Econometrics, kandidatkurs
The population R-squared is affected when heteroskedasticity is present in Var(u|x1, ..., xk). True or false?
False
What is polynominals on multiple regression?
Having exponential explanatory variables, that is as example: B0 + B1logx + B2logx-squared + etc or B0 + B1X + B2X-squared + B3X-3squared + etc
What is the drawback with including proxy variables in a regression model?
It exacerbates multicollinearity.
What does the time series analysis focus on (modeling)?
It focuses on modeling the dependency of a variable on its own past, and on the present and past values of other variables.
Using a multiple linear regression model, what problems can arise in policy analysis and program evaluation?
The model can produce predicted probabilities that are less than zero and greater than one.
Transformations on highly persistent time series, what?
With integrated of order one I(1)
a smaller standard error means?
a larger t statistics
Covariance stationary sequences where Corr( xt + xt+h) 0 as are said to be
asymptotically uncorrelated
The instrumental variables in the two stage least squares estimation method consists of
exogenous variables appearing in either equation
F statistic can be used to test
nested models.
What is underidentification?
null hypothesis: IV not correlated with y2. (not correlated with endog. variable) Using Kleibergen-Paap rk Lagrange multiplier test and evaluating the p-value. • We want to reject the null, if we cannot do so strongly, IV will be (much) worse than OLS (inconsistent and more biased).
What is HAC?
Heteroskedasticityand autocorrelation consistent. Is the same as Serial correlation-robust standard erros. HAC SEs lagged in because of: We generally have more observations with cross-sections than for time series. Newey-West SEs can be poorly behaved if there is substantial serial correlation and the sample size is small. The bandwidth g must be chosen by the researcher and the SEs can be sensitive to the choice of g. Can also use for time series regressions. Heteroskedasticity is automatically corrected for if one uses the serial correlation-robust formulas for standard errors and test statistics.
Dependent variable log(y) and independent variable x, how to interpret it?
%change in y = 100beta*change in x
Dependent variable log(y) and independent variable log(x), how to interpret it?
%change in y = beta%*change in x
Why should a trend be included (time series data)?
* If the dependent variable displays an obvious trending behaviour • If both the dependent and some independent variables have trends • If only some of the independent variables have trends; their effect on the dependent variable may only be visible after a trend has been substracted
What are the advantages and disavantages of the linear probability model (LPM)?
+: * Easy estimation and interpretation * Estimated effects and predictions are often reasonably good in practice. -: • Predicted probabilities may be larger than one or smaller than zero. • Marginal probability effects sometimes logically impossible. • The linear probability model is necessarily heteroskedastic. • Thus, heteroskedasticity consistent standard errors need to be computed. (solve with robust standard errors with OLS)
Summarise FE
Allow for correlation between unobserved effect and explanatory variables Time-constant explantory variables drop out
The definition / criterias for IV?
1) It does not appear in the regression (exclusion restriction) 2) It is highly correlated with the endogenous variable (instrument relevance) 3) It is uncorrelated with the error term (exclusion restriction) (instrument exogeneity)(instrument validity)
What is the linear probability model (LPM)?
A linear regression when the dependent variable is binary. The coefficients describe the ffect of the explanatory variables on the probability that y=1
What are the goodness-of-fit measure for Logit and Probit models?
1. Percent correctly predicted 2. Pseudo R-squared 3. Correlation based measures Use, compare, predict, look at, etc
What are the three cases in which OLS on the selected sample is consistent?
1. Selection is independent of explanatory variables and the error term. 2. Selection is completely determined by explanatory variables. 3. Selection depends on the explanatory variables and other factors that are uncorrelated with the error term.
How many new variables should be created for a multiple regression model where data are always available for y and x1, x2, ..., xk−1 but are sometimes missing for the explanatory variable xk?
2
What is nonnested?
A combination of two variables that are not related. Nested is the contrarywise.
What is maximum likelihood estimators (MLE)?
A method of estimating the parameters of an assumed probability distribution, given some observed data. Hypothesis testing after MLE is with t-test and confidence intervals. Multiple hypothesis is tested with either: 1. Lagrange multiplier 2. Wald test 3. Likelihood ratio test (chi-square?)
