How does price dispersion change with the number of sellers:
An investigation on the German Television market.
Diane Stiemer 10194134
University of Amsterdam
Faculty of Economics and Business Supervisor: dhr. dr. A.P. Kiss
Abstract
In this paper it is investigated what effect the number of sellers will have on the level of price dispersion. Buying products online has lowered search costs, close to zero. Low search costs would imply Bertrand pricing and therefore virtually no price dispersion. However, studies have shown that price dispersion is still present. In this research I investigate if this price dispersion is affected by the number of sellers. In order to do this I used data from a price comparison website. I
performed regressions with the level of price dispersion as the dependent variable and dummy variables for each number of sellers. From this I find that price dispersion increases as the number of sellers increases. However, this does seem to depend on the way price dispersion is measured. Also adding just a single seller doesn't have a significant effect, but adding more sellers eventually does have a big impact. Overall I conclude that the relationship between the number of sellers and the level of price dispersion is a positive relationship.
Statement of Originality
This document is written by Student Diane Stiemer who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
1. Introduction
Since the early 2000's online purchases have become more and more important(CBS, 2016). For electronic devices such as computers and TV's, there has even been a shift. Online purchases have risen and offline purchases have decreased. For example in the Netherlands, online purchases in the first quarter of 2016 have risen by 34% compared to the same period in 2015 (CBS, 2016). Also the number of firms that sell online have risen by 23% in four years (CBS, 2016). Buying electronics online is mostly populair because it is easy for consumers to see all products that are available and also for which price they are being sold. This makes it easy for them to compare the different prices of a single product at different sellers. According to Bertrand pricing, this would eliminate all differences in prices and all sellers would sell a product for the same price. However, price comparison websites offer an insight into these prices and often list a whole bunch of different prices for the same product. The differences between these prices is called the price dispersion. Previous research suggested that this price dispersion could change with the number of sellers that have been listed ( Clemons et all, 1998; Baye, Morgan and Scholten, 2002; Gerardi and Shapiro, 2007, Montgomery et all, 2007). Since the results of these studies aren't clear, in this research I will investigate how price dispersion changes with the number of sellers.
To do this I use a dataset from a price comparison website. I use three different ways to measure the level of price dispersion. On these three measures I will investigate what kind of effect the different number of sellers have. I create dummy variables for each different number of sellers. Then I perform regressions with the level of price dispersion as the dependent variable and the dummy variables as the explanatory variables. In order to control for some time effect, I will extent the regressions with dummy variables for how long a product is up for sale. Then I will also add the minimum price of each product in the regression to control for different pricing strategies at the different price levels. In a next regression I will also control for pricing strategies of the different brands, by adding dummy variables for the different brands. As a robustness check I will do these regressions again, but then I include the shipping costs in the price.
From these regressions the relationship between the number of sellers and the level of price dispersion seems to be positive. For two measures of price dispersion the level of price dispersion clearly increases as more sellers enter the market. For the third measure of price dispersion the results are a little ambiguous. Including the shipping costs in the total price, doesn't affect the results, which leads to the believe that the results are robust. Adding the time dummies to the
coefficient is close to zero. The different brands do give significant results. This leads to the believe that different brands set different pricing strategies.
I used data from a German price comparison website, called billiger.de. This data was retrieved from April 2012 until February 2013. In this dataset for all products the different prices at different sellers can be found. The dataset contains 455 different products. The different dates were used to derive the number of days that a product is up for sale and the lifecycle of the different products. Price dispersion is measured in three ways; the difference between the highest and the lowest price, the difference between the average price and the lowest price and the difference between the two lowest prices. In this dataset a product has at most 44 different sellers.
The outline of this paper will be as follows. In part two the results of previous research will be discussed. From this two hypotheses will be derived. In part three the details of the data and the characteristics of the different variables will be described. After this, in part four, the methodology that is used to answer the research question, will be elaborated. In part five the results will be presented and explained. Then in part six the conclusion will be outlined. The paper ends with the references and some attachments.
2. Literature review
Earlier studies have examined whether the 'law of one price' actually occurs in real life (Clemons et all, 1998; Baye, Morgan and Scholten, 2002; Gerardi and Shapiro, 2007, Montgomery t all, 2007). Most of these studies have been done by looking at price comparison websites. These price
comparison websites allow the user to do a product search on a specific product. The website will then give back a list of all suppliers that are offering this product and at what price they offer it. Picture 2.1 is an example of what a price comparison website looks like. Once a single product has been selected, the website will give back a list of different vendors that offer this product and at what price they offer this product.
