DATA

Data Interpretation

Data Interpretation

The worksheet index contains price and quantity data for 8 products purchased by a company over 10year period. We use the method of Paasche and Laspeyres index numbers to interpret the given data set.

Paasche Index

This index answers the question, "What is the difference in price in today's house in today's dollars versus the price for the same house in base year dollars?" Since "today" is defined as any time period in question, the quality of the house defined above is not held constant. It is newly calculated at each time period.

A hypothetical calculation is made in which the numerator of the calculation is the current house priced in current dollars. The denominator is the current house priced in base year dollars. In the numerator, for each time period the size, characteristics, and geographic mixture of the houses sold reflect the activity of that time period and the prices paid. Base year prices for the same characteristics are held constant in the denominator.

Uses of This Index

Since we are not concerned with new home sales or under construction as an output, we do not publish this index. Our use for this index is to calculate the Fisher Ideal Index as defined below. Data users who are concerned with measuring the value of today's output or production using a constant set of dollars will find this kind of index useful.

By dividing today's output or value of production by this index, one can convert or deflate back to a fixed or standard set of dollars associated with the base year. This enables the data user to determine what the real value of output is for each time period.

Weaknesses of This Index

Given that buyers of new homes can satisfy their housing needs through a variety of means, preferences in housing choices can change at each time period.

If, in effect, the real costs of housing are rising relative to income, the Paasche index will allow the substitution of a smaller house with fewer amenities over the larger house with more amenities in order to increase affordability, because there is no fixed standard quality. By doing this, the Paasche index understates inflation because it allows cheaper options to replace more expensive ones. If certain housing markets become over priced, and housing sales reflect a shift to lower priced markets, a Paasche index will not factor out these changes. All things being equal, this will result in a lower calculated rate of inflation. Paasche can be derived by the following formula:

The statistical index

where is the price per unit in period and is the quantity produced in period .

Paasche Index of given data set

Company 1:

2001 1.450747

1.574193

1.417893885

1.819191167

1.446009081

2.370441459

2.636687293

3.070416835

8.160973278

Company 2:

1.176681

1.636167602

1.47723031

1.479248323

1.407090412

1.458373298

1.458373298

1.419288505

1.405431779

Company 3:

1.124092218

1.437238432

1.346206859

1.469551786

1.334433132

2.513358345

1.365927419

1.833812099

5.183443342

Company 4:

2001 1.150908135

2002 1.539247

2003 1.307534

2004 1.442226

2005 1.388216

2006 1.401622

2007 1.415249

2008 1.426043

2009 1.340761

Company 5:

2001 1.142551

2002 1.543967

2003 1.176382

2004 1.466711

2005 1.39719

2006 1.407057

2007 1.402673

2008 2.926231

2009 6.21071

Company 6:

2001 1.138248

2002 1.49287

2003 1.36352

2004 1.585651

2005 2.926087

2006 2.494077

2007 2.147969

2008 1.673586

2009 1.449344

Company 7:

2001 1.172148

2002 1.472075

2003 0.669785

2004 1.464497

2005 1.331442

2006 1.52818

2007 1.326792

2008 1.595428

2009 1.309216

Company 8:



2001 ...