Example of an Autoregressive Forecasting Model

1.  Background Information on the Time Series Data:

The first purpose of this blog is to demonstrate the model building approach commonly known as Box-Jenkins or ARIMA methodology.  (ARIMA stands for autoregressive integrated moving average.)  The second purpose is to demonstrate how forecasts can be produced from the fitted ARIMA model.

This blog uses a time series consisting of 75 observations.  I call this time series Yt, which is normal for forecasting models.  What this means is that observations were collected over time and entered into the computer (Minitab) in chronological order.

The time series is examined first using autocorrelation and partial autocorrelation functions.  This preliminary examination suggests that an autoregressive model of order 1 fits the data.  This autoregressive model of order 1, also known as an AR(1) model, is built and coefficients are estimated.  The model's adequacy is verified using a number of diagnostic tests to ensure that the residuals are random, normally distributed, and contain few outliers.  Then, four forecasts are made.

Below is the time series plot of Yt.

2.  Identifying a Model to be Tentatively Entertained:

To identify a potential model using the Box-Jenkins methodology, we begin by producing both the autocorrelation function and the partial autocorrelation function for the original time series data.  Then, these two graphical outputs are compared with theoretical graphical outputs to see if a match between them can be found.  This matching process helps narrow down which kind of model we should build.  We have numerous options such as building an autoregressive model, a moving average model, a mixed model, a differenced data model, and even a model with seasonal components.  We have more options, for example, we could pick an autoregressive model of order 1, or of order 2, or of order 3 depending on the number of terms we want to include on the right-hand side of the equation.  Therefore, we use this graphical matching process in order to reduce the number of options that we need to consider.

The autocorrelation function is a graphical display of various autocorrelation coefficients for various time lags. An autocorrelation coefficient is a measure of correlation between two variables:  the original time series variable and the lagged version of this same time series variable.  For example, a lag 2 autocorrelation coefficient is a measure of correlation between the original data and the original data lagged two periods.  For monthly data, lagging two periods means that we shift an observation from January to March and that we shift an observation from February to April and so on.  A lag 3 autocorrelation would involve shifting an observation from January to April and would involve shifting an observation from February to May.  The graph puts the various time lags on the horizontal axis and plots the autocorrelation coefficients as black lines extending upward or downward.  The autocorrelation coefficients are the little black lines that stick up or down and they appear all the way across the middle section of the graph.

The partial autocorrelation function is conceptually very similar to the autocorrelation function.  It too is a graphical output containing various partial autocorrelation coefficients computed for various time lags.  Again, the various time lags are put along the horizontal axis and the partial autocorrelation coefficients are plots as black lines extending upward or downward.  Moreover, a partial autocorrelation coefficient can be thought of as a correlation between the original time series data and a lagged version of the time series data.  The difference between the partial autocorrelation coefficients and the autocorrelation coefficients is that the partial autocorrelation coefficients are computed in such a way that the effects of the intervening time lags are taken into account.  So for example, a partial autocorrelation coefficient at time lag 12 is the correlation between the original time series and the time series lagged 12 periods and we have adjusted for the effects of the intervening values, i.e., we have adjusted for the effects of the lagged 1 through lagged 11 data.

Here are the autocorrelation and partial autocorrelation functions for the original time series data.  The most striking feature of these two plots is the strongly negative (downward pointing) partial autocorrelation coefficient at lag 1.  Then, the rest of the partial autocorrelation coefficients are all very small and close to zero, i.e., the black lines at the other time lags are all very short.  This is suggestive of an autoregressive model of order 1, usually abbreviated AR(1).  The reason it is suggestive is because I compared this partial autocorrelation function to the theoretical graphs from a book that I have and this picture is classified under the AR(1) function.

3.  Estimating Parameters in the Tentatively Entertained Model:

To estimate the autoregressive model of order 1, or AR(1), I utilize Minitab's ARIMA program.  The computer ran 7 iterations and then estimated the parameters of the model.  The Minitab results are presented next.


Final Estimates of Parameters
Type          Coef     SE Coef         T        P
AR   1     -0.5376      0.0986     -5.45    0.000
Constant   115.829       1.356     85.42    0.000
Mean       75.3310      0.8818


Minitab has estimated the following equation:


Y_t = φ₀ + φ₁Y_{t - 1} + ε_t

Minitab also estimates the values of the coefficients.  The estimated values of the coefficients are:

φ₀ = 115.829

φ₁ = - 0.5376

Finally, using these coefficient estimates, we can easily derive the forecasting function.  (In regression terminology, this would be called the Y-hat function).  We can use this function to forecast future values of Yt.  Of course, first we will have to verify that the AR(1) model is adequate.  This forecasting function is:


Y(forecast)_t = 115.829 – 0.5376 Y_{t - 1}


4.  Diagnostic Checking:

A number of tests have to be run in order to make sure that the model is satisfactory.  We want to ensure that the residuals of this AR(1) model are random.  Moreover, we also want to make sure that the residuals are normally distributed and that they contain few outliers.  The individual residual autocorrelations have to be checked to make sure that they are small and close to zero.  An overall test of model adequacy is provided by the chi-square test based on the Ljung-Box Q statistic.  This overall test looks at the sizes of the residual autocorrelations as a group.  (It is a portmanteau test).

