 # Intertemporal consistency

I struggle to understand this concept and it seems to be an important one for the capital markets expectation readings.

Can someone explain it in an easily understandable way?

Back to the Past (Level 1)
In inferential statistics, an estimator is consistent if the probability of estimates close to the value of the population parameter increases as sample size increases (i.e. the standard error becomes lower a.k.a higher likelihood of being close to the population).

Using the standard error of the sampling mean as an example (Level 1 stuff), which is:

\frac{\sigma}{\sqrt n}

The larger the sample size, the lower the standard error of the sampling mean.

Back to Present (Level 3)
Intertemporal consistency means consistency across time horizons, with the statistic being the forecast on capital market expectations.

Having intertemporal consistency means that as we extend the time horizon (something like increasing sample size), our projections will converge to the long-range forecast (as the forecast error decreases).

Hope this explanation helps.

What type of projections are we talking about? Is it as simple as if we predict a 2% inflation rate for our 1y forecast, we should use a 2% inflation rate for our 10y forecast?

Or could you please elaborate with an example of a projection that are being extended into a longer time forecast.

Thanks for the help - much appreciated.

A typical example is the expected risk and return of the asset classes the investor will invest into.

Helpful, thanks. In other words, the risk and return expectations used for an asset class should be the same for both our short term and long term forecasts.

It should not be the same. The right way of describing it is that the method of forecasting should be such that the projections converges to the long-term forecast as we increase the horizon (going from short term to long term).

For example, we can estimate equity market return based on:

1. % change in nominal GDP
2. % change in share of profits in the economy, and
3. % change in P/E ratio.

In the short-term forecasts, the equity market return can be affected by items (1), (2), and (3).

BUT

In the long-term forecasts, the equity market return can only be affected by item (1). Items (2) and (3) will converge towards zero.

See Book 2, page 184 for the formula.

Very helpful, makes sense. Thanks a lot!

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Still a bit confused myself. Would appreciate any other thoughts regarding this.

Suppose we have this simple scenario:

I want to invest for one year. I expect the economy to expand over that one year time period. So, I invest in stocks because valuations will likely be tied to the GDP growth. And if that occurs, then there probably won’t be much of an appetite for risk-free bonds. So my expectation would be for stocks to outperform bonds.

Where does internal and inter-temporal consistency apply in this situation?