<blockquote>
<p>Does money supply growth minus inflation measure economic growth?</p>
</blockquote>
<p>No it does not. Economic growth is defined as the growth of real output, and money supply or inflation do not measure output in an economy.</p>
<blockquote>
<p>Is there some type of accounting equality or economic theory that relates these three quantities?</p>
</blockquote>
<p>There are economic theories that relate these quantities. For example, quantity theory of money states that;</p>
<p><span class="math-container">$$MV= PY$$</span></p>
<p>Where <span class="math-container">$M$</span> is money supply, <span class="math-container">$V$</span> velocity of money, <span class="math-container">$P$</span> price level and <span class="math-container">$Y$</span> real output.</p>
<p>To get to instantaneous growth rates take logs, solving for <span class="math-container">$y$</span> and time derivative we get;</p>
<p><span class="math-container">$$\frac{\dot{M}}{M} + \frac{\dot{V}}{V} - \frac{\dot{P}}{P} = \frac{\dot{Y}}{Y}$$</span></p>
<p>Which say that growth of money supply, plus growth in velocity minus growth in price level (inflation) is equal to real economic growth.</p>
<p>However, this is not an accounting relationship, this is an theoretical relationship.</p>
<blockquote>
<p>One would think that money supply growth that doesn't lead to higher prices must be explained by growth in quantity of goods and services. Obviously, there will be a lag between money supply growth and inflation, but is there a long term relationship that theoretically holds?</p>
</blockquote>
<p>No it doesn't. Depending on various theories this can be explained away with different mechanisms. For example, in dynamic models with uncertainty, people's expectations matter, and sometimes matter more than actual quantities, so it can be explained by people having anchored low inflation expectations. It could also be explained by liquidity trap. There are numerous possible mechanisms that could explain that other than economic growth (you can have a look at models in Romer Advanced Macroeconomics or Woodford Interest and Prices and so on).</p>
<blockquote>
<p>Obviously, there will be a lag between money supply growth and inflation, but is there a long term relationship that theoretically holds?</p>
</blockquote>
<p>There are relationships, as shown before, but that does not mean you can use these relationships for measurement.</p>
<blockquote>
<p>Furthermore, does this relationship have value in econometrics, to double-check whether hedonic adjustments to price level and measurements of money supply were done correctly?</p>
</blockquote>
<p>No, the reason for that is as follows.</p>
<p>These relationships come from theoretical models. All theoretical models have to be falsifiable and need to be checked against empirical data and against each other.</p>
<p>The way how these models are tested is by estimating the relationship from data. For example, to test quantity theory of money you can run some cointegration model where you regress price level (which is considered to be dependent variable by theory, other variables are exogenous according to QTM), on the velocity, money supply and real output. E.g.</p>
<p><span class="math-container">$$p = \beta_0 + \beta_1 v + \beta_2 m + \beta_3 y + e$$</span></p>
<p>And then you can test whether <span class="math-container">$\beta_0=0$</span> while <span class="math-container">$\beta_1 = \beta_2 = \beta_3=1$</span> against alternatives that this does not hold.</p>
<p>Now suppose you actually do find that the QTM is true. Does that mean you can use it to double check measurements of <span class="math-container">$y$</span>? Well no, because in order to find out that QTM is true, you already need to have a measurement of <span class="math-container">$p$</span>, <span class="math-container">$v$</span>, <span class="math-container">$m$</span> and <span class="math-container">$y$</span>. If you find that  <span class="math-container">$\beta_0=0$</span> and <span class="math-container">$\beta_1 = \beta_2 = \beta_3=1$</span>, you found that because of the data generated by possibly flawed methods. So you cannot use it to double check the data, because the beta coefficients are estimated from those data.</p>
<p>Hence, you can only use it check the measure <span class="math-container">$y$</span> if you already a priori believe the model is true. That could be sometimes justified, for example, in physics people often use theoretical models like Newtonian mechanics to estimate some unknowns, but that is because in such field there much more stable relationships. In economics, you could have regime switching when the relationship conditional on some 3rd variable, and even if you would found some stable relationship due to noise in data it is generally difficult to get enough precise parameter estimates that you could use parameters from some general estimation to double check some local measurements.</p>

CC BY-SA 4.0
2024-10-12T16:44:50.877Z
2024-10-12T16:59:20.957Z
2024-10-12T16:59:20.957Z
1muflon1
<p>Does the difference between growth in money supply and growth in the price level tell us something meaningful about economic growth? Is there some type of accounting equality or economic theory that relates these three quantities? One would think that money supply growth that doesn't lead to higher prices must be explained by growth in quantity of goods and services. Obviously, there will be a lag between money supply growth and inflation, but is there a long term relationship that theoretically holds? Furthermore, does this relationship have value in econometrics, to double-check whether hedonic adjustments to price level and measurements of money supply were done correctly?</p>

<econometrics><inflation><economic-growth><money-supply>
Does money supply growth minus inflation measure economic growth?
Betterthan Kwora
# Does money supply growth minus inflation measure economic growth?

