代做ECN6540、代写Java，c++编程语言

日期：2024-01-24 10:00

ECN6540  ECN6540 1

Data Provided:

Mathematical, Statistical and Financial Tables for the Social Sciences (Kmietowicz

and Yannoulis).

DEPARTMENT OF ECONOMICS Autumn Semester 2022/23

ECN6540 Econometric Methods

Duration: 2? Hours

Maximum 1500 words excluding equations

The answers to the questions must be type-written. The preference is that

symbols and equations should be inserted into the document using the

equation editor in Word. Alternatively, they can be scanned and inserted as an

image (providing it is clear and readable).

There are two questions, firstly on microeconometrics and secondly on

macroeconometrics. ANSWER ALL QUESTIONS. The marks shown within each

question indicate the weighting given to component sections. Any calculations

must show all workings otherwise full marks will not be awarded.

ECN654540 2

MICROECONOMETRICS

1. The non-mortgage debt behaviour of individuals is modelled using UK

cross sectional data for 2017 from Understanding Society based upon

11,470 employees. The table below describes the variables in the data.

Variable Definitions

-----------------------------------------------------------------------------------------------------

debtor = 1 if has any non-mortgage debt, 0 otherwise

debt_inc = debt to income ratio (outstanding debt ? annual income)

work_fin = 1 if employed in financial sector, 0 otherwise

lincome = natural logarithm of income last month

ghealth = 1 if currently in good or excellent health, 0 otherwise

sex = 1 if male, 0=female

degree = 1 if university degree, 0 = below degree level education

lsavinv_inc = natural logarithm of saving & investment annual income

age = age of individual in years

agesq = age squared

-----------------------------------------------------------------------------------------------------

a. The following Stata output shows an analysis of modelling the probability that

an individual holds non-mortgage debt using a Logit regression.

logit debtor ib(0).work_fin##c.lincome ghealth sex degree age lsavinv_inc

Logistic regression Number of obs = 11,470

LR chi2(8) = 546.50

Prob > chi2 = 0.0000

Log likelihood = -7067.5606 Pseudo R2 = 0.0372

----------------------------------------------------------------------------------

debtor | Coefficient Std. err. z P>|z| [95% conf. interval]

-------------------+--------------------------------------------------------------

1.work_fin | 5.43774 1.271821 4.28 0.000 2.945017 7.930462

lincome | .4584589 .0384631 11.92 0.000 .3830726 .5338451

|

work_fin#c.lincome |

1 | -.6710698 .1587322 -4.23 0.000 -.9821792 -.3599604

|

ghealth | -.0796141 .0413548 -1.93 0.054 -.160668 .0014398

sex | -.0084802 .0433091 -0.20 0.845 -.0933645 .0764041

degree | .0795525 .0462392 1.72 0.085 -.0110748 .1701797

age | -.0316432 .0020753 -15.25 0.000 -.0357106 -.0275757

lsavinv_inc | -.0819022 .0085226 -9.61 0.000 -.0986062 -.0651983

_cons | -2.638081 .2870575 -9.19 0.000 -3.200703 -2.075458

----------------------------------------------------------------------------------

ib(0).work_fin##c.lincome is an interaction effect between a binary

and continuous variable. Summary statistics on variables used in the analysis

are provided below.

sum ib(0).work_fin##c.lincome ghealth sex degree age lsavinv_inc

Variable | Obs Mean Std. dev. Min Max

-------------+---------------------------------------------------------

1.work_fin | 11,767 .0398572 .195632 0 11

lincome | 11,767 7.650333 .6965933 .0861777 9.847781

work_fin#|

c.lincome 1 | 11,767 .3197615 1.574852 0 9.72120

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ghealth | 11,767 .5457636 .4979224 0 1

sex | 11,767 .4812612 .49967 0 1

degree | 11,767 .3192827 .4662186 0 1

age | 11,767 44.43885 10.39257 18 65

lsavinv_inc | 11,767 1.857315 2.600682 0 11.51294

-------------+---------------------------------------------------------

i) What do the coefficients of work_fin, lincome and the interaction

term imply? Explain whether the estimates can be interpreted.

ii) Showing your calculations in full, find the marginal effects evaluated

at the mean from the above output.

iii) Provide an economic interpretation of the marginal effects found in

(a(ii)).

iv) Given the pseudo R-squared what is the value of the constrained

log likelihood function? Show your calculation.

