**What’s it:** Total factor productivity quantifies the share of economic growth not explained by increases in labor and capital when both are used together in the production process. We also often refer to it as the residual Solow model or multifactor productivity.

There are various explaining factors for total factor productivity. One of them is technological advancement. Advances in technology make workers more productive. For example, they can learn from the internet to acquire new skills or find ways to do their jobs faster.

Advances in technology are also responsible for increasing business output significantly. With more sophisticated machines, manufacturers can produce the same output but faster than before. Or, they can also produce more output using the same quantity of input because machines are more efficient.

## Calculating total factor productivity

Take the Solow growth model. The aggregate economic output formula is as follows:

**Y = A K ^{α} L^{β}**… Equation 1

Where

- Y = Aggregate output
- L = Workers
- K = Capital
- A = Total factor productivity (TFP)
- α = Output elasticity of capital (α <1)
- β = Output elasticity of labor (β <1) and α + β = 1

We can rewrite equation 1 above as output per worker. The results are as follows:

**Y/L = A (K/L) ^{α}**… Equation 2

Where

- Y/L = Output per worker or worker productivity
- K/L = Capital per worker

From the first and second equations, we can take three critical points:

**First**, labor and capital face diminishing marginal returns (you can see, α and β are less than 1). Thus, in the long run, labor and capital contribution to output is at a decreasing rate.

**Second**, investing in capital deepening – which increases the capital-power ratio – is not the solution to sustaining long-term growth. The capital-power ratio has a decreasing rate of return. Thus, when it is high (K/L), the addition of capital investment only contributes less significantly than when it was low.

**Third**, the only way to sustain economic growth in the long run (potential GDP) is to increase total factor productivity (A) through technology.

Technological advances will result in an outward shift in the production function. In the production possibilities curve, it is reflected by shifts in the curved lines to points outside the curve. More advanced technology allows the economy to produce greater output even though labor and capital are fixed.

### Total factor productivity growth

Furthermore, from the previous Equation 1, we can also rewrite it to measure aggregate output growth. The results are as follows:

**∆Y/Y = α*∆K/K + β*∆L/L + ∆A/A**… Equation 3

Where:

- ∆Y/Y = Aggregate output growth rate
- ∆K/K = The rate of capital growth
- ∆L/L = Growth rate of labor
- ∆A/A = Total factor productivity growth

Equation 3 above shows you a regression model. ∆K/K and ∆L/L represent the independent variables (predictors), where α and β show you the impact of growth in capital and labor on aggregate output growth. Meanwhile, ∆A/A represents the residuals of the model.

Thus, to obtain total factor productivity growth (∆A/A), you must have data for ∆K/K, ∆L/L, and ∆Y/Y. Then, you regress ∆K/K and ∆L/L against ∆Y/Y. You will get the error or residual from the regression, and that’s ∆A/A.

Some agencies also provide data. For example, you can find it on the Federal Reserve Bank of St. Louis website for the United States’ private business sector. You can also get it on the OECD website, which covers several countries other than the United States.

## Importance of total factor productivity

**The source of growth.** As I explained earlier, total factor productivity is the key to long-run economic growth because labor and capital have a decreasing marginal return. It becomes even more critical when the capital per worker ratio is high, as in developed countries.

**The gap between developed and developing countries.** Now ignore total factor productivity. Since the capital per worker ratio has a decreasing return rate, the deepening effect of investment has a more significant impact when the ratio is low. In this case, it represents a developing country. They should enjoy high growth, as well as their GDP per capita.

On the other hand, developed countries – with high capital per worker ratio – benefit less from capital deepening. As a result, their economic growth and GDP per capita are also low.

In the long run, because GDP per capita in developing countries grows higher than GDP per capita in developed countries, the two will converge at the same point (convergent or often called the catch-up effect). In the end, developing countries will enjoy the same prosperity as developed countries.

However, you can see, the gap between the two is still huge. The key to the answer is total factor productivity. That explains why the two don’t converge. GDP per capita in developed countries is still much higher than GDP per capita in developing countries.

While developing countries still rely on agriculture and manufacturing, developed countries have relied on services, especially in technology, to spur growth. The emergence of giant companies like Microsoft and Google is an example.

## Factors affecting total factor productivity

Many factors influence total factor productivity. The critical point is, they affect the productivity of existing labor and capital. Apart from technological innovation, other determining factors are:

- Research and development
- Management practice
- Production technique
- General knowledge
- Network effect
- Economies of scale
- Increased competition
- Reallocation of resources

And economists often summarize those factors as technological factors.