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Questions and Answers

What does the parameter $eta_1$ in the regression model measure?

  • The effect of the option price on the spread
  • The effect of risk on the spread
  • The tick size constraint on the spread (correct)
  • The effect of time to maturity on the spread

What is the significance of the adjusted R² value of approximately 0.675 for the first regression?

  • This means the model is overfitting the data.
  • This shows that the model has no predictive capability.
  • This suggests a strong explanatory power of the model. (correct)
  • This indicates a weak relationship between the variables.

Which of the following relationships is suggested between trading volume and bid-ask spread?

  • The spread influences trading volume only.
  • No relationship exists between volume and the spread.
  • A one-way relationship where volume influences the spread.
  • A two-way relationship exists between volume and the spread. (correct)

In the context of the put and call options, what does the paper suggest about their relationship?

<p>They can be viewed as substitutes due to being written on the same underlying. (A)</p> Signup and view all the answers

What does the reduced form equation for Y1 include?

<p>A constant term and two independent variables (C)</p> Signup and view all the answers

What do the parameters $eta_2$ and $eta_3$ measure in relation to the spread?

<p>Effect of option price and time to maturity respectively (A)</p> Signup and view all the answers

When running the regression for Y1 that includes fitted values from Y2 and Y3, what are we specifically testing?

<p>The relationship between Y1 and the combined effects of Y2 and Y3 (D)</p> Signup and view all the answers

Which equation can be estimated using OLS due to the absence of endogenous variables?

<p>The regression for Y1 (A)</p> Signup and view all the answers

What does the symbol $PBA_i$ represent in the regression models?

<p>Bid-ask spread (C)</p> Signup and view all the answers

What is the implication if the null hypothesis for the F-test (that λ2 = 0 and λ3 = 0) is rejected?

<p>Y2 and Y3 are treated as endogenous (C)</p> Signup and view all the answers

What conclusion can be drawn regarding the influence of trading activity on the bid-ask spread?

<p>Higher trading activity makes the spread tighter. (D)</p> Signup and view all the answers

Which adjusted R² value corresponds with the second regression model regarding the relationship between spread size and trading activity?

<p>0.517 (C)</p> Signup and view all the answers

How can OLS be applied to Equation 22?

<p>If the RHS variables are uncorrelated with u2 (A)</p> Signup and view all the answers

What characterizes the system of equations discussed as 'recursive' or 'triangular'?

<p>Certain equations include endogenous variables in a sequential manner (A)</p> Signup and view all the answers

What is a primary method for determining the optimal lag length in a VAR model?

<p>Information criteria (A)</p> Signup and view all the answers

What is necessary for estimating Equation 23 using OLS?

<p>Y1 and Y2 should be uncorrelated with u3 (A)</p> Signup and view all the answers

What is the goal of performing fitted value regression in econometric analysis?

<p>To assess the endogeneity of the dependent variables (C)</p> Signup and view all the answers

What does the likelihood ratio test assess in the context of VAR modeling?

<p>Joint restrictions on lag coefficients (C)</p> Signup and view all the answers

How many degrees of freedom are used in the likelihood ratio test when imposing zero restrictions on 4 lags in a bivariate VAR model?

<p>16 (A)</p> Signup and view all the answers

Which of the following is a disadvantage of conducting the likelihood ratio test in VAR modeling?

<p>It assumes normality of disturbances. (A)</p> Signup and view all the answers

In a bivariate VAR(8) model, if the last 4 lags are restricted, how many total restrictions are imposed?

<p>16 (C)</p> Signup and view all the answers

Which aspect must be considered when performing a likelihood ratio test for VAR models?

<p>Normality of disturbances (A)</p> Signup and view all the answers

What is the structure of the likelihood ratio test statistic in a VAR model?

<p>$LR = T imes log(Σˆ_r - log(Σˆ_u))$ (D)</p> Signup and view all the answers

What type of data is typically used to estimate a bivariate VAR model?

<p>Quarterly time series data (A)</p> Signup and view all the answers

What is a key feature of Vector Autoregressive (VAR) models compared to ARMA models?

<p>They allow for a variable to depend on multiple lags and combinations of noise terms. (C)</p> Signup and view all the answers

How many parameters must be estimated in a VAR model with g equations, each with k lags?

