Applied Econometrics Issues - Assignment Example

APPLIED ECONOMETRICS Q1. Interpretation of estimated coefficients in model 3 from table Table shows the least ordinary squares (OLS) of regressions of log per capita income on protection against expropriation variable in a variety of samples. The values in the brackets are the standard errors, occurred during the research. On average, if a country has a protection against expropriation of 10 percent, then per capita income increases by 4.3%, ceteris paribus (100 ×0.43 × 0.1 = 4.3%). For 0.37, the concept is the same. However, negative values of the estimates (-0.62, -1.00 and -0.25) show a reduction and not an increment in per capita income. The protection against expropriation was measured on a scale from 0-10, where a higher score means more protection against expropriation. Q.2.Suppose the impact of institutions on growth differed between African countries and the rest of the world. First, comment on why the model in equation (1) cannot capture this effect. Second, write out a model which can allow for this differential African effect. Third, develop a test that would allow you to statistically discern if this effect is actually supported by the data. Model 1 cannot capture the effect because the effect of latitude, which greatly has an effect on African countries has not been considered. The model that can incorporate the above phenomenon is Where the parameters in the equation are estimates from the samples taken in Africa, then compared to the rest of the world. The test in this case is the regression diagnostic. The variables in the model, are interpreted as follows: Yi is the impact of institution growth in a country i, Ri the protection against expropriation, Lati is the latitude country I (measured as the distance from the equator, and scaled to lie between 0 and 1), D Africa is a dummy for country i is in Africa and D Other i is a dummy capturing if country I is in any other and continent β as the observations made. The regression diagnostic test, uses the estimates, errors in estimation, and the test statistic, plus the test instrument, in order to come up with the conclusion. Q3. Estimated difference in growth between African and Asian countries ceteris paribus from table 1. From table 1, the dummy for Asia is –0.62 and the dummy for Africa is -1.00. This indicates that African countries have little protection against expropriation. The values are natural logarithms of the stated values over a given base sample. Inverses of the natural logs give 0.5379 for Asia and 0.3679 for Africa. The difference is thus 0.1700. This is also equal to 32.1% growth difference. Q4. Instead of measuring latitude as absolute difference from the equator we measure it as a raw number. Explain how the estimates, standard errors and R2 would change in model (2) in Table 1. By measuring latitude as a raw number, the effect of climate on performance would not be as precise as it is when measured from the equator, which is the central latitude and the correlation between distance from the equator and economic performance would be known, but with extremes. This changes the coefficient of the index of institutions growth. The estimates would increase, errors would increase as well and the regression, now based on raw numbers for latitudes would significantly reduce. Q.5. Suppose heteroskedasticity was a concern in Acemoglu et al.s (2001) framework. Detail how you could test for the presence of heteroskedasticity using model (1) in Table 1. The ordinary least squares are used in testing the heteroskedasticity. The first step is to make OLS estimates, and the residuals saved in exponents squared. Then the squared exponents are regressed on all the variables and their squares. Then obtain R2. If nR2 is too large, the null hypothesis Ho is rejected. The auxiliary model can be seen as trying to `model the variance of the error term. If the R2 of this auxiliary regression were high, then we could explain the behavior of the squared residuals, providing evidence that they are not constant. This is also the general test for heteroskedasticity in the error distribution by regressing the squared residuals on all distinct regressors, cross-products, and squares of regressors. The test statistic, a Lagrange multiplier measure, is distributed Chi-squared (p) under the null hypothesis of homoscedasticity. The test is implemented and executed by a computer program (white test) Q.6. Detail how you would test (including the appropriate regression you would estimate) the hypothesis that the effect of geographic location (Latitude) has the same impact on growth as institutions (R) for model (3) in Table 1. First, a hypothesis is stated. The hypotheses for both latitude effect and institutional growth. The estimates are then analyzed from at various levels of significance. The p value are to be considered. The test is a regression, using least squares. Considering the white test, the estimates are the key variables in this case. Q.7.Does model (3) nest model (2) in Table 1? Explain carefully. Model 3 does not nest model 2 because the values in model two are not part of the values in model 3. A nest could occur if the values in the two models were similar, or nearly similar. Though the observations are similar, the variable factors are missing in model 2. Q.8.Clearly the quality of a countrys institutions is a difficult variable to measure and Ri, taken as an exact measure of institutions, is likely measured with error. In this setting, comment on the implication that β1 is likely to have more variation due to the measurement error inherent in measuring institutional quality and what this implies for testing H0 : β1 = 0 against a two-sided alternative. Would this same implication be true if we thought of Ri as a proxy variable instead of being measured with error? From the table β1 is likely to have more error, because the number of observations made great. It is this number that is likely to create the better percentage of the error. There is also bias in information acquisition information about the quality of the institution as well as lack of quality assessment measures in some of the institutions. In testing H0: β1 = 0 against a two sided alternative, the hypothesis has a different implication in the findings and the error magnitude reduces. The