A Medium-Term Strategy for Raising Gross Domestic Product - Assignment Example

ASB-4501/4601 Research Methods work assignment no. 2 You are a researcher working for the Finance Ministry of a developing country. Your boss, the Minister of Finance has been asked to make recommendations to a government committee that has been charged with formulating a medium-term strategy for raising the country's per capita Gross Domestic Product (GDP) over the next 15 years. Funding of US$ 2 billion has been earmarked by the government for policy measures to support this strategy. At its previous meeting, the committee decided that this funding should be devoted to policy measures that will increase the country's rate of enrolment in secondary education. It is estimated that the expenditure of US% 2 billion will boost the secondary school enrolment rate (expressed as a percentage of the secondary school age population) by about 6%, from the current figure of 55% to an estimated 61%. However, since the previous meeting of the committee, the country has experienced a financial crash. Senior representatives from the banks have been lobbying furiously for financial support to enable the banks to continue lending, in an attempt to avert a full-scale economic recession. They have argued that by providing emergency financial support now, the government can prevent the banks from shrinking their balance sheets, and maintaining a strong and vibrant banking sector is essential if the country is to achieve the targeted growth in its per capita GDP over the medium term. It has been estimated that US$ 2 billion allocated to the banking sector now will prevent a drop in the ratio of Private Credit by Deposit Money Banks and Other Financial Institutions to GDP, from the current figure of 0.52 to an estimated 0.38. You have been asked by the Minister of Finance to investigate the empirical evidence as to whether the sum of US$ 2 billion would be spent more effectively on boosting secondary school education, or on bailing out the banking sector. You can recall an empirical model that addresses exactly this type of question, which was presented in a series of tutorials/workshops in which you participated during your time as a masters student at Bangor University in the UK. You are concerned, however, that the data that were used in this exercise are now several years out of date, and you have decided that it would be a good idea to update the data and re-estimate the model. In order to complete this task, you have been assigned the following electronic resources: 1. An Excel file struct2.xls, which has been downloaded from Ross Levine's website, in which can be found data on the financial development indicator to be used in the empirical model, the ratio of Private Credit by Deposit Money Banks and Other Financial Institutions to GDP (see column M) 2. An Excel file tab396.xls, containing United Nations data on rates of secondary school enrolment per head of the secondary school-age population in selected years: 1980, 1990 and 1997 (see column BI for the 1990 data). 3. A link to the Centre for International Comparisons at the University of Pennsylvania website, from which you can download data on all of the other variables that are used in the model. http://pwt.econ.upenn.edu/php_site/pwt63/pwt63_form.php You intend to use these data sources to compile data for the following 50 countries: Brazil, Canada, Chile, Ecuador, Peru, Venezuela Belgium, France, Germany, Greece, Hungary, Italy, Netherlands, Poland, Spain, Turkey, United Kingdom Algeria, Burkina Faso, Cameroon, Egypt, Ethiopia, Ghana, Ivory Coast, Kenya, Madagascar, Malawi, Mali, Morocco, Nigeria, South Africa, Sudan, Uganda, Zimbabwe Australia, Bangladesh, China*, India, Indonesia, Iran, Japan, Malaysia, Nepal, Pakistan, Phillipines, Saudi Arabia, Sri Lanka, South Korea, Syria, Thailand When downloading Chinese data from the University of Pennsylvania website, select 'China version 2'. The specification of the empirical model is as follows: dlypci = 1 + 2lypc90i + 3lsecedi + 4govgdpi + 5openi + 6infli + 7crediti + ui where ypc05 = per capita GDP (constant prices, chain series) in 2005 ypc90 = per capita GDP (constant prices: chain series) in 1990 dlypc = ln(ypc05) - ln(ypc90) lypc90 = ln(ypc90) seced = percentage of secondary school age population enrolled at secondary school in 1990 lseced = ln(seced) govgdp = government share of real GDP per capita in 1990 open = openness = ratio of (exports+imports) to GDP in 1990 cpi90 = consumer price index value in 1990 cpi85 = consumer price index value in 1985 infl = five-year inflation rate = ln(cpi90) - ln(cpi85) credit = ratio of private credit by deposit money banks and other financial institutions to GDP in 1990 The codes for the variables you should download from the University of Pennsylvania website are as follows: variable (definitions above) code ypc05, ypc90 rgdpch govgdp kg open openk cpi90 and cpi85 pc Your tasks are as follows: 1. Using the three electronic resources, compile the required data for the 50 countries in an Excel spreadsheet (each row should represent a country and each column should contain the data for one variable). Complete Data.xlsx 2. Read the compiled data into Stata, and estimate the empirical model. Test the following null and alternative hypotheses: dlypc = .8278034 - .2069032 lypc90 + .2580744 lseced + .0083719 govgdp - .0003107 open + .1146529 infl + .2214327 credit (.4223974) (.0810695) (.1010336) (.0059635) (.0014735) (.1106607) (.1437047) R-square: 0.1862 Adjusted R-square: 0.0726 The R-square of .2311 means that 18.62 % of the variations in dlypc can be explained by lypc90,l lseced ,govgdp ,open ,infl ,credit. (i) H0:2=3=4=5=6=7=0 against H1:j0 for at least one j(2...7), using a significance level of 0.05. The computed F is .1596, which is smaller than the table value of F = 1.64 ( = 0.05 and df = 6 and 43). Therefore, we accept H0 that we do not reject the null hypothesis, and conclude H0 = 2=3=4=5=6=7=0, these mean that the coefficients are not equal to zero. Given that the null hypothesis is true, the regression equation means that the lypc90, llseced, govgdp , open, infl and credit does not influence response dlypc. (ii) H0:2=0 against H1:20 using a significance level of 0.05. The computed value of t is -2.55, which is less than the tabular value of ----1.96. This means that we reject H0: 2 = 0. Therefore, we conclude that lypc90 is statistically significant at the 5 % level of significance. It implies that the GDP per capita in 1990 significantly explain the changes of GDP per capita in 15 years, from year 1990-2005. (iii) H0:3=0 against H1:3>0 using a significance level of 