<blockquote>
<p>What was the annual real growth rate in the US from 2010 to 2015?</p>
</blockquote>
<p>I presume you mean growth rate of output. You can see the quarterly real growth rate in the US from 2010 to 2015 below (source Fred) with average quarterly growth rate being 0.6%:</p>
<p><a href="https://i.sstatic.net/ezwtL.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ezwtL.png" alt="enter image description here" /></a></p>
<blockquote>
<p>According to the Quantity Equation the US therefore had a yearly real growth of more than 13% in this period?</p>
</blockquote>
<p>No, that is definitely not implied by the quantitative theory of money (QTM) - I assume that is what you mean by the 'quantity equation'. First, you are using wrong data for that (at least for money supply). Second you are not using all data required for  QTM is given by:</p>
<p><span class="math-container">$$MV=PY$$</span></p>
<p>With, <span class="math-container">$M$</span> being total money supply (usually proxied by <span class="math-container">$M2$</span>), <span class="math-container">$V$</span> velocity of money, <span class="math-container">$P$</span> price level, <span class="math-container">$Y$</span> real output. Taking logs and differentiating the expression wrt time 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>The above says that the growth rate in <span class="math-container">$M$</span> + growth rate in <span class="math-container">$V$</span> should be equal to growth rate in <span class="math-container">$P$</span> plus growth rate in <span class="math-container">$Y$</span>.</p>
<p>Now the <em>total growth rate</em> of <span class="math-container">$Y$</span>  between 2010 and 2015 of <span class="math-container">$Y$</span> was <span class="math-container">$\approx 11.7 \%$</span> (see <a href="https://fred.stlouisfed.org/series/GDPC1#0" rel="nofollow noreferrer">Fred data</a>), the total growth rate of <span class="math-container">$P$</span> in between 2010 and 2015 was <span class="math-container">$\approx 9.4 \%$</span> (see <a href="https://fred.stlouisfed.org/series/GDPC1" rel="nofollow noreferrer">Fred data</a>), next the total growth rate of <span class="math-container">$M$</span>, in the same time period,  measured by <span class="math-container">$M2$</span> was approximately <span class="math-container">$39.6 \%$</span> (see <a href="https://fred.stlouisfed.org/series/WM2NS" rel="nofollow noreferrer">Fred data</a>), lastly the total growth in velocity <span class="math-container">$V$</span>  over the same period was approximately <span class="math-container">$-14.9 \%$</span> (again see <a href="https://fred.stlouisfed.org/series/M2V" rel="nofollow noreferrer">Fred data</a>).</p>
<p>Consequently, plugin these into QTM we would get that:</p>
<p><span class="math-container">$$39.5 \%+ (-14.3\%) - 9.4\% =    \frac{\dot{Y}}{Y} $$</span></p>
<p>Hence QTM would predict that the growth rate of <span class="math-container">$Y$</span> would be:</p>
<p><span class="math-container">$$ 15.8 \% \approx    \frac{\dot{Y}}{Y} $$</span></p>
<p>This is still off by approximately <span class="math-container">$4.1\%$</span> given that the actual real GDP growth was <span class="math-container">$\approx 11.7\%$</span>,   however note QTM is extremely simplistic model of money market equilibrium.</p>
<p>More realistic description of money market equilibrium would be given by (see Woodford Interest &amp; Prices pp 295):</p>
<p><span class="math-container">$$M^s_t/P_t = L(Y_t,\Delta_t: \xi)$$</span></p>
<p>where <span class="math-container">$L$</span> is the money demand that is a function of real output and the interest rate differential between nonmonetary and monetary assets <span class="math-container">$\Delta \equiv \frac{i_t-i^m_t}{1+i_t}$</span> conditional on vector of shocks <span class="math-container">$\xi$</span>. You can view this as the more nuanced version of the equilibrium relationship given by QTM since here <span class="math-container">$MV=PY \implies M/P =Y/V$</span> and we replace crude <span class="math-container">$Y/V$</span> with actual money demand that depends on output and interest rates. In this more nuanced model there does not need to be 1:1 correspondence between LHS and RHS since <span class="math-container">$L$</span> will be some function (e.g. it could be <span class="math-container">$\alpha+ \beta Y - \gamma \frac{i_t-i^m_t}{1+i_t}$</span>, where <span class="math-container">$\alpha$</span> and <span class="math-container">$\beta$</span> and <span class="math-container">$\gamma$</span> would have to be empirically fitted).</p>

