Using statistics to understand economic history when data is limited..

The title of the post is a paradox of sorts. It is based on this paper by prof Pter Temin of MIT.

The paper investigates whether there was an integrated wheat market in early Roman empire. However, data available is limited. Prof. Temin shows how to use limited data into stats to get the desired results.

Frankly, I did not understand the stats bit much. What amazed me the approach to figure whether the wheat market was integrated:

If there had been a unified wheat market, the main market would have been in the city of Rome, where the largest number of potential consumers lived and the center of imperial administration was located. In other words, Rome was where the largest supplies and demands for wheat would have come together and where the price of wheat consequently would have been set. The price would have varied over time as supplies fluctuated due to harvests across the Roman world, storms affected the cost of transportation, and government actions altered the value of the currency. Normal variations in supplies and demands elsewhere in the Empire would have affected the price, although most fluctuations would have been small relative to the total production and the consumption at Rome. Most places outside of Rome would have had an excess supply of wheat, and the price would have been set in Rome where the excess supplies and the largest excess demand came together. When local places were isolated, there could have been excess local demand as well as excess local supply, that is, local famines as well as local glut.

Under these circumstances, wheat outside of Rome would be valued by what it was worth in Rome. Wheat at Palermo in Sicily, for example, normally would be worth less than wheat in Rome because it would have to be transported to Rome to be sold. The price of wheat in Sicily  would be the price of wheat in Rome less the cost of getting wheat from Sicily to Rome. This would be true almost always, but there undoubtedly were circumstances when it was not. If storms prevented the shipment of grain to Rome, the Sicilian price might temporarily deviate from the level set by the price in Rome. If a harvest failure in Sicily created a local famine, the price of wheat in Sicily would rise above the level indicated by the Roman price until new wheat supplies could be brought in. In the absence of extreme events like these, a unified market would keep Sicilian prices near the Roman price less the transportation cost. 

More concretely, competition would determine Sicilian prices if there was a unified market. If the Sicilian price of wheat rose above the Roman level minus transportation costs, it would not make sense for merchants to buy wheat in Sicily to sell in Rome. The amount of wheat demanded in Sicily would fall, and the price consequently would fall as well. If the Sicilian price of wheat fell below the Roman level minus transportation costs, merchants would increase the amount of wheat they would buy in Sicily, for they could make an unusually high profit by taking it to Rome and selling it there. Merchants would bid against each other, raising the Sicilian price.

The author has some price data from other papers and  estimates the distance between the cities using maps!:

I approach this test in three steps, the first of which uses a small set of wheat prices from varied locations from Rickman (1980). This familiar sample provided a way to examine monetary integration at least provisionally. When dealing with fragmentary data it is necessary to collect a sample that is not determined by the desired outcome. Rickman was writing about the Roman wheat market, and he collected his sample to show habitual prices in different places. The sample, albeit small, therefore looks like a random sample. It is, in Rathbone’s (2003, 201) felicitous phrase, “thin but nicely random.” The second step is to check these results with a new data set in Rathbone (2011). These data were collected to exhibit the surviving prices from around the Mediterranean. They overlap Rickman’s sample, but the two authors made different choices in collecting data that allow us to delimit more precisely the extent of the Roman Mediterranean wheat market. The third step is to consider an even newer data set from Bransbourg (2012) and the criticisms Bransbourg levels at the first step in this analysis.

I describe the price observations in the order of their distance from Rome, calculated as straight-line distances on a map. This of course is only an approximation to the actual distance that wheat traveled, and this added randomness reduces the possibility of finding evidence of an integrated market.

Based on limited data he goes on to show that indeed there was an integrated wheat market in Roman empire.

This paper explored the usefulness of small-sample regressions when more observations are not available. As I said earlier, my econometric colleagues like to use these regressions to illustrate the usefulness of econometric theory because the students can calculate directly the significance of their results. They are taught regularly to graduate students at MIT. Economics increasingly is using larger and larger data sets, but every once and while a small data set is all that is available. It is useful to understand how useful such a small data set can be.

This paper presents evidence for the presence of a series of unified grain markets that stretched from one end of the Mediterranean to the other in the late Roman Republic and early Empire. The extent of the Roman market has been debated exhaustively, but evidence to date has been restricted to local markets. The presence of localized market activity has ceased to be controversial, but the question of market integration is still alive. The evidence produced here demonstrates that there was something approaching a unified grain market in the Roman Mediterranean.

Great read. Who said econ history was all fluffy non-math stuff? Papers like these help you understand so many perspectives..

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One Response to “Using statistics to understand economic history when data is limited..”

  1. driss Says:

    Robert Solow,an American economist and a Nobel Prize winner in
    Economics,once said:”All theory is based on assumptions which
    are not quite true,this is what makes it a theory.”Former President
    Henry Truman in the USA,avoided having an economist as an ad-
    viser,since “economists use”on the one hand,and on the other
    hand,language.”ONE définition of “economics’is worth reiterating,
    namely”economics is a science of thinking in terms of models,
    joined to the art of using models serving in solving contemporary
    world problems.”Also,Henri Theil,a scholar from the University of
    California,Davis,Ca,once said”Models are to be used ,not believed.”
    Finally,Benjamin Disraéli,former prime minister of the United King-
    dom,referred to three types of lies”three kinds of lies:lies,damned
    lies,and statistics.”

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