<p>(g + k)g^2 (D)</p> Signup and view all the answers

Which of the following is NOT a disadvantage of VAR modeling?

<p>All variables must be specified as exogenous. (B)</p> Signup and view all the answers

What is one of the advantages of VAR models in forecasting?

<p>They allow modeling of all variables as endogenous. (C)</p> Signup and view all the answers

Why might one consider using a Vector Error Correction Model (VECM)?

<p>To include first difference terms and cointegration relations. (C)</p> Signup and view all the answers

What does the notation yt = β0 + β1 yt-1 + ut represent?

<p>A Vector Autoregressive model with one lag. (D)</p> Signup and view all the answers

In VAR modeling, which is a common challenge faced by researchers?

<p>Deciding the appropriate number of lagged terms to include. (D)</p> Signup and view all the answers

Which is true regarding the assumptions of VAR models?

<p>Assumptions about endogenous and exogenous variables are irrelevant. (B)</p> Signup and view all the answers

What is the purpose of the dummy variables CDUMi and PDUMi in the models?

<p>To determine if the option prices are above or below $3. (A)</p> Signup and view all the answers

In equation (1), which of the following variables has a negative coefficient?

<p>CRi (B)</p> Signup and view all the answers

What role does the variable T2 play in the models?

<p>It enables a nonlinear relationship between time to maturity and the spread. (A)</p> Signup and view all the answers

Which of the following best describes the regression adjustment value Adj.R2 in the models?

<p>It is a measure of goodness of fit for the second-stage regression. (C)</p> Signup and view all the answers

What does the model equation for the puts, specifically in equation (3), focus on estimating?

<p>The relationship between put prices and other influencing factors. (C)</p> Signup and view all the answers

What is indicated by the coefficients in parentheses in the results section?

<p>They show the t-ratios for testing the significance of coefficients. (D)</p> Signup and view all the answers

In the context of the models presented, what does the variable M2 signify?

<p>It captures the trading volume of at-the-money options. (C)</p> Signup and view all the answers

Which statistical technique is used to estimate equations (1) & (2) and equations (3) & (4)?

<p>Two-Stage Least Squares (2SLS) (A)</p> Signup and view all the answers

What methodology was employed by Brooks and Tsolacos for their investigation of the UK property market?

<p>VAR Methodology (D)</p> Signup and view all the answers

Which variable was NOT included in the VAR analysis described?

<p>Nominal GDP Growth (D)</p> Signup and view all the answers

What does the notation I(1) suggest about the property index and unemployment variable?

<p>They are non-stationary but can be differenced once to become stationary (C)</p> Signup and view all the answers

In the context of the given data, what does the term 'Marginal Significance Levels' refer to?

<p>The statistical significance of lags in explaining variances (C)</p> Signup and view all the answers

Which variable showed a marginal significance level of 0.0000 when tested against SIR in the VAR?

<p>PROPRES (D)</p> Signup and view all the answers

What is the primary purpose of conducting variance decompositions in the VAR model analysis?

<p>To understand the contribution of each variable to the forecast error variance (C)</p> Signup and view all the answers

What does the term 'Impulse Responses' refer to in the context of VAR models?

<p>The reaction of one variable to a one-time shock in another variable (D)</p> Signup and view all the answers

Which of the following orders was used for variance decompositions and impulse responses in the analysis?

<p>I: PROPRES, DIVY, UNINFL, UNEM, SPREAD, SIR (A)</p> Signup and view all the answers

Flashcards

Reduced Form Equations

Simplified equations where dependent variables are expressed directly in terms of independent variables.

OLS estimation

Ordinary Least Squares is a method for estimating the parameters of a linear model.

Exogeneity

An assumption where the independent (explanatory) variables are not correlated with the error term (the unexplained part of the dependent variable).

Endogenous Variables

Variables whose values are determined within a system of equations.

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F-test in econometrics

Statistical test used to determine if multiple coefficients in a regression model are jointly equal to zero.

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Recursive System

A system of equations where variables are ordered in a way that later equations depend on variables already determined in prior equations.

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Simultaneity Problem

A situation when two or more variables influence each other simultaneously.

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Fitted values in regression

Predicted values of the dependent variable calculated from the estimated regression equation.

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Call Bid-Ask Spread Model

A model (equation 1) predicting call bid-ask spread (CBAi) using dummy variables (CDUMi), option characteristics (Ci, CLi, Ti, CRi), and an error term (ei).

