From 26af033c755ebfbb8aa6594da743e2c5a6479951 Mon Sep 17 00:00:00 2001 From: Matthew Rognlie Date: Fri, 8 Nov 2019 16:03:38 -0600 Subject: [PATCH] Corrected estimation.all_covariances so that the 'sigmas' argument is standard deviations of shocks, as stated in docstring, rather than variances as the code actually was. Changed krusell_smith notebook to be consistent with this. --- docs/krusell_smith.html | 46 ++++++++++++++++++++--------------------- estimation.py | 2 +- krusell_smith.ipynb | 46 ++++++++++++++++++++--------------------- 3 files changed, 47 insertions(+), 47 deletions(-) diff --git a/docs/krusell_smith.html b/docs/krusell_smith.html index c463e58..b287118 100644 --- a/docs/krusell_smith.html +++ b/docs/krusell_smith.html @@ -12110,8 +12110,8 @@

Speed of steady-state solution -
CPU times: user 683 ms, sys: 4.72 ms, total: 688 ms
-Wall time: 686 ms
+
CPU times: user 646 ms, sys: 5.73 ms, total: 652 ms
+Wall time: 651 ms
 

 
 
@@ -12151,8 +12151,8 @@ 
Speed of steady-state solution
-
CPU times: user 3.46 s, sys: 46.9 ms, total: 3.51 s
-Wall time: 1.78 s
+
CPU times: user 3.38 s, sys: 49 ms, total: 3.43 s
+Wall time: 1.73 s
 

 
 
@@ -12723,8 +12723,8 @@ 
4.2 Results

-
CPU times: user 60.8 ms, sys: 18.3 ms, total: 79.1 ms
-Wall time: 40.3 ms
+
CPU times: user 65.7 ms, sys: 19.3 ms, total: 85.1 ms
+Wall time: 44 ms
 

 

 
@@ -12737,7 +12737,7 @@ 
4.2 Results

 

-
The time taken here differs from run to run, but in the current run (like all runs on a personal laptop) it takes 50 milliseconds of "wall time" to compute 10,000 impulse responses means that each impulse response takes less than 5 microseconds. "CPU time" is slightly higher because mild parallelization on two cores is used by the built-in matrix multiplication implementation. By contrast, typical impulse response calculations in heterogeneous agent models in the literature take at least a minute, so this method is more than 10 million times faster as a way of calculating individual impulse responses.

+
The time taken here differs from run to run, but in the current run (like all runs on a personal laptop) it takes less than 50 milliseconds of "wall time" to compute 10,000 impulse responses means that each impulse response takes less than 5 microseconds. "CPU time" is slightly higher because mild parallelization on two cores is used by the built-in matrix multiplication implementation. By contrast, typical impulse response calculations in heterogeneous agent models in the literature take at least a minute, so this method is more than 10 million times faster as a way of calculating individual impulse responses.

 
Although this may seem like an extreme example, repeated calculations of this form are quite useful in the most computationally demanding applications, like estimation (as we will see later).

 
Another important feature of our sequence space methodology is that it is easy to calculate the response to shocks that are difficult to cast into simple recursive form, like news shocks.

 
For example, calculating the response to a news shock where $Z$ is expected to increase at a specific period in the future is trivial -- in fact, that's exactly what the columns of the $G$ matrix are. Below we plot the capital responses to news shocks of $Z$ increases at periods 5, 10, 15, 20, and 25.

@@ -12834,8 +12834,8 @@ 
Step 1. Stacked impulse responses
     

 
rho = 0.9
-sigma_persist = 0.01
-sigma_trans = 0.04
+sigma_persist = 0.1
+sigma_trans = 0.2
 
 dZ1 = rho**(np.arange(T))
 dY1, dC1, dK1 = G['Y'] @ dZ1, G['C'] @ dZ1, G['K'] @ dZ1
@@ -12927,8 +12927,8 @@ 
Step 2. Obtain covarian
 
 
 

-
CPU times: user 970 µs, sys: 10 µs, total: 980 µs
-Wall time: 497 µs
+
CPU times: user 932 µs, sys: 9 µs, total: 941 µs
+Wall time: 478 µs
 

 

 

@@ -13047,8 +13047,8 @@ 
5.2 Log-likelihood
# random 100 observations
 Y = np.random.randn(100, 4)
 
-# 0.01 measurement error in each variable
-sigma_measurement = np.full(4, 0.01)
+# 0.05 measurement error in each variable
+sigma_measurement = np.full(4, 0.05)
 
