1 

Weekly Coal Production Estimation Methodology 

Step 1 (Estimate total amount of weekly U.S. coal production) 

U.S. coal production for the current week is estimated using a ratio estimation from the given equation 

below; 

P̂w(t) = Cw(t) × μpcq × {1 + 2

3

(δpcq

− 1)} (1)

where

P̂w(t) = Estimated total U. S. coal production for the current week

Cw(t) = Total number of U. S. railcar loadings of coal for the current week 

μpcq = A weighted average of the ratio of production over railcar loadings. 

A three ̵quarter average is used to lessen quarter ̵to ̵quarter changes in the

estimated ratio. More weight is given to the quarter one year earlier to account

for any seasonal fluctuations.

i. e. μpcq= 

1

4

(

Pq(t−3)

Cq(t−3)) + 1

2

(

Pq(t−4)

Cq(t−4)) + 1

4

(

Pq(t−5)

Cq(t−5))

where

Pq(t) = Total coal production for the current quarter (U. S. Total) 

Cq(t) = Total railcar loadings of coal for the current quarter (U. S. Total) 

δpcq = A growth rate to allow for change in the ratio of production tons per railcar 

loading of coal. This computes the change in a three ̵quarter average over the

course of one year. This is multiplied by 2 3⁄ to moderate extreme values.

Unlike μpcq, this is computed using the most recent data available from

MSHA, which is usually a two ̵quarter lag, although it may be a one ̵quarter

lag for the last few weeks of a quarter.

i. e. δpcq= 

(

∑(Pq(j)+ Pq(j−1)+ Pq(j−2))

∑(Cq(j)+ Cq(j−1) + Cq(j−2))

⁄

∑(Pq(j−4)+ Pq(j−5)+ Pq(j−6))

∑(Cq(j−4)+ Cq(j−5) + Cq(j−6))

⁄

)

, δpcq

∈ [0.95, 1.05]

where

Pq(j) = Most recently available quarterly coal production (U. S. Total) 

Cq(j) = Total railcar loadings of coal for quarter j (U. S. Total) 
2 

Step 2 (Allocate to state level)

Allocate weekly U.S. coal production estimated in Step 1 above to the state level by using state 

production share of the latest available quarterly coal production data from MSHA. Aggregate state 

level data to get coal basin and other regional level totals. 

The estimated U.S. coal production for the current week in Step 1 is allocated to the state level by using 

the following formula; 

SP̂w(t) = P̂w(t) × μspsq × {1 + 2

3

(δspsq

− 1)} (2) 

where

SP̂ w(t) = Estimated coal production of a specific state for the current week

P̂w(t) = Estimated total U. S. coal production for the current week

μspsq= A weighted average of the coal production share for a state

i. e. μspsq

= 

1

4

(

SPq(t−3)

Pq(t−3) ) + 1

2

(

SPq(t−4)

Pq(t−4) ) + 1

4

(

SPq(t−5)

Pq(t−5) )

where

SPq(t) = Total coal production for the current quarter (State Total) 

Pq(t) = Total coal production for the current quarter (U. S. Total) 

δspsq= A growth rate of the coal production share for a state 

i. e. δspsq= 

(

∑(SPq(j)+ SPq(j−1)+ SPq(j−2))

∑(Pq(j)+ Pq(j−1) + Pq(j−2))

⁄

∑(SPq(j−4)+ SPq(j−5)+ SPq(j−6))

∑(Pq(j−4)+ Pq(j−5) + Pq(j−6))

⁄

)

, δspsq∈ [0.71, 1.41]

where

SPq(j) = Most recently available quarterly coal production (State Total) 

Pq(j) = Most recently available quarterly coal production (U. S. Total) 

The subsequent remainder (if any) of the estimated U.S. weekly coal production amount is allocated 

proportionally to each state using the same methodology as equation (2) above. 

These estimates rely on the most recent MSHA data, which is usually a two-quarter lag, with 

only a one-quarter lag the last few weeks of a quarter. Because of this lag, significant 

industry changes may not be accurately reflected in the estimation process. Estimates are 

revised with actual data once it is available from MSHA.