Linear, Nonlinear: Characterizing the Trend

Figures 6.5 and 6.6 provide the initial evidence of the trend and cyclical patterns of corporate profits for the complete sample period of 1982–2014:Q2. We also divide profit growth and profit margins into period subsamples so that we can apply statistical tools on the series and characterize its behavior in each sample.

First, we test whether profit growth and profit margins contain a time trend. There are two types of trends—linear and nonlinear. A linear trend indicates a constant growth rate, while a nonlinear growth rate is variable (see Silvia et al., 2014, for more detail). One of the tripwires in financial thinking is that all relationships are linear, and linearity is at play in many spreadsheets when strategists and economists operate their models.

In Table 6.1, we examine the sample period of 1982–2014 and provide the results from an identification process, which results in the finding of no trend in the growth rate of profits, while there is evidence of a nonlinear trend in the NFC ratio. This was foreseen given that we saw a clear cyclical pattern around a trend that itself moves up and down and is more characteristic of a nonlinear, rather than linear, trend in Figure 6.5

Stability Ratio over Different Economic Cycles

In addition, Table 6.1 provides the results of calculations of the mean and standard deviation for each subsample since 1982 as well as for the complete sample period of 1982–2014. We do this to identify whether all subsamples have the same mean and standard deviation. Moreover, we calculate a stability ratio—standard deviation as percent of the mean—for each subsample and for the complete period. The stability ratio helps us to identify how profit growth varies by sample. A higher stability ratio indicates a more volatile series.

We find that U.S. corporate profit growth is mean reverting. A high degree of volatility in profits is evident, however, with a higher standard deviation (12.31 percent) than the mean (7.47 percent). Finally, among the subsamples, the 1990–2014 period is more stable in terms of profit growth (lowest stability ratio) and the subsample since the Great Recession (2007–2014) contains the most volatile profit growth rates. The H-P filter reveals that profit growth was higher than its long-run trend growth during the 2003–2006 period, indicating an above-trend (and unsustainable?) pace of profit growth.

Results in Table 6.1 indicate that the average growth in profits since 1982 is remarkably stable at around 7.47 percent, with a standard deviation of 12.31 and a stability ratio of 164.8. However, once we isolate the 2007–2014 period, there is a clear break in the mean growth rate of profits which would be anticipated given the Great Recession in that period. In this case, the standard deviation is also larger than the mean, and as a result the stability ratio is also high. Contrary to popular commentary, profit growth has not picked up in recent years; rather, it has slowed in the most recent period.

For the NFC ratio, there is also remarkable stability in the mean value as well as in its standard deviation. For this ratio, there does not appear to be a significant break with the past for the 2007–2014 period.

Mean Reversion: Key Benchmark for Pursuing Accurate Analysis

Does the rate of growth in profits tend to revert to a mean value over time? This is a critical issue. First, effective statistical analysis requires that an economic series does not exhibit any trend (nonstationary). Second, if profit growth tends to rise continuously (or fall continuously), there are significant consequences for the overall economy. In a similar way, do profits as a percent of nonfinancial sector output also rise or fall over time?

After applying simple statistical tools, we move to the more sophisticated econometric technique of unit root testing. We apply an Augmented Dickey-Fuller (ADF) unit root test on profit growth. The ADF unit root test was introduced by Dickey and Fuller (1979, 1981) and has the null hypothesis of a unit root, with the alternative that the series is stationary.⁷ If a series contains a unit root, we call it nonstationary; if not, it is stationary. A stationary series fluctuates around a constant long-run mean that implies that the series, profit growth in this case, has a finite variance that does not depend on time; hence, it is mean reverting.

In Table 6.2, the results for a test of mean reversion (stationarity) are presented. For the rate of growth of profits, the series is stationary (mean reverting) over the 1982–2014 period, and therefore can be utilized in statistical analysis. Unfortunately, the series for nonfinancial profits as a percent of nonfinancial output is nonstationary, and therefore must be transformed into a series that would be applicable in further statistical analysis.

A common practice is to utilize the mean of a series for decision making, which is naïve, in our view, as average values may not be constant over time. We provide a more accurate framework to analyze a variable of interest for decision making, that is, whether we should utilize the mean for decision making. In addition, the proposed framework is easy to apply, as an analyst can perform statistical tests using Excel and any standard statistical software. First, plot the series to learn about overall behavior. Then the mean, standard deviation, and stability ratio can be calculated for different business cycles to examine variation in these statistics between business cycles. The H-P filter helps to determine current behavior of the series relative to the long-run trend. The ADF test is a more appropriate method to determine whether the long-run average is practical in decision making. For instance, profit growth is mean reverting in our sample period, implying that any deviations from the 7.5 percent average are temporary in nature, statistically speaking.

