An Empirical Examination of the Electric Utilities Industry. December 19, Regulatory Induced Risk Aversion in. Contracting Behavior

Transcription

1 An Empirical Examination of the Electric Utilities Industry December 19, 2011

2 The Puzzle Why do price-regulated firms purchase input coal through both contract Figure and 1(a): spot Contract transactions, versus paying Spot acoal marked Price: premium Mean for contract coal over spot By coal? Date, The contract and spot prices are obtained from monthly FERC Form 423 data on transactions between plant and mine. These prices are quantity-weighted means over all plants in the sample for each month. The contract prices used are the coal prices as delivered, including transport costs. The definition of contract is an agreement to purchase input coal, with repeated deliveries, lasting greater than one year.

3 Why is this interesting? In economics, we typically think of the regulator s objective as inducing firms to procure input coal as if they are (expected) cost minimizing. Considering how the legal and political structure of regulation in practice deviates from this economic intuition has important policy implications. Also, this distortion away from expected cost minimization is quite large; I find the percentage difference in total costs of coal procurement between the observed and cost minimization scenarios to be 18.47%

4 This Paper This paper posits firm-level as-if risk aversion brought about by the regulatory structure in place as an explanation for this contracting behavior. Therefore, this paper sets out to Posit a regulatory-based explanation for firms behaving as if they are risk-averse Document the existence of contracting behavior consistent with this as-if risk-aversion Quantify the magnitude of this behavior, and the extent of its deviation from expected cost minimization. Consider how these effects differ in a later time period primarily characterized by more intense competition from unregulated generators. What is a Contract?

5 This Paper This paper posits firm-level as-if risk aversion brought about by the regulatory structure in place as an explanation for this contracting behavior. Therefore, this paper sets out to Posit a regulatory-based explanation for firms behaving as if they are risk-averse Document the existence of contracting behavior consistent with this as-if risk-aversion Quantify the magnitude of this behavior, and the extent of its deviation from expected cost minimization. Consider how these effects differ in a later time period primarily characterized by more intense competition from unregulated generators. What is a Contract?

6 This Paper This paper posits firm-level as-if risk aversion brought about by the regulatory structure in place as an explanation for this contracting behavior. Therefore, this paper sets out to Posit a regulatory-based explanation for firms behaving as if they are risk-averse Document the existence of contracting behavior consistent with this as-if risk-aversion Quantify the magnitude of this behavior, and the extent of its deviation from expected cost minimization. Consider how these effects differ in a later time period primarily characterized by more intense competition from unregulated generators. What is a Contract?

7 This Paper This paper posits firm-level as-if risk aversion brought about by the regulatory structure in place as an explanation for this contracting behavior. Therefore, this paper sets out to Posit a regulatory-based explanation for firms behaving as if they are risk-averse Document the existence of contracting behavior consistent with this as-if risk-aversion Quantify the magnitude of this behavior, and the extent of its deviation from expected cost minimization. Consider how these effects differ in a later time period primarily characterized by more intense competition from unregulated generators. What is a Contract?

8 This Paper This paper posits firm-level as-if risk aversion brought about by the regulatory structure in place as an explanation for this contracting behavior. Therefore, this paper sets out to Posit a regulatory-based explanation for firms behaving as if they are risk-averse Document the existence of contracting behavior consistent with this as-if risk-aversion Quantify the magnitude of this behavior, and the extent of its deviation from expected cost minimization. Consider how these effects differ in a later time period primarily characterized by more intense competition from unregulated generators. What is a Contract?

9 This Paper This paper posits firm-level as-if risk aversion brought about by the regulatory structure in place as an explanation for this contracting behavior. Therefore, this paper sets out to Posit a regulatory-based explanation for firms behaving as if they are risk-averse Document the existence of contracting behavior consistent with this as-if risk-aversion Quantify the magnitude of this behavior, and the extent of its deviation from expected cost minimization. Consider how these effects differ in a later time period primarily characterized by more intense competition from unregulated generators. What is a Contract?

