Akkaya 2016a - Revision history

Scipediacontent at 08:54, 12 June 2017

2017-06-12T08:54:19Z

Scipediacontent at 08:52, 12 June 2017

2017-06-12T08:52:55Z

Scipediacontent: Scipediacontent moved page Draft Content 928288140 to Akkaya 2016a

2017-06-12T08:47:38Z

Scipediacontent moved page Draft Content 928288140 to Akkaya 2016a

Scipediacontent: Created page with "==Abstract== In this paper, our research question that could analyze how efficiency in Swedish financial enterprises has changed since the banking crisis in 1993. We estimate..."

2017-06-12T08:44:15Z

Created page with "==Abstract== In this paper, our research question that could analyze how efficiency in Swedish financial enterprises has changed since the banking crisis in 1993. We estimate..."

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 [[#bfn0010|1]]. Completing the replications with a fresh set of values of <math display="inline">u_{bt}^{\bullet }</math> generated in each iteration produced virtually the same results. Retaining the fixed set (as shown here) facilitates the analysis of the results in terms of estimation of a set of invariant quantities ([[#bib0100|Greene, 2005]]).<span id='fn2'></span>
-[[#bfn2|2]]. We want to find the fit model in these estimators. We use some hypothesis tests for our estimators. Firstly, we compare the pool model and fix model. The likelihood ratio test enables us to find which model is more fit in our database. In this test, the null hypothesis is the pool model <math display="inline">\left(H_0=The\mbox{\;}Pool\mbox{\;}Model\right)</math>. The likelihood ratio test formulates <math display="inline">\left(Likehood\mbox{\;}ratio_{estimate}=-2[loglike_{pool\mbox{\;}model}-\right. </math><math>\left. loglike_{fix\mbox{\;}model}]\right)</math>. We calculated <math display="inline">Likelihoodratio_{estimate}=582.43\mbox{.}</math><math display="inline">Chi\mbox{\;}square{\left(8,\mbox{\;}0.05\right)}_{table}</math> is 15.507 for our example. We obtained the result of <math display="inline">Likelihoodratio_{estimate}=582.43\mbox{.}</math><math display="inline">Chi\mbox{\;}square{\left(8,0.05\right)}_{table}</math>, which we reject to the null hypothesis.econdly, we could compare the fix model and the random model. The Hausman test enables us to find which model is more fit in our database. In this test, the null hypothesis is the random model <math display="inline">\left(H_0=The\mbox{\;}Random\mbox{\;}Model\right)</math>. The Hausman test formulates: <math display="inline">\left\{H_{estimate}=({\overset{\frown}{\beta }}_{FM}-\right. </math><math>\left. {\overset{\frown}{\beta }}_{RM})cov{\left({\overset{\frown}{\beta }}_{FM}-{\overset{\frown}{\beta }}_{RM}\right)}^{-1}({\overset{\frown}{\beta }}_{FM}-\right. </math><math>\left. {\overset{\frown}{\beta }}_{RM})\right\}</math>. We calculate ''H''<sub>''estimate''</sub> = 50.715. ''Chi-square''(8,0.05)<sub>''table''</sub> as 15.507 for our example. As a result of ''H''<sub>''estimate''</sub> = 50.715. ''Chi square''(8,0.05)<sub>''table''</sub>, we reject the null hypothesis. Thirdly, we compare the fix model and the TRUEfix model. The Hausman test enables us to find which model is more fit in our database. In this test, the null hypothesis is the fix model <math display="inline">\left(H_0=The\mbox{\;}Fix\mbox{\;}Model\right)</math>. The Hausman test formulates:<math display="inline">\left\{H_{estimate}=({\overset{\frown}{\beta }}_{TRUEFM}-\right. </math><math>\left. {\overset{\frown}{\beta }}_{FM})cov{\left({\overset{\frown}{\beta }}_{TRUEFM}-{\overset{\frown}{\beta }}_{FM}\right)}^{-1}({\overset{\frown}{\beta }}_{TRUEFM}-\right. </math><math>\left. {\overset{\frown}{\beta }}_{FM})\right\}</math>. We calculate that ''H''<sub>''estimate''</sub> = 42.469. ''Chi square''(8,0.05)<sub>''table''</sub> is 15.507 for our example. As a result of ''H''<sub>''estimate''</sub> = 50.715. ''Chi square''(8,0.05)<sub>''table''</sub>, we reject the null hypothesis.<span id='fn0020'></span>
+[[#bfn2|2]]. We want to find the fit model in these estimators. We use some hypothesis tests for our estimators. Firstly, we compare the pool model and fix model. The likelihood ratio test enables us to find which model is more fit in our database. In this test, the null hypothesis is the pool model <math display="inline">\left(H_0=The\mbox{ }Pool\mbox{ }Model\right)</math>. The likelihood ratio test formulates <math display="inline">\left(Likehood\mbox{ }ratio_{estimate}=-2[loglike_{pool\mbox{ }model}-\right. </math><math>\left. loglike_{fix\mbox{ }model}]\right)</math>. We calculated <math display="inline">Likelihoodratio_{estimate}=582.43\mbox{.}</math><math display="inline">Chi\mbox{ }square{\left(8,\mbox{ }0.05\right)}_{table}</math> is 15.507 for our example. We obtained the result of <math display="inline">Likelihoodratio_{estimate}=582.43\mbox{.}</math><math display="inline">Chi\mbox{ }square{\left(8,0.05\right)}_{table}</math>, which we reject to the null hypothesis.econdly, we could compare the fix model and the random model. The Hausman test enables us to find which model is more fit in our database. In this test, the null hypothesis is the random model <math display="inline">\left(H_0=The\mbox{ }Random\mbox{ }Model\right)</math>. The Hausman test formulates: <math display="inline">\left\{H_{estimate}=({\overset{\frown}{\beta }}_{FM}-\right. </math><math>\left. {\overset{\frown}{\beta }}_{RM})cov{\left({\overset{\frown}{\beta }}_{FM}-{\overset{\frown}{\beta }}_{RM}\right)}^{-1}({\overset{\frown}{\beta }}_{FM}-\right. </math><math>\left. {\overset{\frown}{\beta }}_{RM})\right\}</math>. We calculate ''H''<sub>''estimate''</sub> = 50.715. ''Chi-square''(8,0.05)<sub>''table''</sub> as 15.507 for our example. As a result of ''H''<sub>''estimate''</sub> = 50.715. ''Chi square''(8,0.05)<sub>''table''</sub>, we reject the null hypothesis. Thirdly, we compare the fix model and the TRUEfix model. The Hausman test enables us to find which model is more fit in our database. In this test, the null hypothesis is the fix model <math display="inline">\left(H_0=The\mbox{ }Fix\mbox{ }Model\right)</math>. The Hausman test formulates:<math display="inline">\left\{H_{estimate}=({\overset{\frown}{\beta }}_{TRUEFM}-\right. </math><math>\left. {\overset{\frown}{\beta }}_{FM})cov{\left({\overset{\frown}{\beta }}_{TRUEFM}-{\overset{\frown}{\beta }}_{FM}\right)}^{-1}({\overset{\frown}{\beta }}_{TRUEFM}-\right. </math><math>\left. {\overset{\frown}{\beta }}_{FM})\right\}</math>. We calculate that ''H''<sub>''estimate''</sub> = 42.469. ''Chi square''(8,0.05)<sub>''table''</sub> is 15.507 for our example. As a result of ''H''<sub>''estimate''</sub> = 50.715. ''Chi square''(8,0.05)<sub>''table''</sub>, we reject the null hypothesis.<span id='fn0020'></span>
 [[#bfn0020|3]]. Technical Efficiency Score = 1 − Technical Inefficiency Scores.

