Regression Analysis for the Netherlands

Regression digest for the NetherlandsTABLE OF FIGURES AND GRAPHSTable 1 Coefficients of prefigured OLS forgeTable 2 abbreviation of Variance and F-statisticTable 3 diametrical t-sample rivuletsTable 4 Analysis of Variance for pre structural set off (b,c)Table 5 Analysis of Variance for stakes structural break (b,c)Table 6 Analysis of Variance and F-statisticTable 7 Pearsons correlations chart 1 Scatterplot with best fit taskGraph 2 Simple scatterplot of instantsIntroductionThe following document dissects the importee aggregate demand for the Netherlands utilising data from the first quarter 1977 to the first quarter 2006. The aim is to watch over the relationship amidst imports and five explanatory variables relative prices (measured as the ratio of import to domestic prices), ho rehearsehold consumption utilize ups, government consumption expenditures, investment expenditures and exports. A regression utilising Ordinary Least Squargons is run and hence a series of a nalyses is done on the results of the estimated regulate.Model EstimationData for the Netherlands was obtained from initiative quarter 1977 to 1st quarter 2006 from the International Monetary Funds International Financial Statistics, giving a sample population N = 117 and 116 degrees of freedom. It is worth noting that due to the use of the euro to report Netherlands accounts starting in 1999, there was a break in the information presented as they were in two currencies pre 1999 (in Dutch gulden) and post 1999 (euros). In order to overcome this, all of the data was transformed into Dutch gulden, using the official euro/gulden ex variety show rate at the time of the entry of the euro.To fix the data for the regression, the natural log of the values for imports (M), relative prices (RP)the index of import prices to consumer prices, household consumption expenditure (HC), government consumption expenditure (GC), investment expenditure (INV) and exports (EXP) were taken. By using SPS S to estimate the model via Ordinary Least Squargons, the aggregate demand function (utilising the unstandardised coefficients) is estimated asM = 0.071 0.966 RP 0.328 HC 0.171 GC + 0.286 INV + 0.808 EXPStd errors (0.041) (0.022) (0.053) (0.035) (0.033) (0.026)The model has an adjusted R2 = 0.992, indicating that 99.2% of the form in imports is explained by the relative price and the four expenditure components. It has a standard error of regression of 0.02715.With regards to the explanatory variables included in the regression, by analysing their t-values we are able to determine that each coefficient is statistically significant at all take aims. Table 1 shows the results of the estimated coefficients along with their corresponding t-values and significance values.Table 1 Coefficients of estimated OLS modela myrmecophilous Variable LN_MPlotting the values of imports (as ln(M)) with regards to the standardised predicted values from the model, we get the best-fit curve shown i n graph 1.Graph 1 Scatterplot with best fit lineInterpretation of slope coefficientsThe estimated coefficients from the regression supra can now be interpreted. The results are presented again for ease of readingM = 0.071 0.966 RP 0.328 HC 0.171 GC + 0.286 INV + 0.808 EXPIn ordinary terms, each slope coefficient is the import elasticity with mention to each of the equation components relative prices, household consumption, government consumption, investment expenditures and exports. Following is the explanation for each coefficientmachinery and tape drive equipment, chemicals, fuels, foodstuffs, clothing from germ, belg and china2 = -0.966 represents the relative price import elasticity. This implies that a 1% plus in relative prices causes a reduction in imports of 0.966%. This is essentially a unitary elasticity, the effect of a change in relative prices is almost identically reflected on imports. This occurs primarily in countries with an open economy that thrives on the balance of trade. Additionally, since the Netherlands most important trade contributionners are within the European Union, who use the same currency, the relative prices are similar for them. (Atlapedia Online, 2006)3 = -0.328 represents the elasticity of imports with respect to household consumption expenditure. It implies that a 1% growing in household consumption expenditure will translate into a 0.328% decrease in imports. The import elasticity of household consumption is inelastic. Household consumption has a small effect on imports, as although Netherlands does import foodstuffs and clothing, the bulk of imports is for machinery and transport equipment as comfortably as chemicals, which have no relation with household consumption. (CIA World Factbook, 2006)4 = -0.171 represents the import elasticity with respect to government consumption expenditures. It follows that a 1% cast up in government expenditure will result in a reduction in imports of 0.171%. The import elastici ty of government consumption is tallly inelastic. delinquent to the nature of imports