Demand Estimation Specifying a Demand Equation General Form: Q = F(P, M, PR,T, Pe, N) Empirical (Regression) Form:

Q = a + bP + cM + dPR + eN You estimated a demand equation

like this in the demand project

The Identification Problem Estimate Q = a + bP + cM + dPR + eN

If P and Q are determined by supply and demand, how do you know that you are estimating a demand relationship?

Answer: You don’t! If you have not estimated a demand

relationship, you have an identification problem. Warning signs:

Coefficient on price (b) is positive Coefficient on price (b) is not statistically significant

Solution to Identification Problem Use a technique called 2-stage Least Squares

Specify Demand and Supply Equations Qd = a + bP + cM + dPR + eN Qs = f + gP +hPI

Run a 2-stage least squares program When is Identification not a problem?

Data are for a single firm setting it’s own price Price not set by market (regulated prices)

Electricity prices are regulated by the states Identification not a problem for demand project

Calculating Elasticities for estimated demand equations Linear equation – demand project

Q = a + bP + cM + dPR + eN E = b(P/Q) = (ΔQ/ΔP)(P/Q) EM = c(M/Q); EPR = d(PR/Q)

Log-linear equation – constant elasticity Ln(Q) = g + h(lnP) + j(lnM) + k(lnPR) Coefficients (h, j, k) are elasticities No calculation needed

Calculate elasticities at the sample means Milkwh= 10800 – 3581(Pkwh) +

0.004(Pop) + 2252(PGas) Elasticity = (coeff.)(value/Milkwh) Sample Means: Milkwh=25365

Pkwh=9.0 Pop=5,756,577 PGas=11.4 E = -3581(9.0/25365) = -1.27 Epop = 0.004(5,756,577/25365) = 0.91 Epgas= 2252(11.4/25365) = 1.01

Exercise: Elasticities Milkwh= 10800 – 3581(Pkwh) +

0.004(Pop) + 2252(PGas) Milkwh=38,526 Pkwh=6.92

Pgas=10.6 Pop=5,900,962 Elasticity = (coeff.)(value/Milkwh) Calculate electricity demand

elasticities with respect to Pkwh, Pop, & Pgas

Forecasting Demand Using Elasticities

Multiply elasticities by projected % changes in explanatory variables

Add the results to get projected % change in demand

Using linear regression equation Multiply coefficients by projected values for

explanatory variables in future period Add results and intercept to get forecast of

demand

Forecasting with elasticities Estimate a log-linear equation

LMilkwh = 0.04 – 0.92(LPkwh) + 1.0(LPop) + 0.4(LPgas) – 0.4(Linc)

Get projected % changes Pkwh:10% Pop:1% Pgas:20% Inc:2%

Calculate the projected % change in Milkwh -0.92(10%)+1.0(1%)+0.4(20%)-0.4(2%) = -

1% Do not use the intercept! It doesn’t change.

Suppose Pgas goes down by 20%, not up?

Exercise: Forecasting with linear demand Estimate a linear demand equation

Milkwh= 10800 – 3581(Pkwh) + 0.004(Pop) + 2252(PGas)

Get forecasts of explanatory variables Pkwh=10 Pop=20,000,000 Pgas=10

Calculate a Forecast for Milkwh Substitute forecast values for explanatory

variables and do the arithmatic