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Consider the Following Model Yt = β0

question 28

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Consider the following model Yt = β0 + Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? + ut where the superscript "e" indicates expected values.This may represent an example where consumption depends on expected,or "permanent," income.Furthermore,let expected income be formed as follows: Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? = Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? + λ(Xt - Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? );0 < λ < 1
(a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process.
(b)Rewrite the expectations equation in the following form: Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? = (1 - λ) Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? + λXt
Next,following the method used in your textbook,lag both sides of the equation and replace Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? .Repeat this process by repeatedly substituting expression for Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? , Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? ,and so forth.Show that this results in the following equation: Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? Explain why it is reasonable to drop the last right hand side term as n becomes large.
(c)Substitute the above expression into the original model that related Y to Consider the following model Yt = β0 + + ut where the superscript e indicates expected values.This may represent an example where consumption depends on expected,or permanent, income.Furthermore,let expected income be formed as follows: = + λ(Xt - );0 < λ < 1 (a)In the above expectation formation hypothesis,expectations are formed at the end of the period,say the 31st of December,if you had annual data.Give an intuitive explanation for this process. (b)Rewrite the expectations equation in the following form: = (1 - λ) + λXt Next,following the method used in your textbook,lag both sides of the equation and replace .Repeat this process by repeatedly substituting expression for , ,and so forth.Show that this results in the following equation: = λXt + λ(1-λ)Xt-1 + λ(1- λ)2 Xt-2 + ...+ λ(1- λ)n Xt-n + (1 - λ)n+1 Explain why it is reasonable to drop the last right hand side term as n becomes large. (c)Substitute the above expression into the original model that related Y to .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions? (d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a Koyck transformation. What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier? .Although you now have right hand side variables that are all observable,what do you perceive as a potential problem here if you wanted to estimate this distributed lag model without further restrictions?
(d)Lag both sides of the equation,multiply through by (1- λ),and subtract this equation from the equation found in (c).This is called a "Koyck transformation." What does the resulting equation look like? What is the error process? What is the impact effect (zero-period dynamic multiplier)of a unit change in X,and how does it differ from long run cumulative dynamic multiplier?

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