10 Main Findings I show descriptively that predictions consistent with risk-aversion, and not readily explainable through other theories, hold in the data Through estimation of a static model of contract versus spot purchases where firms trade off mean and variance of total costs, I find a significant elasticity governing this tradeoff. I find that both the descriptive and structural results diminish in magnitude, but do not disappear, in the post 1992 period characterized by increased competition from unregulated generators

11 Brief Overview of in the 1980s All electric utilities were under rate-of-return regulation. In theory, this entails a regulator actively attempting to set output electricity price such that the firm has an opportunity to recover prudently incurred costs. Also, the majority of the plants in my sample were under some form of fuel adjustment clause, which allows firms to pass through all or a portion of fuel costs into the output price without a corresponding formal review.

12 How does the structure induce as-if behavior? Prudence (and less frequently exorbinance ) bounds on realized profit induce higher order profit moments into the firm s objective function If a firm asking for a rate increase incurs costs that are deemed to be significantly higher than what a reasonable manager acting in the same circumstances would have incurred, these costs may be flagged as imprudent and so not passed through to consumers via the output price. More rarely, if firms faces very low costs relative to the output price set, a consumer or environmental group may intervene through asking the state commission to initiate a rate case. Relevant regulatory literature Graphical Intuition

13 Stylized Motivating of Inducing As-if Risk Aversion Let TC N(µ, σ 2 (µ)), where σ 2 (µ) is decreasing in µ Consider the case of perfect cost passthrough, subject to prudence constraint. Therefore, the firm gets: R(TC realized ) = TC realized if TC TC TC otherwise In words, the case of perfect passthrough is where the firm earns zero profits for any cost realization lower that TC, and earns TC TC realized for any cost realizations higher than TC In this setup, I show that the following two optimization problems are approximately equivalent: max min µ M E[R(TC) TC] = µ M E[TC TC > TC] TC min φ µ M (µ + σ } (1 Φ)

14 Stylized Motivating of Inducing As-if Risk Aversion Let TC N(µ, σ 2 (µ)), where σ 2 (µ) is decreasing in µ Consider the case of perfect cost passthrough, subject to prudence constraint. Therefore, the firm gets: R(TC realized ) = TC realized if TC TC TC otherwise In words, the case of perfect passthrough is where the firm earns zero profits for any cost realization lower that TC, and earns TC TC realized for any cost realizations higher than TC In this setup, I show that the following two optimization problems are approximately equivalent: max min µ M E[R(TC) TC] = µ M E[TC TC > TC] TC min φ µ M (µ + σ } (1 Φ)

15 Stylized Motivating of Inducing As-if Risk Aversion Let TC N(µ, σ 2 (µ)), where σ 2 (µ) is decreasing in µ Consider the case of perfect cost passthrough, subject to prudence constraint. Therefore, the firm gets: R(TC realized ) = TC realized if TC TC TC otherwise In words, the case of perfect passthrough is where the firm earns zero profits for any cost realization lower that TC, and earns TC TC realized for any cost realizations higher than TC In this setup, I show that the following two optimization problems are approximately equivalent: max min µ M E[R(TC) TC] = µ M E[TC TC > TC] TC min φ µ M (µ + σ } (1 Φ)

16 How did Change in the 1990s? For my study, the most important legislation to consider is the Energy Policy Act of 1992 (EPACT), which opened up the national transmission grids to wholesale, unregulated suppliers of electricity. FERC Order 888 set out to implement this vast restructuring of the electricity industry, and the majority of the changes were completed by 1998 Also, the 1990 Amendments to the Clean Air Act made the environmental impacts of burning coal much more salient. These legislative changes may be more pertinent for how we expect transaction cost predictions to differ after these Amendments.

17 How did Change in the 1990s? For my study, the most important legislation to consider is the Energy Policy Act of 1992 (EPACT), which opened up the national transmission grids to wholesale, unregulated suppliers of electricity. FERC Order 888 set out to implement this vast restructuring of the electricity industry, and the majority of the changes were completed by 1998 Also, the 1990 Amendments to the Clean Air Act made the environmental impacts of burning coal much more salient. These legislative changes may be more pertinent for how we expect transaction cost predictions to differ after these Amendments.

18 Section Outline I examine contracting behavior in a descriptive framework, drawing from the transaction-cost based approach implemented in Joskow (1987). I show within this framework that so-called risk aversion covariates have additional explanatory power beyond these transaction cost covariates for my sample of contracts Further, I show that these descriptive findings diminish, but do not disappear, in my post 1992 sample ( ).

