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How Useful Are Forecasts of Corporate Profits? Dean Croushore How Useful Are Forecasts Of Corporate Profits? Dean Croushore* I nvestors’ forecasts of corporate profits affect the prices of corporate stock. When a corporation announces that earnings won’t be as large as expected, its stock price immediately drops. Similarly, when investors think a firm will earn higher profits than they previously thought, the company’s stock rises in value. This positive relationship between forecasts of corporate profits and stock prices must be true for the stock market as a whole. That is, if investors forecast higher overall corporate earnings, that should lead to higher overall stock prices. In the 1990s, stock prices have grown substantially, in part because of forecasts of higher levels of corporate profits.1 But how accurate are those forecasts? To investigate the accuracy of forecasts of overall U.S. corporate profits, we need to have a consistent set of forecasts. One such set comes from *Dean Croushore is an assistant vice president and economist in the Research Department of the Philadelphia Fed. He’s also head of the department’s macroeconomics section. Dean thanks John Duca of the Federal Reserve Bank of Dallas for comments on an earlier draft of this article. 1 For a discussion of how stock prices are related to corporate profitability in the 1990s, see the article by John Cochrane and the article by John Carlson and Kevin Sargent. U.S. data show strong correlations between stock prices, corporate profits, and forecasts of corporate profits. 3 BUSINESS REVIEW SEPTEMBER/OCTOBER 1999 the Survey of Professional Forecasters (SPF), which has collected forecasts of corporate profits and many other macroeconomic variables for over 30 years. The survey is widely respected by academic researchers, and they often use it for investigating the quality of forecasts of various macroeconomic variables, especially inflation.2 In general, the forecasters who participate in the survey are actively involved in forecasting as a part of their jobs. The forecasters include many Wall Street economists, along with chief economists at Fortune 500 companies, a number of bank economists, and some economic consultants. It’s the type of group you’d expect to have a pretty good idea about corporate profits as well as the macroeconomic variables (such as inflation and output growth) they are asked to forecast. DATA PROBLEMS If we look at the raw data on the growth of corporate profits in the U.S. economy, we see that profits are very volatile over time (Figure 1).3 Notice that, on an annualized basis, corporate profits have occasionally risen from one quarter to the next at a rate of over 100 percent. Data on most macroeconomic variables, such as the economy’s output or its industrial production, aren’t nearly as volatile. To eliminate some of the volatility, we’ll look at the growth in corporate profits over a year, not at quarterly data.4 The annual data series is a lot less volatile. Unfortunately, attempts to analyze the forecasts of the growth of corporate profits are subject to a problem that’s also true of many other variables — the data have been modified over time. That is, the data a forecaster or stockholder faced at a particular point in time look quite different from the data available today. For example, let’s take a look at the reported values for the growth of corporate profits from 1986 to 1987. If we look at the national income data in May 1988, the growth rate of corporate profits from 1986 to 1987 was reported as 8.5 percent. In July 1988, the numbers underwent a minor revision, and the growth rate rose to 10.2 percent. But in July 1989, new IRS tabulations of data from corporate tax returns led the Bureau of Economic Analysis (BEA), the statistical 4 The variable we’ll use is the growth rate in the annual average level of corporate profits from one year to the next. FIGURE 1 2 For a look at some of the details of the survey and how it’s run, see my 1993 article; to find out how accurate the inflation forecasts from the survey are, see my 1996 article. I use the SPF, rather than the Blue Chip survey or the IBES survey, because it began in 1968, much earlier than the other surveys. Quarterly Corporate-Profits Growth 3 The precise variable we’re examining is nominal (i.e., not adjusted for inflation) after-tax corporate profits (without inventory valuation and capital consumption adjustments) as reported in the Survey of Current Business from the national income and product accounts. 4 Date FEDERAL RESERVE BANK OF PHILADELPHIA How Useful Are Forecasts of Corporate Profits? Dean Croushore agency that compiles the national income ac- Survey of Professional Forecasters is taken. These counts, to substantially reduce the value of cor- data sets show us what the official data looked porate profits for both 1986 and 1987, but more like at the time. This real-time data set is a better so for 1986. As a result, the growth rate of corpo- source for the numbers forecasters were trying rate profits from 1986 to 1987 rose to 23.2 per- to predict than the data set available today, becent. cause some of the changes in corporate-profits An even bigger change came in December data involved redefinitions of the items included 1991, when the BEA, among other changes, re- in corporate profits; forecasters couldn’t have classified the bad-debt losses of financial insti- foreseen those changes. tutions as financial transactions; those losses How well do the year-ahead forecasts comwere no longer included in the national income pare to the data, using the real-time data set? To accounts and were not to be viewed as reducing find out, we’ll first plot the forecast for the growth corporate profits. The result was a very large re- of corporate profits over a one-year period, then calculation of corporate profits, especially for compare it to the actual value in the real-time 1987, when financial firms recorded very large data set (Figure 2).6 You can see that the forebad-debt losses. The impact was to increase the casts and actual growth rates move together growth rate of corporate profits for 1987 to 44.4 percent. Minor revisions since then have re6 duced the growth rate to 43.5 percent. The forecasts are taken from the November Survey of Professional Forecasters each year, from 1968 to 1996. So, occasionally the data for corporate profits The forecast variable is the growth rate of corporate profare revised quite extensively. Most of the time, its from the year in which the survey was taken to the the revisions aren’t as extensive as they were for following year, based on annual average data. For ex1987, but they can still be substantial. ample, the November 1968 survey forecasts how much Getting around this problem of data revisions higher profits are expected to be in 1969 than they were is not easy. We’re going to attempt to do so using in 1968. the following technique: we’re going to take data sets that FIGURE 2 were created not long after the Corporate Profits forecasts were formulated, be(SPF Forecasts and Real-Time Actuals) cause information available at that time is what affected stock prices. First, we’ve created a special set of data, called a realtime