The first test that I run is the Modified Box-Pierce or Ljung-Box chi-square test.  This test checks a number of residual autocorrelations simultaneously to see whether they are all random or not.  If the p value is small, i.e., less than 0.05, the model is considered inadequate.  Since this test at lags 12, 24, 36, and 48 has p-values that are all much larger than 0.05, the model can be deemed adequate.  What this test is telling us is that a set of residual autocorrelations is not significantly different from what we would expect to find when looking at a set of random residuals.  In other words, the residuals are random.


Modified Box-Pierce (Ljung-Box) Chi-Square statistic


Lag               12        24        36        48
Chi-Square       9.3      29.8      37.2      58.2
DF                10        22        34        46
P-Value        0.508     0.124     0.324     0.107



The next graph is the autocorrelation function of the residuals.  This plot shows the individual residual autocorrelations.  The 95% confidence limit is used to test whether a residual autocorrelation coefficient is significantly different from zero.  A residual autocorrelation coefficient would be significantly different from zero if the black line were to extend upward of downward and penetrate through one of the confidence intervals (the red lines).  Since this never happens in this plot, we can again conclude that the residuals are random; the residual autocorrelations are not significantly different from zero.

The next graph is the partial autocorrelation function of the residuals.  We interpret it using the same general rules that are used for the autocorrelation function.  If a black line penetrated through a red line we have to worry because this suggests non-random residuals.  If the black lines do not penetrate through the red lines then we most likely have random residuals.  We can again conclude that the residuals from this graph.

The next two graphs are used to check the residuals for normality.  The normal probability plot is a visual way of checking for normality.  If the residuals are normally distributed, then the plot should appear to fall along a straight line.  If many residuals diverge radically from the straight line then the residuals are non-normal.  The Anderson-Darling Normality test is another way to check the residuals for normality.  This test has a null hypothesis that says that the residuals follow a normal distribution.  Since the p-value for this test is 0.539, we fail to reject the null hypothesis and conclude that the residuals are most likely normally distributed.

The last test that I run is to plot the residuals against the order of the data.  Notice that almost all of the residuals are clustered around 0, plus or minus 20.  This is an encouraging sign because we expect that the average value of the residuals should be zero and the residuals should have a constant variance across time.  There are only a few residuals that deviate outside of this band.  This suggests that few residuals could be classified as outliers.  We want to have few outliers; this plot confirms that we have few of them.

5.  Using the AR(1) Model for Forecasting:


Since the model passed the diagnosis phase, it can be used to develop forecasts of future values.  I once again use Minitab to produce four forecasts.  The data in the original time series ran from time period 1 to time period 75.  Consequently, the four forecasts are made for time periods 76, 77, 78, and 79.  The results are presented next.



Forecasts from period 75
                             95 Percent Limits
Period      Forecast        Lower        Upper       Actual
  76          77.122       54.102      100.142
  77          74.368       48.232      100.504
  78          75.849       48.879      102.818
  79          75.053       47.847      102.258



The forecasts and presented in the second column above.  The 95% limits give us a range of values for these forecasts because the forecasts contain a degree of uncertainty.  For example, the forecast for time period 76 is 77.122.  However, the 95% limit tells us that the actual value could very likely fall somewhere in between 54 and 100.  This spread of possible values warns the user to keep in mind that the 77.122 figure is not to be taken as an unquestionable truth.  It is simply a point estimate that solves the AR(1) equation.  

Example of Time Series Regression

1.  Background Information:


This time series model is being built in order to predict future electrical usage for a power plant.  In this example, the power plant management have collected quarterly data starting with the first quarter of 1980 and ending with the second quarter of 1996.  In total, we have a sample size of 66, i.e., one observation is taken per quarter.  


First, the regression model has to be built.  Then, four forecasts will be made, i.e., for times 67, 68, 69, and 70; in words, the forecasts will be made for the 3rd Quarter of 1996, the 4th Quarter of 1996, the 1st Quarter of 1997, and the 2nd Quarter of 1997.  Keep in mind that the "current time period" is the 2nd quarter of 1996; consequently, we can view these as future forecasts.  


2.  The Response Variable:


The variable that we want to predict is labeled "Hours" and stands for electrical usage measured in millions of kilowatt hours per quarter.  Basically, we are looking to forecast the demand for electricity at this power plant for the next four quarters in the future.


3.  The Predictor Variables:

1. "Time":  This variable is meant to capture the positive or upward trend in the data.   The coding procedure is fairly straightforward.  The first observation occurs in the first Quarter of 1980 and is coded as "time 1."  The second observation occurs in the second Quarter of 1980 and is coded as "time 2."  The third observation occurs in the third Quarter of 1980 and is coded as "time 3."  This pattern continues, so that the for example, the fifth observation occurs in the first Quarter of 1981 and is coded as "time 5."
2. "2nd Qt":  This dummy variable takes on the value 1 if the observation takes place during the second quarter of the year.  It takes on the value 0 if the observation takes place during any other quarter of the year.
3. "3rd Qt":  This dummy variable takes on the value 1 if the observation takes place during the third quarter of the year.  It takes on the value 0 if the observation takes place during any other quarter of the year.
4. "4th Qt":  This dummy variable takes on the value 1 if the observation takes place during the fourth quarter of the year.  It takes on the value 0 if the observation takes place during any other quarter of the year.
5. (Implied variable):  To capture the situation when the observation takes place during the first quarter of the year, we simply do nothing.  This has already been captured.  This occurs when "2nd Qt" = 0 and "3rd Qt" = 0 and "4th Qt" = 0.  We are saying, that the observation does not happen in the 2nd Quarter, the observation does not happen in the 3rd Quarter, and the observation does not happen in the 4th Quarter.  Therefore, since there are only 4 quarters in the year, the only option left is for it to be in the 1st Quarter.

