A First Tutorial in Stata
Stan Hurn
Queensland University of Technology
National Centre for Econometric Research
www.ncer.edu.au
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Table of contents
1
Preliminaries
2
Loading Data
3
Basic Descriptive Statistics
4
Basic Plotting
5
Simple Data Manipulation
6
Simple Linear Regression
7
Using do files
8
Some Regression Examples
Electricity Data
California Schools Data
Food Expenditure and Income
9
Instrumental Variables Estimation
Wage Data
Artificial Data
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Preliminaries
Stata
Stata is a fast, powerful statistical package with
smart data-management facilities,
a wide array of up-to-date statistical techniques,
and an excellent system for producing publication-quality graphs
The bad news is that Stata is NOT as easy to use as some other statistical
packages, but Version 12 has got a reasonable menu-driven interface. On the
whole the advantages probably outweigh the steepness of the initial learning curve.
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Preliminaries
Stata Resources
One of the major advantages to using Stata is that there are a large number of
helpful resources to be found. For example:
a good web-based tutorial can be found at
http://data.princeton.edu/stata/default.html
a useful introductory book is
An Introduction to Modern Econometrics Using Stata by Christopher F. Baum
published by Stata Press in 2006
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Preliminaries
The Stata 12 Front End for Mac
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Preliminaries
The Stata 12 Front End for Windows
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Preliminaries
Stata 12 Front End
Stata has an menu bar on the top and 5 internal windows.
The main window is the one in the middle (1 on the previous slide). It gives
you the all output of you operations in Stata.
The Command window (2) executes commands. You can type commands
directly in this window as an alternative to using the menu system.
The Review window (3), lists all the operations preformed since opening
Stata. If you click on one of your past commands, you will see the command
being displayed in the Command window and you can re-run it by hitting the
enter key.
The Variables window (4) lists the variables in the current dataset (and their
descriptions). When you double-click on the variable, it appears in the
Command window.
The Properties window (5) gives information about your dataset and your
variables.
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Preliminaries
Changing the Working Directory
To avoid having to specify the path each time you wish to load a data file or
run a Stata program (saved in a ”do” file), it is useful to changed the
working directory so that Stata looks in the directory that you are currently
working in.
Click File – Change Working Directory
Browse for the correct directory and select it.
The result is printed out in the Results window and the appropriate Stata
command is echoed in Review window enabling you to reconstruct a ”do”
file of you session.
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Loading Data
Loading an Existing Stata File
Simply click File – Open and browse for an existing Stata data file.
Stata data files have extensions dta.
Open the file food.dta. You will note that two variables food exp and
income appear in the Variables window of the Stata main page.
In the Properties window you will see the filename food.dta together with
some information about the file. This file has 2 variables, each with 40
observations and the size of the file in memory is also given.
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Loading Data
Loading an Excel File
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Loading Data
Loading an Excel File
Load the Excel file US Macroeconomic Data.xls
Click File – Import – Excel Spreadsheet
Browse for the correct file in the working directory and open it.
Remember to check the radio button asking if you want to use the first row
as variable names.
Changes variable names in Stata is something of a mystery when using the
Menu. But using the command window is easy enough.
rename oldname newname
will do the trick. Try it.
NOTE Case matters: if you use an uppercase letter where a lowercase letter
belongs, or vice versa, an error message will display.
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Loading Data
Loading a CSV File
Load the CSV file taylor.csv which contains data on the output gap, the
inflation gap and the Federal Funds rate for the period 1961:Q1 to 1999:Q4.
Click File – Import – Text data created by a spreadsheet
Browse for the file and load it. You should have data on the variables ffr, infl
and ygap.
To specify this as time series data we need a series of dates. The date vector
(called ”year”) is created using the following commands
generate year = tq(1961q1) + _n-1
To make sure Data understands that this is a time series data set we need to
tell it to use ”year” as the date vector. The command is
tsset year, quarterly
The Stata menu command is to do this is found on the next slide.
