Thousand Big Mac’s Index Project:
Alternative measures of the Real Exchange Rate
Roberto Rigobon
MIT, NBER, CSAC
Types of Data
Designed Data
Organic Data
Representative
Non-representative
Scope is limited
Volume, Velocity, Variety
Costly
Cheap
Difficult Access
Open
Intrusive
Non-intrusive
2
Online Information and Indexes
Our Approach to Daily Inflation Statistics
1
2
Use scraping
technology
Connect to
thousands of online
retailers every day
3
Find individual
items
4
Store and process
key item
information in a
database
5
Develop daily
inflation statistics
for ~20 countries
• Date
• Item
• Price
• Description
3
The Dependent Economy
Surplus
Overheating
e/w
External Equilibrium
Surplus
Unemployment
Deficit
Overheating
Deficit
Unemployment
Internal Equilibrium
Domestic Demand
Salter and Swan 1960’s, Dornbusch 1980
4
Underlying assumptions
•
•
The pricing implications are too stark because the model assumes a very extreme
position for the products.
In the segmentation – labor share space the typical assumptions place two goods
Labor Share
1
N
Very strong assumptions
• T vs. NT
• LOP in T
• NT is more labor intensive
α
T
0
Degree of Segmentation
1
5
Unsustainable Shock
• In the dependent economy, an increase in domestic wages
without an increase in productivity is an example of an
unsustainable shock
–
–
–
–
Prices of NT increase a lot
Prices of T do not move
There is a real exchange rate appreciation
Needs a nominal depreciation or a drop in wages to be
corrected
• How to detect or measure the degree of sustainability?
– Compare identical items internationally
– An increase in the relative prices, without a productivity
increase implies a RER appreciation
The International Comparison Program
• The International Comparison Program (ICP) is the world's
largest statistical initiative.
– Established in 1968
– It is now the largest international data collection exercise
involving five regions and 107 countries.
– The results will be combined with the OECD/Eurostat PPP
program for 43 countries, bringing the total to about 150
benchmark countries.
• Measure disequilibrium two ways:
– Compare the purchasing power across nations for similar goods
or basket of goods
– Compare the time series or international relative prices for
similar goods or basket of goods
Two issues with the ICP
• Comparing identical products
– Any international comparison either compares
individual products or baskets of identical products.
• How to make sure the products are identical?
• How to deal with different statistical capacities worldwide?
• The assumptions on segmentation and labor
market share are too stark.
– In reality technologies differ across products and
across degrees of segmentation.
Assume a single product:
Beer
Pjp
e
Pus
Pus ($)
Pjp (¥)
• Relative price of similar products (or a basket of products) in the same
currency
• One advantage is that if there is a world productivity shock (supply shock
to the production of beer) all beer prices in the world move together and
there is no impact on their relative prices. Only domestic demand shocks
have an impact.
• The disadvantage is that the products might not be identical.
Compare products:
Beer
Japan
?
Belgium
Two issues with the ICP
• Comparing identical products
– Any international comparison either compares
individual products or baskets of identical products.
• How to make sure the products are identical?
• How to deal with different statistical capacities worldwide?
• The assumptions on segmentation and labor
market share are too stark.
– In reality technologies differ across products and
across degrees of segmentation.
Extreme Assumptions
•
•
We expect technologies to exist in all the space
However, the degree of segmentation and the possibility of international arbitrage produce a
correlation between the degree of segmentation and the maximum labor share that the
sector can sustain
Labor Share
1
Degree of Segmentation
0
1
12
International Arbitrage
•
•
The degree of segmentation implies a range in which products are not
arbitraged.
This compresses the distribution of prices at the boundaries
1
Price Distribution for a fully
segmented Item
1
Commodities experience very
narrow price deviations
13
The Dependent Economy and Pricing implications
• Arbitrage:
– Assume there is a no-arbitrage condition and such condition is related to the degree of
segmentation
– Assume that wages in dollars fluctuate between {wmin and wmax}
– Less segmented products cannot sustain large price deviations.
– Shocks to wages imply larger fluctuations for those that have large labor shares
Labor Share
Arbitrage
1
Items with high
labor shares that
are not produced
Items that
ARE
produced
Degree of Segmentation
0
1
14
International Price Dispersion
Relative Absolute
Price Deviation
Small Shock
Degree of Segmentation
15
International Price Dispersion
Relative Absolute
Price Deviation
Different Items have different
labor shares
Degree of Segmentation
16
International Price Dispersion
Relative Absolute
Price Deviation
Maximum Deviation
given wage shock and
labor share
Degree of Segmentation
17
International Price Dispersion
Relative Absolute
Price Deviation
Average
Price
Deviation
Degree of Segmentation
18
International Price Dispersion
Relative Absolute
Price Deviation
Large Shock
Degree of Segmentation
19
International Price Dispersion
Relative Absolute
Price Deviation
No Arbitrage is binding for
some items. Prices are
compressed (or production
stops)
Degree of Segmentation
20
International Price Dispersion
Relative Absolute
Price Deviation
Average
Price
Deviation
Degree of Segmentation
21
How to measure deviations or misalignments of the
real exchange rate?
