LECT: Add lecture on lake model #99
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@maanasee do you have time to review this lecture? The current warnings indicate that |
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This lecture has been upated. Please review and let me know if there is any issue. |
lectures/lake_model.md
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| ```{code-cell} ipython3 | ||
| lm = LakeModel(α=0.01, λ=0.1, d=0.025, b=0.02) | ||
| plot_time_paths(lm, x0=x0) | ||
| ```` |
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extra backtick needs to be removed (CC @Chien-Y )
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Many thanks @Chien-Y . Perhaps we should replace the png file with a graphvis figure, so that it's generated within the lecture. |
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Thank you for the comment, @jstac . |
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Thanks @Chien-Y . @Smit-create or @mmcky , could you please fix the build error. |
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Thanks, @jstac. Fixed the build error. |
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Thanks @Smit-create , much appreciated. |
lectures/lake_model.md
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| The importance of the Perron-Frobenius theorem stems from the fact that | ||
| firstly in the real world most matrices we encounter are nonnegative matrices. | ||
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| Secondly, a lot of important models are simply linear iterative models that |
lectures/lake_model.md
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| Since by intuition if we consider unemployment pool and employment pool as a closed system, the growth should be similar the labor force. | ||
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| We next ask whether the growth rates of $e_t$ and $u_t$ in the long run also dominated by $1+b-d$ as labor force. |
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"growth rates... in the long run" -> "long run growth rates"
lectures/lake_model.md
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| $$ | ||
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| Moreover, the times series of unemployment and employment seems to grow at some constant rate in the long run. | ||
| Hence, the growth rate of $n_t$ is fixed at $1 + b - a$. |
lectures/lake_model.md
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| The rate motion follows $r_{t+1} = \hat{A} r_t$, where $r_0$ is a probability vector: $\sum_j r_{0,j}=1$. | ||
| The dynamics of rates follows $r_{t+1} = \hat{A} r_t$, where $r_0$ is a probability vector: $\sum_j r_{0,j}=1$. |
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"of rates" -> "of the rates"
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Thanks @Chien-Y , please see my comments above. |
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Thank you, @jstac. I've corrected them. |
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Thanks @Chien-Y , nice work. |
This PR adds
lake_modellecture but needs some additional import statements to make the code run etc.