Tuesday, December 20, 2016

Understanding Long-run Price Dispersion

Understanding Long-run Price Dispersion

One sentence summary: At the PPP level, almost all of price dispersion is attributed to unskilled wage dispersion, while at the LOP level, borders and distance contribute about equally to price dispersion that is rising in the distribution share.

The corresponding paper by Mario J. Crucini and Hakan Yilmazkuday has been published at Journal of Monetary Economics.

We use a unique panel of retail prices spanning 123 cities in 79 countries from 1990 to 2005, to uncover six novel properties of long-run international price dispersion. First, at the PPP level, virtually all (91.6%) of price dispersion is attributed to service-sector wages, consistent with a dominant role of the retail distribution margin. Second, at the level of individual goods and services, the average contribution of service-sector wages is significantly reduced, one-third as large (31.9%). This reflects the fact that good-specific sources of price dispersion, such as trade costs and good-specific markups, tend to average out across goods. Third, at the LOP level, borders and distance contribute about equally to price dispersion with distance elasticities consistent with the existing trade gravity literature which links trade volumes (rather than relative prices) to borders and distance. Fourth, in the cross-section, price dispersion is rising in the distribution share consistent with the notion that baby-sitting services and haircuts embody local wages to a far greater extent than highly traded manufactured goods. Fifth, we provide the first estimates of distribution margins at the micro-level and show them to be very different across goods and substantial in the aggregate, where they account for about 55% of consumption expenditure. Sixth, these estimates are broadly consistent with more aggregated U.S. NIPA measures currently used in the literature.

Non-technical Summary
The Law-of-One-Price (LOP) is the theoretical proposition that, absent official and natural barriers to trade, international prices are equated in common currency units, and a laborer's purchasing power (i.e., real wage) is determined only by their labor productivity. A stark empirical implication of this proposition is that the cross-country correlation between price levels and wage levels is zero. As is well known, this implication of goods market integration is grossly at odds with the data. The Penn Effect, in recognition of the ambitious work of Heston, Kravis, Lipsey, who developed the Penn World Tables, shows a strong positive correlation between international price levels and per capita income.

The following figure shows the microeconomic counterpart of this fact using the panel data of our study. Microeconomic in this context means the prices of individual goods and services across cities of the world, as opposed to aggregate price levels at the national level. Specifically, each point in the scattterplot is the price of an individual good or service in a particular city plotted against the hourly wage of domestic cleaning help in that particular city. Prices and wages have been averaged over the period 1990 to 2005 to eliminate transitory deviations associated with business cycles and exchange rate fluctuations.

Specifically, there are 300 goods and services (up to missing observations) for each city and there are 123 cities in total. The prices and wages used to construct these time-averages are from the Economist Intelligence Unit (EIU) World Cost of Living Survey which spans 79 countries. As far as we know, this is the first study to use time-averaged data to study long-run deviations from the LOP and Purchasing Power Parity (PPP). The points labeled with an asterisk are price levels computed as expenditure-weighted averages of the individual prices.

In the figure, the estimated line through the scatter of price levels has a slope of 0.52 and an R-squared value of 0.37. The estimation is by geometric mean regression to consider for possible measurement errors in both the price and wage data. A common set of consumption expenditure weights are used for all cities. These consumption expenditure weights are taken from the PWT, averaged across all OECD nations. 

In words: a doubling of wages is associated with a 52 percent higher price level. This finding is typically associated with the seminal works of Harrod (1933), Balassa (1964), and Samuelson (1964); however, the HBS theory assumes that LOP holds for traded goods but not for non-traded goods. According to this view, called the classical dichotomy, there should be a horizontal line traced out by traded goods for which the LOP holds and a line with a slope of unity for non-traded goods. The trivial example is the hourly wage of domestic help itself, which produces a slope of one by recognizing that the market price of this non-traded service is, in fact, the hourly wage for unskilled labor. The figure above, obviously, is not much more sympathetic to the classical dichotomy than it is to complete market integration.

To help resolve this puzzle, this paper estimates distribution and trade cost wedges using a trade model augmented with a retail distribution sector (developed in Crucini and Yilmazkuday, 2009). We have two sets of results, one for relative price levels (PPP) and the other at the level of individual goods (LOP). 

Regarding PPP, the variance of price levels for international city pairs is found to be almost entirely explained by international wage differences, 92% by our estimate. Both the absolute amount of price dispersion and the relative importance of wage differences falls when the sample is restricted to cities in countries at similar stages of development while the role of retail productivity increases. The contribution of cross-city wage differences falls to 8% when the sample is restricted to city pairs within the same country. It is important to keep in mind that the amount of price level dispersion across cities that are located in the same country is a trivial 3-5%; as such, a modest amount of wage or retail productivity variance goes a long way in terms of accounting for the lion's share of the variance. The thrust of the PPP analysis is that when long run price level differences are consequential, the differences are attributable to the level of economic development, not traditional trade frictions.

The table turns dramatically in favor of borders and trade costs and away from wages and retail productivity, as explanatory factors, when the focus is LOP deviations. Pooling all international city pairs, the explanatory power of the HBS theory (wage dispersion) falls by a factor of three, to about 32%. Traditional theories of trade that emphasis distance and borders now account for the lion's share of price disperison, about 41%. City effects account for almost none of the international LOP variation. Essentially, this is because international LOP deviations are both large and idiosyncratic to the good once we condition on the wage level. The remainder is a residual term, which may reflect good and location-specific markups as well as other variables omitted from the model. The following figure shows how this decomposition changes across goods, where the vertical axis shows the deviations from LOP, while the horizontal axis shows the distribution share of goods.

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