The paperConclusions

Global Divergence in Growth RegressionsM. Battisti, G. Di Vaio, J. Zeira

Comments byGiuseppe De Arcangelis

Sapienza University of Rome

Current Macroeconomic ChallengesMarch 7, 2014

Giuseppe De Arcangelis

The paperConclusions

Plan

I Brief recap of the paper

I Reverse engineering of the empirical model and comments

I Conclusive remarks

Giuseppe De Arcangelis

The paperConclusions

Plan

I Brief recap of the paper

I Reverse engineering of the empirical model and comments

I Conclusive remarks

Giuseppe De Arcangelis

The paperConclusions

Plan

I Brief recap of the paper

I Reverse engineering of the empirical model and comments

I Conclusive remarks

Giuseppe De Arcangelis

The paperConclusions

Main objectives

I Propose an empirical model to disentangle long-run trend(s)and short-run speed(s) of adjustment in growth dynamics;

they are usually confounded together in traditional growthregressions

I Although fully empirical, the paper hinges on some importantconstraints coming from the theoretical model (in theAppendix)

I Many robustness checks (differences vs. panel cointegration,including a correction for human capital)

I Focus on the long-run trends and possible explanations withinthe tradition of growth models (geography, history, education,institutions)

I Related papers: about 123 published papers mentioned in thesurvey by Durlaf, et al. (2005) and 36,091 items in Repec

Giuseppe De Arcangelis

The paperConclusions

Main objectives

I Propose an empirical model to disentangle long-run trend(s)and short-run speed(s) of adjustment in growth dynamics;they are usually confounded together in traditional growthregressions

I Although fully empirical, the paper hinges on some importantconstraints coming from the theoretical model (in theAppendix)

I Many robustness checks (differences vs. panel cointegration,including a correction for human capital)

I Focus on the long-run trends and possible explanations withinthe tradition of growth models (geography, history, education,institutions)

I Related papers: about 123 published papers mentioned in thesurvey by Durlaf, et al. (2005) and 36,091 items in Repec

Giuseppe De Arcangelis

The paperConclusions

Main objectives

I Propose an empirical model to disentangle long-run trend(s)and short-run speed(s) of adjustment in growth dynamics;they are usually confounded together in traditional growthregressions

I Although fully empirical, the paper hinges on some importantconstraints coming from the theoretical model (in theAppendix)

I Many robustness checks (differences vs. panel cointegration,including a correction for human capital)

I Focus on the long-run trends and possible explanations withinthe tradition of growth models (geography, history, education,institutions)

I Related papers: about 123 published papers mentioned in thesurvey by Durlaf, et al. (2005) and 36,091 items in Repec

Giuseppe De Arcangelis

The paperConclusions

Main objectives

I Propose an empirical model to disentangle long-run trend(s)and short-run speed(s) of adjustment in growth dynamics;they are usually confounded together in traditional growthregressions

I Although fully empirical, the paper hinges on some importantconstraints coming from the theoretical model (in theAppendix)

I Many robustness checks (differences vs. panel cointegration,including a correction for human capital)

I Focus on the long-run trends and possible explanations withinthe tradition of growth models (geography, history, education,institutions)

I Related papers: about 123 published papers mentioned in thesurvey by Durlaf, et al. (2005) and 36,091 items in Repec

Giuseppe De Arcangelis

The paperConclusions

Main objectives

I Propose an empirical model to disentangle long-run trend(s)and short-run speed(s) of adjustment in growth dynamics;they are usually confounded together in traditional growthregressions

I Although fully empirical, the paper hinges on some importantconstraints coming from the theoretical model (in theAppendix)

I Many robustness checks (differences vs. panel cointegration,including a correction for human capital)

I Focus on the long-run trends and possible explanations withinthe tradition of growth models (geography, history, education,institutions)

I Related papers: about 123 published papers mentioned in thesurvey by Durlaf, et al. (2005) and 36,091 items in Repec

Giuseppe De Arcangelis

The paperConclusions

Main objectives

I Propose an empirical model to disentangle long-run trend(s)and short-run speed(s) of adjustment in growth dynamics;they are usually confounded together in traditional growthregressions

I Although fully empirical, the paper hinges on some importantconstraints coming from the theoretical model (in theAppendix)

I Many robustness checks (differences vs. panel cointegration,including a correction for human capital)

I Focus on the long-run trends and possible explanations withinthe tradition of growth models (geography, history, education,institutions)

