Data and Analysis : Model Replication
Added on 2021-06-17
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ContentsSummary.....................................................................................................................................................1Critical evaluation........................................................................................................................................1Data and Analysis : Model Replication........................................................................................................2Unit Root Tests........................................................................................................................................2Granger Causality Test.............................................................................................................................6Further Analysis..........................................................................................................................................8Further Structural Analysis using impulse responses...............................................................................8Vector Error Correction Model Forecasts................................................................................................9Bibliography...............................................................................................................................................11SummaryThe paper being replicated is “The long run, causality, and forecasting in the advertising- sales Relationship” by George P Zanias.[ CITATION Zan94 \l 1033 ]The paper conduct a co-integration analysis of the Lydia Pinkham Data set. The Co-intergration analysis is used to analyse the long term relationship between the sales and advertising process. Granger Causality test is used to testthis relationship and model the data, using an error corrected model.The paper takes the logarithmic values of the advertising and sales spending (in US Dollars) . Logarithmic values often depict the growth of a variable, implying that spending in advertising grew, given an increase in sales and vice versa. The study utilized data from 1907 to 1960 i.e 53 years. The study models data in both the long run and short run. The author finds that there is a bi-directional Granger causality between the two variables viz: sales and advertising, in the long run. In simple words, the study concludes that the greater increases in sales revenue are caused by advertising, the greater is the likelihood of an increase in spending in advertising. The study also, compared the results with previous studies using the same data sets and concluded that the forecasts are better of error correction systems are employed and data is modeled in error corrected models i.e. residuals in an equation should not be neglected.
Critical evaluation Granger Causality test is usually, conducted to establish if there is a structural relationship between two variables. The test is well designed since it utilizes the Granger Causality Test with the log of variables. Taking the log of variable helps establish the structural relationship even further since the causality between the logs of variables will help understand how the growth in one variable affects the growth in another variable and it helps understand “elasticity” between two variables.[ CITATION Jef15 \l 1033 ]The paper goes into details about the augmentation of the Dickey Fuller (Augmented Dickey Fuller) test to highlight the importance of lags in the causality.[ CITATION Sjo08 \l 1033 ]However, the use of Dickey Fuller Test and Augmented Dickey Fuller Test seem to be redundant. Co-integration is further established using the Co-integration Durbin Watson (CRDW) Statistic. The logarithmic values of both the series seem to be non-stationary and had to be differentiated. However, the tests conducted in this report provide results to the contrary and establish that the logarithmic values of both the variables are stationary. The reasons for the differing results cannot be , understood. However, the author does, further use the Error Corrected Model for modeling which seems appropriate.[ CITATION Jef15 \l 1033 ]The study does take into account Auto-Correlation or serial co-relation among the variables, which makes the study incomplete. It is possible that the growth is a result of serial co-relation and not exclusively caused by a change in the other variable.[ CITATION Jef15 \l 1033 ]Overall, the study has been well designed and implemented with all the appropriate tests being conducted. The study also, highlights the importance of logarithmic values compared to arithmetic values. The primary achievement of the study, however, lies in the fact that it has contributed to literature by improving the quality of forecasts as compared to previous studies byincluding a vector-error corrected model.Data and Analysis : Model ReplicationThe data taken is sales and advertising data for the period of 1907 to 1960. In this data, the data taken is for both Unit Root TestsThe paper first evaluates the stationarity of the data. The stationarity of the data is evaluated using the Advanced Dickey Fuller Test (separately for both variables). The Null Hypothesis
being that there is a presence of unit roots, the ADF test rejects the null hypothesis for both the variables i.e. sales and advertising. [ CITATION Hei05 \l 1033 ]Table 1 ADF Test for natural log of advertising represented by “la” (Durbin Watson Statistic is highlighted)
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