<p>The PWL (piece-wise linear) model replaces a curve with a sequence of straight line segments joined together to approximate the curve.</p>
<p>I am not familiar with the use of PWL in economics, however, it is the same principle used in science and engineering. This two page reference shows a PWL for a model rocket motor:</p>
<p><a href="https://www.nar.org/SandT/pdf/Estes/A10-0T.pdf" rel="nofollow noreferrer">https://www.nar.org/SandT/pdf/Estes/A10-0T.pdf</a></p>
<p><a href="https://i.sstatic.net/HSAXq.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/HSAXq.png" alt="enter image description here" /></a></p>
<p>The data for a typical thrust-time curve are measured with short sampling time and therefore high sampling rate. This data sampling model is a PWL model with many dense line segments joined to each other to make the curve.</p>
<p>The PWL model below approximates the PWL curve above using fewer line segments for use with a standard rocket simulation software package with a limit of 32 data points for the PWL motor model:</p>
<p><a href="https://i.sstatic.net/g6AEL.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/g6AEL.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-09-30T16:08:45.287Z
2021-09-30T16:08:45.287Z
SystemTheory
<p>I think a picture would best convey the intuition. The red line in the graph below shows a linear trend, the blue piece-wise linear, and the green exponential.</p>
<p><a href="https://i.sstatic.net/kTwHI.png" rel="noreferrer"><img src="https://i.sstatic.net/kTwHI.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-09-30T17:15:01.893Z
2021-09-30T17:15:01.893Z
Herr K.
<p>When the impact of laws diminish over time, it may dissipate by &quot;linear&quot;, &quot;piecewise linear&quot; or &quot;exponential way&quot;.</p>
<p>It is easy to understand that linear mean that the the erosion of the laws impact follows a constant slope coefficient. And exponential way is that the erosion of laws effect would follow a curve.</p>
<p>But I do not fully understand what does &quot;<a href="https://en.wikipedia.org/wiki/Piecewise_linear_function" rel="nofollow noreferrer">piecewise linear</a>&quot; mean intuitively? Is it the mixture between &quot;linear&quot; and &quot;exponential&quot; ?
Could you please explain it to me, thanks in advance.</p>

CC BY-SA 4.0
2021-09-30T14:50:25.323Z
What about breaks in linear trends due to some events? Or it could be just some mathematical model for approximation.
chan1142
CC BY-SA 4.0
2021-09-30T19:36:22.407Z
@chan1142 , I am just simply talking about some mathematical model
Nguyen Lis
<econometrics><nonexpert>
What is the difference between "linear" and "piecewise linear" and "exponential way"?
Nguyen Lis
# What is the difference between "linear" and "piecewise linear" and "exponential way"?

(Asked by: username_0 on 2021-09-29)

When the impact of laws diminish over time, it may dissipate by "linear", "piecewise linear" or "exponential way".

It is easy to understand that linear mean that the the erosion of the laws impact follows a constant slope coefficient. And exponential way is that the erosion of laws effect would follow a curve.

But I do not fully understand what does "[piecewise linear](https://en.wikipedia.org/wiki/Piecewise_linear_function)" mean intuitively? Is it the mixture between "linear" and "exponential" ?
Could you please explain it to me, thanks in advance.

**Tags:** econometrics, nonexpert

> **Comments:**
> **username_1**: What about breaks in linear trends due to some events? Or it could be just some mathematical model for approximation.  
> **username_0**: @username_1 , I am just simply talking about some mathematical model  

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## 2 answers

### Answer by username_3 on 2021-09-30. Score: 5 | Accepted answer

I think a picture would best convey the intuition. The red line in the graph below shows a linear trend, the blue piece-wise linear, and the green exponential.

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


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### Answer by username_2 on 2021-09-30. Score: 2

The PWL (piece-wise linear) model replaces a curve with a sequence of straight line segments joined together to approximate the curve.

I am not familiar with the use of PWL in economics, however, it is the same principle used in science and engineering. This two page reference shows a PWL for a model rocket motor:

<https://www.nar.org/SandT/pdf/Estes/A10-0T.pdf>

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

The data for a typical thrust-time curve are measured with short sampling time and therefore high sampling rate. This data sampling model is a PWL model with many dense line segments joined to each other to make the curve.

The PWL model below approximates the PWL curve above using fewer line segments for use with a standard rocket simulation software package with a limit of 32 data points for the PWL motor model:

[![enter image description here](https://i.sstatic.net/g6AEL.png)](https://i.sstatic.net/g6AEL.png)


---