I Related papers:

about 123 published papers mentioned in thesurvey by Durlaf, et al. (2005) and 36,091 items in Repec

Giuseppe De Arcangelis

The paperConclusions

Main objectives

I Propose an empirical model to disentangle long-run trend(s)and short-run speed(s) of adjustment in growth dynamics;they are usually confounded together in traditional growthregressions

I Although fully empirical, the paper hinges on some importantconstraints coming from the theoretical model (in theAppendix)

I Many robustness checks (differences vs. panel cointegration,including a correction for human capital)

I Focus on the long-run trends and possible explanations withinthe tradition of growth models (geography, history, education,institutions)

I Related papers: about 123 published papers mentioned in thesurvey by Durlaf, et al. (2005) and 36,091 items in Repec

Giuseppe De Arcangelis

The paperConclusions

Most important results

I Long-run trends can be diverging because countries are notable to fully adopt the best technologies and may stay awayfrom the global technology frontier forever;

this is measuredby the parameter d which is significantly lower than 1

I The speed of adjustment to one’s own trend is about 4%(parameter b)

I In explaining the diverging long-run trends, geography andinstitutions have the expected effect, but no significant effectis found for education

Giuseppe De Arcangelis

The paperConclusions

Most important results

I Long-run trends can be diverging because countries are notable to fully adopt the best technologies and may stay awayfrom the global technology frontier forever; this is measuredby the parameter d which is significantly lower than 1

I The speed of adjustment to one’s own trend is about 4%(parameter b)

I In explaining the diverging long-run trends, geography andinstitutions have the expected effect, but no significant effectis found for education

Giuseppe De Arcangelis

The paperConclusions

Most important results

I Long-run trends can be diverging because countries are notable to fully adopt the best technologies and may stay awayfrom the global technology frontier forever; this is measuredby the parameter d which is significantly lower than 1

I The speed of adjustment to one’s own trend is about 4%(parameter b)

I In explaining the diverging long-run trends, geography andinstitutions have the expected effect, but no significant effectis found for education

Giuseppe De Arcangelis

The paperConclusions

Most important results

I Long-run trends can be diverging because countries are notable to fully adopt the best technologies and may stay awayfrom the global technology frontier forever; this is measuredby the parameter d which is significantly lower than 1

I The speed of adjustment to one’s own trend is about 4%(parameter b)

I In explaining the diverging long-run trends, geography andinstitutions have the expected effect, but no significant effectis found for education

Giuseppe De Arcangelis

The paperConclusions

Derivation of the Empirical Model (1)

I Canonical growth regression model: output per efficiencyunits (yE in log) converges and we can derive the traditionalgrowth regression on output per capita (y):

∆T yi = a + Xi + by0,i

where Xi is a vector of explanatory variables

I Extended growth model where domestic TFP is linked tothe global technology frontier (ft):

yi ,t − yi ,t = [1 − bi ](yi ,t−1 − yi ,t−1)

where

yi ,t = ai + yEi ,t + di ft ft ∼ r. w. with drift

Giuseppe De Arcangelis

The paperConclusions

Derivation of the Empirical Model (1)

I Canonical growth regression model: output per efficiencyunits (yE in log) converges and we can derive the traditionalgrowth regression on output per capita (y):

∆T yi = a + Xi + by0,i

where Xi is a vector of explanatory variables

I Extended growth model where domestic TFP is linked tothe global technology frontier (ft):

yi ,t − yi ,t = [1 − bi ](yi ,t−1 − yi ,t−1)

where

yi ,t = ai + yEi ,t + di ft ft ∼ r. w. with drift

Giuseppe De Arcangelis

The paperConclusions

Derivation of the Empirical Model (1)

I Canonical growth regression model: output per efficiencyunits (yE in log) converges and we can derive the traditionalgrowth regression on output per capita (y):

∆T yi = a + Xi + by0,i

where Xi is a vector of explanatory variables

I Extended growth model where domestic TFP is linked tothe global technology frontier (ft):

yi ,t − yi ,t = [1 − bi ](yi ,t−1 − yi ,t−1)

where

yi ,t = ai + yEi ,t + di ft ft ∼ r. w. with drift

Giuseppe De Arcangelis

The paperConclusions

Derivation of the Empirical Model (1)

Constraints from theory (open economy and gradual capitalaccumulation):