Heterogenous trend model, explain
A model where time trends are unique across individuals The policy intervention then is correlated with level differences among units but also by trend differences. Estimates with fixed effect, but T must be 3 or greater
Unbalanced panels, explain
A panel is unbalanced when not all cross-sectional units have the same number of observations. Problem if observations are missing in a systematic way. Can be solved using fixed effects.
What is stationary time series?
A time series is stationary if its stochastic properties and its temporal dependence structure do not change over time. Strong stationarity: the distribution of a time series is exactly the same through time. (the distribution of original time series is exactly same as lagged time series, by any number of lags) Weak stationarity: the time series has constant mean and variance throughout the time.
What is a proxy?
A variable that is not directly relevant, but can replace an unobservable or immeasurable variables, that is omitted variables. A variable that replaces omitted variables, does not belong into the population regression (is uncorrelated to its errors)
Two equations form a nonnested model when:
neither equation is a special case of the other.
What is the problem with a cross section?
All relevant explanatory variables are rarely observed, that is the model is restricted in a way where only a couple of explanatory var. is included. Omitted variable bias arises if: B2 not equal to 0 and covariance not equal to 0. The problem can be reduced using pooled cross-sections and panel data
What is parallel trends?
Any trends in the outcome y would trend at the same rate in the absence (frånvaro) of the intervention prior to the intervention, y should move in the same direction for both groups.
Summarise RE
Assume unobserved effect uncorrelated with all explanatory variables More efficient than fixed effects if this assumption holds Time-constant variables can be estimated
Asymptotic properties of OLS, are?
Assumptions: TS1' Linear in parameters ( as TS1 but the dependent and independent variables are assumed to be stationary and weakly dependent.) TS2' No perfect collinearity TS3' Zero conditional mean (the explanatory variables are assumed to be only contemporaneously exogenous rather than strictly exogenous. (And then, b/c of stationarity, TS.3' holds for all time periods.), correlation between a regressor and the error at time t-1 is allowed)
Type 2 error, what is it?
Beta: risk of not rejecting H0, given that H1 is true 1-Beta: power or probability of rejecting H0, given that H1 is true.
Dependent variable y and independent variable log(x), how to interpret it?
Change in y = Beta/100% change in X
What is policy evaluation?
Comparing treatment and control group after a intervention, (in a randomized control trial) The intresting part is: effects of non-experimental policy changes. That is * Treatment group that was affected by the policy * Control group that was not * But non-random assignment to treatment and control
What is multiple linear regression model? its advantages and its interpretation?
Contains more explanatory / independent variables The model must be linear in the parameters (not in the variables) The model holds the values of other explanatory variables fixed, despite being correlated with the explanatory under consderiation. How much does the dependent variable change if the i-th independent variable is increased by one unit, holding all other independent variabels constant
What model to use if dependent variable (y) is binary?
Could use LPM with estimate multiple linear regression. Is problamatic due to predictions outside the interval and partial effects of explanatory variables are constant. Solve by using: Non-linear models
Summarise CRE
Correlated random effects Simple test for choosing between fixed and random effects Estimates for time-constant variables together with fixed effects estimates for time-varying variables.
Consider the following simple regression model y = 0 + 1x1 + u. Suppose z is an instrument for x. the IV-estimator is always biased if
Cov(x,u) not equal 0
How many types of datasets is there and what are they?
Cross-sectional Time series Pooled corss sections Panel / longitudinal
What model rules out perfect collinearity among the regressors?
Cross-sectional regression
What is measurement error?
Difference between the true measure and what is actually measured. Variables may also not be measured perfectly
What is DiD?
Difference-in-Differences. Assumption: parallel trends Is a way to evaluate policy changes, that is a before/after comparison. or Rewriting the DiD-estimator so interpretation is as followed: • The first term is the difference in means over time for the treated group • The second term is the difference in means over time for the control group. Giving the interpretation as the average treatment effect. Needs: no externals factors changed across the two time periods and having random assignments.
What is Autoregressive Conditional Heteroskedasticity (ARCH)?
