March 8, 2010:  Dallas Burtraw, Harrison Fell, Matt Woerman

Supply Elasticity Estimation

The best estimate of the international supply elasticity of cement from five of the largest cement

suppliers – China, Thailand, Venezuela, South Korea, and Greece1 – into the United States is 3.94. This

indicates that if the price of cement was to increase by 1% within any import district in the United

States, then, ceteris paribus, the quantity of cement imported from each of these five supply countries

into that port would increase by 3.94%. The following memo describes the process by which we arrived

at this estimate, as well as the data used in the econometric models.

All of the models described below were run using an instrumental‐variables regression, with demand

shifters as instruments, to identify supply elasticity separate from changes in demand. The dependent

variable in all of these models is the natural log of the quantity of cement shipped annually from a given

country to a given import district2

. The independent variable for which the instruments are used is the

natural log of the average customs price of the cement (in 2001$, as are all other monetary values in the

models) shipped from a given country to a given import district annually2

. By using this log‐log functional

form, the parameter estimate for this variable is the supply elasticity.

The demand shifters that are used as instrumental variables for the cement price are annual

expenditures for the construction of transportation infrastructure (highways, roads, etc.)2

,

unemployment rate2

, and gross state product2. These state‐level data were aggregated, or averaged in

the case of unemployment rate, for all states within a 300‐mile radius of the import district.

The other explanatory variables used in the models include the GDP of the supply country2

, as the state

of the economy in the supply country can serve as a proxy for the opportunity cost of sending cement

abroad rather than selling it domestically. The models also include the average annual international

price of crude oil3 or price of coal in the United States4

, which accounts for the energy costs required for

the production of cement.

The final explanatory variable used was one of three possible measures of the cost of transporting the

cement from the supply country to the import district in the United States. One of the forms of the

transportation cost used in these models is the average C.I.F. price of the cement shipments2 less the

average customs price. This residual price accounts for the transportation cost on a per unit basis, as

well as the insurance cost and other shipment‐related charges. A second form of transportation cost is

the international price of crude oil interacted with the distance from the supply country to the import

district5

, as well as this interaction with distance squared. The final measure of transportation cost is the

Baltic Dry Index (BDI)6

, an index of international shipping prices for various dry cargoes. This index is also

interacted with distance and distance squared in some specifications.

                                                           

1 These five countries supplied approximately 46% of U.S. cement imports during the years 2001‐2007. 2 Data supplied by EPA. 3 Data from EIA – World Crude Oil Prices, http://tonto.eia.doe.gov/dnav/pet/hist_xls/WTOTWORLDw.xls. 4 Data from EIA – Steam Coal Price for Industry, http://www.eia.doe.gov/emeu/international/stmforind.html. 5 Approximate distances calculated using http://www.timeanddate.com/worldclock/distance.html. 6 Data approximated from graph at http://www.investmenttools.com/futures/bdi_baltic_dry_index.htm.

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March 8, 2010:  Dallas Burtraw, Harrison Fell, Matt Woerman

We initially attempted to use these data to estimate separate supply elasticity for each of seven

countries – the five listed above as well as Canada and Mexico7

. This was done by pooling all of the

observations for each country and then running a separate regression for each country. This method,

however, resulted in a wide variety of supply elasticities, including many negative estimates, and most

of the elasticities were not found to be significantly different from zero. For example, the supply

elasticity for Canada varied from ‐4.47 to 3.15, depending on the model specification, while the

elasticities for South Korea and Greece were never statistically significant.

We then attempted to estimate one, aggregate supply elasticity from all seven of these countries to the

United States. To do this, we pooled all of the data for the seven supply countries, and then included all

of the observations in one regression. Most of the models specified in this way resulted in positive

supply elasticity. Only one elasticity estimate, however, was statistically significant.

After a discussion with representatives from the Portland Cement Association, we learned that cement

imports from Canada and Mexico are structurally different from those from the other countries, so data

for those two countries should not be pooled with the rest when estimating one international supply

elasticity. Thus, we next attempted to estimate a supply elasticity using pooled data for the other five

countries. This also resulted in a wide range of elasticities, and few were significantly different from

zero.

Our next attempt was to take advantage of the panel nature of the data. Since the data include many of

the same country‐import district pairs over multiple years within the seven‐year time period, we used a

fixed‐effects model to account for any special characteristics of the country‐import district pairs, as well

as any special annual characteristics, that might affect the supply elasticity but are not included in the

other explanatory variables. We performed these fixed‐effects regressions for both the set of five

countries (excluding Canada and Mexico) and the full set of seven supply countries. None of the supply

elasticities estimated with these fixed‐effects models, however, were statistically significant.

Finally, we recognized that there is a large variation in prices for some of the smallest shipments of

cement, as shown in the plot on the next page. For example, for annual shipments of 10,000 metric tons

or less, the average price varies from a minimum of $14.29 per metric ton to a maximum of $120.89 per

metric ton, which is also the minimum and maximum price for all shipments of any size. It is unclear why

these small shipments have a larger variation in price than the larger shipments, but one possible

explanation is that these shipments were not originally intended to be shipped in such a small quantity

to the import districts where they arrived. Perhaps a larger shipment was originally intended for a

nearby import district, but the port could not handle the large size of the shipment, so the remainder

was dumped at the closest import district. Thus, these small shipments should not be considered in the

same manner as the large shipments that arrived at the intended import district and received a more

common price.

