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PAGE 1 EMPRICAL ESTIMATION OF ASIAN IMPORT DEMAND FUNCTIONS: BY PRESTON BEBAS A Thesis Submitted to the Division of Humanities New College of Florida In partial fulfillment of the requirements for the degree Bachelor of Arts Under the Sponsorship of Dr. Tarron Khemraj Sarasota, Florida May, 2010 PAGE 2 ii Contents Introduction 1.1 Motivation 1.2 Structural Breaks 1.3 1.4 1.5 Outline 1. Literature R eview 2. 3.2c Balance of Payments Constrained Growth 3. Results 4.2 Coint 3 0 4.3 4.4 Balance of 3 5 Conclusion PAGE 3 1 1. I ntroduction The introduction will proceed with an explanation of the motivation behind and a description o f the research. This will be followed by brief discussions of the concept s behind one the key parameters and one of the key variables used in the research and an introduction to the theory behind the study. 1.1 Motivation Over the past decade, developi ng nations have proven to be fertile ground for empirical research with heavy attention paid in particular to both import demand a nalysis and the analysis of economic growth In this paper we combine these two current interests by empirically testing what effe ct critical parameters (domestic activity domest ic and foreign price levels, and exchange rate volatility) have on the level of demand for imports for four Asian countries. We observe the annual economic data for Jordan, Pakistan Singapore, and Tha iland from 1983 200 7 to accomplish this goal. These four countries are prime examples of developing Asian nations that have had significant shifts towards increased global economic integration over the past several decades. In the process, we attempt to determine if and when structural changes strong shifts in demand behavior in each country occurred and their affect on the coefficients o f the aforementioned variables. In particular we wish to observe how import demand elasticity is affected by structur al shifts While illuminating in its own right the derivation of import demand equations serves a second purpose by supplying the necessary coefficients to test for the validity of national growth hypothesis purported by L aw of economic growth. This paper attempts PAGE 4 2 to distinguish itself from the multitude of studies which have placed econometrically derived import demand functions as their singular goal in addition to those that have incorporated such studies into a n analysis of the legitimacy of various growth theories. We hope to accomplish this goal by focusing specifically on the import demand functions of a select group of developing nations belonging to one continental region while addressing the common model misspecification of erroneously excluding structural shifts developing nations There are many important numerous attempts to empiri cally define models of import demand. Sorting out the key variables of and their contributions to import demand is essential for the understanding of the historical causes of the eco nomic performances of countries. In addition, an adequate demand functio n is essential for forecasting future performance With the knowledge of which variables significantly contribute to the demand for imports in a country and to what extent, an nce of trade net exports can be greatly improved. For instance, knowing the response of imports to the ratio of import and domestic prices can help determine the results of a change in tariffs or deflation as these events change price relativity. Additionally, knowing the income elasticity of import demand in the short term and long term can help us understand better whether or not the balance of trade is more negatively affe cted by growth in one time frame or the other as changes to income may be seen more or less immediately in changes in imports These issues are of particular importance to PAGE 5 3 developing nations which can greatly benefit from the ability to understand where t heir countries are heading economically and how their policies have shaped that course in the past and how they can potentially shift performance in the future. Empirically testing import demand equations and finding the values of significant coefficients has the added benefit of also contributing to the proving or disproving of economic growth theories dependent upon such values. The validation of such theories can help us achieve a higher level of understanding of how aggregate national and internationa l behav ior determine economic growth, an insight which is of vital importance for a more complete unde rstanding of economic theory. Specificall y, investigating the level at which growth levels in these developing nation s is of great interest While more or less confirmed empirically in recent studies for countries belonging to the Organiz ation for Economic Co operation and Development (hereafter referred to as the OECD) (Bagnai 2008 ), a comprehensive analysis for any g eographic union of developing nations employing current considerations of structural breaks has yet, to our for the developed nations under the OECD branding, but when analysis of economic theories is centered on developing nations results have often varied from those pertaining to more economically advanced nations In this paper a primary goal of ours will be concerned with the establishment of the long run impact of aggregate var iabl es on import demand. In order to accomplish this goal we will observe a necessarily large span of data As any study that attempts to analyze aggregate behavior over a long period of time exposes itself to both the possibility of changes in the param eters and the effects of nonstationary series of PAGE 6 4 variables a characteristic typical when dealing with large sample series used in imp ort demand equations we will make use of a method similar to that proposed by Gregory and Hansen (1996) and employed by Bag nai (2008) that attempts to use the occurrence structural breaks in the d emand equations as a method of testing for a result of cointegration an event where a combination of nonstationary variables results in a stationary equation Through this process we hope to discern any long run relationship s that exist between nonstationary variables The observance of structural breaks is o f key importance to the discernment of an accurate import demand function, one that can be used in the determination of the va is often a consideration that is left out in research of import demand equations The inclusion or exclusion of structural breaks in import demand analysis can alter the acceptance of cointegration between variable s and drastically change the results of import demand estimation as if it is excluded while being a relevant variable the model will have been incorrectly specified Therefore, the analysis conducted in this paper will take account of structural breaks. After discovering we turn our and attempt to determine its potential descriptive ness of each cou view of the efficacy of by Bagnai (2008) period following a structural break than the period before. This result was attributed to the notion that these structural breaks might represent moves towards better integration of these economies in the world economy an event that could result in more attention PAGE 7 5 being paid by the governments of the world to the ir exter nal indebtedness. Given these results, we may expect that the validation of the theory amongst these developing countries may prove less successful than amongst the OECD countries commonly examined. A brief introduction to the theory of income elasticity structural breaks and law seems in order at this point 1. 