4.  Graphical Inspection of the Data:

The simplest way to analyze time series data is to plot the response variable of "Hours" against time to see what it looks like.  This simple time series plot appears first below.  The second picture is the autocorrelation function for this "Hours" variable.  The idea behind an autocorrelation function is to lag data and run a correlation analysis between the actual data and the time lagged data.  The purpose for doing so is to help spot whether the data has a trend and/or a seasonal pattern in it.

The autocorrelation function produces these black bars that indicate the different autocorrelations at various time lags.  When the bar breaks through the red line (the confidence interval) then this indicates we have something statistically significant (it implies a correlation that is significantly different from zero).  

What exactly is an autocorrelation?  What exactly does it mean?  A simple example using a lag of 4.  Since this is quarterly data, a lag of 4 means that we are comparing data for a correlation analysis as follows:  Quarter 1 of 1980 will be compared with Quarter 1 of 1981; Quarter 2 of 1980 will be compared with Quarter 2 of 1981 and so on.  Basically, we are seeing whether or not a pattern exists in the data so that Quarter 1's across time are similar, Quarter 2's across time are similar and so on.  We are looking for the seasonal pattern.

In this example, the lag 4 correlation is 0.87.  This means that Quarter 1 of 1980 is very similar to Quarter 1 of 1981; Quarter 2 of 1980 is very similar to Quarter 2 of 1981 and so on.  For example, we can say that Quarter 1 of 1985 is similar to Quarter 1 of 1986 and so on.  We are picking up on the fact that the data has a repeating pattern every year probably driven by the fact that weather influences electricity demand and weather follows fairly predicable seasons year after year.

The easiest way to see the upward trend would be to do a simple linear regression of "Hours" against time and have Minitab (the program used for this analysis) fit a trend line.  The results are presented next.  Visually, you can see the positive upward slope of the blue trend line.  The equation confirms this because the slope of the trend line is positive.

 
5.  The Regression Model Conceptually:

The above analysis suggests that we have to model a trend and seasonal data.  This is why it makes sense to include the trend and season variables.

The general estimation equation that Minitab will estimate takes the following form:

Estimated Hours = b0 + b1 "Time" + b2 "2nd Qt" + b3 "3rd Qt" + b4 "4th Qt"

Where:

b0 is the constant term or intercept term

b1 is the slope term or coefficient on the "Time" variable

b2 is the coefficient on the "2nd Qt" variable

b3 is the coefficient on the "3rd Qt" variable

b4 is the coefficient on the "4th Qt" variable

We can easily derive from this equation the estimation equations for each quarter.  This is done simply by substituting in the appropriate 1's and 0's into this general estimation equation for each case.

The estimation equation for the First Quarter:

The first quarter is captured when "2nd Qt" = 0;  "3rd Qt" = 0; and "4th Qt" = 0.

Estimated Hours for the First Quarter = b0 + b1 "Time"

The estimation equation for the Second Quarter:

The second quarter is captured when "2nd Qt" = 1; "3rd Qt" = 0; and "4th Qt" = 0.

Estimated Hours for the Second Quarter = b0 + b2 + b1 "Time"

The estimation equation for the Third Quarter:

The third quarter is captured when "2nd Qt" = 0; "3rd Qt" = 1; and "4th Qt" = 0.

Estimated Hours for the Third Quarter = b0 + b3 + b1 "Time"

The estimation equation for the Fourth Quarter:

The fourth quarter is captured when "2nd Qt" = 0; "3rd Qt" = 0; and "4th Qt" = 1.

Estimated Hours for the Fourth Quarter = b0 + b4 + b1 "Time"

In other words, we have four estimation equations, all with the same slope (b1) but with different constant terms or intercepts.

6.  The Regression Output and Interpretation:

Here are the regression results.  I have included four forecasts for times 67, 68, 69, and 70, i.e., forecasts of "Hours" for 3rd Quarter 1996, 4th Quarter 1996, 1st Quarter 1997, and 2nd Quarter 1997.

