Econometrics Flashcards
(196 cards)
1
Q
LLN?
A
Law of large numbers - As the sample size increases, the sample mean will converge to the population mean.
2
Q
CLT?
A
Central Limit Theorem - As the sample size increases, the sample converges to a normal distribution.
3
Q
I.I.D?
A
Independent and identical distribution.
4
Q
What does stochastic mean?
A
It is used to signify that a variable picked is random.
5
Q
Why are time series data considered random even thought they are picked at a specific time?
A
Because any change in history could have altered the realised value of the process. By this logic, every realised value is therefore random.
6
Q
Temporal ordering?
A
The ordering of the values is based on the time period.
7
Q
Contemporaneous meaning?
A
Existing at or occurring in the same period of time
8
Q
Why do we sometimes use the term ‘static model’ when referring to time series
A
We are modelling a contemporaneous relationship between y and z, using a certain time as the base year for example and representing changes from this base.
9
Q
How should we therefore think of time randomness in time series? (1. outcomes, 2. time series, 3. sample)
A
The outcomes of economic variables are uncertain, they should therefore be modelled as random variables. Time series are sequences of random variables (= stochastic process). A sample is the one realised path of the time series out of the many possible paths the stochastic process could have taken.
10
Q
FDL meaning and whether it is a static or dynamic model?
A
A Finite Distributed Lag model is a dynamic model where we allow one or more variables to affect y with a lag.
11
Q
FDL and its orders?
A
The order of the FDL will determine how many lags an impact will have an effect on the aggregate value for. A Lag of three will mean that a value will add to the aggregate y for three periods after its original effect. (see notes for example)
12
Q
What is another name for δ0 (gamma 0) in FDL models and how is it found? What is its meaning?
A
The impact multiplier/ propensity. Found by the difference between y and y. It is the immediate change in y due to a one unit increase in the parameter.
13
Q
What is the LRP or LRM?
A
The Long-run Propensity or Long-Run Multiplier. It is the permanent increase in y given a permanent increase in z.
14
Q
What is the likely reason for z to be omitted?
A
Delta<0> (the impact propensity) = 0.
15
Q
Dependent variable?
A
The y value, the explained variable.
16
Q
Independent Variable?
A
x. The explanatory variable.
17
Q
X (bold) meaning?
A
The collection of all independent variables for all time periods. Useful in time series to think of it as n rocks and k columns.
18
Q
What are the five classical assumptions for time series?
A
TS1: Linear in parameters TS2: No perfect collinearity TS3: Strict Exogeneity TS4: Homoskedasticity TS5: No Autocorrelation
19
Q
TS3 intuitive understanding?
A
Strict exogeneity/ zero conditional mean. Implies that the error at time t is uncorrelated with each explanatory variable in every time period. So the expectation of U at time time, given all X, =0.
20
Q
TS1-TS3?
A
Unbiasedness of the OLS estimator.
21
Q
Contemporaneous Exogeneity intuitive understanding and application to consistency and unbiasedness?
A
The error term at time t is uncorrelated with the explanatory valuables also dated at time t. It implies that u and the explanatory variables are contemporaneously uncorrelated. Contemporaneous exogeneity is all that is needed to prove the OLS estimator is consistent but not enough for unbiasedness.
22
Q
When would TS5 fail and what would be the explanation of failure?
A
The error would suffer from autocorrelation or serial correlation, meaning that say the error in the current period is correlated with the previous period (so if the previous period was positive, the chance of the current period being positive is higher)
23
Q
BLUE?
A
Best in linear unbiased estimators. Requires Gauss Markov Assumption (TS1-TS5).
24
Q
Gauss-Markov Theorem?
A
Under TS1-TS5, the OLS estimators are the best linear unbiased estimators conditional on X.
25
Why are dummy variables useful in time series?
A dummy variable will represent whether, in each time period, a certain event has occurred.
26
Detrending a variable?
Can be done by regressing that variable with a linear time trend and computing its residual. Its fundamental use is create a new variable that trends with time, thereby removing the part of the given independent variable/s trending with time.
27
Why might we want to detrend?
Regressing retreaded variables yield the same slope estimates on x as one would when time trend is added. Generally, if you have a variable that is trending, it is a good idea to add a time trend.