data set.5 Based on data published in the Survey of Current Business from 1965 to the present, this data set contains the data available to a forecaster in mid-November each year, the same time at which the 5 Details on this data set can be found in my 1999 paper with Tom Stark. Date 5 BUSINESS REVIEW pretty well in the 1970s, despite the oil-price shocks in that period. Overall, the forecasts were not too bad in the 1980s. The forecasters missed the downturn in profits from 1980 to 1982, and their forecasts didn’t capture the volatility in profits in the late 1980s, but they did get the average about right. Forecasts in the 1990s haven’t been too bad either; they were just a bit too pessimistic about the growth of profits from 1994 to 1997. Another way to see the relationship between the forecasts and the real-time actual data is to use a scatter plot that compares the actual data with the forecasts (Figure 3). If the forecasts are accurate, the points in the scatter plot should lie along the 45-degree line shown in the figure. A data point close to that 45-degree line means that the growth rate being forecast is close to the actual growth rate of corporate profits. The further away a point is from the 45-degree line, the greater the error and the poorer the forecast. From the scatter plot, it looks like the forecasts for the growth rate of corporate profits are SEPTEMBER/OCTOBER 1999 pretty good. The data points are close to the 45degree line, with a few exceptions, which means the forecast errors are usually fairly small. STATISTICAL TESTS FOR FORECAST QUALITY Although examining figures that plot the forecasts along with the actual values is interesting and graphically illustrates how good the forecasts are, we can also use statistical theory to perform more formal tests of the quality of the forecasts. Economists have developed a number of tests that forecasts must pass to be considered high quality. All of the tests that follow look at the relationship between the forecasts and the actual values and allow for the fact that no forecast is perfect. After all, the economy is very difficult to predict, and many things can cause a forecast to go awry. We’re going to look at two different ideas about forecast quality: (1) high-quality forecasts should be rational, and (2) high-quality forecasts should be better than simple alternatives. A forecast is said to be rational when forecast errors are not predictable in advance. If they FIGURE 3 were, it would be possible to Corporate Profits create a better forecast. For ex(SPF Forecasts and Real-Time Actuals) ample, if I knew that the forecasters, on average, predicted a growth rate of corporate profits that was three percentage points too high, I could make a better forecast by taking the survey’s prediction and subtracting three percentage points. For a forecast to be considered rational, no such method of changing a forecast must lead to a better forecast. The second test of forecast quality is a forecast’s ability to beat simple alternative forecasts. We should expect forecasts from our survey to be sig- 6 FEDERAL RESERVE BANK OF PHILADELPHIA How Useful Are Forecasts of Corporate Profits? Dean Croushore nificantly better (in the sense of having smaller result suggests that the forecasts are potentially errors) than some simple alternative methods of useful and can’t be easily improved upon. forecasting. For example, suppose we found that If we look at a plot of the forecast errors (the the forecast errors from the Survey of Professional actual value for the growth rate of corporate profForecasters were larger, on average, than the er- its minus the forecast at each date), we see they rors from a forecast that assumes corporate profit are occasionally large (Figure 4). But the foregrowth will be 10 percent every year. Then we’d cast errors don’t show any predictable pattern, think, with good reason, that the survey’s fore- which means it would be difficult for someone cast was poor because it was worse than a naive to make a better forecast than the one provided forecast. by the survey forecasters. We begin by testing to see if the survey forecasts are rational. We need statistical theory in these tests because, as noted above, there will 7 To perform this test, we regress the actual value for always be errors in forecasts. The statistical ques- corporate-profits growth each year on a constant and the tion is: are the forecast errors unpredictable forecast value. If the forecast were perfect, the constant enough that we should consider the forecasts term would be zero, and the coefficient on the forecast rational? Or are they so predictable that we would be one. But, of course, there are certain to be some should reject the notion of rationality for the fore- errors in the forecasts, which cause the coefficients to differ from zero and one, so we must use statistical casts? The average error in the forecasts for the theory to see how different from zero and one the coeffigrowth rate of corporate profits was one percent- cients are. Thus, we run a statistical test to see whether age point. But in this case, the one-percentage- the constant term is significantly different from zero and point average error is not statistically significant, the coefficient on the forecast is statistically different because the growth rate of corporate profits is so from one. If they are significantly different from zero and one, we say the forecast isn’t rational. Our tests show variable from year to year that finding a one- they are not significantly different from zero and one. percentage-point error isn’t surprising or un- Further details on the statistical tests in this article can be usual. So one could not convincingly argue that found in the Appendix. the forecasts aren’t rational just because on average they FIGURE 4 are slightly higher than acSPF Corporate Profit Forecast Errors tual growth of profits. (Real-Time Actuals) A common statistical test for rationality is a test for unbiasedness, which uses a technique known as regression analysis. The regression analysis determines whether the points lie along the 45degree line in the scatter plot (Figure 3).7 In this case, the test doesn’t reject the hypothesis that the forecasts are unbiased; visually, there is a rough balance between the points below the 45-degree line and those above. This 7 BUSINESS REVIEW SEPTEMBER/OCTOBER 1999 If the value of the test statistic is less than the critical value, the test supports the notion that the forecasts are rational.9 In summary, all the tests support the view that the forecasts of corporate-profits growth from the Survey of Professional Forecasters are rational. The second type of test for forecast quality compares the forecasts from the survey to some alternative forecasts. One alternative is to form a naive forecast, in which the forecast for next year’s growth rate of profits equals the value from last year. Another possibility is to forecast that corporate-profits growth equals its long-run average. Yet another possibility is to assume that corporate-profits growth simply equals its average over the last five years. When we try these alternatives, however, the errors are always much worse than the errors from the survey forecasts. A good summary measure