mentioned in the paragraph above, it is logical to assume that the import composition is not widely affected by government consumption, except maybe in the import of fuels.5 = 0.286 is the import elasticity with respect to investment expenditure. It is a positive inelastic import elasticity as a 1% increase in investment expenditure will result in a 0.286% increase in imports. This energises sense with reality since investment expenditures are in part for importing machinery and transport goods.6 = 0.808 is the import elasticity with respect to exports. It shows that a 1% increase in exports will result in a 0.808% increase in imports. This elasticity is also elastic, although it is more similar to the relative price import elasticity, approximating unit elasticity. This also reflects the Netherlands open economy and its active trading with neighbouring countries as a result of forming part of t he European Union.Overall significance of the regressionNow that we have seen the interpretations of each of the coefficients of our estimated model, and having seen that they are all statistically significant, we have to analyse whether the model as a whole is statistically significant. This is done by analysing the F-value of the regression. If the value of F is sufficiently large with a high confidence level, then it follows that the estimation we have done does indeed predict some of the values we have observed and the regression is statistically significant.For this regression, SPSS calculates the F-value as 2784.8, which is statistically significant at all confidence levels. As mentioned above, this confirms the validity of the predicted equation in estimating the values of the components of imports.Table 2 infra presents SPSS results for the F-statistic and Analysis of Variance for our model.Table 2 Analysis of Variance and F-statistica Predictors (Constant), LN_EXP, LN_RP, LN_INV, LN_GC, LN_HCb Dependent Variable LN_MTest of equality of import elasticitiesAfter having stressed that the model as a whole is statistically significant, we will now test whether each of the import elasticities of final expenditures are equal amongst themselves. In order to do this, we will use a diametric t-test, which will compare each elasticity against each other and determine whether the differences between them are statistically significant or not. If they are not statistically significant, then the elasticities are the same.In the case of our estimated model, the t-statistics are significant at all levels for all of the relationships. This means that we cannot conclude that each of the import elasticities is the same, rather they are statistically significantly different from one another.Table 3 shows the results provided by SPSS paired t-test for each of the import elasticity relationships testedTable 3 Paired t-sample testsThe Behaviour of Imports from 1977 to 200 6Having verified that our model is statistically significant and that each elasticity of imports is different, we now analyse the behaviour of imports during our sample period. The easiest way to do so is graphically. use the scatterplot function from SPSS we plot the observed values of the Netherlands imports from 1st quarter 1977 to 1st quarter 2006. Graph 2 below shoes this relationshipGraph 2 Simple scatterplot of importsA structural break in importsFrom the graph above, there seems to be a structural break around 2nd quarter 2002. This would make sense since it was around this time that the actual euro currency replaced the Dutch gulden (and all other European currencies for that matter). Such a significant change would be reflected in imports.The actual occurrence of such a break, can be tested statistically using our observed data. This is done via a Chow Test, where we test whether the coefficients in our estimated equation are the same before and after the suspected struct ural break point, Q2 2002. However, since SPSS does not have a command for the Chow Test, we do this analysis by calculating an incremental F-value from a constrained (the model divided into the two periods pre Q2 2002 and post Q2 2002) and an unconstrained model (our original estimation).The constrained model used divides our data into two, as mentioned above. The group labelled as pre represents observed values from Q1 1977 to Q2 2002, whilst the group labelled pos represents values from Q3 2002 to Q1 2006. Running a regression and using the Anova functionality on the constrained model yields the results presented in tables 4 and 5.Table 4 Analysis of Variance for pre structural break (b,c)a Predictors (Constant), LN_EXP, LN_RP, LN_INV, LN_GC, LN_HCb Dependent Variable LN_Mc struct_break = preTable 5 Analysis of Variance for post structural break (b,c)a Predictors (Constant), LN_EXP, LN_HC, LN_INV, LN_RP, LN_GCb Dependent Variable LN_Mc struct_break = posUtilising the above with t he results from the original unconstrained modelTable 6 Analysis of Variance and F-statistica Predictors (Constant), LN_EXP, LN_RP, LN_INV, LN_GC, LN_HCb Dependent Variable LN_Mthe