2 Structural Breaks The first steps taken in this study will be to empirically approximate import demand equations for the four countries listed above Vital to this effort will be the determination of whether and when structural breaks occur throughout the observation period. Given a time frame spanning multiple decades (a necessity when considering cointegration of long run variables ) and given that developing nations are prone t o political and economic shifts as they grow to the level of more industrialized nations the likelihood of the existence of significant structural changes that would make an impact on aggregate import demand behavior is almost assured. Conducting the anal ysis without consideration to the possibility of the o ccurrence of structural breaks c ould constitute a specification error and could lead to spurious results with biased and inconsistent s meaning that there would be a large spread between the expected and actual parameter values and that these estimates would fail to converge to their actual values as the sample size was increased The ability to determine the existence of any long run relationships between the varia bles would also be put into jeopardy by ignoring structural breaks as their exclusion from behavioral functions has been shown to bias cointegration tests in the PAGE 8 6 direction of nonco integration ( Gregory and Hansen, 1996 ). When faced with an equation contain ing nonstationary serie s ( time series where mean and variance are not constant over time) if one cannot find evidence of cointegration one will be left with a possibly spurious regression (Yule, 1926) in other words, a regression which displays a signific ant relationship when there is actually not one Non spurious resu lts are vital for 1. 3 In 1979, Anthony Philip Thirlwall published his seminal work The Balance of Payments C onstraints as an Explanation of International G r owth Rate D In that paper Thirlwall set about to provide an alternative view to the neo on of growth rate differentials which he found to be an unsatisfactory d escription for the differences in growth rates The prevailing neo classical theory based heavily on the work of Robert Solow, relied up on the agg regate production function to build its argument that differences in growth rates between countries could be attributed to the result of differences in the growth in both factor supplies and productivity. Thirlwall found the neo classical view to be insufficient as it failed to incorporate into its analysis an explanation for the differences in country to count ry factor supply and productivity levels side that adapts to the demand level and therefore it was assumed that an adequate description of growth differentials should incorporate into i t s analysis an observance of the differences in long run demand growth rates (Thirlwall 1979) PAGE 9 7 Thirlwall that the long run economic growth rate for a country c an be explained by a relationship relying on the growth of exports and the long run income elasticity of imports. Building off of the aforementioned Keynesian concept of adaptive supply and assuming the current account to be balanced in the long run, Thirlwall proposed that difference s in productivity and factor supplies can be attr ibuted to differences in the growth rates of aggregate demand. Thirlwall proceeded to empirically test this assumption on numerous large, developed economies including the United States and the United Kingdom in the period following World War II and found the results to be overall indicative of his income growth rate differentials run growth rates the elasticities used in the procedure must also naturally, be long run est imates ( Thirlwall 1979) As mentioned earlier, when dealing with nonstationary variables (national income, for example, is often nonstationary) one must employ cointegration techniques to analyze their long run relationship. As Thirlwall es were conducted before the emergence of modern cointegration techniques such as that of Engle and Granger (1987) the accuracy there have been numerous attempts to tes t his hypothesis using more contemporary, appropriate econometric methods. These attempts will be reviewed later. None of the se efforts reasonably large sample of developing nations while giving consider ation to the possibility of structural breaks. That the rate of growth of developing nations should depend heavily on the rate of growth of exports makes inherent sense, as the introduction of foreign currencies through exports PAGE 10 8 allows for the financing of the imports inputs necessary for economic growth. We now begins with two basic equations to describe the flows of exports and imports: (1) (2) Above, represent exports, import s, world income and domestic income respectively and all in real terms terms free of the effect of inflation and represent domestic and world prices (measured in a common currency), respectively represent s the price elasticity of exports and is assumed to be less than 0 which implies that as the relative price of goods increases that is, domestic prices rise a rate higher than foreign prices exports will decrease as foreign consumption is shift ed away from is the price elasticity of imports and is assumed to be greater than 0 to convey the notion that as domestic goods become more expensive relative to foreign goods consumption will shift towards the foreign goods. Finally, and > 0 are the income elasticities of exports and imports which as discussed earlier, implies that as incomes rise consumption increases Th e above equations describe import and export demand functions as lo g linear that is, they can be expressed as a linear combination of logarithms and homogeneous of degree zero in prices which is to say that if both domestic and foreign prices are increased by PAGE 11 9 any constant amount, neither the exports nor the imports will be affected (Thirlwall 1979). Following this, our goal is to arrive at an equality that explains how to calculate the growth rate of an economy with a balanced current account. The following function is derived from the log linearization and different iati on with respect to time of equation s 1 and 2 coupled with the long run assumption that = that is, the current account is required to be balanced (3 ) represent the growth rates of each of the previously defined variables. the assumption that over time, relative prices are constant In other words, domestic and foreign prices grow at the same rate. Put simply, we must have ( ) = 0 We can now solve for : ( 4 ) We arrive at our balance of payments equilibrium growth rate and the definition of l aw Given that the current account is balanced we have that Tha t is to say that the grow th rate is now equivalent to a balance of payments constrained growth rate. (5 ) In order to obtain a more accurate estimation for the balance of payments constrained growth rate it would be ideal to estimate as few components of the above equality as PAGE 12 10 possible in order to minimize error Equation 5 requires the estimation of three variables, including the relatively difficult to estimate world income elasticity. Therefore, we attempt to express as only one variable for ease of estimation Returning to equation 3, continuing with the assumption that domestic prices grow at the same rate as foreign prices, and setting the left side equal to we have: (6 ) Equation 5 can now be expressed and will continue to be expressed for the rest of the paper as: (7 ) Equation 7 is the preferred expression of as it requires only the estimatio n of the income elasticity of imports and knowledge of the growth rate of exports to estimate the balance of payments constrained growth rate Though the growth rate of exports can be found easily for many countries, the income elasticity of imports is no t as easy to obtain. First, one must adequately estimate the import demand equation using appropriate econometric techniques to find such elasticity estimates It is this necessity that forms the basis of this paper. 