Regression Analysis for the Netherlands

Regression Analysis for the Netherlands TABLE OF FIGURES AND GRAPHS Table 1: Coefficients of estimated OLS model Table 2: Analysis of Variance and F-statistic Table 3: Paired t-sample tests Table 4: Analysis of Variance for pre structural break (b,c) Table 5: Analysis of Variance for post structural break (b,c) Table 6: Analysis of Variance and F-statistic Table 7: Pearson’s Correlations Graph 1: Scatterplot with best fit line Graph 2: Simple scatterplot of imports Introduction The following document analyses the import aggregate demand for the Netherlands utilising data from the first quarter 1977 to the first quarter 2006. The aim is to determine the relationship between imports and five explanatory variables: relative prices (measured as the ratio of import to domestic prices), household consumption expenditures, government consumption expenditures, investment expenditures and exports. A regression utilising Ordinary Least Squares is run and then a series of analyses is done on the results of the estimated model. Model Estimation Data for the Netherlands was obtained from 1st quarter 1977 to 1st quarter 2006 from the International Monetary Fund’s 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 Netherland’s 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 exchange rate at the time of the entry of the euro. To prepare 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 SPSS to estimate the model via Ordinary Least Squares, the aggregate demand function (utilising the unstandardised coefficients) is estimated as: M = 0.071 – 0.966 RP – 0.328 HC – 0.171 GC + 0.286 INV + 0.808 EXP Std 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 variance 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 levels. Table 1 shows the results of the estimated coefficients along with their corresponding t-values and significance values. Table 1: Coefficients of estimated OLS model a Dependent Variable: LN_M Plotting 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 line Interpretation of slope coefficients The estimated coefficients from the regression above can now be interpreted. The results are presented again for ease of reading: M = 0.071 – 0.966 RP – 0.328 HC – 0.171 GC + 0.286 INV + 0.808 EXP In general terms, each slope coefficient is the import elasticity with respect to each of the equation components: relative prices, household consumption, government consumption, investment expenditures and exports. Following is the explanation for each coefficient: machinery and transport equipment, chemicals, fuels, foodstuffs, clothing from germ, belg and china ÃŽ ²2 = -0.966 represents the relative price import elasticity. This implies that a 1% increase in relative prices causes a reduction in imports of 0.966%. This is basically 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 partners are within the European Union, who use the same currency, the relative prices are similar for them. (Atlapedia Online, 2006) ÃŽ ²3 = -0.328 represents the elasticity of imports with respect to household consumption expenditure. It implies that a 1% increase 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 well as chemicals, which have no relation with household consumption. (CIA World Factbook, 2006) ÃŽ ²4 = -0.171 represents the import elasticity with respect to government consumption 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. Due 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. ÃŽ ²5 = 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 makes sense with reality since investment expenditures are in part for importing machinery and transport goods. ÃŽ ²6 = 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 the European Union. Overall significance of the regression Now 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 below presents SPSS’ results for the F-statistic and Analysis of Variance for our model. Table 2: Analysis of Variance and F-statistic a Predictors: (Constant), LN_EXP, LN_RP, LN_INV, LN_GC, LN_HC b Dependent Variable: LN_M Test of equality of import elasticities After having tested 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 paired 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 tested: Table 3: Paired t-sample tests The Behaviour of Imports from 1977 to 2006 Having 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. 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 relationship: Graph 2: Simple scatterplot of imports A structural break in imports From 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 structural 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 â€Å"pre† represents observed values from Q1 1977 to Q2 2002, whilst the group labelled â€Å"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_HC b Dependent Variable: LN_M c struct_break = pre Table 5: Analysis of Variance for post structural break (b,c) a Predictors: (Constant), LN_EXP, LN_HC, LN_INV, LN_RP, LN_GC b Dependent Variable: LN_M c struct_break = pos Utilising the above with the results from the original unconstrained model: Table 6: Analysis of Variance and F-statistic a Predictors: (Constant), LN_EXP, LN_RP, LN_INV, LN_GC, LN_HC b Dependent Variable: LN_M the incremental F-value is calculated using the residual sums of squares and degrees of freedom of the constrained and unconstrained models. In this case as: F6,105 = [(0.063 -0.082)*(117 – 2*5-2)] / (0.082 * 6) = -4.05 The 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 â€Å"pre† and â€Å"pos† periods we chose. This confirms that there was a structural break in the 2nd quarter of 2002. Autocorrelation We 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 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, otherwise 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 i mply that a new regression must be run and new tests for autocorrelation carried out until this problem is eliminated. Correlation of final expenditure components Only 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 Pearson’s 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: Pearson’s 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 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. Conclusions Through 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 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. References Atlapedia Online, 2006, Netherlands [online], available at: http://www.atlapedia.com/online/countries/netherla.htm [accessed 12 December 2006] Biokin, 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 2006] Central 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 2006] Critical Values for the Durbin-Watson Test: 5% Significance Level [online]. Available at: http://www.stanford.edu/~clint/bench/dw05b.htm [accessed 10 December 2006] Hamilton, 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.

