Price Index Basics* (pg. 146 of Foundations of Economic Analysis)

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2 Price Index Basics* The fundamental problem upon which all the analysis rests is that of determining merely from price and quantity data which of two situations is higher up on an individual s preference scale. - Paul Samuelson (pg. 146 of Foundations of Economic Analysis) *Mostly from Diewert, W. E. (2004). Basic Index Number Theory. Consumer Price Index Manual: Theory and Practice,

3 Why Make Indexes? Aggregation of goods is inevitable UPC level analysis is not feasible Apples: gala, red delicious, granny smith, price index quantity index Compare cost of living across time, space indexes (or indices ) *Mostly from Diewert, W. E. (2004). Basic Index Number Theory. Consumer Price Index Manual: Theory and Practice,

4 1. Define a good PI s are made for goods Making an Index Use Hick s Composite Commodity Theorem If the prices of a group of items always change in the same proportion, that group of items behaves just as if it were a single good. E.g., if prices of all fresh fruit move together, then fresh fruit can be considered one commodity in demand analysis. Separability requires the ordering within the group to be unaffected by non-group choices.

5 Hick s Composite Commodity Theorem Intuition Suppose Then p p 1 1 for some fixed price. e( p, u ) e( p, p, u) e(, p, u) (because p 1 does not vary) e e p p h T T p1 Think of φ as the price, and composite good T ph 1 1 as the

6 Making an Index 2. Define items These are the categories that are averaged to form a PI for the good they are a part of. Aggregation is needed even at this stage UPC is too fine, aggregate across days, months No 2 purchases are the same context, location, prices, all vary across observations. Problems: products disappear, are improved, and new ones are introduced. 3. Determine Item Prices Usually take simple means Problems: quantity discounts (2 nd degree price discrimination), slight changes in quality, zeroes, units of measurement (count vs. weight),

7 Items in Practice

8 Making an Index 4. Determine the Basket Some products disappear from the market Some new products are introduced to the market Some products are improved Some transactions Requires updating

9 Making an Index 5. Choose Item Price Weights Weight by quantity plutocratic PI Weight each household equally democratic PI with plutocratic PI s, the rich are over-represented

10 Making an Index 6. Choose a Functional Form Big Considerations 1. Does it have any bad properties? Ex: Shouldn t depend on units of measurement The Axiomatic Approach 2. Does it reflect the Cost of Living? The Economic Approach is it superlative to a flexible functional form? i.e. is it exact for a demand system that can accommodate any substitution pattern? 3. Does it reflect an underlying stochastic process? The Stochastic Approach

11 Notation Superscripts denote periods (or locations) Subscripts denote items p [ p1,..., p n ] Total Expenditure in period t is V n t t t piqi i 1

12 P and Q Indices Upper case denotes indices P( p, p, q, q ) and Q( p, p, q, q ) are bilateral indices because they compare 2 time periods We want indices that deflate so that V V P p p q p Q p p q p (,,, ) (,,, ) 0 (product test) LHS is observed P defines Q (and vice versa) Only need one functional form to define the other

13 Fixed Base vs. Chained PI s type/ t fixed base 100 P( p, p, q, q ) P( p, p, q, q ) chained 100 P( p, p, q, q ) P( p, p, q, q ) P( p, p, q, q ) Fixed base runs into the problem of needing to update the basket of items Chained PIs update the base every period But chained PIs explode when prices jiggle (chain drift) high frequency chained PI s explode (see Ivancic, L., Erwin Diewert, W., & Fox, K. J. (2011). Scanner data, time aggregation and the construction of price indexes. Journal of Econometrics, 161(1), )

NEW APPROACH TO GROSS DOMESTIC PRODUCT DECOMPOSITION

NEW APPROACH TO GROSS DOMESTIC PRODUCT DECOMPOSITION Ante Rozga, University of Split, Faculty of Economics/Split - Cvite Fiskovića 5, 21 000 Split; CROATIA e-mail: ante.rozga@efst.hr Elza Jurun, University