Question

If a researcher is considering whether to use distributed lags or proceed with a dynamic model, discuss the considerations to use one or the other.

Answer 1

As it’s said before, the most aim of this research is to show that if the advertising
costs have long benefits, it must be shown as an intangible asset in financial
statements and in their useful lives, they must amortize. But if they have not
benefited for more than one period, they must be show as expenses in financial
statements. Also the selection of each one of this policy can have meaningful
effects on reporting of profits. To exist of these hesitation caused many scientist
have done research in this field that will be explained in chapter three. In this
chapter it will be tried to explain about research design as a through.
DEFINING THE RESEARCH PROBLEM:
As we know, the research problem undertaken for study must be carefully
selected Help may be taken from a research guide in this connection. A problem
must spring from the researcher’s mind like a plant springing from its own seed.

AUTOREGRESSIVE AND DISTRIBUTED LAG MODELS
In regression analysis involving time series data, if the regression model
includes not only the current but also the lagged (past) values of the explanatory
variables (the X’s), it is called a distributed-lag model. If the model includes one or
more lagged values of the dependent variable among its explanatory variables, it is
called an autoregressive model. Thus:
(2-8-1) Yt =  + 0Xt +1Xt-1 +2Xt-2+ut
represents a distributed – lag model, whereas:
(2-8-2) Yt =  + Xt+ Yt-1 + ut

is an example of an autoregressive model. The latter are also known as dynamic
model since they portray the time path of the dependent variable in relation to its
past value(s).
Autoregressive and distributed-lag models are used extensively in econometric
analysis, and in this chapter we take a close look at such model with a view to
finding out the following:
1. What is the role of lags in economics?
2. What are the reasons for the lags?

3. Is there any theoretical justification for the commonly used lagged models in
empirical econometrics?
4. What is the relationship, if any, between autoregressive and distributed-lag
models? Can one be derived from the other?
5. What are some of the statistical problems involved in estimating such models?
6. Does a lead-lag relationship between variables imply causally? If so, how does
one measure it?
THE ROLE OF “TIME,” OR “LAG” IN ECONOMICS
In economics the dependence of a variable Y (the dependent variable) on another
variable(s) X (the explanatory variable) is rarely instantaneous. Very often, Y
responds to X with a lapse of time. Such a lapse of time is called a lag. To illustrate
the nature of the lag, we consider example

Link between money and prices. According to the monetarists,
inflation is essentially a monetary phenomenon in the sense that a continuous
increase in the general price level is due to the rate of expansion in money supply far
in excess of the amount of money actually demanded by the economic units. Of
course, this link between inflation and changes in money supply is not instantaneous.
Studies have shown that the lag between the two is anywhere from 3 to about 20
quarters. we see the
effect of a 1 percent change in the M1B money supply (= currency + Checkable
deposit at financial institutions) is felt over a period of 20 quarters. The long-run
impact of a 1 percent change in the money supply on inflation is about 1(= mi),
which is statistically significant, whereas the short-run impact is about 0.04, which is
not significant, although the intermediate multiplies seem to be generally significant.