of overall forecast accuracy is the root mean squared error of the forecast.10 When we look at the root mean squared error of the survey forecasts, compared 8 to the alternative forecasts, we see that the surThe first line of the table reports the test results that vey has a lower root mean squared error than show the forecast is unbiased. Additional information about the other tests can be found in the Appendix. any of the alternatives (Table 2). Although the survey forecasts pass all these TABLE 1 statistical tests, we are left wondering a bit about Tests for Forecast Rationality these results, because the forecast errors are someTest Value of Test Statistic Critical Value Rational? A variety of statistical tests that examine the forecasts show the forecast errors to be unpredictable and balanced, a sign of good-quality forecasts. The various tests run on the forecasts include the sign test, which examines whether there are the same number of positive and negative forecast errors; the Wilcoxon signed-rank test, which examines whether the magnitude of positive and negative forecast errors are the same; the zero-mean test, which examines whether the forecast errors are significantly different from zero; and the Dufour test, which looks to see if the forecast error for one year is independent of the forecast error from the previous year. The forecasts pass all these tests with flying colors (Table 1).8 The table provides the value of the test statistic, along with the critical value to which that test statistic is to be compared, and whether the test supports the rationality of the forecasts. Unbiasedness test 0.23 3.37 yes Sign test 0.56 1.96 yes Wilcoxon signed-rank test 0.07 1.96 yes Zero-mean test 0.64 2.04 yes Dufour test 1.32 1.96 yes Note: The test is consistent with rationality of the forecast when the value of the test statistic is less than its critical value. 8 9 To see how the forecasts would fare in these tests using today’s data, as opposed to the real-time data set, see Corporate Profits Data Today. 10 The root mean squared error is calculated by taking the forecast errors at each date, squaring them, adding them together, dividing by the number of data points, and taking the square root. FEDERAL RESERVE BANK OF PHILADELPHIA How Useful Are Forecasts of Corporate Profits? Dean Croushore Corporate Profits Data Today How much difference would it make to use today’s data on corporate profits, instead of the realtime data set used in this article? The choice of which data to use makes a difference, especially at particular dates. If we plot the data from today over time and compare it to the real-time data, we see that the new definitions and recalculations of the data are important, especially at certain dates, such as 1987 (Figure). The figure shows that the difference in the growth rate of Corporate Profits corporate profits between the differ(SPF Forecasts and Actuals) ent data sets is as much as 33 percentage points! How much difference would this have made to our statistical tests? Using the latest vintage of the data would increase the average forecast error to three percentage points (higher than the one-percentagepoint average error based on the realtime data). Despite that, when we run all the statistical tests reported in Table 1 and the alternative forecasts reported in Table 2, using the latest data, the forecasts still pass all the tests, but not by as large a margin. Date times large. It’s not clear why that should be the case. But a close look at the data reveals a good reason why the forecasts pass the tests despite the occasional large errors: corporate profits are very volatile, as we saw in Figure 1. Forecasting TABLE 2 Tests for Improving Forecasts Alternative Root Mean Squared Error Survey 8.9 Naive 15.8 Constant Average Value 11.9 Five-Year Moving Average Value 13.5 a variable this volatile is bound to lead to large forecast errors, as we’ve seen. However, large forecast errors don’t indicate that the forecasts are bad, just that the variable itself is inherently volatile. WHY ARE CORPORATE PROFITS SO VOLATILE? The main source of volatility in corporate profits seems to be the business cycle. Recessions cause corporate profits to decline substantially (Figure 5). As you can see from the figure, the recessions (the shaded periods in the figure) that began in 1969, 1973, 1980, 1981, and 1990 led to significant declines in the growth rate of corporate profits. Other sources of volatility in corporate profits include: (1) changes in the value of the dollar against other currencies; (2) changes in the in9 BUSINESS REVIEW SEPTEMBER/OCTOBER 1999 porate profits until the economy came out of the recession in late 1982 and began growing strongly in 1983.12 FIGURE 5 Corporate Profits (Real-Time Actuals) Date flation rate; and (3) changes in tax laws. Changes in the value of the dollar against other currencies can influence corporate profits, since large corporations depend heavily on profits from foreign operations, which are affected by the exchange rate. When the dollar rises against foreign currencies, profits earned abroad in foreign currencies convert to fewer dollars, so the dollar profits of international corporations decline. Uncertainty about profits can also stem from changes in the inflation rate. Inflation introduces a number of distortions into our accounting systems, and those systems can’t deal with inflation perfectly. For example, the manner in which accounting methods handle the value of inventories can make a significant difference in nominal profits. As a result of problems like this, changes in the inflation rate make profits hard to predict.11 Changes in tax law obviously influence aftertax corporate profits, though sometimes the effects aren’t apparent for several years. Corporate taxes were cut in 1981, in the middle of a recession, but the effects didn’t show up in cor10 SUMMARY Corporate profits are quite volatile. Even so, forecasts of corporate profits from the Survey of Professional Forecasters pass a variety of statistical tests that show they’re rational and better than simple alternative forecasting methods. The forecasts line up reasonably well with actual values. The value of the stock market may have risen over the past few years partly because of forecasts of high corporate profits. The results reported here, concerning the forecasts of corporate profits from the Survey of Professional Forecasters, suggest that such forecasts have been fairly accurate, though certainly not perfect, over the last 30 years. What is the forecast for corporate profits for this year? In the Survey of Professional Forecasters from the fourth quarter of 1998, the forecasters projected that corporate profits would rise just 0.8 percent in 1999, after declining in 1998. This represents a significant slowdown from the growth rate of corporate profits throughout the earlier part of the 1990s. 11 There is some controversy about this issue, since the biggest increases in inflation were accompanied by large increases in oil prices and economic recession. As a result, it’s hard to tell whether corporate profits really fall because of inflation alone. 