ECO 4321 Hotelling Under Pressure

HUP and Positive demand shocks

Positive global demand shocks lead to an immediate increase in oil prices, drilling activity, and rig rental prices - and that oil prices may gradually fall if the increased rate of drilling causes production to gradually increase. These results are reversed for negative demand shocks

HUP and local supply shocks

The new model correctly predicts that local supply shocks arising either from the discovery of new resources or from cost-reducing technical change lead to a surge in drilling and then production

Hotelling's Rule

A theory stating that in equilibrium the net price (price minus production costs) of a resource must rise at a rate equal to the rate of interest.

Traditional Hotelling Model

Price net of marginal extraction cost must have the same present value whenever production occurs P0 - MC0 = (P1 - MC1) / (r + 1)

Endogenous HUP: Decrease in oil demand

A decrease in oil demand will cause the oil price, rate of drilling, and rig rental rate all to decrease immediately Subsequently, production may fall (if the shock was large enough or if it was falling already - in the latter case, it will fall at a faster rate) leading the oil price to gradually rise after impact For a sufficiently large shock, the price may rise faster than the interest rate, provide that oil demand is sufficiently inelastic

Implication of Darcy's Law on HUP

Extractors want to maximize the present value of net cash flows (drilling rev - drilling cost) It is super inexpensive to extract oil up to the capacity constraint of a well. Drilling today however, means there are fewer untapped wells. If we don't drill anything, the capacity constraint decreases with actual existing flow. If we drill more, we increase the capacity constraint

Exogenous HUP: Unanticipated increase in reserves

If the supply of undrilled wells increases, the rate of drilling and the rig rental rate will immediately jump up and the time interval over which drilling is non-zero will be longer than before.

Oil Production and intensive/extensive margins

the intensive margin does not play a significant role in determining (changes in) oil output

When should new wells be drilled in HUP?

New wells create new capacity. If the value of that capacity is greater than the marginal cost of drilling, one might need to drill For a firm to hold an undrilled well, its value must rise by at least the discount rate and no faster. Thus drilling occurs when the marginal return to drilling rises at rate r TH says the marginal value of barrels rises at the rate of interest HUP says the TH rule applies to wells and not barrels

Keg Tapping vs Cake eating

Oil extraction is more akin to a "keg tapping" problem than a "cake-eating" problem: Extractors choose when to drill their wells (or tap their kegs), but the flow from these wells is (like libations from a keg) constrained because of pressure and decays toward zero as more oil is extracted.

Two facts about Oil production

Oil production from existing wells declines asymptotically toward zero and is almost completely unresponsive to price shocks The drilling of NEW oil wells in Texas and the rental price of drilling rigs both respond strongly to oil price shocks

What causes production to increase? HUP v. TH

The extended model links capacity expansion to drilling activity (and NOT to increased production from existing wells) and links the marginal cost of capacity expansion to the rental rates on drilling rigs

Endogenous HUP: Drilling Incentives

The marginal discounted revenue from drilling initially falls as the oil price falls, but then rises, asymptotically approaching $50 million per well Marginal drilling costs fall with the rate of drilling so that the marginal profit per well rises at the interest rate until drilling ceases (the modified Hotelling Rule)

Darcy's Law

The rate of flow from a well is proportional to the pressure differential between the reservoir and the well

Exogenous Price version of HUP

The model assumes that the oil price is taken as given by extractors. Rig Rental Rates are explained by the model Production is always capacity constrained If drilling is profitable, then the equilibrium rig rate must fall over time, so drilling remains attractive as new wells are drilled Drilling must stop when the initial supply of untapped wells is exhausted (In the graph, production starts at 0 and increases as the stock of drilled wells increases, then falls to 0 as the remaining volume of oil declines)

The HUP model and how production changes over time

The new model correctly predicts that production in a region will initially rise as drilling ramps up but then peaks and eventually declines as drilling slows down and declining flow from existing wells is most of all production

Implications of the "Under Pressure" Model

The new model explains the two facts about oil production Production from existing wells is not sensitive to oil price changes, but drilling of new wells is sensitive to oil price changes Total production evolves only gradually over time, responding to price shocks with a delay (Aggregate oil production is price inelastic)

Endogenous HUP: Implications

The rate of drilling is initially high but decreases rapidly Thus, the rate of oil production rapidly rises from zero initially to a plateau-like peak and then enters a decline as the drilling rate falls to zero. The time path of oil prices is therefore U-shaped.

Key Features of HUP

The rate of drilling is more important than the rate of oil production Hotelling Logic still applies: The difference between MR of drilling and MC of drilling rises at the interest rate.