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Loading Data
Assigning a Date Vector
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Basic Descriptive Statistics
Summary Statistics
Reload the file food.dta.
Now click Statistics and then choose
Summaries, tables, and tests – Summary and descriptive statistics.
Sometimes it is useful to have a look at the histogram of the data. Click
Graphics – Histogram and experiment with some of the options.
Another useful visual tool is the box plot. Click Graphics – Box plot
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Basic Plotting
Simple Scatter
Click File – Open and browse for food.dta. This is a Stata data file.
Click Grahics – Twoway and create a simple scatter plot of weekly food
expenditure versus weekly income.
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Basic Plotting
Time Series Plots
Let’s work through a simple example to construct a plot of the Australian business
cycle.
Click File – Import – Excel Spreadsheet and use the first row as variable
names. This will give you a variable gdp.
Make a time series data set by creating a quarterly date vector from 1959:Q2
to 1996:Q1 and make a time-series data set using dates as the time vector.
The commands are
generate dates = tq(1959q2) + _n-1
tsset dates, quarterly
Plot the data.
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Basic Plotting
Australian GDP
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Simple Data Manipulation
Data Transformations
Stata’s basic commands for data transformation are generate and replace.
generate creates a new variable.
replace modifies an existing variable.
Both commands are accessed via the Data menu item on the main Stata
toolbar.
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Simple Data Manipulation
generate and replace
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Simple Data Manipulation
Growth rate of Australian GDP
Create a growth rate of gdp using the L. operator (lag operator)
generate g = log(gdp)-log(L1.gdp)
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Simple Data Manipulation
Australian Business Cycle
While the plot of the growth rate of gdp is more informative than a plot of the
level of the series, yet more information can be obtained by smoothing g.
generate bcycle = (L3.g+L2.g+L1.g+g+F1.g+F2.g+F3.g )/7
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Simple Data Manipulation
Load the food data set
1
Make sure you are in the right working directory (File – Change Working
Directory)
2
Load the dataset in food.dta and look at the data characteristics.
3
You can experiment using Statistics – Summaries, tables, and tests –
Summary and descriptive statistics but it is simpler to issue the following
commands from the command window.
describe
list
browse
summarize
summarize food exp, detail
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Simple Data Manipulation
Simple scatter plots
1
Use Grahics – Twoway to create a simple scatter plot of weekly food
expenditure versus weekly income.
2
Issue the command
twoway (scatter food exp income)
3
Issue the command
twoway (scatter food exp income), title(Food Expenditure Data)
4
Issue the command
twoway (scatter food exp income) (lfit food exp income), title(Fitted
Regression Line)
The line of best fit is obtained by linear regression of food expenditure on income.
We will now explore this in more detail.
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Simple Linear Regression
A First Regression
1
Load the data set caschool.dta.
2
Run a regression of the test scores, testscr , against the student-teacher ratio,
str . You do this by selecting Statistics – Linear models and related –
Linear regression.
3
A dialogue box will pop up which will require you to fill in the dependent and
independent variable.
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Simple Linear Regression
Regression dialogue box
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Simple Linear Regression
Regression Results
Stata reports the regression results as follows:
The regression predicts that if class size falls by one student, the test scores will
increase by 2.28 points.
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Simple Linear Regression
Predicted Values and Residuals
A common task after running a regression is storing the fitted values, yb, or the
b. Here you must become familiar with the very useful Statistics –
residuals, u
Postestimation menu. One option to select is Predictions, residuals, etc which
gives the dialogue box
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Simple Linear Regression
Predicted Values and Residuals
1
Note that the names you choose for the predicted values and/or residuals
cannot already be taken. Use something obvious like yfit or yhat for the
fitted values and res or uhat for the residuals.
