## Dynamic AD-AS model

I am a big fan of the Cowen/Tabarrok Dynamic AD-AS model. This page contains resources for my students who want more information.

Here is a video:

Here is a presentation:

You can download the slides here.

I published a short blog post called “The policymakers view of the great recession – a dynamic AD-AS analysis.”, and an academic article called “A Dynamic AD-AS Analysis of the UK Economy, 2002-2010“.

There are three components to the dynamic AD-AS model.

The first is the **Solow curve**, which shows the growth rate that would exist (i) if prices were perfectly flexible; (ii) given the existing real factors of production. It can be derived from the Solow growth model and since this treats capacity as being independent of inflation, it is depicted as a vertical line. Improvements in research & development; better infrastructure; increased competitiveness; higher quality education and training; labour market flexibility; or natural events such as more conducive weather would all constitute a positive productivity (or “real” or “supply side”) shock, increase the Solow growth rate, and shift the Solow curve outwards.

The second component is the** Aggregate Demand (AD)** curve. This can be defined as combinations of inflation and real growth for a specified rate of total spending, and is far more intuitive than the traditional AD curve. This is because instead of being based on other curves (necessitating an explanation of the Pigou effect, for example) it is instead based on a dynamic version of the equation of exchange:

M+V=P+Y

M denotes the growth rate of the money supply, V denotes velocity growth, P denotes inflation and Y denotes real GDP growth. Since the AD curve simply shows how any given amount of (M+V) can be split between P and Y, it will only shift if there is a change in M (i.e. the money supply) or V (confidence).* In terms of what constitutes a velocity shock, we can switch from looking at the left hand side of the equation (our posited increase in total spending) to the right hand side of the equation (how it is being spent). After all an increase in spending must be spent on something. The composition of total spending is household spending, business spending, and government spending (we’re assuming a closed economy).

AD=C+I+G

Potential sources of increased spending are thus fiscal policy (either changes to government spending or changes to taxes) or wealth effects (where “wealth” means the value we place on the assets we own). An important caveat is that generally speaking changes in the growth rate of V tend to be temporary and thus only changes in M can generate sustained inflation.**

If prices were perfectly flexible, the Solow curve and AD curve would suffice. For example, if the Solow growth rate were 3% and the central bank increased M from 5% to 10% this would lead to an equivalent increase in inflation (from 2% to 7%).

However if prices aren’t perfectly flexible, the dynamic AD-AS model shows how the economy can deviate from potential GDP growth. This requires the third component, the **Short Run Aggregate Supply curve (SRAS)**. The SRAS shows the relationship between P and Y for a given expected inflation rate. As with the traditional AD-AS model, the labour market plays a key role in economic adjustments, and so “sticky” wages (i.e. those that don’t adjust quickly to new conditions) are problematic. For example, if revenues are rising at a faster rate than wages (which constitute a large share of the firms costs), firms will appear to be profitable and will expand their output. Similarly, if prices fall quicker than wages, production will appear to be unprofitable, and they will reduce output. It is due to inflation expectations that we might expect wages to lag behind prices – if inflation is higher than expected output will *rise*. If inflation is lower than expected output will *fall*. This explains the upward sloping shape of the SRAS curve.

Underpinning the SRAS is the concept of the signal extraction problem, which implies that in the short run (i.e. whilst prices are adjusting) there may be a positive relationship between inflation and real growth. (This is the conventional argument that money is only neutral once prices have adjusted. One of the nice things about moving away from a “short run” vs. “long run” distinction is that it’s less likely that students fall into the trap of treating these concepts as passages of time. To say that prices are “sticky” is not really to say that it takes time for them to adjust, but that there are costs involved in doing so).

The reason the SRAS curve is flatter below Y* is because wages are *especially* sticky in a downwards direction. Basic money illusion means that workers tend to be hostile to nominal wage cuts. And the SRAS curve is steeper above Y* because there’s a limit to how fast the economy can grow – it can’t indefinitely exceed the Solow growth rate.*** Given that the SRAS holds for a given rate of inflation expectations, the only thing that can cause it to shift is a change in those inflation expectations. This may appear to underplay the importance of the SRAS curve, but in fact it clarifies the difference between SRAS and the Solow curve. It is tempting to think of the difference in terms of calendar time, for example that a period of bad weather, causing a poor harvest, will primarily affect the SRAS. This is because it is a temporary event that hasn’t altered the underlying production capacity, and if there is nothing to say that bad weather will cause a reduction in supply in the long run, it shouldn’t affect the long run supply curve. However the dynamic AD-AS model makes it a lot clearer to understand why the above reasoning is *incorrect*. An adverse weather event – even a temporary one – is a real shock, and will therefore impact the Solow curve and not the SRAS. The SRAS shows how the price mechanism facilitates but also can disrupt the adjustments in response to either real (Y*) or nominal (AD) shocks. It can be somewhat complicated (and sometimes arbitrary) to distinguish between SRAS and LRAS shocks in the traditional model. The dynamic model treats all real shocks as Solow shocks and is therefore much easier to use.

* It is tempting to treat M as monetary policy and V as fiscal policy but this wouldn’t be correct. Most central banks use interest rates (specifically a short term risk free rate) as their main policy tool. If the “velocity of circulation” refers to the speed at which money turns over, then this is a function of people’s demand to hold money (relative to their demand to hold goods and services). In other words V is the inverse of the demand for money. If the demand for money is high, people hold onto cash, and velocity is therefore low. Hence central banks can either affect the money supply, or try to influence the demand for money by manipulating the price (i.e. interest rates). This actually helps aid a discussion about quantitative easing. Given that interest rates are very low many central banks have reinstated the quantity of money (through the process of quantitative easing) as a policy tool that can be used in addition to interest rates.

** An increase in C in the dynamic model implies an increase in the growth rate of C, relative to I and G. Indeed this demonstrates a weakness in fiscal stimuli because it is impossible for a permanent increase in the growth rate of G. At some point it is likely that an increase in G that leads to a positive AD shock will at some point reverse itself. Indeed this also implies that when a central bank reduces interest rates this will also be self-reversing. As Cowen and Tabarrok point out (p.257) this reinforces the notion that changes in the growth rate of C, I or G do not change the rate of inflation in the long run. Given that shifts in V will tend to be temporary it is.

*** The above could also be considered a “Lucas” curve, since it follows his islands parable and emphasises the labour market. We might also think of it as a “Hayek” curve if we focus more on the capital market. Entrepreneurs confuse a temporary reduction in real interest rates (due to an increase in the money supply) with a permanent one (or at least one consistent with an increase in real savings) and invest in capital-intensive production plans. The Austrian claim is that this will be self-reversing and bring on a recession. We can incorporate this into the analysis here by stressing that particular increases in AD (i.e. when money supply exceeds the demand to hold it) will – as Cowen and Tabarrok argue happens ordinarily – cause a reverse shift in AD later on, but also end up causing a reduction in Y* through a negative shift in the Solow curve. Monetarists would say an increase in AD ultimately leads to an increase in P. Austrians would say that it increases P *and* reduces Y*.