Probresults if h true 0001 we use the standard error

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Prob[Results IF H 0 True] = <.0001. We use the standard error provided by the ordinary least squares (OLS) regression results to compute the Prob[Results IF H 0 True]. We can also calculate the Prob[Results IF H 0 True] by using the tails probability reported in the regression printout. Since this is a one-tailed test, we divide the tails probability by 2: 0 .0001 Prob[Results IF H True] = .0001 2 < ≈ < Based on the 1 percent significance level, we would reject that null hypothesis. We would reject the hypothesis that disposable income has no effect on the consumption of consumer durables use. There may a problem with this, however. The equation used by the ordinary least squares (OLS) estimation procedure to estimate the variance of the coefficient estimate’s probability distribution assumes that the error term/error term independence premise is satisfied. Our simulation revealed that when autocorrelation is present and the error term/error term independence premise is violated, the ordinary least squares (OLS) estimation procedure estimating the variance of the coefficient estimate’s probability distribution can be flawed. Recall that the standard error equals the square root of the estimated variance. Consequently, if autocorrelation is present, we may have entered the wrong value for the standard error into the Econometrics Lab when we calculated Prob[Results IF H 0 True]. When autocorrelation is present the ordinary least squares (OLS) estimation procedure bases it computations on a faulty premise, resulting in flawed standard errors, t -Statistics, and tails probabilities. Consequently, we should move on to the next step.
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21 Step 2: Consider the Possibility of Autocorrelation Unfortunately, there is reason to suspect that autocorrelation may be present. We would expect the consumption of durables are not only influenced by disposable income, but also by the business cycle: When the economy is strong, consumer confidence tends to be high; consumers spend more freely and purchase more than “usual.” When the economy is strong the error term tends to be positive. When the economy is weak, consumer confidence tends to be low; consumers spend less freely and purchase less than “usual.” When the economy is weak the error term tends to be negative. We know that business cycles tend to last for many months, if not years. When the economy is strong, it remains strong for many consecutive months; hence, when the economy is strong we would expect consumers to spend more freely and for the error term to be positive for many consecutive months. On the other hand, when the economy is weak, we would expect consumers to spend less freely and the error term to be negative for many consecutive months. Economy strong Economy weak Consumer confidence In the last month, consumer was high last month; e t 1 > 0 confidence was low; e t 1 < 0 consumers spent more freely, consumers spent less freely, consume more, last month. consume less, last month.
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