<p>Unfortunately, there isn't a clearcut answer to this question.</p>
<p>The two simplest answers are that the variable is really not involved in the nominal rate or that is a false negative.  The other answer is that there are other variables involved that were omitted.  In that case, your model is misspecified.</p>
<p>Let us begin with the simplest of the answers, it is a true negative.  What you should then do is walk through the economic models related to this and ask if that actually makes sense.  What would it imply for how the world would have to work?</p>
<p>The second is that it is a false negative.  There is absolutely nothing you can do about this if that is true.  False negatives happen.  There is no variable that you could add that would change it.  People forget that a variable being significant just implies that if the null is true, then what you saw was unusual.  However, if the null is false, the measurements tell you nothing.  All of the probability is built around the null being true.  A false negative is a false negative.</p>
<p>The third is a bit more interesting.  What if TFP matters, generally, but not in your chosen country because something else of interest is also happening that is of great importance to your model.  In that case, your model is misspecified.  Your parameters would be biased downward and would tend to not falsify the null.  In that case, you need to investigate more.</p>

CC BY-SA 4.0
2021-10-31T13:28:10.893Z
You're right, especially regarding the third case. And since the TFP doesn't seem to be statistically significative, I've changed it and used as independent variable the net return on net capital stock, as a measure of the capital's productivity. After all, Wicksell himself said that the natural rate corresponds s to the expected yield on the newly created capital (Lectures on political economy) and so my model now is both economically and statistically significant.
Giord
CC BY-SA 4.0
2021-10-31T03:53:17.600Z
2021-10-31T03:53:17.600Z
Dave Harris
<p>I'm conducting an econometric analysis of the natural rate of interest in the euro-area countries using the following variables: as dependent variable I'm using the long term nominal interest rates (i.e.: the yield on 10 year maturity public bonds) and as independent variable I'm using the TFP growth rate, the inflation rate, a dummy variable to show the impact of the common monetary policy and the growth rate of the population aged between 15 and 64 years; so my equation is given by:</p>
<p><span class="math-container">$$r^*= a_0 + \beta_1x_1+\beta_2x_2+\beta_3Dx_3+\beta_4x_4$$</span></p>
<p>Now, I have some problems: first of all the TFP growth does not seems to be statistically significant (since its p-value is greater than the significance level <span class="math-container">$\alpha=0.05$</span>); and that's a problem, because based on the literature about this topic, what I expected to see is that higher TFP growth and higher active population growth were associated with a higher natural rate of interest. So, my question is: why this doesn't seem to happen in my model? And if I'm correct in assuming no statistical significance of the TFP growth, what I have to do to show the impact of productivity in the natural rate of interest? Thanks in advance for the answers.</p>

CC BY-SA 4.0
2021-10-29T19:27:32.750Z
Hi @Giord. Could you attach a link to some of the papers which exhibit a statistically significant relationship? There could be many issues with your specification, ranging from functional form, to controlling for problems with your error term, alongside the specific model you've chosen. Is this a panel model?
EB3112
CC BY-SA 4.0
2021-10-29T19:34:55.663Z
@EB3112, One of these paper is this: https://www.nber.org/system/files/working_papers/w25039/w25039.pdf , in which (as reported here:https://www.lb.lt/en/publications/natural-real-rates-of-interest-across-euro-area-countries-are-r-stars-getting-closer-together) the authors argue that the natural interest rate has been driven down over the past three decades mainly by productivity. And no, my model is cross sectional
Giord
CC BY-SA 4.0
2021-10-29T19:45:03.967Z
I feel you're trying to mimic the 'building block' eq.14 in the Negro paper if I am not mistaken? It has a time subscript. They're estimating a time series model (in fact, they've estimated many in their paper). But, a cross-sectional OLS will average over all euroarea countries and hide many important dynamics.
EB3112
CC BY-SA 4.0
2021-10-29T19:56:16.550Z
@EB3112, Yeah, mee to I'm trying to run a time series estimate for each of the euro area countries. What I'm trying to do is to estimate an equation similar to the one in the Lithuanian National Bank's paper. In fact my problem is to understand why productivity is not statistically significant as seems to be in the abovementioned paper
Giord
CC BY-SA 4.0
2021-10-29T19:58:10.037Z
@EB3112, i.e.: the equation number two in the second paper I quoted (that is, this: https://www.lb.lt/en/publications/natural-real-rates-of-interest-across-euro-area-countries-are-r-stars-getting-closer-together)
Giord
CC BY-SA 4.0
2021-10-29T20:26:59.973Z
You said you were doing cross sectional?
EB3112
CC BY-SA 4.0
2021-10-29T20:40:53.613Z
My point overall is that you have to look in more detail at their (fairly advanced) time series model, rather than take one equation from it.
EB3112
<macroeconomics><econometrics>
No statistical significance of the TFP growth
Giord
# No statistical significance of the TFP growth

