The result are analyzed in the excel worksheet showing all the required data. (2) In order to estimate the empirical model, the previous compile data in excel worksheet would be used. This method is used to test a claim o just hypothesis about a parameter of the entire population using the data measured in the previous sample. This will enable to determine whether the sample statistic would be selected in case the hypothesis regarding such population parameter is true (Barnard, 2007). Therefore the following null and alternative hypotheses would be tested based on the following formula as shown bellow.
Using random method of data selection, let use consider the results for Algeria and United Kingdom for effective calculations. For United Kingdom: i. dlypci = 1 + 2lypc90i + 3lsecedi + 4govgdpi + 5openi + 6infli + 7crediti + ui Since dlypc = ln (ypc05) – ln (ypc90), then dlypc=121.07-102.70=18.37 (a) H0:2=3=4=5=6=7=0 against H1: j0 for at least one j (2.. .7), using 0.05 significance level. =1+102.7*0+93*0+21742.5*0=36.97*0+ (112.62-65.79)*0+1.130044*0+0.05 18.37=1+0+0.05 1=18.32 where as for Algeria the results are: dlypci = 1 + 2lypc90i + 3lsecedi + 4govgdpi + 5openi + 6infli + 7crediti + ui Since dlypc = ln (ypc05) – ln (ypc90), then dlypc=59.77-98.12=-38.35 =1+59.77*0+61*0+5189.55*0+90.65*0+ (49.95-44.38)*0+0.399052*0+0.05 -38.35=1+0+0.05 1=-38.4 Therefore, based on the above computation, the results shows that the data collected is statistically not significant and can be relied upon in making decision.
This is because all the outcomes as per the hypothesis i. e. j0. Thus, the population is a null hypothesis. ii. 2=0 against H0:20 using a significance level of 0.05 dlypci = 1 + 2lypc90i + 3lsecedi + 4govgdpi + 5openi + 6infli + 7crediti + ui =1+102.7*0.1+93*0+21742.5*0+36.97*0+ (112.62-65.79)*0+1.130044*0+0.05 18.37= 1+10.25 1=8.1 while for Algerian =1+59.77*0.1+61*0+5189.55*0+90.65*0+ (49.95-44.38)*0+0.399052*0+0.05 -38.35=1+5.977+0.05 1=-44.28 The hypothesis is not true is null in nature and can not be relied upon in making decision according to the model stated.
(Wellek & Stefan, 2003) iii. H0:3=0 against H0:3>0 using a significance level of 0.05 =1+102.7*0+93*0+21742.5*1+36.97*0+ (112.62-65.79)*0+1.130044*0+0.05 18.37=1+21742.5+0.05 1=-21724.2 where as for Algeria =1+59.77*0+61*0+5189.55*1+90.65*0+ (49.95-44.38)*0+0.399052*0+0.05 -38.35=1+5189.55+0.05 1=-5227.95 The test statistic results are used to determine the likelihood of results computed, for instance, the larger the value of statistic, then the further the number or distance sample mean or standard deviation. Though the result ca be relied on, but is further from the mean value. iv. H0:7=0 against H0:7>0 using a significance level of 0.1 =1+102.7*0+93*0+21742.5*0=36.97*0+ (112.62-65.79)*0+1.130044*1+0.1 18.37=1+1.130044+0.1 1=17.3 on the other side Algeria results are; =1+59.77*0+61*0+5189.55*0+90.65*0+ (49.95-44.38)*0+0.399052*1+0.1 -38.35=1+0.399052+0.1 1=-38.9 The above alternative hypothesis can be relied upon in making decisions, since the population Parameter is less than, more than or not equal to the stated values in the null hypothesis as per the model.
This is contrary to null hypothesis (3) Based on the model determined in the previous computations, An appropriate advise can now be made on whether, the ministry of finance should spend extra money effectively on secondary school education, or consider bailing out banks can be easily arrived at in a more concise and appropriate manner keeping in mind that the main objective is to increase the overall growth in GDP per capita for the coming fifteen years.
For instance, using Algeria and United Kingdom based on H0:7=0 against H0:7>0 using a significance level of 0.1, the results would be as follows, dlypci = 1 + 2lypc90i + 3lsecedi + 4govgdpi + 5openi + 6infli + 7crediti + ui =1+102.7*0+93*0+21742.5*0=36.97*0+ (112.62-65.79)*0+ (1.130044+2)*1+0.1 18.37=1+3.130044+0.1 1=15.24 =1+59.77*0+61*0+5189.55*0+90.65*0+ (49.95-44.38)*0+ (0.399052+2)*1+0.1 -38.35=1+2.399052+0.1 1=-40.9 The ministry of finance should consider investing more money (USD 2 billion) on secondary education as opposed to being spent on bailing out the banks.
