# Variables Affecting Ability To Take Out A Loan Finance Essay

The aim of this study was to test the validity of Purchasing Power Parity (PPP) between Spain & Portugal and Spain & Morocco. PPP is a good metric for standard of living. Let us say $1.50 is the same as £1. In this example, a USD will buy 0.67 Pounds. However, what if $1.50 buys more milk in Atlanta (USA) than 0.67 Pounds will purchase in Birmingham (UK)? This led some economists to look at PPP, in addition to the official currency exchange rate.

Studies previous to mine have come to find that in some cases PPP does hold (similar milk quantities can be bought with the same relative money, but in most cases PPP theory doesn’t seem to function.

My empirical work suggests that in reality, PPP relationship does not hold (at least not exactly, i.e.: exactly the same amount of milk bought). This is due to a number of reasons; the main ones highlighted below:

Trade barriers and non-tradable goods and services – Government trade restrictions like import duty would essentially distort the price and any PPP relation possibility (increasing the price of US milk in the UK)

Imperfect competition – allowing similar products to be sold at different prices perhaps due to geographical or chronological restrictions. (milk likely to ‘go off’ soon sold more cheaply than the same amount of more fresh milk)

Differences in price level measures – One country may value a certain good more than another so even though the items may be identical, people would be willing to pay more for it.

A firm sells the same product at different prices in different markets to maximise profits, based on expectations about what consumers are willing to pay. Simply the prices of identical baskets, when converted to a single currency, differ substantially across countries.

## Introduction:

This project aims to examine and econometrically test the validity of Purchasing Power Parity (PPP) between Spain, Portugal and Morocco. It should focus on finding possible stochastic trends that may exist between their exchange rates and relative prices (CPI) using unit root and co-integration tests. The countries in question have been chosen as they are geographically close, with Spain and Portugal sharing a land-based border whilst Spain and Morocco are separated by the narrowest part of the Mediterranean. Also with Spain and Portugal gaining accession into the European Union (EU) and then European Monetary Union (single currency) in 1999 1&2 and Morocco being in Africa should hopefully provide room for good comparative analysis regarding their PPP relationships.

## Theoretical Foundations:

The PPP theory uses the long-term equilibrium exchange rate of two currencies to equalise their purchasing power and is based on the Law of One Price. The theory states that, in ideally efficient markets, identical goods should have only one price. This law applies only in competitive markets free of transport costs, official barriers to trade, perfect homogeneity of domestic and foreign goods, and (usually) perfect competition. The relationship between PPP and the Law of One Price is that the law of one price applies to individual commodities, while PPP applies to the general price level. Therefore if the Law of One Price holds true for every commodity, PPP must hold automatically for the same reference baskets across countries.

Therefore the elemental concept underpinning PPP theory represents an application of the Law of One Price, where economic agents exploit price differences so to benefit from risk-less profit. Thus the proponents of PPP argue that the exchange rate must adjust to ensure that this law of one price holds internationally for both individual goods and identical bundles of goods. There are two forms of PPP to be discussed.

Absolute (strong) PPP states that, exchange rates equal relative price levels. Therefore a rise in the ‘domestic’ price level relative to the ‘foreign’ price level will lead to a proportionate depreciation of the ‘domestic’ currency against the ‘foreign’ one. This can be algebraically expressed: 3

Where St = Exchange Rate (domestic currency units per unit of foreign currency), Pt = the price of a good (or bundle of goods) in domestic currency and Pt* is the same good (or bundle) expressed in foreign currency terms. Conversely purchasing power does not hold (purchasing power disparities) when: 4

Relative (weaker) PPP states that the percentage change in the exchange rate between two currencies over any period equals the difference between the percentage changes in national price levels and can be algebraically expressed:

Where % ∆St = percentage change in the exchange rate, % ∆Pt = percentage change in the domestic inflation rate and % ∆Pt* = percentage change in the foreign inflation rate.

However in reality (even the proponents of PPP) accept that absolute PPP, though sound in theory, remains difficult to empirically prove due to implications of real world situations such as:

Trade barriers and non-tradables

Departures from free competition

International differences in price level measurement

## Literature Review:

PPP theory being translated into empirical work has been attempted by many economists such as: McNown and Wallace (1989), Bahmani-Oskooee (1993), Mollick (1999), Chinn (2000), Choudhry (2005).

