ECON2000 Chap.1 Models, Income and Growth Accounting
Models, Income and Growth Accounting
This chapter separates three layers that are easy to collapse: national income identities, behavioural models and empirical decompositions. It reviews the expenditure identity, levels versus growth rates, logarithmic changes, the Cobb-Douglas production function and per-capita growth accounting.
The central method weights observed capital and labour-efficiency growth, then recovers total factor productivity growth as the residual needed to match observed output growth. That residual is informative but conditional on the production function and measurement choices.
The paid guide works a full numerical decomposition, shows how to check that contributions add back to total growth and explains why an accounting residual is not automatically a causal technology estimate.
What this chapter covers
- 01
National income and expenditure
- 02
Levels, per-capita values and growth
- 03
Log-change approximation
- 04
Cobb-Douglas production
- 05
Weighted factor contributions
- 06
TFP residual and its limits
Worked example · free
Recovering TFP growth
- +1Capital contributes 0.40 times 3.0, or 1.20 percentage points.
- +1Labour efficiency contributes 0.60 times 1.2, or 0.72 points.
- +2TFP growth is 2.80 minus 1.20 minus 0.72, which equals 0.88%.
- +1The components add to 2.80%, so the accounting check passes.
Key terms
- National income identity
- An accounting equality linking output with consumption, investment, government purchases and net exports.
- Log change
- The first difference of a logarithm, used as an approximation to a proportional growth rate.
- Growth accounting
- A decomposition of output growth into weighted input growth and total factor productivity growth.
- TFP residual
- The output-growth component left after measured factor contributions are removed under the chosen production model.
- Capital share
- The production weight applied to capital growth in a Cobb-Douglas growth-accounting exercise.
Models, Income and Growth Accounting FAQ
Why use logarithms for growth rates?
Log differences provide a convenient approximation to percentage growth, especially for small changes, and turn multiplicative production relationships into additive decompositions. They also make proportional changes easier to compare across series with very different levels. For large movements, calculate the exact percentage change as a check.
Is the TFP residual the same as technology?
Not exactly. It is the portion of measured output growth not explained by the included weighted inputs. Technology can contribute, but institutions, allocation, utilisation, omitted inputs and measurement error can also enter. Interpret it as a model-dependent productivity remainder unless stronger evidence identifies a cause.
What is the difference between an identity and a model?
An identity holds because of definitions and accounting construction, such as expenditure components adding to output. A model adds behavioural claims about how variables respond, such as investment falling with the real interest rate. Evidence can challenge behavioural magnitudes while the identity still balances.
How should a numerical decomposition be checked?
Keep all rates in consistent percentage-point units, apply weights once, and add the measured contributions plus the recovered residual. The total must equal observed output growth. A failed add-back usually reveals a sign error, an incorrectly converted percent or weights that do not sum correctly.
Exam move
Create a three-column revision sheet headed identity, behaviour and accounting decomposition. Place each equation in the right column and write what kind of claim it supports. Practise one growth-accounting problem with positive TFP growth, one with a negative residual and one where the input contributions already explain nearly all output growth.
After every calculation, add the components back to observed growth and write a restrained interpretation that names the production-function assumption. For graph questions, label whether each axis is a level, log level or growth rate before reading the slope. That small discipline prevents a fast-growing low-income economy from being confused with a high-income slow-growing one.
Build a small spreadsheet with columns for output, population, capital and labour efficiency. Create per-capita series before taking growth rates, then calculate each weighted contribution on its own line. Change the capital share and observe how the residual responds; this makes the maintained factor-weight assumption visible.
Next, compare exact percentage growth with log changes for small and large movements, noting when the approximation becomes less close. On paper, practise explaining why Y = C + I + G + NX is an identity while a consumption function is behavioural. For a written prompt, organise the answer as measurement, calculation, interpretation and limitation. Measurement names the variables and period.
Calculation prints weights and contributions. Interpretation states how much observed growth is assigned to each component. Limitation explains that the residual can contain technology, institutions, allocation, utilisation and error. Finish by checking that periods and units match across every input. An annual output rate combined with a quarterly capital rate can produce neat arithmetic but no valid decomposition.
Before the final, reproduce the national-income identity and the per-capita growth equation on blank paper, define every symbol and state which terms are observed versus recovered. Use a calculator only after estimating the sign and approximate magnitude of each contribution. Compare a raw level plot with a log plot and describe what each reveals about proportional growth.
Then write a short answer that distinguishes accounting balance, model assumption, empirical result and causal uncertainty.
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