Applied Econometric Examination - Assignment Example

Applied Econometric Examination Question 1 In the third model, β1 estimates how an increase in the income per capita is brought about by the increase in protection against expropriation (proxy for quality of institutional). From β1, if protection against expropriation variable increases by just one unit, the result will be that income per capita increases by 0.43. Similarly, β2 of 0.37 implies that income per capita in a given economy can rise by up to 37% if the latitude of a country increases by 1 units. However, β3 of -0.62 implies for the countries in the Asian continent, an upsurge by1 unit, results into a decrease, of up to 62 percent, in the income per capita. β 4 of -1.00 and β5 of -0.25 illustrates that for the countries residing in African continent and other continents, an increase by one unit will cause a decline the income per capita to decline by 100% and 25% in the respective countries. Question two If the effect on growth differed between Africa and the other continents, then including variable DAsia, i and variable Dother, i in the model, in equation 1, will be like including two correlated variables. As such, the model cannot effectively capture the differing effect on growth occasioned by African countries and the rest of the countries. This is because we will have two variables (variable DAsia, i and variable Dother, i) that illustrate a similar effect on income per capita. ln (yi) = βo + β1Ri + β2Lati + β3DAsia, i + β4DAfrica,i + β5Dother, i + εi…………………..………..(1) The appropriate model would be as shown in equation 2: ln(yi) = βo + β1Ri + β2Lati + β3DAfrica,i + β4Dother, i + εi……………………………………….(2) We will adopt F-test to prove this theory. As such, the assumption is: Ho: β3 = β4 (effect of institutions is similar across nations) H1: β3 ≠ β4 (effect of institutions vary across nations) Comprehensive procedure for testing this assertion would be to: 1) Obtain the variables of the two models and divide the bigger variable by the smaller variable (calculated F-statistic). 2) Get the critical F-value, depending on the preferred alpha value, from the F-table 3) Do a comparison from the statistics on the table using the calculated statistics and do not use Ho only if the calculated statistics is less than the statistics on the table. Question three A decrease in income per capita by up to 62% will be realized if the countries resides in Asia. Similarly, a 100% decline in the per capita income will be realized if the countries resides in African. As such, the expected difference in growth for the countries in the two continents, averagely, is 48% decline in the income per capita. Question four In an analysis of the regression, the use of raw-score rather than absolute values will cause the value of Lati to be smaller than the value of Ri since the two independent variables incorporate different scales. In the second model, a reduction is expected for R2 and standard error. Question five The presence of heteroscedasticity gives an implication that there is no constant change of errors in all the observations. The existence of heteroscedasticity can best be validated using Breusch-Pagan test. After undertaking the regression, the analyzer should type estat hottest in the command space in stata. The zero hypothesis will be that the change of errors are all similar in comparison with the option that change of error are different. From the test, if a person observes a big chi-square, it implies that there is the presence of heteroscedasticity, and as a result the person should not use the null hypothesis. Question six In an analysis on the assumption that there are similar effect on the locality of and on growth as institutions (R), there is the need to experiment on how the two variables correlate. Consequently, t-test should be conducted to validate whether the means are the same. Ho: μg = μq (correlation ρ ≠ 0) H1: μg ≠ μq (no correlation, ρ = 0) The formula to be used is: sd2 = (σ2g / ng) + (σ2q / nq) where; σ2g and ng refer to variance and sample size of latitude data respectively, and σ2q and nq refer to the variance and sample size of institution data. From this, sd = √ sd2 Thus, the solved value for t value will be: t statistics = (μg – μq)/ sd Finally, go back to the table and look at the value, at (nr + nl – 2) degrees of freedom and alpha of say 5%. If the computed value of t value is greater than the value on the table, ignore Ho and summarize that the two variables have different effects on growth. Question seven Obviously, it can be said that, model 3 in table 1 nests model 2 in the table 1 because the third model has all of the independent constraints found in model 2, and also, some other independent constraints. Question eight In a situation when there are at least two descriptive variable, error in measurement can result into a measure of the coefficient estimate to be increasingly biased or decreasingly biased. By addition of other variables which experience the effect of measurement error, the outcome will most likely be a substantially incorrect. Reliability, will be hard to attain (a function of error variance and cumulative variance) because the error on variance is relied upon by the tool used for measurement. As a result, β1 will record high variations because of the error in measurement. Errors for measurement do not have an impact of the test which shows whether there is proper proof that the β1 is not similar to 0 (β1 = 0 against two-sided alternative assumption). Computation using such a test relies on the p-value, which does not act as representation of measurement error or the chance of error creation. The above case will not be true when a proxy variable is used for Ri. There is the possibility for no biasness in the estimation of coefficient due to lack of measurement error. Question nine E (IQ|R,Lat) = E(IQ|R) illustrates that if institutions were independently allocated, it would be