Structural Break: History Discontinued

Naturally, there is an interest in knowing whether profit growth or the NFC ratio contained a structural break during the 1982–2014 period. The results in Table 6.2 indicate that there were no structural breaks in either series.⁸

We employ the State-Space approach to identify structural changes in the profits series. The approach identifies the change based on the chi-square test. In the present case, the chi-square test determined the five largest breaks in the profits series using the 0.01 level of significance. The null hypothesis is that the underlying variable does not contain a change and the alternative hypothesis is that there is a change in the behavior of the variable during the specified time period. After we are aware of the existence of a break, the State-Space approach would then determine the break date and the nature of the change (e.g., level shift, additive outlier, or temporary change).

Although we are only interested in level shifts (structural breaks), the other forms of breaks in a series are additive outliers and temporary changes. Identifying a level shift demonstrates that a variable has two or more “structures.” Thus, the data set can be divided into multiple subsamples depending on the number of breaks, and each subsample will have statistically significant differences in the descriptive statistics (e.g., mean and standard deviations). An additive outlier indicates that an observation is just that, an outlier in the data set. A temporary change, however, identifies a fixed duration of change in a variable before the variable returns to the previous level. For example, the GDP growth rate will turn negative during a recession, but then returns to positive territory once the recession ends. Where a temporary change is often the result of the business cycle, a structural shift is often due to a change in policy or a more fundamental economic change.

Summing up, profits, as a return to entrepreneurship and real capital investment, play a crucial role as both incentives and rewards in our economic system. While profits are frequently disparaged by many commentators, profits take many forms and are essential for economic growth. Profitable companies find ways to hire, to contribute to their communities, and to pay taxes. When viewed in the context of the business cycle, profits act as a buffer to fluctuations in economic growth. As a buffer, profits fluctuate significantly over the cycle. Over time, however, profit growth tends to remain stable, indicating that the pace of profit growth corresponds with the pace of economic growth and the offsetting effects of changes in input costs and sales revenues. We also note that pricing margins and productivity tend to vary over the economic cycle. This provides a challenge to business leaders and financial investors in determining the profitability of an enterprise at any stage of the economic cycle.

In the first half of this chapter, we have provided an approach to separating trend from cycle so as to help decision makers in these areas. Volatility in corporate profits can be measured by calculating the mean, standard deviation, and stability ratio of data. All three measures should be calculated over several economic cycles to pin down the volatility of profits and provide perspective on equity market volatility and a sense of risk for equity investors. Profit data is also available for different sectors. Calculating measures of volatility will also provide perspective to investors and business leaders to better characterize the behavior of each sector. Later in this chapter, we will focus on modeling economic profits over the business cycle and the drivers in that model.

The Internal Dynamics of Prices, Labor Costs, and Profit Margins

Dynamic partial adjustment under conditions of imperfect information is also a characteristic of profit margins. As we have witnessed with the current cycle, firms tend to be extremely cautious to hire workers early in the economic recovery, and, as a result, employment gains have been modest. Yet labor costs are often the largest component of the marginal costs of any adjustment by a firm while increasing production. As a result, output increases are accompanied by modest price increases but even more modest marginal cost increases. Therefore, the spread between price and marginal cost widens in the early phase of an economic recovery. As the cycle progresses, unit labor costs tend to rise faster as labor productivity slows and compensation rises. The rise in unit labor costs tends to outpace the rise in output prices and thereby profit margins shrink (Figure 6.7). Interestingly, the consumer price index (CPI) outpaces unit labor costs in the early phase of recoveries (1982–1985, 1992–1997, 2001–2004, and 2010–2011) but then lags in the latter phase of the expansion.

Increases in demand in the short run are not fully met by an increase in output as upward price movements along a supply curve come into play. In the short run, the output supply curve is upward sloping. Meanwhile, while short-run marginal costs do increase with increases in output, the price of outputs will rise relative to input prices.

