Learn about binary regressions in an example.
- [Instructor] Ed's boss has asked him to help the firm understand what drives changes in interest rates. In particular, because Ed works for a real estate company, one of the primary interest rates that they're concerned about, is the Federal Reserve rate. Ed wants to understand what factors drive the Federal Reserve rate so that he can apply that understanding to projects the company is working on. I'm in the 03_03_Begin file from the Exercise Files folder.
Ed's gathered data using FRED, the Federal Reserve Economic Database, on the Federal Reserve rate, inflation, industrial production numbers, and on employment figures. In particular, he's gathered this data on a monthly basis from 1960 through present. Let's go ahead and clean up the data a little bit just to help make it more understandable for us. So this first two columns, A and B, is the effective federal funds rate, and value is the value for that.
I'm going to relabel this column, Fed Funds Rate. These next two columns, C and D, are the changes in the consumer price index on a core level. That means, after excluding food and energy prices. So I'm going to relabel value to CPI. And columns E and F, we have industrial production index values and the changes in those on a monthly level. So again, I'm going to label this Industrial Production.
And then finally, in columns G and H, we have nonfarm payrolls changes in every month. So I'm going to label this Payrolls. Having done that, I'll delete these rows because we don't need them anymore. Now, Ed has very kindly gathered the data for us on a monthly basis, so that we don't have to merge it together, so I'm going to remove the extra date columns, which we no longer need.
If you notice, Ed has gathered the change in each value every month. Now, what Ed is interested in is not the change in the Federal Funds Rate but rather what leads the Federal Reserve to raise rates. His firm is happy if the Federal Reserve cuts rates. If interest rates fall, that makes it more feasible for them to pursue various projects. Ed is really only interested in what happens if the Federal Reserve raises rates.
If the Federal Reserve lowers rates, that's good for his real estate company. So we're going to add a new column that we're going to label Fed Rate Hike and we're going to set it equal to one if the Federal Reserve increases rates, so we're going to use an if function here. I've typed =if(. Now I'm going to specify the B column. In this case, B2 and say that B2, if B2 is greater than zero, then we have one.
Otherwise, zero. And I'm going to drag and drop through the bottom. Now we see that since 1960, there have been 342 occasions where the Fed raised rates. That's out of a total of 687 months. Now that we've done that, what we're looking at is a binary variable. Recall that when we're using a binary variable and we're trying to predict a binary outcome, we're really only interested in using a probit or logit style regression.
That's why we had to change this variable to be equal to a one or zero. Now, in this case, Excel has limited capability to do more advanced types of regression analysis, so we're going to use our standard regression that's available under the Data tab. We're going to click Data Analysis and come down and set up our Regression. Please note that if you're interested in doing more advanced types of regressions, like logit and probit regressions, like fixed effects regressions, there are many statistical software packages out there.
SAS, Stata, and R, are all examples of software that you can use, just to name a few. In our case, we're going to stick with Excel because it's simple, straightforward, and easy to use. So our Y Input Range is going to be from C1 through C687. And our X Input ranges are going to be D1 to F1, all the way down to row 687. And again, we're going to have labels.
When we're ready, let's click OK. Now I'm going to neaten up our regression a little bit while widening the columns, and trimming the last couple columns, which we again don't need. Next, I'm going to go through and clean up our numbers to shrink the number of decimal places. And I'm going to change our R-squared values so that they're in percentage terms.
Now, what we see here is that we have a relatively modest R-squared, only about 7%. What this is really telling us is that the variables we've selected, Inflation, Industrial Production, and Payroll, have only limited ability to predict Federal Reserve fund rate changes, at least based on the frequency of the data that we've collected. We might try lagging some of the variables to see if that was more effective, but for right now, we'll just stick with the existing regression.
However, we also see that two of our variables, Payroll and Industrial Production do in fact have a statistically significant impact on whether the Fed hikes rates. Industrial Production measures the strength of the economy, in that it measures how much is being produced by manufacturing firms across the economy. Payrolls of course are also a good measure of strength in the economy. The higher those payroll rates are, that is the more positive the payroll growth is, the stronger the economy is.
It indicates the economy is adding new jobs at a faster rate What we see here is that industrial production is statistically significant. The P-value is less than 0.10, although only marginally so. And Payrolls is highly statistically significant. It has a P-value of zero. What this in essence tells us is that when Payrolls are higher, that is when there's a positive change in payrolls and more people are being employed or when there's a positive change in industrial production, the Fed is also more likely to raise interest rates.
That's a powerful insight that Ed can use to help his firm understand what interest rates might be like in the future. If he identifies payroll and industrial production trends to indicate that both those figures are likely to be strong going forward, his firm should also be aware, there will probably be Fed interest rate hikes coming along the same time.
Professor Michael McDonald demonstrates how to harness the wealth of information available on the Internet to forecast statistics such as industry growth, GDP, and unemployment rates, as well as factors that directly affect your business, like property prices and future interest rate hikes. All you need is Microsoft Excel. Michael uses the built-in formulas, functions, and calculations to perform regression analysis, calculate confidence intervals, and stress test your results. He also covers time series exponential smoothing, fixed effects regression, and difference estimators. You'll walk away from the course able to immediately begin creating forecasts for your own business needs.
- Understanding big data and economic forecasting
- Predicting values with regressions
- Analyzing economic trends and economic cycles
- Using fixed-effects regressions and binary regressions for forecasting
- Assessing the accuracy of an economic forecast
- Using scenario analysis