Manny and list, The most common way of dealing with this issues is through the use of a specific distributed lag structure. Among the most common distributed lag structures are the Almon, Shiller and Koyck distributed lag structures. Choice of a distributed lag structure should be
guided by applicable theory, if any, and the observed pattern of autocorrelations and cross-correlations. Good discussions of distributed lag models can be found in most econometrics texts, including Intrilligator, Section 6.7 and Kmenta, Section 11-4. Most econometric and statistical
packages (such as SAS and Soritec) have specific procedures for estimating distributed lag models. I hope this helps.
Regards,
Dick March
Rafael Emmanuel Macatangay wrote:
> Hello listmembers,
>
> I am searching for a way to summarise the results of a regression of Y on explanatory variables W and Z as well as on N lags of an explanatory variable X,
>
> Y = f[X(t-1), ... , X(t-N), W(t), Z(t)]
>
> in which X positively affects y.
>
> I am thinking of two ways:
>
> 1. Get the mean of the t-statistics of the N lags of X, and test this mean under Ho: mean = 1.64 (an example of a tabulated value associated with a particular significance level). Given that the expected relationship between Y and X is positive, negative values are a form of penalty.
>
> 2. Construct a test statistic (I am told this is called a Z statistic, but I'm not sure) as follows:
>
> a. get the sum of the t-stats of the N lags of X
> b. divide the sum by sqrt(N)
> c. the resulting test statistic is normal [0,sqrt(N)]
> d. conduct a test under Ho: test statistic = 0 (pressumably this is a two-sided test, but I am thinking of a one-sided test because of the positive relationship between Y and X)
>
> Once again, negative values are a form of penalty. Is this a good test even if N=7 only?
>
> Suggestions and comments are most welcome.
>
> Thank you.
>
> Manny
>
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