Picture 2.1
Presentation of the website billiger.de
Since it is easy to compare the different vendors that sell this product, searching different vendors becomes fairly costless. This way consumers can be fully informed. Another aspect of these websites is that the location of the shop becomes irrelevant. Stores all over the country and sometimes maybe even all over the world can compete with each other on these websites. Robert Kuttner (1998) even said in Business Week:
'The internet is a nearly perfect market because information is instantaneous and buyers can compare the offerings of sellers worldwide. This will result in fierce price competition, dwindling product differentiation and vanishing brand loyalty.'
That is why most papers look at price comparison websites. Brynjolfsson and Smith (2000) investigated the difference between price dispersion offline and online. They look at the prices for books and cds. These are homogeneous goods, which according to the model by Bertrand, could result in fierce price competition. They do find that the online prices are lower than offline prices, which indeed suggests higher price competition. Since online selling also reduces search costs, the law of one price would state that there is just one single price in the market. However, Brynjolfsson and Smith (2000) do find some substantial differences in prices across online suppliers and this price dispersion would not be in line with Bertrand pricing. Prices of books differ by an average of
larger than the range of offline prices in 87% of the cases. When they look at weighted prices, price dispersion becomes smaller but is still present. They conclude that price dispersion still can be due to some heterogeneity, for example heterogeneity in customer awareness or retailer branding and trust.
Baye, Morgan and Scholten (2002) suggest that price dispersion might be a disequilibrium and not a phenomenon that is always present. If it is indeed a disequilibrium it will be corrected over time. They use online data on the market for consumer electronic products. This data is retrieved from the price comparison website Shopper.com. They compare daily price quotes. They find little evidence that price dispersion is in fact a disequilibrium. Contrary to their believes, they find that price dispersion is persistent and depends on market structure. Also they find that an increase of the usage of the internet will not result in lower price dispersion.
One reason for price dispersion to occur could be some heterogeneity in the product. A research on Online Travel Agencies (OTA's) finds that the highest price agent is 25% more
expensive than the lowest price agent, even when customer requests are exactly the same (Clemons et all., 1998). To see if this price dispersion can be due to heterogeneity Clemons et al (1998) performed a second regression. In this second investigation they account for quality differences, which indeed leads to a drop in price dispersion. However, there is still a price dispersion of 20% left. This would lead to the conclusion that price dispersion is always present. But, Clemons et all (1998) do point out that products with complex characteristics enable producers to avoid the outcome of pure price competition through product differentiation. Even if this product
differentiation is only perceived by consumers. This would mean that even though the product is homogeneous, there might be some differences that are due to the different vendors. For example a high rating or low shipping costs could result in a higher willingness to pay from the consumer's side. So as the number of sellers goes up, also differentiation goes up. This heterogeneity would then cause price dispersion between different vendors (Clemons et all., 1998). This leads to the first hypothesis that as the number of sellers increases, price dispersion will also increase.
The number of sellers could also affect price dispersion in a different way. If the market contains only a few number of sellers, there might not be enough competition that enforces a general equilibrium price. Also, if there are more sellers in the market, this has the tendency to increase the price elasticity among sellers, which reduces prices. This increase in elasticity compels prices towards marginal costs. When this happens for all sellers, their price dispersion will fall (Barron et all, 2004). Previously mentioned Baye, Morgan and Scholten (2002) incorporated this potential effect in their research. It showed that the level of price dispersion is greater when a small
number of firms lists prices, compared to when a large number of firms does. When there are 2 firms that offer the product, the gap between their prices is 23% and when 17 firms offer the product the gap between the two lowest is only about 3,5%. This suggests that the number of firms is indeed an influencing factor on the level of price dispersion. Another research done by Gerardi and Shapiro (2002) also investigates the effect of an increasing amount of sellers. They use panel data of online travel agencies and find that price dispersion becomes smaller as a new supplier enters the market. This effect will be strongest on markets where first price discrimination takes place; in their data they discriminate between leisure and business travel. Also the effect of a new supplier on the market is bigger during peaks in the business cycle. Montgomery et all (2007) have two ways to measure price dispersion. When they measure price dispersion as the standard
deviation of the mean price, they find a positive relationship between the number of sellers and price dispersion. But when they measure price dispersion as the difference between the two lowest observations, they find a negative relation between the number of sellers and price dispersion. This leads to the second hypothesis of this research, which is: as the number of sellers increases, price dispersion will decrease.
