Water and Economics: Overview of Change and Feedback Bradley T. Ewing, Ph.D. Rawls Professor in Operations Management Rawls College of Business Texas Tech.

Water and Economics:Overview of Change and

Feedback

Bradley T. Ewing, Ph.D.Rawls Professor in Operations Management

Rawls College of BusinessTexas Tech University

WATER & ECONOMICS

• Do water and economics mix?– The Dismal Science– Usual connotations – retirement, investing,…– Decision-making, valuation, human behavior– The diamond-water paradox?

• Water – “place-based”– Water events (abnormal level, rainfall,…)– Water management and use (systems,…)

WATER & ECONOMICS

• General comments– Areas (often) covered

• Business interruption, recovery, mitigation, optimal use,…

– Economics• Decision-making → Effective use of information• Analysis of impacts, growth, etc. (Regional, State, National)

– Approaches• Project management (“portfolio approach”) – e.g., large scale

construction project, treatment plant• Systems analysis (“linkages” among agents/areas) – e.g.,

evacuation plan, policy programs• Quantitative tools

WATER & ECONOMICS Applications & Research

• Individual decisions (involving risk perception)– Construction of structures (homes, mitigation, …)

• Performance of the economy (as measured by “economic indicators”)– Labor market: unemployment, employment, income– Output: production of goods & services, agricultural, power– Supply chain: efficiency (incl. systems – sewer, treatment,…)

• Financial markets– Insurer stock prices– Bank performance– Municipal bond rating

WATER & ECONOMICS Methods & Techniques

• Time Series– Standard: Unit roots, Event study & Intervention

Analysis• ADF, ARIMA, “dummy” variables

– Advanced: VAR, IRF, GARCH, TAR/M-TAR, cointegration

• (Bi)GARCH, regime changes & structural breaks, out-of-sample

• Engineering Economics– EIA: Input-Output (Systems), IMPLAN– LCCA– CBA

RESEARCH – Some Examples

• Water Level and Flow Rate– TAR/M-TAR

• Ecological System and Freshwater Organisms– VAR & GIRF

• Insurer stock performance following weather (wind) event– Event study or intervention analysis

• Weather Risk– Conceptual & applied (time series, other)

Do Flow Rates Respond Asymmetrically to Water Level? Evidence from the Edwards Aquifer

Bradley T. Ewing

Texas Tech University

Teresa Kerr

Baylor University

Mark A. Thompson

University of Arkansas – Little Rock

Published in Journal of Applied Statistics (2006)

Research – TAR/M-TAR

• Determine and model short run and long run relationships between water level and flow rate and model the (possibly asymmetric) return to equilibrium following disturbance– That is, the adjustment back to their long run equilibrium relationship may

be faster or slower depending upon whether the disequilibrium is in the positive or negative phase.

– Additionally, the response is asymmetric if the adjustment exhibits more momentum in one direction than the other.

• Examine whether positive vs. negative changes in disequilibrium have a different effect on the behavior of flow rates and water level.

• Provide useful information as to how and to what extent periods of water shortages differ from periods of water surplus.

Research – TAR/M-TAR

• TSP vs. DSP – short and long memory processes• Common trend? Statistical property known as cointegration

4.8

5.2

5.6

6.0

6.4

6.44

6.46

6.48

6.50

6.52

6.54

6.56

1998 1999 2000 2001 2002 2003

Flow rate Water level

Research – TAR/M-TAR

• TSP vs. DSP – short and long memory processes• Common trend? Statistical property known as cointegration• Engle and Granger (1987) – method to test for cointegration

– Linear combination of nonstationary I(1) variables may form a stationary series

– Error correction models – short run dynamics and long run relationships

• augmented Dickey-Fuller (ADF) test (note: critical values) where H0 is that X is nonstationary and is rejected if (1–1)<0

t

m

1kktk1t10t uXX)1(X

Research – TAR/M-TAR

• Cointegrating relation:

ttt WF

• We test for cointegration based on the null hypothesis of =0. The key point to note is that the alternative hypothesis implicitly assumes a symmetric adjustment process around the disequilibrium, .

t

p

1iiti1tt vˆˆˆ

0 0

Research – TAR/M-TAR

• But… unit root and cointegration tests have low power in the presence of an asymmetric adjustment process

• TAR model allows for asymmetry and highlights discrepancies between positive and negative phases (Enders & Granger, 1998; Enders & Siklos, 2001)– Note: adjustment depends on last period’s disequilibrium

t

p

1iiti1t2t1t1tt v~ˆˆ)I1(ˆIˆ

0ˆif0

0ˆif1I

1t

1tt

Research – TAR/M-TAR

• M-TAR– allows the adjustment to depend on the previous period's change in

disequilibrium. This model is especially valuable when the ad justment is believed to exhibit more momentum in one direction than the other.