The regression equation is

Hours = 968 + 0.938 Time - 342 2nd Qt - 472 3rd Qt - 230 4th Qt

Predictor        Coef     SE Coef          T        P

Constant       968.39       16.88      57.38    0.000

Time           0.9383      0.3377       2.78    0.007

2nd Qt        -341.94       17.92     -19.08    0.000

3rd Qt        -471.60       18.20     -25.91    0.000

4th Qt        -230.23       18.20     -12.65    0.000

S = 52.25       R-Sq = 92.4%     R-Sq(adj) = 91.9%

Analysis of Variance

Source            DF          SS          MS         F        P

Regression         4     2012975      503244    184.34    0.000

Residual Error    61      166526        2730

Total             65     2179502

Durbin-Watson statistic = 1.48

Predicted Values for New Observations

New Obs     Fit     SE Fit         95.0% CI             95.0% PI

1        559.65      17.39   (  524.87,  594.43)  (  449.54,  669.76)  

2        801.96      17.39   (  767.19,  836.74)  (  691.85,  912.08)  

3       1033.13      17.56   (  998.01, 1068.25)  (  922.91, 1143.35)  

4        692.13      17.56   (  657.01,  727.25)  (  581.91,  802.35)  

Values of Predictors for New Observations

New Obs      Time    2nd Qt    3rd Qt    4th Qt

1            67.0      0.00      1.00      0.00

2            68.0      0.00      0.00      1.00

3            69.0      0.00      0.00      0.00

4            70.0      1.00      0.00      0.00

The Minitab output begins with the regression equation.  Instead of using b0, b1, b2, b3, b4 as generic coefficients, the program has substituted in the regression estimates for these values.  The coefficient value of 0.9383 is positive.  This positive value makes sense; it tells us that if we increase "Time" then the Estimated Hours will go up.  To see this, take a look at the First Quarter Estimation equation.

Estimated Hours for the First Quarter = b0 + b1 "Time"

Or, if we substitute in the values for b0 and b1 from the regression equation we get:

Estimated Hours for the First Quarter = 968.39 + 0.9383 "Time"

The t-tests and p-values are meant to determine whether or not the coefficients are significantly different from zero.  We want them to be different from zero.  The fact that all the p-values are much less than 0.05 is very good news.  In fact, all the p-values are below 0.01.  This tells us that we can reject the null hypotheses that each population coefficient is 0.  

The R-sq or R-squared statistic is a measure of the ratio of sum of squares regression divided by sum of squares total.  (These numbers come from the Analysis of Variance chart immediately below this statistic in the chart above.)  In this case, the 92.4% means that 92.4% of the variation in "Hours" is explained by the predictor variables.  This means that most of the variation that we want to explain has been explained.  

The analysis of variance table also reports the F statistic with the associated p-value.  The F-Test tests the null hypothesis that ALL the slope coefficients are zero.  In this case, the null hypothesis is that b1 = b2 = b3 = b4 = 0.  With the p-value virtually zero and the F-value so large, we can conclude that at least one of the four regression slope coefficients is different from zero.  This again is a good sign.  We want this result since we want to find values different from zero.

The Durbin-Watson statistic is important for model checking.  It is meant to check to see whether positive first-order autocorrelation exists in the residuals or error terms of the regression model.  The error terms are supposed to be independent and normally distributed with a mean of zero and a constant variance.  With time series data, we can easily run into the problem where the error term in one period is related to the error term in the preceding time period.  This is the issue that the Durbin-Watson test is addressing.  

I ran the Durbin-Watson test manually (I had to look up the values in a table).  I used n = 65 for the sample size (even though the real sample size is 66) since 65 is the closest entry in my chart.  I used k = 4 since there are four independent variables in this model (i.e., "Time", and the three dummy variables).  I used the significance level of alpha = 0.05.  From the chart we get upper and lower bounds for the Durbin-Watson test.

dL = 1.47 (lower bound)

dU = 1.73 (upper bound)

DW = 1.48 (the Durbin-Watson statistic from the regression results above)

Unfortunately, we have situation where lower bound < DW < upper bound (specifically we have the situation where 1.47 < 1.48 <1.73.  Therefore, the test is inconclusive.

A deeper analysis would continue with the residuals or error terms of the model.  We would investigate the autocorrelation functions to see whether any of the lagged residuals display significant correlations.  When I did this, I found that most of the lagged correlations are fairly small.  The largest value was 0.24.  Also, none of the black bars penetrated through the red-line or confidence interval.  This implies that none of the lagged correlations are significantly different from zero.  This is a good sign.  We want the errors to be random; hence, we do not want to find patterns in the error terms over time.

Then, I did some predictions using Minitab to forecast four future observations on "Hours."  The program first estimates the fitted value.  This is simply done by sticking in the appropriate values of the predictor variables into the appropriate estimation equations.  Then, the program calculates 95% CI (confidence intervals) and 95% PI (prediction intervals).  What is going on here is that the fitted values are guesses and so they have to be interpreted with care.  The intervals are trying to capture certain aspects of uncertainty in calculating these fitted values.  For example, we have to take into account the fact that data points do not fall perfectly on our estimated regression line.  Moreover, we have to also take into account the fact that we are estimating a sample regression line and not the population regression line.  Maybe this company has additional years of data before 1980--maybe going back to the 1920s.  We have not used all of this data and so we cannot know for sure whether our sample regression line is similar to the population regression line.  Because of these uncertainty issues, Minitab gives up these ranges of values--ideally we want the range of possible values for the forecast value to be as small as possible.

