Econometrics Essentials - Assignment Example

Econometric Course Professor’s Name Name of the Institution Date Question one (a) The equation is given by: Ln (𝑝𝑟𝑖𝑐𝑒) = 𝛽1 + 𝛽2𝑐𝑟𝑖𝑚𝑒 + 𝛽3𝑑𝑖𝑠𝑡 + 𝛽4ln (𝑛𝑜𝑥) + 𝛽5𝑙𝑜𝑤𝑠𝑡𝑎𝑡 + 𝛽6ln (𝑝𝑟𝑜𝑝𝑡𝑎𝑥) + 𝛽7𝑟𝑎𝑑𝑖𝑎𝑙 + 𝛽8𝑠𝑡𝑟𝑎𝑡𝑖𝑜 + 𝛽9𝑟𝑜𝑜𝑚𝑠 + 𝑒 The regression results are shown in the table below From the results, the estimated equation will be given by; LPRICE = -0.00899022863382*LOWSTAT + 0.176450565448*LNOX 0.00119235090003*DIST - 0.00667964959875*CRIME + 0.231670438192*LPROPTAX - 0.037923718021*NOX + 3.62441426754e-05*PRICE - 0.00822618311505*PROPTAX + 0.00479484711547*RADIAL - 0.0462807286603*ROOMS - 0.00114227351782*STRATIO + 8.4075273902. From the results, it is clear that distance, lnox, nox and stratio are not statistically significance while the rest of the variables are statistically with p-value < 0.05. (b) Using significance level of 0.15 on rooms, the regression equation is given below From the results, p-value is 0.00 0 hence reject null hypothesis and accept alternative hypothesis that there is autocorrelation. R2 indicates that 11.12% of the total variables were included in the analysis. Steps in doing this is shown below:- Step 1: Estimate the model and obtain the residuals Step 2: Run the full LM model with the number of lags used being determined by the assumed order of autocorrelation. Step 3: Compute the LM statistic = (n-ρ) R2 from the LM model and compare it with the chi-square critical value. Step 4: Conclude d. The model with AR (1) errors was estimated as ̂
𝐷𝐻𝑂𝑀𝐸𝑆𝑡 = −2.124 − 58.61𝐷𝐼𝑅𝐴𝑇𝐸𝑡−1 𝑒𝑡 = −0.3314𝑒𝑡−1 + 𝑣𝑡 T = 216 T value = 1.98 (at 95% confidence interval) Sample size 216 (2.497) (14.10) (0.0649) Standard deviation 0.0649 1.98* 0.0649 =0.128502 Square root 216 = 14.6969 Therefore = 0.128502/14.6969 = 0.0087434 Using aggregate of 2.497+0.0087434 or 2.497- 0.0087434 The results gives = 2.5057 or 2.488 Ignoring autocorrelation on inferences result into increase in the correlation coefficient Question three (a) It is important to understand the cause of endogeneity in the data more so when it comes to the median value like in the case of house prices. In most cases, it results from measurement errors, autoregression with auto-correlated errors. It points out the non-controlled confounder and the loop of causality between independent and dependent variables of the model. This should be of major interest to any analyst doing regression analysis (Baltagi, 2008). (b) Weak instruments From REG2 coefficient is -5.095 indicating a strong instrument and not a weak one, REG3 gives -1.778 indicating declining strength of the instrument while REG4 post the strongest instrument among the three with coefficient of 13.41. Column three, this is not the case as it post weak instruments (Baltagi, 2008). The null hypothesis states that:- The instrument is not weak The instrument is weak Steps in estimating weak instrument include:- Estimate the regression and obtain residuals Estimate ρ from regressing the residuals to its lagged terms. Transform the original variables as starred variables using the obtained from step 2. Run the regression again with the transformed variables and obtain residuals. Continue repeating steps 2 to 4 for several rounds until (stopping rule) the estimates of from two successive iterations differ by no more than some preselected small value, such as 0.001 (Baltagi, 2008). These steps will help in identifying weak and strong instruments in the analysis. The coefficient is very important in establishing the level or strength of the instrument. (c) The result indicates the cause of error in the endogeinity in the regression process. Instrument variables estimations in most cases are used when the model has endogenous variables (Baltagi, 2008). If a variable is endogenous, it is correlated with contemporaneous errors. This is evident in column 4 with the VHAT giving -1.589. This results shows that the first case, there was endogeinity and no autocorrelation between the variables and it supports the answer in the first question that the null hypothesis should be rejected (Baltagi, 2008). (d) The IV/2SLS estimates using the instruments listed in part (b) shows high level of the In using 2 stage least squares (2SLS) In this case, y2 is the endogenous, variable z is the exogyneous In circumstances where we have 2 + IVs, which are; Correlated with y2 and Uncorrelated with u In this case we only need one IV but one which is more efficient to use The different with question one is that The estimates are in reduced form unlike in question b and 2SLS estimators is IV estomators of y1 and y 2 only. The t-statistics are significance at 5% signicance level unlike in the first case (Baltagi, 2008). (e) The variables in column 6 of EHAT shows constant c which is -62.85 with coefficient of 26.95. Others are the coefficient and the t-test that helps in explaining autocorrelation. The results also shows errors in autocorrelation. Question four (a) The book discusses the degree of measurement error in estimates required schooling for jobs and the bias which are created by errors when estimating the returns to over education (Robst, 1994). The study used panel data of income dynamics and it finds substantial differences between estimates of required schooling. This shows that errors in measurement may seriously bias previously results examining the wage effects of over education (Robst, 1994). (b) An estimator is consistent if as the sample size increases, the estimates, converge to the true value of the parameters being estimated. When it states that estimators are consistent if the sample size increases and the distribution of the estimators become increasingly concentrated at the true parameters values. If it is unbiased if an average, it hits the true parameter value. It shows that sampling distribution of the estimator is equal to the true parameters as per the author of this book (Robst, 1994). (c) On whether I think the DOT estimates provide good instrument for the PSID measures, Yes, they do provide good estimates instruments. Furthermore, on whether you think that the PSID measures provide good instruments for the DOT measures, yes, it provides good instrument from the PSID and DOT from the book (Robst, 1994). (d) Instrument exogeneity and instrument relevance are two crucial requirements in empirical analysis using GMM. It now appears that in many applications of GMM and IV regressions, instruments are only weakly correlated with included endogenous variable. The 2SLS estimator with weak instruments is biased in small samples (Robst, 1994). Reference Baltagi, B. (2008). Econometric analysis of panel data. John Wiley & Sons. Robst, J. (1994). Measurement error and the returns to excess schooling. Applied Economics Letters, 1(9), 142-144. Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. MIT press. Read More