• Four alternatives
Characteristic
Real Exchange Rate
Big Mac
Measure the average price deviation in the economy
• Need all items in the economy
• Need weights for each item
• Usually relies on statistical office inflation indexes
Measure the price deviation of one NT item
• Stick to the model: measured as the price of non tradables relative to the exchange rate (the
price of tradables)
Sectorial Real Exchange
Rate
Measure the average price deviation of a subset of items (better matched) with different
degrees of segmentation
• Similar to the RER computed from official statistics
• Representativeness of the subset is important
Proportion of Extreme
Observations
Measure the percentage of items close to the tradability constraint.
• Compute how many items are on the top quintile of price dispersion (for each item)
22
International Price Dispersion
Relative Absolute
Price Deviation
Average
Price
Deviation
Degree of Segmentation
23
How to measure deviations or misalignments of the
real exchange rate?
• Four alternatives
Characteristic
Real Exchange Rate
Big Mac
Measure the average price deviation in the economy
• Need all items in the economy
• Need weights for each item
• Usually relies on statistical office inflation indexes
Measure the price deviation of one NT item
• Stick to the model: measured as the price of non tradables relative to the exchange rate (the
price of tradables)
Sectorial Real Exchange
Rate
Measure the average price deviation of a subset of items (better matched) with different
degrees of segmentation
• Similar to the RER computed from official statistics
• Representativeness of the subset is important
Proportion of Extreme
Observations
Measure the percentage of items close to the tradability constraint.
• Compute how many items are on the top quintile of price dispersion (for each item)
24
International Price Dispersion
Relative Absolute
Price Deviation
Big Mac
Degree of Segmentation
25
How to measure deviations or misalignments of the
real exchange rate?
• Four alternatives
Characteristic
Real Exchange Rate
Big Mac
Measure the average price deviation in the economy
• Need all items in the economy
• Need weights for each item
• Usually relies on statistical office inflation indexes
Measure the price deviation of one NT item
• Stick to the model: measured as the price of non tradables relative to the exchange rate (the
price of tradables)
Sectorial Real Exchange
Rate
Measure the average price deviation of a subset of items (better matched) with different
degrees of segmentation
• Similar to the RER computed from official statistics
• Representativeness of the subset is important
Proportion of Extreme
Observations
Measure the percentage of items close to the tradability constraint.
• Compute how many items are on the top quintile of price dispersion (for each item)
26
International Price Dispersion
Relative Absolute
Price Deviation
Sectorial RER: Average of a
subset of items
Degree of Segmentation
27
How to measure deviations or misalignments of the
real exchange rate?
• Four alternatives
Characteristic
Real Exchange Rate
Big Mac
Measure the average price deviation in the economy
• Need all items in the economy
• Need weights for each item
• Usually relies on statistical office inflation indexes
Measure the price deviation of one NT item
• Stick to the model: measured as the price of non tradables relative to the exchange rate (the
price of tradables)
Sectorial Real Exchange
Rate
Measure the average price deviation of a subset of items (better matched) with different
degrees of segmentation
• Similar to the RER computed from official statistics
• Representativeness of the subset is important
Proportion of Extreme
Observations
Measure the percentage of items close to the tradability constraint.
• Compute how many items are on the top quintile of price dispersion (for each item)
28
International Price Dispersion
Relative Absolute
Price Deviation
Degree of Segmentation
29
Comparison
Advantages
Real Exchange Rate
•
True Measure
•
International matching of products is extremely
hard
•
•
Close to the true model
Non-tradable highly labor
intensive
•
Price fluctuations of one item might be driven by
idiosyncratic shocks and not aggregate
fluctuations
The measure of the deviation is related to the
true measure but tends to overstate the degree of
appreciation
Big Mac
•
•
•
Sectorial Real Exchange Rate
Proportion of Extreme
Observations
Disadvantages
•
•
•
Goods can be matched better
In our case they are matched
exactly in many retailers
•
Goods can be matched better
In our case they are matched
exactly in many retailers
Solves the price compression
from the tradable products
•
•
•
•
The measure of the deviation is related to the
true measure but not identical.
