<p>Ignore the other variables. Let $g$ be growth, $C$ corruption and $A$ aid. You look at</p>

<p>$$g = \alpha C + \beta A + \gamma A\cdot C$$</p>

<p>You ask, "does <em>lower</em> corruption increases the effectiveness of foreign aid?"</p>

<p>For this you have indeed to examine the cross-partial derivative</p>

<p>$$\frac {\partial g}{\partial A\partial C} = \gamma$$</p>

<p>This is "how growth is affected at the margin by Aid, if corruption changes"... So if <em>lower</em> corruption increases the effectiveness of Aid, $\gamma$ should be <em>negative</em>, not positive...</p>

<p>...<em>if</em> your corruption index is mapped as "the higher the value of $C$ the higher the corruption".</p>

<p>If your "corruption index" is mapped in reverse (and so in reality it measures "non-corruption"), the anticipated sign reverses also.</p>

CC BY-SA 3.0
2017-02-24T14:53:22.330Z
2017-03-28T14:38:36.650Z
2017-03-28T14:38:36.650Z
Alecos Papadopoulos
<p>Say I have an augmented growth regression, where my Y is GDP growth, and my Xs are the classical MRW variables, + international aid + corruption + the interaction term between the two.<br>
Basically, I'm interested in seeing if lower corruption increases the effectiveness of international aid, which means I'd like to see a positive sign on my interaction term.<br>
However, I also think I should see a negative sign on corruption, as the higher corruption, the lower should growth be.<br>
Now, my questions:<br></p>

<ol>
<li>Is this possible as I describe it? Can I see a negative component but a positive interaction term? In which case, how should I interpret it?<br></li>
<li>Or is there a reason the coefficient on corruption should be positive, and still indicate that higher "institutional quality" has a positive impact on growth by itself and also in interaction with aid?<br></li>
</ol>

<economic-growth><regression>
Positive interaction term with one negative component?
Margherita
# Positive interaction term with one negative component?

(Asked by: username_0 on 2017-02-24)

Say I have an augmented growth regression, where my Y is GDP growth, and my Xs are the classical MRW variables, + international aid + corruption + the interaction term between the two.  
Basically, I'm interested in seeing if lower corruption increases the effectiveness of international aid, which means I'd like to see a positive sign on my interaction term.  
However, I also think I should see a negative sign on corruption, as the higher corruption, the lower should growth be.  
Now, my questions:

1. Is this possible as I describe it? Can I see a negative component but a positive interaction term? In which case, how should I interpret it?
2. Or is there a reason the coefficient on corruption should be positive, and still indicate that higher "institutional quality" has a positive impact on growth by itself and also in interaction with aid?

**Tags:** economic-growth, regression

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## 1 answers

### Answer by username_1 on 2017-02-24. Score: 1

Ignore the other variables. Let $g$ be growth, $C$ corruption and $A$ aid. You look at

$$g = \alpha C + \beta A + \gamma A\cdot C$$

You ask, "does *lower* corruption increases the effectiveness of foreign aid?"

For this you have indeed to examine the cross-partial derivative

$$\frac {\partial g}{\partial A\partial C} = \gamma$$

This is "how growth is affected at the margin by Aid, if corruption changes"... So if *lower* corruption increases the effectiveness of Aid, $\gamma$ should be *negative*, not positive...

...*if* your corruption index is mapped as "the higher the value of $C$ the higher the corruption".

If your "corruption index" is mapped in reverse (and so in reality it measures "non-corruption"), the anticipated sign reverses also.


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