## **Learning Outcomes**

On completing this article, you will be able to explain causal forecasting models, use and interpret learning curves, and discuss experience effects. You will understand model limitations, be able to critically assess forecasting assumptions, and identify key risks in model-based predictions. You should be able to apply these techniques to exam scenarios requiring cost, production, or performance forecasting in a strategic management accounting context.

## **ACCA Advanced Performance Management (APM) Syllabus**

For ACCA Advanced Performance Management (APM), you are required to understand and apply advanced forecasting and modelling techniques, assess their suitability, and evaluate the risks when using them for performance management decision-making. Revision should focus on:

- The use and evaluation of causal (explanatory) models in forecasting future business results
- The application and interpretation of learning curves and experience effects for cost and time prediction
- Model risk: limitations of quantitative forecasting and the dangers of over-reliance or misuse
- Critical appraisal of model assumptions and their fit to business scenarios
- Awareness of how model risk can impact planning, performance evaluation, and decision-making

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. Which of the following best describes a causal forecasting model?
   a) A model that projects future results based solely on past values of the series.
   b) A model that predicts outcomes based on one or more identified independent factors.
   c) A model using manager judgment alone.
   d) A model that ignores relationships between variables.

2. A company’s average labour hours per unit decrease as cumulative output doubles during initial production. What is this effect called?
   a) Random fluctuation
   b) Economies of scale
   c) The learning curve
   d) Price discounting

3. True or false? Learning curve effects apply equally regardless of whether output is made in batches or individually.

4. Briefly explain one key risk of using forecasting models for performance management.

## **Introduction**

Accurate forecasting is a critical element in advanced performance management. Organisations use quantitative techniques to estimate future costs, times, or outcomes. Two important tools are causal models—which link outcomes to specific drivers—and learning curves, which capture how performance improves with repetition. However, all models carry risk, especially if their limitations are overlooked. This article explains these forecasting techniques, their practical application, and highlights model risk.

## **CAUSAL (EXPLANATORY) MODELS**

Causal models are quantitative methods that aim to predict a dependent variable (such as cost, sales or production hours) based on changes in one or more independent variables (e.g. sales volume, labour hours, advertising spend).

> **Key Term: causal model**
> A quantitative method that seeks to explain or forecast an outcome variable by identifying and using one or more influencing factors (independent variables).
>
> **Key Term: dependent variable**
> The outcome or result that is predicted in a forecasting model.
>
> **Key Term: independent variable**
> A variable believed to affect or drive changes in the dependent variable.

One common causal technique is **linear regression**, which fits a straight line through historical data points to quantify the relationship between variables. If a strong correlation exists, managers can use the derived equation to forecast future results—providing the fundamental relationship is stable.

> **Key Term: linear regression**
> A statistical technique that models the linear relationship between a dependent variable and one or more independent variables in the form y = a + bx.

A causal model may be more reliable than a simple extrapolation, as it is based on real business drivers. However, its accuracy depends on the stability and strength of the relationship and the relevance of all included variables. Omitted or poorly chosen variables, changes in the business environment, or limited data can invalidate forecasts.

### **Worked Example 1.1**

A budget analyst finds that advertising spend (x) and monthly sales (y) are strongly correlated. Over the past 6 months, regression analysis produces the equation:  
y = 55,000 + 6.3x, where x is in \$1,000s.

Forecast sales if next month's advertising spend is \$20,000.

> **Answer:**  
> Substitute x = 20:  
> y = 55,000 + (6.3 × 20,000 ÷ 1,000) = 55,000 + 126,000 = \$181,000.

### **Exam Warning**

Do not assume correlation is always causation. A strong statistical relationship does not automatically mean there is a direct cause—there may be hidden variables or coincidental patterns. In exams, be prepared to explain or evaluate this risk.

## **LEARNING CURVES AND EXPERIENCE EFFECTS**

Repetitive tasks often become quicker or cheaper as experience increases. The **learning curve** models this, showing that each time cumulative output doubles, the average time or cost per unit falls by a constant percentage. This is relevant in new product launches or labour-intensive operations.

> **Key Term: learning curve**
> A mathematical model showing that the average time or cost per unit declines by a fixed percentage each time cumulative production doubles, due to increased worker efficiency.

The learning curve formula is commonly written as:  
y = ax^b  
where:

- y = average labour time or cost per unit for x units
- a = time or cost for the first unit
- x = cumulative number of units produced
- b = learning index (log of learning rate ÷ log 2), where the learning rate is expressed as a decimal (e.g. 80% as 0.8).

The **experience effect** is a more general principle that includes efficiencies gained not just by workers, but also through process redesign, scale economies, and technological improvements. It is often observed over a longer period or with wider operational changes.

> **Key Term: experience effect**
> The broader reduction in cost per unit occurring as cumulative output increases, due to accumulated organisational learning, technological improvement, and process changes.

### **Worked Example 1.2**

StarTech launches a new device. The first unit takes 100 hours to make. The learning rate is 80%.  
a = 100;  
b = log 0.8 ÷ log 2 ≈ -0.322.

What is the average time per unit for 4 cumulative units?

> **Answer:**  
> y = 100 × (4)^-0.322  
> 4^-0.322 ≈ 0.8 (since at double output, time per unit is 80%, and at quadruple (i.e. double, then double again), it's 0.8 × 0.8 = 0.64).  
> y = 100 × 0.64 = 64 hours per unit (average for first 4 units).

### **Exam Warning (Learning Curves)**

Learning curves primarily affect direct labour in manual, repetitive processes. Their impact becomes negligible once a "steady state" is reached. Do not apply the curve beyond reasonable output levels or to processes where learning has already stabilised.

## **MODEL RISK: LIMITATIONS AND DANGERS**

Any quantitative forecasting model, however sophisticated, has limitations. Management must be alert to the risks including:

- Over-reliance on modelled relationships that may not hold in future periods
- Changes in technology, process, market, or workforce that alter the relationship between variables
- Extrapolation outside the observed data range (e.g. scaling a learning curve prediction beyond realistic production runs)
- Ignoring factors not included in the model, such as one-off events, competitor actions, or regulatory changes
- Failing to regularly test model assumptions and outcomes against actual results

### **Worked Example 1.3**

A manager uses a regression model based on past three years to forecast sales as a function of economic growth. An unexpected global pandemic occurs, disrupting normal business patterns.

> **Answer:**  
> The forecast will be unreliable because the historical relationship no longer holds. External shocks or regime changes reduce model validity. Management should supplement model output with judgment and contingency analysis.

### **Revision Tip**

When asked to discuss or apply forecasting models, always state the key model assumptions and specific risks if those assumptions change. This will attract credit for professional scepticism.

## **Summary**

Causal models and learning curves are powerful tools for forecasting and planning, especially in settings where workload, cost, or efficiency are influenced by identifiable drivers or by accumulated experience. However, careful attention must be paid to model risk: the limitations and dangers if forecasts are not kept under review or if model assumptions are violated.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain the difference between causal and extrapolative forecasting models
- Apply linear regression to predict future results based on independent variables
- Calculate and interpret learning curve forecasts, including use of learning rates
- Recognise the experience effect for broader cost or time reductions
- Describe the concept of model risk and its consequences for forecasting accuracy
- Critically assess when a forecasting model may become unreliable or misleading
- Apply caution when using model output for decisions, always considering real-world context

## **Key Terms and Concepts**

- causal model
- dependent variable
- independent variable
- linear regression
- learning curve
- experience effect

Forecasting techniques and model risk - Causal models learning curves and experience effects