12 For more on the sources of volatility in corporate profits, see the article by John Duca. FEDERAL RESERVE BANK OF PHILADELPHIA How Useful Are Forecasts of Corporate Profits? Dean Croushore REFERENCES Carlson, John B., and Kevin H. Sargent. “The Recent Ascent of Stock Prices: Can It Be Explained by Earnings Growth or Other Fundamentals?” Federal Reserve Bank of Cleveland Economic Review (1997 Quarter 2), pp. 2-12. Cochrane, John H. “Where Is the Market Going? Uncertain Facts and Novel Theories,” Working Paper 6207, National Bureau of Economic Research (1997). Croushore, Dean. “Introducing: The Survey of Professional Forecasters,” Federal Reserve Bank of Philadelphia Business Review, November/December 1993. Croushore, Dean. “Inflation Forecasts: How Good Are They?” Federal Reserve Bank of Philadelphia Business Review, May/June 1996. Croushore, Dean, and Tom Stark. “A Real-Time Data Set for Macroeconomists,” Working Paper 994, Federal Reserve Bank of Philadelphia, June 1999. Diebold, Francis X., and Jose A. Lopez. “Forecast Evaluation and Combination,” in G.S. Maddala and C.R. Rao, eds., Handbook of Statistics. Amsterdam: North Holland, 1996, pp. 241-68. Duca, John V. “Has Long-Run Profitability Risen in the 1990s?” Federal Reserve Bank of Dallas Economic Review, Fourth Quarter 1997. 11 BUSINESS REVIEW SEPTEMBER/OCTOBER 1999 APPENDIX For the interested reader, this appendix explains the tests discussed in this article in more detail (see Table 1 in the text). More information about all these tests can be found in the 1996 article by Diebold and Lopez. BIAS TESTS The first test discussed in the paper is a test for unbiasedness. A set of forecasts over time is unbiased if a regression of the actual values (the dependent variable) on a constant term and the forecasted values (the independent variable) yields coefficients that are not significantly different from 0 for the constant term and 1 for the forecast term. That is, the regression is: pt = a + b ptf + et, where pt is actual profits and ptf is the forecast at each date t. The bias test is simple and sensible: over a long sample period, you’d expect ^ a to be close to zero and ^ b to be close to one. When we estimate this equation, we get the following results: _ pt = 1.380 + 0.949 p tf, (2.15) (0.216) R2 = 0.21, D.W. = 0.17, F = .23, F* = 3.37, _ where R2 is the adjusted R2 statistic, D.W. is the Durbin-Watson statistic, numbers in parentheses are standard errors, F is the value of the test statistic for the joint hypothesis that a is zero and b is one, and F* is the critical value of that statistic. Since F < F*, we don’t reject the null hypothesis. Sign Test. If a forecast is optimal, the forecast errors should be independent with a zero median. The sign test examines this null hypothesis by examining the number of positive forecast errors in the sample, which has a binomial distribution. Since the studentized version of the statistic is standard normal, we assess its significance with the normal distribution. The test statistic has a value of 0.56, less than the critical value of 1.96, so we don’t reject the null hypothesis that the forecast errors have zero median. Wilcoxon Signed-Rank Test. The Wilcoxon signed-rank test is related to the sign test, since it has the same null hypothesis, but requires distributional symmetry. It accounts for the relative sizes of the forecast errors, not just their sign. The test statistic is the sum of the ranks of the absolute values of the positive forecast errors, where the forecast errors are ranked in increasing order. The studentized value of the statistic is normally distributed. The test statistic has a value of 0.07, while the critical value is 1.96, so we don’t reject the null hypothesis. Zero-Mean Test. Optimal forecasts should pass a simple test: the mean of the forecast errors should be zero. The mean of the forecast errors divided by its standard error is 0.64, which is less than the critical value of 2.04, so we don’t reject the null hypothesis that the mean of the forecast errors is zero. Dufour Test. Dufour adapts the Wilcoxon signed-rank test and applies it to the product of successive forecast errors. This is a stringent test of the hypothesis that the forecast errors are white noise and serially independent, in particular that they are symmetric about zero. The value of the test statistic is 1.32, less than the critical value of 1.96, thus we don’t reject the null hypothesis that forecast errors are white noise. 12 FEDERAL RESERVE BANK OF PHILADELPHIA How Useful Are Forecasts of Corporate Profits? Dean Croushore The Philadelphia Story: A New Forecasting Model For the Region Theodore M. Crone and Michael P. McLaughlin* F orecasts of the national economy have long been a staple of the planning and budgeting process for large corporations and the federal government. But for small firms and state and local governments, a forecast of the regional economy may be more important to their planning process. This demand for regional forecasts challenges the professional forecaster to develop models that produce accurate predictions of the major economic variables for states and metro- politan areas. Several years ago, the Philadelphia Fed developed a small forecasting model for each of the three states in the Third Federal Reserve District — Pennsylvania, New Jersey, and Delaware.1 This article introduces a similar model that forecasts major economic variables for the Philadelphia metropolitan area and the city of Philadelphia. For the metro area as a whole, the model suggests continued job growth through mid-year *Ted Crone is a vice president and economist and Mike McLaughlin is a research associate at the Federal Reserve Bank of Philadelphia. 1 Theodore M. Crone, “A Slow Recovery in the Third District,” Federal Reserve Bank of Philadelphia, Business Review (July/August 1992). 13 BUSINESS REVIEW 2000. For the city of Philadelphia, the outlook is not so bright. The model predicts that the city will lose a significant number of jobs between the second quarter of 1999 and the second quarter of 2000. GOOD REASONS TO FORECAST THE PHILADELPHIA ECONOMY The Philadelphia metropolitan area is a natural choice as a region for developing an economic forecast. It is one of the nation’s largest metro areas, and it has a diverse economy. Moreover, the area’s business cycle is similar, though not identical, to the national cycle. Metropolitan areas in general represent logical geographic divisions for forecasting economic activity because “the general concept adopted for the determination of a standard metropolitan area was that each area should represent an integrated economic unit with a large volume of daily travel and communication between a central city and the outlying parts of the area.”2 The Philadelphia metropolitan area is the fourth largest in the United States and still conforms to the classic description of a metropolitan area — an integrated economy with a densely populated central city to which a large number of workers commute from surrounding suburbs. In 1990, almost a quarter of a million people commuted to the city of Philadelphia to work — about one-third of the wage and salaried workers in the city. The Philadelphia metro area has a population of almost 5 million and supplies more than 2.25 million nonfarm jobs, slightly less than 2 percent of the national totals 2 U.S. Bureau of the Census, County and City Data Book, 1949. Washington, DC: U.S. Government Printing Office, p. iv. The Philadelphia metropolitan area includes five counties in Pennsylvania (Philadelphia, Bucks, Chester, Delaware, and Montgomery) and four counties in New Jersey (Burlington, Camden, Gloucester, and Salem). 