1. Broda Weinstein Paper
G6904

2. What this paper does
First paper to compare prices of identical goods at barcode level across borders – test law of one price
First paper to construct consistent price indexes for identical goods across borders instead of using official CPI data – test PPP for tradables and explain puzzles in the literature that use aggregated data

3. Notation and definitions
Law of One Price
Relative LOP
Relative LOP Index
Existing Literature
Existing literature compares price indexes comprised of different goods using different weights. This paper is able to look at identical goods and use identical weights because indexes constructed from ground up.

4. Data
Compare the number of product groups (which is at most the level of aggregation of previous studies) with number of products. While the is almost complete overlap in product groups, there s much less overlap in actual products. Thus tests of LOP or PPP may fail because of apples and oranges problem.

5. Product Groups vs. Barcodes

6. A lot of Products are City and Country Specific
This suggests that the amount of overlap in city or regional price indexes in national statistics data is quite small.

7. The fact that price indexes across regions or countries are largely composed of different goods would not be a problem for understanding the LOP or PPP if goods within categories are fairly homogenous. But they are not!
Distribution of all changes in log deviations from LOP in Canadian Cities 2001:1 – 2004:4

8. Price Dispersion for Identical Goods in 2003:4
The first interesting number presented in the table is the standard deviation of the median price differential in the city pairs. The standard deviation of means that the typical price differential between cities in the US is very close to zero (upper panel). We repeat the same exercise for Canadian regions and obtain very similar results (middle panel). These results suggest that whatever price differentials exist within countries, they are distributed around zero.
“This is strong indication that absolute PPP holds in different locations within countries.”
Note that statistics are on left are moments of the stats in the columns where each column stat, for US, based on 45 observations for each product category. There are 10,616 different US products.

9. In columns 3 and 4 we present the standard deviation of the log relative prices and the median absolute price deviation. The table reveals that the typical standard deviation of log price differences between any two cities is 22.3 percent in the US and 18.7 percent in Canada. These numbers reveal something very important about the LOP: even within a country the standard deviation of prices of identical goods is typically 20 percent. To put this number in perspective, Consider the results of Froot, Kim, and Rogoff’s [1995] study of international violations of the law of one price. In that study, they concluded, “the volatility of law of one price deviations is both remarkably high (typically on the order of 20% or more per year for most commodities in most centuries) and remarkably stable over time.” The important fact to bear in mind is that the LOP deviations that these authors found internationally are approximately the same magnitude as those we observe within countries. In other words, the prices of individual goods vary substantially across space regardless of whether two regions are in the same country or not .
This point notwithstanding, we can see that the dispersion of prices of individual goods vary slightly more when crossing the border. The lower panel of Table 2 shows that the standard deviation of prices of identical goods across the border is typically 26.7 percent, roughly 4 percentage points larger than within the US and 8 percentage points larger than within Canada. Results are similar using the typical absolute price difference between cities.

10. Price Dispersion for Identical Goods in 2003:4

11. Overview of Data Summary
First, there are a vast number of goods in the market and the composition of consumption varies systematically with distance and across borders. This implies that one must take great care about how samples are constructed when comparing relative price movements across space and borders.
Second, the prices of these goods vary substantially even for narrowly defined commodities. This implies that absolute deviations in the LOP will be quite sensitive to whether precisely the same goods are compared.
Third, one should not equate the international violation of the law of one price with a barrier at the border. The data strongly suggests that there are substantial violations of the law of one price within countries and that these violations are of similar magnitudes as international violations. A corollary of this lesson is that one should not be surprised at the existence of LOP deviations – these happen all the time within countries – the more interesting question is how much larger international deviations are than the regional ones.
Fourth, there is vastly more volatility in individual price quotes than in price indexes. This means that much of the price variation is eliminated when one focuses on price indexes. As we will see in the next few sections, each of these stylized facts will play a key role in understanding why absolute price convergence holds and why it has been so hard to find evidence in favor of it.

12. How Wide is the Border?
Where we compute dispersion in absolute LOP for identical goods u in group g

13. How Wide Was the Border in 2003:4
How Wide Was the Border in 2003:4? There was no Engel Rogers (1996) Puzzle
They find as little as 36 miles or a much as Engel and Roger found 3.8 million miles wide and Parsley and Wei found 43 quadrillion!

14. Is This Result due to Aggregation of Price Indexes?
Three Different Constructed Indexes – common goods/weights, common goods, nothing in common

15. Is This Result due to Aggregation of Price Indexes?

16. How Wide Was the Border 2001:1 - 2003:4 Using the Engle Roger (1996) Definition
Following Engel and Rogers, for each region pair, they compute the standard deviation of the relative log price changes of the goods common to that pair. In particular, they calculate

17. Absolute Convergence to PPP
Estimate Speed of convergence in product prices relative to Ontario Canada
Note that they allow border to impact speed of adjustment and well as rest of dynamics

18. There is No (Rogoff 1996) PPP Puzzle!
This is strong evidence in favor of a small role played by the border in terms of market segmentation. Can reject absolute LOP, but long run deviations are small.

19. Is Rogoff PPP Puzzle due to Aggregation?
Estimate dynamic adjustment at index level not product level
Two different indexes are considered - common goods/common weights
Two different indexes are considered - different goods/different weights

20. Is Rogoff PPP Puzzle due to Aggregation? Yes

21. But is this Due to Group Specific Speeds of Adjustment (Imbs (2005)? No
Allow the speed of adjustment to vary by product group and then aggregating up does not explain the Rogoff PPP puzzle.

22. Are There Non- Linearities PPP Convergence (Obstfeld – Taylor(1997))
Are There Non- Linearities PPP Convergence (Obstfeld – Taylor(1997))? Yes
A number of papers have estimated non linear models in which speed of adjustment depends on distance from equilibrium. When β2 < 0, we find this sort of non linearity.

23. The use of barcode data reveals a very different picture of international price differences
than what one sees with coarser data.
In particular we find that the LOP and PPP hold in their absolute forms as well across the border as they do within countries.
Moreover, the importance of distance for price differences is five to ten times larger in aggregate data than in barcode data. Much of this is driven by the fact that the set of common goods falls systematically with distance leading price indexes to diverge because their composition diverges.
Finally, we find that rates of price convergence within and across borders are fast and completely in line with micro studies.
Our study also explains why prior work has failed to identify these facts.
In particular ,our examination of the barcode data reveals that there is enormous heterogeneity in individual goods even when one examines goods that strike most researchers as homogeneous.
This heterogeneity gives rise to very large relative price deviations that are lost when one examines price aggregates. The combination of using price indexes that are comprised of non-comparable goods and averaging away the large idiosyncratic price changes gives rise to a biased picture of how fast price differentials dissipate.

24. Engel, C. and J.H. Rogers (1996), .How Wide Is the Border?., American
Economic Review, 86, pp
Jean Imbs & Haroon Mumtaz & Morten Ravn & Hélène Rey, "PPP Strikes Back: Aggregation and the Real Exchange Rate," The Quarterly Journal of Economics, MIT Press, vol. 120(1), pages 1-43, January.
Obstfeld, M. and A.M. Taylor (1997), .Nonlinear Aspects of Goods-Market Arbitrage and Adjustment: Heckscher.s Commodity Points Revisited,. Journal of the Japanese and International Economies, 11, pp
Rogoff, R. (1996), .The Purchasing Power Parity Puzzle, Journal of Economic Literature, 34, pp