Facts about Industry costs that explain these responses

The rate of production from a well is physically constrained and declines asymptotically toward zero as a function of cumulative production. The marginal cost of production below a well's capacity constraint is small relative to oil prices The fixed cost of operating a producing well is non-zero. There may be costs for re-starting a shut in well, but they aren't too high to be overcome Drilling rigs and crews are pretty fixed in the short run, so higher rental rates are required to attract more rigs into use so rent rigs have an upward sloping supply curve

Hotelling "Under Pressure" Model

The stream of revenues a well earns over its lifetime, net of the cost of drilling the well, must have the same present value whenever drilling occurs Well Rev0 - Cost of drilling0 = (Well Rev1 - Cost of Drilling1) / (r + 1)

Exogenous HUP: Initial Flow Shock

This can be viewed as an increase in technology. Doubling the initial flow will have the same effects on the paths of drilling and rental rates as doubling the price

Why do existing wells not respond to price shocks?

This is because initially reservoir pressure is high when a well is first drilled so production is high. However, over time as extraction depletes reserves, pressure declines and production converge to zero. This pressure constraint makes it expensive to withhold selling oil from existing wells, so shocks do not affect it. This means that drilling incentives are what determine production

Can Oil Prices rise faster than the rate of interest in equilibrium? HUP v. TH

Traditional Hotelling model: NO Revised Hotelling model: YES This phenomenon is implied by oil futures price data

Production from existing wells and price changes

Production from Existing Wells does not respond to prices.

Why can ccp be optimal when oil prices rise faster that the interest rate?

Any production that is deferred today cannot be completely recovered at the future instant in which it is most valuable. Instead, the deferred production must be recovered over the full remaining life of the well, including the time period when the oil price is higher than the current price in present value. If the value lost during the latter period outweighs the value gained during the former period, ... [it will be] optimal to operate at the capacity constraint even though the oil price will (temporarily) rise faster than r.

Exogenous HUP: Oil Price

Because the stock of wells is fixed, the oil price can affect the timing of drilling but not the total drilling. For a high oil price, the initial rate of drilling and rig rate will also be high. In this case, wells are drilled more quickly, and production happens earlier in time. Higher prices also increase the wealth generated from the well

Exogenous HUP: Unanticipated price shock

Comparing low and high oil prices can be interpreted as an analysis of the effects of an unanticipated (but permanent) price shock Suppose the price of oil is expected to be low forever, but then suddenly increases to a higher level Drilling and rig rates immediately jump up Production increases more quickly so the curve is steeper and more narrow

Endogenous HUP: Increase in oil demand

Expected oil price rises Oil drilling increases immediately Rig Rental rate also rises Production cannot immediately increase because it is capacity constrained Actual oil price rises immediately If the shock is large enough, the jump in drilling will be sufficient to cause production to gradually increase as new wells come online, causing prices to gradually fall subsequent to the initial impact

Why does production fall? HUP v. TH

HUP: production falls because of the flow constraint that declines with cumulative extraction TH: Production falls because of rising Hotelling rent. Extractors move production into the future in anticipation of higher discounted expected returns

Exogenous HUP: Marginal cost of drilling new wells shock

Halving the marginal drilling cost (due to technological progress) has the same effect on drilling as initial flow doubling, but the increase in wealth would only be half as much as with the price doubling.

Endogenous HUP: Oil Prices

Price adjusts to equate supply and demand As with the exogenous price case, drilling is initially high but then decreases monotonically over time. Starting with initial capacity of zero, we initially have no production so that the oil price is very high, generating a strong incentive to drill at a rapid rate. From there, the oil price must initially decline as capacity, and therefore production (and supply) is added. In order to have the current value of an undrilled well increase at rate r, the marginal drilling cost and therefore the rate of drilling must initially be decreasing. If the initial capacity is sufficiently low, the drilling rate will be decreasing not just initially but throughout the entire equilibrium path, yielding a single-peaked production profile. Production will be capacity constrained along the entire path. If the initial capacity is sufficiently large relative to oil demand, the initial rate of drilling with endogenous prices will be low, owing to the initially low price. As capacity is exhausted, the oil price will rise, which can cause the drilling rate to initially increase over time (though it must eventually fall as the stock of undrilled wells nears exhaustion).

Endogenous price version of HUP

Price of oil is determined by the model Drilling can never steadily increase To account for the persistent technological progress that resulted from the development of hydraulic fracturing, the model may be augmented to allow the marginal cost of drilling to decrease at an exogenous rate This means that the drilling rate increases over time only if the revenue earned by a newly drilled well is sufficiently far above the value of an undrilled well

Intensive Margin

Production from existing wells

Extensive Margin

Production from newly drilled wells

Rig activity and price changes

Rig Activity DOES Respond to Price Incentives

Rig day rate and price changes

Rig day rates do respond to price changes

Endogenous HUP: Technological Progress

Sufficiently rapid downward shifts in the drilling supply curve (due to technological progress) initially lead drilling activity to increase, even as the value of an undrilled well grows at the rate of interest. However, drilling costs are bounded from below by zero. Thus, the relentlessly growing scarcity rent must eventually dominate, driving a decline in drilling. For low rates of technological progress, the rising scarcity rent always dominates, so the drilling rate never increases.

Novel feature of HUP

capacity-constrained production can be optimal during periods when the oil price increases strictly faster than the interest rate (r), provided that the magnitude and duration of this increase are limited.