# Why is GDP growth so important that central banks are trying to impose negative interest rate?

BoJ just announced its negative interest rate policy in an effort to drag Japanese out of a deflationary mindset and hoping to shift the demand curve to boost the economy. However, my question is, if people don't want to spend, why bother?

Consider the following simple model of an ideal economy. Suppose this economy has a maxium output is 100 units of bread. Further suppose it is a one-factor economy, i.e. all output is produced by labor. Suppose everyone in the country is considered a labor and there is a total of 100 units of labor in the economy. Suppose the most comfortable level of consumption of bread by people is a total of 10 units. Then my question is why would the cnetral banks impose policies to force people to demand more of it when they do not want to? It only made sense under the following circumstance: since only 10 units of bread is needed, maybe only 10 units of labor is employed to do all the production and the rest of the people is not employed, which means they do not have any money to buy the bread. In this case, it made sense for government to raise demand so the rest of the people can have a job and earn money, and therefore spend money, which further helps the economy. However, in Japan's case, unemployment rate looks fine, around $3.5\%$ as I checked yesterday, partly because Japanese companies are reluctant in cutting employees. Connecting to the simple model I had beforehand, Japan's case is like having all the 100 units of labor employed to produce 10 units of bread, althought they really only needed 10 units of labor. This implies that all the people are getting what they want.

So why is there anything to worry about that the central bank of Japan even start to adopt these agressive monetary policies?

Central banks do not try to increase growth. Instead, they commonly have two targets: 1) to maintain price stability and 2) to minimize the output gap. Let us ignore the first goal for a moment. The minimization of the output gap implies that if output falls short of what the central bank believes to be the natural level of output, then it will try to use economic policies which promote growth.

In your example, 10 units of bread being produced seems to be the natural level of output. If the central bank sees that the economy produces only 9 units of bread, it will try to stimulate the economy with low interest rates. If it observes 11 units being produced, it will raise interest rates to reduce the output. (Note that this is still possible even if firms produce 9 units of bread using 10 (or even 100) units of labor, i.e. if firms are not cutting employees efficiently.). Thus, if the central bank of Japan currently has low interest rates, it believes that current output falls short of the natural level of output, despite low unemployment rates.

You may still ask why the central bank tries to minimize the output gap in the first place. Why should it not just focus on price stability or why not even do something random. It turns out that up to second order approximations, an interest rate policy which minimizes a combination of price volatility and output gap volatility maximizes people's welfare in so-called new-Keynesian models. This was first shown by Woodford and Rotemberg in several articles:

Woodford, Michael. "Inflation stabilization and welfare." B.E. Journal of Macroeconomics, 2, (2002).