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Call Volume Model

A model (equation 2) predicting call volume (CLi) based on the call bid-ask spread (CBAi), time to maturity (Ti), and time-squared (Ti^2), trading volume of ATM options(Mi^2), and an error term (vi).

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Put Options Model

Models (equations 3 & 4) symmetric to call options, predicting put bid-ask spreads (PBAi) and volumes (PLi) using similar variables.

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Dummy Variables (CDUMi, PDUMi)

Variables taking value 0 if option price is below $3, and 1 if it is at least $3.

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Bid-Ask Spread (CBAi, PBAi)

The difference between the prices at which traders buy and sell an option

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Trading Volume (CLi, PLi)

The frequency/count of options traded in the market.

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Time to Maturity (Ti)

The time remaining until an option expires.

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Bid-Ask Spread

The difference between the highest price a buyer is willing to pay (bid) and the lowest price a seller is willing to accept (ask) for an asset.

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Trading Volume

The total number of shares or contracts traded over a specific period (e.g., a day).

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What is the relationship between Bid-Ask Spread and Trading Volume?

There's a two-way relationship where higher trading volume tends to lead to smaller spreads, and narrower spreads can encourage more trading.

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Tick Size Constraint

The minimum price increment allowed for trades, affecting the bid-ask spread.

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Option Price

The current price of an option contract, which is influenced by factors like underlying asset price, volatility, and time to maturity.

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Trading Activity

The frequency and volume of trades in an asset, which can impact the bid-ask spread.

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Time to Maturity

The period remaining until an option contract expires, influencing bid-ask spread.

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Risk

The potential for loss on an investment, affecting the bid-ask spread.

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VAR Lag Length

The number of past periods used to predict current values in a Vector Autoregression (VAR) model. It's crucial for capturing the relationship between multiple time series.

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Cross-Equation Restrictions

A constraint imposed on a VAR where all equations in the system are assumed to have the same lag length. This simplifies the model but may miss specific dynamics.

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Likelihood Ratio Test (LR)

A statistical test used to compare nested models (one model is a simplified version of the other). It helps determine if simplifying assumptions are justified.

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Information Criteria

Methods for selecting the optimal lag length in VAR models by balancing model fit with complexity. This helps to find the most parsimonious representation.

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AIC (Akaike Information Criterion)

An information criterion that penalizes models with more parameters, balancing model fit with complexity. Lower AIC values suggest a better model.

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BIC (Bayesian Information Criterion)

Another information criterion. It penalizes model complexity more heavily than AIC, favoring parsimony. Lower BIC values indicate better models.

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Residuals Variance-Covariance Matrix

A matrix that summarizes the relationships between error terms across different equations in a VAR model, providing insights into the model's overall fit.

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Degrees of Freedom (df)

The number of independent pieces of information available to estimate model parameters. In a hypothesis test, df reflects the number of restrictions imposed.

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VAR Model

A statistical model that analyzes the relationships between multiple time series variables and how they influence each other over time.

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What are some macroeconomic variables that can influence property returns?

Key macroeconomic indicators like interest rates, inflation, and unemployment rates can significantly impact the property market.

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What does it mean when a variable is I(1)?

A variable is I(1) if it needs to be differenced once to become stationary, meaning its statistical properties remain consistent over time.

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Variance Decomposition

A statistical technique that shows how much of the variation in a particular variable is explained by each of the other variables in a VAR model.

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Impulse Response

A statistical tool that shows how a variable responds to an unexpected change in another variable within a VAR model.

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Lag

A time delay used in time series analysis to account for the fact that past values of a variable can influence its current value.

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F-test

A statistical test used to determine if a group of variables (coefficients) in a regression model jointly have a statistically significant effect on the dependent variable.

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Vector Autoregression (VAR) Model

A statistical model that explains the relationship between multiple time series variables by considering their past values. It assumes that each variable depends on its own past values and the past values of other variables in the system.

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VAR Model Notation

In a VAR model, 'yt' represents a vector of variables at time t, '0' is a vector of constants, '1' is a matrix of coefficients representing the effect of lagged variables on current values, and 'ut' is a vector of error terms.

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Lagged Variables in VAR

Lagged variables in a VAR model are past values of the variables in the system. They are used to predict the current values of the variables.

