A framework for applied macroeconomic forecasting (part 1)

Most economists who have worked as macro economists for governments, central bank or commercial banks will sooner or later be engaged in doing macroeconomic forecasting.

Oddly enough most economists are not really educated to do forecasting. What we learn in university is mostly theoretical. We learn about different economic schools and models (Keynesian, New Keynesian, RBC, monetarist etc). And maybe we learn about econometric methods to estimate different “models”, but that is very far from the daily realities of real-world macroeconomics forecasters.

The fact is that the challenges that real-world macroeconomic forecasters are facing are of a completely different type than the theoretical models that we learn in university.

Just think about the present discussion about how the weather has influenced US macroeconomic data recently. Or think about the discussion that we constantly have about the quality of Chinese macroeconomic data – can we really trust the data produced by a communist government or any government? Think about the problems of seasonal adjustments. Are seasonal patterns really constant over time? And we could go on about such technical issues. Something we never heard about in the university.

This are the kind of challenges those of us who do macroeconomic forecasting deal with on a daily basis. It is not very sexy, but it is a very large part of real-world macroeconomic forecasting.

I believe that these unsexy challenges actually are among the main reasons why so many macroeconomic forecasters become quite ignorant about theoretical issues and why they tend to practise a quite vulgar form of “Keynesianism” – or what I have earlier termed national accounting economics.

That basically means that most real-world forecasters start out with the familiar national account identity – Y=C+I+G+X-M. And then they simply make “sub-forecasts” for private consumption growth (C), investment growth (I), public expenditures (G), exports (X) and imports (M) and then add up all these elements to a forecast for real GDP growth (Y). This would often (always!) include some fiddling with the data so to ensure a nice “profile” for the forecast path for real GDP as most forecasters prefer that the real GDP growth returns to trend growth within 2 or 3 years.

What is notable about this form of forecasting is that it ignores a lot of factors. Most important in my view is that the monetary policy rule/regime is totally ignored. To the extent any monetary policy is thought about it is mostly considerations about the impact of interest rates on private consumption and investments. Second, supply shocks are mostly reduced to a quasi-demand side story in the sense that for example an increase in the oil price is something, which reduces real disposable incomes rather than something, which is increasing production costs. There is no direct relationship between the production and demand side of the economy and inflation and inflation forecasts are mostly made in other “parallel” models, that are not directly related to the rest of the modeling.

An alternative approach – applied AS/AD forecasting and modelling

I am no saint and I have also for years used a similar approach when I have been involved in macroeconomic forecasting – both working for government and in the financial sector. In many ways I have for years lived in a parallel universe or rather one universe where I was thinking in a certain way (as a Market Monetarist) and another universe where I was doing macroeconomic forecasting (national accounting style).

I had the same problem as everybody else – I had to overcome a lot of practical problems. That led me to continue to do forecasting in a way I fundamentally found unsatisfactory. I am still not fully satisfied with the way I do macroeconomic forecasting in my day-job, but I think I am a lot closer to getting it right now than before. It has been a nearly 20 years journey.

In this post – and more to come – I will try to sketch an alternative approach to do real-world macroeconomic forecasting. Not because I necessarily think it will produce more accurate forecasts (we can’t forecast shocks!), but because I think the approach I will outline here will make a lot more sense economically speaking.

My starting point is a simple AS/AD framework in the spirit of Cowen and Tabarrak. We start with a familiar graph.

ASAD

In the AS/AD framework we basically have only two macroeconomic variables – inflation (p) and real GDP (y). Of course from this we also get nominal GDP (n=p+y).

I think we from this can estimate fairly simple AS and AD curves that will be easy and simple to use in real-world macroeconomic forecasting and analysis.

A four-equation model

In later blog posts I will get into more details with my overall framework, but for now we will start out with a four-equation model.

We start with the AS curve. The important thing is to differentiate between when we “move along” the AS curve and when the AS curve shifts left or right.

It follows from economic theory that the (short-term) AS curve is upward sloping. This means that there is a positive correlation between on the one hand real GDP growth (y) and inflation (p) and therefore also nominal GDP growth. We can use this insight to write a simple equation for our AS curve:

(1) y = a0 + a1*n + SS

Where y is for example the quarterly real GDP growth rate, while n is nominal GDP growth. a0 and a1 are coefficients. SS is a shift variable that will capture exogenous supply shocks (shifts in the AS curve). In a slightly more advanced model we could also include the (real) output gap in model – so real GDP growth would be higher as long as the output gap is negative. That would mean that the output gap would gradually close even if nominal GDP (aggregate demand did not change). That would account for the long-run AS being vertical.

And variations of that equation are easy to estimate and my experience is that there is a very good fit to such models for most countries I have tried to apply this type of model to. The clever reader will realise that this is basically a simple form of a Phillips curve.

In a later post I will return to discuss the AS curve in more detail and I will particularly discuss how to use financial market information to forecast the impact of supply shocks on real GDP growth and to discuss different forms of supply shocks.

In the spirit of Cowen and Tabarrak our AD curve is basically the equation of exchange (in growth rates):

(2) n = m + v

Where n is nominal GDP growth, m is the money supply (for example M2) growth rate, while v is the growth rate of money-velocity.