2
You can also use the Postestimation option to obtain confidence intervals
for the prediction using the option Standard errors of the prediction. Save
this as yhatci. The commands
. gen yhatu = yhat+1.96*yhatci
. gen yhatl = yhat - 1.96*yhatci
will now generate a 95% confidence interval for the prediction.
3
To be more precise you could use the t-distribution rather than hard-code
1.96. The commands are
. gen ttail = invttail(e(df_r),0.975)
. gen yhatu = yhat+ttail*yhatci
Note that e(df_r) is the way Stata stores the degrees of freedom for the
residuals and invtttail computes the relevant critical value from the
t-distribution.
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Simple Linear Regression
Predictions with 95% Confidence Interval
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Simple Linear Regression
Out-of-sample Prediction
Obtaining out-of-sample predictions is a bit clunky and using the command line is
probably the way to go. Suppose there are 40 observations in the data sample and
you want to obtain an out-of-sample prediction for a value of the explanatory
variable income = 20. The code is
// add observation to data file
edit
set obs 41
replace income=20 in 41
// obtain prediction
predict yhat0
list income yhat0 in 41
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Simple Linear Regression
You should explore other visualisation options
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Using do files
Using do files
A nice thing about Stata is that there is a simple way to save all your work steps
so you or others can easily reproduce your analysis.
The way to do so is using a so-called do file.
Remember that all Stata does is to execute commands, which you either
clicked on using the menu or directly typed in the Command window.
A command is just one line of text (or code). If you want to save this
command for later use, just copy it (simply click on it in the Review window
and copy the line of text that comes up in the Command window) and paste
it into the do file.
The next slides describe how you can open and use a do file.
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Using do files
Where to open a new do file
You can open a new do file by clicking on the “New Do file Editor” button below
the menu (or press Ctrl+9):
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Using do files
Using a do file
A do file is just a list of commands. Each command has to start with a new line.
Normally you will start your do file telling it which data to load in the first line. In
the following lines you can then include analysis commands. If you leave a row
empty – no problem. If you want to write comments or text, which are not Stata
code, you have to start the row with // or a * symbol; using these symbols tell
Stata that this line is not to be executed.
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Using do files
Executing commands with a do file
If you want to re-run a command from the do file, just highlight the line and press
the “Execute (do)” button (or press Ctrl+d). If you don’t mark any specific line,
Stata will run all the commands in the do file you have currently opened from first
to last. The results of the command(s) are displayed in the main view as if you
were using the menu.
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Some Regression Examples
Electricity Data
Demand for Residential Electricity
The Excel file elecex.xls has quarterly data on the following variables from
1972:02 to 1993:04.
RESKWH
NOCUST
PRICE
CPI
INCOME
CDD
HDD
POP
=
=
=
=
=
=
=
=
electricity sales to residential customers (million kilowatt-hours)
number of customers (thousands)
electricity tariff (cents/kwh)
consumer price index
nominal personal income (millions of dollars)
cooling degree days
heating degree days
population (thousands)
Import the data into Stata using the Import wizard. Take care to check the Radio
Button asking whether or not to treat the first row as variable names! Once done
you can save this as elecex.dta for your own convenience.
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Some Regression Examples
Electricity Data
Time Series Data
Most multiple regression exercises involve data manipulation. This is where
writing ”do” files is a powerful way of ensuring that you can recover your previous
work and others can reproduce it.
1
This is time series data, so we need to create a date vector set dates as the
date vector.
generate dates = tq(1972q2) + _n-1
tsset dates, quarterly
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Some Regression Examples
Electricity Data
Data Manipulations
1
Generate the dependent variable:
gen LKWH=log(RESKWH/NOCUST)
2
We want to explain this demand in terms of real per capita income so create
the variable
gen LY=log((100\ast INCOME)/(CPI\ast POP))
3
Another important determinant is price — we want to use the real average
cost of electricity
gen LPRICE=log(100 \ast PRICE/CPI)
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Some Regression Examples
Electricity Data
Getting a Feel for the Data
You should always try to understand your data before beginning to model it. A
useful starting point is the Graphics – Scatterplot matrix option. As the name
suggests this creates a matrix of scatterplots of the variables against each other.
