18 Sept 2000

Demand Forecasting

Accurately forecasting future demand is very difficult, but is necessary if firms are to succeed in their current capital investment, product development and introductions, advertising, pricing, and other decisions that have implications for future profit. Thus demand forecasting is central to the planning and control functions of the firm. I will be rather closely following the material presented in the Hirschey and Pappas text in this chapter.

Lecture Outline

• Motivation: Why is Forecasting Useful? What are Some Common Problems?
• Qualitative Analysis
• Trend Analysis
• Cyclical and Seasonal Variation
• Exponential Smoothing Techniques
• Econometric Methods
• Input-Output Analysis
• Judging Forecast Reliability

Lecture Notes

Motivation: Why is Forecasting Useful? What are Some Common Problems?

Forecasting should not be confused with the goal-setting process in firms. Managers (and others) with particular strategic interests (e.g., the agency problem) in the goal-setting process can subvert the forecasting process to serve their interests, destroying the objective, unbiased properties essential to quality forecasting.

Macroeconomic forecasting involves the prediction of economic aggregates such as inflation, unemployment, GDP growth, short-term interest rates, and trade flows. Macro forecasting is very difficult because of the complex interdependencies in the overall economy. For example, how would implementation of a 'flat tax' affect the macroeconomy and real GDP growth? Such a scheme may lower interest rates because the super-rich will have more after-tax income to invest, but may lower the value of the existing housing stock if the mortgage interest deduction is eliminated. To make the scheme revenue-neutral (yield the same level of tax revenue to the Federal government), low-income and some upper-middle income people will have less after-tax income, which will reduce consumption spending, which will reduce aggregate demand and GDP growth.

Microeconomic forecasting involves the prediction of activity of particular firms, branded products, commodities, markets, and industries. Microeconomic forecasting is usually much more reliable than macroeconomic forecasting because the dimensionality of important factors is lower and often can more easily be incorporated into a modeling structure.

There can be a problem of self-fulfilling prophesy in forecasting analysis. If auto industry consensus is that rising consumer debt and a slowing macroeconomy will create sluggish auto sales, and as a consequence automakers reduce production and lay off workers, these actions can be interpreted by others as a leading indicator of a macroeconomic recession, causing them to take actions that future lead us into recession. This is similar to how 'jitters' by mutual fund managers, or sensitive program-trading algorithms, can cause a downward spiral in financial markets.

The term 'garbage in, garbage out' refers to the critical role of data quality in forecasting analysis. Issues include the care taken in the data gathering process, and the number of observations from which the future is projected. Often times preliminary data are released that include estimates which must later be revised when actual observations can replace the estimates. Preliminary data are less valuable than final revisions, but there is great pressure to produce forecasts as far into the future as possible, which leads business economists to rely on preliminary data.

Common forecast techniques that we shall discuss below include:

• Qualitative analysis
• Trend analysis and projection
• Econometric methods
• Input/output analysis

Qualitative Analysis

Survey methods are another qualitative analytical technique in which consumers, managers of various sort, and government agencies are asked for information on their status and future plans. Two common sources of survey data are the US Department of Commerce and the Conference Board (a private industry organization). Barrons weekly market survey of economic indicators is a good source of information on the outcome of recurrent surveys. Table 6.1 in the Hirschey and Pappas text offers an example of reported economic indicators for 27 Jan 1997.

Trend Analysis

Regression analysis of micro time series data can include explanatory (independent) cyclical variables such as season and quarterly real GDP or unemployment. One can simply average out the cycles and derive a simple linear trend line:

Sales, year T = A + BxT,

where A would be the 'y-intercept' value of sales (year 0), and B would be the average growth rate in sales per year. This is a very simple linear projection, and so its reliability will tend to decline the further out one hopes to extend the forecast.

If one believes that growth occurs at a roughly constant percentage rate rather than a roughly constant rate, as assumed in linear estimation, then one could specify an exponential growth function in the underlying trend model:

Sales, year T = [Sales, base year](1+G)^T,

in which it is assumed that year T sales are base year sales compounded at constant annual growth rate G.

Example: Suppose that Dr. John's Medicine Show is a band whose annual sales revenues have risen from $10 million to $30 million over the last 10 years. Calculate the company's growth rate in sales over this period using the constant growth rate model with annual compounding.

$30,000,000 = $10,000,000[1+G]^10

3 = [1+G]^10

ln(3) = 1.0986 = 10[ln(1+G)]

.10986 = ln(1+G)

e^.10986 = 1 + G

1.116 - 1 = G

Constant (annually compounded) annual sales revenue growth rate G = .116 or 11.6%

Now lets use this 11.6% annual growth rate to derive a 5 year forecast of sales revenue:

Annual sales, 5 years hence = $30,000,000[1+.116]^5 = $51,932,853.

To estimate this trend model using ordinary least squares regression techniques, one must perform a logarithmic transformation of the model equation:

log (sales, year T) = log (base year sales) + log (1+G)xT,

which you can see is of the linearized form 'y=b+mx' that allows for traditional linear regression analysis. In this case, regression analysis will yield a constant-term estimate for log (base year sales) = b, and a constant-term estimate for log (1+G) = m. These can be transformed back into a sales forecast as follows:

sales, year T = (antilog b)x[(antilog m)^T].

When T = 0, the model yields us base year sales. To forecast 20 years into the future from the base year, one uses T = 20, which enters exponentially in the equation above.