Even if there is no heteroskedasticity in the usual sense (the error variance depends on the explanatory variables), there may be heteroskedasticity in the sense that the variance depends on how volatile the time series was in previous periods: Consequences of ARCH in static and distributed lag models: * If there are no lagged dependent variables among the regressors, i.e. in static or distributed lag models, OLS remains BLUE under TS.1-TS.5. * Also, OLS is consistent etc. for this case under assumptions TS.1'-TS.5' * As explained, in this case, assumption TS.4 still holds under ARCH. Consequences of ARCH in dynamic models: • In dynamic models, i.e. models including lagged dependent variables, the homoskedasticity assumption TS.4 will necessarily be violated: • This means the error variance indirectly depends on explanatory variables. • In this case, heteroskedasticity-robust standard error and test statistics should be computed, or a FGLS/WLS-procedure should be applied. • Using a FGLS/WLS-procedure will also increase efficiency
What is and what is the difference of exogeneity and strict exogeneity?
Exogeneity: The mean of the error term is uncorrelated to the explanatory variables of the same period Is sufficient for OLS consistency Strict exogeneity: The mean of the error term is uncorrelated to the values of the explanatory variables of all periods. Is necessary for OLS unbiasedness.
Types of observations?
Experiment Controlled observation Uncontrolled observation Rumour
What is policy analysis: two periods without controls?
First period: no intervention Second period: intervention in some units T=2, leads to no difference between fixed effect and first differencing. Produces the DiD estimator Bdd
Dummy variables and fixed effects, explain
Fixed effects can be replaced as dummy variables, that is introducing a dummy for each individual in the original regression and using pooled OLS. • Explain what the unobserved individual specific effects stand for, and how they are accounted for. • What are the obvious unobserved variables? • Are these variables likely to be constant over time within units?
Definition of causal effect (x on y)
How does variable X change if variable Y is changed, but all other relevant factors are held constant.
Describe significance level (alpha) - p-value
How likely is a difference of X, due to random variation, gien no difference (H0 is true)? Is type 1 error (risk of false alarm / false positive, is not the probability!) P-values less 5% is statistically significant (on 5% alpha) If H0 is true, then alpha can be interpreted as probability of a false positive.
Serial correlation-robust inference after OLS, explain
If a model contains serial correlation, the OLS standard errors will overstate statistical significance because of less independent variation. It can be solved by using Serial correlation-robust inference after OLS. Might be a better choice than FGLS-est due to it requires strict exogeneity and assumes specific form of serial correlation (AR(1)) Using Newey-West standard errors.
How does 2SLS/IV solve errors-in-variables problems?
If a second measurement of the mismeasured variable is available, this can be used as an instrumental variable for the mismeasured variable.
How does 2SLS/IV solve omitted variables problems?
If a variable that is not observed is correlated with an observable we want to include as a regressor, the estimator will be inconsistent and biased. But using an IV, can address the inconsistency and reduce bias.
what are the problems with IV?
If the instrumental variable is not completly exogenous and only weakly related to X, then it gets incosistent. OLS, is a better fit then.
How does 2SLS/IV solve simultaneity/reverse causality problems?
If the outcome and explanatory variable are jointly determined such that x affects y and y affects x, x will not be exogenous. Using an IV is a potential solution, as are, e.g., natural experimental approaches.
What is dummy variable trap?
Implementering a dummy variable in a model, using both versions causes perfect collinearity , leading to not eastimating. ex: wage = B0 + B1male + B2female + etc When using dummy variables, one category always has to be omitted (using female, then male gets omitted)
What is Heckman model?
Incidental truncation Is a truncation model, but is now instead dependent of another variable. Is used to correct sample selection bias
What is cross sectional dataset? and its disavantages?
Includes samples of individuals (households, firms, cities, etc) Observations are more or less independent - pure random sampling is usually violated due to example people refuse answering surveys or clustering in sampling.
What is integrated of order I(), both 0 and 1?
Integrated of order zero I(0): weakly dependent time series Integrated of order one I(1): the time series is differenced one time, in order to obtain a weakly dependent series.
What is seasonality in time series data?
Is a dummy variable where 1= the seasonality 0= not the seasonality. Modelling seasonality in time series: ex, BetaDec where Dec is 1=if obs. from december, 0= otherwise
Feasible generalized least squares-estimator (FGLS), explain
Is a method for autocorrelation, that is correcting for serial correlation with strictly exogenous regressors. There is two variants: Cochrane-Orcutt estimation: omits the first observation Prais-Winsten estimation: adds a transformed first observation (useful/efficient if small sample)
What is qualitative information?