Yet despite econometric techniques ever improving there is evidence against PPP as well as supporting PPP. Bahami-Oskooee (1993) strongly disagrees with real exchange rate stationarity for the majority of economies he studied. Piet Sercu, Raman Uppal and Cynthia Van Hulle (1995) concluded that absolute PPP does not generally hold. Nor is it likely that this ratio would be a constant over time, because it is unlikely that, for each and every good, there is trade at all times and in the same direction. They went on to also comment that in general, relative PPP does not hold either. Their reasoning; a deviation between the marginal utilities will be related to a deviation between the composite prices in exactly the same way as it is in the one-good case.

Against Rogoff’s (1996) work on half lives, Sarno and Taylor (2002) disputed the merit of it, as they found that PPP corrects more quickly in the short run. Contradicting that Dimitrios (2006) finds that the analysis provides support for long-run equilibria, but the coefficients of the estimated cointegrating vectors violate the symmetry and proportionality hypotheses suggested by the weak and strong PPP versions, respectively.

Since the being awarded the Nobel Prize in 2003 (Robert F Engle and Briton Clive W J Granger) for their work in analysing economic time series there has been an increase in related literature. It can be noted that in previous and even current studies there is much ambiguity surrounding empirical evidence. However it seems that applying non linear unit root techniques find greater evidence in favour of PPP. This study aims to further analyse the question over the PPP relationship and its validity within the countries discussed.

## Data & Possible Statistical Problems:

The nominal exchange rates (implied PPP conversion rates) and the consumer price index (CPI) are from 1980-2010 with the base year of 2000 and all other values are relative to that particular year. They were taken from the IMF world economic outlook (WEO) database.9

The time period under analysis (1980-2010) is a long enough period to observe the hypothesis. The time period for strong forms of PPP to become ‘apparent’ can be months and weaker forms may take years.

Modelling the data for PPP analysis discussed above could have some problems which are outlined:

As the notion of PPP is comparisons of identical baskets of goods and/or services though sound in theory, poses a flaw in real life situations. Different countries may value (apply different weights) to particular goods and/or services. A MEDC (more economically developed country) would place less weighted value on luxury goods than a LEDC (less economically developed country). Conversely and LEDC would place higher value of foods than a MEDC.

Also a problem that needs to be known is whether PPP is applicable to traded or non-traded goods. Assumptions that traded goods should be more relevant are being made in the study, even though it is agreed in some literature that this poses a grey area. In addition to this the consumer price index (CPI) is being used for price levels. This illustrates further as the use of CPI for PPP analysis was disagreed with by Xu 2003 who stated PPP is less likely to hold when using CPI than when using TPI (tradable price index). The study suggested that the estimated half life of deviation from PPP to be more when CPI is used.

Another issue is that when testing for PPP using any price index should ideally have a base year where PPP holds best. In this study 2005 is the base year and it is unknown if it’s a best fit for PPP.

Further research has led to some more possible problems. These are less connected to the structure of data but may have as much of an effect on the empirical output. Spain, Portugal and Morocco have been primarily chosen as they are geographically close and have high volumes of trade. However the European Trade Study Group Conference 2007 Athens, 13-15 September 2007 shows findings that although separated by a land border may not have as high a trade volume as initially thought. This lack of ‘free-trade’ affects how PPP performs as will be later discussed.

‘’…there has not been significant trade levels until the last decade of the 20th century. An explanation for this lack of trade between what should be natural partners can be trade on the political system in both countries. For centuries they have seen each other as enemies. Only recently, a European approach has emerged, from which the conditions to develop trade among each other rose.’’

Similarly political unrest between Spain and Morocco has had an effect on their willingness to trade. The following is an extract from EU-Morocco Summit & Spain’s Internal Political Battle by Hassa Masiky:

‘’…be it on immigration, national security, agriculture, or fishing policy, Morocco’s standpoints have a direct and implicit effect on Spain’s internal political discourse on these subjects. Therefore, accommodating postures from the Moroccan will make it easier on several key economic sectors of a sluggish Spanish economy.’’

