Introduction

In economics, there is a strong history trying to understand market behavior. Properly identifying a market demand function is hard, but various authors have studied fish markets as examples of markets where a relatively homogeneous good (fish) with a short lifespan (its quality deteriorates if not bought promptly) is sold in competitive regional markets, such as the fish markets at Saumaty in Marseille, France or MERITAN in Ancona, Italy. Alan Kirman has been involved in a lot of this work in the past few decades trying to understand the complex interactions that produce market demand functions from not particularly consisten individual demand functions. Härdle and Kirman (1995) was one of his first papers to study the Marseille fish market, which he returned to for his book (Kirman 2010). He has also done a variety of work with co-authors on fish markets, such as that on the Ancona fish market (Gallegati et al. 2011). Prof Kirman has kindly provided me with the data from his Marseille studies and so we have the opportunity to look at this rather marvellous data set.

Go here on Moodle to download the data: https://moodle.smith.edu/mod/resource/view.php?id=405319
The codebook to understand what the data means is available on Moodle here: https://moodle.smith.edu/mod/resource/view.php?id=405318

library(tidyverse)

Import the data as follows. Notice that this is different to how we’ve historically imported data. This is because the data are in a .txt file and so we can’t use read.csv(). Instead, we use read_table() from the readr package in the tidyverse.

MarseilleBase <- read_table("../more/MARS.txt", col_names = FALSE)

## Parsed with column specification:
## cols(
##   X1 = col_character(),
##   X2 = col_double(),
##   X3 = col_character(),
##   X4 = col_double(),
##   X5 = col_character(),
##   X6 = col_character(),
##   X7 = col_double(),
##   X8 = col_double()
## )

Look at the .txt file. Why do you think we had to specify the option col_names = FALSE?

head() the data to look at it. It has an issue in one column (find the issue)

head(MarseilleBase)

## # A tibble: 6 x 8
##   X1       X2 X3                     X4 X5    X6       X7    X8
##   <chr> <dbl> <chr>               <dbl> <chr> <chr> <dbl> <dbl>
## 1 002   18064 ESCALE BASTIA 1002 880105 05415 077     110  4000
## 2 002   18070 ESCALE BASTIA 1002 880105 05415 044     120  2200
## 3 002   18078 PSS DE L'OPERA1002 880104 05505 214      90  6500
## 4 002   18081 GENTY PERTUIS 1002 880105 10080 214     150  6500
## 5 002   18085 MONTLAUR      1002 880102 10090 077     205  3600
## 6 002   18088 MONTLAUR      1002 880102 10090 044      60  1800

As you can see, we need to solve this problem. We can do this using the separate() function in dplyr, which is part of the tidyverse.

Marseille <- 
  MarseilleBase %>% 
  separate(X3, c("X3a", "X3b"), sep = 14)
head(Marseille)

## # A tibble: 6 x 9
##   X1       X2 X3a              X3b       X4 X5    X6       X7    X8
##   <chr> <dbl> <chr>            <chr>  <dbl> <chr> <chr> <dbl> <dbl>
## 1 002   18064 "ESCALE BASTIA " 1002  880105 05415 077     110  4000
## 2 002   18070 "ESCALE BASTIA " 1002  880105 05415 044     120  2200
## 3 002   18078 PSS DE L'OPERA   1002  880104 05505 214      90  6500
## 4 002   18081 "GENTY PERTUIS " 1002  880105 10080 214     150  6500
## 5 002   18085 "MONTLAUR      " 1002  880102 10090 077     205  3600
## 6 002   18088 "MONTLAUR      " 1002  880102 10090 044      60  1800

What did I do above?

Create a new data frame called Marseille
Using the data frame MarseilleBase
I use separate on the variable X3
I ask separate to create two new variables: X3a and X3b
Because the txt file has the names of the buyers limited to 14 characters, I ask separate to separate the variables at the 14th character
I can now work with this data frame and rename my variables sensibly.

