The Governor of the RBNZ called upon the government to spend more money. Since the interest rate is low, the RB is obviously encouraging spending. The government responded later by an investment package.
Spending will stimulate aggregate demand and buy votes. However, If the government wants to expand demand and increase inflation to meet the inflation target of 2 percent, then the question is how much money it has to spend to achieve that?
I will show here that the government must spend a huge amount of money to achieve a 2 percent inflation.
We know from John Taylor and Valerie Ramey research that the government spending multiplier is small in the U.S. and the Obama fiscal package did not have a significant impact.
Today, I answer a more specific question. Suppose that the Zero Lower Bound constraint is binding so the nominal interest rate is zero. Hence, monetary policy is ineffective. The inflation target is 2 percent. How much the government have to spend in order to restore the inflation target?
To answer this question we have to have a theory for the natural rate of interest. I am working on this now and I thought it would be a good idea if I do the calculations for NZ and share it with you. This is not the place to do all the math, and there is a lot of it in this research, but I will explain and hope that it would be clear.
The natural rate is an unobservable variable, Wicksell (1898. Here is a translation of the main point regarding price change[Boldface and italic is my emphasis].
“… These
two rates of interest, the natural rate and the money rate, which is quoted on
the market, tend of course, to coincide. If the former differs from the latter,
money can no longer be said to be “neutral,” and monetary consequences in the
shape of change in prices are bound to ensue. If the money rate were kept below
the natural rate prices would rise, if above they would fall.”
So that means if r* is the natural rate of interest, and i is the nominal rate, r* - i = inflation.
The story goes like this. Let the economy be made of three optimizing agents, a household, a firm, and a government. The household maximizes a utility function subject to a budget constraint. The utility function has two arguments: a consumption good and leisure. The household makes a decision about saving-consumption, and consumption-leisure. The household holds bonds and stocks, and owns the capital stock, which is rented out to a firm that uses it along with labor to produce output. The household pays taxes on consumption, on investments, on income from capital, and on labor income. All tax revenues, except those used to finance pure public consumption good (e.g., education, defense, etc.) are given back to the household in the form of lump sum transfers from the government. This is a simple model that covers the basics.
The story goes like this. Let the economy be made of three optimizing agents, a household, a firm, and a government. The household maximizes a utility function subject to a budget constraint. The utility function has two arguments: a consumption good and leisure. The household makes a decision about saving-consumption, and consumption-leisure. The household holds bonds and stocks, and owns the capital stock, which is rented out to a firm that uses it along with labor to produce output. The household pays taxes on consumption, on investments, on income from capital, and on labor income. All tax revenues, except those used to finance pure public consumption good (e.g., education, defense, etc.) are given back to the household in the form of lump sum transfers from the government. This is a simple model that covers the basics.
The solution of this simple model results in a parsimonious equation for the natural rate of interest, which could be easily computed (no estimation) using observable raw data. The natural rate r* would be zero when consumption grows at the same rate of leisure and capital grows at the same rate of labor. Once these gaps open up, r* changes. The natural rate depends positively on the growth rate of consumption, negatively on the growth rate of leisure, negatively on the growth rate of the stock of capital, and positively on the growth rate of labor.
Note that there is a great degree of uncertainty about the value of r* because people have different ways of modelling Wicksell's idea. Thus, r* is model-dependent. Therefore, what I have may well be very different from what the RB has in mind, and both of us are different from what Wicksell had in mind.
Here are Some measurements.
Consumption is private consumption plus government consumption less military spending less indirect taxes on consumption. Military spending is trivial in NZ.
Labor is measured by working age population (15-64 years). I assume that the household has 100 hours a week available for work in the market to make money and pay taxes. Therefore, leisure is 100 minus the average weekly hours worked. For example, if a household average weekly hours worked are 30 hours, leisure time would be 70 hours. That is all we need to measure r*, but I am asking about the projection of r*, the future.
Labor is measured by working age population (15-64 years). I assume that the household has 100 hours a week available for work in the market to make money and pay taxes. Therefore, leisure is 100 minus the average weekly hours worked. For example, if a household average weekly hours worked are 30 hours, leisure time would be 70 hours. That is all we need to measure r*, but I am asking about the projection of r*, the future.
I look at the period 2018 to 2024 as the projection horizon because the IMF has this horizon and some data are taken from the IMF - World Economic Outlook. I assume that consumption follows a random walk(Robert Hall).
I assume that military spending and the indirect taxes on consumption are unchanged from 2018 to 2024, which is also reasonable.
Capital stock evolves according to a typical Perpetual Inventory equation, (1-depreciation rate)*last period capital stock plus investment. The stock of capital and the depreciation rate are published by the World Penn Table 9.1. The investment forecasts are reported by the IMF, except that they are nominal percentages of current GDP. Given current GDP, we compute the level and deflate it by the GDP implicit price deflator to obtain real investments.
Working age population is from the OECD population projections. Leisure requires measuring average weekly hours worked. This is hours worked by employed people from the OECD statistics times (multiplied by) employment/working age population ratio. Then we compute 100- average weekly hours worked.
I assume that military spending and the indirect taxes on consumption are unchanged from 2018 to 2024, which is also reasonable.
Capital stock evolves according to a typical Perpetual Inventory equation, (1-depreciation rate)*last period capital stock plus investment. The stock of capital and the depreciation rate are published by the World Penn Table 9.1. The investment forecasts are reported by the IMF, except that they are nominal percentages of current GDP. Given current GDP, we compute the level and deflate it by the GDP implicit price deflator to obtain real investments.
Working age population is from the OECD population projections. Leisure requires measuring average weekly hours worked. This is hours worked by employed people from the OECD statistics times (multiplied by) employment/working age population ratio. Then we compute 100- average weekly hours worked.
I solve the model for the level of government sending needed to make r*=2, which is needed to achieve the 2 percent inflation target when nominal interest rate is zero.
The average growth rate of consumption over the period 2018 - 2019 is projected to be 9 percent. It is high because it includes the increase in government spending that we need to achieve the inflation target. The stock of capital average growth rate is projected to be 7.8 percent, also high. Working age population growth rate average is 0.8, and leisure average growth rate is zero because there is no change in future average weekly hours worked. Hence,r* is 2. To get to this, government spending must increase by 20% on average over the period 2018 t 2024. This is a relatively very high growth rate knowing that the average growth rate between 2000 and 2017 was 3% only. I conclude that it is very costly to use fiscal policy to achieve the inflation target.
The average growth rate of consumption over the period 2018 - 2019 is projected to be 9 percent. It is high because it includes the increase in government spending that we need to achieve the inflation target. The stock of capital average growth rate is projected to be 7.8 percent, also high. Working age population growth rate average is 0.8, and leisure average growth rate is zero because there is no change in future average weekly hours worked. Hence,r* is 2. To get to this, government spending must increase by 20% on average over the period 2018 t 2024. This is a relatively very high growth rate knowing that the average growth rate between 2000 and 2017 was 3% only. I conclude that it is very costly to use fiscal policy to achieve the inflation target.
