# Determining the price of vintage clocks

**Determining the price of vintage clocks**

Contents

Introduction……………………………………3

Literature review……………………………. 3

Results and discussion……………………..5

Model specifications………………………..6

Analysis…………………………………………10

Discussion of econometric problems..10

Discussion of hypothesis test results..10

Discussion of estimated coefficients..11

Conclusion……………………………………11

References……………………………………12

**Introduction**

The paper discusses the value of vintage products and the reasons that make them to be in demand. Vintage products were often luxury products with proven performance and were durable to the present age. Authenticity is among the issues that influence the interest of buyers. This interest is expressed in bids. The research assessed how age of vintage clocks and the number of bids.

**Literature review**

People like collections of old and antique products for various reasons. Cars and clocks and anything with historical value tend to offer collectors and owners’ sentimental satisfaction. Kostecki (Kostecki, 2013) noted there is a kind of satisfaction in owning popular and rare products such as red Ferrari cars that always get attention from onlookers, regardless of how the car is acquired. There is a value that certain products have. Where there may be economic reasons, owning these products seems to have economic sense due to positive reception and appreciation of value with age. However, not all products have similar values. As Carney (Carney, 2005) explained, the value of antiques is determined by time, scarcity, and condition. It means once people identify products to have value to them, the oldest, rarest, and well-conditioned products will attract the highest number of bidders, which is the mode in which these are usually sold.

Baudrillard (2005) described the motive for the search for old products as “authenticity, period style, rusticity, craftsmanship, hand-made products” because they want to relate to their own time and space and in accordance with their own cultural systems. Once acquired, it acts as a family portrait that has a sense of immemorialization. Thus, there is a search for authenticity and the feeling of nostalgia that is associated with certain products. There are certain people who are obsessed with certainty which is defined as the authenticity of specific works especially if they are done by certain people who are known to produce certain qualities that people are fascinated with. They are authentic especially if they have certain unique features and are recognized as the creator’s signature, meaning that they cannot reproduced. This rarity is what makes such products unique and in demand. Russell (2009) also noted that authentic and vintage products tend to attract high demand from customers given that they cannot be found anywhere, giving an example of Gutenberg Bibles that are the reserve of museums and libraries. They are very valuable in this sense. Banning especially for books is also one reason that makes them rare. As time elapses, certain products become even rarer and therefore more valuable and expensive. Husfloen et al. (2006) added that some Victorian attire might not have been unique but because of the passage of time, their present value has increased.

Noting the essence of durability or condition of products and rarity, Kapferer and Bastien (2012) observed that these often luxury products in their time range from all classes of products. Vintage products tend to have a quality of historicity and to maintain their value and demand, they are often judged to have no equal, hence the bidding process that is used. This also means they have to pass the par of performance and ownership to tell stories, hence the nostalgia that was described above. George (2003) also noted that vintage products were often in the class of luxuries, designed to be durable and lasting through generations. This means they were expensive and therefore not necessarily available to the usual market where the price of a product or service would be influenced by forces of demand and supply.

Vintage clocks too are identified by the same characteristics such as craftsmanship, type of materials used to make them, and finish given to them. Mechanical watches were identified with various finely organized parts that made them adorable. The website selling these clocks (sellingantiques.co.uk), dates back to 1750 and prices ranged to as low as £135 to £13,500 for 1770s musical quarter Chiming Clock (Selling Antiques, 2017).

**Hypotheses **

- There is a positive relationship between the age of clocks and the price at which they are sold
- The number of bids has a strong positive influence on the price at which vintage clocks are finally sold.

**Results and discussion**

The data was on prices of clocks that were classified as vintage, dating several hundreds of years. The data presented age, number of bidders, and prices for 50 clocks were presented.

**Dependent variables**

- Price

These are predicted values that are determined by others.

**Independent variables**

These were the variables that determined the price at which the clocks were finally sold.