Marseille <- 
  Marseille %>%
  rename(sellerb = X1, 
         lot = X2, 
         nbuyer = X3a,
         seller = X3b,
         date = X4, 
         buyerc = X5, 
         fish = X6, 
         tempa = X7, 
         tempb = X8) 
Mars <- 
  Marseille %>%
  mutate(weight = tempa/10, 
         price = tempb/100, 
         fish = parse_number(fish))
head(Mars)

## # A tibble: 6 x 11
##   sellerb   lot nbuyer  seller   date buyerc  fish tempa tempb weight price
##   <chr>   <dbl> <chr>   <chr>   <dbl> <chr>  <dbl> <dbl> <dbl>  <dbl> <dbl>
## 1 002     18064 "ESCAL… 1002   880105 05415     77   110  4000   11      40
## 2 002     18070 "ESCAL… 1002   880105 05415     44   120  2200   12      22
## 3 002     18078 PSS DE… 1002   880104 05505    214    90  6500    9      65
## 4 002     18081 "GENTY… 1002   880105 10080    214   150  6500   15      65
## 5 002     18085 "MONTL… 1002   880102 10090     77   205  3600   20.5    36
## 6 002     18088 "MONTL… 1002   880102 10090     44    60  1800    6      18

DO NOT run the code below yourselves.
The sample size is huge and we don’t want to overload the server.
Just look at the plot. What does it suggest?
What does the line correspond to?
What kind of pattern are you able to see?

Mars %>% 
  ggplot(aes(x = weight, y = price)) + 
  geom_point() + 
  stat_smooth(method = "lm", formula = y ~ x,  size = 1) +
  ylim(0, 100)

Note, we don’t need a linear downward-sloping function…

(Again DO NOT RUN THIS CODE)

Mars %>% 
  ggplot(aes(x = weight, y = price)) + 
  geom_point() + 
  stat_smooth(method = "auto", size = 1) +
  ylim(0, 100)

A basic linear regression

Notice that you can run a linear regression with the whole sample of fish:

m1 <- lm(price ~ weight, data = Mars)
summary(m1)

## 
## Call:
## lm(formula = price ~ weight, data = Mars)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -52.63 -20.45  -8.68  15.94 616.91 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 54.365659   0.065227  833.49   <2e-16 ***
## weight      -0.123012   0.001865  -65.97   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29.56 on 237159 degrees of freedom
## Multiple R-squared:  0.01802,    Adjusted R-squared:  0.01802 
## F-statistic:  4353 on 1 and 237159 DF,  p-value: < 2.2e-16

What is the sign on the coefficient for weight?
What is weight’s significance?
What does the relationship mean in terms of economic theory?

Filtering the Fish

Consult the Marseille Data Description document to check what the different kinds of fish are.

I have generated the following graph for one of the kinds of fish (Merlan) by filtering and then graphing the data.

Filtering for Merlan:

MarsFish44 <- 
  Mars %>%
  filter(fish == 44)

Graphing the Merlan data:

MarsFish44 %>% 
  ggplot(aes(x = weight, y = price)) + 
  geom_point() + 
  stat_smooth(method = "lm", formula = y ~ x, size = 1) +
  ylim(0, 100)

We can also run a linear regression just with the filtered Merlan data.

OLSMerlan <- lm(price ~ weight, data = MarsFish44)
summary(OLSMerlan)

## 
## Call:
## lm(formula = price ~ weight, data = MarsFish44)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -31.37  -8.03   0.45   7.45 345.26 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 33.461832   0.060521  552.90   <2e-16 ***
## weight      -0.181625   0.003097  -58.64   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.08 on 53679 degrees of freedom
## Multiple R-squared:  0.06021,    Adjusted R-squared:  0.06019 
## F-statistic:  3439 on 1 and 53679 DF,  p-value: < 2.2e-16

Do the following:

Choose a fish in which you are interested and construct a data frame that contains only that kind of fish.
Construct a plot for that fish’s quantity-price observations
Run a linear regression model of that fish’s price-quantity relationship
Summarize the regression output.
Submit your html of this later.