– A consistent estimator is avialable for the “threshold” (zero or tau)

1t

1tt ˆif0

ˆif1I

Research – TAR/M-TAR

• Null hypothesis of no cointegration can be tested by the restriction:

t

p

1iiti1t2t1t1tt v~ˆˆ)I1(ˆIˆ

021

• Null hypothesis of symmetry can be tested by the restriction:

21

Research – TAR/M-TAR

Symmetric Asymmetric

Engle-Granger TARM-TAR

(=0)M-TAR

(consistent)

1a -0.021

(-4.745)-0.022

(-2.836)-0.032

(-5.160)-0.053

(-6.292)

2a ---

-0.021(-3.803)

-0.009(-1.411)

-0.009(-1.662)

b --- 11.252 14.310 21.174

1 = 2c ---

0.004(0.952)

6.186(0.013)

19.766(<0.001)

a Entries in parentheses are the t-statistic for the null hypothesis =0.b Entries represent the sample values of (see Enders and Siklos, 2001).c Entries represent the sample F-statistics for the null hypothesis 1 = 2 (adjustment coefficients are equal, i.e., symmetric adjustment).Entries in parentheses are p-values.

Research – TAR/M-TAR

• Asymmetric Error Correction Model (and Granger-causality), t-stats in parentheses

• Comment:– “Granger-causality” tests on joint null hypothesis that a particular subset of

variables has no effect on the current change in flow rate. The F-statistics indicate that past changes of flow rates, water level, and (level of) precipitation each Granger-cause current changes in flow rates.

t

01.0F

p

1kktk

01.0F

n

1jjtj

04.0F

m

1iiti

1tt)65.2(

1tt)12.5()08.3(

t

PΔWΔF

ˆI10123.0ˆI0.03760009.0ΔF

),0.(D.I.I~u 2t 1t1t1t WˆˆFˆ

Time Series Analysis of a Predator-Prey System:Application of VAR and Generalized Impulse Response Function

Bradley T. Ewing

Texas Tech University

Kent Riggs

Stephen F. Austin State University

Keith L. Ewing

Kent State University

Published in Ecological Economics (2007)

Research – VAR & Impulse Response Analysis

• Time series econometric approach to study ecological systems and freshwater organisms

• Understand the dynamics of organisms and population densities within an ecological system for successful environmental management and sustainability

• How will organisms respond to the introduction (or invasion) of additional plant or animal species, natural and/or man-made environmental disruptions, as well as other perturbations and unexpected changes in population densities? (intended and unintended abrupt changes)

Research – VAR & Impulse Response Analysis

• Vector Autoregression (VAR) – multiple equation system

– VAR methodology makes minimal theoretical demands on the structure of the underlying model

– Nonstructural VAR model

(L)Xt = A0 + vt

Research – VAR & Impulse Response Analysis

• Impulse Response Analysis– Intuition:

• Model produces expectation, M

• Realized value is X

• Equilibrium (baseline) is v = X – M = 0

• v = X – M, where X > M v > 0 in period t

• How does X respond to “shock” going into the future?

Research – VAR & Impulse Response Analysis

• Consider MA representation of the VAR

Xt = (L)vt

• Let E(vtvt) = v

(shocks may be contemporaneously correlated)

• GIRF of Xi to a one s.d. shock in Xj is given by:

ij,h = (ii)-1/2 (e'jvei)

where e is a selection vector

Research – VAR & Impulse Response Analysis

t

m

i iti

m

i itit

t

m

i iti

m

i itit

vPREDGbPREYGaaPREDG

vPREDGbPREYGaaPREYG

21 21 220

11 11 110

-1

0

1

2

3

4

5 10 15 20 25 30 35 40 45 50

PREYG PREDG

Research – VAR & Impulse Response Analysis

Notes: PREYG denotes the population density growth rate of the prey and PREDG denotes the population density growth rate of the predator. The forecast horizon (h) is measured in 12 hour intervals and is given on the horizontal axis. The vertical axis measures the magnitude of the response to the impulse, scaled such that 1.0 equals one standard deviation. Confidence bands, used to determine statistical significance of an impulse response at horizon h, where h = 1,2 ,…20, are shown as dashed (----) lines and represent 2 standard errors.

