Descriptive Statistics

Descriptive Statistics

 

Juice dataset (OJ). For simplicity, the products and stores of the dataset represent the whole market.

Description

The data contains 1070 purchases where the customer either purchased Citrus Hill or Minute Maid Orange Juice. A number of characteristics of the customer and product are recorded.

A data frame with 1070 observations on the following 18 variables.

Purchase

 

 A factor with levels CH and MM indicating whether the customer purchased Citrus Hill or Minute Maid Orange Juice
WeekofPurchase Week of purchase
StoreID Store ID
PriceCH Price charged for CH
PriceMM Price charged for MM
DiscCH Discount offered for CH
DiscMM Discount offered for MM
SpecialCH Indicator of special on CH
SpecialMM Indicator of special on MM
LoyalCH Customer brand loyalty for CH
SalePriceMM Sale price for MM
SalePriceCH Sale price for CH
PriceDiff Sale price of MM less sale price of CH
Store7 A factor with levels No and Yes indicating whether the sale is at Store 7
PctDiscMM Percentage discount for MM
PctDiscCH Percentage discount for CH
ListPriceDiff List price of MM less list price of CH
STORE Which of 5 possible stores the sale occured at

 

 

 

 

Basic summary statistics of the OJ data frame

##  Purchase WeekofPurchase     StoreID        PriceCH         PriceMM

##  CH:653   Min.   :227.0   Min.   :1.00   Min.   :1.690   Min.   :1.690

##  MM:417   1st Qu.:240.0   1st Qu.:2.00   1st Qu.:1.790   1st Qu.:1.990

##           Median :257.0   Median :3.00   Median :1.860   Median :2.090

##           Mean   :254.4   Mean   :3.96   Mean   :1.867   Mean   :2.085

##           3rd Qu.:268.0   3rd Qu.:7.00   3rd Qu.:1.990   3rd Qu.:2.180

##           Max.   :278.0   Max.   :7.00   Max.   :2.090   Max.   :2.290

##      DiscCH            DiscMM         SpecialCH        SpecialMM

##  Min.   :0.00000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000

##  1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000

##  Median :0.00000   Median :0.0000   Median :0.0000   Median :0.0000

##  Mean   :0.05186   Mean   :0.1234   Mean   :0.1477   Mean   :0.1617

##  3rd Qu.:0.00000   3rd Qu.:0.2300   3rd Qu.:0.0000   3rd Qu.:0.0000

##  Max.   :0.50000   Max.   :0.8000   Max.   :1.0000   Max.   :1.0000

##     LoyalCH          SalePriceMM     SalePriceCH      PriceDiff       Store7

##  Min.   :0.000011   Min.   :1.190   Min.   :1.390   Min.   :-0.6700   No :714

##  1st Qu.:0.325257   1st Qu.:1.690   1st Qu.:1.750   1st Qu.: 0.0000   Yes:356

##  Median :0.600000   Median :2.090   Median :1.860   Median : 0.2300

##  Mean   :0.565782   Mean   :1.962   Mean   :1.816   Mean   : 0.1465

##  3rd Qu.:0.850873   3rd Qu.:2.130   3rd Qu.:1.890   3rd Qu.: 0.3200

##  Max.   :0.999947   Max.   :2.290   Max.   :2.090   Max.   : 0.6400

##    PctDiscMM        PctDiscCH       ListPriceDiff       STORE

##  Min.   :0.0000   Min.   :0.00000   Min.   :0.000   Min.   :0.000

##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.140   1st Qu.:0.000

##  Median :0.0000   Median :0.00000   Median :0.240   Median :2.000

##  Mean   :0.0593   Mean   :0.02731   Mean   :0.218   Mean   :1.631

##  3rd Qu.:0.1127   3rd Qu.:0.00000   3rd Qu.:0.300   3rd Qu.:3.000

##  Max.   :0.4020   Max.   :0.25269   Max.   :0.440   Max.   :4.000

 

(Answers max 30 characters per question)

 

  1. How many stores are available in the dataset?
  2. How many weeks does the dataset cover?
  3. Which one of the two orange juice products is more expensive on average?
  4. Which one of the two orange juice products is more often on special offer?
  5. Which one of the two orange juice products has the greatest discount percentage on average?
  6. How are prices, discounts, and sales prices related in the dataset?