Development of long-run estimable models: 3

In developing an estimable long run model one can deduce whether the PPP holds in a relatively long time scale one can assume that the law of one price will also hold. Hence when measured in the currency, the assumption that the foreign and domestic price levels remain unchanged can be made

In this instance:

Where St = Exchange Rate (domestic currency units per unit of foreign currency), Pt = the price of a good (or bundle of goods) in domestic currency and Pt* is the same good (or bundle) expressed in foreign currency terms.

By expressing the above in logarithm form, the new (log) variable approximates the percentage change in the variable.

It becomes:

From the above a testable model can be then built. This testable model can be used to determine whether the hypothesis should be rejected or accepted. The equation for the testable model follows:

(1)

Where εt is the error term, β1 and β2 are the testable coefficients and α is the constant. The long run model that is developed will not be valid if an error term of order I(1) occurs; I(0) is required. Thus any conclusions made about the values of the coefficients become impossible.

Considering that, there are three forms under which the extent of PPP holds. These are strong, weaker and weak.

Strong PPP holds when the long run parameter for the domestic price is equal to 1 and the foreign price equal to -1.

This can be depicted:

Hence the equation (1) becomes:

Weaker PPP holds when the long run parameters of the domestic and foreign prices the same magnitude but of opposite signs, for example -2 and 2.

This can be depicted:

Hence the equation (1) becomes:

Weak PPP is said to hold long run parameters are not restricted.

This can be depicted:

Hence the equation (1) becomes:

## Testing for stationarity:

A variable is said to be stationary if it exhibits a constant mean and a finite variance whilst remaining time independent. Conversely a variable displaying characteristics of a changing mean with an increasing variance (dependant of time) is said to be non-stationary. When considering time-series data for analysis, stationarity is vital as the ordinary least squares (OLS) will otherwise give rise to spurious regression and thus invalid results. Pre 1980’s many economists used linear regression on non-stationary data but was proved a dangerous (as important long run information is likely to be omitted rendering incorrect functional form) approach by Clive Granger. In 1987 his paper with Robert Engle formalised the cointegrating vector approach, coining the term.6

A non-stationary series is made stationary through the process of differencing. If the series requires to be differenced once before reaching stationarity it is denoted as I(1) and twice as I(2) an so forth. However it is unlikely that a series will remain non-stationary after I(2) and is referred as I(0). The use of cointegration allows retaining such long run information that is essential to analysing PPP. Cointegration is said to happen when multiple non-stationary variables, trend over time to form a stationary gap which in turn leads to a stationary error term. Simplistically the drift processes of the variables cancel out leaving an error term with no drift; concluding a long run relationship between the variables in question.7

Considering the formula defining cointegration: 3

Where components of X are cointegrated of order d,b

Also for cointegration to be possible series’ must have the same level of integration, discussed earlier, for example: either two I(1) or two I(2) variables, but not one I(1) variable and one I(2) variable and vice-versa. An error term is produced post cointigration, of a lower integration level (εt) for example: two I(1) variables cointegrate to produce a stationary error of order I(0). It is possible to cointegrate different levels of integration but by and I(2) being integrated first to I(1) and then cointergration to I(0) providing a stationary error term.

From the formal definition: 3

Where X is I(d) and there exists a non-zero vector such that if X has n components then there may be up to (r) co-integrating vectors, where r is at most n-1. This implies the presence of n-1. This basically implies the presence of n-r common stochastic trends, when n is greater than 1 (n>1). 3

Provided cointegration is possible and a stationary error term results an Error Correction Model (ECM) can be created. According to Engle & Granger ECM exists provided that cointegration is possible. Simplistically the ECM incorporates long-run information into the model and represents a short-run relationship between successfully cointegrated variables. The Engle-Granger 2 method will be used to create an ECM. Should no cointegration be possible then it show no PPP relationship present.

To summarise it is now required to determine the levels of dereferencing required in order to render the variables in question as stationary stochastic trends. Drawing back to the introduction, the tests to be carried out follows:

Actual Plot: This is a standard plot of the variable. When interpreting the output upward or downward trends imply non-stationarity. After differencing ‘I(1) or I(2)’ if the plot fluctuates roughly around one value it that in turn implies a constant mean and thus considered stationary.