Direction is the same, but bias is unknown
The smaller the degree of segmentation the more
compressed the price dispersion is and the less
informative is the index
This is not a true measure of the average
deviation.
It is correlated with the average price deviation
30
Thousands Big Mac’s Project
Illustration: International Prices
• Online prices represent an effective tool to
measure PPP fluctuations
– Identical items sold around the world
– Detailed descriptions to achieve a nearly
perfect matching
– Daily Prices
• PPP indices:
– More than 300 narrow product
categories
– With thousands individually matched
items
Compare prices for a bottle of Coke
across countries
– In food, fuel, and electronics: we are
missing clothing, personal care,
household products.
– Cars we will never match
Apply similar approach to hundreds of products
on a daily basis
PPP Indices
31
http://www.zara.com/us/en/m
an/beachwear/basic-shortswim-trunksc721501p2708544.html
32
US
UK
p2708544
Japan
http://www.zara.com/jp/ja/メンズ/
ビーチウェア/ベーシックショート水着c721501p2708544.html
Spain
33
Thousands Big Mac’s Project
• Construct an item level real exchange rate
pit
qit = * et
pit
– Bilateral Comparisons: All products are compared against
the equivalent product in US (*)
• Aggregate the items within a category (narrowly
defined)
– Categories:
• Sony TV, LCD, 52-60in, Smart
• Tomatoes
• Fuel
– Weights: Simple average within the category
34
Big Mac for Brazil
Relative Price of Big Mac
1.35
1.3
1.25
1.2
1.15
1.1
1.05
1
0.95
2013
2013.5
2014
2014.5
2015
BigMac Approach to all tradables
Tomato
36
BigMac Approach to all tradables
Gasoline and Diesel
37
BigMac Approach to all tradables
TV 60-66in Sony LCD
38
BigMac Approach to all tradables
39
BigMac Approach to all tradables
40
Thousands of Big Mac’s Indexes
41
Average Price Deviation
• Average the prices within categories
• Aggregate to sectors
• Aggregate to the whole economy
Aggregation to average price deviations per sector
Food
43
Aggregation to average price deviations per sector
Fuel
44
Aggregation to average price deviations per sector
Electronics
45
RER for the three sectors
46
PPP: Sectorial Real Exchange Rate Indexes
Fuel
Food
Electronics
All three
47
Proportion of Extreme Observations
• Pressure index per item (quantile)
• Aggregate to sectors
• Aggregate to economy
Brazil: Product Category 3
49
Brazil: Product Category 3
50
PPP Score
Food
Fuel
Electronics
Argentina
74.6
100.0
69.1
Australia
56.3
33.3
22.7
Brazil
33.3
0.0
52.3
China
55.0
100.0
25.0
Germany
75.0
50.0
50.0
Japan
35.0
100.0
29.7
South Africa
59.6
33.3
25.0
UK
66.2
100.0
35.1
Example: Nov 16, 2013. PS Calculations
To create an aggregate measure each sector is
weighted by its share in consumption
51
Proportion of sectors on the top quintile
(Brazil)
52
Event Study
• Event Definition
– First time the index reaches 70%
• This means that 70 percent of the items are on the top 20 percent
quintile in the last year (or two years)
• After crossing once, the event is assumed to last 220 days
– Only concentrate on appreciations
• Adjustment Process:
– Track the path of
• The real exchange rate as computed by us
• The nominal exchange rate
• And the relative prices
– Aggregate across all countries:
• Australia, Brazil, Germany, Japan, UK, South Africa
• I excluded Argentina and China
53
After Appreciation Signal
After 50 days, 76% of the paths experience a depreciation!
54
Sensitivity to Threshold
Threshold
% Overvaluation
% Over-% Under
0.50
63%
27
74%
23
0.60
76%
21
73%
15
0.70
77%
17
89%
9
0.80
100%
6
100%
4
0.85
100%
4
100%
2
Proportion of exchange rate paths that
are negative after 50-60 days
55
Conclusions
•
Measuring Price Imbalances
– The Real Exchange Rate
•
The usual measure relies on prices collected from statistical offices
–
–
Products are not perfectly matched
Statistical capacity differs across countries
– Single Product Indexes
•
•
Have the advantage of perfect matching
Have the disadvantage that are not representative
–
•
Meaning, the price deviation might be idiosyncratic
Measuring imbalance through Online Price Indexes
– Sectorial RER
•
•
Similar to single product indexes, but averaging many across categories and sectors
The tradability of the products masks large shocks
– Proportion of extreme price observations
•
•
•
•
Perfect matching
Measures pressure by categories
Might be a better measurement of macroeconomic imbalance
What is next?
– Need to finish all sectors and categories
– Need to compute multilateral deviations
56