The two hypotheses in this research are contradicting. The first hypothesis states that as the number of sellers increases, heterogeneity increases and so price dispersion increases. The second hypothesis states that as the number of sellers increases, competition increases, which results in lower price dispersion. In order to investigate which will actually be the case, the research question will be: “How does price dispersion change with the number of sellers?” Since more evidence points towards the second hypothesis (Montgomery et all, 2007; Gerardi and Shapiro, 2009; Baye, Morgan and Scholten, 2002; Barron et al, 2004), this will be the main hypothesis of this research. However, if the results are contradicting this hypothesis, price dispersion is clearly more affected by heterogeneity.
3. Data
To investigate whether the price dispersion depends on the number of sellers, I will use a dataset on TV's. This data was retrieved from the German price comparison website billiger.de1. Data was
collected for a period of nine months, starting at April 2012 and ending at February 2013. There are several variables in this dataset. Since I will look at price dispersion, the price is one of the most important variables in this dataset. From the data I find that the average price is 789.19, but the
between the highest price, which is 8144, and the lowest price, which is 99. This would suggest that the variety of the products in this dataset is very large. So even though only TV's are being
investigated, there is still some differentiation. To check for robustness I also made a figure of the distribution of the total price, which is the price plus shipping costs. This distribution can be found in figure 3.2.
Figure 3.1 Distribution of the price
Figure 3.2
Distribution of the price with shipping costs
There are more variables in this dataset, besides the price. Previously I mentioned the shipping costs, which are the costs that a seller sets to ship their products to the consumer. Two other
variables are the rating and the times that a vendor is rated. The rating is a number between zero and a hundred, which is given to a vendor by consumers. In the dataset we can also find an id for the vendor and an id for the product. These two variables will only be used to create other variables, which are either seller specific or product specific. One variable that depends on both is the number of sellers. This is a variable that I will create by counting how many different vendors offer the same product at each day. The last important variable is the date.
A variable that I had to create is the time that a product is up for sale. This variable lists the number of days that a product can be bought from this price comparison website. It will be used to see how the number of sellers can change over time. It will also be used to create time dependent dummy variables. To create this variable I took the difference between each date and the first date that the product came up in the dataset. Since I do not know when the products that are already present at the first day of the dataset, became available on the market, I had to dismiss all these products. This left me with a dataset where all products became available on the price comparison website at some point between April 2012 and Februray 2013. Then in order to see how long a product is actually up for sale, the product also had to go out of sale somewhere within the dataset. For products that are still in the dataset at the last day, it is unclear how long they will be up for sale after the dataset has ended. Therefore I also dismissed the products that are still up for sale at the last day of the dataset. Then all the products that were left started and ended selling somewhere within the current dataset. The mean of the number of days that a product is up for sale in this dataset is about 93 days. From this variable the lifecycle in days of each product, could be retrieved. There are 455 different products in this dataset. The distribution of the lifecycle of the different products can be found in figure 3.3. The average lifecyle of all observations in this dataset is close to 200 days.
Figure 3.3
Distribution of the lifecycle of the different products
After this I created a variable which enlisted the number of different sellers of a single product at each day. This variable then lists how many sellers sell a given product at each day. The distribution of the number of sellers is in figure 3.4 The average number of sellers is 13.2.
Figure 3.4
Distribution of the number of sellers
In figure 3.5 we can see how the number of sellers changes as a product is up for sale for a longer period of time. On the x-axis we see the number of days that a product is up for sale, which is just the variable that was created before. On the y-axis we see the mean of the number of sellers by the time that a product is up for sale.
Figure 3.5
How the number of sellers changes with over the time that a product is up for sale
From this figure we can see that the the number of sellers increases at the start of the sale. But after about a hundred days the number of sellers decreases. At around 180 days the number of sellers makes a relatively big drop. This could be the result of a drop in average prices, that occurs just
before this drop. This can be seen in figure 3.6.
Figure 3.6
Average prices between 150 and 210 days
This decrease in prices could make sellers drop out of the market. Another possibility is that this decrease in prices is an indication that sellers set their products up for sale at this point in the lifecycle. This could mean that the actual lifecycle would be around 180 days and all sales after this point are just to sell the leftover stock. However, these are all speculations, the actual reason for this sudden drop in the number of sellers is hard to determine from the dataset. It is interesting to notice that prices go up again after the sellers at 180 days have dropped out.