28
A time trending variable?
A variable that appears to increase in time with no reason aside other factor being the causal reason for this
29
Why might exponential time trends be more realistic?
It is often the case that growth is more exponential, whereby it is increasing at an increasing rate.
30
Pareto rule?
80/20 almost natural law. Roughly states that 80% of the effects come from 20% of the causes.
31
Spurious regression problem and how to correct for it?
Occurs when a relationship between two or more trending variables (in time) simply because each is growing over time. Adding a time trend eliminates this problem.
32
When might a time trend variable be added?
If a trend term is statistically significant and the results change in important ways when a time trend is added to a regression
33
Seasonal dummies?
Dummy variables used to alter the dependent variable at certain times of the year..
34
Dummy trap?
Violates 'No perfect correlation'. Occurs when the base year variable isn't omitted in the equation.
35
De-seasonalising the data?
Similar to detrending the data. It makes a new dummy variable to account for seasonal changes in y.
36
Week3....
...
37
When is a time series stationary?
A stationary time series process is one whose probability distributions are stable over time in the following sense: If we take any collection of random variables in the sequence and then shift that sequence ahead h time periods, the joint probability distribution must remain unchanged.
38
What two assumptions does stationaity simplify?
The LLN and CLT.
39
What does stationaity in simple terms have to do with?
The joint distributions of a process as it moves through time. The mean, variance and autocorrelation structure do not change over time.
40
When is a time series weakly dependent?
A time series consisting of elements that are generally less correlated the further away they are from each other. Basically nearly independent, so that correlation between x and x goes to 0 sufficiently quickly as h approaches infinity.
41
Asymptotically uncorrelated?
With respect to weakly dependent time series, stating that as h tends to infinity, the joint correlation between two sets of values along the trend with the same sample size will be uncorrelated. Covariance stationary processes are said to be asymptotically uncorrelated.
42
When is an OLS estimator consistent?
Under assumptions TS.1-TS.3
43
When are OLS estimators asymptotically normal?
Under assumption TS.1-TS.5
44
EMH?
Efficient Market Hypothesis - States that the most recent information contains all that is required to make prediction.
45
Why does it make sense that time series data are weakly dependent/ correlated?
Otherwise all the data would give us no information about future data. This dependence will fall as t approaches infinity though.
46
Noise process?
Just a time series of i.i.d variables. This enables it to be modelled in processes.
47
What would be the assumptions of a MA(1) process?
There will be joint correlation between two observations next to each other in a time series, but any association between variables two or more period apart will be independent. e will be independent across t, meaning, time is independent across t with a more than 1 period difference. Therefore MA(1) is weakly dependent, stationary and the law of large numbers and the central limit theorem can be applied for x.
48
What is the stability condition with regards to an AR process?
The crucial assumption for the weak dependence of AR1. The stability condition would be the |Row| < 1, which intuitively means that -----------
49
When would we determine that a series is nonstationary?
If it violates one of the stationary principle.
50
What are the properties of a covariance stationary process and when is this definition used?
1.E (yt) = 𝛍
2. Var(yt) = 𝛔^2
3. Cov(yt,ys) = Cov(y*t+h*, Y*s+h*).
Used when there is a finite second moment.
51
A stationary stochastic process?
xt has the same distribution for all t. It is identically distributed. The stationarity definition means that the covariance between two sets will be dependent on h.
52
What is stationarity generally?
Involves the joint distributions of a process as it moves through time.
53
Weak dependency?
Assumes that the relationship between x*t* and x*t+h* are 'almost independent' as h increases without a bound.
We assume a series is weakly dependent if the covariance
54
Why is weak dependency important for regression analysis?
It replaces the assumption of random sampling in implying that the LLN and CLT hold.
55
In which way is a time series data expected to be different to cross sectional data?
d) Time series tend to be serially-correlated
56
If β₀ = 0 but β₁ ≠ 0 and/or β₂ ≠ 0, is the model static?
No
57
If β₀ ≠ 0 but β₁ = β₂ = 0, is the model dynamic?
No
58
What is the impact propensity that captures the immediate change in y due to a one-time unit increase in x?
