.73 46.41 0.179161 17.779 20.34 0.0285902 2.87 2.8923 Table 4: Test for Co-integration Rank Table 2 shows the results of the largest Eigen value as well as the trace statistics. Additionally, the plot for the repeatedly approximated maximum Eigen value shows the co-integrating links with the constant variables. Figure 3 below shows the covariance test matrix. Figure 3: Covariance Coefficient Matrix 1.5. Empirical evidence followed by comment and interpretation The results for the interest rates in the US and European Union are compared in US Dollars and Euro respectively. Figure 4 and 5 shows the interest rates obtained in the two currencies. This is in line with the autocorrelation results, which shows residual value of 0.9644 for the US $ and 1.391 for the Euro. Likewise, the normality test shows 1.664 for the US $ and 7.745 for the Euro, proving that indeed, the EURO has the greatest long-term purchasing Power than the US Dollar. Figure 4: Interest Rate - US Figure 5: Interest Rate – European Union Figure 6: Currency Exchange Rate US$ / EURO Essay Selected Question: Question 2 2. Interest Rate Parity This study suggests a different method to be applied to agents and the interest rate markets using certain forms of rationality as well as efficiency. The Heterogeneous agent (HAM) models ignore the idea of one rationality agent and discuss different manners of agents and their behaviours based on their expectations (Mixon, 2005). As a result, this study builds a model to act as the simulation of the exchange rate using the expected values and behaviours of three different agents. One of the agents in the simulation is the carry trader; this paper will also explore the statistical features available in the simulations of exchange rate and the sample of the data. The present heterogeneous model includes the carry traders, which serve the statistical features available in the empirics. Through the carry traders’ behaviour against UIP, this model explains a section of the forward premium concept. This study uses the interest rate factors in the US compared to those of France, for which it compares the behaviours of US $ and EURO. a. Why the exchange rate used in forward contracts differ from the current Spot rate The exchange rates used in the forward contracts have rational expectations on each of the agents leading to the efficiency of the dominant markets. In spite of the continuous challenges from the by perpetual fabrication of the two rational agent, the efficiency of the interest rates in the US and France remains firm and stable. An example of the fabrications is that of the REEM models which allows the flowing of the carry traders. These traders thrive on the difference in the interest rates used in the forward contracts and the current spot rate. The interest rate differentials arises because of the weaknesses in the in the rationality theory (Mixon, 2005) and the efficiency theory which argue that the carry trade has profitable strategic plans . The fundamental reasoning displays the fact that as the carry traders operate, their operations influence the rates of currency exchange. This eventually becomes the main reason for the weakness in efficiency and rationality (Mixon, 2005). The inequality between the forward contracts and the spot rate is the basic factor that supports the majority of the international markets dealing with the foreign exchange and their efficiencies. The study on efficiency will reveal the interest parity (UIP). Additionally, the study takes the equality to represent the starting point. UIP argues that when an assumption is made of a condition of no arbitrage, the expected rate of currency exchange becomes equal to the present spot currency exchange rate rectified for the difference created by the interest rates during the same period. The mathematical representation for the UIP is shown as: E (St + K) = St (1 + idt, k) / 1 + ift, k In this model, represents the K number of period the desired spot rate of currency exchange; is represents the present spot rate of exchange; and are the interest rates of the k-period in the domestic country currency (US$) and the foreign country currency (Euro). The definition of the exchange rate in this simulation is given as the product price in the US$ but the amounts in the domestic currency market. As the UIP undergoes test, this study takes the logarithms developed on the two sides, leading to the equation below: Many economics experts have made tests on this connection and relationships. A large number of the connections test the link between the forward and the expected spot rate. The test for the relationship measures the changes relative to the forward rates, but uses the safe covered interest parity (CIP). The equation for the CIP is: , In the equation, represents the k – period of the forward exchange rates. From the assumption raised by the CIP the equation changes to Of Course, the UIP argues under the economic conditions that the value of alpha (α) is zero and the value of beta is 1. The variable represents the white-noise error-term. Many of the researchers who have made the discovery, made conclusion that the UIP is not rational and hence does not hold. The mean value of beta found by the research practitioners averaged to about -0.88 and that of the alpha is insignificant but not a zero). Intriguingly, more than 75% of the research studies obtain the