1.4 Income Elasticity As the purpos e of the estimation of the import demand equation s outside of informative nature these equations have on their own is based heavily on the need to obtain income elasticity of import demand values for the four countries to use in the PAGE 13 11 law, a few words should be spent to define income elasticity. Basically, the income elasticity of import demand is a value equal to the percent change in quantity demanded divided by the percent change in income. In other words, the income elasticity of import demand describes the responsiveness of imports to changes in income. When the absolute value of the elasticity is evaluated at less than 1, demand is considered income inelastic. This means that demand reacts at a slower rate than the increase in income When the absolute value of elasticity is evaluated to be greater than 1, demand is called income elastic. This means that demand reacts at a greater rate than the increase in income Naturally, if the income elasticity of import demand were 0 t he implication would be that import demand does not change at all when income changes. It is assumed that if the actual value of the income elasticity is negative, then the good under consideration is an inferior good a good whose demand is reduced as inc ome increases. Similarly, if the actual value of elasticity value is between 0 and 1, or greater than 1 the good can be considered normal or superior, respectively. 1.5 Outline The paper is comprised of five sections and will proceed as follows. Se ction II will provide a review of the literature, examining the empirical work done on developing import demand functions and their use in testing for growth Section III will present t he data (import, GDP, price leve ls etc. ) for each of the countries under consideration and will then develop the econometric model and process that will be used to create import demand functions and test for the validity of the growth PAGE 14 12 theory. Section I V will present and discuss the res ults. Finally, in Section V conclusions and summation will be provided 2. Literature Review The attempts to conduct a satisfactory empirical analysis of been numerous, with the history of such attempts spanning decades beginning with As discussed above, is a rule that establish es an explanation for differentials in long run growth rates between nations by observing a city of imports To verify this rule for any given country one needs to obtain an estimate of the income elasticity of import demand. Naturally, obtaining this long run value requires the estimation of a long run import demand equation to discern accurat e coefficients for verification. study did not concern itself with the obtainment of import demand equations o f its own, but instead employed the estimates for income elasticity of imports previously derived in a study conducted by Hou thakker and Magee in 1969 to test its hypothesis. As mentioned earlier, these estimates possess the apparent defect of having been derived prior to the advent of more recent methods of cointegration testing. In addition to this, the study was conducted w ithout direct ly accounting for the possibility of structural breaks though Thirlwall admits the possibility of their occurrence Since run parameter estimation of import demand equations mostly looking at those belonging to countries in the OECD using cointegration techniques to attempt to discern long run relationships between variables and to locate significant coefficients of PAGE 15 13 variables for use in the s law. More recent studies have begun to thoughtfully incorporate structural breaks into the analysis. Leading the charge in recent years was Bairam (1993) who first attempted to test for cointegration in the import demands functions to derive accurate long run values while not explicitly test ing Bairam studied the import functions for five European countries France, the United Kingdom, Belgium, Germany and the Netherlands with annual data spanning 1970 through 1989 Unable to reach a conclusion of cointegration and yet finding variables of the import function to be I (1), Bairam instead decided to use pre differenced values of the variables to obtain I (0) series in an attempt to find an estimate that would have nonb iased and consistent standard errors Bairam (1993) take s the lack of cointegration as evidence of the need for the predifferencing of variables and continuing with the estimation, finds the income elasticities of the differenced import equations all to be statistically significant and the price elasticities not to be. However, several point s stick out that se em to imply that the conclusion s of the test may be less than wholly accurate To start with, the 2 value of the pre differenced equation 0.8 does not drop significantly from that of the original equation 0.97. However, differencing an equation with cointegrating variables will not lead to a significant decrease in the 2 value whi le differencing a noncointegrating equation will lead to a significant drop in the 2 value. This suggests the possibility that the variables in the import demand equat ion s tested in Bairam (1993) do in fact, cointegrate as has been addressed by Bagn ai (2008) Following this line of thought, it is relevant to note as has been pointed out by Hieke (1997) and Atesoglu (1997 ) that the implementation of PAGE 16 14 differenced variables in an equation with cointegrati ng variables will le ad to the loss of long run i nformation As explained by Bagnai (2008), this is due to the fact that differencing the standard import demand equation eliminates the cointegrating residual from the dynamic error correction representation that would normally explain the cointegrating r elation between any n I (1) variables. The overall effect of this is a specification error that likely leads to biased and inconsistent estimates of the elasticities estimated in the differenced import demand equations. Additionally, t here exist at least two potential explanations for the conclusion of (1993) First, as Bagnai (2008) points out as t he test conducted by Bairam employed a sa mple of 20 annual observations the study needed to employ appropriate critical va lues. When critical values inappropriate for a given sample size are used incorrect conclusions may be reached When the analysis is conducted with t he critical values of Bla n giewic z and Charemza (1990) critical values that are specifically intended for use in tests with small sample sizes the procedure returns cointegration results for three of the five countries (Bagnai, 2008) Additionally, the omission of key variables in an y equation estimation represents a type of specification error and may change the conclusions drawn from the results a specification error that will carry over to the differenced form. As admitted by Thirlwall (1979), structural breaks most likely represent a relevant consideration in the analysis of long run estimates he asserts that their prevalence may have increased towards the end of his sample period and that they may have chang ed the value s of the estimated coefficients. As subsequent studies by Gregory and Hansen (1996) have suggested it is most likely the exclusion of st ructural breaks as variables in the analysis that represents a significant PAGE 17 15 misspecification, one that may result in an incorrect conclusion of noncointegration. Bairam followed up this initial 1993 study into the matter with another in 1997 that helped d esignate the current investigation into the connections linking to the import and export income elasticities using similar cointegratio n techniques Bairam (1997) reaches the conclusion that due to the income versio law seen in equation 7 would be the preferable version to be studied in f uture analyses. S ubsequent studies have incorporated structur al breaks into the analysis. Another similar study was conducted in 1997 by Hubert Hieke Hieke analysis focused on the United States and was one of the first to incorporate structural break s into the analysis as variables chosen at various intervals A dditionally, the study made use of the relative prices of imports as variables in the equation Several important points on previous research are made and improved upon within the study and m ore are recognized for future research. First Hieke employed a decently large sample in his study that consisted of quarterly data from January 1950 through April 1990, a forty year span double th e span which Howeve r, the use of quarterly data is fairly irrelevant as the determination of long run parameters is more concerned with span than with frequency of data and