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 {| style="text-align: center; margin:auto;"
 |-
-| <math>C_b=C(\boldsymbol{\mbox{y}}_i,p_k,{\epsilon }_b),\mbox{ }b=</math><math>1,\mbox{\;}\ldots ,\mbox{\;}n</math>
+| <math>C_b=C(\boldsymbol{\mbox{y}}_i,p_k,{\epsilon }_b),\mbox{ }b=</math><math>1,\mbox{ }\ldots ,\mbox{ }n</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (1.1)
@@ Line 103: / Line 103: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>lnC_b=f(\boldsymbol{\mbox{y}}_i,p_k)+{\epsilon }_b\mbox{ }\mbox{where}\mbox{\;}{\epsilon }_b=</math><math>u_b+e_b\mbox{ }[\mbox{the}\mbox{\;}\mbox{Pooled}\mbox{\;}\mbox{Model}](\mbox{PM}\mbox{\;}\mbox{hereafter})</math>
+| <math>lnC_b=f(\boldsymbol{\mbox{y}}_i,p_k)+{\epsilon }_b\mbox{ }\mbox{where}\mbox{ }{\epsilon }_b=</math><math>u_b+e_b\mbox{ }[\mbox{the}\mbox{ }\mbox{Pooled}\mbox{ }\mbox{Model}](\mbox{PM}\mbox{ }\mbox{hereafter})</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (1.3)
@@ Line 117: / Line 117: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>\mbox{ln}\mbox{\;}C_b=f(\boldsymbol{\mbox{y}}_i,p_k)+</math><math>{\epsilon }_b\mbox{ }[\mbox{the}\mbox{\;}\mbox{Fixed}\mbox{\;}\mbox{Effects}\mbox{\;}\mbox{Model}](\mbox{FM}\mbox{\;}\mbox{hereafter})</math>
+| <math>\mbox{ln}\mbox{ }C_b=f(\boldsymbol{\mbox{y}}_i,p_k)+</math><math>{\epsilon }_b\mbox{ }[\mbox{the}\mbox{ }\mbox{Fixed}\mbox{ }\mbox{Effects}\mbox{ }\mbox{Model}](\mbox{FM}\mbox{ }\mbox{hereafter})</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (1.4)
@@ Line 143: / Line 143: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>lnC_b=f(\boldsymbol{\mbox{y}}_i,p_k)+u_b+e_b\mbox{ }[\mbox{the}\mbox{\;}\mbox{Random}\mbox{\;}\mbox{Effects}\mbox{\;}\mbox{Model}](\mbox{RM}\mbox{\;}\mbox{hereafter})</math>
+| <math>lnC_b=f(\boldsymbol{\mbox{y}}_i,p_k)+u_b+e_b\mbox{ }[\mbox{the}\mbox{ }\mbox{Random}\mbox{ }\mbox{Effects}\mbox{ }\mbox{Model}](\mbox{RM}\mbox{ }\mbox{hereafter})</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (1.6)
@@ Line 186: / Line 186: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>\mbox{ln}\mbox{\;}C_{bt}^\ast ={\rho }_b+f(y_b,p_k)+</math><math>u_{bt}^{\bullet }\mbox{ }[\mbox{the}\mbox{\;}\mbox{TRUE}\mbox{\;}\mbox{Fix}\mbox{\;}\mbox{Effects}\mbox{\;}\mbox{Model}](\mbox{TRUE}\mbox{\;}\mbox{FM}\mbox{\;}\mbox{hereafter})</math>
+| <math>\mbox{ln}\mbox{ }C_{bt}^\ast ={\rho }_b+f(y_b,p_k)+</math><math>u_{bt}^{\bullet }\mbox{ }[\mbox{the}\mbox{ }\mbox{TRUE}\mbox{ }\mbox{Fix}\mbox{ }\mbox{Effects}\mbox{ }\mbox{Model}](\mbox{TRUE}\mbox{ }\mbox{FM}\mbox{ }\mbox{hereafter})</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (1.8)
 |}
-By this device, the underlying data to which we will fit the fixed effects model are actually generated by an underlying mechanism that exactly satisfies the assumptions of the TRUE fixed effects stochastic frontier model. Additionally, the model is based on a realistic configuration of the right-hand side variables. Each replication, ''r  '', is then produced by generating a set of disturbances <math display="inline">e_{bt}C_{bt}^\ast ={\rho }_b+f(y_b,p_k)+u_{bt}^\ast </math> from the normal distribution, with mean 0 and standard deviation. The data that enter each replication of the simulation are then <math display="inline">lnC_{bt}(r)=lnC_{bt}^\ast +e_{bt}^\ast (r)</math>. The estimation was replicated 100 times to produce the sampling distributions. We computed the sampling error in the computation of the inefficiency for each of the 96 observations in each replication, <math display="inline">du_{bt}(r)=estimation\mbox{\;}u_{bt}(r)-u_{bt}^\ast </math>. The values are not scaled, as these are already measured as percentages (changes in log cost); we analyse the raw deviations, <math display="inline">du_{bt}(r)</math>. The mean of these 96 deviations is computed for each of the 100 replications ([[#bib0100|Greene, 2005]]).
+By this device, the underlying data to which we will fit the fixed effects model are actually generated by an underlying mechanism that exactly satisfies the assumptions of the TRUE fixed effects stochastic frontier model. Additionally, the model is based on a realistic configuration of the right-hand side variables. Each replication, ''r  '', is then produced by generating a set of disturbances <math display="inline">e_{bt}C_{bt}^\ast ={\rho }_b+f(y_b,p_k)+u_{bt}^\ast </math> from the normal distribution, with mean 0 and standard deviation. The data that enter each replication of the simulation are then <math display="inline">lnC_{bt}(r)=lnC_{bt}^\ast +e_{bt}^\ast (r)</math>. The estimation was replicated 100 times to produce the sampling distributions. We computed the sampling error in the computation of the inefficiency for each of the 96 observations in each replication, <math display="inline">du_{bt}(r)=estimation\mbox{ }u_{bt}(r)-u_{bt}^\ast </math>. The values are not scaled, as these are already measured as percentages (changes in log cost); we analyse the raw deviations, <math display="inline">du_{bt}(r)</math>. The mean of these 96 deviations is computed for each of the 100 replications ([[#bib0100|Greene, 2005]]).
 We first need to specify a relationship (function) between bank production and bank cost in order to estimate the inefficiency ''u''<sub>''b''</sub> and random ''e''<sub>''b''</sub> factors of the composite <math display="inline">{\epsilon }_b</math> error term. To that end, we specify banks as multi-product and multi-input firms and estimate the following translog cost function:
@@ Line 267: / Line 267: @@
 <span id='sec0020'></span>
 ==4. Data and definition of variables==

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