Example of Correspondence Analysis

1.  Background Information for this Study

This hypothetical study involves 18 respondents doing in-depth interviews.  It is written from the perspective of Allergan, i.e., I am assuming that Allergan is the client that I am advising.  We ask these 18 respondents to evaluate Allergan as well as nine of Allergan’s competitors on eight firm attributes.  We are asking them simply “does the firm possess this attribute or not.”  In other words, we are creating a tally.  Each time the respondent says yes, we make a tick to symbolize that the respondent agrees to the idea that the specific firm does in fact have the attribute in question.  At the end, we count the number of ticks or yes responses; these counts form the data matrix or cross-tabulation table or contingency table results.  The attributes are:  Product Quality, Strategic Orientation, Overall Service Level, Delivery Speed, Price Level, Sales Force Image, Price Flexibility, and the firm’s Image.  I picked the following companies to represent the pharmaceutical industry:  Biodel, Merck, Bayer, Allergan, Novo Nordisk, Shire, Roche, Pfizer, Glaxo, and Novartis.


2.  Discussion of the Contingency Table

The numbers in the chart, which appears at the bottom of this section, represent the number of times we get ‘yes’ responses.  In the first row and first column, we see a 4 in the cell created by Product Quality and Biodel.  This means that 4 of our 18 respondents said in their interviews that Biodel has product quality.  If we move one cell to the right, we see a 3 in the Product Quality and Merck cell.  This means, of our 18 respondents, 3 said that Merck has product quality and consequently 15 said that Merck does not have quality in its products.  

Contingency Table

              Biodel     Merck     Bayer  Allergan      Novo     Shire

Quality            4         3         1        13         9         6

Strategi          15        16        15        11        11        14

Service           15        14         6         4         4        15

Speed             16        13         8        13         9        17

Price             14        14        10        11        11        14

Sforce             7        18        13         4         9        16

Flexibil           6         6        14        10        11         8

Image             15        18         9         2         3        15

Total             92       102        76        68        67       105

               Roche    Pfizer     Glaxo  Novartis     Total

Quality            3        18         2        10        69

Strategi          16        12        14        14       138

Service           14        13         7        13       105

Speed             15        16         6        12       125

Price             12        13        10        14       123

Sforce            14         5         4        16       106

Flexibil           7         4        14         4        84

Image             16         7         8         8       101

Total             97        88        65        91       851

3.  Correspondence Analysis and Perceptual Mapping

Now, this gigantic collection of counts in the contingency table is hard to interpret.  It hides a bunch of important strategic findings.  To make these findings obvious, I use correspondence analysis.  The general idea is to draw an attribute-company combination close together if they are strongly associated with each other.  Similarly, if an attribute-company combination is not strongly associated with each other, they are drawn apart.  Moreover, the creation of dimensions or ‘components’ lets us know the key drivers in this industry when it comes to perceptions in the minds of the respondents.

A simple way of explaining the thought process behind correspondence analysis is as follows.  Suppose that a new car brand is being presented to the public for the first time.  This car brand offers a value proposition to the customers that can be described as fun, sporty, sexy, energetic, and cool.  Suppose that two customer groups are being evaluated to see their degree of correspondence with this brand’s value proposition.  The first group consists of 18 to 25 year old males.  This group is looking for a fun, sporty, sexy, energetic, and cool looking car.  Consequently, the value proposition that this car brand offers and the value proposition that the 18 to 25 year old males want are highly similar.  This implies that the number of sales of this car brand to this customer group will be above average.  The correspondence analysis will pick this up as actual sales to this group exceed expected sales (technically the expected cell value used to compute the chi-square statistic).  The analysis will assign to this result a positive value and draw 18 to 25 year old males and this car brand close together on the perceptual map.  Suppose further, that a second group consists of 55 to 65 year old males.  This group is looking for a car that can be defined as refined, elegant, safe, dignified, and expensive.  The value proposition offered by the car brand and the value proposition desired by this 55 to 65 year old group of males are dissimilar.  Correspondence analysis will pick this up as actual sales to this group will be below the expected value.  Intuitively, this makes sense.  Since the car brand does not satisfy the needs of this customer group, then few sales will take place.  The analysis will draw the 55 to 65 year old group and this car brand far apart on the perceptual map.

The graphical output or perceptual map is provided in this blog at the bottom of this section.  The attributes are plotted with red squares; the companies are plotted with blue squares.  To understand the competitive landscape, we look for the extreme attribute cases to try to figure out what the components (the axes in the graph) mean.  Component 1, the y-axis, (i.e., why we can move up and down in this picture) is driven by Product Quality (at the top of the picture) and Firm Image (at the bottom).  Component 2, the x-axis, (i.e., why we can move right and left in this picture) is driven by Price Flexibility (on the left) and Service (on the right).  So now, we have the four key drivers that explain most of what is going on in this market space.  We also know that component 1 (i.e., product quality and firm image) is more important than component 2.  This is because component 1 explains 53.1% of the variation while component 2 explains only 33.2%.  Moreover, when I look at the “explanation by component” information, Allergan is very heavy (88.2%) on component 1 and much lower on component 2 (9.3%).  Further, when looking at the similarity values (i.e., signed chi-square values), the two largest values for Allergan are +10.165 on Quality and –4.566 for Image (the minus implies dissimilarity).  All of this suggests that component 1, i.e., product quality and firm image are the most important things for the marketing manager at Allergan to address.  The secondary issue to address is component 2, i.e., service and price flexibility.

