# Using Spreadsheets to Teach Economics

### What can Spreadsheets Do for Economics Teachers?

Spreadsheets not only speed calculation so more examples may be covered, they allow students to explore models that are too complex for undergraduates to solve analytically. As such, using spreadsheets increases the breadth and depth of what a course can cover.

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### Useful tools for economists

Spreadsheet programs may be used to assist with such core learning activities as:

**Exploring and analyzing data**

The advanced plotting and statistical features make it easy to create data charts and calculate summary statistics.

The Okun's Law parameter value and potential GDP growth rate are easily estimated by constructing a scatter plot of the change in unemployment versus the GDP growth rate. Excel can easily insert a linear regression line and display associated equation in the chart that is an estimate of the growth rate version of Okun's Law, as shown on the right (click to enlarge). This is a scatter plot of the change in unemployment (*dU*, on the*x*-axis) and the percent GDP growth (*dY/Y*, on the*y*-axis). The equation of the regression line is therefore*dY/Y*= -*w**dU*+*dY*/Y**where*w*is the Okun's Law parameter and***denotes potential GDP. On the chart, Excel estimates Okun's Law parameter to be about 2.2 and potential GDP growth to be 4.1%. See full example instructions.**Estimating and plotting regression lines**

The time trend of any series may be estimated and plotted easily by inserting a "trendline" (regression line) on a chart, estimating a trend using the Fill command, or using basic regression functions of Excel.As shown in the example above, the Okun's Law parameter may be easily estimated and the relationship plotted by inserting a "trendline" regression line into a scatter plot of unemployment and GDP growth data.

The Fill command is easily used to generate regression-estimated data for a time trend. Simply select the data for which the trend is to be estimated, select Fill/Series..., and check the Trend box and Linear or Growth options as shown in the image on the right (click to enlarge).**Solving complex systems of equations numerically**

Models with several equations or non-linear equations may be explored numerically by Excel. The most straightforward way to do this is to assign cells to left-hand variable names (e.g., Q, C, I) and enter the right-hand side of the equation in the cell, referring to other cells as appropriate. Excel reports this as a "circular reference" error but when the "Iteration" Excel option is activated, Excel will solve the system numerically. See instructions on solving equations.For example, the effect of parameter changes on models like the Cobb-Douglas function, the Keynesian Cross model, the IS-LM model and Solow growth model may be easily found numerically.

Consider the screen capture from Keynesian cross model example to the right. (Click image to enlarge. Full instructions are available). The consumption (C) function cell is selected, showing how consumption is related to parameters and disposable income (DI). The disposable income (DI) formula refers to the income (Q) cell, which refers back to the consumption function cell. The columns explore what happens to the model when various parameters are changed. this would be a tedious exercise without Excel, and allows for more model exploration.**Creating large tables of simulation data**

Because spreadsheets can make many calculations quickly, they can be used for generating large data sets for analysis and plotting. For example, data for generating three dimensional plots of utility and production functions may be generated through the Data Table command. The Data Table command can be difficult to use at first, but detailed instructions are available. Another useful application for large amounts of data is to solve dynamic macroeconomic models over many periods to allow for exploratory analysis.The Data Table command can generate a matrix of numbers corresponding to the value of a three-variable equation, like a 2-good utility function or a 2-input production function. These data can then be plotted in a 3D chart called a "Surface Chart", and the chart rotated to see the function from different axis perspectives (i.e. level curves). For example, the data for the three dimensional Cobb-Douglas production function above to the left (click to enlarge) was created using the Data Table command. The chart can be rotated to show the familiar total product curve for one of the inputs, as shown in the other image. (These images were originally produced for the web supplement to Cahill and Kosicki (2000).)

The Solow growth model is a difficult topic to tackle in undergraduate classes, partly because its abstract and technical nature makes it difficult to work through numerical examples. The simultaneous equation solving feature of Excel (described above) can be used to generate many periods of simulation data, allowing the behavior of an economy after a shock to be explored. The image on the right (click to enlarge) depicts a Solow economy that experienced an increase in the capital depreciation rate in year 5. The bottom line is the (shifting) balanced growth path, and the top line is the transition path converging to the balanced growth path. Full instructions for the Solow neoclassical balanced growth model analysis exapmple are available.

**Solving optimization problems**

Numerical examples of constrained and unconstrained optimization models are relatively easy to program using Solver or Goal Seek in Excel.For example, consider the multiplant cost minimization problem where a firm is dividing a fixed amount of production between plants with different cost functions. Such a problem is presented in the image on the right (click to enlarge), where a firm produces 32 total units over two plants with cost functions*C1*=16+6**q1*^2 and*C2*=240+2**q2*^2 (and an aggregate total cost*C*=*C1*+*C2*) with associated marginal cost functions*MC1*and*MC2*and average cost functions*AC1*and*AC2*. The model is set up so the firm initially splits production evenly between the plants. To minimize total cost, Solver is used by clicking the Solver button on the Analysis section of the Data tab (as circled on the image, click to enlarge). In the Solver window, the objective "Target cell" is the total cost cell, which is minimized. An equality constraint is added so that the total production (*Q*=*q1*+*q2*) is set at 32. The result (not shown) is the firm divides production so*q1*=8 and*q*2=24. Interestingly, the average cost of good 2 is higher than good 1, but this is the optimal decision because the marginal cost of the plants is equalized. This demonstrates a key economic principle. Students may manually change the production numbers to try to "beat" this optimal result, or Solver can be used to equalize average cost to further demonstrate this result. (These images were originally produced for the web supplement to Cahill and Kosicki (2000).)**Conducting statistical analysis**A full range of statistical functions may be used to calculate summary statistics, statistically test hypotheses, and calculate p-values.This is part of the example that simulates the well-known Taylor Rule for monetary policy. (Full instructions are available.) The Taylor Rule is a simple equation proposed in the Taylor (1993) conference paper to guide monetary policy. The equation provides a federal funds rate target based on the measured inflation rate and GDP gap and assumed values for target inflation, long run real interest rate and preferences for fighting inflation and unemployment. The Taylor (1993) paper plots the actual federal funds rate with the rule target rate to argue that the early Greenspan administration policy was close to what the rule would have prescribed. However, no statistical analysis is done to back this claim. One of the parts of the Taylor Rule example is to calculate the correlation coefficient between the rule target and actual federal fund rates (using Excel's =CORREL function) and test the hypotheses that the correlation coefficient is statistically different from 1 or 0 by manually entering the formula for the t statistic and using Excel's =TDIST function to compute the p-value of the test. The screen shot image from the spreadsheet (click to enlarge) shows the TDIST formula is displayed on the formula bar.

Furthermore, spreadsheets can be integrated with a a variety of assignments and settings and may be tailored to support or replace technical skills. However, implementing a spreadsheet activity may take some care. Find more information about how to teach with spreadsheets Furthermore, while some spreadsheet tools are straightforward to find and use, others are hidden or take some know-how. The spreadsheet tools page provides and overview of some spreadsheet tools and gives instructions on how to use these tools in Excel. Basic information on how to use Excel can be found on the What is Excel page of the Mathematics and Statistical Models SERC module.

### Economics Examples

Nearly any topic in economics can be approached using spreadsheets, as suggested by the examples above. A large number of examples have already been developed for use by instructors:- Internal list of economics examples organized by topic
- These examples have been reviewed by module coordinators and are ready to be used in a classroom to cover specific topics
- A complete list of spreadsheet examples may also be searched
- A large number of examples in the existing literature available. See a list of external links
- There are several references and resources available for using spreadsheets, Excel, and related teaching approaches.