03 March 2011

Forecasts how we like them

by Jaromir Benes

Practitioners know that a good forecast is about a good story in the first place and – contrary to popular belief – not so much about very accurate numbers. And also that good forecasts can only be produced by putting together a large amount of information that has often little to do with a particular model itself while still using that model, and not by pushing a button on a black box. In other words, we usually need to add lots of various types of judgmental adjustments (or tunes, or whatever we call them) to our models and forecasts. In this post, I show a simple taxonomy of judgmental adjustments (JAs) that are available in IRIS.

  • Structural versus reduced-form JAs.

    We can either translate our judgment into changes in the distribution of current or future structural shocks (typically their mean values, but can be also time-varying changes in their std deviations), or impose certain restrictions on the paths or distributions of some of the endogenous variables.

    An example of the first type is, for instance, an expected change in an indirect tax (say VAT), and its effect on the marginal cost of producers. If the tax itself is not part of the model, we need to translate its impact into cost-push shocks in a Phillips curve. An example of the other type is a situation in which a central bank's staff is asked by the governor to produce a scenario in which the policy rate, an otherwise endogenous variable, remains constant for the next couple of quarters.

  • Anticipated versus unanticipated JAs.

    Because almost every contemporary macroeconomic model has some forward-looking expectation element built in (in one way or another), it matters what we assume about the information set: today's outcomes are affected by what agents think of the future. Adjustments that occur in the future can be therefore introduced either as expected by everyone from the very beginning, or as a sequence of surprises.

    If the government announces the tax increase from the above example a year ahead of its actual implementation, it surely is an anticipated event, and should be simulated or forecast as such. On the other hand, the constant rate example may be different. Although it is against the transparency principle of monetary policy, some governors really like to keep the rates flat contrary to inflationary pressures and market expectations under certain circumstances, not communicating the decision much. Such a flat rate track scenario can be then seen as a sequence of unexpected shocks to the behaviour of the central bank.

I now turn to the reduced-form JA techniques, that is to the question how to adjust the paths or distributions of endogenous variables.

  • Endogeneity/exogeneity swap versus conditioning.

    E/e swaps and conditioning are two basic methods that allow us to force an endogenous variable (or a whole lot of them, for that matter) move in a desired direction. Although the first technique is under certain circumstances just a special case of the second one, it is still useful to think of the two separately.

    In an e/e swap, we just do literally that. We temporarily (in a certain number of simulation or forecast periods) exogenise a certain endogenous variable, and endogenise a certain shock. In other words, we re-write the system so that the shock temporarily occurs in the state-space vector on the left-hand side, wile the variable becomes an exogenous thing and moves to right-hand side (yes, this is possible in both unanticipated and anticipated modes). Then we simply specify our assumptions about the exogenised variable – the other endogenous variables together with the endogenised shock are now a function of the assumptions and react to them accordingly. Note that in an e/e swap, the number of data points exogenised must match the number of data points exogenised. For instance, we can have three different variables exogenised in two periods, and three different shocks endogenised in two periods. Or three variables in two periods, and two shocks in three periods (not sure why you would like to do that but it is technically possible).

    Conditioning, on the other hand, works a little bit differently. We want to find such a combination of all model shocks that reproduces the desired paths of some endogenous variables. In general, there will be infinitely many such combinations, simply because the total number of shocks in the model will be usually larger than the number of judgmentally adjusted endogenous variables. So how do we discriminate among all the combinations, and pick one? Statistics to the rescue. If we know the distribution of the shocks (or are able to make an informed choice – impose judgmentally adjusted assumptions – about the distribution) we can simply choose the most likely combination: the one that maximises the likehood function of the shocks. For a normal distribution, it obviously boils down to a minimum square error kind of criterion: The smaller the std deviation of a shock, the less we want to use it in imposing our judgment, and vice versa. If a shock has a zero std deviation it will not move from its mean a bit.

    Examples? We use the constant rate exercise again. The question we ask now is, Why does the governor want to see a flat rate track scenario when the baseline projection suggests, say, an interest rate increase. From a model-based forecast perspective, she can have two basic reasons for that. First, she may buy into the overall forecast of inflation, output, and so on, but may be concerned about, for example, financial stability. In other words, she may want to deviate from the systematic monetary policy reaction function (relating the policy rate to macroeconomic conditions) for other than macroeconomic considerations. In this case, endogenising the policy rate while exogenising a monetary policy shock is an appropriate approach.

    The second reason, though, may be that the governor disagrees to some extent with the baseline staff view on inflation, output, and so on, and does not see room for interest rate increases under current macroeconomic conditions. At the same time, she is not very specific about what exactly should be adjusted in the model. At that point, we could use the conditioning technique to find the most likely combination of shocks other than policy shocks that would reproduce the governor's preferred policy setting. In other words, we would answer the question, what kind of judgmental adjustments to the model forecast would align the staff and the governor's views keeping the policy rule untouched?

  • Hard numbers versus soft numbers.

    This one is easy. When imposing judgment on some of the endogenous variables, we may either want the variables to follow a specific exact path (hard numbers) or add some uncertainty, or play, around such paths (soft numbers). The latter case can be thought of, and also dealt with, as "measurement errors".

    Perhaps the most common judgmental adjustment added to structural models is very short-term forecasts based on econometric or time-series tools. These short-term (or near-term, as they are often termed) forecasts have obviously some errors associated with them. By incorporating some measures of uncertainty in the judgment we effectively allow these short-term forecasts interact with the structural model mechanisms. The result is a sort of weighted average of the two, with the weight on the judgmental adjustments inversely proportional to their std deviations.

The IRIS function jforecast allows you to produce forecasts with almost any combination of the above types of JAs imposed on it.

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