Hopefully this reveals some pattern to the relationships between the dependent
and explanatory variables and no discernible pattern between the explanatory
variables themselves.
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Some Regression Examples
Electricity Data
Matrix Plots
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Some Regression Examples
Electricity Data
Regression Results
The results from running the linear regression of the base model of demand on
price, income and the weather variables are as follows:
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Some Regression Examples
Electricity Data
ACF and PACF
This is time series data, so one of the problems may be autocorrelation in the
residuals. The autocorrelation function and partial autocorrelation function of the
residuals look as follows
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Some Regression Examples
Electricity Data
AR(1) Estimation Options
The following dialogue box under the Time Series Prais-Winstein regression allows
you to correct for autocorrelation in the residuals.
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Some Regression Examples
Electricity Data
AR(1) output
The results from running the linear regression of the AR(1) model of demand on
price, income and the weather variables are as follows:
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Some Regression Examples
California Schools Data
California Test Score Data
1
Load the file caschool.dta.
2
Run the regression relating test scores to the student teacher ratio
testscr = β0 + β1 str + u
3
The concern is that this equation suffers omitted variable bias which we can
correct using multiple regression. Try relating test scores to the student
teacher ratio and the percentage of English learners
testscr = β0 + β1 str + β2 el pct + u
Note that the size of the effect of str is halved!
4
Now try adding expenditure per student to the regression
testscr = β0 + β1 str + β2 el pct + β3 expn stu + u
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Some Regression Examples
California Schools Data
Presenting Results
This exercise has shown that the coefficient on str in the simple two variable
model is biased. But the question remains as to how to present this in a
reasonable way so that we can see the pattern immediately. The answer is to store
the results of the regressions and then to use Stata’s Postestimation menu item
to help organise the presentation of the results.
Unfortunately this is going to involve estimating the regressions again and then
using
Statistics – Postestimation – Manage estimation results – Store in memory
After each estimation you will need to name your model. Lets be original and call
them Model1, Model2 and Model3. As you do this, watch how Stata echoes your
command and think how easy it would be to use a ”do” file instead.
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Some Regression Examples
California Schools Data
Table of Estimation Results 1
Show the results: estimates table Model1 Model2 Model3
Here both coefficients and standard errors of the various models are summarised
in an accessible way and the reduction in the significance of str is clear.
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Some Regression Examples
California Schools Data
Table of Estimation Results 2
Further detail on the results: estimates table Model1 Model2 Model3,
star(.05 .01 .001)
This is a particularly useful way of summarising the results as the significant
coefficients are marked. Note how str is insignificant in Model 3. Essentially the
t-tests on the individual coefficients are interpreted for you!!
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Some Regression Examples
California Schools Data
Joint Significance Test
Now let’s test the hypothesis that both str and exp stu are zero.
The tests are to be found at:
Statistics – Postestimation – Tests – Test linear hypotheses
Obviously you are going to have to give Stata some information on which
coefficients you wish to test. Once you have selected Test linear hypotheses,
click on Create and the following dialogue box with appear.
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Some Regression Examples
California Schools Data
Testing Joint Hypotheses
The result shows that the p-value of the F-test of the joint hypothesis that
β1 = β3 = 0 is 0.0004 so we would reject the null hypothesis. At least one of str
and exp stu is a significant factor in the regression.
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Some Regression Examples
California Schools Data
Testing Joint Hypotheses for Windows
The result shows that the p-value of the F-test of the joint hypothesis that
β1 = β3 = 0 is 0.0004 so we would reject the null hypothesis. At least one of str
and exp stu is a significant factor in the regression.
