Applied Econometrics Issues - Assignment Example

Sur Lecturer Applied Econometric: Final Exam Introduction This paper gives answers to certain questions that relate to the research article, “Colonial Origins of Comparative Development,” by Acemoglu, Johnson & Robinson (2001). They assert that “nations with superior “institutions”, less distortionary policies and secure property rights will achieve better level of economic growth. To first examine this assertion, they collected data on 110 nations and formulated the model of interest. As such the following questions concern the above article. Question one In model 3, β1 measures how income per capita increases as a result of the increase in quality of institutions (protection against expropriation variable). From β1, income per capita will increase by 43% if protection against expropriation variable increases by 1 unit. Similarly, β2 of 0.37 specifies that when the latitude of a country increases by 1 units, income per capita of that country increases by 37%. However, β3 of -0.62 put forward that an increase, by 1 unit, in countries residing in Asia will cause income per capita to fall by 62%. β4 of -1.00 and β5 of -0.25 shows that one unit increase in countries residing in Africa and other part of the world will cause income per capita of the countries to fall by 100% and 25% respectively. Question two If at all the influence of institutions on income per capita differed between counties in African and other countries in other parts of the world, the current model (equation 1) cannot show the different effect since independent variables DAsia, and Dother, will be practically related hence they describe the same effect on income per capita. Variable DAsia is a subset of variable Dothers hence we will have collinearity. Such collinearity can extremely distort the results of the model in equation 1. The role of correlated variable is just to enhance inaccuracy, as conveyed through bias in the coefficients. Collinearity also increases uncertainty as conveyed through the standard errors. Therefore, regression estimates biased by such collinearity can cause the effect of institutions on growth not to demonstrate significant different in the outcome. As such, we might have false-positive results in the model in equation 1. ln(yi) = βo + β1Ri + β2Lati + β3DAsia, i + β4DAfrica,i + β5Dother, i + εi…………………..………..(1) The best model would be: ln(yi) = βo + β1Ri + β2Lati + β3DAfrica,i + β4Dother, i + εi……………………………………….(2) We will F-test to verify this claim. As such, the hypothesis is: Ho: β32 = β41 (impact of institutions differ) H1: β32 ≠ β41 (impact of institutions don`t differ) A detailed steps for the test would be to: Get the variances of the two models and divide the bigger variance using the smaller variance (calculated F-statistic). Obtain the critical F-value, based on the desired alpha value, from the F-table Compare the table statistics with the calculated statistics and reject Ho only if the calculated statistics < the table statistics. Question three Increasing the variable “countries residing in Asian” by a unit will occasion 62% fall in per capita income while increasing the variable “countries residing in African” by 1 unit will occasion 100% fall in per capita income. Therefore, the projected difference in economic growth between these two countries, on average, is 48% fall in per capita. Question four Using raw-score instead of absolute values in the regression analysis will make the estimate of Lati smaller than that for Ri because the two independent variables use dissimilar scales. R2 and standard error will also be reduced in model 2. Question five The existence of heteroskedasticity implies we do not have a constant variance of errors across observations. Breusch-Pagan test is best designed to sense the presence of heteroscedasticity. After running your regression analysis, you type estat hottest in the command space in stata. The test hypothesis will be: Ho: The variance of errors are all equal H1: The variance of error are not equal. From the test, if you get a big chi-square, the implication will be that heteroscedasticity is present hence reject the null hypothesis. Question six In testing the hypothesis that geographic location has a similar impact on growth as institutions (R), we need to test for correlation of the two variables. As such, we will test if there is no difference in their means. Ho: μl = μr (correlation) H1: μl ≠ μr (no correlation, ρ = 0) We will use the formula sd2 = (sl2 / nl) + (sr2 / nr) where; sl2 and nl are variance and sample size of geographical location data respectively and sr2 and nr are the variance and sample size of institution data. From this, sd = √ sd2 Therefore, our computed t value will be: t = (μl – μr)/ sd Lastly, check the table value, at (nr + nl – 2) degrees of freedom and alpha of say 0.05. If the computed t value > table value, reject Ho and conclude that the effect of the two variables on growth are not the same. Question seven Yes, we can confidently say model 3 in table 1 nests model 2 in table because model 3 has every of the independent variables found in model 2 plus some other independent variables. Question eight When we have at least two explanatory variable, measurement error may cause a coefficient estimate to be upwardly biased or downwardly biased. As we add more variables that suffer from measurement error, the results will possibly be a little wrong. We will not achieve reliability (a function of error variance and total variance) since error variance is depended on measuring instrument. As such, β1 will have high variations as a result of this measurement error. The measurement error cannot influence the test that proves whether there is strong proof that the β1 is different from 0 (β1 = 0 against two-sided alternative hypothesis). Such a test rely on the p-value, which is not a representative of measurement error or the probability of making errors. When we use a proxy variable for Ri, the above cases will not hold. The coefficient estimate