easy to notice any causality. The question is; does changes in quality of institutions constraint link with variations in geographical position or growth? If there exists a correlation, it can be safely said that institutions, most likely are the cause for an adamant growth of an economy. Unplanned assignment makes sure that the units used in measurement in our treatment group, those available to the ultimate quality institutions, shall be affiliated with the same units in the control group. There are both unobserved and observed procedures which result into the recognition and preservation of institutions around the world, and such attributes, some extent have a direct or indirect correlation with economic growth. Thus, these elements have to be done away with in order to avoid creating a calculation which is biased for the safeguarding effect on the quality of growth in the institutions. If not, then there is to be a resulting change in measurement of growth between the treatment and control group earlier than exposure to treatment. To be exact, the key idea is that any correlation between variables of the institution and geographical place that have a correlation with growth of the economy permit the choice made in "treatment group" and are dependent. As an auxiliary for, assignment to the treatment group exists a function for the geographical place. As such, E(IQ|R,Lat) = E(IQ|R) attempts to explain the estimator will be not be a biased determiner of the actual population factors. Question ten A comparison cannot be made between the R2s in Table 1 with the equivalent R2s in Table 2 because the models used in the two tables did not have similar sizes. Fewer samples, of size 64 were used in Table 2, while a sample size of 110 was used in table 1. Generally, as sample size increases, R2 will be precise. Thus, a comparison between the R2s in table 2 are more biased than R2s in Table 1. Question eleven Comparing the estimates in model (2) for the two Tables, the estimations for Table 1 seem to be exact because the sample sizes used in Table 1 were larger. Increasing the sample size may have enhanced the accuracy of estimates. Question twelve A comparison cannot be drawn in the distinctions in β2 in the two Tables because the outcomes of the regression are on the basis of different sample size. The second table comprised of lesser sample size. This shows that its approximation is related with higher, which is contrary to the lower variation recorded from the estimations of Table 1. Therefore, certain factors varied in the two Tables and as a result we it is not possible to do a comparison on the estimate of β2. Question thirteen This does not come as a surprise since model 3 consisted of more variables than those of the other two models. Particularly, model 3 is set on certain dummy constraints set and it is better than model 1 and 2 that are fixed on few constraints. The third model also has higher R2 thus there is the probability that it boosted the model’s suitability, of model 1 and 2, with the data. As a result, it possibly used a larger and a sample that was illustrative. Question fourteen No. It does not imply that estimation of country produce is substandard since R2 just estimates the fraction of the change in income per capita that is explained by institutional factors (independent variable). It is used by the explanatory variable, which is the quality of any institution in the country). As such, a R2 less by 10% implies that the change in income per capita is described, with an estimated lower value of 10%. The variation is in accordance with the quality of the institutions in the country. Question fifteen β1 should not be interpreted as a causal impact since there is a connection between the quality of a country`s institution and certain variables, like the settler mortality, which has a correlation with the growth of the economy. Thus, these elements must be discarded to evade making a biased estimation on the impact of the quality of treatment in relation to the income per capita. In addition, since the quality of institutions are not solely allocated, it becomes difficult to discover causality since β1 will biased measure and should not be regarded as a causal consequence. Question sixteen To determine which direction the endogeneity bias, it is crucial to study the sign of β1 and δ1. This coefficient is positive. If we feel β1 and δ1 are closer to true values, then we can argue that β1, which will exaggerate the effect growth with regard to quality of institution. Question seventeen Bear in mind that if there exists a correlation between the geographical location and institution are in the sample, then the standard deviation will be equivalent to zero, and subsequently there will be bias. This means that, the bias approximation of concern because there exists a correlation between the misplaced independent variable and other variables. The model that uses this relation would be: ln(yi) = βo + β1Ri + β2Lati + β3DAsia, i + β4DAfrica,i + β5Dother, i + β6 Lati * Ri + εi Comprehensive procedure for the test if there exists such precise statistical relations would be: a) Obtain the variances of the two models and divide bigger variance by the smaller variance (calculated F-statistic). b) Get the critical value of F, in the basis of the preferred alpha value, from the F-table c) Compare the table value with the computed statistics and reject Ho only if the calculated statistics is less than the table statistics. Question eighteen The F-test is to be used to ascertain if: Ho: β1 = β3 = β4 = β5 (there is no difference between the institutions and the continental perspective) H1: β1 ≠ β3 ≠ β4 ≠ β5 (institutions are different from a continental perspective) For the following two models ln(yi) = βo + β1Ri + β2Lati + β3DAfrica,i + β4Dother, i + εi…………………………………..(a) ln(yi) = βo + β1Ri + β2Lati + εi…………………………….……………………….…….