0.05. The value of the computed t is 2.55, which is greater than the table value of 1.96 (5% level of significance and 42 degrees of freedom). We reject H0: 3 = 0, and conclude that the lseced is statistically significant. Therefore, the percentage of secondary school age population enrolled at secondary school in 1990 significantly explain the changes of GDP per capita in 15 years, from year 1990-2005. (iv) H0:7=0 against H0:7>0 using a significance level of 0.1. The computed value of t = 1.54 is less than the tabular value of t = 1.645 at the 5% level (two-tail test) with 43 degrees of freedom. This explains that we cannot reject H0, that 7 = 0. We therefore conclude that the credit is not statistically significant at the 10 % level of significance. This means that the ratio of private credit by deposit money banks and other financial institutions to GDP in 1990 does not significantly explain the changes of GDP per capita in 15 years, from year 1990-2005. Provide a brief interpretation/commentary (a couple of sentences each) on the results of these hypothesis tests. Explain the apparent contradiction between the test results in (i) and (iii). In testing the x's as a pool, it turned out that they are not related to y's. This was the interpretation in testing F-statistic. But there is an apparent contradiction on the hypothesis testing in H0:3=0 against H0:3>0 using a significance level of 0.1, because the null hypothesis was rejected and was therefore concluded that the lsced is statistically significant at the 10 % level of significance. So what's true for the part is not true for the whole, as the fallacy of composition states. This means that even the lsced variable is significant, and it does not necessarily reflect the significance of the explanatory variables as a whole to explain the changes the response variable (dlypc). 3. On the basis of the model you have fitted and tested in Q2, formulate your advice to the Finance Minister on the question as to whether US$ 2 billion would be spent more effectively on secondary education, or on bailing out the banks, assuming that the policy objective is to increase growth in GDP per capita over the next 15 years. (Hint: work out the effects of the additional expenditure on the values of lseced and credit, and multiply by the relevant coefficients to calculate the effect on GDP per capita.) The government should prioritize the secondary education, because it is perceptible that there is an effectual augmentation in boosting the growth in terms of GDP per capita over the next 15 years. The US$ 2 billion bailout spent in secondary education will result to a 25.81% growth in GDP per capita over the next 15 years. When we spend it on banks, it will only have a 22.14 % increase. 4. Carry out diagnostic tests for the validity of the following statistical assumptions underlying the model you have estimated and the hypotheses you have tested in Q2: (i) The linearity assumption. (ii) The homoscedasticity assumption. Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of dlypc chi2(1) = 0.12 Prob > chi2 = 0.7290 (iii) The normality assumption. The distributions of the normal probability plots are normal, except for lsced, which is approaching a horizontal line. Those points on the plot that fall close to the diagonal line are normally distributed probability plots, because it exhibited a bow-shaped pattern of deviations from the diagonal, which indicates that the residuals have excessive skewness. It means that they are not symmetrically distributed, with too many large errors in the same direction. Unlike lsced, this has an S-shaped pattern of deviations that indicate residuals with excessive kurtosis. It means that there are either too many or too few large errors in both directions. 5. It has been suggested that a possible remedy for a non-normality problem is to create a 0-1 dummy variable for any 'outlier' observation with a residual larger than three times the standard error of the regression. Investigate whether there are any such outlier observations in the data you have used to estimate your model. If there are any outlier observations, create a 0-1 dummy variable for each outlier you find, and re-estimate the model. Using the new specification, repeat the diagnostic tests you carried out in Q4, and comment briefly on the results. (i) Linearity assumption The computed F value is 0.7086, which is greater than 0.59 (tabular value). This means that we do not accept the null hypothesis that there is a relationship between lypc90, llseced, govgdp, open,i nfl, credit,dummy variable to dlypc. The plot of residuals versus the predicted values clearly shows this notion. See graphs. (ii) The homoscedasticity assumption. The computed Chi square-statistic is 0.8539, which is greater than the tabular value of 0.03. Therefore, we reject the null hypothesis and conclude that homoscedasticity was not violated in the emperical test. It is evident in residual plots versus the predicted values. Please see graphs on (i) . Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of dlypc chi2(1) = 0.03 Prob > chi2 = 0.8539 (iii) The normality assumption. The distributions of the normal probability plots are normal, except for dummy variable, which is heading away from the horizontal line. Those points on the plot that fall close to the diagonal line are normally distributed probability plots, because it exhibited a bow-shaped pattern of deviations from the diagonal, which indicates that the residuals have excessive skewness. It means that they are not symmetrically distributed, with too many large errors in the same direction. Unlike dummt, this has an S-shaped pattern of deviations that indicate residuals with excessive kurtosis. It means that there are either too many or too few large errors in both directions. 6. Does having respecified and re-estimated the model cause you to alter the advice you would give to the Finance Minister concerning the most effective means of spending US$ 2 billion (Hint: To set up a dumy variable, use the gen command to create a new variable equal to zero on all observations, then use the Data Editor - 4th icon from the right along the top - to change the required observation from 0 to 1.) No, because the result is still favourable in bailing out the banks. The government should still prioritize the bailing out the banks, because it is perceptible that there is an effectual augmentation in boosting the growth in terms of GDP per capita over the next 15 years. The US$ 2 billion bailout will result to a 16.84% growth in GDP per capita over the next 15 years. When we spend it on secondary education, it will only have a 0 % increase. Read More