The Dynamic Impact of Random Fluctuations - Article Example

Student Name: Course Title: Instructor Name: Date: Part A 1). Base group is a group that is used in testing, for example, when testing the ability of patients to quit smoking ,a base group will be one group that is under treatment and another one not under treatment. The one under treatment is the base group. 2.) AR (1) Model is Autoregressive model that is used for forecasting interrelated time series data and for analyzing the dynamic impact of random fluctuations on given factors. AR (1) is a linear autoregression time series model which can be expressed as In order to change AR (1) Monte Carlo analysis is done with exogenous repressor as shown in the equation below ARDL - A combination of simultaneous equation models and univariate time series models form the vector autoregressive model are treated as a function of lagged values of all the endogenous variables in the system. That is to say, current values depend on previous values of all variables and error terms. Variables in a VAR model are taken as endogenous and no restrictions are imposed. Least square method is used for each equation with assumption of all of the components being stationary. Assume that is exogenous, therefore the Monte Carlo analysis is 3). a transformed model in the context of heteroskedasticity is Autoregressive Conditional Heteroscedastic Model. This is used to model and forecast conditional variances in the factors being tested. The model specifications, the variance of the dependant variable depends upon the past values of internal variables and external variables. For basic Autoregressive Conditional Heteroscedastic Model model, conditional variance of a shock at time t is a function of the squares of past shocks:. (Where, h is the variance and  is a “shock,” “news,” or “error”). Since the conditional variance needs to be nonnegative, the conditions have to be met. If 1 = 0, then the conditional variance is constant and is conditionally homoscedastic. 4). The main difference between OLS and GLS estimation techniques when estimating β. OLS estimates unknown parameters in a regression model after one has y observation such as . It provides maximum probable value for coeficient on assumption that the parameters have equal variance and error uncorrelated. GLS provides the same error is correlated. 5). instrumental variable is needed when X is endogenous. The properties of the variables are - Omitted variable bias from a variable that is correlated with error term but is unobserved,; - has causality bias -Errors-in-variables bias 6). The reduced form equation in instrumental variable estimation Yit = β1 +  + δ t + Uit Where Uit = αi + εit Hausman test is used to specification for distinction among coefficients. This test is sufficient to check for instrument validity. If it showcases that random effects are present, it would definitely be more advisable to use random effects regression. 7). fixed effects panel data model Firstly, the average values of the variables with respect to every individual observation of the sample is calculated and then deducted from the overall data for that particular person. Therefore, the form of the model becomes as follows. Yit - Y = ) + δ (t – t) + εit - ε This form of the model does not have the unobserved effect. That is, it diminishes. This is essentially the within group regression model. However, any predictor variable X that has remained the same for each person in the sample will drop out of the model. Another problem is the loss of several degrees of freedom when the form of the model is manipulated to remove the unobserved effect. The next version known as the first differences regression model, the unobserved effect is completely diminished by deducting prior observation from the present ones, with respect to all the periods of time. For individual i, the model may be written as follows. Again, the problem of loss of degrees of freedom and drop out of variables that remain constant over time persist with this approach. 8). the concept of 2SLS (two-stage least squares) estimation in a systems framework- This uses instrumental variables which are uncorrelated with the error. It uses computed values at the first stage to compute a linear regression model the second stage giving the optimal value. 9). In the random effects model, it is assumed the probability of treating each Zp variables that were not observed to be a random drawing with respect to a particular distribution. If so, then each of the αi variables may be treated as random variables and can be rewritten as follows. Yit = β1 +  + δ t + Uit Where Uit = αi + εit In this way, the unobserved effect is dealt with respect to its inclusion in the disturbance term. Because of the obvious auto-correlated nature of term of disturbance, the customary OLS method is not utilized, since it reports the accurate computation of the parameter estimates’ standard error; they are unbiased but effective 10). Chow test is an econometric test that finds out whether the coefficients in different linear regressions from different data sets are equal. 