situation is similar when a proxy variable is used. Q.9.Recall that for Ri to be a valid proxy variable, it must be the case that E (IQjR; Lat) = E (IQjR) where IQ is unobserved institutional quality. Comment on the precise meaning of this condition and if this condition is likely to hold A valid proxy is a variable that is not in itself directly relevant, but that serves in place of an unobservable or immeasurable variable. The statement means that the institutional quality, a key variable that is used in the models has been unobserved. The condition is unlikely to hold due to the fact that the entire research this paper was based majorly on institutional quality and growth. Q.10.Can the R2s in Table 1 be compared to the corresponding R2s in Table 2? Why or why not? The values can be compared. The square of regressions in table 1 is 0.62, 0.63 and 0.73 respectively while in table 2, the values are 0.54, 0.56 and 0.69 respectively. The values are gradually increasing in a similar margin, indicating the efficiency of the methods used. Q.11.Are the estimates from model (2) in Table 1 closer to the truth than the estimates from model (2) in Table 2? Explain carefully. The estimates from table 1 are closer to the truth than the estimates in table 2, because the error in table 1 for the second value 0.89 (0.49) is less than the value for the second value in table 2 1.60 (0.70) and the first value is similar in both cases. The less the error, the more precise the value. Q.12.Notice that the impact of geographic location, as measured through absolute latitude, has a much larger effect on economic output in models (2) and (3) in Table 2 compared to Table 1. Can you compare the differences in β2 in Table 1 and 2? Why or why not? The difference in geographic location, in the two tables, 1 & 2, is evident, in table 1, the latitude effect is 0.89, whereas in table 2, the latitude effect is at 1.6. The difference is due to the differences in latitudes of the countries sampled in the two tables. Q.13.The effect of geographic location has gone from being statistically significant in model (2) in Tables 1 and 2 to being statistically insignificant in model (3) in both Tables at the 5% level. Comment on why this is not that surprising. The effect of geographic location, is statistically insignificant in model 3 of both table 1 and 2 because the sample countries from Africa and Asia do not have enough geographic variation, and the role such variations could play are thus rendered insignificant. However, in model 1 and 2, the geographical location is significant in the sense that the samples observed in the two models have greater geographical variation Q.14. In Table 2 in Acemoglu et al. (2001) they report estimates from model (1) but use a different measure of output per capita; they use output per worker in 1988 as opposed to output per capita in 1995. Their estimates for β1 are roughly similar, but R2 is about 10% lower. Does this suggest that this measure of country output is inferior to their measure? The lower values of the square of regressions, does not insinuate that country output per worker is not inferior to the output per capita. Differences among countries can be attributed greatly to differences in human capital, physical capital and productivity. Therefore the method is not inferior, but the variables used in the two methods are diverse. Q.15.Detail two reasons why we should not interpret β1 as a causal effect The first reason is that rich economies may be able to afford, or perhaps prefer, better institutions. Arguably more important than this reverse causality problem, there are many omit-ted determinants of income differences that will naturally be correlated with institutions. And the second reason is that the measures of institutions are constructed ex post, and the analysts may have had a natural bias in seeing better institutions in richer places. Q.16.If OLS estimation of β1 is likely to suffer from endogeneity bias, comment on the likely direction of this bias. Endogeneity bias happens as a result of measurement errors that arise from use of alternative variables. In this case, if the bias in the ordinary least squares could be in the direction of variables- the samples been used for the research. Q.17.Acemoglu et al. (2001) suggest using settler mortality as an instrument for institutions to estimate a causal relationship between economic growth and institutions. However, suppose that no endogeneity bias existed, but instead an omitted interaction between institutions and geographic location arose. First, explain how this omitted nonlinearity could lead to biased estimates. Second, construct a model that incorporates this interaction and discuss if this model has a ceteris paribus interpretation for the effect of institutions on growth. Lastly, detail how you could test if the presence of this specific interaction belonged in the model statistically. If no endogeneity bias existed but interaction between institutions and geographic variations arose, then the general findings could have bias. In the model by the author, geographic variation has led to precision in the estimates. The model to be developed will be minus the latitude section, but similar to the one developed by the author. That is The test is the typical white test in which, by regressing the squared residuals on all distinct regressors, cross-products, and squares of regressors. The test statistic, a Lagrange multiplier measure, is distributed Chi-squared (p) under proves the hypothesis formulated. Q.18.Consider the hypothesis that institutions differ from a continental standpoint. Using model (1) from Table 1, detail how you could test this hypothesis at the 10% level. Further, suppose that if you were to conduct this test you obtained a p-value of 0.023. Discuss what this implies about the estimates in model (1) in Table 1 as it pertains to bias and variance. If I fail to reject at the 10% level this means that I must have a test statistic with a p Value that is greater than 0.023. The test statistic assumes that the value of p does not lower than the stated one. Then from statistical tables at 10% level of significance, the test can be proven. Then failure to rejection or the hypothesis is done. Q.19. Suppose you wished to test the continental hypothesis on model (1) from Table 2 instead. Why