Autocorrelation Function: Stationarity is defined by examing how fast the autocorrelation function fades. If it fades away slowly (sloping downward on visual output) it would imply non-stationarity. After differencing ‘I(1) or I(2)’, if it dies away quickly (within 6 lags) this means that it looks like it is fluctuating around a central point This can be deemed as stationary. 10 lags will be used as a sufficient amount.

Spectral density: If the visual output (graph) peaks at zero, it implies stationarity. After differencing ‘I(1) or I(2)’ if the peak is situated not at zero it will imply the data is stationary.

Although the three tests above are useful as an indication of stationarity, graphical plots can be inconclusive and relies partly on judgement. Therefore alongside them a unit root test will be carried out to further clarify whether variables are stationary.

A unit root test: is a statistical test for the suggestion that in an autoregressive statistical model of a time series, the autoregressive parameter is equal to one.8

Hence the following equation:

Where yt represents the variable in question at a time t, b equals the slopes coefficient, and as the error term. If the coefficient |b| (modulus of b) = 1 then a unit root exists. In that case it is said that the time series is non-stationary with a stochastic trend yet again giving rise to spurious regression. For larger sets of time series data it is advised to used the Augmented version of the renown Dickey-Fuller thus accomodating for higher order autoregressive processes.

Interpreting the results, means that the condition of stationarity leads to the rejection of the null. The ADF will use 3 lags, as too many would result in reducing the power of the overall test. The ADF (t-adf) will produce negative results and if the t-adf is less negative than the hypothesis, it will imply non-stationarity. Conversely a more negative value suggests stationarity. There will be 2 intervals (1% & 5%) shown, and 5% utilised. Another notable summary of the ADF result is Akaike's Information Criterion (AIC). This shows an inverse relationship between the models’ fit and its complexity. The strongest negative AIC value highlights the best minimalist of serial correlation.

## Stationarity Results:

Log (Spain/Portugal):

Level term graphical analysis: Actual Plot (fig. 1) has a strong positive slope with two kinks, peaking in the year 2000, followed by a downward slope kinking at the end at 2009. ACF (fig. 2) shows slow decay and the Spectral Density (fig. 3) peaks at 0. All of these imply non-stationarity. This means that further differencing is required.

Unit root tests: ADF tests (fig. 4,5,6): shows no lag of the ADF value and t-adf is less negative than the hypothesis, thus implying non-stationarity. AIC does not need to be consulted and this means that further differencing is required.

## -----------------------

DLog Spain/Portugal:

Level term graphical analysis: Actual Plot (fig. 7) has a general negative slope but does fluctuate. This can be seen with a peak of 5 in 1988 and a low point at around 2006. ACF (fig. 8) shows slow decay (after 6 lags) and the Spectral Density (fig. 9) peaks at 0. All of these imply non-stationarity. This means that further differencing is required.

Unit root tests: ADF tests (fig. 10,11,12): shows the ADF value and t-adf is less negative than the hypothesis, thus implying non-stationarity. AIC does not need to be consulted and this means that further differencing is required.

## -----------------------

DDLog Spain/Portugal:

Level term graphical analysis: Actual Plot (fig. 13) fluctuates around a point and no general slopes can be noted. ACF (fig. 14) shows quick decay (within 6 lags) fluctuating also. The Spectral Density (fig. 15) does not peak at 0. All of these imply stationarity. This means that it becomes stationary at I(2).

Unit root tests: ADF tests (fig. 16,17,18): shows the ADF value and t-adf is more negative than the hypothesis, on all lags thus implying stationarity. AIC is also supports stationarity. This means that it becomes stationary at I(2).

## -----------------------

Log (Spain/Morocco):

Level term graphical analysis: Actual Plot (fig. 19) has a strong arced positive slope. ACF (fig. 20) shows slow decay (more than 6 lags) and the Spectral Density (fig. 21) peaks at 0. All of these imply non-stationarity. This means that further differencing is required.

Unit root tests: ADF tests (fig. 22,23,24): shows the ADF value and t-adf is more negative than the hypothesis, thus implying stationarity but the AIC does is large and negative implying non-stationarity. Overall this means that further differencing is required.

## -----------------------

DLog Spain/Morocco:

Level term graphical analysis: Actual Plot (fig. 25) has a general negative slope but does fluctuate. This can be seen with peaks of 5 at 1983 and 1986 and a low point at around 2009. ACF (fig. 26) shows slow decay (after 6 lags) and the Spectral Density (fig. 27) peaks at 0. All of these imply non-stationarity. This means that further differencing is required.