-.3

-.2

-.1

.0

.1

.2

.3

2 4 6 8 10 12 14 16 18 20

Response of PREYG to PREYG

-.3

-.2

-.1

.0

.1

.2

.3

2 4 6 8 10 12 14 16 18 20

Response of PREYG to PREDG

-.3

-.2

-.1

.0

.1

.2

.3

2 4 6 8 10 12 14 16 18 20

Response of PREDG to PREYG

-.3

-.2

-.1

.0

.1

.2

.3

2 4 6 8 10 12 14 16 18 20

Response of PREDG to PREDG

Employment Dynamics and the Nashville Tornado

Bradley T. Ewing

Texas Tech University

Jamie Kruse

East Carolina University

Mark Thompson

UALR, Institute for Economic Advancement

Published in Journal of Regional Analysis and Policy (2005)

Research – Event Study & Intervention Analysis

• Weather event = Nashville tornado on April 16, 1998

• Economic theory– Growth & recovery due to improvements in supply chain, systems, etc.

• Methodology – time series intervention analysis (Data 1980-2002)– Basically used to examine pre- vs post-event

• Define the intervention

otherwise

DecemberMayt ,0

20021998,1

Research – Event Study & Intervention Analysis

• Model of mean and variance (estimated simultaneously via MLE)

tttt scLL 0

2,0~ tt hN

ttth 2

1102

Research – Event Study & Intervention AnalysisExample: Nashville Tornado and Regional Employment

TOT CMN FIR GOV MFR SRV TPU WRT

Mean

Constant 0.270b -1.211 -0.155 0.056 0.264c -0.326 0.519 0.516a

EG(t-1) 0.819a 0.752a 0.880a 0.603a 0.824a 0.894a 0.814a 0.746a

State EG 0.164a 0.428a 0.147a 0.250a 0.172a 0.172a 0.167a 0.231a

Tornado -0.066 0.194 -0.517b -0.411 0.101 0.074 1.222a 0.155

Variance

Constant 0.370a -- -- 1.768a 1.085a 1.027a 3.461a 0.805a

ARCH 0.286a -- -- 0.838a 0.052 0.660a 0.178a 0.111c

Tornado -0.254a -- -- -0.290 -0.379c -0.893a -0.867a -0.573a

RESEARCH – Weather Risk

• Weather Risk is financial gain or loss due to variability in climatic conditions

• Weather Risk Management (WRM)– Currently there exists a global WRM market (started 1997)– Temperature based not water or wind

• Water “events” affect operations of businesses– Cause delays, affect physical properties of materials, damage

• Excess water → construction projects, theme parks, …• Insufficient water (threshold) → agriculture, recreation, …

RESEARCH – Weather Risk

• Water affects revenues & expenses of firms

– Volatility in water → fluctuations in cash flows

– Risk averse firms prefer to “smooth” cash flow

RESEARCH – Weather Risk• Economics, Operations and Finance intertwined

– Manage risk via financial contract• Define risk: the exposed firm determines how $ change with

respect to water (Note: operations → $)

• Design the hedge: includes defining the “water event” relative to some benchmark or underlying index

• Define the risk to be transferred: cost related to amount

– Manage risk through operations• Define risk

• Design plan for business disruption: “self-protection”

RESEARCH – Weather Risk

Approach WRM through financial contracts & operations

• Strategies for insulating the firm from water risk– Financial

• Derivatives

– Operational (“preparedness”)• Reduce (expected) revenue loss from any event through

improved systems, planning & processes

• Requires forecasting & modeling water– Understand how water impacts:

• Distribution, Manufacturing, Service, Plant & Employees,…

Example: Hedging Wind Delays

• Define the risk– Highway expansion project to begin 8/1/04 and to be

completed by 10/31/04– XYZ Construction Company estimates that 50 mph wind

in a 24 hour period creates delay costs of $25,000– Maximum protection desired is $500,000

• Design the hedge– Use local weather station wind data– Define a “wind event” (relative to benchmark or index)