I output per efficiency units is constant: yEi

I theoretical derivation of bi = (1 − α)(r + δ) ∂∆k∂MPK ; this is

actually measurable (as it is done in the paper)

Final dynamic reduced form:

yi ,t = ηi + (1 − bi )yi ,t−1 + bidi ft−1 + ui ,t

Two different representations

Giuseppe De Arcangelis

The paperConclusions

Derivation of the Empirical Model (1)

Constraints from theory (open economy and gradual capitalaccumulation):

I output per efficiency units is constant: yEiI theoretical derivation of bi = (1 − α)(r + δ) ∂∆k

∂MPK ; this isactually measurable (as it is done in the paper)

Final dynamic reduced form:

yi ,t = ηi + (1 − bi )yi ,t−1 + bidi ft−1 + ui ,t

Two different representations

Giuseppe De Arcangelis

The paperConclusions

Derivation of the Empirical Model (1)

Constraints from theory (open economy and gradual capitalaccumulation):

I output per efficiency units is constant: yEiI theoretical derivation of bi = (1 − α)(r + δ) ∂∆k

∂MPK ; this isactually measurable (as it is done in the paper)

Final dynamic reduced form:

yi ,t = ηi + (1 − bi )yi ,t−1 + bidi ft−1 + ui ,t

Two different representations

Giuseppe De Arcangelis

The paperConclusions

Derivation of the Empirical Model (1)

Constraints from theory (open economy and gradual capitalaccumulation):

I output per efficiency units is constant: yEiI theoretical derivation of bi = (1 − α)(r + δ) ∂∆k

∂MPK ; this isactually measurable (as it is done in the paper)

Final dynamic reduced form:

yi ,t = ηi + (1 − bi )yi ,t−1 + bidi ft−1 + ui ,t

Two different representations

Giuseppe De Arcangelis

The paperConclusions

Panel Cointegration Approach

From:yi ,t = ηi + (1 − bi )yi ,t−1 + bidi ft−1 + ui ,t

They obtain an equivalent representation:

(yi ,t − di ft) = biei + (1 − bi )(yi ,t−1 − di ft−1) + ui ,t (1)

Hence:

I Obtain di and the (possible) cointegrating parameter betweenyi ,t and ft

I Equation (1) is the short-run representation from which toobtain an estimate of bi

I Obtain an estimate of ei ≡ ai + yEi , i.e. the the own frontier(even when di = 0) but depends on the normalization(reference year)

Giuseppe De Arcangelis

The paperConclusions

Panel Cointegration Approach

From:yi ,t = ηi + (1 − bi )yi ,t−1 + bidi ft−1 + ui ,t

They obtain an equivalent representation:

(yi ,t − di ft) = biei + (1 − bi )(yi ,t−1 − di ft−1) + ui ,t (1)

Hence:

I Obtain di and the (possible) cointegrating parameter betweenyi ,t and ft

I Equation (1) is the short-run representation from which toobtain an estimate of bi

I Obtain an estimate of ei ≡ ai + yEi , i.e. the the own frontier(even when di = 0) but depends on the normalization(reference year)

Giuseppe De Arcangelis

The paperConclusions

Panel Cointegration Approach

From:yi ,t = ηi + (1 − bi )yi ,t−1 + bidi ft−1 + ui ,t

They obtain an equivalent representation:

(yi ,t − di ft) = biei + (1 − bi )(yi ,t−1 − di ft−1) + ui ,t (1)

Hence:

I Obtain di and the (possible) cointegrating parameter betweenyi ,t and ft

I Equation (1) is the short-run representation from which toobtain an estimate of bi

I Obtain an estimate of ei ≡ ai + yEi , i.e. the the own frontier(even when di = 0) but depends on the normalization(reference year)

Giuseppe De Arcangelis

The paperConclusions

Panel Cointegration Approach

From:yi ,t = ηi + (1 − bi )yi ,t−1 + bidi ft−1 + ui ,t

They obtain an equivalent representation:

(yi ,t − di ft) = biei + (1 − bi )(yi ,t−1 − di ft−1) + ui ,t (1)

Hence:

I Obtain di and the (possible) cointegrating parameter betweenyi ,t and ft

I Equation (1) is the short-run representation from which toobtain an estimate of bi

I Obtain an estimate of ei ≡ ai + yEi , i.e. the the own frontier(even when di = 0) but depends on the normalization(reference year)

Giuseppe De Arcangelis

The paperConclusions

Empirical Implementation

I Use Gronigen data set rather than PWT (more countries andtime periods)

I Global technology frontier is proxied with US data:ft = yUSt − yUSR where R= 1950 or 2008 Alert: for somecountries di > 1 My first remark: isn’t then di measuringproximity (divergence) to US dynamics rather than proximity(divergence) from a global frontier? Aren’t there variousfrontiers in the world that may depend on the area where youare? Is it possible a model of (competiting) frontiers?