An increase by $2billion has a considerable increase in the countries GDP. This is because education is the key pillar of economic stimulant which is channeled to other sectors of economy. In the longer run i. e. 15 years to come, all sectors including banking institutions will be much better having improved so much. Employment level will increase, income per person would also rise and as a result of this, the overall well being of all the citizens will be better. (4) Diagnostic test on the empirical model and the hypothesis tested previously in question two following; i.
Linearity assumption. According to linearity assumption, the general rule is that, for any regression model which has an independent variable (Hardy & Melissa1993). Then such variable is represented by both non-square and squared terms which have significance. If the value chosen is less than the significance level, then it is recommendable to accept the hypothesis that the entire population represented by the variable is statistically significant. This is contrary to the null hypothesis, which the reverse is true.
Therefore based on the following hypothesis, H0:7=0 against H0:7>0 using a significance level of 0.1. As computed earlier the results should be accepted. dlypci = 1 + 2lypc90i + 3lsecedi + 4govgdpi + 5openi + 6infli + 7crediti + ui For instance since the result obtained 1=-40.9 which is less than 0 then the hypothesis should be accepted and be used in making decisions. ii. Homoscedasticity assumption The model assumes that all dependent variables have the same amount of variables across the range of values for each independent variable.
It requires that, all independent variables be non-metric (Lehmann, 2010). Once this is the case, then it can be evaluated as one of the residual analysis in the multiple regressions. Since the diagnostic hypothesis test for homogeneity of the variances and the degree of confidence is 0.1 which is much higher, then the result can be relied upon. 18.37=1+3.130044+0.1, 1=15.24, according to United Kingdom results, since the degree of confidence is over 0.05 as is the case with other hypothesis, the result is significant. iii.
Normality assumption Statistical method includes hypothesis test for the linearity i. e. the thumb rule which assumes that a relationship is always linear if the difference between the non-linear and the linear correlation coefficient is small. If the transformations for an independent or a dependent variable are statistically significant, then the problem is linear (Koch, 1999). And incase, the transformation is not statistically significant, then there is no relationship at all. The results computed in the previously indicate that the problem is linear, thus statistically significant. (5) Dummy variable represents a number of data categories; it is used to find out if being in a certain category has a comparable difference with being in the other category.
The value for dummy is either one or zero (Kooyman, 1976). For instance, the number of student enrolment in secondary school for different levels could be used based on the empirical model computed earlier. dlypci = 1 + 2lypc90i + 3lsecedi + 4govgdpi + 5openi + 6infli + 7crediti + ui Supposed the value of students enrolled is 0 and the government share on GDP is 1, then this means that less money will be stent on education.
Though in the normal case, the government incurs expenditures on its projects such as education before considering having its share. The same effect will be on other variable incase they are assumed to be dummy. The result will be that the overall per capita GDP of the country will be lower. In case the value changes from 0 to a much higher value like 3, then the result will no longer be dummy. A slighter change in any variable will significantly affect the entire result for per capita GDP. (6) The main objective of altering or changing of variables is necessary in testing the effectiveness and the accuracy of the empirical model and does not really change the decision of using the $2 billion to foster secondary education rather than investing the funds in the banking institution.
In order to realize the value of $2 billions, the Ministry of finance should consider investing the funds in education sector which will in tern be realized in less than a span of 15 years. This is evidenced as per the tests and computations determined above. Reference: Barnard, C. 2007, Asking questions in biology: a guide to hypothesis-testing, analysis and presentation in practical work and research.
Harlow: Pearson Education. Hardy & Melissa1993, Regression with dummy variables, Newbury Park: Sage Publications. Koch, 1999, Parameter estimation and hypothesis testing in linear models S. l: Springer. Kooyman, M. 1976, Dummy variables in econometrics, Tilburg: Tilburg University Press. Lehmann, E. 2010, Testing statistical hypotheses. New York: Springer. Wellek & Stefan, 2003, Testing Statistical hypotheses of equivalence, Boca Raton, Fla: Chapman & Hall/CRC.