Fresh from the Fridge: Imagine you have collected data on quit rates experienced by a set of firms during a given year and data on the firms' avarage wage rates (sample size = 100). The data are presented grafically in the figure below:
Each dot in this figure represents a quit-rate/hourly-wage combination for one of the hundred firms. From a visual inspection of all data points, it appears from this figure that firms paying higher wages in our (hypothetical) example do indeed have lower quit rates. But would it make sense to explain the quit rates solely with the wage rates? Definitely not. Economic theory suggests there are many factors besides wages that systematically influence quit rates. These include characteristics both of firms (e.g. employee benefits offered, working conditions, and firm size) and of their workers (e.g. age and level of training).
If any of these other variables that we have omitted from our analysis tend to vary across firms systematically with the wage rates that the firms offer, the resulting estimated relationship between wage rates and quit rates will be incorrect. In such a cases, we must take these other variables into account by using a model with more than one independent variable.
The data in the plot given above were generated under the assumption that the only variable affecting a firm's quit rate besides its wage rate is the average age of its workforce. Older workers are, ceteris paribus, less likely to quit their jobs for a number of reasons (as workers grow older, ties to friends, neighbors, and co-workers become stronger, and the psychological costs involved in changing jobs--which often require a geographic move--grow larger). To cut a long story short: Half of the firms of our sample employed mainly young workers and paid an average wage of 8 Euro, the other half employed mainly old workers and therefore paid an average wage of 10 Euro. In both cases the standard deviation of the wage rate was two Euro. Furthermore, at any level of wages a firm's quit rate was 10 percentage points lower if it employed mainly old workers.
The red line is what we get when we do not control for age and run a regression over the whole sample. The blue regression lines emerge when we run separate regressions for firms with an old workforce and firms with a young workforce*. It can easily be seen that the first model exaggerates (=omitted variable bias) the effect of a wage increase (slope of -3.5 instead of -2.5 (= true slope)). In words: A wage increase of one Euro decreases the quit rate by 2.5 % and not by 3.5 %.
Example taken from "Modern Labor Economics - Theory and Public Policy" (Ehrenberg & Smith).
*Actually, one should run a single regression that includes a dummy variable for age.
Each dot in this figure represents a quit-rate/hourly-wage combination for one of the hundred firms. From a visual inspection of all data points, it appears from this figure that firms paying higher wages in our (hypothetical) example do indeed have lower quit rates. But would it make sense to explain the quit rates solely with the wage rates? Definitely not. Economic theory suggests there are many factors besides wages that systematically influence quit rates. These include characteristics both of firms (e.g. employee benefits offered, working conditions, and firm size) and of their workers (e.g. age and level of training).If any of these other variables that we have omitted from our analysis tend to vary across firms systematically with the wage rates that the firms offer, the resulting estimated relationship between wage rates and quit rates will be incorrect. In such a cases, we must take these other variables into account by using a model with more than one independent variable.
The data in the plot given above were generated under the assumption that the only variable affecting a firm's quit rate besides its wage rate is the average age of its workforce. Older workers are, ceteris paribus, less likely to quit their jobs for a number of reasons (as workers grow older, ties to friends, neighbors, and co-workers become stronger, and the psychological costs involved in changing jobs--which often require a geographic move--grow larger). To cut a long story short: Half of the firms of our sample employed mainly young workers and paid an average wage of 8 Euro, the other half employed mainly old workers and therefore paid an average wage of 10 Euro. In both cases the standard deviation of the wage rate was two Euro. Furthermore, at any level of wages a firm's quit rate was 10 percentage points lower if it employed mainly old workers.
The red line is what we get when we do not control for age and run a regression over the whole sample. The blue regression lines emerge when we run separate regressions for firms with an old workforce and firms with a young workforce*. It can easily be seen that the first model exaggerates (=omitted variable bias) the effect of a wage increase (slope of -3.5 instead of -2.5 (= true slope)). In words: A wage increase of one Euro decreases the quit rate by 2.5 % and not by 3.5 %.Example taken from "Modern Labor Economics - Theory and Public Policy" (Ehrenberg & Smith).
*Actually, one should run a single regression that includes a dummy variable for age.
Mahalanobis - am 2005-09-15 03:15 - Rubrik: EconoSchool