There are different ways to measure price dispersion. One way, for example, could be the difference between the highest and the lowest price. Another way could be the difference between the lowest and the daily average for each product. A study by Baye et all (2001) suggests that price dispersion should be measured as the difference between the two lowest prices, so this has also been included. In the previously mentioned research by Brynjolfsson and Smith (2000) weighted prices gave a smaller and more true measure of price dispersion. So in this research price dispersion will be computed as a percentage of the lowest price. Statistics about these different measures are given in table 3.1. Graphical presentations of these distribution are in figures 3.7, 3.8 and 3.9.
Table 3.1
Figure 3.7 Figure 3.8
Distribution difference highest and lowest price Distribution difference average and lowest price
Figure 3.9
Distribution difference two lowest prices
From table 3.1 it becomes clear that the highest price is on average 25% higher than the lowest price. Also the average price is 7,5% higher than the lowest price. The second lowest price is on average 3% higher than the lowest price. The minimum for all is zero since for some products, there are only two sellers that set the same price. In figures 3.10, 3.11 and 3.12 we see a scatterplot of each of these measures of price dispersion and how it coincides with the number of sellers. We see the number of sellers at the x-axis. At the y-as we see the average price gap.
Figure 3.10 Figure 3.11
Difference between highest and lowest price Difference between the average and lowest price
Figure 3.12
Difference between the two lowest prices
From these figures it seems that as the number of sellers increases, also the dispersion in prices becomes larger. This is an interesting result since it contradicts the main hypothesis. Regressions have to be performed in order to see if this relationship between price dispersion and the number of sellers is indeed positive.
There is a number of different products in this dataset. In total there are 455 different products. However, there are only a nine brands. Table 3.2 provides an overview of the different brands and how many products each has times in this dataset. We see that Samsung has the biggest share of the market and Thomson sells the least products.
Table 3.2
Statistics about the different brands
4. Methodology
In order to investigate if price dispersion actually changes with the number of sellers I have to do a regression. To see if the results will hold for all three measures of price dispersion, I will do this regression for all three measures. To investigate what kind of effect the number of sellers has, I should create dummy variables. There will be 44 dummy variables. The first one will be numbrsellers2 which will be equal to one if the number of sellers is two. Then we have numbrsellers3 which will be one if the number of sellers is equal to three. Then we have
numbrsellers4 etc. The last dummy variable will be equal to one if the number of sellers is equal to 44. The first linear regression that will be done, will look like:
PRICERANGEit = β0 +Σ βj*Numbersellersjit + εit
In this regression 'j' will be the 43 different dummy variables for the different number of sellers, 'i' will refer to the different products and 't' will be the different days. It is assumed that the number of sellers influences the price dispersion, but price dispersion doesn't affect the number of sellers. Here I assume that the number of sellers is an exogeneous variable. However, it could be the case that the number of sellers is actually enodogeneous. This would imply that the level of price dispersion either attracts or repels sellers and therefore price dispersion influences the number of sellers. However,from this dataset we cannot observe causality. So for simplicity I will assume that the number of sellers influences the level of price dispersion and not the other way around. But it should be noted that we cannot be completely sure of this. Another assumption is that the error is uncorrelated with the other variables within the regression.
regression that will show the relationship between the number of sellers and the range in prices. The last dummy, for all observations that are equal to 44, has been left out. This is done to avoid the dummy trap. This also means that all results I find for the other dummies, have to be compared to the last dummy. This means that if price dispersion decreases with the number of sellers, then all beta's have to be positive. If price dispersion would increase with the number of sellers then all beta's will be negative.
The results from this regression will probably be higher than the impact of the number of sellers actually is. This is because some other things may change simulateneously with the number of sellers, like other effects that change over time. Baye, Morgan and Scholten (2002) suggested that price dispersion is a disequilibrium, that might dissolve over time. This would lead to the believe that time can be of influence on it's own. So in order to control for some other time effects, there will be dummy variables on time in this regression. I created a dummy variable for each month that a product is up for sale. This resulted in 10 dummy variables for time. In the next regression I included nine of these dummy variables. The 10th month has been left out to avoid the
dummy trap.This also has to be done for all different measures of price dispersion. In this
regression all effects that time will have on the price dispersion will be investigated. This will then also give a more clear result in the beta for the number of sellers, which will probably be closer to zero than in the first regression.