19 Joskow (1987) Contract Duration Regression, with Risk-aversion covariates, Table 3: Duration Results with Risk-aversion covariates, (1) (2) VARIABLES Log(duration) Log(duration) Spot Price NA ( ) Sd(Spot Price) ** NA ( ) Consumption -3.13e e-05** (3.99e-05) (3.93e-05) Sd(consumption) 6.12e-06*** 5.31e-06** (2.22e-06) (2.10e-06) Inventory 1.75e e-05*** (1.29e-05) (1.46e-05) Midwest Indicator 0.458*** 0.443*** (0.0866) (0.0714) West Indicator 0.631*** 0.630*** (0.240) (0.184) Minemouth Plant Indicator *** (0.139) (0.704) Log(Contract Quantity) *** *** (0.0207) (0.0191) Observations 881 1,037 R-squared Contract year signed fixed effects are included Unit of observation is a contract signed between plant and mine, at the year of signing The spot price (sd of spot price) are calculated from average (std. deviation) of monthly transaction-level data over the year of the contract signing. Inventory and consumption are summed from monthly plant-level data, using the within-year standard deviation for std(con) The spot price data come from monthly, transaction-level data from FERC Form 423. The inventory and consumption data are from FERC Form 759. Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

20 Contract Proportion Regression using VAR model with GARCH errors, Table 6: Quantity Regression using VAR(1) model with GARCH errors, Comparing versus VARIABLES Contract proportion Contract proportion Contract proportion Contract proportion Contract Premium ** *** *** ( ) ( ) ( ) ( ) Var(Spot Price) *** ** ( ) (8.66e-05) (0.0310) ( ) Var(consumption) 8.28e-11*** 1.23e-10*** 2.34e e-09 (1.68e-11) (2.37e-11) (1.55e-09) (8.90e-09) Midwest or West Plant *** *** Date Fixed Effects? Plant Fixed Effects? (0.0130) (0.0105) (0.0152) (6.193) Y Y N N N N Y Y Observations 1,065 1,349 1,065 1,349 R-squared Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Unit of Observation is Plant-month of sample, using a subsample of plant that transact on both contract and spot markets in all periods Contract Premium = contract price E[spot price], and these prices are from monthly FERC Form 423 data on transactions. The variances for consumption and spot price are computed using a VAR(1) model with GARCH errors, and I divided Contract Quantity, Stock, and Consumption scaled to be in 10 billion BTU Spot Price scaled to be in $/1millionBTU In the sample, there are no West cost plants; there is only one West coast plant in the sample

21 Overall s from the Section The overall descriptive findings for both duration and contract quantity suggest that as-if risk aversion plays an important role in explaining contract behavior, in addition to the traditional transaction cost explanation. These findings are diminished, but do not disappear, in the descriptive analysis on post 1992 data These results indicate further investigation of the role of risk aversion in fuel procurement behavior. Duration Regression Comparison with Quantity Regression with Full Sample

22 Description I consider a static model where a plant with preferences over mean and variance of total costs can purchase a fixed amount of coal from either contract or spot transactions This plant faces spot price risk, as well as demand risk, noting that these two are likely correlated The primary goal of this modeling effort is to assign magnitudes to the plant-level distortion from the expected cost minimization benchmark.

23 Timing The plant first chooses contract quantity, facing uncertain demand and spot price (but knowing the contract price) Demand and spot price are realized The plant purchases its residual demand from the spot market

24 Assumptions The information set at the beginning of time t is {p C s } t s=1, {p S s } t 1 s=1, and {Y s} t s=1 Revenue is fixed by regulation, and so does not enter the mean or variance of the plant s objective function. The plant takes contract and spot prices, as well as electricity demanded as given; it cannot affect these magnitudes through its behavior.