We can think of different ways to model both m and v. That is our two next equations.

Equation (3) is an equation for the central bank’s policy rule. We assume that the central bank directly controls the money supply. This is of course not necessarily a realistic assumption and in an alternative formulation we could write (2) as n=k*b*v, where k is the money multiplier and b is the money base. However, for simplicity we will start with the simple version here.

We can obviously think of all kind of policy rules – inflation targeting, nominal GDP targeting or some kind of exchange rate targeting. This is the general form of our policy rule:

(3) m = f(TARGETS) + PS

m is the policy instrument, the money supply, while TARGETS is whatever policy target(s) we can think of and PS is discretionary changes in monetary policy (policy shocks).

Whether we want to estimate or “simulate” (3) will depend on whether or not there has been any changes (structural breaks) in the overall monetary policy regime or not.

Finally we have an equation for the development in money-velocity (v). This is basically a model for the development in money demand. There is a huge literature on this, but overall I think it is useful to apply a fairly eclectic approach to modelling v:

(4) v=f(V0, V1,…, VN) + VS

Where velocity is determined as a function of a number of variables – for example the yield curve or the exchange rate etc. VS is a velocity shock, which we should think of as unpredictable shocks to money-velocity – policy induced or not.

Overall, I think this framework can easily be applied to most economies in the world and a major advantage is that we can get down to the basics by just looking at three macroeconomic variables: (the growth rates of) Real GDP, Nominal GDP (or the GDP deflator) and the money supply.

Based on these variables and equations we can basically decompose the actual development in any economy between on the one hand supply shocks and on the other hand demand shocks (monetary policy shocks and velocity shocks).

How will we do forecasting with this model?

Operationally we could think of a set-up where we keep (the growth of) money-velocity (v) constant in the forecasting period. Furthermore, we would assume that our three shocks (supply, monetary policy and velocity) are zero as we by definition cannot forecast shocks. However, we could also think of these shocks as “forecastable” in the very short-term (within a quarter). I will in later posts return to this topic – how to use financial variables as an approximation of the expected impact of shocks to aggregate demand and supply.

If we want to apply our model to actual forecasting we first see that the monetary policy rule is the rule that “closes” the model. The central bank is assumed to set the money supply growth rate to hit a given monetary policy target – for example a NGDP target.

So if we for example have a given money supply growth rate at our starting point and NGDP growth is at a rate slower than the targeted growth rate and we are assuming that the central bank will try to hit the target NGDP growth rate in 2 or 3 years then we get a “growth path” for the money supply. We could think of this growth being implemented by the central bank or by the market (for example through a Scott Sumner style NGDP futures market).

This will give us a forecast for the growth rateof  not only the money supply, but also for real GDP and inflation (the GDP deflator). Obviously we can build more or less sophisticated models for private consumption, investments, unemployment, the trade balance etc. to expand the model, but the overall framework would be the same.

What is important is that we with this four-equation set-up can both get an understanding of what shocks are driving the business cycle in real-time and we can at the same time use the model to forecast RGDP growth and inflation (and obviously NGDP growth). And most important – this will not only be empirically useful, but it will also – and this is much more important – allow us to make economically meaningful forecasts.

In the coming weeks I will try to go more into detail with a discussion of the individual equations in the model – including how we can use financial market data to improve macroeconomic forecasting.

And then hopefully at a point I will be able to present a model for a “random” country to show that this set-up actually has a practical application.

PS Returning to the US weather and the macroeconomic development in the US I believe that the framework presented above should make it fairly easy to decompose present US growth to better understand whether we are now seeing a negative demand shock (monetary tightening) or just a short-term negative supply shock (bad weather).

 

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6 Comments

  1. Lars,
    It’s a good start but two things need to be addressed or the model won’t work: money demand and the transmission of monetary policy.

    I insist the money multiplier cannot be part of any useful model. There needs to be a more honest look inside the “black box.” I suggest this is where the banking sector comes in and using net interest margins, loan demand, lending standards and liquidity to replace reserve ratios. The exchange rates impact on net exports could play here too.

    The money demand function needs to be disaggregated. People demand money in different forms for different reasons. It makes a difference if people are demanding currency, checkable deposits, or time deposits.

    Reply
  2. Integral

     /  March 26, 2014

    Lars,

    I use a similar setup to do qualitative forecasting exercises in my Principles of Macro course. I’m interested to see how you take it to a more quantitative direction.

    Reply
  3. I have an improvement on the equation of exchange, motivated here:

    http://informationtransfereconomics.blogspot.com/2014/03/how-money-transfers-information.html

    that you’re welcome to use … I’ve been able to extract some quantitative forecasting results from it (we’ll see how accurate they are):

    http://informationtransfereconomics.blogspot.com/2014/03/macroeconomic-predictions-for-2016.html

    Reply
  4. What about things like input output models like those developed by Leontief? I’ve never seen any analysis on how well they perform in the real world but they seem both theoretically sound and highly applicable.

    Reply
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  2. A framework for applied macroeconomic forecasting (part 2) | The Market Monetarist

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