From a strategic point of view, we see that Allergan is viewed as being very strong on product quality and very weak on firm image.  With regard to component 2, Allergan does fine on price flexibility but not so well on service.  This suggests an advertising strategy based on product quality mainly with a secondary focus on price flexibility, assuming the plan is to play to the existing strengths.  We also observe that Allergan is perceived as being very similar to Pfizer since both firms are very strong on product quality.  We might expect competition here because these two firms are very similar. 

Moreover, suppose that you are no longer Allergan but rather a new entrant into this industry.  One thing you might want to consider is where to position your new brand.  One possible solution would be to analyze this perceptual map to see if any ‘gaps’ exist.  Are there any areas where existing firms have not yet been positioned?  For example, the top-left hand corner of the graph is currently unoccupied.  No firm is currently offering the combination of strong product quality and strong price flexibility.  Consequently, this could be one area to further study using a feasibility analysis (since one needs to verify the profitability of such a combination).  If this combination were to be profitable, the new entrant would have achieved a successful differentiation strategy.

Blog 9: The Global Communist Ideology of the Venus Project

A few weeks ago, I came across a rather heavily commented on Facebook post regarding the Venus Project in my Facebook news-feed.  I have heard on the Zeitgeist/Venus movement for some time now, but I had never really looked into it seriously.  What motivated me to launch a more thorough investigation was a comment posted about how ‘airtight’ the arguments are in favor of the Venus Project.  This commenter mentioned how he had never seen anyone present any solid arguments against the Venus Project.  Case closed apparently.  Such self-assured comments are suspicious because I have never seen any social science debate that is ‘airtight.’  Social science debates normally are quite passionate and quite divisive and are not normally settled in any way.  Consequently, I launched this investigation into the Venus Project.  I wanted to see whether this ‘airtight’ claim could stand up to a thorough criticism.  My conclusion is that it cannot be considered ‘airtight’ because the arguments are all unconvincing.  There are also many issues I have with the logic of their arguments, and with the historical accuracy of what they say.  I also wanted to see if I could figure out the ideology driving this project.  My conclusion is that it is a form of global communism mixed in with anarchist rhetoric, or some sort of global anarcho-communism system.  

The Venus Project flatly denies my claims that they have anything to do with communism.  Here are some quotes from their website where they explicitly reject my linking of their project to communism, to Karl Marx, etc. 

This first quote is the first half of their answer to Question 55 “How does The Venus Project Compare with Communism?”

Communism being similar to a resource-based economy or The Venus Project is an erroneous concept. Communism has money, banks, armies, police, prisons, charismatic personalities, social stratification, and is managed by appointed leaders. The Venus Project's aim is to surpass the need for the use of money. Police, prisons and the military would no longer be necessary when goods, services, healthcare, and education are available to all people.

This second is part of their answer to Question 54 “Is this what Karl Marx advocated?”

Although Marx was a brilliant man for his time, he did not foresee the methods and advantages of a high-tech resource-based economy. Communism used money and labor, had social stratification, and elected officials to maintain the communists' traditions. Most importantly, Communism did not eliminate SCARCITY nor did they have a blueprint or the methods for the production of abundance.

The global nature of this plan is stated explicitly in their answer to Question 2 entitled “What is a Resource-Based Economy?”

To transcend these limitations, The Venus Project proposes we work toward a worldwide, resource-based economy, in which the planetary resources are held as the common heritage of all the earth's inhabitants. The current practice of rationing resources through monetary methods is irrelevant, counter-productive, and falls far short of meeting humanity's needs.

Simply stated, a resource-based economy utilizes existing resources - rather than money - to provide an equitable method of distribution in the most humane and efficient manner. It is a system in which all goods and services are available to everyone without the use of money, credits, barter, or any other form of debt or servitude.

Terminological Issues:

One of the major problems is that the terms ‘communism’ and ‘socialism’ and even the terms ‘communist’ and ‘socialist’ have historically had inconsistent meanings.  Initially, these terms were all synonymous.  However, over time, shades of difference in meaning of all of these four terms emerged.  Part of the reason for this has to do with changes in tactical issues pertaining to how to implement communism or socialism.  One view held that communism would come about inevitably and would be achieved in a manner independent of the wills of individuals.  Another view held that communism had to be achieved by revolutionary means.  A further view held that communism had to be achieved through parliamentary means because it was important that the public supported the cause.  Moreover, further refinements in terminology differentiated between an early stage and a late stage with socialism being the early stage and with communism being the later stage.  Further hairsplitting could be raised over whether a proposal should be classified as ‘interventionist’ or ‘petty bourgeois’ or whether it is legitimately communist or socialist.  Furthermore, the history of communism and socialism is full of examples of one communist party accusing other parties of not being ‘true’ communists or being sellouts to capitalism. 

To address these issues, I will try to add modifiers to my use of the terms socialism and communism.  So for example, if I am alluding to revolutionary communism, I might add in a modifier such as the Bolshevik or Leninist or Sorel approach.  My plan is to keep these terms as clearly differentiated as possible.  This will not only cut down on confusion but it will also help classify what the Venus Project is and what it is definitely not.  