Until now I assumed that price dispersion could be constant over all products. However, this might not be the case. Price dispersion could be lower in the products with a relatively low price. If prices are low, price elasticity is high and consumers might not be willing to pay even the slightest bit extra (Barron et all, 2004). To control for this effect, in the third regression I will include the minimum price. This would make the results of the other variables independent of the different prices.
Another factor that might influence the level of price dispersion is the brand of the TV. Different brands could have different pricing and selling strategies. If one brand only sells their product through one distributor, then all vendors buy their product for the same price. The only factor that influences price dispersion in this case are the pricing strategies of the different vendors. However, if a brand sells their product through different distributors, the price that a vendor pays can also differ. In this case the price dispersion that the consumer faces could increase. Therefore in the fourth regression I will include dummy variables for the different brands. Again, in order to control for the effect the price level could have, I will still include the minimum price. The dummy
In the last regression all variables that have previously been mentioned, will be included. This last regression is the most extensive and will probably give the most clear results. In this regression all variables have been added. In this regression 'p' will be eight different brands, except for the brand Thomson. Then 'm' will be the first nine months and the tenth month has been left out. Also the minimum price was included. It will look like:
PRICERANGEit = β0 +Σ βj*Numbersellersjit + Σ δp*brandpit + Σ τm *monthmit + β61*minpriceit + εit
To do a robustness check, in a last set of regressions I redefine the prices. In the previous regression I only used the actual price of the different products. The shipping costs were not included in this price, but consumers do have to pay these costs. Since some consumers might let this extra costs for shipping, influence their decision on whether to buy a product at a single vendor, I will do the same regressions with the shipping costs included in the price. This will be done for all three measures of price dispersion, but only on the last most extensive regression.
5. Results
In table 1 of the attachments we see the first results. The dependent variable in table 1 is always the difference between the highest and the lowest price of each product at each day, as a percentage of the lowest price. A negative result in this table would mean that price dispersion is smaller,
compared to the case where there are 44 sellers in the market. In the first regression only the dummy variables for the number of sellers have been included. The constant in this regression is 59.06. This means that when there are 44 sellers in the market, their price dispersion is around 59%. When we look at the value of the coefficient for when there are only 2 firms in the market, we see that this has a value of -49.14. This means that the price dispersion is around ten percent when there are only two sellers. The value of the coefficients seems to be closer to zero as the number of sellers increases. Towards the end the coefficients even seem to become positive. This would mean that as the number of sellers increases, so does price dispersion. In figure 5.1 we see a graphic presentation of these results. The difference between two consecutive results isn't really significant. But when comparing a small number of sellers to a relatively large number of sellers, the result is clearly positive. When there are more than 38 sellers, the results seem to become very high, very instantly. These results are still significant, but there are only five different products that have this many sellers. The reason these results are significant is probably because there are a lot of observations, but since there is only a small number of products, the results might be biased.
Figure 5.1
Regression results on highest minus lowest price
When in the second regression the time dummies have been included, all coefficients seem to become less negative. To conclude that the effect is smaller, would be wrong, since the constant has also decreased to 56.84. Because previous research suggested that price dispersion could resolve over time (Baye, Morgan and Scholten, 2002), a time effect was included in this regression. The 10th month has been left out, so all coefficients should be compared to this month. The effect of
these time dummies isn't a clear one, since the results don't evolve linearly over time. Some of these time dummies aren't even significant. The time dummies do not seem to have that much effect on the level of price dispersion.
Lower prices could have a higher price elasticity, which could bring prices closer together (Barron et all, 2004). For this reason, in the next regression the I included the minimum price. This led to an increase in the constant to 58.05. The results of this regression are fairly similar to the previous case. The results are a little less negative, but then again the constant has increased. The value of the coefficient of the minimum price is only -0.003. It seems as though adding a price level to the regression isn't very effective. The price level doesn't seem to have an impact on the level of price dispersion.
the different brands, there seems to be relation between the brand and the level of price dispersion. The most negative value is for Philips, which has a coefficient of -9.526. This would mean that the level of price dispersion is almost ten percent lower when it concerns a TV from Philips compared to TV's from Thomson. Adding these different brands in the regression also increased the constant up to 66.36. Again, overall the effect of the number of sellers seems to be a positive one. It should be noted that the value of the coefficients stays very close to the results in the previous regression, even though the constant has increased.
