<p>The <span class="math-container">$k+1$</span> parameters are <span class="math-container">$k+1$</span> unknowns. In general, you need at least <span class="math-container">$k+1$</span> equations (which are observations in the context of OLS estimation) to uniquely pin down those <span class="math-container">$k+1$</span> unknowns.</p>

CC BY-SA 4.0
2019-11-18T12:29:34.930Z
So the ‘observations’ are the equations which comprise the OLS first order conditions?
Ali Lodhi
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2019-11-18T17:26:32.480Z
@AliLodhi: I'm not sure what you mean by "OLS first order conditions", but I have in mind the OLS regression model $y_i=\beta_0+\beta_1x_{1i}+\cdots+\beta_k x_{ki}+\epsilon_i$, where each observation $i$ is an instantiation of this equation.
Herr K.
CC BY-SA 4.0
2019-11-17T20:27:02.077Z
2019-11-17T20:27:02.077Z
Herr K.
<p>The intuition is that OLS is a linear model and to estimate any linear model you need at least 2 points in 2D space. The reason for that is that with a single point you can’t uniquely identify any line. </p>

<p>Adding extra parameter increases the dimensions and in each higher dimension you need one more point to estimate linear model. You can think about it in a way that you need at least one point per dimension but in 1D space there is no line since 1D would be just Y axis hence you get minimum k+1 points.</p>

CC BY-SA 4.0
2019-11-17T20:19:51.727Z
"with a single point you can’t crate any line" --- I would beg to differ: through a single point you can create *infinitely many* lines.
Herr K.
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2019-11-17T20:45:57.687Z
@HerrK. You are right it should be identify unique line I changed it
1muflon1
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2019-11-17T15:08:37.080Z
2019-11-17T20:46:43.460Z
2019-11-17T20:46:43.460Z
1muflon1
<p>Wooldrige says that ‘intuitively, to estimate k+1 parameters, we need at least k+1 observations’. Why is this the case?</p>

<econometrics>
Uniqueness of OLS estimates
Ali Lodhi
# Uniqueness of OLS estimates

(Asked by: username_0 on 2019-11-17)

Wooldrige says that ‘intuitively, to estimate k+1 parameters, we need at least k+1 observations’. Why is this the case?

**Tags:** econometrics


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## 2 answers

### Answer by username_1 on 2019-11-17. Score: 3

The $k+1$ parameters are $k+1$ unknowns. In general, you need at least $k+1$ equations (which are observations in the context of OLS estimation) to uniquely pin down those $k+1$ unknowns.

> **Comments:**
> **username_0**: So the ‘observations’ are the equations which comprise the OLS first order conditions?  
> **username_1**: @username_0: I'm not sure what you mean by "OLS first order conditions", but I have in mind the OLS regression model $y_i=\beta_0+\beta_1x_{1i}+\cdots+\beta_k x_{ki}+\epsilon_i$, where each observation $i$ is an instantiation of this equation.  

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### Answer by username_2 on 2019-11-17. Score: 1

The intuition is that OLS is a linear model and to estimate any linear model you need at least 2 points in 2D space. The reason for that is that with a single point you can’t uniquely identify any line.

Adding extra parameter increases the dimensions and in each higher dimension you need one more point to estimate linear model. You can think about it in a way that you need at least one point per dimension but in 1D space there is no line since 1D would be just Y axis hence you get minimum k+1 points.

> **Comments:**
> **username_1**: "with a single point you can’t crate any line" --- I would beg to differ: through a single point you can create *infinitely many* lines.  
> **username_2**: @HerrK. You are right it should be identify unique line I changed it  

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