I Estimation with a 5-year window: isn’t there a problem ofoverlapping periods? (Go for corrections in the standard errorsa la Newey-West?)

Giuseppe De Arcangelis

The paperConclusions

Empirical Implementation

I Use Gronigen data set rather than PWT (more countries andtime periods)

I Global technology frontier is proxied with US data:ft = yUSt − yUSR where R= 1950 or 2008

Alert: for somecountries di > 1 My first remark: isn’t then di measuringproximity (divergence) to US dynamics rather than proximity(divergence) from a global frontier? Aren’t there variousfrontiers in the world that may depend on the area where youare? Is it possible a model of (competiting) frontiers?

I Estimation with a 5-year window: isn’t there a problem ofoverlapping periods? (Go for corrections in the standard errorsa la Newey-West?)

Giuseppe De Arcangelis

The paperConclusions

Empirical Implementation

I Use Gronigen data set rather than PWT (more countries andtime periods)

I Global technology frontier is proxied with US data:ft = yUSt − yUSR where R= 1950 or 2008 Alert: for somecountries di > 1

My first remark: isn’t then di measuringproximity (divergence) to US dynamics rather than proximity(divergence) from a global frontier? Aren’t there variousfrontiers in the world that may depend on the area where youare? Is it possible a model of (competiting) frontiers?

I Estimation with a 5-year window: isn’t there a problem ofoverlapping periods? (Go for corrections in the standard errorsa la Newey-West?)

Giuseppe De Arcangelis

The paperConclusions

Empirical Implementation

I Use Gronigen data set rather than PWT (more countries andtime periods)

I Global technology frontier is proxied with US data:ft = yUSt − yUSR where R= 1950 or 2008 Alert: for somecountries di > 1 My first remark: isn’t then di measuringproximity (divergence) to US dynamics rather than proximity(divergence) from a global frontier?

Aren’t there variousfrontiers in the world that may depend on the area where youare? Is it possible a model of (competiting) frontiers?

I Estimation with a 5-year window: isn’t there a problem ofoverlapping periods? (Go for corrections in the standard errorsa la Newey-West?)

Giuseppe De Arcangelis

The paperConclusions

Empirical Implementation

I Use Gronigen data set rather than PWT (more countries andtime periods)

I Global technology frontier is proxied with US data:ft = yUSt − yUSR where R= 1950 or 2008 Alert: for somecountries di > 1 My first remark: isn’t then di measuringproximity (divergence) to US dynamics rather than proximity(divergence) from a global frontier? Aren’t there variousfrontiers in the world that may depend on the area where youare?

Is it possible a model of (competiting) frontiers?

I Estimation with a 5-year window: isn’t there a problem ofoverlapping periods? (Go for corrections in the standard errorsa la Newey-West?)

Giuseppe De Arcangelis

The paperConclusions

Empirical Implementation

I Use Gronigen data set rather than PWT (more countries andtime periods)

I Global technology frontier is proxied with US data:ft = yUSt − yUSR where R= 1950 or 2008 Alert: for somecountries di > 1 My first remark: isn’t then di measuringproximity (divergence) to US dynamics rather than proximity(divergence) from a global frontier? Aren’t there variousfrontiers in the world that may depend on the area where youare? Is it possible a model of (competiting) frontiers?

I Estimation with a 5-year window: isn’t there a problem ofoverlapping periods? (Go for corrections in the standard errorsa la Newey-West?)

Giuseppe De Arcangelis

The paperConclusions

Empirical Implementation

I Use Gronigen data set rather than PWT (more countries andtime periods)

I Global technology frontier is proxied with US data:ft = yUSt − yUSR where R= 1950 or 2008 Alert: for somecountries di > 1 My first remark: isn’t then di measuringproximity (divergence) to US dynamics rather than proximity(divergence) from a global frontier? Aren’t there variousfrontiers in the world that may depend on the area where youare? Is it possible a model of (competiting) frontiers?