In contrast to the perfectly competitive economic model, input prices do not respond quickly to variations in demand—labor compensation flexibility is limited. As we have witnessed in the current recovery, employment is not perfectly flexible. We are in an economic world characterized by frictions rather than perfect competition. Firms require specific skills, preventing perfect labor mobility, so firms prefer steady employment levels since decreases in employment engender trained workers to leave or have their skills depreciate. Moreover, varying employment is costly to firms’ reputations as workers prefer stable employment.

Productivity improves in the early phase of an economic recovery while compensation picks up in the latter phase of an economic expansion (Figure 6.8). Although productivity gains are certainly tied to real wages over a longer time frame, within a business cycle the slack in the labor market is a more important driver of wages. As a result, the marginal costs for labor are extremely pro-cyclical. Therefore, profit margins decline as the economic expansion continues. Imperfections in the labor and goods markets play a central role in the cyclical pattern of corporate profits.

Corporate Profits and the Midpoint of the Business Cycle

One of the most basic metrics for business decision makers is corporate profitability. With such an emphasis placed on this one metric, it is important to understand how profits evolve over the business cycle in order to anticipate the future needs of the business. For example, as we reach further into the current business cycle, it is time to contemplate cost-cutting strategies in order to mitigate potential losses as profitability growth begins to slow. Conversely, if profitability growth is anticipated to increase, it would be in a firm’s best interest to take advantage of expansion opportunities sooner in order to build or maintain a competitive advantage over time. In addition to the importance of understanding the economic operating environment, we find that, through analyzing corporate profits and their economic determinates, we can apply these metrics to more precisely identify the midpoints of business cycles. In addition, we explore one of the most commonly employed metrics to gauge business optimism, the debt-to-equity (D-E) ratio, which we find may not be the most applicable metric in determining fluctuations in corporate profits or business cycles.

Productivity and Unit Labor Costs

Now that we have a sense of how corporate profits evolve throughout the business cycle, we turn to metrics that can provide some framework for determining future growth in corporate profits. There are two key metrics that economists exploit as inputs to determine the trend behind corporate profit cycles: labor productivity and unit labor costs. Although capital is also an important component of the business input-output equation, in a large, service-driven economy like the United States, labor productivity and unit labor costs explain most of the variance in corporate profits since 1947.⁹

Labor productivity is a measure of output per hour worked. Unit labor costs refer to the rise in labor compensation per hour relative to the labor’s real output per hour. Monitoring the trends behind these two metrics can provide some predictive power in understanding future trends in corporate profits (Figure 6.9 and Figure 6.10). Productivity tends to decline rapidly as output slows heading into a recession (2006–2007). More telling is the trend in unit labor costs, which tends to accelerate before an economic downturn as the labor market tightens and wages rise (1990, 2000, and 2006). Thus, the higher labor costs in light of falling output places downward pressure on corporate profits. Conversely, during the early recovery phase of an economic expansion, growth in output and profitability outpaces labor compensation and unit labor cost decline. The net result is higher corporate profit growth (1992–1994, 2002, and 2010).

The relationship between corporate profits and productivity and unit labor costs can be utilized to define turning points in the business cycle. As can be borne out during the past three expansions, the point at which productivity growth begins to exceed corporate profit growth has typically signaled the midpoint of a business cycle (1985–1986, 1996–1997) and a danger signal toward the end of the cycle (1989, 2000, 2007). Looking at unit labor costs compared to corporate profits, the midpoint of business cycles since the 1980s has been marked by unit labor costs growing more rapidly while at the same time corporate profits begin to contract (1985–1986, 1998, 2006–2007).

Saving vs. Spending Decisions

Profits are the major source of corporate cash flow and dividend payments, which serve as a return to savers and investors over time. Corporate cash flow roughly equals profits less dividend payments and inventory adjustment (often negative) plus deductions for capital consumption allowances (depreciation). Profits and retained earnings are the driving sources for dividend payments that, in turn, provide the returns to savers and investors via their 401(k)s, pensions, and individual retirement accounts (IRAs). As illustrated in Figure 6.11, there is a clear, positive link between profits and dividends. Two points are worth mentioning. Profits tend to lead dividends, as illustrated in the periods 1988–1991, 1994–2000, 2002–2007, and, most recently, from 2009 to 2012. This leading relationship exists on both the up- and downside of the economic cycle. This link establishes the importance of profits to the returns on financial investments and is a key to middle-income households in achieving a certain standard of living in retirement. Dividends, in turn, are a major, and increasingly sizeable, component of personal income, as illustrated in Figure 6.12, as pensions and other investment vehicles become more widely held among all households.

