Chapter 3: Methodology
3.0 Introduction
The theory of purchasing power parity is essential for the study of international trade since it argues that there exist a relationship between prices of products and exchange rates. This theory provides a framework for assessing long-term changes in the exchange rates. It states that similar goods and services in various countries should have the same cost in the long-run (Frankel 153). Essentially, the PPP theory is based on the assertion that the exchange rates tend to adjust themselves in such a way that there no opportunity costs for buying particular goods or services in a particular country and selling them in another country can be realized. In other words, the exchange rates do not significantly determine the opportunity cost involved in international trade. It asserts that a particular basket of goods should have the same cost no matter the country from which it was purchased. Thus, the theory tends to approximate the adjustments that should be made on the countries’ exchange rates so that the purchasing power is the same for all countries. This section will discuss the methodology that will be utilized in the analysis of the purchasing power parity in different countries to test whether PPP theory holds.
3.1 Hypothesis and research question
The paper focuses on the movement of the Chinese Yuan and USA and Canadian dollar on the long-run. It uses the monthly data for the period from 1990 to 2015. Additionally, the paper employs various statistical techniques to analyze the CPI, PPI and exchange rates data for the period considered and use the data to test the hypothesis. The main hypothesis in the study is that PPP holds. The study suggests that the PPP theory holds. Therefore, there is a long-run relationship between the exchange rates and PPP. The purchasing power is determined by both producer and consumer prices. As such, the study aims at testing the relative and absolute PPP ad use various statistical techniques to test whether PPP is equal to the exchange rates. The purchasing power parity theory holds that the adjustments in the exchange rates tend to offset the price differentials in various countries making the purchasing power to be the same. It assets that since the exchange rates are equal to purchasing power, no opportunity cost is involved in the international trade. The null hypothesis in the study is that PPP theory holds true. Thus, the research question is whether PPP holds.
3.2 Research methods and approach
Various researchers who have undertaken research on the validity of PPP theory have failed to agree because of the contradicting outcomes they obtain. Different economic factors have been revealed to contribute these contradicting research findings. The methods of data collection and the time considered during various empirical studies were found to be the main determinants of the results found by different researchers. The study utilizes Eview tool to generate the regression results as well as several inferential statistics. The regression analysis will be used to test for the significance of the difference between PPP and the exchange rates to show whether there is sufficient empirical evidence to accept or reject the hypothesis.
3.3 Methods of data collection
The data used in the study was collected in three countries using various data collection methods. The samples were taken in time intervals and the average values of the variables were calculated. The information collected was used to compare CPI and PPI for the three countries. These values were then used to compute both absolute and relative PPP, which were then compared with the real exchange rates to test the stated hypothesis. To test the validity of PPP theory, the calculated PPP is expected to be equal to the exchange rates. The PPI data and CPI data was collected from various industries in the countries considered.
The graphical representation of the information was used to make relevant comparison of the variables. The graphs show the trends in the CPI as well as the producer price indexes in the three countries, and help to compare the variations in the two variables among the countries. Obtaining the data from the industries’ records was significant because it ensured that the study utilized data from original sources. The computation of the coefficient of determination (R2) helps to determine how much variation in the factors affecting PPP influence the outcomes of the analysis. The correlation coefficient helps to determine the strength of the relationship between variables. It shows how one variable is related to the other in a regression model. The computation of PPP values at different economic periods helped to understand how changes in the economic conditions can lead to contradicting research findings. Various facts presented in the graphs help to provide a preliminary insight about the correlation between the PPP and the exchange rates.
3.2.1 Graphs for comparing CPI and PPI between the countries between 1990 and 2015
3.4 Samples and the time period
The scientific sampling designs were deployed in the study to ensure that the samples obtained provide reliable information that could be generalized for the entire population. Various economic conditions affect the variables in different ways. Additionally, the time period during which the study was conducted is a major factor in the analysis of PPP theory. The study involved dividing the entire period into small samples and comparing the PPP and the exchange rates for these periods. Using the small samples in this study was advantageous because different results were obtained for the same analysis in different periods. Therefore, the results of each sample were used to make particular inferences as well as to relate the prevailing economic conditions with the outcomes. Further, it was possible to identify the trends in exchange rates and purchasing power parity among the countries by using small samples. The study collected information for the exchange rates, purchasing power parity, consumer price index, and the producer price index from 1990 to 2015for the exchange rates, and from 1997 and 2012 for the CPI and PPI. The study drew particular outcomes for the relationship between the exchange rates and purchasing power parity during some specific periods like the financial crisis of 2008. The samples were taken randomly by considering the average monthly data for the entire period of study. Since it was not possible to analyze the data for each month over fifteen years, the annual data was obtained as mean value for the twelve months. This data was then used to calculate PPP values that were compared with the exchange rates values to test the hypothesis.