14 SEPTEMBER/OCTOBER 1999 in both cases. The area has more people and jobs than 30 states, and the city of Philadelphia alone has a larger population and more jobs than 12 states. The Philadelphia metro area contains more than 40 percent of the population in the Third Federal Reserve District and about 50 percent of the jobs. The Philadelphia economy is not only large, it’s also diverse. We would expect the distribution of jobs in few, if any, metropolitan areas to exactly mirror the distribution in the nation as a whole, but the distribution in Philadelphia comes close. Jobs in the Philadelphia area are somewhat more concentrated in financial and nonfinancial services than in the nation as a whole, and the other major job categories (construction, manufacturing, transportation and utilities, trade, and government) are somewhat underrepresented in the Philadelphia economy.3 Despite these differences, the distribution of jobs in the Philadelphia area mirrors the national distribution fairly closely when compared to the other nine largest metropolitan areas in the country. (See Measuring the Relative Importance of Industries Across Metropolitan Areas.) Even though the structure of the Philadelphia economy has closely resembled the national economy in recent decades, significant shifts have occurred in the last 30 years. Prior to the 1980s, the Philadelphia area had a larger proportion of its jobs in the manufacturing sector than the nation. But Philadelphia has been losing manufacturing jobs at a much faster pace than the nation, so the region’s economy is now less manufacturing oriented than the U.S. 3 The Philadelphia area has about 6.8 percent more of its jobs in nonfinancial services and about 1.1 percent more in financial services than the nation. The area has an especially high concentration of jobs in the insurance industry, legal services, health services, social services, and private education. The underrepresentation in Philadelphia ranges from 0.5 percent for transportation and public utilities to 3.1 percent for government (federal, state, and local). FEDERAL RESERVE BANK OF PHILADELPHIA HowPhiladelphia Useful Are Forecasts of Corporate Profits? The Story: A New Forecasting Model for the Region Croushore Theodore M. Crone and MichaelDean P. McLaughlin Measuring the Relative Importance Of Industries Across Metropolitan Areas One measure of a metro area’s relative specialization in a given industry is the “location quotient.” This quotient is calculated as the proportion of an area’s employment (or output) in a given industry divided by the proportion of the nation’s employment (or output) in that industry. A location quotient equal to one indicates that the industry in question is neither over- nor underrepresented in the region relative to the nation. Industries with location quotients greater than one have relatively more importance in the region than in the nation. The reverse is true for industries with location quotients less than one. The table presents location quotients for the major industry divisions in the 10 largest metropolitan areas. Since output measures are not available at the metropolitan level, these location quotients are based on nonfarm employment. Philadelphia’s location quotients range from 0.75 for construction and mining to 1.23 for nonfinancial business and personal services.* This means that the proportion of jobs in construction and mining in the Philadelphia metro area is 25 percent less than the proportion nationwide. Similarly, the proportion of jobs in nonfinancial services in Philadelphia is 23 percent higher than the proportion in the United States. Three of the other top 10 metro areas (Los Angeles, New York, and Boston) have a lower percentage of their jobs in construction and mining than does Philadelphia. And New York, Washington, and Boston have a higher percentage of jobs in nonfinancial services than Philadelphia. Every one of the other nine metro areas in the table except Chicago has at least one location quotient that is lower than Philadelphia’s lowest, and every one has at least one location quotient that is higher than Philadelphia’s highest. For each of the major industry divisions, Philadelphia’s location quotient ranks between fourth and seventh among the top 10 metropolitan areas. None of Philadelphia’s location quotients are at the extremes among the nation’s largest metro areas. TABLE Location Quotients for Major Industries in the 10 Largest Metropolitan Areas Metro Area Construction and Mining* Los Angeles New York Chicago Philadelphia Washington Detroit San Francisco/ Oakland Houston Atlanta Boston Manufacturing Transportation and Public Utilities Trade Finance, Insurance and Real Estate Nonfinancial Services Government 0.59 0.61 0.77 0.75 1.00 0.77 1.14 0.52 1.07 0.89 0.27 1.39 1.09 1.11 1.19 0.91 0.89 0.87 0.95 0.75 0.96 0.94 0.80 1.01 0.98 2.19 1.31 1.20 0.94 0.92 1.10 1.25 1.07 1.23 1.32 1.04 0.87 1.00 0.76 0.80 1.45 0.70 0.90 2.00 0.98 0.61 0.68 0.74 0.73 0.77 1.38 1.36 1.64 0.83 0.93 0.97 1.14 0.92 1.41 0.91 1.14 1.43 1.12 1.03 1.00 1.32 0.93 0.82 0.80 0.75 *Because there are so few jobs in the mining and extractive industries in the Philadelphia area, the Bureau of Labor Statistics combines the employment data for this sector with data for the construction industry. 15 BUSINESS REVIEW SEPTEMBER/OCTOBER 1999 economy.4 The loss of manufacturing jobs has been a major factor in keeping Philadelphia’s overall job growth below the U.S. average.5 Nonfarm job growth in the metro area has averaged less than 1 percent a year since 1967, compared with 2 percent a year for the nation. Although trend growth in the Philadelphia area has been slower than the national average, the business cycles have been similar. Since the late 1960s, both the nation and the metro area have suffered five periods of sustained job losses (losses lasting two consecutive quarters or more). The national and regional downturns have occurred at approximately the same time, but downturns in the Philadelphia area have tended to begin a bit earlier and last a bit longer. In most cases, the differences in timing have been narrow. At all but two of the 10 turning points, the cyclical high or low employment levels in the metro area were within one quarter of the cyclical highs and lows in the nation (Figure 1).6 Job growth in the metro area is also much more vola- tile than job growth in the nation, and there have been isolated quarters in some expansions when the metro area has lost jobs. USING NATIONAL AND REGIONAL DATA TO FORECAST THE PHILADELPHIA ECONOMY Since the cyclical patterns of the national and regional economies are similar, one way to forecast the metro area’s economy would be to take a national forecast and assume that the Philadelphia economy would follow the same pattern, 6 The history of job growth in the city of Philadelphia has been somewhat different. For most of the past 30 years, the city has been losing jobs. Nevertheless, the national and metro area patterns are reflected in the city data. When national job growth has been strong, losses in the city have been less severe, and when the nation was losing jobs, losses in the city were even larger. The city’s tax structure sets its economy apart as a distinct segment of the metro area’s economy. For evidence of how the city’s tax structure affects its job growth relative to the nation’s, see Robert P. Inman, “Can Philadelphia Escape Its Fiscal Crisis With Another Tax Increase?” Federal Reserve Bank of Philadelphia, Business Review (September/October, 1992). 