(Asked by: username_0 on 2024-10-12)

Does the difference between growth in money supply and growth in the price level tell us something meaningful about economic growth? Is there some type of accounting equality or economic theory that relates these three quantities? One would think that money supply growth that doesn't lead to higher prices must be explained by growth in quantity of goods and services. Obviously, there will be a lag between money supply growth and inflation, but is there a long term relationship that theoretically holds? Furthermore, does this relationship have value in econometrics, to double-check whether hedonic adjustments to price level and measurements of money supply were done correctly?

**Tags:** econometrics, inflation, economic-growth, money-supply

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## 1 answers

### Answer by username_1 on 2024-10-12. Score: 1 | Accepted answer

> Does money supply growth minus inflation measure economic growth?

No it does not. Economic growth is defined as the growth of real output, and money supply or inflation do not measure output in an economy.

> Is there some type of accounting equality or economic theory that relates these three quantities?

There are economic theories that relate these quantities. For example, quantity theory of money states that;

$$MV= PY$$

Where $M$ is money supply, $V$ velocity of money, $P$ price level and $Y$ real output.

To get to instantaneous growth rates take logs, solving for $y$ and time derivative we get;

$$\frac{\dot{M}}{M} + \frac{\dot{V}}{V} - \frac{\dot{P}}{P} = \frac{\dot{Y}}{Y}$$

Which say that growth of money supply, plus growth in velocity minus growth in price level (inflation) is equal to real economic growth.

However, this is not an accounting relationship, this is an theoretical relationship.

> One would think that money supply growth that doesn't lead to higher prices must be explained by growth in quantity of goods and services. Obviously, there will be a lag between money supply growth and inflation, but is there a long term relationship that theoretically holds?

No it doesn't. Depending on various theories this can be explained away with different mechanisms. For example, in dynamic models with uncertainty, people's expectations matter, and sometimes matter more than actual quantities, so it can be explained by people having anchored low inflation expectations. It could also be explained by liquidity trap. There are numerous possible mechanisms that could explain that other than economic growth (you can have a look at models in Romer Advanced Macroeconomics or Woodford Interest and Prices and so on).

> Obviously, there will be a lag between money supply growth and inflation, but is there a long term relationship that theoretically holds?

There are relationships, as shown before, but that does not mean you can use these relationships for measurement.

> Furthermore, does this relationship have value in econometrics, to double-check whether hedonic adjustments to price level and measurements of money supply were done correctly?

No, the reason for that is as follows.

These relationships come from theoretical models. All theoretical models have to be falsifiable and need to be checked against empirical data and against each other.

The way how these models are tested is by estimating the relationship from data. For example, to test quantity theory of money you can run some cointegration model where you regress price level (which is considered to be dependent variable by theory, other variables are exogenous according to QTM), on the velocity, money supply and real output. E.g.

$$p = \beta\_0 + \beta\_1 v + \beta\_2 m + \beta\_3 y + e$$

And then you can test whether $\beta\_0=0$ while $\beta\_1 = \beta\_2 = \beta\_3=1$ against alternatives that this does not hold.

Now suppose you actually do find that the QTM is true. Does that mean you can use it to double check measurements of $y$? Well no, because in order to find out that QTM is true, you already need to have a measurement of $p$, $v$, $m$ and $y$. If you find that $\beta\_0=0$ and $\beta\_1 = \beta\_2 = \beta\_3=1$, you found that because of the data generated by possibly flawed methods. So you cannot use it to double check the data, because the beta coefficients are estimated from those data.

Hence, you can only use it check the measure $y$ if you already a priori believe the model is true. That could be sometimes justified, for example, in physics people often use theoretical models like Newtonian mechanics to estimate some unknowns, but that is because in such field there much more stable relationships. In economics, you could have regime switching when the relationship conditional on some 3rd variable, and even if you would found some stable relationship due to noise in data it is generally difficult to get enough precise parameter estimates that you could use parameters from some general estimation to double check some local measurements.


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