Incidentally, note that since P and M are both in percent forms, the mi (i
in our usual
notation) give the elasticity of P with respect to M, that is, the percent response of prices to a
1 percent increase in the money supply. Thus, m0 = 0.041 means that for a 1 percent increase
in the money supply the short-run elasticity of prices is about 0.04 percent. The long-term
elasticity is 1.03 percent, implying that in the long run a 1 percent increase in the money
supply is reflected by just about the same percentage increase in the prices. In short, a 1
percent increase in the money supply is accompanied in the long run by a 1 percent increase
in the inflation rate.
DETECTING AUTOCORRELATION IN AUTOREGRESSIVE MODELS
: DURBIN h TEST
As we have seen, the likely serial correlation in the errors vt make the estimation
problem in the autoregressive model rather complex : In the stock adjustment model
the error term vt did not have (first-order) serial correlation if the error term ut in the
original model was serially uncorrelated, whereas in the Koyck and adaptive
expectation models vt was serially correlated even if ut was serially independent. The
question, then, is: How does one know if there is serial correlation in the error term
appearing in the autoregressive models?
A noted the Durbin-Watson d statistic may not be used to detect (first- order)
serial correlation in autoregressive models, because the computed d value in such
models generally tends towards 2, which is the value of d expected in a truly random
sequence. In other words, if we routinely compute the d statistic for such
models , there is a built-in bias against discovering (first-order) serial correlation.
Despite this , many researchers compute the d value for want of anything better.
Recently, however, Durbin himself has proposed a large-sample test of first-order
serial correlation in autoregressive models. This test, called the
h statistic, is as follows:
n
(2-12-1) h= 
1-n [(var(2)]

Where n = samples size, var(2) = variance of the coefficient of the lagged Yt-1, and
=estimate of the first-order serial correlation , which is given by the Eq. (2-11-5).
For large sample size, Durbin has shown that if =0, the h statistic follows the
standardized normal distribution, that is, the normal distribution with zero mean and
unit variance. Hence, the statistical significance of an observed h can easily by
determined from the standardized normal distribution table .
In practice there is no need to compute  because it can be approximated from the
estimated d as follows :
1
(2-12-2)  = 1- d
2
Where d is the usual Durbin-Watson statistic. Therefore (3-12-1) can be written as

1 N
(2-12-3) h = 1- d
2 1-N[(var (2)]
The steps involved in the application of the h statistic are as follows :
1. Estimate (Yt = 0 + 1Xt + 2Yt-1 + vt ) by OLS (don’t worry about any
estimation problems at this stage)

3. Compute p as indicate in (3-12-2).
4. Now compute h from (3-12-1), or (3-12-3).
5. Assuring n is large, we just saw that:
(2-12-4) h  AN (0.1)
that is h is asymptotically normally(AN) distributed with zero mean and unit
variance. Now from the normal distribution we known that
(2-11-4) Pr (-1.96  h  1.96) = 0.95
that is, the probability that h (i.e., any standardized normal variable) lying between –
1.96 and +1.96 is about 95 percent. Therefore, the decision rule now is
(a) if h  1.96 reject the null hypothesis that there is no positive first order
autocorrelation, and
(b) If h  -1.96 reject the null hypothesis that there is no negative first order
autocorrelation, but
(c) If h lies between – 1.96 and 1.96 do not reject the null hypothesis that there is no
first-order (positive or negative) autocorrelation.
As an illustration, suppose in an application involving 100 observations it was found
that d = 1.9 and var(2) = 0.005. Therefore:

(2-12-3) h = [1- (1.9)] = 0.7071
2 1-100 (0.005)
Since the computed h value lies in the bounds of (2-11-5), we cannot reject the
hypothesis, at the 5 percent level, that there is no positive first-order autocorrelation.
Note these features of the h statistic :
1. It does, not matter how many X variables or how many lagged values of Y are
included in the regression model. To compute h, we need consider only the
variance of the coefficient of lagged Yt-1.
2. The test is not applicable if [n var (2)] exceeds 1. (Why?) In practice, though this
does not usually happen.
3. Since the test is a large-sample test, its application in small samples is not strictly
justified

LIMITATIONS OF THE STUDY
The study had following limitations:
1. The period of the study was 1998 to 2004 for generalization of the findings. This
period was limited.
2. 1512 food companies were divided in 9 groups for testing.
3. Since detailed data for each firm was not available, they were tested as a group.
4. Since observations for each group were small (1999 to 2004), all of them were tested
as one group( 9 groups  6 periods = 54 periods). For this reason we used only 6
periods because the sales of the last year were necessary for the equation. Since the
data for 1997 was not available, the year was taken to be 1999 and 1998 was taken as
previous year for it.