The data for this assignment can be found in the csv file named ‘PS4_Savings_And
ID: 3272482 • Letter: T
Question
The data for this assignment can be found in the csv file named ‘PS4_Savings_And_Income.csv’. It contains data on annual household income (Yt) and annual household savings (St) for households in the United States. Both of these variables are in billions of dollars.
DATA PROVIDED:
14008.69036
The data for this assignment can be found in the csv file named ‘PS4_Savings_And_Income.csv’. It contains data on annual household income (Yt) and annual household savings (St) for households in the United States. Both of these variables are in billions of dollars.
Part 1:
You decide to model household savings as a function of household annual income. For now, you decide to assume CR3 holds.
1. Write the linear regression model used to estimate this relationship, using your time series data.
Sample Model: St = b0 + b1Yt + ei
2. Estimate the model and report the regression results.
Part 2
You think back to class, and remember that autocorrelation is often a problem in time series data.
3. In your own words, describe what autocorrelation is, and how it can affect our estimates.
4. First, try using the Breusch-Godfrey/LM test manually. Predict (and save) the residuals from the estimated model in part 1, and create a lagged residual. Estimate the following model and report the results.
errort = errort-1 + 0 + 1Incomet + ut
Answer:
Source | SS df MS Number of obs = 39
-------------+---------------------------------- F(2, 36) = 40.15
Model | 703719.312 2 351859.656 Prob > F = 0.0000
Residual | 315453.027 36 8762.58408 R-squared = 0.6905
-------------+---------------------------------- Adj R-squared = 0.6733
Total | 1019172.34 38 26820.3247 Root MSE = 93.609
------------------------------------------------------------------------------
e | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
elag | 1.046828 .1168573 8.96 0.000 .8098306 1.283826
income | -.0091536 .0037628 -2.43 0.020 -.0167849 -.0015223
_cons | 46.20118 28.21931 1.64 0.110 -11.03023 103.4326
------------------------------------------------------------------------------
5. Using the results from question 5, construct the Breusch-Godfrey/LM test statistic.
(t-m)*R^2 = 39 * .6905 =
6. Now use the stata command bgodfrey to test for autocorrelation. Report the results from the test and state the conclusion.
. estat bgodfrey, lags(1)
Breusch-Godfrey LM test for autocorrelation
---------------------------------------------------------------------------
lags(p) | chi2 df Prob > chi2
-------------+-------------------------------------------------------------
1 | 7.284 1 0.0070
---------------------------------------------------------------------------
H0: no serial correlation
7.Try using correcting for autocorrelation by correcting the standard erros using the Newwy-West procedure. Try assuming lag = 1, lag = 2, lag = 4. Report your results and explain whether or not this is a sufficient solution to your problem. (do stanard errors stabilize?)
8. Try estimating an autoregressive distributed lag model:
Report your results and explain whether or not this is a sufficient solution to your problem. You will need to create new variables to estimate this model. (repeat the test for autocorrelation no the new test)
Help with problems 5-8. The rest of the problems have been answered. Additionally, these problems deal with econometrics and the program stata.
Obs Year Savings Income 1 1970 184.55 1024.139845 2 1971 205.76 1109.816613 3 1972 236.24 1224.675998 4 1973 288.29 1374.118208 5 1974 293.58 1491.768293 6 1975 290.92 1619.821826 7 1976 332.49 1802.113821 8 1977 386.31 2013.079729 9 1978 465.41 2271.400683 10 1979 520.17 2528.779776 11 1980 528.3 2755.868545 12 1981 632.3 3099.509804 13 1982 598.25 3260.217984 14 1983 574 3493.609251 15 1984 714.67 3905.300546 16 1985 695.26 4168.22542 17 1986 664.572 4375.062541 18 1987 728.635 4682.744216 19 1988 845.027 5093.592526 20 1989 872.12 5410.173697 21 1990 862.44 5703.968254 22 1991 899.201 5892.536042 23 1992 882.0661 6211.733099 24 1993 914.2892 6507.396441 25 1994 1053.535 6944.858273 26 1995 1180.627 7337.6445 27 1996 1306.783 7787.741359 28 1997 1495.239 8316.123471 29 1998 1624.513 8843.293413 30 1999 1676.473 9397.270179 31 2000 1767.655 10072.10826 32 2001 1663.113 10387.96377 33 2002 1523.952 10664.46466 34 2003 1511.005 11143.10472 35 2004 1675.438 11907.87491 36 2005 1850.428 12752.77739 37 2006 2115.119 13628.34407 38 2007 1882.452 14100.76404 39 2008 1636.974 14334.2732 40 2009 1379.85614008.69036
Explanation / Answer
We are allowed to do 1 question at a time. Post again for second question.
3)
Autocorrelation is a characteristic of data in which the correlation between the values of the same variables is based on related objects. It violates the assumption of instance independence, which underlies most of the conventional models. It generally exists in those types of data-sets in which the data, instead of being randomly selected, is from the same source.
It seems that OLS residuals autocorrelation is not always an issue, depending on the problem at hand. ... While it does not bias the OLS coefficient estimates, the standard errors tend to be underestimated (and the t-scores overestimated) when the autocorrelations of the errors at low lags are positive.
OLS is not the best estimation method. It will underestimate the true variance. the t values will look too good will reject H0 when it is true So estimates will be unbiased but inefficient (not least variance) Focus on simplest form of relation over time: Obviously there could be more complicated forms. T
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