11). We normally required to use methods of moments estimation when the distribution converges to a probability distribution thus the need to estimate. For example, if a sample is taken and it is seen to exhibit characteristics of probability distribution, this method will be used. 12). Probit model is use when there are only two values that are expected. For example when there is a likelihood of obtaining male or female. Logit model is when there are many likelihoods and the logit functioning is negative. Logit functioning is a logistic distribution while probit is a normal distribution. Part B Question1. Dependent variable Constant POP INV IGDP SEC R2 G60 0.0231 -0.2435 0.1280 -0.0001 0.0410 0.289 (S (0.0195) (0.2384) (0.0333) (0.0001) (0.0172) G70 0.0185 -0.4336 0.1870 -0.0001 0.0127 0.302 (S (0.0313) (0.4029) (0.0397) (0.0001) (0.0184) G80 0.0423 -0.8156 0.1155 -0.0001 0.0028 0.387 (S (0.0265) (0.2997) (0.0297) (0.0141) (0.0141) Part i. Comment on the signs of coefficients. Can you explain these signs in terms of the expected impact of the explanatory variables on growth rate? From the model negative coefficients means that the growth rate for years under consideration will reduce while the positive coefficients will mean increase in growth rate. This means that POP and IGDP have negative impact on the growth rate. However, their P-values are significantly higher than the threshold value of 0.05. This indicates that these factors significantly influence growth rate. Part ii. Does human capital appear to influence growth rate?(use 5% critical value of 1.96 to answer this question) Human capital has coefficients that are positive and there their P-values are significantly lower than the threshold value of 0.05. This indicates that it significantly influence growth rate. Part iii The estimated correlations between the errors for the three equations are Carry out a hypothesis test to see if SUR estimation is preferred over separate least squares estimation (use the sample size 86 and 5% percent critical value of 7.81 to make a decision). The null hypothesis F = = 20.76 The F-value for the test is 20.76 and critical F 5%, 1% and 10% level of significance is 2.70, 5.36 and 2.14 with df 86-3 = 83 which indicates a highly significant population correlation coefficient. Hence we can conclude that the SUR estimation is preferred. Question 2.( This question has three parts, I, ii, ii) Consider a simple model to estimate the effect of personal computer (PC) ownership on college grade point average for graduating seniors at a large public university: Where, PC is a binary variable indicating PC ownership. Part i Why might PC ownership be correlated with u? This is a case of ordinal least square regression model thus slope is correlated to error term. Where the ei are uncorrelated error variables with mean 0 and common variance 2. Part ii Explain why PC is likely to be related to parents’ annual income. Does this mean parental income is a good IV for PC? Why or why not? The PC is related to parental income because the parents are the main financials of the purchase of PC. Parental income is a good IV for PC since it has an effect on pc although it is not being evaluated Part iii Suppose that, four years ago, the university gave grants to buy computers to roughly one-half of the incoming students, and the students who received grants to buy computers to roughly one half of the incoming students, and the students who received grants were randomly chosen. Carefully explain how you would use this information to construct an instrumental variable for PC. To solve this we need a program that will solve this by generating variables for the interaction terms. Question 3. Consider the following labour supply equation specification for married women HOURS= Where, HOURS is the supply of labour, WAGE is hourly wage, EDUC is years of education, KIDSL6 is the number between 6 and 18 years old, and NWIFEINC is household income from sources other than the wife’s employment. Part i. Explain why this supply equation cannot be consistently estimated by least squares regression. This cannot be constantly be used to estimate estimated by least squares regression since the error term is not constant and there are many variables. Part ii. Suppose we consider the woman’s labour market experience EXPER and its square, EXPER2, to be instruments for WAGE. Explain how these variables satisfy the logic of instrumental variables. These variables satisfy the logic of instrumental variables as it provides the square of the variable which will have an inverse function. Part iii It is not identified since its log will be required. However it will be rearranged to have an equation as 2 HOURS=2 Question 4 + Where, denotes per capital public expenditure on health and X1 denotes per capita gross domestic product for 80 countries in the year 2008. Part i There may be evidence of heteroskedasticity from the above model since there is no constant variance of the error term. Part ii Heteroskedastic partition” concept can not be used to estimate the variance function since there is only one variable. It can only be used where there is more than one variable Part iii Say the variance of the error term from the above model takes the following structure: Transform the original model using the above information regarding the variance of the error term in your transformed model is a constant. + Always homoscedasticity assumes the error term has constant variance, σ2. Question 5 Part i Looking at the equation above and estimates nonblack males scored of 45 points more than nonblack females. The statistical differences of coefficient support this assertion. This simplified by use of one nonblack female and one nonblack male. Their differences is 45.0 when other factors are constant. Part ii Test the null hypothesis that there is no difference between their scores, against the alternative that there is a difference. The following is used to test H0: black = 0 H1: black ≠0 The test statistic = -169.81/12.71=13.36. This figure is statistically significant at any 5% significance level. Therefore, the result highly statistically significant Part iii Controlling for other conditions, black females score about 107.5 points lower than Non-black females. Accordingly black females score about 107.5 points more than non-black females. To test whether the difference is statistically significant, a t-test will be necessary through a statistical program Read More