Econometric Methodology Chapter 3

Step 1 Review the literature and develop a theoretical model Keyword Search Databases (EBSCO, EconLit) Journal of Economic Literature (JEL)

Sample Model Y = Erie Mfg Employment X1 = Total Employment X2 = Exchange Rate X3 = Economic Activity X4 = Stock Market Activity

Step 2 Specify the model’s variables and functional form Measurement issues for Y and X Dummy variables Determine appropriate functional form

Example Choosing Y Measuring Erie Manufacturing Employment (Y) Number of Manufacturing Employees Manufacturing/Total Employment Change in Manufacturing Employment Change in Manufacturing/Total Employment

Options for the Dependent Variable

Options for the X Variables

Total Employment – X1

Expressed as Differences

Exchange Rate – X2 U.S. versus a particular currency? Broad exchange rate index? Major currencies exchange rate index? Values in levels or differences?

Economic Activity – X3 Level or Difference in: PA Manufacturing Employment U.S. Manufacturing Employment Regional or National Unemployment Rate Index of Industrial Production Capacity Utilization Rate Real GDP (quarterly)

Stock Market – X4 Level or Difference in: S&P 500 Stock Index Dow Jones 30 Stock Index Price/Earnings Ratio (SP500) NASDAQ Stock Index

Dummy Variables Measure qualitative characteristics or events

Dummy Example To measure the impact of the 9/11/2001 attacks, use a dummy for September through November of 2001.

Determining if there is a Relationship between Y and X Scatter Plots

Determining if there is a Relationship between Y and X Correlation Coefficient

Correlation Coefficient r = 0 (no relationship between Y and X) r > 0 (positive relationship) r < 0 (negative relationship) |r| → 1.0 (strong relationship)

Example from EViews ERMFG SP500 USTOT XCHBRD 1.000000 -0.562928 -0.737109 -0.579849 0.943997 0.873023 0.925830

Functional Form of Equation Linear: Quadratic

Step 3 Hypothesize the expected signs of the variable relationships Base the decision on theory Assists in validating the model

Example Y = Erie Mfg Employment X1 = Total Employment X2 = Exchange Rate X3 = Economic Activity X4 = Stock Market Activity

Step 4 Collect the data Use sufficient data to maximize degrees of freedom (d.f.) for the model d.f. = n-k-1 Larger data sets allow + and (-) errors to offset – maximizing model accuracy

Special Considerations with Time-Series Data “More data the better” not necessarily true for T-S data Data far in the past may no longer be relevant The issue of “spurious regression” Two variables may “trend” together over time because they are both affected by a third variable Consider use of “real” instead of “nominal” variables when possible

Step 5 Estimate & evaluate the regression model Estimate β values using OLS or other method Validate the model to determine usefulness

Forms of Validation Testing sign of slope coefficients “Goodness-of-Fit” – (sy,x, R2, Adj-R2) Testing for significance of relationship (t) Testing model (OLS) assumptions Testing for correct functional form

Step 6 Documenting the results Make results clear to the non-technical reader Include sufficient statistical evidence of model usefulness Thoroughly document variable definitions and data sources