β₀ = 0
59
What is the long-run propensity that captures the permanent change in y due to a permanent unit increase in x?
β₀ + β₁ + β₂
60
What type of exogeneity is sufficient to fulfil the Gauss Markov assumption require on xt?
Strict exogeneity
61
Is it true that contemporaneous exogeneity implies strict exogeneity?
No
62
Is heteroskedasticity of the error term required for Gauss Markov assumption with time series?
Yes
63
Is strict exogeneity necessary for consistent estimation of an OLS estimator?
No, only contemperaneous exogeneity (along with TS1' and TS2')
64
The statement, "An R² is harder to compute with cross sectional data compared to time series data", is
not true
65
Which of the following properties is/are necessary for a time series to be a stationary process {Xt}?
a) E(Xt)=E(Xt+h) for all t,h
b) Var(Xt)=Var(Xt+h) for all t,h
c) Cov(Xt,Xt+h)=Cov(Xs,Xs+h) for all t,s,h
d) All of the above.
a) E(Xt)=E(Xt+h) for all t,h
b) Var(Xt)=Var(Xt+h) for all t,h
c) Cov(Xt,Xt+h)=Cov(Xs,Xs+h) for all t,s,h
d) All of the above.
d
66
Is it true that an autoregressive process of order 1 is stationary?
Cannot say with the given information
67
Is it true that a trend stationary time series is stationary?
No
68
Which processe is the most appropriate for modelling time series that have correlation persistence across a finite number of time periods?
Moving average
69
How is a weakly dependent process similar to a noise process?
Correlations between variables that are far apart in time have either no or weak correlation
70
How is a trend stationary time series similar to a noise process?
They have constant variance
71
Is it true that an autoregressive process of order 1 is asymptotically uncorrelated?
Cannot say with the given information.
72
Is it true that a moving average process of order 1 is asymptotically uncorrelated?
Yes
73
Let {yt} be a time series on stock returns. What does the efficient market hypothesis (EMH) imply?
E(yt|y₁,…,yt-1) = E(yt)
Not:
E(yt|y₁,…,ys) = E(ys) for 1
74
Which of the following regressions may be useful for studying the EMH?
yt = α + βyt-1 + ut
75
ΔYt = 0.513 - 0.106ΔXt + 0.076ΔXt-1
(0.218) (0.437) (0.013)
where ΔXt = Xt - Xt-1 and ΔYt = Yt - Yt-1.
Suppose you are told that the first order autocorrelations for {Yt} and {Xt} are 0.901 and 0.923 respectively. What you may expect to observe if you run a linear regression of Yt on Xt?
The slope parameter is significant and R-squared may be very high
76
ΔYt = 0.513 - 0.106ΔXt + 0.076ΔXt-1
(0.218) (0.437) (0.013)
where ΔXt = Xt - Xt-1 and ΔYt = Yt - Yt-1
What may a regression on first differences instead of levels achieve?
First differences may be weakly dependent
77
ΔYt = 0.513 - 0.106ΔXt + 0.076ΔXt-1
(0.218) (0.437) (0.013)
where ΔXt = Xt - Xt-1 and ΔYt = Yt - Yt-1.
What is the expected permanent change a unit increase in ΔXt has on ΔYt?
-0.03
78
What is the purpose of the Breusch-Godfrey test?
Test if the error terms are correlated to one another
79
What is the first step you need to do to apply the Breusch-Godfrey test?
Perform OLS on all the regressors to obtain the residuals
80
Generally what happens if the error terms in a regression are correlated?
The OLS estimator is both unbiased and consistent
81
What is an argument for applying a Cochrane-Orcutt procedure?
The Cochrane-Orcutt procedure may yield a more efficient estimator than OLS
82
Can you do hypothesis testing with OLS estimators when the error terms are correlated?
Yes, serial correlation-robust standard errors can be used
83
The statement, OLS estimates are harder to compute with cross
sectional data compared to time series data, is
not true
84
Which of the following property is necessary for a time series to be a stationary process fXtg?
a. ) E (Xt) = E (Xt+h) for all t; h
b. ) V ar (Xt) = V ar (Xt+h) for all t; h
c. ) Cov (Xt;Xt+h) = Cov (Xs;Xs+h) for all t; s; h
d. ) All of the above
a.) E (Xt) = E (Xt+h) for all t; h
b.) V ar (Xt) = V ar (Xt+h) for all t; h
c.) Cov (Xt;Xt+h) = Cov (Xs;Xs+h) for all t; s; h
d.) All of the above
All of the above
85
Is it true that an i.i.d. sequence of random variables is stationary?