Unit root tests: ADF test (fig. 28): shows the ADF value and t-adf is more negative for the report only than the hypothesis, thus implying stationarity but ADF tests (fig. 29&30) shows t-adf values that are less negative. AIC is still largely negative implying non-stationarity. Overall this means that further differencing is required.

## -----------------------

DDLog Spain/Morocco:

Level term graphical analysis: Actual Plot (fig. 31) fluctuates around a point and no general slopes can be noted. However there is an anomaly in 1987. ACF (fig. 32) shows quick decay (within 6 lags) fluctuating also. The Spectral Density (fig. 33) does not peak at 0. All of these imply stationarity. This means that it becomes stationary at I(2).

Unit root tests: ADF tests (fig. 34,35,36): shows the ADF value and t-adf is more negative than the hypothesis, on all lags thus implying stationarity. AIC is also supports stationarity. This means that it becomes stationary at I(2).

## -----------------------

Log CPI Portugal:

Level term graphical analysis: Actual Plot (fig. 37) has a strong positive arced slope. ACF (fig. 38) shows slow decay (after 6 lags) and the Spectral Density (fig. 39) peaks at 0. All of these imply non-stationarity. This means that further differencing is required.

Unit root tests: ADF tests (fig. 40): shows the ADF value and t-adf is less negative for the report only than the hypothesis, thus implying non-stationarity. ADF tests (fig. 40,41,42): show t-adf values more negative that the hypothesis implying stationarity but AIC supports non-stationarity. Overall this means that further differencing is required.

## -----------------------

DLog CPI Portugal:

Level term graphical analysis: Actual Plot (fig. 43) has a general negative slope but does fluctuate at some points. This can be seen near 1988 and a low point at around 2010. ACF (fig. 44) shows slow decay (after 6 lags) and the Spectral Density (fig. 45) peaks at 0. All of these imply non-stationarity. This means that further differencing is required.

Unit root tests: ADF tests (fig. 46,47,48): all show the ADF value and t-adf is more negative than the hypothesis, thus implying stationarity yet AIC implies non-stationarity and so overall further differencing is required.

## -----------------------

DDLog CPI Portugal:

Level term graphical analysis: Actual Plot (fig. 49) fluctuates around a point and no general slopes can be noted. Although it should be noted that more drastic fluctuations occur at the beginning of the time period ACF (fig. 50) shows quick decay (within 6 lags) fluctuating also. The Spectral Density (fig. 51) does not peak at 0. All of these imply stationarity. This means that it becomes stationary at I(2).

Unit root tests: ADF tests (fig. 52,53,54): shows the ADF value and t-adf is more negative than the hypothesis, on all lags thus implying stationarity. AIC is also supports stationarity. This means that it becomes stationary at I(2).

## -----------------------

Log CPI Spain:

Level term graphical analysis: Actual Plot (fig. 55) has a strong positive arced slope. ACF (fig. 56) shows slow decay (after 6 lags) and the Spectral Density (fig. 57) peaks at 0. All of these imply non-stationarity. This means that further differencing is required.

Unit root tests: ADF tests (fig. 58): shows the ADF value and t-adf is less negative for the report only than the hypothesis, thus implying non-stationarity. ADF tests (fig. 59,60): show t-adf values more negative that the hypothesis implying stationarity but only on the 0th lag. AIC supports non-stationarity. Overall this means that further differencing is required.

## -----------------------

DLog CPI Spain:

Level term graphical analysis: Actual Plot (fig. 61) has a general negative slope but does fluctuate at some points. This can be seen near the end of the time period. ACF (fig. 62) shows slow decay (after 6 lags) and the Spectral Density (fig. 63) peaks at 0. All of these imply non-stationarity. This means that further differencing is required.

Unit root tests: ADF tests (fig. 64): shows the ADF value and t-adf is more negative than the hypothesis, thus implying stationarity but ADF tests (fig. 65&66): show 2 lag points that are less negative than the hypothesis (lag 0 and 2 respectively). AIC implies non-stationarity and so overall further differencing is required.