 # calculate log-likelihood
 est.log_likelihood(Y, Sigma, sigma_measurement)
@@ -13070,8 +13070,8 @@ 
5.2 Log-likelihood
-
CPU times: user 3.96 ms, sys: 148 µs, total: 4.11 ms
-Wall time: 2.07 ms
+
CPU times: user 3.71 ms, sys: 153 µs, total: 3.87 ms
+Wall time: 1.94 ms
 

 

 

@@ -13084,7 +13084,7 @@ 
5.2 Log-likelihood
-
-1036409.6757086646

+
-52212.80116916728

 

 
 
@@ -13160,7 +13160,7 @@ 
5.3 P
 
 

 

-
Now let's plot the log-likelihood of $w$ as a function of the standard deviation of the persistent component (the true value of which is 0.01), given correct values for all other parameters. Note that evaluating the log-likelihood 100 times takes well below one second.

+
Now let's plot the log-likelihood of $w$ as a function of the standard deviation of the persistent component (the true value of which is 0.1), given correct values for all other parameters. Note that evaluating the log-likelihood 100 times takes well below one second.

 
 

 

@@ -13170,7 +13170,7 @@ 
5.3 P
 
In [34]:

 

     

-
sigma_persist_values = np.linspace(0.005, 0.02, 100)
+
sigma_persist_values = np.linspace(0.05, 0.2, 100)
 %time lls = np.array([log_likelihood_from_parameters(rho, sigma_persist, sigma_trans, sigma_measurement, Y) for sigma_persist in sigma_persist_values])
 

 
@@ -13188,8 +13188,8 @@ 
5.3 P
 
 
 

-
CPU times: user 534 ms, sys: 40.5 ms, total: 574 ms
-Wall time: 294 ms
+
CPU times: user 608 ms, sys: 43.3 ms, total: 651 ms
+Wall time: 349 ms
 

 

 

@@ -13204,7 +13204,7 @@ 
5.3 P
 

     

 
plt.plot(sigma_persist_values, lls)
-plt.axvline(0.01, linestyle=':', color='gray')
+plt.axvline(0.1, linestyle=':', color='gray')
 plt.title(r'Log likelihood of simulated data as function of $\sigma_{persist}$')
 plt.show()
 

@@ -13225,7 +13225,7 @@ 
5.3 P
 
 
 

-
 

@@ -13240,7 +13240,7 @@ 
5.3 P
 

 

 

-
Reassuringly, the mode is near (although not exactly at, since we're simulating a finite sample with only 100 periods) the value of $\sigma_{persist}=0.01$ with which the data was simulated!

+
Reassuringly, the mode is near (although not exactly at, since we're simulating a finite sample with only 100 periods) the value of $\sigma_{persist}=0.1$ with which the data was simulated!

 
 

 

diff --git a/estimation.py b/estimation.py
index dfb5996..ff1b992 100644
--- a/estimation.py
+++ b/estimation.py
@@ -21,7 +21,7 @@ def all_covariances(M, sigmas):
     """
     T = M.shape[0]
     dft = np.fft.rfftn(M, s=(2 * T - 2,), axes=(0,))
-    total = (dft.conjugate() * sigmas) @ dft.swapaxes(1, 2)
+    total = (dft.conjugate() * sigmas**2) @ dft.swapaxes(1, 2)
     return np.fft.irfftn(total, s=(2 * T - 2,), axes=(0,))[:T]
 