Yes
86
Is it true that an autoregressive process of order 1 is stationary?
Cannot say with the given information
87
Is it true that a nonstationary time series must be a unit root?
No
88
Is it true that a moving average of order 1 is stationary?
Yes
89
Which of the following processes is the most appropriate for modelling persistence that only lasts for one period?
MA(1)
90
Is it true that a noise process is asymptotically uncorrelated?
Yes
91
Is it true that an autoregressive process of order 1 is asymptotically
uncorrelated?
Cannot say with the given information
92
Is it true that a moving average process of order 1 is asymptotically
uncorrelated?
Yes
93
Is it true that a trend stationary process is asymptotically uncorre-
lated?
Yes
94
Which of the following statement is true about a trend stationary time series?
It is nonstationary
95
Which of the following statement is true about a time series that has
seasonal e¤ects?
It is nonstationary
96
What is the purpose of the Cochrane-Orcutt procedure?
To improve the e¢ ciency on the OLS estimator
97
What is the di¤erence between the Cochrane-Orcutt (CO) and Prais-
Winsten (PW) procedure?
CO omits the
rst observation while PW uses all observations
98
Is the OLS estimator better than the Prais-Winsten estimator?
Cannot say. Depends on sample size
99
What is the
first step you need to do to apply the Breusch-Godfrey
test?
Perform OLS on all the regressors to obtain the residuals
100
What is the
final regression you need to run to apply the Breusch-
Godfrey test?
Regress the residual on its lagged values, as well as the other regres-
sors in the original model
101
Why is it important to perform unit root tests?
Regression involving highly persistent dependent and independent
variables may be spurious
102
How can AR or MA processes be used to measure the covariance structures?
```
AR can be used to model time series that exhibits persistence
that may (or may not!) disperse over time
MA only allow correlations over a
nite time lag
```
103
Persistence?
Persistence intuitively is the reverse of weak dependence
104
Are unit routes, where 𝝆=1, stationary and why. weakly depending?
Will be a non stationary process since variance alters. Not weakly dependent
105
What process is a unit root process?
a persistent time series.
106
spurious correlation?
when two variables are correlated through a
third variable. E.g., if you regress y on x, you may
nd a highly signi
cant relationship but this disappears as soon as you add another variable, say w.
107
Role of the Dickey-Fuller test?
To test for a unit root. Contruct the t-ratio to check for critical values.
108
GLS method?
General Least squares. More efficient estimator than OLS if ut is autocorrelated (TS5 violated).
109
Another name for the Breusch-Godfrey test?
The Lagrange Multiplier (LM) test.
110
OLS vs FGLS?
- OLS is unbiased and inefficient.
- FGLS is biased but more efficient with large sample
- Both estimators are consistent with large sample
- Preference of one over another will depend on the sample size
111
When is OLS not BLUE?
When errors are autocorrelated and inference needs adjusting.
112
How can you detect correlation in the error terms?
The Lagrange multiplier (LM) test.
113
When is estimation still possible with the FGLS?
When the sample size is large enough. With a large sample size FGLS may be better than the OLS estimator.
114
What are the GM assumptions for Time Series?
```
MLR1: Linear in Parameters
MLR2: Random Sampling
MLR3: No Perfect Multicollinearity
MLR4: Zero Conditional Mean on Unobserved Term
MLR5: Homoskedasticity
```
115
When is our OLS estimator unbiased and BLUE for any n?
Under GM 1-5.
116
Lecture 5
- Book and Slides
117
Unbiasedness intuitive meaning?
An estimator is unbiased if we take a random draw of Beta1(HAT) many times, the average is Beta1.
118
Consistency intuitive meaning?
For a single draw of B1,n(HAT) as n tends to infinity, we expect B1,n(HAT) ->Beta1
119
How can you deal with omitted variable bias?