Google vs. Yahoo

Many people around the world use search engines everyday to find information quickly. However, not many people realize that each search engine is different from each other. Every search engine is unique because they will all produce different links when a word or phrase is searched for. This means that some search engines will be better than others. Two main search engines are Yahoo and Google. Although Yahoo and Google both perform the same task, Google is a better search engine because it has a simple layout and provides links that are more relevant to the item that is being searched for.Google has a simple homepage that is about 90% white with a search bar in the center below its logo. Yahoo's homepage has a variety of items on it such as moving images and attention-grabbing headlines. This argument may seem like it is in favor of Yahoo, but in reality Yahoo's flashy homepage can distract people for a long time. People that go to Yahoo can waste their time reading about topics tha t have nothing to do with what they originally wanted to search for while people who go to Google aren't distracted by their almost blank layout.Google and Yahoo both provide links with information about the topic that is searched for but Google's links have information that are more related to the topic. Surveys have been done where the most popular search engines (including Google and Yahoo) were tested to see which one gave them the best information about the topic that was searched for. The end result was that 94 out of the 100 people that did the testing agreed that Google was the best search engine because its results were the most relevant.Most of Yahoo's results displayed pages with irrelevant information after the first three or four results. When Google was used, the information that the testers wanted was found in the first or second link. They all said that they didn't have to even go on to the second page because the first page of links was more than enough for them. Go ogle's search engine has been tested and proven to be superior to Yahoo. Although the Internet may seem like a very common thing, many people are still getting introduced to it and its many functions.These types of people will not be used to something such as a search engine so it is important to keep the search engine simple and easy to use. While it is true that Yahoo's homepage can give people an idea about all the things that the Internet can do for them, it may be hard to navigate to something such as the search bar amidst the cluttered bundles of information. I think that we should keep search engines simple so that it will be easy for people new to the Internet to utilize it.

Making History Fun - Free Essay Example

Sample details Pages: 2 Words: 588 Downloads: 4 Date added: 2017/09/14 Category Advertising Essay Did you like this example? Steve Berg Period 2 08/28/10 Descriptive Essay Making History Fun Mr. Leonard is the AP American History teacher at Horizon High School. He has been teaching for more than twenty five years and uses his experience to educate the minds of young Horizon students. While Mr. Leonard can be a bit much, he always gets his point across. And if the student shows up for class and pays attention they will be forced to learn the material, even if they don’t realize it. To some, history can be a dull and boring subject but Mr. Leonard makes history an experience. He’s been to historical sites and has seen the things he teaches which helps him explain these historical events to his students. A teacher cannot teach directly from a book, anyone can do that; a teacher must use their own experiences and their own knowledge to truly enlighten young disinterested high school students. Mr. Leonard is a very strange, very loud, and very well educated history teacher that can pass his own personal knowledge down to open minded high school juniors. While some teachers bore students to death with monotonous lectures that seem to last for days; Mr. Don’t waste time! Our writers will create an original "Making History Fun" essay for you Create order Leonard shows students that lectures, even in high school, can be interesting. He takes events from that past and tells stories that seem to almost have no point, but while studying or even taking his tests those stories stick in student’s brains and help them remember and understand events and concepts relevant to the time period being studied. Even though he can be a little over the top his methods are proven. Generally, almost all of his students at least pass the Advanced Placement test with the score of a three. This shows his off the wall teaching techniques don’t just work on his tests, but also work on college level exams. Mr. Leonard is a very interesting and extraordinary teacher that prepares his students with outrageous, yet proven, methods. Most high school educators could care less about the students they teach. These lazy teachers would rather talk nonsense for fifteen minutes, and then turn their kids loose for the rest of class. When these under taught students take their tests it isn’t surprising they fail, but it is surprising at how little remorse their teachers feel for not properly preparing them. Mr. Leonard always prepares his students, even if they don’t realize it. He can lecture for the entire hour and some kids in class feel as if they’re only there for fifteen minutes. This is a sign that the man actually knows and cares about what he teaches. He has visited all the battlefields and all the monuments. He doesn’t just teach history, he has a passion for it, and this passion gets passed down to some of his students. This approach of â€Å"stealth teaching† evokes thoughts and ideas never before dreamed of by young high school juniors. If students really want to succeed, they can look to Mr. Leonard not only to help them with grades, but also provide them with knowledge that will make them better overall students and people. He sheds light on history and life, proving to kids that school can in fact be fun and interesting, teaching them things that will help them later on down the road. It is these qualities and much more that make Mr. Leonard one of the best teachers in not only Horizon but in the entire Paradise Valley Unified School District.

The Lucifer Effect Is An Eye Opener For Me - 1919 Words

Reading The Lucifer Effect was an eye opener for me. It got me thinking do we really know anyone for that matter do we know ourselves? There are times in of our lives, have we been astonished to learn about the activities of someone we thought we knew very well. Are those who commit atrocities people with serious character defects or psychopathology, or are they ordinary people responding to an extraordinary situation? The Lucifer Effect delivers some possible rationalizations for these personal mysteries in which we deal with. This book also gives some prospective on perplexed ideas of our own actions that may contradict our previous thought of our own identities. In this reflection paper I will be In The Lucifer Effect Zimbardo addresses a question, â€Å"What makes people go wrong?† (p. 5) He defines the word: â€Å"Evil consists in intentionally behaving in ways that harm, abuse, demean, dehumanize or destroy innocent others—or using one’s authority and systemic power to encourage or permit others to do so on your behalf† (p. 5). As is evident from this definition, the study of evil is the study of particular behaviors and motivations. As such, it could be argued that such a study is within the legitimate province of psychology, although some may be disturbed by this. Zimbardo begins by pointing out that the predominant paradigm in our culture for explaining human behavior is known as the dispositional model, a model that focuses on inner individual personality traits andShow MoreRelatedEssay about Galileo Galilei2120 Words   |  9 Pageshow they saw the world. â€Å"For example, a serious discussion among academics at that time was about the size and shape of hell as depicted in the poem Dantes Inferno, which was another eye opener for the community. Galileo gave a well-received lecture on the topic, including his scientific opinion about how tall Lucifer was† (Bellis). As a result of his lecture, there were positive criticism that helped Galileo score a position at the University of Pisa. â€Å"When he was born there was no such thing as