# STATA Homework Help

Time series data was provided and certain statistical modelling techniques were applied to it in Stata. The report contains a good use case of how to use statistical techniques like regression, ARCH, GARCH and ARIMA. Students seeking Stata homework help can refer to this sample report as reference, which demonstrates the skill set of our tutors for Stata assignment help. Results like heteroskedasticity were interpreted and appropriate conclusions were drawn accordingly.

**Answer 1:**

**a. **We will want to use an instrumental variable if there is reason to believe that there is measurement error in an independent variable X or if there is reverse causation between X and Y, i.e., X and Y are jointly determined. Measurement error in X will generally bias the estimated relationship between X and the dependent variable Y toward 0 and the STATA homework help estimated coefficient on X will be biased if X is endogenous.To be a valid instrument for STATA assignment help X, Z must be correlated with X but uncorrelated with the regression error. We need Z to be correlated with X because in effect we are going to use Z and any other independent variables inSTATA project help the regression model to predict values for X which we will then use in the regression model. We need Z to be uncorrelated with the error because if Z is correlated with the error, then so will be our STATA homework help predicted value of X, which will lead to biased estimation.

We can check to see if Z is correlated with observed X because observed X is available to us. We cannot check to see if Z is correlated with the error in STATA assignment help the regression model because the errors in the regression model are not available and cannot be obtained given that there is measurement error in X. The best we can do is STATA homework solution choose a Z that logically seems to be independent of the error, perhaps because it comes from an earlier time period or because for some other reason it is correlated with X but not Y.

I used the pairwise correlation command in Stata, with the command and output as follows:

Clearly, X and Z are very strongly correlated, with a correlation coefficient of 0.9726, which is statistically significantly different than 0 at less than the 0.0001 level of significance.

Stata command and results for the regression of Y on X:

Stata command and output for the IV regression of Y on STATA homework help X using Z as an instrument for X, showing results of first stage regression of X on Z as well:

From the IV regression of X on Z in the first stage, we have an R^{2} of 0.946, which is the square of STATA assignment help the correlation coefficient between X and Z that we found earlier as 0.9726. In the second stage, where Y is regressed on X predicted from Z, the estimated coefficient on X only changes from 1.862 in the regression that uses X to 1.833 in the regression that uses Z to predict X, which suggests that neither endogeneity bias or measurement error are problems here. Observe that the intercept changes from 3.779 to 3.833, again a very small change, which is due to our being able to predict X very well with Z, so that the mean of predicted X is similar to the mean of X (i.e., in general the intercept is equal to ). Finally, note that both the intercept and have numerically smaller p values when Z is used to STATA homework help predict X than when X is used directly.

**Answer 2:**

Ignoring iteration history, the Stata commands and output for the ARMA(1,1) model are as follows:

In general, an autoregressive moving average process for Y with 1 period autoregression and 1 period moving average can be written as

The dependent variable is the change in annual real GDP. The Wald chi square for the model has a significance level of less than 0.0001, which suggests that the model predicts the change in real GDP from year to year significantly better than the average change in real GDP.

The estimated constant 56.832, which is STATA expertssignificantly different than 0 at the 0.052 level of significance implies if there were no change in GDP in the previous year and the previous year’s prediction error were 0, then GDP would increase by an average of 56.832. The estimated value for γ, the coefficient on the previous period’s change in real GDP, is 0.798, which isSTATA assignment help significantly different than 0 at less than the 0.001 level of significance, and indicates that the annual change in real GDP is on average equal to 0.798 times the previous year’s change in real GDP in STATA project help addition to the average change of 56.832. The positive sign indicates that increase in GDP tend to be followed by increases of a smaller amount, which is STATA homework help consistent with business cycles in which GDP increases for several years until hitting a peak and then decreases. The estimated value for θ, the moving average term, is negative, suggesting that if GDP were underestimated in the previous period (i.e., a positive value for ε_{t-1}) then the change help with STATA assignment in real GDP for this period is decreased, on average. Both the moving average term and the autoregressive term are statistically significant at less than the 0.001 level of significance.

Ignoring iteration history, the Stata command and output for the ARMA(2,2) model are as follows:

In general, an autoregressive moving average process for Y with 2 period autoregression and 2 period moving average can be written as

Here, neither of the terms thatSTATA problems with answers involve two period lags are statistically significantly different than 0, with a p value of 0.137 for STATA homework for money the autoregressive term γ_{2} and a p value of 0.2 for the moving average term θ_{2}. Once again, both of the first order terms are statistically significantly different than 0 at less than the 0.001 level of significance. The estimate on the one period autoregressive term, 1.203, implies that changes in pay for STATA homework annual GDP are amplified from one year to the next and the estimated coefficient for the one period moving average error term, -0.747, again suggests that an underestimate in the previous period will lead to a lower forecast help with STATA homework for the change in rel GDP for the current period.

Ignoring iteration history, the command for the GARCH(1,1) model and its output follow:

In the generalized autoregressive conditional heteroskedasticity model with 1 period autoregression and 1 period moving average, the variance in period t conditional on information available in period t is an ARMA(1,1) process in the variance and the innovation, so that the variance for period t conditional on information in period t is written as

The regression for the mean has anAR(1) term similar to the first model in part a that is statistically significant (p value less than 0.001) and similar coefficient on pay for STATA assignment the lagged value for the difference in real GDP, 0.789 here versus 0.798 in part (a), which again suggests that help with STATA homework changes in GDP from one period to the next are damped versions of the previous change. Interestingly, the constant in the STATA questions with answers regression for the mean is only a small fraction of the constant expressed in part a, as the Garch model apparently attributes much of the value of the constant in part a to increasing variance in the change in real GDP, which we turn to next.

The model for the variance has terms that are statistically significant for both the previous period’s variance and the previous periods innovation, ε_{t-1}. The estimate on the autoregressive variance, γ, is slightly larger than 1, 1.084, which is consistent with increasing conditional variance in the change in real GDP over time. The estimated coefficient for STATA assignment for money the moving average error term, θ, is 0.433, which suggest that the conditional variance in a given period will be larger (smaller) if the previous period’s forecast for the change in real GDP was underestimated (overestimated).

For the span of time considered, roughly the Revolutionary era to the present, it makes sense to think that the variance of the change in STATA assignment solution real online STATA tutorsGDP has grown because both real GDP and the change in real GDP have grown over time. For example, any simple percentage of real GDP change is a much different number in STATA homework help 1793 than in 2013, so that if we imagine the variance as some percentage of real GDP over time, the same percentage would yield an increasing variance over time.