Is added to use dummy variables, that is incorporating qualitiative information to the model. Example: gender, race, industry, region, rating grade, etc
What is DDD?
Is the same as DiD-estimator, but with one additional control group. The assumption, parallel trends, is violated. That is, trends between the two groups do not differ in third group leading to second component vanishing.
What is: the fundamental problem of causal inference? and how to solve it?
It is impossible to observe a observation that is both affected and unaffected by an intervention. That is, the observations differ for various unknown reasons. Solve: the intervention must be independent of observation's attributes. giving every observation the same chance of being affected by the intervention. By doing both, the selection bias is even out, due to groups do not differ. AND: using randomness.
a reason for using the correlated random effects approach?
It provides a way to include time-constant explanatory variables in a fixed effects analysis.
Using trends, how does modeling looks like and its problems?
Linear time trend: y = B0 + B1X + u Exponential time trend: log(y) = B0 + B1X + u A spurious relationship may arise if not including trends.
What is omitted variables
Many variables are not observed and are correlated with observables
What is instrumental variables method (IV)?
Method to address endogeneity problems. Can also be used to obtain consistent estimators and to reduce their bias.
What is average partial effects?
Models with quadratics, interactions and other nonlinear functional forms, the partial effect depends on the values of one or more explanatory variables It is a summary measure to describe the relationship between dependent variable and each explanatory variable
What are the measurement scales?
Nominal - categorical or unordered data (colour, nationality, postcode, etc). Dependence of nominal variables uses chi-squared test. Ordinal - ordered data (survey). Correlation between ordinal variables uses spearmans rank correlation coefficient: r. Interval scale - with a constant measurement unit (year, IQ, etc). Differences have meaning. Ratio scale - interval scale with a zero point (income, sales, unemployment, etc) Ratios have meaning
What is the endogeneity problem?
OLS is inconsistent and biased 1. Omitted variables 2. Measurement error 3. Simultaneity / reverse causality Could be solved with proxy variables and fixed effects. Only works if proxy is available and fixed effect requirements are fulfilled. Popular solvement is instrumental variables method (IV)
Properties of OLS with serially correlated errors, comment:
OLS will be unbiased and consistent, but OLS standard errors and tests will be invalid. OLS will also be unefficient. Correcting for serial correlation (with strictly exogenous regressors): using FGLS-estimator. (Could transform the model so GM-assumptions are satisfied but the problem is AR(1) coefficients are unknown) or serial correlation-robust inference (after OLS)
What is time series data?
Observations of variables over time Observations typically serially correlated Typically contains trends and seasonality
Definition of ceteris paribus
Other relevant factors being equal.
What are non-linear models?
Probit and logit models Probit model is a normal distribution Logit model is a logistic function
The sampling variance for the instrumental variables (IV) estimator is larger than the variance for the ordinary least square estimators (OLS) because
R2 < 1 the IV variance is always larger than the OLS variance.
What to use, FE or RE?
Random Effects (RE): regressors unrelated to individual specific effects Fixed effects (FE): regressors related to individual specific effects However: * unobserved individual effects are seldomly uncorrelated with explanatory variables → FE more convincing However: * only RE allows estimating effects of time invariant variables. Include as many time invariant controls as possible in RE
What is the margin of error?
Randomization bias Confidence interval in which the real effect probably is loacted.
What is panel / longitudinal data?
Same cross sectional units are followed over time (Follow the same N units across T time periods) Has cross sectional and time series dimension Can be used to account for time invariant unobservables Can be used to model lagged responses Observations are not independently distributed across time Differencing removes time-constant unobserved effects
What is static models (time series)?
Static time series models, the current value of one variable is modeled as the results of the current values of explanatory variables. EX: current Y (dependent) is determined by the current X, X2, X3 (independent)
What is trend-stationary process (time series)?
Stationary around the trend and weakly dependent. Satifies assumption TS1' Time series with deterministic time trends are nonstationary (not trend stationary process)
What is highly persistent time series (time series)?
Strongly dependent Is not weak dependent and OLS methods is invalid. Can be transformed to weak dependent.
