13. Valuing Impacts from Observed Behavior: Slopes, Elasticities, and Data

Transcription

1 3. Valuing Impacts from Observed Behavior: Slopes, Elasticities, and Data Reading: BGVW, Chapters 3. Introduction Need to measure social surplus. These are found as areas under demand and supply curves. Triangles, trapezoids and so forth. Curves are usually unknown, so analyst need to find ways to estimate them the curves and, in turn, calculate the triangles. Well look at some direct estimation techniques and then some indirect ways to measure shadow values -- infer values indirectly from other markets and behaviors.

2 2. Direct Estimation One point plus slope or elasticity. Usually know one point (current & ). If slope is also known (literature on demand for the good you are interested in studying), then it is a simple matter to extrapolate the demand curve. α in the basic demand equation below, for example, may be estimated from various studies q = α + α p 0 slope If so, it is a simple matter to sketch out the shape of the curve around this point. slope = α p 0 q 0 2

3 Or, plug in current p and q to get intercept. Then you have an estimate of the equation. α 0 q = α + α p 0 Refuse fee example from book. Current is zero, town plans to raise fee to $.05 per pound. Graph: Social cost is $.06 initial zero point Robin Jenkins. The Economics of Solid Waste Reduction: The Impact of User Fees lb/p/d Note: External and Internal Validity. 3

4 Elasticities and linear demand. If you know demand is linear and you have an elasticity measure instead of a slope, you can calculate the slope as Elasticity is ε = α p / q. d Solving for α gives α = ε q / p. d You need to know at which elasticity was calculated in the original study. Same basic strategy can be followed for constant elasticity demand curves See example in book (p. 39) initial point of p,q q = β p 0 β ln q = ln β + β ln p 0 / β [ + (/ β )] q0 ( q ) Area = β0 + (/ β) 4

5 initial point of p,q q = β p 0 β ln q = ln β + β ln p 0 / β [ + (/ β )] q0 ( q ) Area = β0 + (/ β) Extrapolating from a few points. You know a few points of p,q from historic data and you try to fit a line through these points. Usually 2 or 3 points. Example from book Known data points 5

6 Notes sensitivity to functional form controlling for other factors validity of measures from only 2 points Extrapolating beyond relevant range Many Points/Econometrics Suppose you have many observations of and from a time series or cross sectional data set. OLS, ML or other. 6

7 Regress q on p, or fit a line to this scatter of points. You d have something like the red linear regression or blue non-linear regression. q = f ( p;! β ) Estimted demand Regress q on p, or fit a line to this scatter of points. You d have something like the red linear regression or blue non-linear regression. q = α 0 + α p + α 2 I + α 3 T + ε ln(q) = α 0 + α ln(p) + α 2 ln(i) + α 3 ln(t ) + ε q = f ( p;! β ) Estimted demand 7

8 Use the estimated line in your analysis Types of data individual vs. aggregate time series (annual/monthly) vs. cross sectional examples: electricity, farm crops, water, consumer goods galore, automobiles, oil, minerals markets, traffic, computers, wine Major econometric issues () Omitted variable bias q = f ( p, p, y, d) own subst (2) Autocorrelation in time series data (3) Identification Problem: Are you estmating a deamnd curve or a supply curve when you estimate the relationship between p and q?» The ideal case. (Rain example. Cross sectional stories.) Shifting supply is sketching out a demand curve. Shifting supply curves Stable demand curve 8

9 (3) Identification Problem: Are you estmating a deamnd curve or a supply curve when you estimate the relationship between p and q?» The ideal case. (Rain example. Cross sectional stories.) Shifting supply is sketching out a demand curve. Shifting supply curve Observations Stable demand curve» But it could have been supply that was sketched out 9

10 » Trouble and likely outcome is that you observe and relationships that get both shifts.» Simultaneous equations/instrumental variables quanity 0