25 Setup and Results In each period t, the plant maximizes: max c t 0 U(E t[ p C t c t p S t (Y t c t )], Var t [ p C t c t p S t (Y t c t )]) Solving this problem: p C t = E t [p S t ] + 2λ(c t Var t [p S t ] + Cov t [p S t, p S t Y t ]) However, note that λ as defined is not unitless: Define ɛ i U2Var[ pc t ct ps t (Yt ct)] U 1E[ p C t ct ps t (Yt ct) The above is an elasticity governing the plant s trade-off between mean and variance of total costs

26 First-Stage VAR with GARCH errors I use within-plant, time-series variation in order to obtain the price and demand moments for the above equation However, some plants do not transact on both the spot and contract markets in every period Therefore, I simply estimate for the subsample of plants transacting via both spot and contract transactions. I estimate this first-stage model separately for the periods and I do not estimate for both due to sample considerations and due to the 1986 Oil Price Collapse.

27 First-Stage VAR with GARCH errors I use within-plant, time-series variation in order to obtain the price and demand moments for the above equation However, some plants do not transact on both the spot and contract markets in every period Therefore, I simply estimate for the subsample of plants transacting via both spot and contract transactions. I estimate this first-stage model separately for the periods and I do not estimate for both due to sample considerations and due to the 1986 Oil Price Collapse.

28 First-Stage VAR with GARCH errors I use within-plant, time-series variation in order to obtain the price and demand moments for the above equation However, some plants do not transact on both the spot and contract markets in every period Therefore, I simply estimate for the subsample of plants transacting via both spot and contract transactions. I estimate this first-stage model separately for the periods and I do not estimate for both due to sample considerations and due to the 1986 Oil Price Collapse.

29 Counterfactual of Expected Cost Minimization First, I simply construct the counterfactual where firms are only interested in minimizing expected total costs. I can compare this counterfactual to the observed expected total costs. I compute a finite difference elasticity based on the actual versus counterfactual costs I show that MRS C > MRS A ( ɛ C > ɛ A ) In words, under utility maximization, the cost-minimizing bundle contains too much variance relative to the optimum. The firm is willing to trade for relatively more mean in total costs for a one unit decrease in the variance.

30 Counterfactual of Expected Cost Minimization First, I simply construct the counterfactual where firms are only interested in minimizing expected total costs. I can compare this counterfactual to the observed expected total costs. I compute a finite difference elasticity based on the actual versus counterfactual costs I show that MRS C > MRS A ( ɛ C > ɛ A ) In words, under utility maximization, the cost-minimizing bundle contains too much variance relative to the optimum. The firm is willing to trade for relatively more mean in total costs for a one unit decrease in the variance.

31 Full Table of Results Table 7: Statistics relating to Contract Timing using Complete Price Data plants Variable Mean Std. Dev. Mean Std. Dev Elasticity Mean Actual Costs ($) Mean Cost Minimization Counterfactual Costs ($) Variance of Actual Costs ($) (%change in mean counterfactual actual cost)/(%change in variance of counterfactual actual cost) ( ) ( ) E E E E ( ) Note that the standard error of the elasticity is for and for ( ) Unit of observation is plant-date Elasticity is calculated as (U 2 *vartc)/(u 1 *meantc) = λvartc/meantc, where λ varies by plant, and costs vary by plant-date The counterfactual profits correspond to a case where λ=0 (%change in mean counterfactual actual costs) = (counter_mean_costs actual_mean_costs)/actual_mean_costs (%change in mean counterfactual actual costs) = (counter_variance_costs actual_variance_costs)/actual_variance_costs

32 Overall s from the Section Without estimation of the fuel procurement model, we can still compare the expected cost minimization counterfactual to the expected total costs in actuality. I find the difference in these (expected) costs to be 18.47/ From the fuel procurement model, the elasticity governing the tradeoff between mean and variance of total costs is significant both economically and statistically, at ɛ = 2.48 Both of these results are diminished in magnitude when you re-run the analysis for

33 From the descriptive analysis, I demonstrate that firm risk-aversion provides additional explanatory power to the more traditional transaction-cost explanations for contracting behavior The static model with mean-variance preferences over total cost provides an economic magnitude for the above result, indicating that the tradeoff firms make between mean and variance of costs is non-trivial (ɛ = 2.48) These results are diminished, but do not disappear, when the analysis is performed on data from after 1992.