the structural breaks were taken as occurring between the fourth and first quarter of consecutive year s rather than occurring throughout the year The use of structural breaks in the analysis is an important step forward in this realm of research as long run estimates of trade equations are very likely to be subject to PAGE 18 16 change over sizeable sample periods sample periods the size of which are clearly needed to ascertain long run behavior and incorporate cointegration techniques. Additionally, Hieke not only took into account the role of structural breaks in long run coefficient determination, but also corr ectly asserted that structural breaks need not occur at the same points in various countries While obviously not a relevant comparison point in his study, as focus is only on one country, the observation is a much needed one to motivate more involved res earch as many studies have simply taken a single break point as the standard break point for all countries tested. Hieke found that all the variables used in the study were but there was no evidence of cointegration in the sam ple as a whole. However, cointegration is verified when the sample is broken into multiple subsamples. This continues to reaffirm the assertion that previous results of noncointegration may have been the result of a model specification error through the exclusion of relevant structural break variables. Between the two subsamples split between 1966 and 1967, the income elasticity of imports nearly doubles. Additionally, the variable represented by the relative prices of imports appears to be relevant in long run trade equations Though t he method used by Hieke (1997) helped encourage the adoption of the line of reasoning that structural breaks and the relative price of imports play considerable roles in the determination of long run parameters, room for expansion still exists in the analysis. While the use of a longer sample period in the study is most useful the utilization of only one country does little for multi law Similarly, th ough the use of structural break s in the analysis helped address the issue of evolving trade parameters and though the use of subsamples allowed for PAGE 19 17 confirmation of cointegration, this result is more likely the result of the fact that small subsamples more accurately captur e changes in p arameters rather than capture the actual changes. In other words, the use of arbitrarily defined points as the locations of structural breaks may not satisfactorily produce accurate long term parameters and this leaves room for further refinement The p roblem of limited country data is further addressed and slightly relieved in the similar examination of t hree countries by McCombie in 1997 Using a sample period from 1952 through 1993 McCombie (1997) like Hieke (1997), looks for cointegration in the i mport demand equations of the United States while additionally bringing Japan and the U nited Kingdom into the analysis. McCombie asserts that the income elasticities should come from demand equations tha t are inclu sive of the relative price term, though the term possesses a quantitatively low impact on trade flows in the long run. He addresses the relevance of structural the key variable relationships that fails to recognize a potential break in the trend will open itself to biased results in favor of rejecting the unit root. McCombie assumes break point s between 1973 and 19 74 modeled after the collapse of the Bretton Wo ods system and the recession spurred by the oil shocks Initially, McCombie approaches the trade equations as possessing a segmented trend with an intercept shift between 1973 and 19 74 He then examines the plausibility of the break point resulting in a one that not only shifts the intercept after the break point between 1973 and 19 74 but one that also alters the income elasticity coefficient. In both case s McCombie reaches conclusion s of nonstationarity of the imports and income for any of the countries studied, except for PAGE 20 18 Japan in the second scenario As addressed earlier, it does not seem to be entirely reasonable to assume the same points of structural breaks for all countries under analysis as the oil shocks had varying effects on d ifferent countries and other economic developments may represent more significant structural shifts for any of the observed countr ies After reaching the conclusion of noncointegration in the variables in both the ombie, like Ba iram (1993) before him concludes that these results must be indicative of the need to pre difference the involved variables. This decision to pre difference the variables does just as little in the effort to obtain accura te long As a model s pecification likely arises due to the arbitrary and homogenous determination of structural break points, pre differencing does little to correct the model. The relevance of signal point structur al breaks is somewhat downplayed as McCombie asserts that changes in the income elasticities of imports most likely come as a result of changes in the degree of nonprice competitiveness a change that would occur slowly rather than at any one point time. I n his attempt to verify the null hypothesis of nonstationarity Augmented Dickey Fuller (ADF) test (Dickey and Fuller, 1979 ) (1993 ). Overall, McCombie reaches the conc lusion that the three countries studied all grew at roughly their balance of payments equilibrium growth rates. As elaborated on above, there are many reasons for applauding the efforts of McCombie, while noting their capacity for improvement. The study c onducted by Bairam and Ng in 2001 attempts to correct for the flaw of arbitrary structural break dates present in previous studies Bairam and Ng analyze the PAGE 21 19 import functions of Canada, New Zealand, and the UK using a sample of annual time series data that spans from 1973 through 1995. The choice of the three countries was based on the contrasting nature of their trade patterns (Bairam and Ng, 2001). Proceeding with the assumption that structural breaks occur at a specific point in time rather than throug h gradual economic change, Bairam and Ng take a result of noncointegration in the import demand equation of a country as an indication of structural breaks in the income elastici ties and acknowledge that any such unaccounted for break is likely to change t assumption by use of the CUSUM test of Brown et al. (1975). Cointegration is only found initially for New Zealand, which may hint at a more gradual change of trade conditions for this nation compar ed to the other, more developed economies. Overall, when structural breaks are accounted for. Unfortunately, as addressed by Bagnai (2008), it is incorrect to use the CU SUM test for such verification as its distributional characteristics are tied firmly to the assumption of stationarity of the variables in question which in the trade equations of Canada and the UK are found to be nonstationary In o ne of the more recent attempts at analysis of the empirical validity of Bagnai (2008) continues along the same lines of inquiry as previous research while making marked improvements on the various areas left flawed or unanalyzed in the previous economet ric studies. The flaws from previous studies paid particular attention to and addressed are the small number of countries under consideration, short sample periods, the use of arbitrarily identified structural breaks, the PAGE 22 20 use of the same break point for a ll countries observed, the use of pre differenced variables as a means for overcoming noncointegration and the exclusion of the relative price of imports as a variable in the trade equations Bagnai (2008) addresses the first issue by deriving imp ort dem and equations for 22 OECD countries which in addition to the United States, the United Kingdom, and Japan include Australia, Austria, Belgium, Canada, Denmark, Finland, France, Greece, Iceland, Ireland, Italy, Mexico, the Netherlands, New Zealand, Portugal Spain, Sweden, Switzerland, and Turkey. Even when positive results were achieved, previous studies uses of only a handful of countries