## -----------------------

DDLog CPI Spain:

Level term graphical analysis: Actual Plot (fig. 67) fluctuates around a point and no general slopes can be noted. Although it should be noted that more drastic fluctuations occur at the end of the time period ACF (fig. 68) shows quick decay (within 6 lags) fluctuating also. The Spectral Density (fig. 69) does not peak at 0. All of these imply stationarity. This means that it becomes stationary at I(2).

Unit root tests: ADF tests (fig. 70,71,72): shows the ADF value and t-adf is more negative than the hypothesis, on most lags thus implying stationarity. AIC is also supports stationarity. This means that it becomes stationary at I(2).

## -----------------------

Log CPI Morocco:

Level term graphical analysis: Actual Plot (fig. 73) has a strong positive slope with a sudded rise in 200. ACF (fig. 74) shows slow decay (after 6 lags) and the Spectral Density (fig. 75) peaks at 0. All of these imply non-stationarity. This means that further differencing is required.

Unit root tests: ADF tests (fig. 76,77,78): shows the ADF values and t-adf that are less negative for the report only than the hypothesis, thus implying non-stationarity. AIC supports non-stationarity. Overall this means that further differencing is required.

## -----------------------

DLog CPI Morocco:

Level term graphical analysis: Actual Plot (fig. 79) fluctuates around a point but a sharp increase and fall can be noted in the year 2000. ACF (fig. 80) shows quick decay (within 6 lags) fluctuating also. The Spectral Density (fig. 81) does not peak at 0. All of these imply stationarity. This means that it becomes stationary at I(1).

Unit root tests: ADF tests (fig. 82,83,84): shows the ADF value and t-adf is more negative than the hypothesis except on the 2nd lag in (fig. 84); most lags are implying stationarity. AIC is also supports stationarity. This means that it becomes stationary at I(1).

To summarise:

Log Spa/Port

Log Spa/Mor

Log CPI Spa

Log CPI Por

Log CPI Mor

I(2)

I(2)

I(2)

I(2)

I(1)

Testing for absolute and relative PPP will now follow:

Cointegration Log Spain Morocco:

As discussed earlier cointegration occurs when the difference levels are the same. From the above table it can be noted that there are four I(2) variables and one I(1) variable, therefore the two I(2) variables can be co-integrated to an I(1) variable. This can then be co-integrated to and I(1) variable with the other I(1) variable, and further to become I(0).

To proceed with testing if co-integration exists, we will use HongKong/Korea log and use this as out dependant variable. We will use Hong Kong CPI log and Kor CPI log, which is South Korea’s CPI log, as our two independent variables. An OLS regression was carried out using all the variables stated above. These variables were added with no lags, and the OLS was run. If the residual process of this OLS regression is stationary, then we can say that the relationship that is being modelled holds in the long run equilibrium. This being the case, residual being stationary, the long run relationship will be represented by the regression. However if this is not the case, residuals being non stationary, the coefficients of the independent variables, HongKong CPI log and Kor CPI log, will be assumed to be zero and we can reject the relationship.

Lets us now proceed to test for the possible existence of the Absolute PPP relationship between Hong Kong and South Korea. We will need to use HongKong/Korea log, Hong Kong CPI log and Kor CPI log. As stated we have two I(2) variables and one I(1) variable, therefore the two I(2) variables can be co-integrated to an I(1) variable. This can then be co-integrated to and I(1) variable with the other I(1) variable, and further to become I(0).

To proceed with testing if co-integration exists, we will use HongKong/Korea log and use this as out dependant variable. We will use Hong Kong CPI log and Kor CPI log, which is South Korea’s CPI log, as our two independent variables. An OLS regression was carried out using all the variables stated above. These variables were added with no lags, and the OLS was run. If the residual process of this OLS regression is stationary, then we can say that the relationship that is being modelled holds in the long run equilibrium. This being the case, residual being stationary, the long run relationship will be represented by the regression. However if this is not the case, residuals being non stationary, the coefficients of the independent variables, HongKong CPI log and Kor CPI log, will be assumed to be zero and we can reject the relationship.

## Error Correction Model (ECM):

Following the previous results it is possible to carry out an ECM. An error correction model will need to now be carried out. The ECM will incorporate long-run information into the model and represent it in a short-run relationship between successfully cointegrated variables. The Engle-Granger 2 method will be used to create an ECM.