- Number of bidders
- Age of the clocks

Descriptive statistics

This is a summary of the variables that were used where average, median, minimum, and maximum variables are provided. The oldest clock was 194 years while the newest was 108 years and all had an average of 144 years. average price was £1327.16

Summary Statistics, using the observations 1 – 50

(missing values were skipped)

Correlation matrix

This is used to illustrate how various variables relate to each other. It indicates the nature and strength of the relationship of the variables presented. Pearson correlation varies between -1 and +1. In Table 2, the age and number of bidders have a weak negative correlation of -0.25 but a number of bidders and price have a strong positive correlation of 0.73. Price and number of bidders have a positive relationship as suggested by Pearson correlation coefficient of 0.35. This is a moderately strong positive relationship.

The overall critical value of 0.394 was obtained, which means that the null hypothesis was not rejected. There is evidence to suggest that the variables do not have a statistically significant relationship in the values that were used.

Correlation coefficients – using the observations 1 – 32

5% critical value (two-tailed) = 0.3494 for n = 32

**Model specifications**

The model represents more than one independent variable that is used to explain the change in the price of vintage clocks. Age and number of bids were used to represent this relationship with price. Coefficients are used to explain the significance of the models from the equation presented.

Model 1: OLS, using observations 1-32

Dependent variable: PriceA

Table **above presents the multiple regression analysis of the variables of price as the dependent or predicted variables against the number of bids and age as the independent or predictor values. The R-Square in the relationship is 0.89. This indicates there is a strong positive relationship between the dependent and independent variables. 0.89 of 89% meant that the independent variables were used to explain the relationship with price, the dependent variable. This suggested that there is a high likelihood that the price of the clock was predicted by the two independent variables, age and number of bidders.

Multiple regression is expressed in the format indicated below:

Y = β_{0} + β_{1}X_{1} + β_{2}X_{2} + ε

Where X_{1} and X_{2} are independent variables for age and bidders. β is the coefficient for each of these variables.

The coefficient for age is 12.73. The t-test statistic is 14.11 while the p-value is <0.001. This is less than 0.05, the confidence limit that was used in this regression. This means the null hypothesis is rejected at this level. The null hypothesis stated that there is no relationship between the predictor or independent and dependent (predicted) variables. There is enough evidence to suggest that there is a significant relationship between the dependent variable, price, and age of the clocks as the independent variable.

The coefficient for Bidders is 85.81 and a p-value of less than 0.001. This was less than 0.05 which was used as the confidence limit as well. Again, the null hypothesis is rejected and a conclusion is made that there is enough evidence to suggest that the number of bidders was strongly correlated with the price at which the clocks were sold.

Representing the estimated variables make the equation to be:

Price=12.74_{Age }+85.82_{Bidders}-−1336.72+ ε

F-test results are given to indicate the nature of the relationship between the independent and dependent variables. According to the findings, the F(2, 29), 120.65, p=0.000. The F test is big while the p-value was less than 0.05. This confirmed that the model used to compare the variables for dependent and independent variables was good. It meant that the independent variables had an effect on the dependent variables, hence the strong relationship as was also suggested by the R-Square coefficient of 0.89.

Analysis of Variance:

Sum of squares df Mean square

Regression 4.27716e+006 2 2.13858e+006

Residual 514035 29 17725.3

Total 4.79119e+006 31 154555

R^2 = 4.27716e+006 / 4.79119e+006 = 0.892713

F(2, 29) = 2.13858e+006 / 17725.3 = 120.651 [p-value 8.77e-015]

Ramsey RESET Test

The test was done to assess if there were any mis-specified or inappropriate and or omitted variables in the equation that could have influenced the findings that were presented. The results are presented below:

Auxiliary regression for RESET specification test

OLS, using observations 1-32

Dependent variable: PriceA

Test statistic: F = 3.280319,

with p-value = P(F(2,27) > 3.28032) = 0.0531

The critical F value was

*F*_{0.05}_{,2,32 }*= **3.280304*

F Test and F critical were compared as indicated below:

*120.65 (F) > 3.28(F _{critical})*

Thus, the null hypothesis is rejected and a conclusion is made that all independent variables, age, and bidders, influenced price.