(b) To conduct f-test, we will: Get the variances by squaring standard deviation from model (a) & (b). Divide the bigger variance by the smaller variance so as to obtain the calculated F-statistic. Obtain the critical F-value, at 10% alpha value, from the F-table Perform a comparison between the critical value of F and the calculated F-value and ignore Ho if calculated F-value is less than the table F-value. The p-value of 0.023 suggests a lower threshold for attaining a significant outcome. Question nineteen It is a bad idea since the degrees of freedom in Table 2 is smaller but the higher the degree of freedom, the higher the possibility of attaining a significant measurement. Thus, in Table 2 it is quite impossible to attain significant result. Question twenty To be a valid tool, settler mortality (Si) must meet the following two conditions: a) Instrument relevance, that is, Cov (Si, Ri) ≠ 0. The covariance between settler mortality and institution should be zero or any other value above zero. b) Instrument exogeneity, that is, Cov (Si, εi) = 0. This implies that covariance between the instrumental variable and error term should be equivalent to zero. Question twenty one 100% increase in the dependent variable (income per capita) will be realized if the quality of institutions increases by 1 unit, that is (β1 = 1.00). However, there exists an inverse relation between the income per capita and the latitude of a country increases, that is (β2 = -0.65). Question twenty two Yes, β1 in Table 3 was measured by the use of instrumental variables method. The approximation is thus control for estimation and confounding error in the sample observation. This method allowed for the chance of using causal conclusions with observational data concerning the quality of institutions. The evaluation is also accustomed for both the unobserved and observed confounding impacts; something dominant when estimating the quality of institutions. In the other table, β3 does not have the above conditions. Question twenty three The hypothetical implication of this large estimate of β1 just proves the outcomes of Acemoglu, Johnson and Robinson (2001) and what not only several economists but also social scientists accept to: the variations in quality of institutions and rules of state are the main cause of large inequality in economic growth around the world. There is negligible agreement, however, regarding what defines quality of institutions towards economic growth, baring the isolation exogenous determining factor of change in quality of institutions. Question twenty four In table 1, the meaning of the higher standard error is that the sample is not a well representation of the entire population (quality of institution), rather the assessment is nearer to the actual value of β1. As such, great standard error implies that the data was extensively distributed in model 1 & 3 in Table 1. The other implication is that the Table 2 altered the unit of measurement approved for quality of institution (proxy variable). Thus, it recorded a smaller amount for the standard error. Question twenty five Since there exists a correlation between some variables which might refer to the similar alteration in income per capita, which is the dependent variable, β2 in table 3 was measured in a manner (instrumental variable approach) that scrapped the biasness of concurrent causality (settler mortality variable results into alterations of the in income per capita and vice versa) and errors of bias constraints. Thus, β2 had a resilient sign which is statistically of no importance in relevance to p-values that are above 0.15. Question twenty six Contradicting Acemoglu, Johnson and Robinson (2001) argument that settler mortality was an effective tool is hard to disprove from a statistical view since the outcome in the covariance between settler mortality and quality institution was not equivalent to zero. The two variables have a good correlation. This follows one of the two reasons for an effective instrument. However, there could have been a zero outcome on the determination of the covariance between settler mortality and the error term. Question twenty seven If “disease environment” variable has a positive correlation with “quality of institution” variables but negative impact on growth, the Acemoglu, Johnson and Robinson (2001) estimation would not be reliable because there would be no zero outcome on the variance. Conversely, this cannot be an effective concern because each quality assessment in a institution has no capability in explaining the actual effect on the growth, which is a dependent variable as might be the situation if that institutional quality were to be the only constraint in the model. Question twenty eight Viewing all the models in first, second and third table, there is a positive result on the evaluation of institutional quality. This suggests that the difference in quality of institutions of the country are the major cause of large changes in economic growth globally. There is a positive effect on the income per capita, as a result of Institutional quality. Study of the factors that influence economic growth has shown that specific factors in some countries result into significant effects on the performance of the economy. Maintaining the rule of law and better institutional quality encourage economic progress. Such inferences are too delicate to the estimation of sample and techniques in choosing. When countries with similar sample are used, the states with quality institutions advantages from countries with larger growth and performance in the economy. Approximations incorporating instrumental variable approaches admit that democratic institutions experience better performance in the growth of the economy. Work Cited Daron Acemoglu, Simon Johnson, & James A. Robinson. The Colonial Origins of Comparative Development: An Empirical Investigation. The American Economic Review, Vol. 91, No. 5 (Dec., 2001), pp. 1369-1401. http://economics.mit.edu/files/4123 Read More