 
diff --git a/krusell_smith.ipynb b/krusell_smith.ipynb
index ed87860..8b5b714 100644
--- a/krusell_smith.ipynb
+++ b/krusell_smith.ipynb
@@ -294,8 +294,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 683 ms, sys: 4.72 ms, total: 688 ms\n",
-      "Wall time: 686 ms\n"
+      "CPU times: user 646 ms, sys: 5.73 ms, total: 652 ms\n",
+      "Wall time: 651 ms\n"
      ]
     }
    ],
@@ -319,8 +319,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 3.46 s, sys: 46.9 ms, total: 3.51 s\n",
-      "Wall time: 1.78 s\n"
+      "CPU times: user 3.38 s, sys: 49 ms, total: 3.43 s\n",
+      "Wall time: 1.73 s\n"
      ]
     }
    ],
@@ -762,8 +762,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 60.8 ms, sys: 18.3 ms, total: 79.1 ms\n",
-      "Wall time: 40.3 ms\n"
+      "CPU times: user 65.7 ms, sys: 19.3 ms, total: 85.1 ms\n",
+      "Wall time: 44 ms\n"
      ]
     }
    ],
@@ -777,7 +777,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The time taken here differs from run to run, but in the current run (like all runs on a personal laptop) it takes 50 milliseconds of \"wall time\" to compute 10,000 impulse responses means that each impulse response takes less than **5 microseconds**. \"CPU time\" is slightly higher because mild parallelization on two cores is used by the built-in matrix multiplication implementation. By contrast, typical impulse response calculations in heterogeneous agent models in the literature take at least a minute, so this method is more than **10 million** times faster as a way of calculating individual impulse responses.\n",
+    "The time taken here differs from run to run, but in the current run (like all runs on a personal laptop) it takes less than 50 milliseconds of \"wall time\" to compute 10,000 impulse responses means that each impulse response takes less than **5 microseconds**. \"CPU time\" is slightly higher because mild parallelization on two cores is used by the built-in matrix multiplication implementation. By contrast, typical impulse response calculations in heterogeneous agent models in the literature take at least a minute, so this method is more than **10 million** times faster as a way of calculating individual impulse responses.\n",
     "\n",
     "Although this may seem like an extreme example, repeated calculations of this form are quite useful in the most computationally demanding applications, like estimation (as we will see later).\n",
     "\n",
@@ -872,8 +872,8 @@
    "outputs": [],
    "source": [
     "rho = 0.9\n",
-    "sigma_persist = 0.01\n",
-    "sigma_trans = 0.04\n",
+    "sigma_persist = 0.1\n",
+    "sigma_trans = 0.2\n",
     "\n",
     "dZ1 = rho**(np.arange(T))\n",
     "dY1, dC1, dK1 = G['Y'] @ dZ1, G['C'] @ dZ1, G['K'] @ dZ1\n",
@@ -934,8 +934,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 970 µs, sys: 10 µs, total: 980 µs\n",
-      "Wall time: 497 µs\n"
+      "CPU times: user 932 µs, sys: 9 µs, total: 941 µs\n",
+      "Wall time: 478 µs\n"
      ]
     }
    ],
@@ -1040,14 +1040,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 3.96 ms, sys: 148 µs, total: 4.11 ms\n",
-      "Wall time: 2.07 ms\n"
+      "CPU times: user 3.71 ms, sys: 153 µs, total: 3.87 ms\n",
+      "Wall time: 1.94 ms\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "-1036409.6757086646"
+       "-52212.80116916728"
       ]
      },
      "execution_count": 31,
@@ -1059,8 +1059,8 @@
     "# random 100 observations\n",
     "Y = np.random.randn(100, 4)\n",
     "\n",
-    "# 0.01 measurement error in each variable\n",
-    "sigma_measurement = np.full(4, 0.01)\n",
+    "# 0.05 measurement error in each variable\n",
+    "sigma_measurement = np.full(4, 0.05)\n",
     "\n",
     "# calculate log-likelihood\n",
     "est.log_likelihood(Y, Sigma, sigma_measurement)\n",
@@ -1125,7 +1125,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Now let's plot the log-likelihood of $w$ as a function of the standard deviation of the persistent component (the true value of which is 0.01), given correct values for all other parameters. Note that evaluating the log-likelihood 100 times takes well below one second."
+    "Now let's plot the log-likelihood of $w$ as a function of the standard deviation of the persistent component (the true value of which is 0.1), given correct values for all other parameters. Note that evaluating the log-likelihood 100 times takes well below one second."
    ]
   },
   {
@@ -1139,13 +1139,13 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 534 ms, sys: 40.5 ms, total: 574 ms\n",
-      "Wall time: 294 ms\n"
+      "CPU times: user 608 ms, sys: 43.3 ms, total: 651 ms\n",
+      "Wall time: 349 ms\n"
      ]
     }
    ],
    "source": [
-    "sigma_persist_values = np.linspace(0.005, 0.02, 100)\n",
+    "sigma_persist_values = np.linspace(0.05, 0.2, 100)\n",
     "%time lls = np.array([log_likelihood_from_parameters(rho, sigma_persist, sigma_trans, sigma_measurement, Y) for sigma_persist in sigma_persist_values])"
    ]
   },
@@ -1158,7 +1158,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "
"
       ]
@@ -1169,7 +1169,7 @@
    ],
    "source": [
     "plt.plot(sigma_persist_values, lls)\n",
-    "plt.axvline(0.01, linestyle=':', color='gray')\n",
+    "plt.axvline(0.1, linestyle=':', color='gray')\n",
     "plt.title(r'Log likelihood of simulated data as function of $\\sigma_{persist}$')\n",
     "plt.show()"
    ]
@@ -1178,7 +1178,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Reassuringly, the mode is near (although not exactly at, since we're simulating a finite sample with only 100 periods) the value of $\\sigma_{persist}=0.01$ with which the data was simulated!"
+    "Reassuringly, the mode is near (although not exactly at, since we're simulating a finite sample with only 100 periods) the value of $\\sigma_{persist}=0.1$ with which the data was simulated!"
    ]
   },
   {