CC BY-SA 4.0
2021-05-04T23:19:11.727Z
2021-05-04T23:19:11.727Z
1muflon1
<p>If we look at the US M0 money supply after the global financial crisis (GFC):
<a href="https://i.sstatic.net/M7ezd.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/M7ezd.png" alt="enter image description here" /></a>
we see that it doubled from 2010 to 2015.</p>
<p>If we look at the Consumer Price Index in the same period:
<a href="https://i.sstatic.net/zYOOw.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/zYOOw.png" alt="enter image description here" /></a>
it rose by 8%.</p>
<p>So over the 5 year period from 2010 to 2015 the M0 had a geometric average of 15% and the CPI a geometric average of 1.6%.</p>
<p>According to the Quantity Equation the US therefore had a yearly real growth of more than 13% in this period?</p>
<p>Which sounds way to much.</p>

CC BY-SA 4.0
2021-05-04T21:59:35.907Z
Real growth of what? GDP?
Giskard
<inflation><money-supply><nonexpert><united-states>
What was the annual real growth rate in the US from 2010 to 2015?
Andy
# What was the annual real growth rate in the US from 2010 to 2015?

(Asked by: username_0 on 2021-05-04)

If we look at the US M0 money supply after the global financial crisis (GFC):
[![enter image description here](https://i.sstatic.net/M7ezd.png)](https://i.sstatic.net/M7ezd.png)
we see that it doubled from 2010 to 2015.

If we look at the Consumer Price Index in the same period:
[![enter image description here](https://i.sstatic.net/zYOOw.png)](https://i.sstatic.net/zYOOw.png)
it rose by 8%.

So over the 5 year period from 2010 to 2015 the M0 had a geometric average of 15% and the CPI a geometric average of 1.6%.

According to the Quantity Equation the US therefore had a yearly real growth of more than 13% in this period?

Which sounds way to much.

**Tags:** inflation, money-supply, nonexpert, united-states
> **Comments:**
> **username_1**: Real growth of what? GDP?  

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## 1 answers

### Answer by username_2 on 2021-05-04. Score: 1 | Accepted answer

> What was the annual real growth rate in the US from 2010 to 2015?

I presume you mean growth rate of output. You can see the quarterly real growth rate in the US from 2010 to 2015 below (source Fred) with average quarterly growth rate being 0.6%:

[![enter image description here](https://i.sstatic.net/ezwtL.png)](https://i.sstatic.net/ezwtL.png)

> According to the Quantity Equation the US therefore had a yearly real growth of more than 13% in this period?

No, that is definitely not implied by the quantitative theory of money (QTM) - I assume that is what you mean by the 'quantity equation'. First, you are using wrong data for that (at least for money supply). Second you are not using all data required for QTM is given by:

$$MV=PY$$

With, $M$ being total money supply (usually proxied by $M2$), $V$ velocity of money, $P$ price level, $Y$ real output. Taking logs and differentiating the expression wrt time we get:

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

The above says that the growth rate in $M$ + growth rate in $V$ should be equal to growth rate in $P$ plus growth rate in $Y$.

Now the *total growth rate* of $Y$ between 2010 and 2015 of $Y$ was $\approx 11.7 \%$ (see [Fred data](https://fred.stlouisfed.org/series/GDPC1#0)), the total growth rate of $P$ in between 2010 and 2015 was $\approx 9.4 \%$ (see [Fred data](https://fred.stlouisfed.org/series/GDPC1)), next the total growth rate of $M$, in the same time period, measured by $M2$ was approximately $39.6 \%$ (see [Fred data](https://fred.stlouisfed.org/series/WM2NS)), lastly the total growth in velocity $V$ over the same period was approximately $-14.9 \%$ (again see [Fred data](https://fred.stlouisfed.org/series/M2V)).

Consequently, plugin these into QTM we would get that:

$$39.5 \%+ (-14.3\%) - 9.4\% = \frac{\dot{Y}}{Y} $$

Hence QTM would predict that the growth rate of $Y$ would be:

$$ 15.8 \% \approx \frac{\dot{Y}}{Y} $$

This is still off by approximately $4.1\%$ given that the actual real GDP growth was $\approx 11.7\%$, however note QTM is extremely simplistic model of money market equilibrium.

More realistic description of money market equilibrium would be given by (see Woodford Interest & Prices pp 295):

$$M^s\_t/P\_t = L(Y\_t,\Delta\_t: \xi)$$

where $L$ is the money demand that is a function of real output and the interest rate differential between nonmonetary and monetary assets $\Delta \equiv \frac{i\_t-i^m\_t}{1+i\_t}$ conditional on vector of shocks $\xi$. You can view this as the more nuanced version of the equilibrium relationship given by QTM since here $MV=PY \implies M/P =Y/V$ and we replace crude $Y/V$ with actual money demand that depends on output and interest rates. In this more nuanced model there does not need to be 1:1 correspondence between LHS and RHS since $L$ will be some function (e.g. it could be $\alpha+ \beta Y - \gamma \frac{i\_t-i^m\_t}{1+i\_t}$, where $\alpha$ and $\beta$ and $\gamma$ would have to be empirically fitted).


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