did little in the way of broad cross cointegration te chniques an d a necessarily large span of annual data ranging from 1960 2006 while accounting for structural breaks in the data Accepting that the omission of structura l breaks from the analysis can result in a conclusion of noncointegration, structural breaks are considered to occur at definite points in the sample period and not to reflect slowly evolving changes in trade. Bagnai tests for long run relationships between the variables of the import demand equations using th e Engle and Granger (1987) Cointegrating Residual Augmented Dickey Fuller (CRADF) test, asserting that the supposed superiority of the Johansen (1988) approach of cointegration testing is invalid in his analysis as it s application of the maximum likelihood principle rests upon the assumption of a known and constant distribution of data an assumption he claims is invalid due to the very nature of structural breaks. Further, when the null of noncointegration fails to be rejected by the ordinary cointegration test, Bagnai adopts the stance that such a result likely depends on the presence of structural breaks in the long run parameters. Overall, cointegration is found in 16 out of 22 of the countries PAGE 23 21 run estimates in the periods follow hypothesis as that economy become s more open and integrated clearly tends to consider trade equation parameter values as being subject to abrupt structural breaks at explicit points in the sample period rather than as expressing slowly evolving economic changes that may be indicative of more abstract notions such as changing preferences an d non price competitiveness Much of the literature reviewed tends to treat structural breaks as occurring at the same point for multiple countries and either makes arbitrary decisions about when such breaks would occur or just assumes, perhaps incorrect ly, specific events, such as the oil shocks of 1973, as likely repres entatives for the points where structural breaks occur. Some studies, such as those of Bairam and Ng (2001) and Bagnai (2008) take into account the differing nature of different countrie equations with respect to structural breaks and explicitly tackle the issue of the potentially unknown All previous studies look solely at more developed nations, tending to focus attenti on on the member nations of the OECD. Using modern econometric techniques focusing on the import demand form, and accounting for and overcoming previous study flaws, recent attempts to verify Thirlwall have returned positive res ults. Using the advancements in the understanding of and in the techniques used to verify can be made on applying this knowledge to analyze those countries left previously unstudied, mainly those countries not belonging to the O ECD. PAGE 24 22 3. Methodology The discussion of the methodology will proceed in several sections. The first section will address the variables and data employed in the analysis with theoretical discussion of their relevance. The second section will explain the step s involved in the practical application of the concepts 3 .1 Variables This study utilizes time serie s data on real GDP, real exports, real imports, and import relative prices, calculated as the rati o of the GDP deflator to the imports deflato r, for Jordan, Pakistan Singapore, and Thailand over the period 1983 to 2007 Because intermediate goods comprise a large amount of imports their demand is likely tied to total count ry output, and therefore, the real GDP variable is employed in the model rather than other measures of aggregate domestic activity. Other variables have been proposed for use in import demand equation s, such as a measure of exchange rate volatility Howe ver, while exchange rate volatility has been shown to have an effect on trade flows, the results have shown that that effect can be both negative and positive depending on the industry The results are roughly split with the aggregate effect of the exchan ge rate volatility being insignificant (Bahmani Oskooee, & Hegerty, 2007) Additionally, an attempt by Atesoglu (1993 94 ) which was generally supportive of finds growth of capital flows to be insignificant in the analysis. Real GDP was c alculated as the nominal GDP multiplied by 100 and divided by the GDP deflator. Real exports was calculated as the nominal exports multiplied by 100 PAGE 25 23 and then divided by the exports deflator. Similarly, was calculated as the nomi nal imports multiplied by 100 and divided by the imports deflator. All data were retrieved (IFS) database in November 2009. A measure for price relativity (domestic prices over for eign prices) was taken as the GDP deflator divided by the import deflator Real imports, real GDP, and real exports are all calculated in bi llions of the domestic currency. 3. 2 Application A basic model of imports on regressors would take the form of eq uating imports over time to GDP over time, the relative price term over time a constant, and an error term: (8 ) Here, we would expect the level of GDP to have a positive effect on imports, i.e. Here we mean to say that as the level of national income increases so too will the money spent on foreign goods increases it eventually shifts demand from intermediary input goods to final form consumption goods. Similarly, as the price of domestic goods rises re lative to that of foreign goods, becoming relatively more expensive, we would expect imports to increase, i.e. > 0. However, while equation 8 serves well to explain how an increase in income leads to a proportional increase in import consumption, t his analysis is concerned primarily PAGE 26 24 with obtaining estimates of the income elasticity of imports and b ecause the coefficient of a logged term in a regression represents the unlogged following form for our import demand equation (9 ) where are the va riables defined above, is the constant term, is the error term, and and are the income and relative price elasticities of imports. In this form of the model we expect > 0, which implies that import s as a whole are not an inferior good. As to its elasticity type, it is uncertain whether it will be elastic or inelastic. One of the possible results of a structural break may be that that structural break signifies a shift towards improved economic int egration and perhaps this economic development will lead to the elasticity term increasing to a value greater than 1 in the second subsample as import demand shifts from necessity input goods to superior goods. Of course, similar explanations could be mad e for an opposite shift. Additionally, we also expect > 0 as a percentage change in price relativity signifying an increase in domestic prices relative to foreign prices will likely lead to a positive percentage change in import demand as imports become relatively more affordable. Again, we are unsure as changing status from inputs to luxury goods may hold. PAGE 27 25 3.2a Unit Roots We expect the series of both GDP and imports to be nonstationary and test whether or not the log linear import demand function reflects the presence of a cointegrating relationsh ip between the variables. To begin to test this hypothesis we start by testing for the presence of a unit root in these time series using the Augmented Dickey Fuller (ADF) unit root test. The basic Dickey Fuller test for unit roots looks at whether or not the difference between consecutive time series observations is equal to a random error term. This is to say tha t in the equation where the series Y has a unit root if If a unit root is found then the series are nonstationary. The above equation can be modified to accommodate for a drift and a trend in the series with the addition of a constant value and a time dependent value, respectively. The ADF test simply tweaks the basic Dickey Fuller test by accounting for lagged differences etc.) in the above equat ion to reach a state where the white noise error term is serially uncorrelated. The order of lags in the ADF regression is determined by model reduction using the Schwartz Bayesian Information Criterion (SBIC) a method used for model selection. 