might this not be such a good idea from a practical standpoint? The data tested for the entire research to be accepted is randomly across the world, with 64 observations made. If continental hypothesis was to be used, the number of observations are to be uniform per continent, and random across each continent, including America which had been excluded earlier on. This will make the research expensive and quite unrealistic. Q.20.Detail the two main conditions that settler mortality must satisfy for it to be considered a valid instrument. Be precise Settler mortality must use the logarithm of the settler mortality rates, since there are no theoretical reasons to prefer the level as a determinant of institutions rather than the log, and using the log ensures that the extreme African mortality rates do not play a disproportionate role. And the samples used must be taken randomly to avoid bias. Q.21.Please interpret both coefficient estimates in model (2) in Table 3. On average, if a country has a protection against expropriation of 10 percent, then per capita income increases by 1 ceteris paribus (100 ×1.00 × 0.1 = 10%). The protection against expropriation was measured on a scale from 0-10, where a higher score means more protection against expropriation. The value in the bracket (0.22) is an error term. For -0.65, the same explanation occurs. However it means that there is a reduction and not an increment because of the negative sign. 1.34 is an error term as well. Q.22. Can we say that the estimates of β1 in Table 3 are closer to the true value of β3 than those in either Table 1 or 2? Why or why not? No. the estimates cannot be said to be said to be closer, due to the fact that in β3, dummies from Africa, and other countries are used. This is not the case in β1 where the sample variables used are not the same. Q.23.Note that in models (1)-(3) in Table 1, the estimates of β1 are larger than their counterparts in Table 2. Comment on the theoretical implications that these larger estimates carry. Theoretical implications of the larger estimates, for β1 are large because of the large observations (110) compared to the less observations of 64 in table 2. Theoretically, the estimates in table 1 are thus more precise, and near the truth than the estimates in table 2. Accuracy in terms of the large samples observed, and the trends in the samples noted and analyzed. Q.24.For models (1)-(3) in Table 1, the standard errors for bβIV are larger than their counterparts in Table 2. Detail why this is not that surprising to you. The standard errors in table 1, are larger than their counterparts in table 2 because the number of observations made in table 1 is larger than the number of observations made in table 2, 110 and 64 respectively. Statistically, larger samples incur larger errors as compared to smaller samples. The case that happened in the two tables. Q.25.The estimates of β2 which appear in Table 3 now have the wrong sign and are statistically insignificant with p-values larger than 0.15. Comment on the implication of this as it pertains to correlation between institutional quality and settler mortality. The wrong sign and statistical insignificance with p values larger than 0.15, implies that the correlation between the variables of institutional quality and settler mortality is not strong. The less correlation factor is due to many factors including bias and errors within the data collection and analysis. Q.26.If you disagreed with Acemoglu et al.s (2001) assertion that early settler mortality was a valid instrument for current institutional quality, explain how you are hamstrung from a statistical standpoint. The estimation and analysis of settler mortality in relation to the institutional quality is biased, and dependent on latitude, it is severe in countries within the tropics that it was in other countries. With the issue of bias, data analysis and design of a suitable model to avert the biasness is required. Q.27.McArthur and Sachs (2001) suggest that the `disease environment and health characteristics of country belong in the Acemoglu et al. (2001) model. If disease environment was positively correlated with institutional quality and had a negative impact on growth, comment on the likely bias of Acemoglu et al.s (2001) estimates? Further, discuss, given the magnitude found, why this may not be a valid concern pertaining to ruling out institutions as a driver of cross-country economic growth. The bias in the estimates would significantly reduce if disease environment had a negative impact on growth. However, the disease environment could not be a valid concern pertaining the development of institutions because diseases are caused by various predisposing factors and only attack a given race. Malaria and yellow fever are the examples cited by the author, and they attacked Europeans reducing their mortality. But the same diseases again attacked locals who moved away from their regions to other places. The same cases were very dependent on many other factors making them not ideal as study instruments. Q.28.Having considered the estimates appearing in Tables 1 through 3, detail to the best of your ability the likely impact that institutional quality has on economic growth. Be careful not to overstep your bounds, but to also say something with economic and statistical substance. It is evident from the tables that institutional quality is directly proportional to economic growth of a country. From the estimates analyzed and the models used, the quality of institutions in rich countries, and those in poor countries, show great variation. In the whole world sample there is a strong correlation between our measure of institutions and income per capita. The impact of the institutions variable on income per capita in the base sample is quite similar to that in the whole world. The regression indicates that over 50 percent of the variation in income per capita is associated with variation in this index of institutions. To get a sense of the magnitude of the effect of institutions on performance, two countries, Nigeria, which has approximately the 25th percentile of the institutional measure in this sample, 5.6, and Chile, which has approximately the 75th percentile of the institutions index, 7.8, were compared. The results proved that the model used was effective. Read More