Analysis of Question 55:

The Venus Project states that it is not communism because, unlike communism, the Venus Project does not have police, prisons, and military.  All that has been proven is that the Venus Project is not planning for revolutionary communism.  It opposes the Leninist Bolshevik brand of communism.  The Venus Project openly rejects the George Sorel approach of ongoing bloody riots and violence.  I conclude that the Venus Project is not revolutionary communism.

But this is insufficient proof for the Venus Project to go on to claim that their non-violence makes them non-communists.  Take for example Ludwig von Mises’s 1947 work entitled Planned Chaos (which appears as an appendix to his larger treatise Socialism:  An Economic and Sociological Analysis.)  Back then, the socialist authors that Mises was debating against said exactly the same thing the Venus Project says today.  Mises writes on page 521 (Emphasis is mine.):

Socialism, they asserted, will bring true and full liberty and democracy.  It will remove all kinds of compulsion and coercion.  The state will “wither away.”  In the socialist commonwealth of the future there will be neither judges and policemen nor prisons and gallows.

Of course, this 1947 quote does not conclusively prove that the Venus Project is socialist.  Moreover, Mises does not specify which socialist authors he is alluding to in this quote so I cannot give any modifying phrase here.  In fact, one could easily quote modern day anarcho-capitalists who vehemently attack the state as a tool of coercion and compulsion.  This is not surprising given their openly anarchistic views as espoused especially by Murray Rothbard.  Furthermore, one could also quote a classical liberal, such as Mises himself to support this claim.  Mises said in Liberty and Property that, “Government is essentially the negation of liberty.”  (Classical liberals call for the ‘minimal state’ that would be restricted to a narrow range of activities usually only the protection of life, liberty, and property.)

However, neither a classical liberal nor an anarcho-capitalist would ever advocate for the abandonment of money.  The advocating for the elimination of money by the Venus Project is, however, a staple of communist literature.  Here are three historical examples of communist experiments that all tried to eliminate money.

Murray Rothbard’s book, Economic Thought before Adam Smith, discussed, what he called the totalitarian communism of Munster.  Munster in northwest Germany in the 1530s provides a nice historical lesson of an early attempt at money-less communism.  From page 153 (Emphasis is mine.):

After two months of severe and unrelenting pressure, a combination of propaganda about the Christianity of abolishing private money, and threats and terror against those who failed to surrender, the private ownership of money was effectively abolished in Munster. The government seized all the money and used it to buy or hire goods from the outside world.

         

Rothbard’s essay entitled The Myth of Monolithic Communism points out the failure of the Soviet’s experiment with abolishing money.  They quickly learned from experience that the plan to abolish money is impracticable even in a fairly economically backward nation, i.e., 1917 Russia.  One has to wonder how this plan could ever be applied to an advanced capitalistic nation.  (Emphasis is mine.)

When the Bolsheviks assumed power in late 1917, they tried to leap into full "communism" by abolishing money and prices, an experiment so disastrous (it was later dubbed "War Communism") that Lenin, always the supreme realist, beat a hasty retreat to a mere semisocialist system in the New Economic Policy (NEP).

Finally, in his book entitled Classical Economics, Murray Rothbard provides, on page 333, historical information on the Pol Pot attempt to abolish money in order to abolish the division of labor (i.e., specialization in production).  To abolish the division of labor is also a rather typical Marxian theme mainly because capitalist production is based on the division of labor.  (Emphasis is mine.)

Perhaps the closest approximation was the short-lived communist regime of Pol Pot in Cambodia which, in attempting to abolish the division of labour, managed to enforce the outlawry of money - so that for their tiny rations the populace was totally dependent upon the niggardly largesse of the communist cadre.

Obviously, this does not prove that the Venus Project will turn into the totalitarian dictatorships that appeared in Munster, in Bolshevik Russia, or in Pol Pot’s Cambodia.  The Venus Project certainly could turn into a global totalitarian dictatorship especially because of their global common holding of property idea.  The point is that historical examples do not prove future events.  They do, however, suggest that communist regimes have a tendency to favor plans that will abolish money.  A capitalist regime can never suggest a plan that would abolish money because money facilitates indirect exchange.  Indirect exchange (i.e., trading goods and services for payment in money) exists because of the division of labor.  The division of labor is specialization in production and so requires exchange between the different specialized producers.  These exchanges are facilitated by the use of a medium of exchange, i.e., by money.

The Venus Project is correct when it asserts that communism tends to lead to social stratification.  In Planned Chaos, page 506, Stalin’s regime suffered from the creation of a small ruling elite that lived very well while the masses of people lived in horrific poverty.

Stalin finds it necessary to explain to the vast majority of his subjects why their standard of living is extremely low, much lower than that of the masses in the capitalist countries and even lower than that of the Russian proletarians in the days of Czarist rule.  He wants to justify the fact that salaries and wages are unequal, that a small group of Soviet officials enjoys all the luxuries modern technique can provide, that a second group, more numerous than the first one, but less numerous than the middle class in imperial Russia, lives in “bourgeois” style, while the masses, ragged and barefooted, subsist in congested slums and are poorly fed.