Profits and Risk

In economics, profits are a signal of financial success and credit quality. As a result, there is a sense that profits are negatively related to risk. As profits improve, there is less risk associated with the provision of credit in any given economic activity. For equity investors, an increase in profits is associated over time with a rise in dividends and, thereby, a reduction in the cost of equity finance. This tends to make profits and equity issuance pro-cyclical. For example, profits have a tendency to lead gains in equity prices, benchmarked here by the Standard & Poor’s (S&P) 500 index (Figure 6.13). In turn, gains in initial public offering (IPO) issuance and merger-and-acquisition activity tend to follow the S&P 500 (Figure 6.14). The cost of equity finance reflects the anticipated dividend yield plus expected nominal growth of dividends. Gains in profit growth provide the basis for dividend growth and lower the cost of equity finance.

Profit growth also tends to lead credit finance activity. Profit growth is again a signaling device for greater opportunity and a reduction in the credit risk associated with bank lending. Gains in profit growth in 1993–1994, 2002–2004, and again in 2012 are associated with growth in bank loans (Figure 6.15). On the bond side, improvement in profit growth tends to be associated with declines in credit spreads (Figure 6.16). Strong profit growth in 1988, 1994–1996, 2004–2006, and 2009–2011 is associated with a decline in the Baa over the 10-year Treasury spread. As a result, profits provide a signal about the viability of repayment from the lender’s point of view. Improvement in profit growth signals an improving view of credit quality and likelihood of repayment down the road by borrowers to lenders.

Profits as Return for Innovation, Entrepreneurship: Signals of Success, Opportunity

Profit growth alters the nonfinancial corporate ratio of capital spending minus internally generated funds (Figure 6.17). The rise in profits leads to gains in internally generated funds that, in turn, can provide greater financial support for investment and encouragement to entrepreneurial spirits—as proxied by improving profit expectations and equity valuations (Figure 6.18).

Finally, profit growth tends to be associated with gains in business investment in plants and equipment (Figure 6.19). Profit growth that is directed to capital spending will tend to maintain the capital-output ratio and, along with that, the hiring of workers. Moreover, the investment undertaken would be anticipated to increase corporate share values and thereby feed back into earnings and dividends and the improvement of household incomes over time.

One Final Note: Cyclical Profits and Stationary Benchmarks

Many investment decisions reflect a judgment on profits as a return on equity, and yet we see that this measure of investment performance has a distinct cyclical character. Given this cyclical character, establishing an absolute level of value attached to any return on equity is likely to be a misleading guide to investing, since both profit growth and profits as a percentage of GDP vary significantly over the economic cycle. Establishing a single value for the return on equity would run counter to the cyclical character of the series. Therefore, an investor would view values above average as too expensive when, in fact, those values would reflect an improving economy. In turn, a slower pace of profit growth, especially when equity valuations look attractive, may reflect a weakening economy and might represent a challenge to current market valuations.

Moreover, the cyclical behavior of profit growth will also vary between economic sectors over the business cycle. Two sectors of the economy could exhibit different returns on equity patterns over the same economic cycle. At the sector level, some economic sectors, such as manufacturing, may be more sensitive to the economic cycle than other sectors, such as health care. This reinforces the view that any absolute benchmark for value in investing might be misleading when dealing with a cyclical series such as the return on equity, that itself varies by the sector under study. There is not a uniform standard for all sectors or for a uniform standard for the stage of the economic cycle.

Some Fundamental Rules of Building a Forecasting Model

We present a model-based forecasting approach to generate reliable forecasts of an economic/financial variable, such as corporate profits.¹⁰ Here are some fundamental rules. First, a preferred model should perform better (produces a smaller forecast error, on average) than a benchmark or competing models in a simulated out-of-sample forecasting experiment. Second, it is necessary to establish a benchmark forecasting approach for comparison, so we adopt an autoregressive of order one, AR(1), method as a standard benchmark. All competing models should perform better than the AR(1) model’s forecasts.

Third, different forecasting approaches should be employed in a modeling process. That is, one possible approach would be a pure statistical method, which does not include any additional variables. One such technique is called an Autoregressive Integrated Moving Averages (ARIMA) model. In the forecasting process, it is always preferable to include as much information (in terms of predictors) as possible, along with a better econometric method to lead to a better forecast. In the Bayesian Vector Autoregressions (BVAR) modeling procedure, we can incorporate more information than a traditional econometric framework. The AR, ARIMA, and BVAR techniques are explained in great detail in Silvia et al. (2014).

