by Michael Hatcher
A major challenge for macroeconomics is to model the linkages between financial markets and the economy. These ‘financial linkages’ are a key transmission mechanism through which financial markets can exacerbate cycles in the real economy. The most prominent recent example is, of course, the Global Financial Crisis (GFC).
In our Rebuilding Macroeconomics project, we focus on the link between the stock market and macroeconomic stability. Most existing models do a fine job of matching Rama Cont’s stylized facts of market behaviour. Our challenge is to include macroeconomic effects with an aim of providing some guidance for monetary and macro-prudential policy. This blog is an update of our work-in-progress.
We begin with a simple model of the stock market which has two types of investors: fundamentalists and chartists. This can be considered as an application of the canonical ‘noisy trader’ model. Each investor type chooses holdings of a risky stock (in fixed supply) and a riskless bond (in flexible supply) to maximize expected next period wealth. Demand for shares is based on investors’ subjective expectations of variable stock prices and dividends. However, re-weighting of a portfolio of shares is subject to a transaction cost.
Fundamentalists believe that stock prices will revert to their fundamental value next period; however, they only trade on this belief if the current price differential exceeds a critical value. They buy when the market price is well below the fundamental value and sell when price is well above the fundamental value. Chartists, by contrast, use the past trend in stock prices as a basis for forecasting future prices. They buy when the past trend is positive and sell when the trend turns negative.
There is good evidence that real-world investors behave along these lines. Following Brock and Hommes (1998), the fractions of fundamentalist and chartist investors are determined by the past profits of each trading strategy.
Figure 1 shows a simple example. The stock price (blue) is initially set equal to the fundamental value (red). Four unanticipated positive ‘news shocks’ occur in the form of rising dividends that last for 4 periods. The news shocks raise the fundamental value of the stock for four periods then remains unchanged (left panel). The stock price rapidly increases as chartists expect the positive trend to continue and buy additional shares, pushing the price above fundamental value.
Fig 1 – Stock price and volume after 4 positive dividend shocks
The gap between the actual stock price and its fundamental price may be interpreted as a ‘bubble’. The bubble collapses because fundamentalists sell shares (expecting prices to return to their fundamental value) and chartists eventually become less bullish because they place most weight on recent price changes, which are less impressive than the initial price increases backed by strong fundamentals. Trading volume is high throughout the bubble – a phenomenon again noted in the literature.
This simple model does a good job in matching some stylized facts of stock market returns, including weak predictability of stock market returns and volatility clustering. It is worth noting that stock market returns in the model are largely unpredictable even if the dividend process – the only exogenous shock – is calibrated to be somewhat predictable (i.e. persistent).
Next step is to embed our simple stock market model into a macro model. This is a three-equation model of aggregate demand (IS curve), inflation determination (Phillips curve) and the stock market described above. Following Nistico (2012), we assume that an increase in stock prices raises consumption and aggregate demand through a wealth channel. Demand is a negative function of the nominal interest rate set by the central bank. Attempts to stabilize inflation and output growth could take the form of macro-prudential measures aimed at stock market or directly using interest rates. We consider both cases below.
As a macro-prudential policy we consider a limit on the short-selling of shares. Short-sellers borrow and sell shares with the hope of buying them back more cheaply at a later date. The SEC has short-selling limits in the US and the UK also introduced limits during the GFC. In our model, such limits are a restriction on the size of negative positions. It is not obvious whether this will stabilize or exacerbate market volatility.
Figure 3 introduces a short-sales limit in the ‘bubble’ example above. Fundamentalists are prevented from selling as many shares as they would like around the peak. As a result, the bubble peaks at a higher level than before, as well as undershooting the fundamental value on the way back down (left panel). The increased fluctuations in stock prices imply greater macroeconomic volatility in output and inflation via the wealth channel (right panel).
Fig 2: Short-selling limit and the economy
We now turn to monetary policy. Rather than asking whether monetary policy should respond directly to stock prices, we consider a more standard interest rate rule that raises interest rates in response to increases in inflation and output growth. Our interest is in whether the ‘wealth channel’ between the stock market and the real economy justifies a more aggressive response to inflation and output than a standard Taylor rule.
The results are shown in Figure 4. We see that an aggressive response to inflation and output growth lowers the volatility of both inflation and output relative to a standard Taylor rule. Whereas the aggressive policy rule permits less of an increase in output in response to the stock market boom, it also avoids a lengthy period of low output after the bubble collapses, and stabilizes inflation at the same time. An important question is whether these results would survive in a richer macroeconomic model with additional sources of volatility.
Fig 3: Aggressive monetary policy versus the Taylor rule
The model presented so far is obviously highly stylized. In the remainder of the project we plan to extend the model in two directions. First, we will model the stock market as a network of agents. An interesting question is which network structures will produce greater stock market volatility and hence imply greater spill-overs to the macroeconomy. The interactions between agents may have important implications for macro-prudential policy.
Second, we plan to extend the macroeconomic model with a housing sector. A question we hope to answer is whether booms built on rising house prices call for a different policy response to those built on rising stock prices. Empirical evidence hints that this may be the case because house price busts are associated with larger reductions in consumption than equity price busts, as well as with larger declines in GDP growth.