The Venus Project’s assertion that communist leaders are appointed is questionable.  Lenin did not get appointed; he seized power from the Constituent Assembly at gunpoint (see Planned Chaos, p. 502).  Stalin moreover eliminated his competitor, Trotsky, by forcing him to have to flee the country (see Planned Chaos, p. 514).  Historically speaking, these communists are not appointed; they like to appoint themselves.

Analysis of Question 54:

Question 54 begins by asserting that Marx was a brilliant man.  Given the historical context, this is probably a fair statement to make.  In the Preface to the Second German Edition of Socialism:  An Economic and Sociological Analysis, Mises (pages 5-6) points out that socialism was basically a dead philosophy by the middle of the nineteenth century and that Marx successfully resurrected it.

Thus, about the middle of the nineteenth century, it seemed that the ideal of Socialism had been disposed of.  Science had demonstrated its worthlessness by means of strict logic and its supporters were unable to produce a single effective counter-argument.  It was at this moment that Marx appeared. 

Then, this Venus Project quote mentions that Marx’s major failure was that he did not anticipate a high-tech economy.  However, this claim is contradicted by Rothbard’s discussion on pages 327 to 328 in his book Classical Economics.  Although not technically from Marx, this quote is from Marx’s collaborator, Engels.  Notice that Engels, like the Venus Project, links a discussion of the use of new technology with a discussion of the abolishment of scarcity and the creation of superabundance to satisfy the needs of everyone.  (Emphasis is mine).

Furthermore, in 'The Principles of Communism', an essay written in late 1847 that became the first draft for the Communist Manifesto, Engels laid bare one of the crucial, usually implicit, assumptions of the communist society – that superabundance will have eliminated the problem of scarcity:

Private property can be abolished only when the economy is capable of producing the volume of goods needed to satisfy everyone's requirements...The new rate of industrial growth will produce enough goods to satisfy all the demands of society... Society will achieve an output sufficient for the needs of all members,

This superabundant production somehow will have been achieved by a wondrous technological progress that would eliminate the need for any division of labour.

The Venus Project laments the fact that communist failed to eliminate scarcity.  Ironically, on page 54 (everything is 54 I guess in this section!), George Reisman, in is treatise entitled Capitalism, explains that it is impossible to eliminate scarcity.  As he says, “The desire for goods will always remain far greater than the ability to produce them.”  In his book, Young Lessons for the Young Economist, Robert P. Murphy that scarcity means that at any particular point in time we have limited resources but unlimited desires and so tradeoffs have to be made.  Reisman does differentiate between pre-capitalistic (i.e., food, clothing, and other necessities) and capitalistic definition of scarcity (e.g. I do not want to take the bus, now I want a car).   At first, I thought that maybe the Venus Project was using a pre-capitalistic definition of scarcity as opposed to the capitalistic definition and that a terminological issue existed.  It is certainly possible to eliminate the pre-capitalistic version of scarcity.  However, the Venus Project seems to go beyond the pre-capitalistic definition and wants to provide a superabundance of all goods.  This then makes the wishes of the Venus Project unattainable.  You cannot eliminate the capitalistic version of scarcity because the invention of any new technology creates even more desires on the part of individuals and so desires will always be greater than the ability to produce them.

To conclude my analysis of Question 54, the Venus Project said that communism did not have a plan for the creation of superabundance.  This is not historically accurate.  The revolutionary communists certainly had plans.  The Soviet Union was notorious for having Five-Year Plans.  It seems contradictory to me to claim that communism, which has always been about central planning, does not have any plans for abundance.

Analysis of Question 2:    

Question 2 begins by admitting openly that the Venus Project is global communism.  To abolish private ownership of the means of production is the essence of all socialist and communist plans (and interventionist plans as well.)  Going back to Rothbard’s historical Munster example, from page 153 of Economic Thought before Adam Smith, we clearly see that communist experiments eliminate private property, want to redistribute everything equitably, and also plan to eliminate manual labor.  (Emphasis is mine).

This compulsory communism and reign of terror was carried out in the name of community and Christian 'love'. All this communization was considered the first giant steps toward total egalitarian communism, where, as Rothmann put it, 'all things were to be in common, there was to be no private property and nobody was to do any more work, but simply trust in God'. The workless part, of course, somehow never arrived.

Conclusions:

The Venus Project is global anarcho-communism.  They certainly are not calling for revolutionary communism because of their views against violence and against government coercion that comes in the form of police and prisons.  They are also not for the parliamentary version of socialism because they do not want any government at all (I took this fact from some of their other frequently asked questions—they explicitly state that they want to abolish all government).  I suppose that this makes them orthodox Marxians—that is, they think that global communism is inevitable.  Or in the Venus Project’s case, this new technological revolution is inevitable and so their global communist scheme is therefore inevitable.  But they certainly are kidding themselves if they think they are not communists.  They want to eliminate prices and money—that is pure communism.  They want to hold all property in common—that is pure communism on a global scale.  They want to distribute all goods equitably—that is communism.  They want to somehow violate all known laws of economics and abolish scarcity—that is communism.  They want to create superabundance through all this new radical technological innovation—that is communism.  They want to eliminate manual labor—that is communism.  Everything that they want is some variation of communism of ideology.  Therefore, I conclude that the Venus Project is global communism and is most consistent with the orthodox Marxian version of the inevitable communism.