As the ECM will only contain variables which are all I(0) the only lag of the stationary residual produced in the OLS regression, the stationary difference of the lag shall be included. This should identify any long run relationship between the variables. This will ensure that the existence of the long-run relationship will be acknowledged.

Firstly the lag length required that causes the residual term to be white noise needs to be found. To do this the model shall start with 4 lags and then progressively removed by order of insignificance. With the change (removal of insignificant lags) the output values will change hence passing the test summary. This is known as a Parsimonious model

Following the above we will look at the results from the tests to see whether the OLS estimator assumptions are satisfied or not. For a correct conclusion, it is essential to have a well specified model, one that produces residuals of the normal distribution, and the emergence of white noise.

## Test Summary Definitions:

The RESET Test: The Ramsey Regression Equation Specification Error Test, is the general specification test for linearity. More specifically, it tests whether non-linear combinations of the estimated values help explain the endogenous variable. The intuition behind the test is that, if non-linear combinations of the explanatory variables have any power in explaining the endogenous variable, then the model is mis-specified.10

The LM Test: is a robust test for autocorrelation in the residuals from a regression analysis and is considered more general than the standard Durbin–Watson statistic (or Durbin's h statistic). The null hypothesis is that there is no serial correlation of any order up to p.11

The Hetersocedasticity Test: a model featuring autoregressive conditional heteroskedasticity considers the variance of the current error term or innovation to be a function of the actual sizes of the previous time periods' error terms: often the variance is related to the squares of the previous innovations. Such models are often called ARCH models. 12

Normality Test: To be white noise the residuals should be normally distributed. This will be the null hypothesis in this case.

## Relative (weaker) PPP model:

Owing to the fact that absolute PPP did not hold a relative model will be built. This has been covered earlier:

Therefore the following model is deduced: ∂lnSt = ∂lnPt - ∂lnPt *

Now using the above it is possible to arrive at a testable forom of the wearker variation PPP model: ∂lnSt = α + ∂β1 lnPt + ∂β2 lnPt * +∂ εt

The definitions have been previously established and ∂ depicts that the variable has been differenced once.

## Conclusions:

To summarise I have not found any solid validity in the PPP relationship theory. However looking at previous empirical works and understanding the difference between ‘theory’ and ‘real-world situations’ means that the overall outcome was not a surprise. I have already established that there is little empirical support for purchasing power parity and some of the reasons are:

Trade barriers and non-tradable goods and services

Imperfect competition

Differences in price level measures

## Trade barriers and non-tradables

Government trade restrictions (import duty for example) and transport costs make trade expensive and in some cases (this in turn affecting PPP validity) and also create non-tradable goods or services. Services that are often not tradable are generally offered within a limited geographic region. This means that it’s not accessible and so relative price differentials may occur i.e. one price need not hold in two markets. Also the greater the transport costs, the greater the range over which the exchange rate can deviate from its PPP value.

## Imperfect competition

This means that ‘pricing to market’ may differ and cause price discrimination, again going against the concept of PPP relationship. Other forms of imperfect competition (eg: flight tickets) differ even within a single geographic region, so its effect on PPP is obvious.

## Differences in price level measures

The way representative groups ‘baskets’ of goods and services are measured differ across countries affecting relative price levels. This can be due to measures of goods and services being different and/or the measure of their prices also being different.

## Comparative Analysis:

Although I have been able to establish that no definite (proponent to PPP) conclusions can be made, quantitatively from the data it can be observed that between Spain and Morocco a parsimonious model using ECM can be created. However between Spain and Morocco there is no PPP validity. For this there could be a variety of reasons including lower transport costs between land borders. Also the fact that Spain and Portugal are part of the EU, a body created with goals to increase and promote free-trade. Coupled with that both Spain and Portugal adopted the euro in 1999 1&2 again reducing transaction cost of currency exchange.

To conclude, overall findings suggest that empirical support for PPP is weak, agreeing with many other literatures in the same field. However the results do not completely disregard the notion in some cases it would seem. It seems that trade barriers, non-tradable products, imperfect competition and differences in price measures factor enough to distort an otherwise sound theory (equalisation though risk free profits) and compose the effects on the empirical shortcomings of PPP. Relative PPP is more consistent with data, but it also performs poorly to predict exchange rates.