34 Future Similar as-if risk -aversion is potentially observed in the coal inventory behavior of these plants. Are there important dynamic considerations in the behavior of these regulated plants? I plan on more explicitly examining the interaction between regulator and regulated; what types of strategic behavior do we expect from the utility (ex: cost-padding prior to a regulatory meeting), and to what extent is the regulator inhibited by asymmetric information (and how does this disadvantage change over time within a given relationship?)

35 Thanks for your time

36 PPI for Coal Graph,

37 PPI for Coal Graph,

38 Contract versus Spot Prices Difference, Mean over plants for each date, Figure 1(b): Contract Minus Spot Coal Price Difference: Mean By Date, The contract and spot prices are obtained from monthly FERC Form 423 data on transactions between plant and mine. These prices are quantityweighted means over all plants in the sample for each month. The contract prices used are the coal prices as delivered, including transport costs (spot prices also include transport charges). The definition of contract is an agreement to purchase input coal lasting greater than one year.

39 Contract versus Spot Prices, Mean over plants for each date, Figure A2(b): Contract versus Spot Coal Price: Mean By Date for The contract and spot prices are obtained from monthly FERC Form 423 data on transactions between plant and mine. These prices are quantity-weighted means over all plants in the sample for each month. The contract prices used are the coal prices as delivered, including transport costs. The definition of contract is an agreement to purchase input coal, with repeated deliveries, lasting greater than one year.

40 Aggregate Contract versus Spot Quantities, Sum over plants for Figure 2(a): Contract versus Spot Coal Quantities: Sum By Date, The contract and spot quantities are obtained from monthly FERC Form 423 data on transactions between plant and mine. The definition of contract is an agreement to purchase input coal, with repeated deliveries, lasting greater than one year.

41 Aggregate Contract Proportion, Figure 2(b): Proportion of Coal Purchased Via Contract: By Date, The contract and spot quantities are obtained from monthly FERC Form 423 data on transactions between plant and mine. The definition of contract is an agreement to purchase input coal, with repeated deliveries, lasting greater than one year.

42 Summary Stats for Contract Dataset, Table 1: Summary Statistics for Contract Dataset, Name Description Mean Std. Dev N Quantity Contracted Total distance Quantity shipped by contract in year of signing (in 1000 short tons) Total distance from mine to plant Indicator of whether the plant is located adjacent to a mine Minemouth Indicator Duration Contract Duration (in years) Inventory Coal inventory for year of contract signing (in 1000 short tons) Consumption Coal consumption for year of contract signing (in 1000 short tons) Spot Price Average Spot price, gross of transport (in $/100 million BTU) Sd(consumption) Standard deviation, within the year the contract was signed, from monthly data Sd(Spot Price) Standard deviation, within the year the contract was signed, from monthly data Midwest Indicator if plant is located in the Midwest West Indicator Indicator if plant is located in the West The unit of observation for this table is a contract between mine and plant at the time of signing. The spot price is averaged over the year of signing from monthly FERC Form 423 data on transactions,whereas consumption and inventory variables are summed over the year of signing from monthly plant-level data obtain from EIA Form 759

43 Summary Stats for Contract Dataset, Table A1: Summary Statistics for Contract Dataset, Name Description Mean Std. Dev N Quantity Contracted Total distance Minemouth Indicator Quantity shipped by contract in year of signing (in 1000 short tons) Total distance from mine to plant Indicator of whether the plant is located adjacent to a mine Duration Contract Duration (in years) Inventory Coal inventory for year of contract signing (in 1000 short tons) Consumption Coal consumption for year of contract signing (in 1000 short tons) Spot Price Average Spot price, gross of transport (in $/100 million BTU) Sd(consumption) Standard deviation, within the year the contract was signed, from monthly transaction data Sd(Spot Price) Standard deviation, within the year the contract was signed, from monthly transaction data Midwest Indicator if plant is located in the Midwest West Indicator Indicator if plant is located in the West The unit of observation for this table is a contract between mine and plant at the time of signing. The spot price is averaged over the year of signing from monthly FERC Form 423 data on transactions,whereas consumption and inventory variables are summed over the year of signing from monthly plant-level data and obtained from EIA Form 759