Try to find and use a suitable Proxy variable for the unobserved variable. If not we can try and leave the unobserved result in the error term, and rather than using OLS we use an estimation method that presence of the omitted variable (the method of instrumental variables).
120
If we put a variable in the error term and estimate by OLS, when is the estimate biased and inconsistent?
If the remaining variables in the model being estimated are correlated with the extra variable put into the error term.
121
How would we attain consistent estimators for Beta values if a variable in the model is correlated with the error term?
Instrumental variables.
122
What properties does an instrumental variable for x have, say Z? Also, when combined, what can we say about these with relation to 1?
Z will be an instrumental variable for x, or simply and instrument for x if:
1. Cov(z,u) = 0 (uncorrelated)
2. Cov(z,x) ≠ 0 (correlated)
We also call this instrument exogeneity (from the equation). These allow us to identify the parameter β1.
123
What does instrument exogeneity infer?
That z should have no partial effect on y (after x and omitted variables have been controlled for), and z should be uncorrelated with the omitted variables. So z should only be correlated with the explanatory variable it is an instrument for
124
Endogeneity?
A variable generated by a statistical model that is explained by the relationships between functions within the model.
125
Exogeneity?
An exogenous change is one that comes from outside the model and is unexplained by the model.
126
For the equation:
y = β0 + β1x + u, and given that x is exogenous,
How would you calculate β1?
β1 = Cov(x,y) / Var(x)
127
With y = β0 + β1x + u, say we attain a proxy z, how would we test if z and x are correlated and why would this test be needed?
We can estimate a simple regression between x and z:
x = 𝛌0 + 𝛌1z + v. As 𝛌1 = Cov(z,x)/Var(z), we know that our instrument variable is good only if Cov(z,x) ≠ 0. Thus we reject the null of 𝛌1 = 0 against the alternative if we are at a significantly small significance level.
128
So what is the key difference between proxy variables and instrumental variables?
Instrumental variables are correlated an explanatory variable and not with any unobserved terms. A proxy variable must be highly correlated with the an unattainable or unobserved term, as to best approximate it.
129
What could be some good proxy variables for Ability?
IQ, family background, number of siblings
130
what problem do IV methods tend to solve?
They can be used to solve the errors in variables problem and the problem of endogeneity of one or more explanatory variables.
131
When would we say the xi is endogenous?
When MLR4 is violated, and so Cov(xi, ui) ≠ 0
132
What must be noted about IV estimators in finite samples?
Corr ≠ Corr(hat), so that an IV estimator can be worse than an OLS, especially if Corr(Hat)(zi,xi) is low, meaning it is a weak instrument.
Also an IV estimator will always be biased in finite sample.
133
Inconsistent OLS?
When regressor is endogenous.
134
What Rule is crucial for a consistent OLS?
The Zero conditional mean rule.
135
Lecture 7
-
136
Take the structural equation:
| y1 = β0 + β1y2 + β2z1 + u1. What is the new notation added here?
y used to signify that we think it is correlated with u.
| z used to signify that we think the explanatory variable is exogenous of u.
137
Take the structural equation:
| y1 = β0 + β1y2 + β2z1 + u1. Providing z1 is correlated with y2, can it be used as an instrumental variable for y2?
No, as it already appears as an explanatory variable., thus we need another exogenous variable.
138
Reduced form equation?
We have written an endogenous variable in terms of exogenous variables.
139
What additional assumption must we have when adding more explanatory variables and then creating a reduced form equation?
No perfect linear relationships among the exogenous variables; which is analogous to the assumption of no perfect collinearity in the context of OLS.
140
Suppose for an endogenous variable we have two ways to consistently estimate the corresponding β, what do we then do?
Any combination of instruments is in fact also an instrument, e.g.
a1z1 + a2z2.
2SLS is then used to figure out the best combination.
141
What does 2SLS do and why does this work?
Picks the best linear combination for instruments. If we have multiple IV estimators that wouldn't be efficient, as each one is uncorrelated with u, any linear combination is also uncorrelated with u.
142
What is the process in performing a 2SLS test?
1. Use OLS to regress y2 on 1, z1, z2 to obtain the fitted value y(HAT)2
2. Use to regress y1 on 1, y(HAT)2 to obtain the 2SLS estimators for β0 and β2.
143
How does 2SLS compare to IV?