3.2b Coin te gration Tests We test for the pres ence of a long run relationship cointegration between the variables using the Engle Granger CRADF test. The Engle Granger CRADF test tests for a cointegrating relationship between two or more nonstationary time series. Possible cointegrating equations those containing nonstationary variables are estimated over PAGE 28 26 the whole sample period and the residuals are tested for the presence of a unit root using the appropriate Engle Granger CRADF critical values. If results of no cointegration are returned then the model is tested under the assumption of structural breaks. The structural breaks are modeled using a dummy variable 1 = ( ) where I is the indicator function, is the sample size ( ), is the relative timing of the breakpoint and is the integer part function This is to say that the point of break is taken to be the beginning of the year reported. The null hypothesis of n o cointegration is tested in the presence of two forms of structural break. The first is where the structural change only affects the intercept term. log = 0 + 0 + log + log log + (10 ) The second is where all coefficients experience a shift in the second subsample. log = 0 + 0 + 0 + 1 log + 0 + 2 log log + (11 ) w here 0 0 and 0 indicate the values taken in the first subsample, 1 is the shift dummy variable defined above the ( = 0, 1, 2) are the parameter shifts, and is second (post bre ak) subsample can be defined as 1 = 0 + 0 1 = 0 + 1 and 1 = 0 + 2 break, and it takes the value 1 = 0 + 0 As can be seen above, the exclusion of structural breaks, should PAGE 29 27 they occur, would constitute a specificati on err o r as an estimation of Equation 9 over the entire sample would omit the se key shift dummy variables. It is this type of specification error that could lead to the spurious rejection of cointegration in the import demand equations that we want to avoid. W e test the cointegrating equation over the whole sample under the assumption of no structural break. We also test for each type of break in each possible year af ter the first if a result of no cointegration is returned ; a break in the f i r st year correspon ds to no break at all When a result of cointegration in a model (level or regime) with structural break was found the model was chosen in one of two ways. Either the level of the CRADF was taken into account or the economic relevancy of the parameters. We are thus choosing the model with the breakpoint that most strongly indicates the presence of cointegration. We argue that this is justified because our goal is to estimate the income inelasticity of imports for each country, and we believe the import demand function will reflect a long run relationship when the presence of a structural break is properly accounted for. 3.2c Balance of Payments Constrained Growth Once a long run income inelasticity of impo rts estimate is found for each country, we test cross the group of countries. We use the estimated value of income inelasticity of imports to estimate the balance of payments constrained growth rate u sing equation 7 We then estimate the following equation using the actual average rate of growth of income (1 2 ) PAGE 30 28 for the four countries in our sample, using the Wald test to examine the null hypothesis 0 : [ ] = [ 0 1 ] This is the method of verification employed by McGregor and Swales (1985 ) McCombie (1992), and Bagnai (2008). The idea is that by doing cross ty estimates, when broken into subsamples. Other methods for exist such as that utilized in McCombie ( 1989, 1997) which finds the income elasticity of imports necessary to equate the balance of pay ments constrained growth rate with the actual gr owth rate. Following equation 7 : One can proce ed to test for significant difference between the estimated income elasticity and the elasticity necessary for growth under long run balanced trade. 4. Results The results will be presented as follows. First, unit root results for the three variables includ ed in the import demand function (real imports, real GDP, and relative prices) will be presented. Second, cointegration results for the aggregate import demand function will be discussed. Third, import demand functions will be presented for the four coun tries. Finally, balance of payments constrained growth in the face of structural breaks will be analyzed. PAGE 31 29 4.1 Unit Roots The results of the unit root tests for the four countries studied are presented in Table 1. The time series of real imports appears to be nonstationary in all four countries. Similarly, the unit root tests for the logarithms of real GDP all appear to be nonstationary a s well. However, as far as the relative price series are concerned, the unit root hypothesis is rejected for Jordan a nd Singapore. These results lead us to conclude that the following cointegration approach for the import demand functions is justified as a stochastic trend in the import time series is matched by a stochastic trend in both explanatory variables for Pakis tan and Thailand and at least one explanatory variable in Jordan and Singapore. Table 1. Unit Root Tests of the Import Demand Function Variables Notes : represent the Augmented Dickey Fuller stat istics of the hypothesis of integration under processes with trend and drift, with drift, and with neither trend nor drift, respectively. indicates a significant statistic at the 5% level PAGE 32 30 4.2 Cointeg ration Tests The results for the cointegration tests for the four countries are displayed in Table 2. None of the four countries appear to possess stable long run import functions when consideration to structural breaks is not gra nted When a level break is considered, all countries studied return cointegration results at the 10% level of significance and only the import function for Pakistan fails to cointegrate at the 5% level of significance. When regime shifts are considered, all import functions appear to cointegrate at the 5% level of significance. All of the breaks happe n in the mid 1990s (1995 1997). Table 2. Cointegration Results Countries CRADF P CRADF(L) BREAK p CRADF(R) BREAK p Jordan 3.09 0 4.18 1997 0 5.68* 1995 0 Pakistan 3.12 1 4.01 1994 1 5.52* 1997 1 Singapore 3.14 1 4.95* 1996 1 4.7 3 1996 1 Thailand 3.35 1 5.36* 1996 1 6.78* 1996 1 Notes: CRADF is the Engle Granger statistic of cointegration. The three CRADF statistics represent the cointegrat ion statistic over the whole sample, over the sample with a level shift, and over the sample with a regime shift, respectively. p is the number of lag of the dependent variable included in the auxiliary regressions *indicates a significant statistic at the 5% level In terestingly, t he da tes of these structural shifts sometimes appear to correspond with significant events such as international trade or relationship treaties in some countries but not in all In Jordan the shift seen in 1995 corresponds with the late 1994 signing of a peace treaty with Israel which led to more normalized relations Additionally, in 1996 Jordan made further steps towards global economic integration with the signing of a trade treaty with Israel, the effects of which would be felt in the ate in the second subsample. Thailand made many changes to encourag e increased economic integration in 1995 that would have had their effects noticed in 1996. The major change was its accession to the World Trade Organization (WTO). This move led to the PAGE 33 31 r eductions of the maximum tariff and the tariff rates on many items. Additionally, a bill was proposed to create an intellectual property and international trade court. Singapore also experienced some positive economic and trade policy shifts directly a round the break point between 1995 and 1996. The most significant change would appear to be that which occurred in the beginning of January 1996 when Patent Act came into effect that made the act meet standards imposed by the W TO Agreement on Trade Related Aspects of Intellectual Property Rights In regards to Pakistan break point, no major institutional change is readily apparent. 