4 Since their peak in 1967, manufacturing jobs in the Philadelphia metro area have declined almost 50 percent, while the nation has lost about 4 percent of its manufacFIGURE 1 turing jobs. Manufacturing jobs in the nation did not peak until 1979. Some of the reasons for the (Seasonally Adjusted Annual Rate) decline of manufacturing jobs in the Third District states are outlined in Theodore M. Crone, “Where Have All the Factory Jobs Gone—and Why?” Federal Reserve Bank of Philadelphia, Business Review (May/June 1997). Quarterly Job Growth 5 The loss of manufacturing jobs is not the only factor, however. Nonmanufacturing jobs have been increasing in the area, but not nearly as fast as in the nation. Nonmanufacturing jobs in the Philadelphia area have increased almost 80 percent since 1967, but nationally they have risen more than 130 percent. 16 Shaded areas represent national recessions. FEDERAL RESERVE BANK OF PHILADELPHIA HowPhiladelphia Useful Are Forecasts of Corporate Profits? The Story: A New Forecasting Model for the Region but at a somewhat slower pace. For example, we might assume that in expansions, job growth in the Philadelphia area would be half as strong as growth at the national level, and that in economic downturns, job losses would be half again as great in Philadelphia as in the nation. But this type of forecast would ignore the relationship between job growth in the Philadelphia area and other measures of the national economy, such as industrial production and housing construction. Job growth in the Philadelphia area may be systematically related not only to overall job growth in the nation but also to which segments of the national economy are growing. Moreover, growth in the Philadelphia area has its own momentum. In the 1970s, annual job growth in the Philadelphia metropolitan area was almost 2 percent below the national average; in the 1980s, it was only one-third of 1 percent below the national average; and in the 1990s, it has been somewhere in between. To capture as many of these relationships as possible, forecasters build models that relate several national and regional variables to one another, then estimate the strength of the relationships from historical data. We have built such a model using variables for the nation, the metro area, and the city. Our Focus Is the Region. We are most interested in a forecast of nonfarm employment and the unemployment rate for the metropolitan area and the city. Nonfarm employment is the most comprehensive, timely measure of economic activity available for the metro area or the city.7 And economic analysts regularly point to changes in nonfarm employment and the level 7 We would like to have a broad measure of regional output such as “gross regional product” that would be analogous to gross domestic product — the most comprehensive measure of output for the nation. Unfortunately, we do not have such a measure. Personal income data are available for the metropolitan area, but they are published with a considerable lag and only on an annual basis, so we cannot use them in our quarterly model. Croushore Theodore M. Crone and MichaelDean P. McLaughlin of the unemployment rate as indicators of the strength or weakness of regional economies, and not without justification. At the national level, changes in these two variables are important factors in determining official business cycles.8 At the metropolitan level, there are no official business cycles, and changes in employment and the unemployment rate are the best indicators of the cycle. Our forecast model includes two other regional variables: housing permits and initial unemployment claims, both for the metro area.9 Housing permits and initial unemployment claims follow a cyclical pattern, but they tend to lead the general business cycle at the national level. That is, housing permits tend to decline and initial unemployment claims tend to rise before the onset of a downturn or recession. For this reason, changes in permits and initial unemployment claims are useful in forecasting more comprehensive measures of the economy, such as employment and the unemployment rate.10 Thus, our Philadelphia model contains six regional variables: four for the metropolitan area and two for the city of Philadelphia. These six variables are the ones we are most interested in forecasting. We supplement these with eight national variables, which are mainly used to 8 Geoffrey H. Moore, Business Cycles, Inflation, and Forecasting, NBER Studies in Business Cycles No. 24, Cambridge, MA: Ballinger, 1983. Peaks and troughs in nonfarm employment and the unemployment rate do not always coincide with the official beginning or end of national business cycles, however. 9 Housing permits are also available for the city of Philadelphia, but the numbers are very small and the pattern is erratic, so we did not use the city housing permits in our model. 10 There is independent interest in forecasts of housing permits because they are the best regional measure of residential construction, and our model produces a forecast of housing permits for the Philadelphia area. 17 BUSINESS REVIEW help forecast the metro-area and city variables.11 We include all the national counterparts to the regional variables in the model. We also include some national variables, such as real gross domestic product, because they are comprehensive measures of the U.S. economy. Finally, we include some financial variables, such as the difference between the yield on 10-year Treasury bonds and the federal funds rate (the overnight interbank loan rate) because they have been found useful in forecasting the national economy and are valuable in forecasting some of the metro-area and city variables in our model.12 A Small Time-Series Model. Our Philadelphia model differs from the large structural models used by most major consulting firms to predict the nation’s economy. These structural models attempt to specify a full range of economic relationships among many variables, and economic theory plays a critical role in how the variables are allowed to interact. Good structural models of this type require a large number of variables.13 Since few regional variables are available on a quarterly basis, these large structural models are not a practical option for forecasting the Philadelphia economy. In the late 1970s and early 1980s, researchers at the Minneapolis Fed developed small time11 The national variables in the model are real gross domestic product, nonfarm employment, the unemployment rate, industrial production, housing permits, initial unemployment claims, the difference between the yield on 10-year Treasury bonds and the federal funds rate, and the inflation rate. All the variables in the model except the unemployment rates, the inflation rate, and the spread in interest rates are included as logarithms of the quarterly levels. 