incremental F-value is calculated using the correspondence sums of squares and degrees of freedom of the constrained and unconstrained models. In this case asF6,105 = (0.063 -0.082)*(117 2*5-2) / (0.082 * 6) = -4.05The f-value of -4.05 when compared to the critical value of F6,105 = 2.19 at the 5% confidence level and 2.98 at the 1% confidence level, causes us to reject the null hypothesis which means that there is a difference in the coefficients between the pre and pos periods we chose. This confirms that there was a structural break in the 2nd quarter of 2002.AutocorrelationWe can now check if our estimated model suffers from autocorrelation by examining the Durbin-Watson statistic. According to a statistical table for Durbin-Watson statistics, the critical values for the Durbin-Watson statistic with N = 117 and k = 6, at the 5% confidence level are dL = 1.61045 and dU = 1.78828. In this model, the D-W statistic was calculated by SPSS as 0.661. This implies that the model does suffer from autocorrelation, as the statistic travel below the lower critical value. It has positive autocorrelation. To correct this, we have to determine whether or not the aggregate demand relation is in fact linear, other than we need to choose a different functional form and re-run our regression. If we do have the correct functional form, we need to determine whether there are whatever other variables which can be included in the model to help explain the effect on imports and which may eliminate this autocorrelation. Any changes that are make to the model or the data itself will imply that a new regression must be run and new tests for autocorrelation carried out until this problem is eliminated.Correlation of final expenditure componentsOnly because the model as a whole suffers from autocorrelat ion, it does not mean that each of the explanatory variables is significantly correlated. In order to test this, we must calculate Pearsons correlation coefficient. SPSS can calculate these coefficients by analysing the relationship between each one of the variables with the others in the equation. Table 7 below shows the results from SPSS, as well as the statistical significance of each of the calculated correlation coefficients.Table 7 Pearsons Correlations** Correlation is significant at the 0.01 level (2-tailed).As can be seen, all of the correlation coefficients are statistically significant at all levels, thus they are positively correlated. The highest correlations are between household consumption expenditures and the other three expenditure components government consumption, investments and exports with correlation coefficients of 0.954, 0.950 and 0.933 respectively. This means that these variables vary together in a linear manner. Due to this high level of statistically si gnificant correlation, the premise of regressing the model via OLS and the corresponding interpretations are put into question, as one of the basic premises is that the value of each coefficient represents the change it causes on the independent variable, leaving the rest of the explanatory variables unchanged. Yet, if they are so highly correlated, you cannot assume that they can ever be unchanged.ConclusionsThrough the analysis of the Netherlands every quarter statistics on imports, relative import/domestic prices, household consumption, government consumption, investments and exports, we estimated via OLS a model to explain elasticity of imports. We underwent a series of analysis of the results of the model, finding that our estimate is statistically significant, as are each of the individual import elasticities. Additionally, we were able to demonstrate that the switch of currency to the euro caused a structural break in the import relationship. Notwithstanding this, the estimat ed model suffers from autocorrelation, which brings into question whether the OLS approach and its findings are in fact correct. Additionally, the high correlations that exist between the various expenditure components also puts into question our interpretations of the estimated coefficients, as none of them can be fully isolated to measure the effect on imports.ReferencesAtlapedia Online, 2006, Netherlands online, available at http//www.atlapedia.com/online/countries/netherla.htm accessed 12 celestial latitude 2006Biokin, Ltd., 2006, Critical values of F-statistics online, (updated 16 November 2006), Available at http//www.biokin.com/tools/fcrit.html accessed on 10 December 2006Central Intelligence Agency, 2006, The World Factbook Netherlands online, updated on 30 November 2006, available at https//www.cia.gov/cia/publications/factbook/geos/nl.html accessed on 11 December 2006Critical Values for the Durbin-Watson Test 5% Significance Level online. Available at http//www.stanford.ed u/clint/bench/dw05b.htm accessed 10 December 2006Hamilton, J.D., 1994, Time Series Analysis, New jersey Princeton University Press.International Monetary Fund (IMF), International Financial Statistics (IFS) November 2006, ESDS International, (MIMAS) University of Manchester.