(Asked by: username_0 on 2021-10-29)

I'm conducting an econometric analysis of the natural rate of interest in the euro-area countries using the following variables: as dependent variable I'm using the long term nominal interest rates (i.e.: the yield on 10 year maturity public bonds) and as independent variable I'm using the TFP growth rate, the inflation rate, a dummy variable to show the impact of the common monetary policy and the growth rate of the population aged between 15 and 64 years; so my equation is given by:

$$r^\*= a\_0 + \beta\_1x\_1+\beta\_2x\_2+\beta\_3Dx\_3+\beta\_4x\_4$$

Now, I have some problems: first of all the TFP growth does not seems to be statistically significant (since its p-value is greater than the significance level $\alpha=0.05$); and that's a problem, because based on the literature about this topic, what I expected to see is that higher TFP growth and higher active population growth were associated with a higher natural rate of interest. So, my question is: why this doesn't seem to happen in my model? And if I'm correct in assuming no statistical significance of the TFP growth, what I have to do to show the impact of productivity in the natural rate of interest? Thanks in advance for the answers.

**Tags:** macroeconomics, econometrics
> **Comments:**
> **username_1**: Hi @Giord. Could you attach a link to some of the papers which exhibit a statistically significant relationship? There could be many issues with your specification, ranging from functional form, to controlling for problems with your error term, alongside the specific model you've chosen. Is this a panel model?  
> **username_0**: @EB3112, One of these paper is this: https://www.nber.org/system/files/working_papers/w25039/w25039.pdf , in which (as reported here:https://www.lb.lt/en/publications/natural-real-rates-of-interest-across-euro-area-countries-are-r-stars-getting-closer-together) the authors argue that the natural interest rate has been driven down over the past three decades mainly by productivity. And no, my model is cross sectional  
> **username_1**: I feel you're trying to mimic the 'building block' eq.14 in the Negro paper if I am not mistaken? It has a time subscript. They're estimating a time series model (in fact, they've estimated many in their paper). But, a cross-sectional OLS will average over all euroarea countries and hide many important dynamics.  
> **username_0**: @EB3112, Yeah, mee to I'm trying to run a time series estimate for each of the euro area countries. What I'm trying to do is to estimate an equation similar to the one in the Lithuanian National Bank's paper. In fact my problem is to understand why productivity is not statistically significant as seems to be in the abovementioned paper  
> **username_0**: @EB3112, i.e.: the equation number two in the second paper I quoted (that is, this: https://www.lb.lt/en/publications/natural-real-rates-of-interest-across-euro-area-countries-are-r-stars-getting-closer-together)  
> **username_1**: You said you were doing cross sectional?  
> **username_1**: My point overall is that you have to look in more detail at their (fairly advanced) time series model, rather than take one equation from it.  

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## 1 answers

### Answer by username_2 on 2021-10-31. Score: 2

Unfortunately, there isn't a clearcut answer to this question.

The two simplest answers are that the variable is really not involved in the nominal rate or that is a false negative. The other answer is that there are other variables involved that were omitted. In that case, your model is misspecified.

Let us begin with the simplest of the answers, it is a true negative. What you should then do is walk through the economic models related to this and ask if that actually makes sense. What would it imply for how the world would have to work?

The second is that it is a false negative. There is absolutely nothing you can do about this if that is true. False negatives happen. There is no variable that you could add that would change it. People forget that a variable being significant just implies that if the null is true, then what you saw was unusual. However, if the null is false, the measurements tell you nothing. All of the probability is built around the null being true. A false negative is a false negative.

The third is a bit more interesting. What if TFP matters, generally, but not in your chosen country because something else of interest is also happening that is of great importance to your model. In that case, your model is misspecified. Your parameters would be biased downward and would tend to not falsify the null. In that case, you need to investigate more.

> **Comments:**
> **username_0**: You're right, especially regarding the third case. And since the TFP doesn't seem to be statistically significative, I've changed it and used as independent variable the net return on net capital stock, as a measure of the capital's productivity. After all, Wicksell himself said that the natural rate corresponds s to the expected yield on the newly created capital (Lectures on political economy) and so my model now is both economically and statistically significant.  

---