12 See Ben S. Bernanke, “On the Predictive Power of Interest Rates and Interest Rate Spreads,” Federal Reserve Bank of Boston, New England Economic Review (November/December 1990). 13 The national models produced by DRI and Macroeconomic Advisers, for example, consist of more than 250 variables. 18 SEPTEMBER/OCTOBER 1999 series models that overcame the need for such a large number of economic variables and that were useful for forecasting state and regional economies.14 Our Philadelphia model is a variant of those models. Time-series models emphasize the statistical regularities among economic variables over time rather than the underlying theoretical relationships, but they are not totally divorced from theory. For example, theory suggests which variables should be included in the models. Moreover, some basic assumptions can help solve the problem of “overfitting,” which occurs when we try to forecast a particular variable, say, the metro-area unemployment rate, using a relatively large number of other variables.15 If we use too many variables, the model we estimate based on past relationships may explain the historical data well but may not produce a very good forecast. In other words, we can overfit the model by estimating influences of one variable on another that reflect not only the stable relationships among the variables but also those relationships that were peculiar to the period from which the data were drawn. When the model is used to forecast, these temporary patterns will be projected into the future, diminishing the accuracy of the forecast. A common way to limit the number of explanatory variables in time-series models is to allow the national variables to affect the regional 14 See Paul A. Anderson, “Help for the Regional Economic Forecaster: Vector Autoregression,” Federal Reserve Bank of Minneapolis, Quarterly Review (Summer 1979). 15 In our Philadelphia model we have 92 observations for each variable (quarterly data from 1976 to 1998). Our explanatory variables include four lagged values for each of the 14 variables in the model, so there are 56 potential explanatory variables in each equation. If we allow all the potential explanatory variables to help account for the historical pattern of a particular variable, we may end up overfitting the model for forecasting purposes. FEDERAL RESERVE BANK OF PHILADELPHIA HowPhiladelphia Useful Are Forecasts of Corporate Profits? The Story: A New Forecasting Model for the Region ones, but not vice versa. In effect, this assumes that the regional variables, such as the unemployment rate for the metro area or the city, have no independent effect on the national economy. We apply the same principle to the metro-area and city variables. The metro-area variables are allowed to affect the city variables, but not vice versa.16 Researchers at the Minneapolis Fed made some other major assumptions that helped address the overfitting problem. Most important, they assumed that the best predictor of a given variable, say, this quarter’s unemployment rate, is its value in the most recent past.17 So, the first stage in developing a model is to forecast each variable using only its own past values. Past values of other variables are added to the equation only if including them lowers the forecast error for the time beyond the period in which the model is estimated. For example, using data up to the fourth quarter of 1988, we would estimate a model in which the equation for the unemployment rate contains only past values of the unemployment rate. We would then estimate a model in which the equation for the unemployment rate also contains the past values of another variable, such as initial unemployment 16 In technical language, the model is “block recursive.” Any national variable can be affected only by its past values and the past values of the other national variables. Any metro-area variable can be affected by its past values and the past values of the national or other metro-area variables. And each of the city variables can be affected by the past values of any variable in the model. 17 In the literature, this is known as one of the Minnesota priors. Another Minnesota prior is that recent values of a variable are more important than distant values in determining its current level. Because of the role of prior beliefs in developing these time-series models, they are called Bayesian vector autoregression models. For a full technical description of the models, see Thomas Doan, Robert Litterman, and Christopher Sims, “Forecasting and Conditional Projection Using Realistic Prior Distributions,” Econometric Reviews, 3 (1984), pp. 1-100. Croushore Theodore M. Crone and MichaelDean P. McLaughlin claims. If the model that includes unemployment claims results in a smaller forecast error in the period after 1988, initial unemployment claims are included in the final equation for the unemployment rate.18 This process limits the number of variables that influence each of the regional variables in our model (Table 1). We decided on which variables to include in the Philadelphia model and how much influence they would have on the regional forecast in this way: We included any variable that reduced the out-of-sample forecast errors over the past 10 years. Thus, we assumed that the pattern of relationships among the variables in the near term would follow this recent historical pattern more closely than the pattern over the entire period for which we have data.19 THE NEAR-TERM FORECAST FOR THE METRO AREA AND THE CITY Even though we have included many national variables in our forecast model, our primary interest is in the variables for the metropolitan area 18 We also restrict the degree to which a variable such as initial unemployment claims influences the unemployment rate to provide the best “out-of-sample” forecast of the unemployment rate. For each equation in our model, we test the forecast value of each of the variables one by one. We add a variable and re-estimate the model using data through the end of 1988; we then calculate the root mean squared errors of the forecasts after that date. We then re-estimate the model through the first quarter of 1989, and so on quarter by quarter, producing forecasts and calculating the out-of-sample forecast errors from those models. In our final model, we incorporate those variables that result in the lowest root mean squared error based on the four-quarter-ahead forecasts over a 10-year period. 19 We also experimented with a model in which the parameters would change over time to pick up any change in the relationship among the variables. This model with time-varying parameters lowered the outof-sample forecast errors for some of our regional variables but increased the errors for others. Therefore, we did not incorporate time-varying parameters in our model. 