can be unbiased due to the absence of measurement error. Question nine E(IQ|R,Lat) = E(IQ|R) explains that if institutions were independently assigned, detecting causality would be very easy. The question is; does variation in quality of institutions variable map onto changes in geographical location or growth? If they were correlated, we could safely deduce that institutions are certainly a cause of obstinate economic growth. Random assignment guarantees that the measurement units in our treatment group, those open to superior quality institutions, shall be aligned with an equal units in our control group. There exist both unobserved and observed processes which lead to the acceptance and preservation of institutions across nations, and such factors are somehow directly or indirectly correlated with economic growth. These factors thus have to be offset to avoid making a biased calculation of our treatment effect of quality of institutions on growth. Or else, they will produce variation in measures of growth between the treatment and control group before disclosure to treatment. To be precise, the key concept is that any correlation between institution variable and geographical location that are also correlated with economic growth render the selection into our "treatment group" dependent (non‐random); as a replacement for, assignment to our treatment group become a function of geographical location. As such, E(IQ|R,Lat) = E(IQ|R) tries to asserts the estimator will be an unbiased predictor of the true population parameters. Question ten We cannot compare the R2s in Table 1 with the corresponding R2s in Table 2 since the models used in the two tables had different sample sizes. Table 2 used fewer sample size (64) while table 1 used a sample size of 110. Generally, as sample size upsurges, R2 will not be that biased. As such, the R2s in Table 2 can be said to be biased compared to the R2s in Table 1 which are not that biased. Question eleven Comparing the estimates in model (2) for the two Tables, estimates in Table 1 are closer to the truth since Table 1 used larger simple size. Increasing the samples increase your chance of significance. Moreover, standard deviations of model of larger sample size are smaller compared to the standard deviations of model of smaller sample size. Question twelve We cannot compare the differences in β2 in the two Tables since the regression results in the two tables are based on dissimilar sample size. Table 2 had lesser sample size. Standard error, which reflects the standard deviation of geographical location data from its sample means, is estimated σ/√n. Remember n is the sample size and so decreasing the sample size will increases standard error and vice-versa. That is, as the sample size become smaller, our standard error will increase. The law of bigger numbers hold at this point: the bigger the sample size, the closer our estimate will be. This implies estimates in table 2 are associated with higher variance as opposed to the estimate in Table 1, which has lower variance. As such, certain parameters were not constant in the two Tables and hence we cannot compare their estimate of β2. Question thirteen This is not surprising since model 3 has more variables than any of the two models. In particular, model 3 is based on some dummy variable set and it is better than model 1 and 2 that are anchored on few variable. Model 3 also has higher R2 hence there is the possibility that it enhanced the model’s fit, of model 1 and 2, with the data. Therefore, it gives perhaps used a larger and more representative sample. Question fourteen No this does not suggest that measure of country output is inferior since R2 just measures the percentage of the change in the income per capita (dependent variable) accounted for by quality of a county`s institution (the explanatory variables). As such, a R2 less by 10% just means that the variation in income per capita is explained, at10% less, by the quality of a county`s institution. Question fifteen we should not interpret β1 as a causal effect since there exist a correlation between the quality of a country`s institution and some other variable (settler mortality) that is correlated with the economic growth. These factors hence must be offset to avoid making a biased computation of treatment effect of quality of institutions on income per capita. Furthermore, since the quality of institutions are not independently assigned, finding causality is difficult since β1 will not be unbiased estimate and should not be interpreted as a causal effect. Question sixteen To find which direction the endogeneity bias, we will classically examine 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 will overstates the impact of quality of institution on growth. Question seventeen Note that if geographical location and institution are correlated in the sample, then the standard deviation will not equal to 0 and thus there will be bias. In simple words, the bias estimate is a concern since the omitted independent variable is correlated with another variables. The model that incorporates this interaction would be: ln(yi) = βo + β1Ri + β2Lati + β3DAsia, i + β4DAfrica,i + β5Dother, i + β6 Lati * Ri + εi A detailed steps for the test if presence of such specific interaction statistically belonged to the model would be to: a) Get the variances of the two models and divide the bigger variance using the smaller variance (calculated F-statistic). b) Obtain the critical F-value, based on the desired alpha value, from the F-table c) Compare the table statistics with the calculated statistics and reject Ho only if the calculated statistics < the table statistics. Question eighteen We will use F-test to ascertain if: Ho: β1 = β3 = β4 = β5 (institutions does not differ from a continental standpoint) H1: β1 ≠ β3 ≠ β4 ≠ β5 (institutions differ from a continental standpoint) For the following to 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: obtain the variances by squaring standard deviation from model (a) & (b). use the