Multiple regression with dummy variables

We want to include dummy variables for the different kinds of fish in our regressions. So we need to check whether the fish variable is numeric or a factor. We could head() the data and see, but we can also get a “TRUE” or “FALSE” report using the is.numeric() or is.factor() functions.

is.numeric(Mars$fish) #This must be true because I made it numeric

## [1] TRUE

is.factor(Mars$fish) #This must be false unless you change it

## [1] FALSE

As you can see, we need to change fish into a factor variable because we want to use the factors as dummy variables.

How would you do this?
Do the variables have the labels you’d like them to have? (i.e. the names of the fish)
Is there a way to remedy this?

Some ideas for factors

We need to take the information from the Marseille Data Details document and create two sets of columns using the following idea: ObjectName <- c(content1, content2, ..., contentn).

I would recommend you call the one object (with the numbers) FishLevels because it corresponds to the levels of your factor variable.

I would recommend you call the second object FishLabels because it corresponds to the labels of the fish that you want.

You will then use the function factor() inside the function mutate() (which you already know).

You would then do something like the following (note this won’t work because I don’t have actual values attributed to these objects yet).

MarsFactorFish <- 
  Mars %>% 
  mutate(fishvariablename = factor(fishvariablename, 
                                   levels = FishLevels, 
                                   labels = FishLabels))

You should get something like the following when you head your data:

FishLabels <- c("Merlan", "Carrelet", "Cabillaud", "Loup/Bar", " Raie Ange", "Raie (Entiere)", "Sole", "Turbot", "Cabillaud (Tranches)", "Sole (Filet)", "Annarrhyque (Filets)", "Loup (Filets)")
FishLevels <- c(44, 62, 77, 122, 204, 205, 214, 244, 285, 289, 314, 315)
Mars <- 
  Mars %>%
  mutate(fish = factor(fish, 
                       levels = FishLevels, 
                       labels = FishLabels))
head(Mars)

## # A tibble: 6 x 11
##   sellerb   lot nbuyer  seller   date buyerc fish  tempa tempb weight price
##   <chr>   <dbl> <chr>   <chr>   <dbl> <chr>  <fct> <dbl> <dbl>  <dbl> <dbl>
## 1 002     18064 "ESCAL… 1002   880105 05415  Cabi…   110  4000   11      40
## 2 002     18070 "ESCAL… 1002   880105 05415  Merl…   120  2200   12      22
## 3 002     18078 PSS DE… 1002   880104 05505  Sole     90  6500    9      65
## 4 002     18081 "GENTY… 1002   880105 10080  Sole    150  6500   15      65
## 5 002     18085 "MONTL… 1002   880102 10090  Cabi…   205  3600   20.5    36
## 6 002     18088 "MONTL… 1002   880102 10090  Merl…    60  1800    6      18

Fish Factors in the Multiple Regression

Now, include the fish variables as factors in our regression

m2 <- lm(price ~ weight + fish, data = Mars)
summary(m2)

## 
## Call:
## lm(formula = price ~ weight + fish, data = Mars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -108.07   -7.61   -0.01    8.19  559.08 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               32.373332   0.070891 456.665  < 2e-16 ***
## weight                    -0.071872   0.001057 -67.992  < 2e-16 ***
## fishCarrelet             -15.228267   0.416955 -36.523  < 2e-16 ***
## fishCabillaud             -0.762175   0.111204  -6.854 7.21e-12 ***
## fishLoup/Bar              79.294592   0.126323 627.712  < 2e-16 ***
## fish Raie Ange             4.903407   0.128050  38.293  < 2e-16 ***
## fishRaie (Entiere)        19.105380   3.316580   5.761 8.39e-09 ***
## fishSole                  33.302315   0.090079 369.702  < 2e-16 ***
## fishTurbot                40.010028   0.247857 161.424  < 2e-16 ***
## fishCabillaud (Tranches)   9.517823   0.630584  15.094  < 2e-16 ***
## fishSole (Filet)          46.448343   0.683419  67.965  < 2e-16 ***
## fishAnnarrhyque (Filets)  12.531891   0.299675  41.818  < 2e-16 ***
## fishLoup (Filets)         13.706294   0.208501  65.737  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.24 on 237042 degrees of freedom
##   (106 observations deleted due to missingness)
## Multiple R-squared:  0.7036, Adjusted R-squared:  0.7036 
## F-statistic: 4.689e+04 on 12 and 237042 DF,  p-value: < 2.2e-16