With one instrument, it is the same, with more it is more efficient.
144
What would we test if we had multiple IVs?
Whether the extra IVs are correlated with the exogenous variable also used to represent y2. If both = 0 we will suffer from perfect collinearity. Thus we use an F-test and make the null that each one =0.
145
How would we generally use 2SLS with multiple variables?
1. Use OLS to regress each endogenous variable in a reduced form equation, and collect the fitted values.
2. Use OLS to regress y on the structural equation with all endogenous variables replaced by their fitted values from stage (1)
146
With 2 instruments, when would we be wasting out time with IV estimation?
If the two instruments are not jointly significant.
147
Order condition?
We need at least as many excluded exogenous variables as there are invoiced endogenous explanatory variables in the structural equation.
148
What is the letter used for the number of endogenous variables and for the number of instruments?
Number of endogenous variables: k
| Number of instruments: q.
149
When is a model just, over or under identified?
k=q, we can just identify the parameters of interest.
If k > q then we cannot identify (under)
If k < q then we can use different instruments, (over)
150
How would you perform a over identification test?
1. Estimate the structural equation using 2SLS and obtain the residuals.
2. Regress the residuals on all exogenous variables to obtain R(SQUARED).
3. Construct a test statistic of the form nR(SQUARED) that has Chi Squared with q - k df distribution, with df equal to the degree of over identification.
151
How would you perform a over identification test?
1. Estimate the structural equation using 2SLS and obtain the residuals.
2. Regress the residuals on all exogenous variables to obtain R(SQUARED).
3. Construct a test statistic of the form nR(SQUARED) that has Chi Squared with q - k df distribution, with df equal to the degree of over identification.
Rejecting the null means at least one of the two instruments is invalid, but not rejecting the null doesn't necessarily mean both instruments are valid.wa
152
Overidentifying restrictions?
Comparing different IV estimates of the same parameter. The idea is that we have more instruments to estimate the parameter than we need.
153
Relevance and endogenous meaning?
Relevance means that the instrument is partially correlated with the explanatory variable.
Exogeneity means that the instrument is uncorrelated with the error term.
154
Reason behind over identification tests.
If we have two instruments for y2, we will be able to estimate the equation twice. If the instruments are both exogenous and relevant, the only difference between the two results will be sampling error. If the estimates are statistically different from each other then we must conclude that either of the instruments or both fail the exogeneity requirement.
155
Where does the Hausman test fail?
Even if both the instruments are similar just by nature of picking them and them haveing a similar outcome,, this may lead to similar estimates despite the instruments being inconsistent.
156
Where does the Hausman test fail?
Even if both the instruments are similar just by nature of picking them and them haveing a similar outcome,, this may lead to similar estimates despite the instruments being inconsistent.
157
Lecture 8
-
158
What are the two endogeneity problems and what can be used to solve them
Measurement error and omitted variables. Instruments can be used to solve these.
159
Simultaneity?
Arises Shen one or more of the explanatory variables is jointly determined with the dependent variable. This basically means that x causes y but y also causes x.
160
SEM?
Simultaneous equation model. Used when we have two structural equations but
161
What would be the problem of using SEM for amount of time studying and amount of time working?
Neither equation can stand on its own as the two endogenous variables are chosen by the same economic agent. The agent will choose these amount of time working and studying simultaneously. Therefore, it makes no sense to specify two equations where each is a function of the other.
162
What must be the case to use and SEM and what then is the purpose of SEMs?
Each equation must have a clear ceteris paribus interpretation. We us SEMs to postulate another relationship, namely one that takes an essentially removes endogenous variables from the two structural equation, making a third equation through substitution that contains only exogenous variable, being the reduced form equation of y2.
163
What bias is present in SEMs and when would this occur?
Simultaneity bias due to the second equation being a function of the first equation, so the error in the second equation will be contained in the first equation when substituted in. There will be bias if y2 is correlated with u1. Therefore using OLS in a simultaneous system lead to biased and inconsistent results.
164
In SEM, what are π12, π22 and V2 commonly known as?
π: Reduced form parameters
| V2: Reduced form error.
