Session 9 Case 3: Utilizing Available Software Statistical Analysis

Transcription

1 Session 9 Case 3: Utilizing Available Software Statistical Analysis Michelle Phillips Economist, PURC michelle.phillips@warrington.ufl.edu With material from Ted Kury Session Overview With Data from Cases 1 and 2, participants will utilize a standard software package to estimate production and cost functions Evaluating Analyses What are the strengths and limitations of statistical methods? How sensitive are results to model specification? 1

2 3 Estimation of Cost Functions Engineering studies: complicated Regression estimates allow decision makers to: Summarize cost & quantity relationship Interpolate between observations and extrapolate beyond firm s experience Conduct Benchmarking Studies 4 2

3 Empirical Observations Total Cost () is a Function of the Level of (Q) 5 Picture of the Relationship 6 Is the LIE a good estimate of the relationship between output and total cost? Why? 3

4 Regression Analysis Control for Factors affecting Cost Level, Quality and other factors Input prices eed data for period of stable input prices, or eed to account for changes in input prices Technology eed period of stable technology Make sure cost data reflects opportunity costs 7 Ordinary Least Squares Minimize the sum of The errors squared (residuals squared), where the residual is the difference between actual and predicted values 8 4

5 The Effect of Outliers ew Regression Old Regression What if we drop This observation? Why would you drop it? 9 COLS: Corrected Ordinary Least Squares OLS COLS All the difference between what the model predicts and the actual is assumed to be due to inefficiency. 10 5

6 SFA: Stochastic Frontier Analysis SFA Much more complicated estimation process. COLS Differences due to both errors in variables AD Inefficiency (requires Assumptions about Distribution of errors). 11 on Linear Relationships = a + b Q + c Q 2 Quadratic Cost Function What if Total Cost does not rise in a linear way? 12 6

7 Specification: Technology Identical O=Old Technology =ew Technology o o o o o o o Control for differences in technology, density, input prices, and other factors affecting Cost Multiple Regression: multiple independent variables Q 13 Multiple Regression If Total Cost depends on (Q) and Quality (Z), then multiple variables explain total cost For example, if the relationship is still linear, = a + b Q + e Z Model specification: functional form and variables Other cost drivers: number of customers, density, age of system, input prices, and

8 Production Functions depends on Inputs (example below shows output as a function of labor) Many functional forms for model specification: Quadratic Cobb Douglas Translog Labor 15 Case 3: Using Software Regression Analysis in Excel Use the full dataset for the twenty utilities Variable Selection Model Specification Explanatory Power Analysis of Coefficients 16 8

9 Some Technical Issues Model Specification: dependent and independent variables (omitted?) R 2 : coefficient of determination ( fit ) t statistics for significance of individual coefficients Initial Assumptions Residuals (error terms) randomly scattered around zero o Heteroscedasticity (assume error terms unrelated to size of dependent variable) o Multicollinearity (assume independent variables are unrelated to each other) Stochastic Frontier Analysis to be discussed later. 17 Appendix: Math of the Linear Total Cost Function $ = a + b Q a Q / week 18 9

10 Constant Marginal Cost $ = a + b Q AC = (a / Q) + b b MC = b Q / week 19 Linear Functional Form = a + b Q MC = b AC = a /Q + b Fits only a limited range of output Evidence: a>0 AC falls as Q increases 20 10

11 on Constant Marginal Cost (MC) a = g(q) If b = 1 and c=1 Slope at Q=20 is 1+2X = 41 = MC = g(q) = a + bq+ cq 2 d dq = b + 2cQ Q 21 Increasing Marginal Cost = a + b Q + c Q 2 MC = b + 2 c Q AC = a/q + b + c Q $ MC Slope of MC is 2c AC b 22 Q 11