3.5 Methods of data analysis
The absolute PPP version defines the exchange as the ratio of the price levels between two countries. That is Et=Pt/Pt*, where Et is the exchange rates and Pt is the price levels at a particular time t. The PPP theory predicts that there is a proportionality of depreciation or appreciation of the domestic currency when there are changes in domestic prices in relation to foreign prices. The data obtained was analyzed using various statistical tools. One the tools used is the descriptive statistics. This method is important in any statistical analysis because it helps the researcher to define statistics, explain various parameters, and give some statistical interpretation of the values obtained. The statistical method was used to describe the time series obtained by plotting various variables. It also helped to relate some economic variables with others be describing how they affect each other. Furthermore, the descriptive statistics method was used to provide statistical interpretations of the values obtained from the regression analysis. For example, we use the descriptive statistics to interpret the result of the ratio between PPP and the exchange rates. The Eview results were also interpreted using descriptive statistics.
The correlation analysis helps to estimate and describe the relationship between variables used in a statistical model in terms of the strength of the relationship between the variables. According to the purchasing power theory, the PPP rates are supposed to coincide with the exchange rates. Therefore, the time series for both exchange rates and the PPP should have the same stationarity properties. The correlation analysis is useful in establishing the strength of the relationship between factors that affect variables and the variables themselves in the model. It also yields the adjusted R, also known as the coefficient of determination that determines the percentage of variations of the variables that can be explained by the model. The econometric view module provides different statistics that are highly useful making statistical decisions. The decision involved in the study was to accept or reject the PPP theory on the basis of the obtained results and the pre-determined criterion. The Eview provided the standard errors for the model coefficients, which were essential in determining and interpreting the spread of the data. If the PPP theory holds true, the exchange rates and the PPP rates are expected to conitegrate. Therefore, conitergration analysis was useful in the evaluation of the conitergration of the two variables both in the short and long-run. The econometric analysis was used for comprehensive estimations of the relationship between PPP and the exchange rates. The ordinary least squares method was another analytical tool that was deployed during the study. This technique involves establishing the linkage between the considered variables as well as drawing a scatter diagram to measure how distantly or how closely the variables in the model are. The ordinary least square method helped to establish the spread of the data for the variables by fitting a line between the plotted observations. Additionally, this technique helped to estimate the errors in the statistical model by estimating the deviations of values from the true values.
3.6 Limitations of the study
The study involved establishing the relationship between the PPP and the exchange rates to test whether PPP theory holds. The test criterion was that PPP rates must converge with the exchange rates for the theory to be validated. However, the outcomes of the study were influenced by various factors. The two variables considered as main variables are influenced by different factors or similar factors in different ways. The inflation rate is one of the factors that significantly influence both producers and consumers’ prices. Additionally, the barriers imposed by the government in different countries tend to have serious implications for the products’ prices. The analysis made various assumptions which had significant impacts on the results. Changes in the economic conditions and the economic behavior during different periods were the main limitations of the study.
bb3.6.1 Table 1: Table for exchange rates between China, USA, and Canada
3.6.2 Graph for the exchange rates comparison
3.6.3 Testing for purchasing power parity between China and USA
3.6.4 Table 3: Table of St, Pt, P*t, and the absolute PPP
3.6.5 Graph of PPP and exchange rates
3.6.6 Testing for purchasing power parity between China and Canada
Results of regression analysis
Dependent variable: percentage exchange rates
Method: simple OLS
Sample April 2014- August 2016
3.7 Conclusion and comments
The study involves the investigation of the relationship between the exchange rates and purchasing power parity. It hypothesized that PPP theory does not hold and collected empirical data to test this claim. It examined the relative and absolute purchasing power parity in the determination of the exchange rates between China and USA and between China and Canada. A careful examination of the data used in the study as well as the results obtained shows that the prices move slowly and do not support the co-movement suggested in the PPP theory. The analysis of PPP between the countries considered indicates that the absolute purchasing power parity does not hold. In the short- run, prices tend to adjust themselves slowly. The absolute purchasing power parity does not hold in this analysis because the criterion for accepting the hypothesis was not satisfied. No long-run relationship could be predicted using the results. Additionally, the relative purchasing power parity does not hold, although it is argued that the failure for absolute PPP to hold does not automatically imply that the relative PPP will not hold. However, the rate of PPP is a significant determinant of the exchange rates between the countries, although if sufficient data is used and adequate period considered, a careful application of econometric analysis will lead to the invalidation of the PPP hypothesis.
Works Cited
Frankel, Jeffrey. Purchasing power parity: Doctrinal perspective and evidence from the 1920s. Journal of International Economics, 8.2: (1978), 169-191. Print