• 50 mph wind in 24 hour period equals 1 event

Example: Hedging Wind Delays

• Historical (time series) data give number of wind events per period of time

• Data provide mean and standard deviation– E.g., mean = 20 and s.d. = 8

Note: computation of mean and s.d. is very important and are used in Guassian (option) pricing models

Example: Hedging Wind Delays

• Define risk to be transferred via weather contract

– If XYZ wishes to reduce wind event risk, then a swap contract can be structured

– If XYZ is willing to absorb some wind event risk, but wishes to be protected in case of an extreme number of wind events, then a cap contract may be appropriate

Example: Hedging Wind Delays

• Compare alternatives– Alternative 1: swap contract for 20 wind events

• No upfront cost (premium)• XYZ receives $25,000 for each wind event above 20 events• XYZ pays $25,000 for each wind event below 20 events• XYZ is protected against above average wind events, but

exchanges benefit of below average wind events

– Alternative 2: cap contract for 24 wind events (1/2 s.d. above historical average)

• XYZ receives $25,000 for each wind event above 24 events• Cost of above normal wind protection is upfront premium

required to purchase a cap contract (say, $75,000)

Example: Hedging Wind Delays

-400

-200

0

200

400

0 5 10 15 20 25 30 35 40

Wind Events

PAYSWAP PAYCAP

Example: Some other points

• Swap or cap on max or average daily wind speed

• Contract can be written to hedge wind risk at various locations (vertical or horizontal distance)

– Basis risk depends on correlation or relationship between two locations

WIND AND RISK

• Manage risk through financial contracts & operations

• Strategies for insulating the firm from wind risk– Financial

• Derivatives – must know how $ change with respect to wind

– Operational (“preparedness” or “self protection”)• Reduce (expected) revenue loss from any event through

improved systems, planning & processes• Strategy impacts the $ change associated with event to be

hedged in the financial market

• Requires forecasting & modeling wind– Understand how event impacts:

• Distribution, Manufacturing, Service, Plant & Employees,…

WATER AND RISK

• Research agenda

– VAR• Related to basis risk, facility design, planning and scheduling

of operations,…• VAR-ECM models short-run dynamics and long term trends

– GARCH-M• Related to pricing models (which must use a mean and

standard deviation), facility design, planning and scheduling of operations,…

Time Series Analysis of Rainfall with Time-Varying Volatility

• Option Pricing depends on mean & standard deviation to define “event”– Weather contracts use historical sample mean and s.d.

• Rainfall may have a nonconstant variance (in the conditional sense)

• Our focus is on the measurement of standard deviation for use in financial options & contracts– However, information about the conditional variance of rainfall and

how (mean) rainfall responds to conditional variance has many economic & engineering uses

Water Analysis

• GARCH-M model of Engle, Lilien, and Robins (1987)

ttj

t hLWL )()(

),0(~ 2tt hN

2

1

2

102

jt

p

j jit

q

i it hh

Example of methodology:

Ewing, Bradley T., Jamie B. Kruse and John Schroeder (2006) "Time Series Analysis of Wind Speed with Time-Varying Turbulence," Environmetrics.

Utilized WERFL data (same location, different heights on tower)

)( 21t

)( 21th

Mean equation W13 W33 W70 W160

Constant (μ) -0.1654(0.0137)

-0.0151(0.7823)

0.0764(0.0001)

0.1084(0.0045)

AR(1) 1.3188(0.0000)

1.1380(0.0000)

1.5030(0.0000)

1.0635(0.0000)

AR(2) -0.1454(0.0000)

0.0573(0.0005)

-0.4165(0.0000)

0.1306(0.0000)

AR(3) -0.1844(0.0000

-0.2051(0.0000)

-0.0920(0.0000)

-0.2013(0.0000)

Cond. Vol. (ht) 1.2289(.0000)

0.6047(0.0005)

0.1819(0.0313)

0.2125(0.1629)

Variance equation

Constant (α0) 0.0212(0.0000)

0.0111(0.0000)

0.0011(0.0000)

0.0005(0.0034)

ARCH 0.0569(0.0000)

0.0464(0.0000)

0.0441(0.0000)

0.0130(0.0000)

GARCH 0.6674(0.0000)

0.8414(0.0000)

0.9279(0.0000)

0.9790(0.0000)

Questions?