The theroems of time series data (BASIC)?
T10.1 Unbiasedness of OLS T10.2 OLS sampling variances (in a finite sample, the sampling variability coming from the randomness of the regressors are ignored) T10.3 Unbiased estimation of the error variance T10.4 Gauss-Markov Theorem (the OLS estimators have the minimal variance of all linear unbiased estimators (BLUE) of the regression coefficients) T10.5 Normal sampling distributions (the OLS estimators must have normal distribution, leading to F and T-test being valid) Following the assumptions!
The theroems of time series data (IMPROVED)?
T11.1 Consistency of OLS (not necessarity unbiasedness), following TS1'-3' T11.2 Asymptotic normality of OLS, following TS1'-5'. The usual OLS standard errors, t-statistics, F-statistics, and LM statistics are asymptotically valid.
Sample properties of OLS under classical assumptions?
TS1: Linear in parameters TS2: No perfect collinearity TS3: Zero conditional mean (the mean value of the unobserved factors is uncorrelated to the values of the explanatory variables in all periods. exogeneity/strict exogeneity) TS4: Homoskedasticity (the volatility of the error is independent of the explanatory variables and that it is constant over time) TS5: No serial correlation / no autocorrelation (the unobserved factors must not be correlated over time, the independent variable can be temporally correlated) TS6: Normality (follows normal distribution)
Which test helps in the detection of heteroskedasticity?
The Breusch-Pagan test
What is the Chow test? and when is it only valid?
The Chow test is just an F test, it is only valid under homoskedasticity.
Testing for serial correlation (AR(1)), which tests are used?
The Durbin-Watson test (classical assumptions) - replaced with t-test as it is only valid asymptotically. General Breusch-Godfrey test for AR(q) serial correlation.
What is the issue with using OLS estimator in presence of lagged dependent variables?
The OLS is biased, but consistent, due to contemporaneous exogeneity.
Issues with OLS, what are they (time series data)? How to solve?
The assumptions might be too restricted (strict exogeneity, homoskedasticity, serial correlation), that is are very demanding. The statistical inference (conclusion) rests on the validity of the normality assumptions. Solving: Using large sample sizes, the assumptions can be relaxed. Weak assumptions are acceptable if the sample size is large, given that the requirements are fulfilled, that is the time series is stationary and weakly dependent.
What is the benchmark group?
The benchmark group is the group against which comparisons are made
What is finite distributed lag models? and how to interpret?
The explanatory variables are allowed to influence the dependent variable with a time lag. Effect of a transitory shock: one time shock in a past period, the dependent variable will change temporarilyby the amount indicated by the coefficient of the corresponding lag. Effect of a permanent lag: a permanent shock in a past period, the explanatory variable permanently increases by one unit, the effect on the dep. variable will be the cumulated effect of all relevant lags. This is a long run effect on the dep. variable.
What is the difference between a fixed effects estimator and a first-difference estimator?
The fixed effects estimator is more efficient than the first-difference estimator when the idiosyncratic errors are serially uncorrelated.
Random effects, explain
The individual effect is assumed to be random, that is unrelated to explanatory variables assumption: covariance equals 0 and error (a + u) is serially correlated for observations coming from the same i. Estimation is done with pooled OLS, but transforming is necessary. The transformation is done with quasi-demeaned data. (due to violating GM-assumptions)
What is the difference between the White test and the Breusch-Pagan test?
The number of regressors used in the White test is larger than the number of regressors used in the Breusch-Pagan test. (The White test includes the squares and cross products of all independent variables. Therefore, the number of regressors is larger for the White test.)
What is simultaneity/reverse causality?
The outcome variable and the explanatory variables may also be affecting each other
What problem does not exist in dynamically complete models.
The problem of serial correlation
What is Autoregressive process of order one [AR(1)]?
The process carries over to a certain extent the value of the previous period (plus random shocks from an i.i.d series e(t)). The estimated coefficient will be biased, but if sample is large and the coefficient is not close to 1, the estimator of the coefficient is good. If the stability condition | p1 | < 1 holds, the process is weakly dependent because serial correlation converges to zero as the distance between observations grows to infinity.
What is Moving average process of order one [MA(1)]?