[10 marks]

[25 marks]

[10 marks]

[5 marks]

b. There is also information on the amount of debt held as a proportion of

income. This outcome is modelled using the Heckman sample selection

estimator. The Stata output is shown below.

heckman debt_inc age agesq sex degree lsavinv_inc,

select(debtor = ib(0).work_fin##c.lincome ghealth sex degree age lsavinv_inc)

Heckman selection model Number of obs = 11,470

Wald chi2(5) = 249.22

Log likelihood = -13437.59 Prob > chi2 = 0.0000

------------------------------------------------------------------------------------

| Coefficient Std. err. z P>|z| [95% conf. interval]

-----------------------+------------------------------------------------------------

debt_inc |

age | -.1341474 .0629505 -2.13 0.033 -.2575282 -.0107667

agesq | .0003505 .0001265 2.77 0.006 .0001026 .0005985

sex | .1517503 .0607726 2.50 0.013 .0326382 .2708623

degree | .157981 .0661602 2.39 0.017 .0283095 .2876525

lsavinv_inc | .1130368 .0124696 9.06 0.000 .0885968 .1374767

_cons | 9.727016 .2615992 37.18 0.000 9.214291 10.23974

-----------------------+------------------------------------------------------------

debtor |

1.work_fin | 1.130109 .3719515 3.04 0.002 .4010974 1.85912

lincome | .2965059 .0113274 26.18 0.000 .2743045 .3187072

|

work_fin#c.lincome |

1 | -.1360006 .0461592 -2.95 0.003 -.2264709 -.0455303

|

ghealth | -.0106065 .0106393 -1.00 0.319 -.0314592 .0102462

sex | -.0488734 .0236997 -2.06 0.039 -.095324 -.0024229

degree | -.0369117 .0256652 -1.44 0.150 -.0872146 .0133912

age | -.016944 .0011782 -14.38 0.000 -.0192532 -.0146349

lsavinv_inc | -.0468348 .0047518 -9.86 0.000 -.0561482 -.0375214

_cons | -1.828795 .0961843 -19.01 0.000 -2.017312 -1.640277

-------------------+----------------------------------------------------------------

lambda | -2.579767 .039169 -2.656537 -2.502997

--------------------------------------------------------------------------------

i) Interpret the estimates in the outcome equation.

ii) In the context of the above Stata output what does the estimate of

the inverse Mills ratio (lambda) suggest? What does lambda

provide an estimate of in terms of the theory?

[5 marks]

[15 marks]

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c.

iii) What assumption has been made about the covariates

work_fin, lincome and ghealth in the treatment equation?

What are the implications if these assumptions are not met? Are

they individually statistically significant? If these variables are also

included in the outcome equation explain whether the model is

identified or not.

In the context of the above application the following figure shows the

distribution of debt as a proportion of annual income.

Describe a situation in which a Tobit specification would be the preferred

modelling choice rather than a sample selection approach. What

assumptions would the Tobit modelling approach have to make with

regard to the   treatment   and   outcome   equations?

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ECN6540 5

MACROECONOMETRICS

2. a.