19 BUSINESS REVIEW SEPTEMBER/OCTOBER 1999 TABLE 1 National and Other Regional Variables That Affect Each of the Regional Variables in the Philadelphia Model* National Variables Used in Forming the Forecast Variable Being Forecast Metro-area nonfarm jobs Metro-area unemployment rate Metro-area housing permits Gross domestic product Unemployment rate Unemployment rate Housing permits Gross domestic product Unemployment rate Nonfarm employment Housing permits Housing permits Inflation rate Housing permits Housing permits Unemployment Initial rate unemployment claims Industrial production Inflation rate Metro-area City nonfarm City initial jobs unemployment unemployment rate claims Spread between 10-yr Treasuries and fed funds rate Inflation rate Housing permits Initial unemployment claims Spread between 10-yr Treasuries and fed funds rate Metro- Area Variables Used in Forming the Forecast Inflation rate Unemployment Initial rate unemployment claims Housing permits Unemployment rate Housing permits Housing permits Initial unemployment claims Initial unemployment claims *Each equation also contains four lags of the variable being forecast. 20 FEDERAL RESERVE BANK OF PHILADELPHIA HowPhiladelphia Useful Are Forecasts of Corporate Profits? The Story: A New Forecasting Model for the Region and the city of Philadelphia, especially nonfarm employment and the unemployment rate. From the second quarter of 1998 to the second quarter of 1999, nonfarm jobs increased 1.3 percent in the Philadelphia metro area and 1.2 percent in the city, the first meaningful job growth in the city since 1987. By the second quarter of 1999, the unemployment rate in the city had fallen to 5.4 percent, its lowest level in almost a decade, and the unemployment rate in the metropolitan area was just 4.0 percent. Croushore Theodore M. Crone and MichaelDean P. McLaughlin What does our forecast model predict for the second half of 1999 and the first half of 2000? For the metropolitan area, our new Philadelphia model is predicting job growth of 1.6 percent between the second quarter of 1999 and the second quarter of 2000, and the unemployment rate is predicted to fall slightly to 3.8 percent (Table 2).20 The model forecasts that total housing per20 For the national variables, our model predicts real GDP growth of 2.0 percent from 1999:II to 2000:II, and TABLE 2 Forecasts from the Philadelphia Model Variable Previous period 1998:II-1999:II Forecast 1999:II-2000:II Root mean squared error of four-quarters-ahead forecast 1989-1998* Percentage points Metro-area nonfarm job growth 1.3% 1.6% 1.2 City nonfarm job growth 1.2% -1.5% 1.3 Previous period 1999:II Forecast 2000:II Metro-area unemployment rate 4.0% 3.8% 0.6 City unemployment rate 5.4% 5.3% 0.8 Previous period 1998:III to 1999:II over 1997:III to 1998:II Forecast 1999:III to 2000:II over 1998:III to 1999:II 1.0% -2.6% Metro-area housing permits** *The square root of the average of the squared values of the errors in the forecasts for four quarters ahead for the years 1989 to 1998. **Since housing permits at the metropolitan area level are so volatile from quarter to quarter, we report growth on a four-quarter-average basis. 21 BUSINESS REVIEW SEPTEMBER/OCTOBER 1999 mits issued in the metro area from the third quarter of 1999 through the second quarter of 2000 will be 2.6 percent lower than in the previous four quarters. The forecast for the city of Philadelphia is not as rosy. Our model predicts that job losses will resume, and the city will give up most of the jobs it has gained since the end of 1997. The unemployment rate in the city, however, is expected to be just 5.3 percent in the second quarter of 2000. Unlike the situation with most published forecasts from large structural models, no forecaster’s independent judgment was used to alter the forecasts generated by our model. How accurate are these forecasts likely to be? No forecasting model is 100 percent accurate, and our Philadelphia model is no exception. Moreover, forecasts of smaller segments of the economy tend to be less accurate than forecasts of the national economy as a whole. One way to gauge the accuracy of a forecast is to look at the forecast errors from the model over the recent past. In Table 2, we have reported the root mean squared errors over the past 10 years of the forecasts produced by our model.21 Using the root mean squared errors as a guide, we can say that about two-thirds of the time, metro-area job growth will be within 1.2 percentage points of what we report in Table 2.22 The dashed line in Figure 2 shows the four-quarter-ahead forecast for metropolitan employment from 1989 to 1998, with a band of 1.2 percent (shaded area) on either side of the forecast. The solid line shows the actual level of employment in this period; it was within the band around the forecast more than 75 percent of the time. Based on the root mean squared error, city job growth will likely be within 1.3 percentage points of what we report in Table 2. For example, our model is forecasting a substantial decline in city jobs (1.5 percent), but based on the forecast errors over the past 10 years, squared errors, dividing by the total number of forecast errors (40), and then taking the square root. This measure of accuracy puts more emphasis on large errors than on small ones. 22 This assumes that the recent forecast errors are a good estimate of future ones and that the errors are normally distributed. FIGURE 2 DRI and Macroeconomic Advisors are forecasting growth of 2.3 percent. Our model’s predicted unemployment rate for 2000:II is within 0.2 percentage point of their forecasts. Our time-series model is predicting considerably faster job growth than these large macro models (about 230,000 new jobs per month versus 130,000 new jobs for the two commercial forecasters). Four-Quarter-Ahead Forecasts and Actual Employment Levels (Philadelphia Metropolitan Area) 21 We concentrated on the root mean squared errors of the forecasts for the period four quarters ahead of the actual data. This statistic is calculated by squaring the four-quarter-ahead forecast error for each quarter from 1989:I to 1998:IV, adding these 22 FEDERAL RESERVE BANK OF PHILADELPHIA HowPhiladelphia Useful Are Forecasts of Corporate Profits? The Story: A New Forecasting Model for the Region there is some chance (about 15 percent) that job losses will be negligible or that the number of jobs in the city will increase, not decline, over the next four quarters. CONCLUSION It remains difficult to accurately forecast the economy for metro areas and individual cities, 23 Technical details about the model are available in Theodore M. Crone and Michael P. McLaughlin, "A Bayesian VAR Forecasting Model for the Philadelphia Metropolitan Area," Working Paper 99-7, Federal Reserve Bank of Philadelphia. Croushore Theodore M. Crone and MichaelDean P. McLaughlin but the development of time-series models has made the process easier and, in many cases, well worth the effort. The size and diversity of the Philadelphia metropolitan area make it a natural candidate for which to develop a forecasting model. For many local businesses, organizations, and governments, a reasonable forecast for the area’s economy can be helpful to the planning process. The time-series model we have developed provides an additional tool to the economist in charting the course of the Philadelphia economy. The historical errors in the forecast are a reminder, however, that this tool should not be used alone. 23
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