In the last regression I have added all variables that could affect the level of price dispersion. The constant is 65.38, which is still on the high site. In this case too, the number of sellers seems to have a positive effect on the level of price dispersion. Surprisingly enough, adding extra variables doesn't seem to do much for the significance of the coefficients of the number of sellers. The effect of the time variables seems to be that price dispersion grows over time. However, this effect is very small, especially when compared to the constant of around 65. The effect of the different brands seems to increase slightly.
Overall from this regression I would conclude that price dispersion increases when the number of sellers increases. The time variables don't seem to have many effect, just like the price level. The different brands do have an effect on the level of price dispersion. The difference between different brands could even be close to ten percent.
In table 2 of the attachment is the second set of results. In these regressions the dependent variable is the difference between the average price and the lowest price. In the first regression I only included the dummy variables for the different number of sellers. At first there seems to be a clear increase in the level of price dispersion. This lasts until there are eightteen sellers in the market. When there are more sellers, the results aren't that clear anymore. There are some numbers that are very close to zero like -0.419, but there can also be some substantial difference, for example -3.533. In addition to the ambiguous results, most variables aren't significant anymore. When there is a relatively high number of sellers, the variables even become positive. These variables are significant. However, there are only five different products that have this many sellers. So even though the results are significant, the coefficients may be biased. When comparing a very small number of sellers with a very high number of sellers, it seems clear that the level of price dispersion goes up with the number of sellers. The results of this regression are in figure 5.2. Indeed the relationship seems to be a positive one, even though adding just one seller doesn't seem to have a significant effect.
Figure 5.2
Regression results on average minus lowest price
In the second regression I have added the time dummies again. This doesn't seem to effect the coefficients for the number of sellers all that much. An interesting point is that, contrary to the expectations, the results seem to become less significant by adding the time variables. The effect that the time dummies have on the level of price dispersion isn't clear at all. Even though most of the results are significant, no real conclusions can be derived from the results.
In the third regression I have added the minimum price to make sure that the price level will not influence the level of price dispersion. This doesn't seem to be the case, since the coefficient for the minimum price is only around -0.002, even though it is highly significant. However, this does slighty decrease the effect that the number of sellers has, since the values are closer to zero. But the positive relationship between the number of sellers and the level of price dispersion seems more prominent.
In the next regression I included the different brands, but left out the time dummies. To avoid the dummy trap I have left out the dummy for the brand Thomson. The results suggest that the different brands do have some different pricing strategy that influences the price dispersion. Price dispersion is smallest among Philips TV's, but Grundig is a very close second. The effect that
significant, but the conclusion would still be the same.
In the last regression I added all variables to the regression. This makes the results of the number of sellers less significant. Except for when there are a lot of sellers in the market, then the results are more significant. The overall effect is still that the level of price dispersion increases with the number of sellers. Again, the effect of the time dummies isn't clear and not always significant. Including all variables does seem to increase the effect of the different brands.
In table 3 of the attachments are the last results. In these regressions the dependent variable is the difference between the two lowest prices. In the first regression I have only included the dummy variables for the number of sellers. When there are only two sellers in the market, the level of price dispersion starts out high. The constant is close to zero, which would mean that the level of price dispersion is 9.920% when there are only two sellers in the market. There is an immediate drop, which suggests that adding more sellers in the market decreases the level of price dispersion. After this immediate drop, price dispersion stays around two percent for the most part. Only when more than thirty sellers enter the market, price dispersion starts to increase again. More towards the end, the high results seem unlikely. But since these results are based on only five different products, these findings could actually be insignificant. The only reason they are significant in this regression, is because there are a lot of observations.
Figure 5.3
Figure 5.3 above shows these results. Indeed, price dispersion starts out high and is significantly different between two consecutive results. This could mean that the level of price dispersion decreases with the number of sellers, which is the opposite of what was found in the previous regressions. However, overall there doesn't seem to be a clear relation between the number of sellers and the level of price dispersion. It appears to be constantly at around two percent.
In the second regression I have added the time variables. This increases the significance that the number of sellers has on the level of price dispersion, but the results stay the same. The time dummies don't imply a clear trend. In the first few months price dispersion seems to increase. In the fifth month this trend disappears and the results become insignificant. So just like in the previous regressions a time effect isn't present. Adding the minimum price as a way to level out price differences, only affect the results slightly. The effect of the minimum price in itself is very minimal. In the fourth regression again I have added the different brands. The brands do influence the level of price dispersion. Of all the brands Grundig has the lowest level of price dispersion.