The following Stata output is based upon modelling aggregate

savings as a function of Gross Domestic Product (GDP), both

measured in constant prices, over time () using data for the U.S.

over the period 1960 to 2020. The savings function is a double

logarithmic specification as follows:

log = 0 + 1log +

Where log is the natural logarithm of savings and log is the

natural logarithm of GDP. The Stata output also shows the results

of ADF tests for savings and GDP. Note that in the output L

denotes a lag and D a difference.

regress logS logY

Source | SS df MS Number of obs = 61

-------------+------------------------------ F( 1, 59) = 180.39

Model | 29.3601715 1 29.3601715 Prob > F = 0.0000

Residual | 9.6029125 59 .162761229 R-squared = 0.7535

-------------+------------------------------ Adj R-squared = 0.7494

Total | 38.963084 60 .649384734 Root MSE = .40344

------------------------------------------------------------------------------

logS | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

logY | 1.16096 .0864398 13.43 0.000 .9879948 1.333926

_cons | -4.007335 .6861211 -5.84 0.000 -5.38026 -2.63441

------------------------------------------------------------------------------

Durbin-Watson d-statistic( 2, 61) = .7252386

predict e, resid

i) Interpret the OLS results. Explain whether the analysis is likely

to be spurious?

ii) What do the results of the ADF tests on savings and GDP imply

at the 5 percent level? Show the test statistic used, the null

hypothesis tested and the appropriate critical value.

iii) Explain whether savings and GDP are cointegrated at the 5

percent level. Explicitly state the null hypothesis, show

algebraically the estimated test equation based upon the

output, and provide the appropriate critical value.

dfuller logS, lag(4) regress

Augmented Dickey-Fuller test for unit root Number of obs = 56

------------------------------------------------------------------------------

D.logS | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

logS |

L1. | -.129875 .0534553 -2.43 0.019 -.2372431 -.0225069

LD. | .2335003 .099153 2.35 0.022 .0343457 .4326549

L2D. | .1939032 .0807975 2.40 0.020 .0316167 .3561897

L3D. | -.0834007 .0858594 -0.97 0.336 -.2558545 .089053

L4D. | -.2258198 .0784568 -2.88 0.006 -.3834049 -.0682348

cons | .7246592 .2840536 2.55 0.014 .1541207 1.295198

------------------------------------------------------------------------------

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dfuller logY, lag(4) regress

Augmented Dickey-Fuller test for unit root Number of obs = 56

------------------------------------------------------------------------------

D.logY | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

logY |

L1. | -.0175739 .0092468 -1.90 0.063 -.0361467 .000999

LD. | .4530274 .1290377 3.51 0.001 .1938476 .7122072

L2D. | -.0699222 .1306402 -0.54 0.595 -.3323208 .1924765

L3D. | -.1351664 .1297451 -1.04 0.303 -.3957672 .1254344

L4D. | -.1774947 .1177561 -1.51 0.138 -.4140149 .0590255

_cons | .1720878 .076104 2.26 0.028 .0192285 .3249471

------------------------------------------------------------------------------

dfuller e, lag(4)

Test Statistic

----------------------------

Z(t) -4.042

----------------------------

b. Explain why the Johansen approach to cointegration may be

preferable to the Engle-Granger two step approach, in each of the

following two scenarios:

i) In the above example (part a) when there are variables in the

model, i.e. = 2?

ii) When ?3. In this scenario what is the maximum number of

cointegrating vectors?

c. A researcher has modelled the relationship between personal

consumption expenditure and the money supply as measured by

M2 based upon a double logarithmic specification as follows:

log() = 0 + 1log(2) +

They then build a dynamic forecast of consumption. Two

alternative models are estimated over the period 1969q1 through

to 2008q4: Model 1 an ARIMA(1,1,2) and Model 2 an

ARIMA(1,1,1). Then the researcher forecasts out of sample

through to 2010q3. The results are shown below along with

diagnostic statistics.

i) Based upon the output below for the ARIMA(1,1,1) model draw

both the ACF and PACF for the AR and MA components.

ii) Explain whether the models are stationary and invertible, along

with any potential implications.

iii) Explain in detail which of the above two models is preferred

and why. Outline any further analysis you may want to

undertake giving your reasons.