44 Summary Stats for Quantity Dataset, Table A2: Summary Statistics for Quantity Regressions, Name Description Mean Std. Dev N Quantity Contracted Consumption Profile Inventory Profile Contract Premium Sd(consumption) Sd(Spot Price) Midwest Indicator West Indicator Monthly Contract quantity delivered (in 10 billion BTUs) The mean over the entire sample of consumption for the plant (in 10 billion BTUs) The mean over the entire sample inventory for the plant (in 10 billion BTUs) Contract price Spot price (in $/100 million BTU) Standard deviation over the year of the observation (in 10 billion BTUs) Standard deviation over the year of the observation (in $/100 million BTU) Indicator if the plant corresponding to the observation is from the Midwest Indicator if the plant corresponding to the observation is from the West The unit of observation for this table is a plant in a given month. Consumption and inventory profiles are means over the entire sample taken from monthly plant-level data obtain from EIA Form 759. The remaining variables are taken from monthly transaction level data from FERC Form 423.

45 Summary Stats for Dataset, Table A3: Summary Statistics for sample, Name Description Mean Std. Dev N Contract Proportion Amount Purchased Contact Price Expected Spot Price Var(Amount Purchased) Var(Spot Price) Midwest or West Indicator Monthly Contract quantity delivered (in 10 billion BTUs) The mean over the entire sample of consumption for the plant (in 10 billion BTUs) The mean over the entire sample inventory for the plant (in 10 billion BTUs) E[Spot price] (in $/100 million BTU) Variance from the VAR+GARCH model (in $/100 million BTU squared) Variance from the VAR+GARCH model (in $/100 million BTU squared) Indicator if the plant corresponding to the observation is from the Midwest The unit of observation for this table is a plant in a given month. Contract proportion, total quantity purchased, and the prices are taken from monthly transaction level data from FERC Form 423. The variance variables are derived from a VAR model with GARCH(1,1) errors (see paper for the exact specification)

46 Summary Stats for Dataset, Table A4: Summary Statistics for sample, Name Description Mean Std. Dev N Contract Proportion Amount Purchased Contract Price Expected Spot Price Var(Amount Purchased) Var(Spot Price) Midwest or West Indicator Monthly Contract quantity delivered (in 10 billion BTUs) The mean over the entire sample of consumption for the plant (in 10 billion BTUs) The mean over the entire sample inventory for the plant (in 10 billion BTUs) E[Spot price] (in $/100 million BTU) Variance from the VAR+GARCH model (in $/100 million BTU squared) Variance from the VAR+GARCH model (in $/100 million BTU squared) Indicator if the plant corresponding to the observation is from the Midwest The unit of observation for this table is a plant in a given month. Contract proportion, total quantity purchased, and the prices are taken from monthly transaction level data from FERC Form 423. The variance variables are derived from a VAR model with GARCH(1,1) errors (see paper for the exact specification)

47 Joskow (1987) Contract Duration Regression, using data from Table : Estimation of Contract Duration Regressions from Joskow 1987 (1) (2) (3) VARIABLES Duration Duration Log(Duration) Quantity Contracted *** NA NA ( ) (Quantity Contracted)^2-4.04e-07 NA NA (4.50e-07) Minemouth Plant Indicator (9.562) (9.623) (0.790) Midwest Plant Indicator 2.615*** 2.822*** 0.455*** (0.394) (0.401) (0.0686) West Plant Indicator 4.742*** 4.875*** 0.629*** (1.403) (1.377) (0.186) Log(Quantity Contracted) NA 0.354*** *** (0.114) (0.0196) Constant 5.018*** 4.258*** 0.931*** (0.518) (0.648) (0.118) Contract Year Signed Fixed Effects? Y Y Y Observations 1,047 1,047 1,047 R-squared Unit of observation is a contract signed between plant and mine, at the year of signing. These data come from the Coal Rate Transportation Data Base. Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Back to Duration Regression