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Some Regression Examples
Food Expenditure and Income
Food Data Set
Study the relationship between food expenditures and income
reg food exp income and plot residuals
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Some Regression Examples
Food Expenditure and Income
Functional Form
It may be that a linear relationship between food expenditures and income is
not a good choice.
Let us try to fit a linear - log model.
food exp = β0 + β1 ln(income) + u
Unfortunately Stata doesn’t recognise ln(income) and you have to generate a
new variable, say
gen lincome = log(income)
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Some Regression Examples
Food Expenditure and Income
Fitted Values
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Some Regression Examples
Food Expenditure and Income
Elasticities
Now you can calculate the percentage change in food expenditure given a 1
percent change in income using the marginal effects options on the
Postestimation menu.
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Instrumental Variables Estimation
Wage Data
Wage Data
This example looks at wage data. The datafile is mroz.dta and the focus is on
modelling the wage of married women only. The variables that are important are
as follows:
educ
= years of schooling
wage
= estimated wage from earns., hours
motheduc = mothers years of schooling
fatheduc
= fathers years of schooling
exper
= actual labor mkt exper
lfp
= 1 if in labor force, 1975
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Instrumental Variables Estimation
Wage Data
Estimating a Wage Equation
Suppose we wish to estimate the equation that relates wages to education and
experience:
ln(wage) = β0 + β1 educ + β2 exper + β3 exper 2 + ut .
The problem is that educ may be correlated with u because it is an imperfect
proxy for ”ability” and that using OLS may therefore result in biased coefficient
estimates.
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Instrumental Variables Estimation
Wage Data
OLS Results
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Instrumental Variables Estimation
Wage Data
The IV Estimator
We can now try estimate the regression by IV using mothereduc as an instrument
for educ. A mother’s education does not itself belong in the daughter’s wage
equation, but it is reasonable to propose that more educated mothers are more
likely to have educated daughters.
Click Statistics – Edogenous Covariates – Single-equation
instrumental-variables estimator
This sequence will open a Dialogue Box which will prompt for more
information like
1
2
dependent variable, independent variables, endogenous variables and
instrumental variables;
other options for the constant and standard error correction etc.
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Instrumental Variables Estimation
Wage Data
The IV Estimator
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Instrumental Variables Estimation
Wage Data
IV Results
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Instrumental Variables Estimation
Wage Data
Some Observations
1
Although not shown here mothereduc is highly significant in the first-stage
regression of the IV estimation indicating it is a strong instrument for educ.
2
The estimated return to education is about 10% lower than the OLS
estimate. This is consistent with our earlier theoretical discussion that the
OLS estimator tends to over-estimate the effect of a variable if that variable
is positively correlated with the omitted factors present in the error term.
3
The standard error on the coefficient on educ is over 2.5 times larger than
the standard error on the OLS estimate. This reflects the fact that even with
a good instrument the IV estimator is not efficient. Of course this situation
can be remedied slightly by adding more valid instruments for educ.
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Instrumental Variables Estimation
Artificial Data
The Data
The datafile is ivreg2.dta contains 500 artificially generated observations on x, y ,
z1 and z2 . The variable y is generated as
y t = β0 + β1 x t + e t ,
β0 = 3, β1 = 1
with
x ∼ N(0, 2) ,
e ∼ N(0, 1) , cov(x, e) = 0.9 .
Note that
ρz1 ,x = 0.5
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Instrumental Variables Estimation
Artificial Data
Summary of Estimation Results
Table was generated by using the Postestimation menu option to store results
and create a table.
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Instrumental Variables Estimation
Artificial Data
Hausman Test
To Implement the Hausman test assuming that you have stored the output from
the IV and OLS regressions you click
Postestimation – Tests – Hausman specification test
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Instrumental Variables Estimation
Artificial Data
Hausman Test
This indicates a strong rejection of the null hypothesis of exogeneity — indicating
that cov(x, u) 6= 0 — which we know to be true by construction.
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