**Analysis**

**Discussion of econometric problems**

The aim of using statistical measurements was to measure the possible relationship between predictor and predicted values. However, these are only estimations and may not indicate actual relationships especially when the relationship is shown to be weak, although for this analysis, the relationship was strong, it was not necessarily indicative of complete variables. There may be other variables such as authenticity as was seen in the literature review that influence the value of clocks. The omission of some variables may affect prediction but will not indicated in the regression equation presented.

One is also needed to do a full analysis to assess the complete effect of coefficients on price. Using the Pearson correlation matrix, age appeared to have a stronger relationship compared to the number of bidders. However, when they were regressed, the effect for a number of bidders had the strongest effect as suggested by a higher coefficient compared to age.

**Discussion of hypothesis test results**

Hypotheses were stated to guide the statistics that were conducted and enable solutions to be made on the same. The first hypotheses involved the relationship between independent and dependent variables. This was done using F-Test where the null hypothesis suggested that all means were equal and therefore there was no relationship between independent and dependent variables. F=120 is statistically significant from 0. This was confirmed by the p-value of 0.001. Being less than the 0.05 confidence limit, it was concluded that the means were not equal and the correlation was not equal to zero.

Hypotheses of the relationship between dependent and independent variables were also tested, with the null hypothesis stating there is no difference between the means or no relationship. This was tested individually and as illustrated, both had p-values (p<0.05), which justified rejection of the null hypothesis. Thus, it was concluded that following statistical results, both independent variables have a significant relationship with the dependent variable, price.

Though these suggested a positive correlation, the Pearson correlation coefficient of 0.89 had a p-value of 0.34. With a p-value of greater than 0.05, it meant that the alternative hypothesis was accepted that there was no relationship between independent and dependent variables.

**Discussion of estimated coefficients**

All coefficients affected the price of vintage clocks. However, the number of bidders has a stronger effect than age. This indicated that if clocks were older and more people bid for them, their prices also increased. Given that they were all positive, they had to be considered to mean what was suggested. The relationship may also be applied to indicate that old vintage clocks attracted the most bids, which means that higher demand led to its increased price. These coefficients can be used to predict the price of vintage clocks in the future.

**Conclusion**

This research analyzed the effect of age and the number of bids on the price at which vintage clocks were sold. Regression analysis was carried out to assess the impact Results suggested that there was enough statistical evidence to suggest that the oldest clocks and those that attracted the highest number of bids were most valuable in terms of prices at which they were finally sold. Using the coefficients that were fitted into a multiple regression equation, these two determinants can be fitted to forecast the average price at which these clocks will sold. It implied that clocks with the highest number of bids will be more valuable although the age will also be significant. Sellers can use this simple guide to have an idea of what a vintage clock might sell at auction.

However, this is a suggestion and not the conclusion of prices at which vintage will sell. There is a need to assess other factors or characteristics that are likely to determine the price of these vintage clocks. Suggested attributes include the designer or creator of the craftmanship, materials used to make them, and mode of operation.

# References

Baudrillard, J., 2005. *Le Système Des Objets. *London: Verso.

Carney, M., 2005. *Trade Me Success Secrets. *Victoria: Trafford Publishing.

George, W., 2003. *William George. *Victoria: Trafford.

Husfloen, K., Kirsch, M. & Wolfe, N., 2006. *Antique Trader Vintage Clothing Price Guide. *Iola: Krause Publications..

Kapferer, J.-N. & Bastien, V., 2012. *The Luxury Strategy: Break the Rules of Marketing to Build Luxury Brands. *London: Kogan Page Publishers..

Kostecki, M., ed., 2013. *The Durable Use of Consumer Products: New Options for Business and Consumption. *New York: Springer Science & Business Media.

Russell, R., 2009. *Antique Trader Book Collector’s Price Guide. *3rd ed. Iola: Krause Publications.

Selling Antiques, 2017. *Seling Antiques. *[Online]

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