The final rule to building a reliable forecasting model is that the model selection criterion should correspond with the forecast objective. For instance, our objective is to forecast the near-term (up to one year ahead) outlook of corporate profits. That implies we are interested in a four-quarter-ahead out-of-sample forecast of corporate profits growth. Therefore, we set a four-quarter-ahead simulated out-of-sample root mean square error (RMSE) as the forecast evaluation criterion for the competing models. The model that produces the smallest four-quarter-out RMSE (i.e., smallest average forecast error) would be the preferred model.

A Recursive Method of Model Selection

To calculate the out-of-sample RMSE, we assume that data is available between t = 1 and t = T for modeling purposes, where T represents the most recent data point—in this case, 2014:Q2. In addition, we are interested in h-step-ahead forecasts, where h = 1, 2, 3, 4, up to four quarters ahead. Assume an integer variable q that varies from 1 to q using one quarter as a unit. For each q, we choose data between t = 1 and t = T – q to build a model and apply it to generate h-step-ahead forecasts. We then calculate the out-of-sample RMSE for each step (from one quarter ahead to four quarters ahead). The magnitude of the RMSE statistic is utilized to compare the out-of-sample performance of each model, and the model with the smallest RMSE is the best model among its competitors.

We estimate all three models using data from the sample period 1982:Q1—2002:Q4 and generate four-quarter-out forecasts. Then, we move one quarter ahead, using data from 1982:Q1 to 2003:Q1, and again produce forecasts for the next four quarters. We employ this recursive method until we reach the final data point that is 1982:Q1–2013:Q2. We then calculate the out-of-sample RMSE for each quarter. In total, we have 42 forecast errors for each quarter ahead forecast. Table 6.3 shows the out-of-sample RMSE for each quarter ahead, up to four quarters, as well as the average RMSE for corporate profit growth rates.

The one-quarter-ahead RMSE for the BVAR model is 4.59 and four-quarter RMSE is 7.44. On average, as well as for each quarter, the BVAR model produces the smallest RMSE compared to the benchmark AR(1) model and the competing ARIMA model. Therefore, the BVAR model is our preferred model to generate forecasts for corporate profits.

As suspected, the RMSE values increase with the forecast horizon for all three models, which indicates forecast uncertainty increases with the forecast horizon. A model selection criterion should be consistent with the forecast objective, since values of the four-quarter-out RMSE are much larger than those of one-quarter-out RMSE. In fact, for the AR and ARIMA models, four-quarter RMSE values are more than twice the values of one-quarter-ahead RMSE. That corresponds with the notion that further-out forecasting contains higher uncertainty. In addition, the out-of-sample RMSE is a practical statistic to build a forecast band (upper and lower limit). If we build a forecast band based on the one-quarter-out RMSE value, then that band will be narrower (and, ideally, more precise) than the one based on the four-quarter-ahead RMSE.

Table 6.4 shows the out-of-sample RMSE for the ratio of nonfinancial corporate profits to output of nonfinancial corporate business (NFC ratio). The BVAR model produces the smallest RMSE for each quarter as well as the average RMSE.

The forecasting performance of the BVAR approach is the best among all three models as it produces the smallest out-of-sample RMSE, on average, or the smallest average forecast error. Therefore, we employ the BVAR approach to forecast corporate profits growth rates (Figure 6.20) and the NFC ratio (Figure 6.21). In addition, in Figures 6.20 and 6.21, we plot the out-of-sample forecast with actual data and in-sample fitted values from all three approaches for corporate profits and NFC ratio.

One observation from the out-of-sample forecast from these three models is that the AR and ARIMA models produce similar forecasts and connote a continuously upward trend in corporate profits. That is one potential issue with both AR and ARIMA approaches, especially during multiperiod-out forecasting. Typically, and in the present case, both AR and ARIMA models linearly extend the series for the out-of-sample period. However, many economic and financial series experience nonlinear growth rates. For instance, profit growth rates are volatile over time, that is, profit growth was 4.7 percent for 2013:Q4 and –4.8 percent for 2014:Q1. The BVAR model, however, shows a bounceback for 2014:Q4 and then slower growth for the next couple of quarters, which is more realistic than the linear upward trend indicated by the AR and ARIMA models. The same observation can be observed in the case of the NFC ratio as the AR/ARIMA models both produce a linear downward trend.