A New Method of Estimating Inflation By Bruce Hamilton Easier than standard method More accurate than standard method Works well when economy is unstable Relative price shocks Rapid policy adjustments Change in structure of economy

I. How Inflation is Measured Define a Consumption Bundle This is (supposed to be) the bundle of goods bought by a typical consumer in a month. This bundle is updated very rarely.

Observe the prices of all of the goods in the Consumption Bundle in month t: {p 1t,…,p nt } Multiply and get the cost of the bundle at time t:

Pick base period 0 Arbitrarily set CPI 0 = 100 Future values of CPI given by If CPI t = 110 there has been 10% inflation since t 0. Annual inflation is % growth in CPI.

II.Problems with Traditional Method 1.New Products 2.Unmeasured Technical Progress 3.Substitution Bias NOTE: All biases tend to OVERSTATE inflation

Substitution Bias (When relative prices change, consumers can substitute away from newly expensive goods) 2 goods, x 1 and x 2 p 1 rises, p 2 unchanged What happens to Cost of Living?

x1x1 x2x2 Consumption Bundle

Black: C 0 (time-0 cost of bundle) Red: Budget constraint when P 1 rises Purple: C 1 (time-1 cost of original bundle) Green: True C 1 (cost of reference indifference curve in period 1) The height of line C overstates inflation between periods 0 and 1 because consumers substitute away from x 1.

CPI growth (inflation) overstated when --- Relative prices changing Innovation in products or economy rapid Fixing CPI VERY difficult Measure and value each quality change Estimate benefits of substitution

III. Estimating Inflation with Engel Curves Engel’s Law: Food budget share declines as income rises

Graphical Demonstration

2008 and 2009 Engel Curves “should” be same If they are not, assume p 2009 is overstated => y 2009 is understated Experimentally reduce p 2009 (raising y/p) until two Engel curves overlap. Use “corrected” p 2009 as new measure of inflation.

In graph above: If 2009 consumers ACT rich (low food share of expenditure) We will assume they really ARE rich and we didn’t know it because we overstated inflation

Translate this idea into estimating equation: Data on individual households Income Food Expenditure Year Family Structure

ω it is household i’s food budget share in year t D t =1 in year t D t = 0 otherwise X it are household characteristics If CPI t is correct, all α t ‘s = 0 If α t < 0, CPI t biased upward Use α t values to estimate correct CPI

Data Requirements very limited Ideal for countries with poor central data- gathering services Superior (I think) for countries undergoing rapid economic transformation

IV Other Applications Russia (John Gibson,, Steven Stillman and Trinh Le, CPI Bias and Living Standards in Russia During the Transition, Journal of Development Economics, Vol. 87, pp ) Dismantle command economy Wild changes in relative prices Huge quality improvements in goods Huge improvements in distribution system CPI inflation overstated up to 1% PER MONTH ( ) when not using “corrected” CPI

Brazil Irineu de Carvalho Filho and Marcos Chamon, “The Myth of Post-Reform Income Stagnation: Evidence from Brazil and Mexico,” IMF Working Paper. Major Economic Reforms in mid 1980s – Relax exchange controls – Relax import restrictions – Relax controls on domestic economy Economic results (income/household) – Official: 1.5% growth – CPI corrected: 4.5% annual growth – Cumulative difference 55%

Mexico Major reforms including NAFTA Official results disappointing (2%) Corrected results impressive (4.5 – 5.5%)