What do the different coefficients on the categorical (dummy) variables mean?
Can you provide new output for the fish regressions using stargazer?

m3 <- lm(price ~ weight + fish + weight*fish, data = Mars)
summary(m3)

## 
## Call:
## lm(formula = price ~ weight + fish + weight * fish, data = Mars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -108.88   -7.86   -0.03    8.04  559.41 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      33.461832   0.080694 414.676  < 2e-16 ***
## weight                           -0.181625   0.004130 -43.982  < 2e-16 ***
## fishCarrelet                    -16.045520   0.509098 -31.518  < 2e-16 ***
## fishCabillaud                    -2.939527   0.122115 -24.072  < 2e-16 ***
## fishLoup/Bar                     79.198454   0.148148 534.591  < 2e-16 ***
## fish Raie Ange                    4.262459   0.149862  28.443  < 2e-16 ***
## fishRaie (Entiere)               35.941919   5.033931   7.140 9.36e-13 ***
## fishSole                         33.210235   0.101279 327.908  < 2e-16 ***
## fishTurbot                       40.505680   0.298213 135.828  < 2e-16 ***
## fishCabillaud (Tranches)          8.618767   0.969096   8.894  < 2e-16 ***
## fishSole (Filet)                 46.469263   0.737629  62.998  < 2e-16 ***
## fishAnnarrhyque (Filets)          9.922578   0.332157  29.873  < 2e-16 ***
## fishLoup (Filets)                11.438594   0.224946  50.850  < 2e-16 ***
## weight:fishCarrelet               0.085692   0.026419   3.244  0.00118 ** 
## weight:fishCabillaud              0.156957   0.004408  35.610  < 2e-16 ***
## weight:fishLoup/Bar              -0.017133   0.009590  -1.787  0.07400 .  
## weight:fish Raie Ange             0.037671   0.011757   3.204  0.00135 ** 
## weight:fishRaie (Entiere)        -4.018855   0.877712  -4.579 4.68e-06 ***
## weight:fishSole                   0.019803   0.004686   4.226 2.38e-05 ***
## weight:fishTurbot                -0.033145   0.015344  -2.160  0.03076 *  
## weight:fishCabillaud (Tranches)   0.098372   0.044602   2.206  0.02742 *  
## weight:fishSole (Filet)          -0.086347   0.051126  -1.689  0.09124 .  
## weight:fishAnnarrhyque (Filets)   0.149352   0.005607  26.634  < 2e-16 ***
## weight:fishLoup (Filets)          0.150366   0.004985  30.164  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.11 on 237031 degrees of freedom
##   (106 observations deleted due to missingness)
## Multiple R-squared:  0.7085, Adjusted R-squared:  0.7085 
## F-statistic: 2.505e+04 on 23 and 237031 DF,  p-value: < 2.2e-16

What does the model say? (that is, interpret the equation of the regressionl line)
What is an interaction term?
What do the coefficients on each of the variables mean now?

References

Gallegati, Mauro, Gianfranco Giulioni, Alan Kirman, and Antonio Palestrini. 2011. “What’s That Got to Do with the Price of Fish? Buyers Behavior on the Ancona Fish Market.” Journal of Economic Behavior & Organization 80 (1): 20–33. doi:https://doi.org/10.1016/j.jebo.2011.01.011.

Härdle, Wolfgang, and Alan Kirman. 1995. “Nonclassical Demand: A Model-Free Examination of Price-Quantity Relations in the Marseille Fish Market.” Journal of Econometrics 67 (1): 227–57. doi:https://doi.org/10.1016/0304-4076(94)01634-C.

Kirman, Alan. 2010. Complex Economics: Individual and Collective Rationality. Routledge.