FEModels - Mgmt 469 Fixed Effects Models Suppose you want...

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Mgmt 469 Fixed Effects Models Suppose you want to learn the effect of price on the demand for back massages. You have the following data from four Midwest locations: Table 1: A Single Cross-section of Data Location Year Price Per capita Quantity Chicago 2003 $75 2.0 Peoria 2003 $50 1.0 Milwaukee 2003 $60 1.5 Madison 2003 $55 0.8 This is cross-section data – data from several locations at a single point in time. If you eyeball this data, you will see that across the four cities, price and quantity are positively correlated. In fact, if you regress per capita quantity on price, you will obtain a coefficient on price of 0.45, suggesting that each $1 increase in price is associated with a .45 increase in per capita massages! You highly doubt that the demand curve for massages is upward sloping so you think a bit more about the data. You wonder if, perhaps, the quality of massages is higher in Chicago. Or perhaps “sophisticated urbanites” have a higher demand for massages. This could boost the demand for massages and simultaneously drive up the price. In other words, the regression probably suffers from endogeneity bias in the form of omitted variable bias (because quality and “sophistication” are omitted.) You really can’t say very much about the role of price with this cross-section data.
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2 Now suppose you had the following cross-section/time series data (data from multiple cities and multiple years): Table 2: A Cross-section/Time Series Location Year Price Per capita Quantity Chicago 2003 $75 2.0 Chicago 2004 $85 1.8 Peoria 2003 $50 1.0 Peoria 2004 $48 1.1 Milwaukee 2003 $60 1.5 Milwaukee 2004 $65 1.4 Madison 2003 $55 0.8 Madison 2004 $60 0.7 If you eyeball this data, you will see that within each of the four cities, price and quantity are inversely correlated, as you would expect if demand is downward sloping. By obtaining multiple observations about each city and looking at the effect of price within each city, we have removed the pernicious effect of omitted variable bias. This is the intuition behind fixed effects regression. If you examine the sales data (per capita quantity) in Table 2, you will observe that there is considerable variation (“action”) from one row to the next. This variation/action comes in two “flavors”” - Intercity (across city) variation : variation in the average quantity from one city to the next - Intracity (within city) variation : variation within each city over time. The single cross-section of data (Table 1) offered only intercity (across) variation. We now know that regressions relying on intercity variation are problematic due to potential omitted variable bias. The solution is to focus on intracity (within) variation.
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3 We must make one key assumption if we are to believe we have really removed omitted variable bias by focusing on within variation. We must assume that there are no changes in quality or demand over time within each city that we cannot control for. For example, suppose
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FEModels - Mgmt 469 Fixed Effects Models Suppose you want...

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