165
Is an IV estimator consistent/ inconsistent, biased/unbiased?
An IV estimator is consistent and based.
166
What method do we use to solve the simultaneous equation method with an endogenous variable?
2SLS.
167
What is the difference between using 2SLS in simultaneous equations compared to proxy variables or testing?
We have two structural equations already so can immediately see if we have enough IVs.
168
What does IV stand for?
Instrumental Variable.
169
The identified equation?
The equation that we will be able to us IVs for to get rid of endogenous variables. In the case of simultaneous equations it is the equation that has less z values generally.
170
How does the existence of an unobserved demand shifter affect our results?
It causes us to estimate the demand equation with error, but the editors will be consistent provided z1 is uncorrelated with U2.
171
What prevents identification of a demand or supply curve?
If we do not have nay exogenous observed factors shifting the other equation, which would allow us to trace out the former equation. e.g. if we have an observed exogenous variable in demand, we can trace out the supply curve and vice versa.
172
Structural error terms?
Error terms in a structural equation.
173
When an equation is over/just/under identified, what are the solutions?
Over: Several options f IVS and 2SLS to be used.
Just: IV can be used.
Under: it cannot be generally consistently estimated.
174
Stopped on page 554
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175
Continued
-
176
Strict, sequential and contemporaneous exogeneity in formula.
```
1. Strict exogeneity:
E(ut | X) = 0
2. Sequential exogeneity:
E (ut | x1, . . . , xt ) = 0
3. Contemporaneous exogeneity:
E (ut | xt ) = 0
```
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Asymptotically uncorrelated?
A time series process in which the correlation between random variables at two points in time tends to zero as the time interval between them increases.
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Autoregressive Process of Order One [AR(1)]
A time series model whose current value depends linearly on its most recent value plus an unpredictable disturbance.
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Contemporaneously Exogenous
In time series or panel data applications, a regressor is contemporaneously exogenous if it is uncorrelated with the error term in the same time period, although it may be correlated with the errors in other time periods.
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Contemporaneously Homoskedastic
In time series or panel data applications, the variance of the error term, conditional on the regressors in the same time period, is constant.
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Covariance Stationary
A time series process with constant mean and variance where the covariance between any two random variables in the sequence depends only on the distance between them.
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First Order Autocorrelation
For a time series process ordered chronologically, the correlation coefficient between pairs of adjacent observations.
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Highly Persistent
A time series process where outcomes in the distant future are highly correlated with current outcomes.
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Moving Average Process of Order One [MA(1)]
A time series process generated as a linear function of the current value and one lagged value of a zero-mean, constant variance, uncorrelated stochastic process.
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Nonstationary Process
A time series process whose joint distributions are not constant across different epochs.
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Random Walk
A time series process where next period's value is obtained as this period's value, plus an independent (or at least an uncorrelated) error term.
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Random Walk with Drift
A random walk that has a constant (or drift) added in each period.
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Sequentially Exogenous
A feature of an explanatory variable in time series (or panel data) models where the error term in the current time period has a zero mean conditional on all current and past explanatory variables; a weaker version is stated in terms of zero correlations.
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Serially Uncorrelated
The errors in a time series or panel data model are pairwise uncorrelated across time.
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Stable AR(1) Process
An AR(1) process where the parameter on the lag is less than one in absolute value. The correlation between two random variables in the sequence declines to zero at a geometric rate as the distance between the random variables increases, and so a stable AR(1) process is weakly dependent.
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Stationary Process
A time series process where the marginal and all joint distributions are invariant across time.
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Trend-Stationary Process
A process that is stationary once a time trend has been removed; it is usually implicit that the detrended series is weakly dependent.
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Unit Root Process
A highly persistent time series process where the current value equals last period's value, plus a weakly dependent disturbance.
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Weakly Dependent
A term that describes a time series process where some measure of dependence between random variables at two points in time?such as correlation?diminishes as the interval between the two points in time increases.
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What is a unit root?
A unit root (also called a unit root process or a difference stationary process) is a stochastic trend in a time series, sometimes called a “random walk with drift”; If a time series has a unit root, it shows a systematic pattern that is unpredictable.
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What is an example of a unit root test?
The Dickey-Fuller Test.