The process is weakly dependent because observations that are more than one time period apart have nothing in common and are therefore uncorrelated.
What does stochastic mean?
The property is well described by a random probability distribution. That is, its random.
What is Tobit models?
The range of the dependent variable is constrained in some way. That is, regression models with those. Is also called: model of limited dependent variables. OLS cannot be used.
Say one limitation of serial correlation-robust standard errors
The serial correlation-robust standard errors can be poorly behaved when there is substantial serial correlation and the sample size is small.
What assumption is required for obtaining unbiased random effect estimators?
The unobserved effect is independent of all explanatory variables in all time periods.
Why randomized experiments?
To achieve constancy: evens out disturbing differences (observed and unobserved) to remain causal effects
What is the poisson regression model used for?
To count data It models a count variable as a function of explanatory variables Uses MLE Interpretation: by what percentage does the mean outcome change if X is increased by one? The problem: it assumes the expected value of y is equal to the variance of y (a feature of the Poisson distribution).
What is a spurious relationship?
Trending variables are regressed on each other and the variables is driven by a common trend. Solving it with including a trend in the regression.
What is pooled cross sections?
Two or more cross sections are combined in one dataset. Cross sections are drawn independently of eachother Usually used to evaluate policy changes Independently pooled cross section: Sampling randomly from a population at different points in time Increase sample size --> precision and power Observations are independently sampled Observations are not identically distributed Allow intercepts to differ across periods
Explain 2SLS estimation
Two stage least squares 1. A IV estimation is done, y1 2. First stage: endogenous variable y2 is predicted using only exogenous information 3. Second stage: OLS with y2, replaced by its prediction from the first stage. Why to use 2SLS: * All variables in second stage regression are exogenous * y2 is purged of its endogenous part (due to exogenous information) Properties: * Standard errors from OLS second stage is wrong! Solved by 2SLS-IV using two instruments • 2SLS/IV is typically much less precise because there is more multicollinearity and less explanatory variation in the second stage regression. • Corrections for heteroskedasticity/serial correlation analogous to OLS. • 2SLS/IV easily extends to time series and panel data situations.
How do we test for requirements for IV/2SLS?
Under-identification Weak identification Overidentification Nature of relationship
Unrestricted and restricted models: what is that?
Unrestricted model: contains all variables Restricted model: removes some variables from the unrestricted model The regression is same for both models. It is for testing for differences in regression functions across groups.
Transformating with quasi-demeaned data, explain
Uses FGLS because of the quasi-demeaned parameter is unknown. Is used to estimate the effect of time-invariant variables If the random effect is relatively unimportant compared to the idiosyncratic error, FGLS will be close to pooled OLS If the random effect is relatively important compared to the idiosyncratic term, FGLS will be similar to fixed effects (because λ goes to 1). Advantages: is likely to have less bias than pooled ols
What is fixed effect?
Variables that are constant across inviduals (age, sex, ethnicity, etc), dont change at a constant rate over time. Could be correlated to explanatory variables. That is, any change to an individual is the same, that is being a woman, a person of color or 17 year old will not change over time. Following must be satisfied: * strict exogeneity in the original model * Degrees of freedom must be adjusted (to NT-N-k) Bear in mind: • The R-squared of the demeaned equation is inappropriate. • The effect of time-invariant variables cannot be estimated. • The effect of interactions with time-invariant variables can be estimated (e.g. the interaction of education with time dummies). * If a full set of time dummies are included, the effect of variables whose change over time is constant cannot be estimated (e. g. experience).
What does weakly dependent mean (time series)?
Xt is almost independent of Xt+h as h grows to infinity (for all t). Then the stochastic process is weakly dependent. Discussion of: It replaces the random sampling assumption the correlation between Xt and Xt+h must converge to zero (if h grows to infinity)
Consider the following simple regression model y = 0 + 1x1 + u. The variable z is a poor instrument for x if
a low correlation between z and x.
What is nature of relationship?
a nature relationship between x and z * statistical significant relation key, but also need to discuss its nature, e.g., positive or negative and magnitude.
Under adaptive expectations, the expected current value of a variable adapts to
a recently observed value of the variable.