smaller variance to divide the bigger variance so as to get the calculated F-statistic. Obtain the critical F-value, at 10% alpha value, from the F-table compare the critical F-value with the calculated F-value and reject Ho if calculated F-value < table F-value. The p-value of 0.023 implies that if institutions differed from a continental viewpoint, will obtain this observed difference in institutions from continental viewpoint or more in 2.3% of studies because of random sampling error. In simple terms, p-values address just one concern: how likely are our sample data, assuming the null hypothesis (institutions` effect on growth differ from a continental viewpoint) is true? This small p-value implies that the indifferent effect (due to biasness occasioned by correlation) we observed will occur rarely because of random sampling. Question nineteen It is not good idea since the degrees of freedom in Table 2 is lower but the higher the degree of freedom, the higher the likelihood of getting a significant test. Hence, in Table 2 we may not get a significant result. Question twenty To be a valid instrument, settler mortality (Si) must satisfy these two conditions: i. Instrument relevance, that is, Cov (Si, Ri) ≠ 0. The covariance between settler mortality and institution must not be zero. ii. Instrument exogeneity, that is, Cov (Si, εi) = 0. This means covariance between the instrumental variable and error term should be zero. Question twenty one When quality of institutions increase by 1 unit, income per capita increases by 100% (β1 = 1.00). However, when latitude of a country increases by 1 unit, income per capita decreases by 65% (β2 = -0.65). Question twenty two Yes, β1 in Table 3 was estimated using instrumental variables approach. The estimate is thus control for measurement and confounding error in the sample observation. This approach allowed for the probability of making causal conclusions with observational data regarding quality of institutions. The estimate is also adjusted for both the unobserved and observed confounding effects; something prevalent when measuring quality of institutions. β3 in other tables lack the above qualities. Question twenty three The theoretical implication of this large value of β1 just confirm the findings of Acemoglu, Johnson and Robinson (152): most economists as well as social scientists agree to: the differences in quality of institutions and policies of state are the root cause of large disparity in economic growth across nations. There is little consensus, however, concerning what determines quality of institutions towards economic growth, making it hard to isolate exogenous determinant of variation in quality of institutions. Question twenty four In table 1, higher standard error just means the sample is not more representative of the whole population (quality of institution) but the estimate is closer to the true value of β1. As such, high standard error simply means the data was greatly spread in model 1 & 3 in Table 1. It might also means that Table 2 changed the unit of measurement adopted for quality of institution (proxy variable). Therefore, it registered a lower value of standard error. Moreover, Model 1 and 3 in table 1also has higher R2 than there counterpart in model 2. Hence and despite the larger values, there is high possibility that the independent variable (income per capita) was explained better in model 1 and 2 in table 1 than it was in table 2. Question twenty five Since there is correlation between some variables which might describe the same change in dependent variable (income per capita), β2 in table 3 was estimated in a way (instrumental variable approach) that eliminated simultaneous causality bias (settler mortality variable causes change in income per capita and vice versa) and errors of variables bias. As such, β2 had a strong sign which is statistically insignificant with regard to p-values greater than 0.15. Question twenty six Disagreeing with Acemoglu, Johnson and Robinson (2001) `s assertion that settler mortality was a valid instrument is difficult to refute from a statistical perspective since the covariance between settler mortality and quality institution could not be zero. There is correlation between this two independent variables. This has conforms to one of the two conditions for a valid instrument. However, the covariance between settler mortality and the error term could have been zero. Question twenty seven If “disease environment” variable was positively correlated with “quality of institution” variables but negatively influence growth, the estimate for Acemoglu, Johnson and Robinson (2001) would be bias since the variance would not be zero. Nonetheless, this cannot be a valid concern since each institutional quality cannot explain the true impact on the growth (dependent variable) as might be the case if that institutional quality were to be the single variable in the model. Question twenty eight Looking at every model in table 1, 2 and 3, the estimate of institutional quality are all positive. This implies that the disparity in quality of institutions of state is the leading cause of large variation in economic growth across different nations. Institutional quality positively influence income per capita of a country. Analysis of the determinants influencing economic growth has revealed that country-specific features have important impact on economic performance. According to (Geweke, 114), upholding the rule of law and better institutional quality promotes growth. We see that such deductions are so sensitive to the sample estimation and selection technique. When similar sample of nations is used, nations with quality institutions merits from superior economic performance. Estimates adopting instrumental variable methods submit that democratic institutions witness better economic growth performance. 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 Geweke, John. Complete and Incomplete Econometric Models. Princeton: Princeton University Press, 2010. Internet resource. Read More