48 Joskow (1987) Contract Duration Regression, with Risk-aversion covariates, Table 5: Duration Regression comparing to Risk Aversion Covariate Results (1) (2) VARIABLES Log(duration) Log(duration) Sd(Spot Price)*(year<=1992) *** NA ( ) Sd(Spot Price) * (year>1992) NA ( ) Sd(Consumption)*(year<=1992) 5.00e-06** 4.06e-06* (2.19e-06) (2.07e-06) Sd(Consumption)*(year>1992) 5.25e-06*** 6.21e-06*** (1.86e-06) (1.73e-06) Inventory*(year<=1992) 1.94e e-05*** (1.20e-05) (1.26e-05) Inventory*(year>1992) -2.90e e-06 (1.35e-05) (1.31e-05) Observations 1,299 1,501 R-squared Additional covariates are log(tons_shipped), minemouth indicator, plant consumption, region indicators and contract year signed fixed effects Unit of observation is a contract signed between plant and mine, at the year of signing The spot price (sd of spot price) are calculated from average (std. deviation) of monthly transaction-level data over the year of the contract signing. Inventory and consumption are summed from monthly plant-level data, using the within-year standard deviation for std(con) Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Contract year signed fixed effects included Back to Duration Regression

49 Contract Quantity Regression, with Risk-aversion covariates, Table 4: Quantity Regression with Risk-aversion covariates, (1) (2) (3) (4) VARIABLES Contract quantity Contract Quantity Contract quantity Contract quantity Contract Premium Sd(Spot Price) Sd(consumption) Inventory Profile Consumption Profile Midwest West Date Fixed Effects? Plant Fixed Effects? Observations R-squared * *** NA NA (0.0498) (0.0592) 0.934*** 0.262** NA NA (0.153) (0.125) *** 0.142*** * (0.0475) (0.0629) (0.0347) (0.0520) *** ** *** ( ) (0.0125) ( ) ( ) 0.709*** 0.922*** 0.852*** 1.067*** (0.0146) (0.0412) ( ) (0.0594) ** 16.81*** * (2.872) (4.525) (1.791) (3.218) *** 43.46*** 46.56*** (4.518) (8.049) (2.993) (4.911) Y N Y N N Y N Y 13,250 13,250 32,558 32, Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Unit of Observation is Plant-month of sample Contract Premium = contract price - spot price, and these prices are from monthly FERC Form 423 data on transactions. The inventory and consumption variables are means for each firm over the entire sample. The standard deviations for consumption and spot price are taken within year, over months from the corresponding datasets Contract Quantity, Stock, and Consumption scaled to be in 10 billion BTU Spot Price scaled to be in $/1millionBTU Back

50 What is a contract? The definition of a contract in the data is any coal purchase agreement between firm and mine lasting in excess of one year. These contracts specify repeated delivery of coal, and typically allow for adjustments by the firm in delivered quantity of coal. The typical contract is base price plus escalation, where some base price is set at the time of signing, and formulaic adjustments to this price are made based on market and cost conditions. Back

51 Relevant Literature on Constraints Joskow (1974) describes a passive regulator for whom the nominal output price is salient. In this framework: Realized profits below a level Π L correspond with a utility-initiated rate review, though realized profits below Π L may be deemed to be imprudently incurred, and so will be incurred by the firm. Realized profits above a certain level Π H trigger a consumer/environmental group initiated rate review, and may subsequently be confiscated by the regulator. Schmidt (1980) argues that some FACs in practice exercise partial passthrough, where 100 percent of the cost decreases are automatically passed through, yet less than 100 percent of the cost increases are passed through to the consumer. Back

52 Relevant Literature on Constraints Joskow (1974) describes a passive regulator for whom the nominal output price is salient. In this framework: Realized profits below a level Π L correspond with a utility-initiated rate review, though realized profits below Π L may be deemed to be imprudently incurred, and so will be incurred by the firm. Realized profits above a certain level Π H trigger a consumer/environmental group initiated rate review, and may subsequently be confiscated by the regulator. Schmidt (1980) argues that some FACs in practice exercise partial passthrough, where 100 percent of the cost decreases are automatically passed through, yet less than 100 percent of the cost increases are passed through to the consumer. Back

53 Graphical Intuition of Bounds Figure B1: Normal Distribution of Profits, with Bounds pdf Prudency Bound 0 Exorbitance Bound Profits The green portions of the graph are ranges of profits where the firm keeps that realization of profits; the yellow portions are ranges of profits where the regulator steps in and sets realized profit to zero. Back