Stamp Price Increase Prediction.

year rate(in cents)
1919 2
1932 3
1958 4
1963 5
1968 6
1971 8
1974 10
1975 13
1978 15
1981 20
1985 22
1988 25
1991 29
1994 32
1997 33
1999 34
2002 37

When we look at the Stamp Price Table, we see that stamp price increased aggressively after 1971.

I plotted this data on spreadsheet and it seemed like a linear model can predict future increases.

But there is a problem with this model, and that is the prediction on x-axis values.

Since x-axis doesn't increase linearly, we cannot apply a linear model to this data.

To prevent this problem I created a new data which I filled the blanks in some years without an increase

1919 2   1939 3   1959 4   1979 15   1999 34
1920 2   1940 3   1960 4   1980 15   2000 34
1921 2   1941 3   1961 4   1981 20   2001 34
1922 2   1942 3   1962 4   1982 20   2002 37
1923 2   1943 3   1963 5   1983 20   2003 37
1924 2   1944 3   1964 5   1984 20   2004 37
1925 2   1945 3   1965 5   1985 22   2005 37
1926 2   1946 3   1966 5   1986 22   2006 39
1927 2   1947 3   1967 5   1987 22      
1928 2   1948 3   1968 6   1988 25      
1929 2   1949 3   1969 6   1989 25      
1930 2   1950 3   1970 6   1990 25      
1931 2   1951 3   1971 8   1991 29      
1932 3   1952 3   1972 8   1992 29      
1933 3   1953 3   1973 8   1993 29      
1934 3   1954 3   1974 10   1994 32      
1935 3   1955 3   1975 13   1995 32      
1936 3   1956 3   1976 13   1996 32      
1937 3   1957 3   1977 13   1997 33      
1938 3   1958 4   1978 15   1998 33      

Plotting this data will be more accurate that plotting the original data.

As you seen on the graph above, curve look like an half parabola.

To generate this kind of curve I have two ideas. One if them is Parabola Prediction and other is Average Inflation Prediction.

 

Parabola Prediction:

I simply treat the data as points from an parabola in the form of  . I tried to find a and b values using first data set and last data set.

so I used {x=YEAR-1919} transformation to use YEAR values more accurately.

Then

Using these values gives us

   .

Then we know b=2, using it in the second equation gives us . Therefore a=0.00488836  .

When we plugged these values , our parabola is

or

Plotting this function together with original data gives

It seems very good model especially for last 20 years

 

Average Inflation Prediction:

My second idea was a Average Inflation Prediction model.

We know all prices are related to each other and I tried to find a average inflation rate for stamp to predict future prices.

To find average inflation in Excel, I created a column that is like

"Price of next Year" = "Price of this Year" x ( 1+Inflation rate)

Say Inflation rate is a

so it is like

Year1=Year0*(1+a)

Year2=year1*(1+a)=Year0*(1+a)*(1+a)

Year3=Year2*(1+a)=Year0*(1+a)*(1+a)*(1+a)

So it is actually an exponential function , and summary of it looks like

.

Since we know 1919 as a starting year, we can make it Year0, then 2006 becomes Year87.

If we use plug this transformation to equation above, we get

After I tried several a values for, I found that for a=0.03475 is the nearest values to make Year2006=39 cents. When we plotted this one

Now we can plot all models together

It seems like Average Inflation Prediction is better for overall but Parabola Prediction is more accurate for last 23 years.

So both models have advantages and disadvantages.

 

When will the cost of a first class postage stamp reach $1.00?

When we extended our model far from 2006, we see that our parabola model predicts 1 dollar in 2061 and average inflation model predicts 1 dollar in 2034.

 

When will the cost be 74 cents?

Parabola model predicts 74 cents in 2041 and average inflation model predicts 74cents in 2025.

 

How soon should we expect the next increase?

According to last years, Price increases 3 cents as average so we can predict next price will be 42 cents.

 In this case, parabola model say it as a 2010 event, and average inflation model says it is 2009 (may be 43 cents).

 

In 1996, the analysis of stamp data historically seemed to show that the postage doubled every 10 years approximately. The cost in 2006 would seem to argue that pattern is no longer valid. Is there evidence to show a change in the growth pattern? Or, was the 'doubles every ten years' just a bad model?

For both model, "Doubles every ten years" may occur for specific time periods but it cannot be a generalization.

 

You can download Excel file of this models from HERE.