4.3 Import Demand Functions Below the import demand equations for the four countries with struc tural shifts are presented. Jordan Regime Shift 1995: Pakistan Regime Shift 1997: PAGE 34 32 Singapore Level Shift 1996 : Thailand Level Shift 1996: As can be seen, our initial hypothesis of a positive coefficient for holds in both subsamples for all countries observed implying that in none of the countries are imports as a whole deemed an inferior good In Jordan, it appears that income elasticity of imports shifted from being elastic in the first subsample to being inelastic in the second subsample. In Pakistan, imports appear to be inelastic in respect to income in both subsamples. In both Singapore and Thailand, imports appear to be elastic in both periods as there is no shift in the elasticity value. In regards to the coefficients of relative pr and negative in both subsamples. This result is surprising as one might naturally expect a positive increase in relative prices to lead to a positive increase in imports as demand is shifted away from domestic goods. We reach a similar result for Pakistan. Here imports are elastic with respect to relative pr ices in the first subsample. However, after the break point, imports appear to be nearly unit elastic but negatively so implying that a positive percentage chan ge in relative prices leads to an equivalent percentage decrease in imports. In both Singapore and Thailand we recover more conventional results with positive but price inelastic demand for imports. PAGE 35 33 4.4 Balance of Payments Constrained Growth Table 3 pre sents the estimated income elasticities of imports for all four countries over the whole sample and in each subsample pre and post structural break. The income elasticities remain the same between the two subsamples for Singapore and Thailand as their st ructural breaks take the form of level shifts and in this form the in come elasticity is unaffected. Table 3. Income Elasticities of Imports Countries Break Date Jordan 0.856 202 1995 1.533978 0.665892 Pakistan 0.650705 1997 0.950163 0.690959 Singapore 1.074462 1996 1.243226 1.243226 Thailand 1.635846 1996 1.763962 1.763962 Notes : a re the estimates of the elasticities over the whole sample, in the first subsample, and in the second subsample, respectively. Table 4. Whole Sample Balance of Payments Constrained Growth Rates Countries Jordan 4. 64155 0.856202 5.42109 4.01374 Pakistan 7.379067139 0.650705 11.34011132 4.925462081 Singapore 12.52581767 1.074462 11.65775772 6.78283402 Thailand 11.92788235 1.635846 7.291568004 6.003408846 Notes : is the growth rate of real exports, is the income elasticity of imports, is the balance of payments constrained growth rate, and is the actual growth rate. Table 4 presents the balance of payments constrained growth rates g iven the ave rage export growth rates as well as the estimated whole sample (free of breaks) income elasticities of import demand For comparison, the actual real income growth rates are calculated and shown. As can be seen, the estimated balance of payments constrai ned growth rates vary significantly from the actual growth rates. The Mean Absolute Deviation or MAD a measure of variance between estimated values and actual values between and for the whole sample per iod is approximately 3.50 percent. PAGE 36 34 Table 5 presents the estimated balance of payments constrained growth rates and the actual growth rates in the pre break subsample. As can be clearly seen, the balance of payments constrained growth rates more closely re semble the actual growth rates for all countries than do the whole sample estimates The improvement is particularly noteworthy for the case of Pakistan. between the balance of payments constrained growth rate and the actual growth rate remains rather large. The MAD value in the pre break subsample drops significantly to approximately 1.99 percent a decrease of over 1.5 percentage points from the whole sample period. Table 5. Pre Break Balance of Payments Cons trained Growth Rates Countries Break Date Jordan 1995 4.835817771 1.533978 3.15246879 2.300328054 Pakistan 1997 7.382674595 0.950163 7.76990326 4 6.532662662 Singapore 1996 15.38591234 1.243226 12.37579679 7.680539943 Thailand 1996 17.50575518 1.763962 9.92411128 8.767964039 Table 6 presents the post break estimated and actual growth rates. Again, the estimated balance of payments constraine d growth rate estimates more closely resemble the actual growth rates than do the whole sample estimates. However the difference between the balance of payments constrained growth rate and the actual growth rate for Pakistan in the post break period is r oughly the same as that when considering the whole sample. This is in contrast to the dramatically closer estimate s in the pre break period for Pakistan. The MAD value between the estimated and actual growth rates in this post break subsample is approxim ately 2.44 percent. This is a worsening of mean absolute deviation of 0.45 percentage points compared to the pre break sample, but is still an PAGE 37 35 improvement as far as a decrease in deviation of 1.06 percentage points compared to the whole sample deviation. Table 6. Post Break Balance of Payments Constrained Growth Rates Countries Break Date Jordan 1995 4.477169984 0.665892 6.723567761 5.463547166 Pakistan 1997 7.374803781 0.690959 10.6732871 4.30240875 Singapore 1996 9.665723007 1.243226 7.77471112 5.885128098 Thailand 1996 7.209656119 1.763962 4.08719469 3.238853653 The Spearman rank correlation coefficient is a value which describes the mono tonicity (the preservation of ranked order) between two series. Over both the whole sample and the pre break subsample the rank correlation coefficient is equal to 0.8 between the two income growth rate series. Over the post break subsample, the rank cor relation coefficient is equal to 0.4. However, while the observed values would tend to indicate a strong monotonic relationship between the two series in the whole sample and pre break subsample and a weak relationship in the post break subsample, the ran k correlation coefficient is not statistically significantly different from zero in any of the above cases. Despite an apparent lessening of the difference between the estimated and actual growth rates, with a sample size of countries of only 4 statistica l significance of ranked order is likely harder to obtain. This helps to explain why the correlation coefficient apparently drops between the whole sample and post break subsample despite a decrease in mean absolute deviation between the two growth rates in the post break period compared to the whole sample deviation. Table 7 presents th e results of the estimation of e quation 1 2 Though F value for a Wald statistical test conducted on the hypothesis of a=0, b=1 cannot be rejected in the whole sample n eit her can the null hypothesis of b=0, individually. This result leaves PAGE 38 36 Also, the adjusted coefficient of determination ( ), which is a measure of the regression takes as its maximum value 1, is quite low. The best results appear to be in the pre break subsample. The hypothesis a=0 cannot be rejected, while the h ypothesis can be rejected at the 10% level of significance. Also, the joint hypothesis of a = 0, b=1cannot be rejected with the F test. Additionally, the adjusted value is very high at 0.727480. Howev er, the post break sample does not return very convincing results about the balance of The hypothesis that b = 0 cannot be rejected and the adjusted value is low. Table 7. Estimation of Equation 1 2 Whole Sample Pre Break Post Break a 0. 