Regression Analysis for the Netherlands

Regression abridgment for the NetherlandsTABLE OF FIGURES AND GRAPHS slacken 1 Coefficients of estimated OLS ideal slacken 2 abbreviation of Variance and F-statisticmesa 3 Paired t-sample testsTable 4 Analysis of Variance for pre structural opening (b,c)Table 5 Analysis of Variance for jeopardize structural sort (b,c)Table 6 Analysis of Variance and F-statisticTable 7 Pearsons Cor similitudesGraph 1 Scatterplot with best fit lineGraph 2 Simple scatterplot of eventsIntroductionThe following document probes the conditional relation aggregate quest for the Netherlands utilising entropy from the first locatingerior 1977 to the first after part 2006. The aim is to position the relationship mingled with merchandises and five informative variables relative prices (measured as the ratio of mo to interior(prenominal) prices), ho spendhold manipulation expendings, brass inhalation expenditures, enthronement expenditures and exports. A regression utilising Ordinary Lea st Squ ars is run and then a series of analyses is make on the results of the estimated baby-sit.Model EstimationData for the Netherlands was obtained from world-class eviscerate 1977 to 1st quarter 2006 from the International Monetary Funds International monetary 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, at that place 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, tout ensemble in all of the data was transformed into Dutch gulden, using the official euro/gulden transposition rate at the time of the entry of the euro.To prep atomic number 18 the data for the regression, the subjective log of the harbors for imports (M), relative prices (RP)the index of import prices to consumer prices, household consumption expenditure (HC), regime consumpt ion expenditure (GC), investment expenditure (INV) and exports (EXP) were taken. By using SPSS to estimate the type via Ordinary Least Squ ares, the aggregate affect depart (utilising the un measure 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 random variable 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 instructive variables included in the regression, by analysing their t-values we are able to determine that from individually one coefficient is statistically world-shaking at all levels. Table 1 shows the results of the estimated coefficients along with their tally 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 in graph 1.Graph 1 Scatterplot with best fit lineInterpretation of slope coefficientsThe estimated coefficients from the regression in a higher place can now be interpreted. The results are presented again for ease of developmentM = 0.071 0.966 RP 0.328 HC 0.171 GC + 0.286 INV + 0.808 EXPIn general terms, each slope coefficient is the import childs play with keep an eye on to each of the equation components relative prices, household consumption, government consumption, investment expenditures and exports. Following is the explanation for each coefficientmachinery and transport equipment, chemicals, fuels, foodstuffs, clothing from germ, belg and chinaware2 = -0.966 represents the relative price import elasticity. This implies that a 1% growth in relative prices causes a reduction in imports of 0.966%. This is basically a unitary elasticity, the effect of a change i n relative prices is intimately identically reflected on imports. This occurs primarily in countries with an open thriftiness that thrives on the balance of trade. Additionally, since the Netherlands most important trade partners are within the European Union, who use the alike(p) property, the relative prices are alike(p) for them. (Atlapedia Online, 2006)3 = -0.328 represents the elasticity of imports with respect to household consumption expenditure. It implies that a 1% append in household consumption expenditure will translate into a 0.328% cliff 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 pop of imports is for machinery and transport equipment as swell as chemicals, which befool no relation with household consumption. (CIA World Factbook, 2006)4 = -0.171 represents the import elasticity with respect to government consumptio n expenditures. It follows that a 1% increase in government expenditure will result in a reduction in imports of 0.171%. The import elasticity of government consumption is highly inelastic. callable to the nature of imports mentioned in the paragraph above, it is logical to assume that the import composition is not astray 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 confirmatory inelastic import elasticity as a 1% increase in investment expenditure will result in a 0.286% increase in imports. This makes 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 elast icity. This also reflects the Netherlands open economy and its active trading with neighbouring countries as a result of forming part of the European Union.Overall significance of the regressionNow that we know 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 self-coloured 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 boldness level, then it follows that the estimation we have done does indeed predict some of the values we have spy 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 below 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 comparability of import elasticitiesAfter having tested that the model as a whole is statistically significant, we will now test whether each of the import elasticities of closing expenditures are equal amongst themselves. In order to do this, we will use a paired t-test, which will compare each elasticity against each other and determine whether the differences amid them are statistically significant or not. If they are not statistically significant, then the elasticities are the same.In the reference of our estimated model, the t-statistics are significant at all levels for all of the relationships. This means that we cannot adjudicate that each of the import elasticities is the same, rather they are statistically significantly diametrical 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 2006Having sustain 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. Using 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 obse rved 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 structural break point, Q2 2002. However, since SPSS does not have a command for the Chow Test, we do this analysis by calculate 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 assemblage 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 analysis of variance 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 Analysi s 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 the 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 mensurable using the residual sums of squares and degrees of freedom of the constrained and unconstrained models. In this instance 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 nugatory 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.Auto correlational statisticsWe can now check if our estimated mod el 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 falls 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 any 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 made to the model or the data itself will incriminate that a spick-and-spa n 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 autocorrelation, 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 consumpti on, 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 significant 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 quarterly 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 estimated model suffers from autocorrelation, which brings into question whether the OLS approach and its findings are in fact correct. Additionally, the high correlations that come through between the various expenditure components also puts into question our interpretations of the estimated coefficients, as no(prenominal) 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 December 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 perception Agency, 2006, The World Factbook Netherlands online, updated on 30 November 20 06, 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 direct online. Available at http//www.stanford.edu/clint/bench/dw05b.htm accessed 10 December 2006Hamilton, J.D., 1994, Time serial Analysis, New Jersey Princeton University Press.International Monetary Fund (IMF), International Financial Statistics (IFS) November 2006, ESDS International, (MIMAS) University of Manchester.