It could be argued that the number of sellers and the level of price dispersion have a negative relationship, but this effect is only present when there is a very small number of sellers. When looking at the overall trend, there doesn't seem to be any relation between the two. It does seem to be that price dispersion is always present at a level of about two percent. The time dummies don't have a clear effect. The different brands do have a different pricing strategy.
In table four of the attachments is the last set of regressions. These are the most extensive regressions that have been done before, but now the price is the total of the price of the product and the shipping costs. This has been done as a robustness check. The results are very close to the results that were found in the previous regressions. This would imply that the level of price dispersion isn't very sensitive to how prices are measured.
A small note to this research is that the value of the R2 isn't very high. In the most extensive
regressions the values are 0,28, 0,26 and 0,13. This could be due to limited information in the dataset. Other factors that aren't in the dataset, could have an effect on the prices and therefore also affect the level of price dispersion. But even though the R2 isn't that high, most results are still
significant, so the conclusion remains in place.
Overall the conclusion of this research would be that an increase in the number of sellers, also increases the level of price dispersion. Therefore, the number of sellers and the level of price dispersion have a positive relationship. The regressions that look at price dispersion as the
According to Bertrand pricing, buying online from a price comparison website would decrease all prices to marginal costs and eliminate price dispersion. However, this isn't in line with the results that are found in this research. One possible reason for price dispersion to still exist, is that there are different kinds of consumers. Some consumers go out ot their way to find the lowest price and are unwilling to pay anything but the lowest price. These consumers want to be fully informed of all prices by all different vendors. If all consumers would do this, then indeed prices would all be equal. But there are those consumers who are willing to pay a little extra, because they value a particular seller higher than another seller (Baye, Morgan and Scholten, 2002). Then there is a part of consumers who pay a higher price, because they are uninformed (Varian, 1980). A part of consumers is uninformed, because they do not look at this price comparison website. Since they aren't fully aware of the alternatives, they end up paying a higher price. If a new entrant on the TV market offers a lower price, the uninformed consumers may not know about this new price. Since the high-priced product is still available on the market and a lower price has entered the market, price dispersion will increase. This way new entrants could create a higher level of price dispersion. This is especially true in this research, since the lowest price is used as a level to measure
percentual price dispersion.
6. Conclusion
In this research the effect that the number of sellers has on the level of price dispersion has been investigated. The research question was: “How does price dispersion change with the number of sellers?” In order to investigate the effect properly I have used three different measures of price dispersion. For all these measures I performed a few regressions to see how the different variables will affect the level of price dispersion. The number of sellers has been included into the regressions by dummy variables for each of the different numbers. When looking at price dispersion as the difference between the highest and the lowest price and as the difference between the average and the lowest price, price dispersion seems to increase with the number of sellers. Adding a single extra seller onto the market doesn't seem to have a significant effect, but adding multiple sellers onto the market will increase the level of price dispersion. In a third set of regressions, price dispersion was measured as the difference between the lowest two observations. Overall it seemed that price dispersion doesn't depend on the number of sellers, but remains constant. Contrary to the other two measures of price dispersion, adding a single seller onto the market does make a
difference, but only if there is a very small amount of sellers. Then adding a seller to the market decreases the level of price dispersion. From this it could be concluded that a rise in the number of sellers, decreases the level of price dispersion. Since this effect is only present when there are very
few sellers, this conclusion cannot be drawn at large.
The general conclusion of this research is that price dispersion increases with the number of sellers. This means that the relationship between the two is a positive one. This isn't in line with the main hypothesis, that stated that the relationship between the number of sellers and the level of price dispersion is a negative one. A possible explanation is that consumers value a single seller more than another and are therefore willing to pay a higher price (Baye, Morgan and Scholten, 2002). Another explanation for this is that not all consumers are completely informed about the different prices (Varian, 1980). These consumers aren't aware that sellers that enter the market, might offer a lower price. This leads to a higher level of price dispersion.
In this research I also looked at time effects. To control for time effects, I introduced dummy variables for the different months that a product is up for sale. Adding these dummies into the regressions, didn't give a clear time trend. Some of these results aren't even significant, so no clear conclusion can be drawn as to how price dispersion changes over time. Also dummy variables have been added to control for different pricing strategies of the different brands. This does give some significant results, which would mean that the level of price dispersion changes among the different sellers.
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