933835 (0.9182) 0.394204 (0.9018) 3.479861 (0.6800) b 1.471785 (0.4178) 1.251724 (0.0953) 0.812036 (0.6440) F test(a=0, b=1) 2.671154 2.070068 1.390634 (0.2724) (0.3 257) (0.4183) 0.008363 0.727840 0.309869 Notes : p values of the t tests are reported in parentheses under the coefficients and F test value. These results indicate that of the three samples y supported in the pre break subsample. All countries appear to have grown below their estimated balance of payments constrained growth rates. Additionally in all subsamples there is one country that grew at a rate at least four points lower than its ba lance of payments constrained growth rate. Given the above regression results, acknowledging that the date of structural breaks corresponds with actual, apparent changes in the economic and trade related policies of all countries except Pakistan, and obs erving that only the estimate of PAGE 39 37 break subsample, it seems reasonable to suggest that the regression should be tested again with Pakistan excluded. With Pakistan excluded the mean absolute deviations between the estimated and actual income growth rates in the whole, pre break, and post break subsamples are now approximately equal to 2.53, 2.23 and 1.33, respectively. As can be clearly seen, with the exclusion of Pakistan the mean absolute deviation significantl y reduce in all three periods We now test equation 12 for the three remaining countries. Table 8 shows the results. Table 8. Estimate of Equation 12 without Pakistan Whole Sample Pre Break Post Break A 3.042799 (0.6949) 0.602229 (0.9008) 0. 242773 ( 0.8270) B 1.993979 (0.3019) 1.261182 (0.2656) 1.323788 (0.0833) F test(a=0, b=1) 2.707515 1 108757 23.39100 (0.3948) (0.5575) (0.1447) 0.582938 0.671693 0.965934 Notes : p values of the t tests are reported in parenthes es under the coefficients and F test value As can be seen from table 8 with the exclusion of Pakistan from the analysis the the post break period compared to the pre break period and whole sample. The adjusted value has increased to nearly 1 in the post break period an increase in the goodness of fit of more than 0.23 over the pre break subsample when four countries were considered the pre viously best fit model. The F test cannot reject the joint hypothesis of a = 0 and b = 1. Individually, in the post break period, the hypothesis that a = 0 cannot be rejected while the hypothesis that b = 0 can at the 10% level of significance. These re tends to become a more accurate descriptor of growth behavior in post break periods as those breaks are often associated with shifts towards improved global economic PAGE 40 38 in tegration and economic policy savvy. In that vein, we see an improvement in the post break points that actually coincide with economic and trade reforms. 5. Conclusions T his study was conducted with the hope of fill ing an apparent void in research using cointegration techniques under the assumption of structural breaks in the import demand fun ctions This is not to stay that there has not been m uch work done to explain the ability of hypothesis Much interest has been paid to this topic since it was formalized in 1979. The comple xity of these analyses has grown over the decades to allow for cointegration analysis and the possible existence of structural breaks. The initial ambivalence towards structural breaks that resulted in mere assumptions as to the dates of shifts has given way towards more methodical investigations into the exact point in time a structural change occurred While more recent studies have claimed at explaining long run growth behavior they have foc used almost entirely on member countries of the OECD with little attention paid to the behavior of developing nations. Positive results for these countries have often been found in periods after a structural break with the explanation offered that further global economic integration an d openness has been the main cause of strengthening of the relationship proposed by Thirlwall as these developments lead to more homogeneity in the economic and trade related policies of these now globalized economies This study w as aimed at address ing T PAGE 41 39 accuracy at d escribing the growth behavior of several small er Asian economies with a contemporary history of development and global economic integration. When estimated over the whole sample from 1983 to 2007, every one of the estimated import d emand functions possessed nonstationary variables and failed to reject the null hypothesis of noncointegration. However, it seemed unwise to assume that such a function of aggregate behavior would remain consistent over any prolonged period of time espec toward increased economic integration. It was postulated that structural breaks in the import demand functions could exist and that their existence could have an effect on the inco me elasticity estimates. W hen structural breaks are taken into consideration all four countries appear to possess import demand functions with a cointegrating relationship between their nonstationary series It appears necessary then that to obtain descr iptive estim ates of import demand functions the possibility of structural breaks should always be considered. The result that single break points change the results of cointegration indicates that structural changes in the income elas ticities of imports o we much to discrete events rather than to slowly changing conditio ns. law is concerned, the results we re mixed when all four countries were initially considered When broken into sub samples, ed to hold better in the pre break period for the four nations However, its strength in the post break period and the sample as a whole appear ed weak. In the pre break period all countries except Singapore grew near their balance of payments constrained growth rates. However, this changed as i n the post break period all countries except Pakistan grew less than but near their balance of payments constrained PAGE 42 40 growth rates whereas Pakistan had a growth rate over 6 percentage points lower in the post break than pre break sample It appears worth noting that all the countries that had structural break points that could be tied to actual real world institutional changes grew at a rate closer to the estimated growth rate in the post break period. This leaves Pakistan out as the one country that violates the conditions and also apparently fails to have a real world proxy for a structural break event. For this reason Pakistan was considered inappropriate to When it is excluded from the analysis, it appears that the major institutional changes apparent around the structural breaks for descriptive performance for these countries. As with most analyses, all results should be taken with some mild skepticism. There are many potential issues that may affect the analysis negatively. It would be ideal, as in the case of Bagnai (2008) to analyze a larger selection of countries to test T (four and three ential to distort overall results in regards to the estimation of Equation 12 than would be the case if several more countries were included. If sufficient data could be obtained, it would be ideal to run this analysis again with a minimum of 10 countries. In ad dition, as consideration is paid to the estimation of long run parameters, a fittingly large sample size is ideal. While a 25 observation sample is considerably large, an even larger sample size could only aide in the attainment of a more accurate view of PAGE 43 41 long run behavior. Previous studies on this topic have often employed data sets of 40 or more years. Again, limitations of the data retrieval syst em necessitated the sample size as reliable data for certain variables could not be found outside of this sample period for all four countries. In line with the previous comments it should seem obvious that with any empirical study the results are always subject to the accuracy of the data used. Any inaccuracies in the data obtained from the IMF could very we ll skew the results to either end of acceptance. Absolute accuracy in data is sometimes questionable when considering those at the national level especially for developing nations. Additionally, the analysis rests upon the assumption that domestic and for eign price levels rise at the same rate. This assumption may lead to complications as some countries have persistently high levels of inflation. Finally, there remains the possibility that there are multiple breaks in any given sample period rather than m erely one. The presence of different break points may affect the analysis. 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