 

Sale prices histograms for the Citrus Hill and Minute Maid Orange Juices.

 

 

(Answers max 500 characters per question)

 

  1. Based on the above summary and histograms, what is your initial assessment concerning the quality relationship between the two products?

 

  1. Based on the above, what is your assessment concerning the pricing strategies followed by the firms in the market?

 

Product Market Shares

 

Examine the market shares for each orange juice product and the market power of the producing firms.

summary of sharesCH and sharesMM data.

##                CH        MM## Min.    0.2121212 0.1250000## 1st Qu. 0.5000000 0.2794444## Median  0.6372180 0.3627820## Mean    0.6057768 0.3942232## 3rd Qu. 0.7205556 0.5000000## Max.    0.8750000 0.7878788

  1. Based on the above, which product has the larger market share on average? How do you interpret the result?

(Answers max 500 characters per question)

  1. Based on the above, which product has more weekly purchases more often? How do you interpret the result? Is this result in line with your interpretation of market shares?

 

  1. Do you observe a date at which the behavior of the purchases of the two products changes? Are your interpretations in questions 1 and 2 driven by the whole sample? Are they driven or from a subset of dates in the sample?

 

 

Market Estimation

 

Estimating a market-clearing model using panel data and examining the resulting demand and supply elasticities for both Citrus Hill and Minute Maid Orange Juice.

 

Estimates of the market model for the Citrus Hill data.

## Equilibrium Model for Markets in Equilibrium:##   Demand RHS        :   D_SalePriceCH + D_SalePriceMM +    D_WeekofPurchase##   Supply RHS        :   S_SalePriceCH + S_WeekofPurchase + S_SpecialCH##     + S_StoreID##   Market Clearing   : NoPurchases = D_NoPurchases = S_NoPurchases##   Shocks            : Correlated##   Nobs              : 653##   Sample Separation : Not Separated##   Quantity Var      : NoPurchases##   Price Var         : SalePriceCH##   Key Var(s)        : StoreID, WeekofPurchase##   Time Var          : WeekofPurchase## ## Maximum likelihood estimation:##   Method              : BFGS##   Convergence Status  : success##   Starting Values     :##    D_SalePriceCH          D_CONST    D_SalePriceMM D_WeekofPurchase ##       -27.285550        26.221912         1.888320         0.095356 ##    S_SalePriceCH          S_CONST S_WeekofPurchase      S_SpecialCH ##        33.089373       -58.766139         0.007735        11.647788 ##       S_StoreID2       S_StoreID3       S_StoreID4       S_StoreID7 ##        -1.378343        -4.403546        -4.351425         4.342338 ##       D_VARIANCE       S_VARIANCE              RHO ##        11.914957        23.541607        -0.202668 ## ## Coefficients:##                      Estimate Std. Error    z value      Pr(>|z|) ##  D_SalePriceCH    -31.55390901 1.52064629 -20.750328  1.217585e-95 ***##  D_CONST           32.50536839 3.54508561   9.169135  4.768300e-20 ***##  D_SalePriceMM      2.48326026 0.67694951   3.668309  2.441596e-04 ***##  D_WeekofPurchase   0.09616766 0.01025188   9.380487  6.566858e-21 ***##  S_SalePriceCH     27.03270999 1.18338671  22.843513 1.695317e-115 ***##  S_CONST          -50.97312757 1.33755482 -38.109188  0.000000e+00 ***##  S_WeekofPurchase   0.01678551 0.01346038   1.247031  2.123860e-01  ##  S_SpecialCH        9.96840294 0.55663702  17.908264  1.016563e-71 ***##  S_StoreID2        -0.83092819 0.61990117  -1.340420  1.801087e-01  ##  S_StoreID3        -2.68217094 0.71065990  -3.774198  1.605235e-04 ***##  S_StoreID4        -2.24175614 0.67065001  -3.342662  8.297898e-04 ***##  S_StoreID7         5.43156610 0.57886201   9.383179  6.401268e-21 ***##  D_VARIANCE        14.18923357 1.24852964  11.364755  6.263989e-30 ***##  S_VARIANCE        18.72063266 1.26470325  14.802391  1.413657e-49 ***##  RHO               -0.26716528 0.05220004  -5.118105  3.086211e-07 ***## —## Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1## ## -2 log L: 1986.905