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Advantages of VAR Models

VAR models are versatile because they don't require specifying which variables are caused or influenced by others. They can handle complex relationships and often provide better forecasts than traditional structural models.

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Disadvantages of VAR Models

VAR models can have a lot of parameters to estimate, which can make them difficult to interpret and prone to overfitting. They are also a-theoretical, meaning they do not rely on underlying economic theory to guide their structure.

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Stationarity in VAR

Stationarity is an important assumption in VAR models, meaning the statistical properties of the time series variables remain constant over time. This is important for accurate model estimation and interpretation.

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Estimating VAR Model Parameters

VAR model parameters can be estimated using ordinary least squares (OLS) separately for each equation in the system, provided there are no contemporaneous terms (current values of other variables) in the equations.

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Interpreting VAR Model Coefficients

Understanding the coefficients in a VAR model can be challenging, as they represent the impact of lagged variables on current values without specifying causality. Interpreting them requires careful consideration within the context of the model.

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Study Notes

Multivariate Models

  • Multivariate models extend single equation models by analyzing the relationships among multiple variables simultaneously.

Simultaneous Equations Models

  • Single equation models assume all independent variables are exogenous.
  • In simultaneous models, variables can be endogenous, meaning they influence each other.
  • The structural form defines the simultaneous relationships.
  • Reduced form equations are derived by solving the structural equations, isolating each endogenous variable.

Simultaneous Equations Bias

  • OLS estimation of structural equations within a simultaneous system yields biased and inconsistent estimates.
  • Endogenous variables are correlated with the error term, violating a key OLS assumption.

Avoiding Simultaneous Equations Bias

  • Employing reduced form equations, which are estimated using OLS avoids simultaneity bias.
  • Instrumental Variables (IV) & Two-Stage Least Squares (2SLS) techniques are suitable for overcoming the simultaneity problem, particularly in over-identified systems or for situations with reduced form equations.
  • IV & 2SLS involve substituting fitted endogenous variables, obtained from the reduced form, into the structural equations, resulting in consistent estimators.

Identification of Simultaneous Equations

  • Identification of simultaneous equations addresses the possibility of multiple structural forms leading to non-unique coefficients.
  • Underidentification: insufficient information to uniquely identify the structural parameters.
  • Just identification: precisely sufficient information to estimate the structural coefficients.
  • Overidentification: more information than necessary, facilitating more robust estimates and performing tests of model adequacy.

Tests for Exogeneity

  • Hausman test helps determine whether variables should be treated as endogenous.
  • The test assesses if the OLS and 2SLS estimates differ significantly.
  • A significant difference points to endogeneity.

Recursive Systems

  • Recursive systems exhibit a strict ordering of variables; there's no simultaneous effect.
  • OLS is applicable to recursive systems because of this ordering or 'triangular' structure of variables.

Indirect Least Squares (ILS)

  • ILS is a method used to estimate structural parameters from the reduced form when the model is just-identified.
  • Solving back to obtain the structural parameters after the reduced form is obtained using OLS is a bit tedious.

Estimation of Systems Using Two-Stage Least Squares (2SLS)

  • Two-stage least squares is a common technique used to estimate structural models that have endogenous variables.
  • Stage 1: Obtain reduced form equations, estimating the relationships between endogenous variables and exogenous variables.
  • Stage 2: Using fitted values from stage 1, substitute into the structural equations, employing OLS to estimate the coefficients.

Instrumental Variables Estimates

  • Instrumental variables (IV) are correlated with endogenous variables, but uncorrelated with the error term, solving the simultaneity problem.
  • The IV methods use instruments, which are other variables that help account for parts of the endogenous variable without the direct correlation with the error term

Vector Autoregressive Models (VARs)

  • VAR models are a way to investigate the relationships between multiple variables over time.
  • VARs allow for feedback relationships among variables.
  • They provide impulse responses, which illustrate how a shock in one variable affects other variables over time.
  • Variance decompositions give information about the proportion of variance in each variable attributed to shocks in other variables.
  • VARs do not require specifying which variables are exogenous or endogenous, making them more flexible.

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Multivariate Models PDF

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Explore the complexities of multivariate models and simultaneous equations through this quiz. Understand the implications of endogenous variables and methods to avoid bias in estimation. Test your knowledge on using Instrumental Variables and Two-Stage Least Squares techniques.

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