mean beta to be approaching 1. This is an abnormality referred to as the equity premium or forward premium puzzle. b. Why the Forward Rate Differ from the future spot rate It has been mentioned that a vital feature of the carry traders is about their capacities. Most of the economy scholars attempt to weigh the sizes the flows of carry trades. It has been observed in many tests that the forward rates are always different from the expected future spot rates. Even so, it is very difficult to identify an exact measure of the size because the flows of carry trader are often components of the monetary flows (Mixon, 2005). Economists have suggested that the forward rate be monitored indirectly against the future spot rate. The data is viewed on the open points of the futures of the exchange rates traded, and by observing the specific sectors in which the carry traders are able to produce higher results on the flows of money. However, the actual size of the flows of carry trade was not identified; it was generally acceptable that the forward rates and the future spot rate be used to influence the currency exchange rates arising. According to Mixon (2005), this legitimizes the application of carry trades, being a section of the cause of the failure and weakness of the UIP interest parity. b. Effect on the value of the Euro and U. S. dollar (1) A decrease in U. S. interest rates As the interest rates in the US reduces, the value of the EURO increases such that whenever a trader purchases products, he or she spends less when using US dollars than when using EURO. The carry trades are therefore frequent at the point of borrowing money in the US, than in France, since the US has low rates of interest. When purchasing in France, the best option is to purchase in a single currency (EURO) rather than convert to US $. This reduces the risk of currency exchange losses. It is also logical to convert any currency to the currency of the country of purchase, which has higher rates of interest rates. This study identifies France as the best country for purchase when the interest rates of the US$ reduces. The US becomes the major low interest countries, while France is the main country with high rates of interest. Because of the fall in the US interest rates, the trade strategy of the investors shits to the interest rate differential on which the demand for EURO grows rapidly. The strategic plans for the carry traders increase in profitability owing to the weakness of Unidentified Interest rate Parity (UIP). There are three revenue sources, on which carry traders will choose to operate. Principally, there is a more open source of profits, being the trade on the interest rate difference. Secondly, the fact that UIP does not have sufficient argument, the Euro (because of high interest rates) will have to appreciate. This implies that as the convert the invested funds to the repayment of debts, it make a profit from foreign currency exchange. The final possible source of profit is the growth in the country of high rates of interest (France) as an impact of carry trading. This is however only important if the resultant capacity of the carry trade will flow with a significant effect on the rates of currency. (2) An increase in France’s interest rates As we look at the Unidentified Interest Rate Parity, it is evident that as the interest rate in France increases, the domestic interest rate in the US also grows higher and possibly exceeds the foreign rates (in France) when trading at the forward premium. The domestic currency (US$) is thus forced to depreciate in relation to the Euro. Nevertheless, this effect is logical, but it does not happen in reality. Instead, the data exhibits the possibility of the Euro rate of exchange will appreciate. Some economic surveys tend to solve the forward premium puzzle in this situation. A simulation performed on the short-term and the long-term rates of exchange concludes that eventually, the forward rates puzzle will be eliminated. This is the effect of the vital macro-variables in the behaviour of the two country currencies owing to the cross-rates. Even though there are efforts to find solution to the difference between the forward rate and the spot rate, there exists no absolute solution to the violation of the parity in interest rates. (3) A decrease in the expected future exchange rate, Ee$/€ The other effect of the forward rates and the future spot rate on the US$ and Euro is the expectation concerning the future rates of currency exchange (Mixon, 2005). Speculative traders expect that the future rates will converge to reach the fundamental threshold. This feature can be presented mathematically as follows: , where α > 0 In this equation, represents the expected variation in the rate of exchange for one period and represents the present spot rate of exchange. Moreover, the variable alpha (α) represents the speed that the fundamentalists expect the rate of exchange to revert to the fundamental position. Other category of traders is the chartists, who believe that the exchange rate will follow the very pattern it followed during the previous period. This essentially implies that if the period increases then the future rates to increase. On the other hand, if the rate reduces during the current period, then it will reduce in the subsequent period. The expectation is represented by the following model: , where 0 Read More