Corresponding plot

 

Estimates the market model for the Minute Maid Orange Juice data.

## Equilibrium Model for Markets in Equilibrium:##   Demand RHS        :   D_SalePriceMM + D_SalePriceCH +    D_WeekofPurchase##   Supply RHS        :   S_SalePriceMM + S_WeekofPurchase + S_SpecialMM##     + S_StoreID##   Market Clearing   : NoPurchases = D_NoPurchases = S_NoPurchases##   Shocks            : Correlated##   Nobs              : 417##   Sample Separation : Not Separated##   Quantity Var      : NoPurchases##   Price Var         : SalePriceMM##   Key Var(s)        : StoreID, WeekofPurchase##   Time Var          : WeekofPurchase## ## Maximum likelihood estimation:##   Method              : BFGS##   Convergence Status  : success##   Starting Values     :##    D_SalePriceMM          D_CONST    D_SalePriceCH D_WeekofPurchase ##         -4.05336          4.86909          2.29706          0.00738 ##    S_SalePriceMM          S_CONST S_WeekofPurchase      S_SpecialMM ##         12.81679        -18.01234         -0.01540          5.37839 ##       S_StoreID2       S_StoreID3       S_StoreID4       S_StoreID7 ##          0.17442         -1.46987         -3.31595          1.07991 ##       D_VARIANCE       S_VARIANCE              RHO ##          2.73589         16.22803          0.32686 ## ## Coefficients:##                      Estimate  Std. Error     z value      Pr(>|z|) ##  D_SalePriceMM     -4.16029559 0.655198389  -6.3496731  2.157729e-10 ***##  D_CONST            5.03677872 1.464823191   3.4384892  5.849699e-04 ***##  D_SalePriceCH      2.35378804 0.812712511   2.8962124  3.776967e-03 **##  D_WeekofPurchase   0.00710339 0.005344794   1.3290296  1.838382e-01  ##  S_SalePriceMM     11.20393559 0.460852032  24.3113512 1.486977e-130 ***##  S_CONST          -15.38509574 0.564571536 -27.2509235 1.620499e-163 ***##  S_WeekofPurchase  -0.01014977 0.004994532  -2.0321763  4.213581e-02 *##  S_SpecialMM        4.60431309 0.527088316   8.7353731  2.428532e-18 ***##  S_StoreID2        -1.01396030 0.619718139  -1.6361637  1.018053e-01  ##  S_StoreID3        -2.33929111 0.621746380  -3.7624523  1.682554e-04 ***##  S_StoreID4        -2.45869406 0.841625287  -2.9213643  3.485021e-03 **##  S_StoreID7         0.13272188 0.645712370   0.2055434  8.371476e-01  ##  D_VARIANCE         2.73202247 0.193621293  14.1101344  3.289505e-45 ***##  S_VARIANCE        13.97708062 0.574493295  24.3294060 9.578197e-131 ***##  RHO                0.40122479 0.104070105   3.8553318  1.155728e-04 ***## —## Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1## ## -2 log L: 1533.975

Corresponding plot

(Answers max 500 characters per question)

  1. What are the signs of the demand and supply price coefficients? Are they as expected?
  2. Which product’s demand is more elastic? How do you interpret this?
  3. Which product’s supply is more elastic? How do you interpret this?
  4. What are the signs of the estimated cross-price demand coefficients? Are the products substitutes or complements?

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