Another common growth formula is to assume continuous growth based on the growth formula:

sales, year T = (Sales, base year)e^GT,

where e^GT requires the use of the natural log (base e) to transform for linear regression analysis:

ln(sales, year T) = ln (base year sales) + GT

By accounting for the cyclical variables in this way we can uncover the fundamental secular trend -- meaning the fundamental trend in the variable of interest once cyclical factors are accounted for. Once the secular trend (slope) is determined, one can forecast the future value of the variable under analysis by extrapolating the trend and utilizing forecasts of the cyclical factors and their estimated impact on the variable. (see Figure 6.1 in Hirschey and Pappas Text)

Cyclical and Seasonal Variation

Fortunately for forecasters, there are economic indicators that typically lead the general business cycle trend, as well as indicators that are coincident with or lag the aggregate business cycle trend. The Conference Board (formerly tracked in the Survey of Current Business, a monthly publication of the Bureau of Economic Analysis at the Department of Commerce) provides data on the following economic indicators:

• Leading Economic Indicators of Business Cycle Peaks:
  • Average work week for manufacturing workers (+)
  • Average weekly new claims for state unemployment insurance (-)
  • Manufacturers' new orders for consumer goods and materials (+)
  • Vendor performance in input delivery speed (-)
  • Manufacturers' new contracts and orders for capital equipment (+)
  • Index of new building permits for residential housing (+)
  • Index of stock prices (e.g., S&P's 500) (+)
  • M2 money supply (+)
  • Interest Rate Spread (10 year Treas. Bond rate minus Fed Funds rate)
  • Index of consumer expectations (+)
  
  
  
• Coincident Indicators of Business Cycle Peaks:
  • Employee on nonagricultural payrolls
  • Personal income (minus transfer payments)
  • Index of total industrial production
  • Manufacturing and trade sales
  
  
  
• Lagging Indicators of Business Cycle Peaks:
  • Average duration of unemployment
  • Ratio of (real inventories to sales) for manufacturing and trade
  • Change in labor cost per unit of manufacturing output (unit labor cost)
  • Average prime interest rate charged by banks
  • commercial and industrial loans outstanding
  • Ratio of consumer installment credit to personal income
  • Change in prices for consumer services

The Conference Board creates a well-known index of 10 leading economic indicators that is a weighted average of each of the 10 leading economic indicators listed above. As Figure 6.3 in the Hirschey and Pappas text indicates, the index of leading economic indicators has generally done a good job signaling peaks and troughs in the business cycle. Barometric forecasting means using variables such as the index of leading economic indicators to forecast the business cycle. Barometric methods are good at predicting change, but may be poor at predicting the timing of the change, and the magnitude of the change.

Another macro cycle is generated by earth's seasons of the year. Seasonality tends to differ a lot from region to region. For example, cold-weather areas have a much more marked seasonal cycle to housing construction than warm-weather areas. In the Northcoast region and much of the Pacific Northwest, rainy winters traditionally halt logging operations in the field, leading to seasonally unemployed loggers. Thus timber companies hoping to have a roughly continuous stream of lumber production build up an inventory of logs on the deck that can feed the mills over the winter season. The Christmas season has a substantial effect on retail sales of consumer goods, candy, and small appliances. Soft drink sales tend to rise during the hotter summer months. Turkey sales peak during Thanksgiving and Christmas, while hot dog sales peak during summer in general, and the 4th of July, Memorial Day, and Labor day in particular.

Exponential Smoothing Techniques

Companies commonly gather data at point-of-sale using cash register records, such as those from optical bar code scanners, or using sales statistics reported by commission sales agents. The data are assumed to be explained by a relatively small number of cyclical variables. Experience and judgement are often times used to determine the appropriate smoothing technique, perhaps by first printing out the raw data time series.

A simple, one-parameter exponential smoothing equation is appropriate when it is felt that the variable in question has an average level that varies very slowly over time. It is given in recursive form as follows:

S(T) = AxY(T) + (1-A)xS(T-1),

where A is a smoothing parameter typically ranging between 0 and 1, and S is the smoothed value of the observed variable Y in period T. The smaller is A, the less responsive is the series to short-period fluctuations in the observed Y value. The smoothed value S(T) is the forecast of Y into the future.

If it is felt that there is a cyclical fluctuation occurs around an average level that is itself experiencing a linear trend, then a two-parameter (one for the cycle, one for the linear trend) is appropriate. An example would be in established markets in which an average trend is discernable, rather than in new or declining markets. The equation is given by:

Y(T,M) = S(T) + MxTREND(T),

where Y is the observed value of the variable at time period T, M is the forecast period into the future, T is the time period of the observation, S(T) is the smoothed average level at time T, and TREND is the linear secular growth rate per unit of time, estimated through time period T. To compute a two-parameter exponential smoothing function one must derive one equation for the smoothed value S, and one for the linear trend rate TREND.

Three-parameter exponential smoothing functions include a cyclical factor such as for the business cycle, a seasonal cyclical factor, and a linear secular trend facor.

Econometric Methods

Input-Output Analysis

Judging Forecast Reliability

Choosing the best forecast technique requires an understanding of the particular forecasting problem and the characteristics of the available data. Table 6.13 in the Hirschey and Pappas text provides a useful subjective comparison of alternative forecast techniques.