I had decided to use CPI as my large time period was large enough to compensate for Xu’s predicted half life as well as Chinn (1998) proposal that the composition of tradable bias indices are less comparable. This was my reasonong to conclude that CPI would be the best choice. Having said that if I was to extend my project, I would definitely consider running different analyses, involving TPI, WPI and even perhaps, a possible GDP deflator as suggested by António Portugal Duarte in his study.

Furthermore I could have used dynamic analysis providing more detail in the structure of the lags. Outliers (that have been pointed out in the stationarity results) could have been omitted prior to any regressing and thus cointegration. With weak conclusive results little changes may have strengthened the overall validity of the PPP claim.

Your project should contain the following elements. Each element will carry a fixed share of the marks, given in brackets.

The project report should begin with an executive summary, giving the main features and conclusions of the study in not more than 300 words. You should pay careful attention to the clarity of this summary. [10%]

You will have chosen a title from those suggested (below) or have a title of your own which has been discussed with Professor Charemza. The main focus of the project is your ability to formulate an empirical model for a relevant and well defined economic problem, use of appropriate econometric techniques and the interpretation of results using an econometric package. You should write a clear account of what problems your project addresses. [10%]

3. The economic theory behind the model should be clearly identified and in particular any additional assumptions imposed on a theory with an aim to derive an empirical (estimable) model should be stated. In order to find appropriate literature using Internet search resources is encouraged. [10%]

4 You need to discuss the properties of data that you have collected to undertake your study, including any problems in coverage and any adjustments you have made to the data set. In particular, any shortcomings and deficiencies of data should be noticed and acknowledged. This could include, for instance, the splicing together of series measured from different base values, conversion of nominal series to ‘real’ values, measurement problems, interpolations, reliability and completeness of data sets, etc.). Also, time series properties (order of integration of series, outliers, structural breaks, etc.) should be identified. [20%]

5 The main section of the project will be to build, estimate and apply (for forecasting and/or policy analysis) the model developed in part 3 above. The model has to be developed on the grounds of the properties of data found in part 4, and in particular the integration/cointegration properties of the series have to be explicitly exploited. In most cases this should lead to a development of an error-correction model through a general-to-specific modelling. Modelling of real life data is always difficult and rarely leads to positive results; it is therefore important that students are able to look critically at their results and are able to identify drawbacks and shortcomings of their findings. [30%]

6 The project should always be completed by appropriate conclusions. These conclusions should relate to (i) the model (its ability to forecast, policy analysis, its drawbacks, advantages, consistency with the economic theory, etc) and (ii) also the economic problem. Special emphasis should be put on transparency and clarity of conclusions. [20%]

There should be two appendices which accompany the main text of the assignment. The first one should contain all relevant computer output (estimated parameters, statistics, etc.) as it has been produced by STATA and the second one should contain all original data used and details of all transformations of the variables, interpolations etc. The principle is that anyone who uses the same data as you do should be able to obtain exactly the same statistical results.

## Indexed References:

1 http://en.wikipedia.org/wiki/Spain#Economy

2 http://en.wikipedia.org/wiki/Portugal#History

3&4 http://www.le.ac.uk/ec/teach/ec3064/documents/lecture1.pdf

5 http://wps.aw.com/wps/media/objects/2029/2078401/ppt/ch15.ppt

6 http://en.wikipedia.org/wiki/Cointegration

7 http://en.wikipedia.org/wiki/Stochastic_drift

8 http://en.wikipedia.org/wiki/Unit_root_test

9 http://www.imf.org/external/pubs/ft/weo/2010/01/weodata/index.aspx

10 http://en.wikipedia.org/wiki/RESET_test

11 http://en.wikipedia.org/wiki/Breusch%E2%80%93Godfrey_test

12 http://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity

## Other references:

-http://www2.sas.com/proceedings/sugi30/192-30.pdf

-http://www.moroccoboard.com/viewpoint/68-hassan-massiki/924-eu-morocco-summit-a-spains-internal-political-battle- (EU-Morocco Summit & Spain’s Internal Political Battle by Hassan Masiky)

-European Trade Study Group Conference 2007 Athens, 13-15 September 2007, Ricardo Carvalho Bruno Ferreira

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