                                                           

7 These seven countries supplied approximately 71% of U.S. cement imports during the years 2001‐2007.

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March 8, 2010:  Dallas Burtraw, Harrison Fell, Matt Woerman

In order to account for this wide variation in these small shipments, we used several different statistical

methods. First, we dropped all of these small shipments from the set of pooled data and then

performed a standard instrumental‐variables regression, as described above. We then included all of the

observations in the pooled data, but used a weighted instrumental‐variables regression8 to account for

the additional variance in the smallest quantities. Finally, we combined methods, dropping the smallest

quantities and using a weighted regression. All of these regressions were run for both the set of all

seven supply countries and the set of five countries. All but one of the estimates of supply elasticity

from the seven‐country sample were not significantly different from zero. The estimates for the set of

five countries, however, resulted in several international supply elasticities that are positive and

statistically significant. Some of these parameter estimates are shown in the table below.

The table of results on the next page includes several of the better estimates of international supply

elasticity, as well as several specifications that led to the identification of the best model. Each

numbered column represents one econometric model, with some defining characteristics of the model

listed at the top. The leftmost column is the list of explanatory variables used in these models. Each

number in the table is the parameter estimate of that variable in the given model, which is the amount

the dependent variable would change with a one unit increase in the explanatory variable. The numbers

in parentheses below the parameter estimates are the standard errors. If a model does not show a

parameter estimate for a given variable, then that variable was not included in that model specification.

The first model is what we have identified as the best model, which estimates the international supply

                                                           

8 Stata documentation describes these analytical weights as “weights that are inversely proportional to the

variance of an observation; i.e., the variance of the jth observation is assumed to be sigma^2/w_j, where w_j are

the weights. Typically, the observations represent averages and the weights are the number of elements that gave

rise to the average.” Because each observation represents an average annual price for a quantity of cement

shipped, these weights are most appropriate.

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March 8, 2010:  Dallas Burtraw, Harrison Fell, Matt Woerman

elasticity of cement from five countries – China, Thailand, Venezuela, South Korea, and Greece – into the

United States is 3.94.

   1 2 3 4 5 6

  

Five countries

Weighted IV

Five countries

Weighted IV

Only Q > 10

Seven countries

Weighted IV

Only Q > 10

Five countries

Standard IV

Five countries

Standard IV

Five countries

Standard IV

ln(P_cement) 3.94** 3.85** 6.22** 3.15 1.98 0.976

(1.81) (1.79) (3.05) (3.82) (3.88) (3.89)

GDP 0.306*** 0.316*** ‐0.205 ‐0.507 ‐0.426 ‐0.305

(0.101) (0.101) (0.279) (0.358) (0.366) (0.343)

P_oil ‐0.086*** ‐0.084*** ‐0.079** ‐0.102 ‐0.013

(0.030) (0.030) (0.036) (0.064) (0.046)

P_coal ‐0.164

(0.183)

P_oil * Distance 0.016*** 0.016** 0.021** 0.031* 0.017

(0.006) (0.006) (0.012) (0.018) (0.015)

P_oil * Distance2 ‐0.001** ‐0.001* ‐0.001 ‐0.002* ‐0.001

(0.0005) (0.0005) (0.001) (0.001) (0.001)

BDI ‐1.19*

(0.649)

BDI * Distance 0.441

(0.297)

BDI * Distance2 ‐0.034

(0.023)

Constant ‐6.56 ‐6.25 ‐16.31 ‐5.28 ‐1.39 6.66

   (5.82) (5.77) (10.66) (12.72) (12.84) (8.01)

Observations 278 256 384 278 278 278

Standard errors in parentheses

* p<0.10, ** p<0.05, *** p<0.01

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March 8, 2010:  Dallas Burtraw, Harrison Fell, Matt Woerman

How to Use the Supply Elasticity Estimate

Supply elasticity is the percentage change in quantity supplied of a good given a 1% change in the price

of the good. Thus, if we consider a price and quantity in time period and a new price and

quantity in , then the elasticity is given by

This equation can be rewritten as

If we assume , , , and are known, then we can solve for an unknown by

We can now view price as the price for cement in import district , quantity as the quantity of cement

shipped to import district from supply country , and elasticity as the supply elasticity of cement to

import district from supply country . Then

As discussed above, we have estimated an international supply elasticity for cement from five of the

largest cement supply countries into any import district in the United States. Since these nations

represent a significant portion of the cement supplied to the United States (excluding Canada and

Mexico, which are discussed below), then we can assume the supply elasticity from these five countries

approximates the supply elasticity from the world (excluding Canada and Mexico). Thus, for every

import district and supply country , , our supply elasticity estimate. We can also assume

that we are using a reference year of 2005 and estimating the quantity supplied in a future year . Then

Since every country in the world (excluding Canada and Mexico) is assumed to have the same elasticity,

and since every country sees the same price in import district , then we can sum this equation over all

supply countries to get

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March 8, 2010:  Dallas Burtraw, Harrison Fell, Matt Woerman

6

So we can estimate total cement imports into import district in year (excluding imports from

Canada and Mexico) by

It is important to note that supply countries react to the price they actually receive for the products they

supply, not the C.I.F. price paid by the importer, which would also include the cost of transportation,

insurance, and other shipment‐related costs. Thus, the price included in the above equations should be

the customs price, not the C.I.F. price.

Imports from Canada and Mexico, however, are structurally different from the imports supplied by the

rest of the world. As we learned in our discussions with representatives from the Portland Cement

Association, many of the Canadian and Mexican plants are owned by American companies and are

located close to the border. Consequently, production decisions at these plants are made along with

domestic production decisions in the United States. For these reasons, cement producers in Canada and

Mexico are more like domestic producers than overseas suppliers, so they should be modeled in the

same manner as domestic cement producers in the United States.