The model: Y t = 0 + 1c t + u t, t = 1,2,......., n is an example of a(n):
a static model
2SLS should be applied to simultaneous equation models with panel data only
after removing the unobserved effects from the equations of interest
In a truncated regression model, the samples
are not included randomly from an underlying population but are based on a given rule. (the rule that was used to include units in the sample. This rule is determined by whether the dependent variable is above or below a certain threshold.)
The model xt = 1xt - 1 + et, t =1,2,.... , where et is an i.i.d. sequence with zero mean and variance 2e represents a(n):
autoregressive process of order one.
Consistency of feasible generalized least square estimators requires the error term to
be uncorrelated with lags of the explanatory variable
Dependent variable y and independent variable x, how to interpret it?
change in y = beta*change in x
A common form of sample selection that does not observe the dependent variable because of the outcome of another variable is called
incidental truncation
All standard count data distributions exhibit
heteroskedasticity
What is a censored model?
if one can at least observe the exogenous variables. The dependent variable is censored in the sense that values are only reported up to a certain level. Can use MLE
A test for heteroskedasticty can be significant if
if the functional form of the regression model is misspecified.
What is tuncated model?
if the observations outside a specified range are totally lost In a truncated regression model the outcome and the explanatory variables are only observed if the outcome is less or equal to some value ci. The sample is not a random sample from the population Can not use OLS Can use MLE
The correlated random effects approach can be applied to
models with many time-varying explanatory variables.
The model yt = et + 1et - 1 + 2et - 2 , t = 1, 2, ..... , where et is an i.i.d. sequence with zero mean and variance 2e represents a(n):
moving average process of order two.
What is weak identification?
null hypothesis: IV only weakly correlated with with y2. (weakly correlated with endog variable) Using Kleibergen-Paap Wald test and evaluating the F-statistic. We want to reject the null with some margin, for IV to perform better than OLS (consistent and less biased).
What is overidentification?
null hypothesis: IVs are orthogonal to the error term, that is the IV is exogenous. Using Hansen J test. • We do not want to reject the null, because if we do reject the null, then we know for sure that the IV performs worse than OLS (inconsistent and more biased). The test requires more than one IV.
The necessary condition for identification of an equation is called the
order condition.
Which of the Gauss -Markov assumptions is violated by the linear probability model?
the assumption of constant variance of the error term.
The following simple model is used to determine the annual savings of an individual on the basis of his annual income and education. Savings = β0 + 0 Edu + β1Inc + u The variable 'Edu' takes a value of 1 if the person is educated and the variable 'Inc' measures the income of the individual. Refer to the model above. The benchmark group in this model is
the group of uneducated people
The classical errors-in-variables (CEV) assumption is that
the measurement error is uncorrelated with the unobserved explanatory variable
If the Breusch-Pagan Test for heteroskedasticity results in a large p-value, what null hypothesis is rejected?
the null hypothesis of heteroskedasticity is rejected
The test for overidentifying restrictions is valid if
the regression model exhibits homoskedasticity.
What is the assumptions of the white test?
the square of the error term in a regression model is uncorrelated with all the independent variables, their squares and cross products.
What does The Least Absolute Deviations (LAD) estimators in a linear model minimize?
the sum of the absolute values of the residuals.
Identification fails when
there are more endogenous explanatory variables then exogenous. (The rank order condition for identification specifies that we need at least as many excluded exogenous variables as there are included endogenous explanatory variables in the structural equation.)
In the correlated random effects approach, the regression model includes
time averages as separate explanatory variables.
Idiosyncratic error is the error that occurs due to
unobserved factors that affect the dependent variable and change over time.
A static model is postulated when:
when a change in the independent variable at time 't' is believed to have an immediate effect on the dependent variable.
The value of the estimated transformation parameter in generalized least square estimation that eliminates serial correlation in error terms indicates
whether the estimates are likely to be closer to the pooled OLS or the fixed effects estimates.
Methods used in panel data?
• Pooled OLS: (random effects assumption, serial correlation of error terms, needs contemporaneous (only occur in the same period of time) exogeneity) • Random effects estimation: (random effects assumption, more efficient than pooled OLS, needs strict exogeneity) • Fixed effects estimation: (fixed effects assumption, problem with time invariant regressors, needs strict exogeneity) • First differencing: similar to fixed effects, good for longer time serie