I Estimation with a 5-year window: isn’t there a problem ofoverlapping periods? (Go for corrections in the standard errorsa la Newey-West?)

Giuseppe De Arcangelis

The paperConclusions

Robustness

I Alternatively to panel cointegration, estimation with firstdifferences with similar results (w/o outliers and oil-exportingcountries);

however, authors preferred panel cointegration toobtain an estimate of ei

I Reformulation with human capital by rescaling labor withhuman capital coefficients (Caselli, 2005);similar result forbi ∼= 4%, but lower values of di (not reassuring?)

I Various countries’ aggregations and an extension (for 30countries) to 1870-2010

I My suggestion: try alternatives to disentangle short-run andlong-run components, e.g. work on the frequency domain(probably only for growth rates)

Giuseppe De Arcangelis

The paperConclusions

Robustness

I Alternatively to panel cointegration, estimation with firstdifferences with similar results (w/o outliers and oil-exportingcountries);however, authors preferred panel cointegration toobtain an estimate of ei

I Reformulation with human capital by rescaling labor withhuman capital coefficients (Caselli, 2005);similar result forbi ∼= 4%, but lower values of di (not reassuring?)

I Various countries’ aggregations and an extension (for 30countries) to 1870-2010

I My suggestion: try alternatives to disentangle short-run andlong-run components, e.g. work on the frequency domain(probably only for growth rates)

Giuseppe De Arcangelis

The paperConclusions

Robustness

I Alternatively to panel cointegration, estimation with firstdifferences with similar results (w/o outliers and oil-exportingcountries);however, authors preferred panel cointegration toobtain an estimate of ei

I Reformulation with human capital by rescaling labor withhuman capital coefficients (Caselli, 2005);

similar result forbi ∼= 4%, but lower values of di (not reassuring?)

I Various countries’ aggregations and an extension (for 30countries) to 1870-2010

I My suggestion: try alternatives to disentangle short-run andlong-run components, e.g. work on the frequency domain(probably only for growth rates)

Giuseppe De Arcangelis

The paperConclusions

Robustness

I Alternatively to panel cointegration, estimation with firstdifferences with similar results (w/o outliers and oil-exportingcountries);however, authors preferred panel cointegration toobtain an estimate of ei

I Reformulation with human capital by rescaling labor withhuman capital coefficients (Caselli, 2005);similar result forbi ∼= 4%, but lower values of di (not reassuring?)

I Various countries’ aggregations and an extension (for 30countries) to 1870-2010

I My suggestion: try alternatives to disentangle short-run andlong-run components, e.g. work on the frequency domain(probably only for growth rates)

Giuseppe De Arcangelis

The paperConclusions

Robustness

I Alternatively to panel cointegration, estimation with firstdifferences with similar results (w/o outliers and oil-exportingcountries);however, authors preferred panel cointegration toobtain an estimate of ei

I Reformulation with human capital by rescaling labor withhuman capital coefficients (Caselli, 2005);similar result forbi ∼= 4%, but lower values of di (not reassuring?)

I Various countries’ aggregations and an extension (for 30countries) to 1870-2010

I My suggestion: try alternatives to disentangle short-run andlong-run components, e.g. work on the frequency domain(probably only for growth rates)

Giuseppe De Arcangelis

The paperConclusions

Robustness

I Alternatively to panel cointegration, estimation with firstdifferences with similar results (w/o outliers and oil-exportingcountries);however, authors preferred panel cointegration toobtain an estimate of ei

I Reformulation with human capital by rescaling labor withhuman capital coefficients (Caselli, 2005);similar result forbi ∼= 4%, but lower values of di (not reassuring?)

I Various countries’ aggregations and an extension (for 30countries) to 1870-2010

I My suggestion: try alternatives to disentangle short-run andlong-run components, e.g. work on the frequency domain(probably only for growth rates)

Giuseppe De Arcangelis

The paperConclusions

Explaining Country Differences in Long-Run Trends

I Cross section regression of di (and others) on different sets ofexplanatory variables, representing geography, history,education, institutions

I Main advancement: avoid confounding short run and long run

I My main concern: representativeness of di per country since itmay have changed over time

I Surprising results: public expenditure (G/Y) has a negativeeffect on the own frontier level (parameter ei ) and uncertainon long-run growth (di ); education does not have along-runeffect (!!);we should probably be reminded that the globalfrontier is given by US growth

Giuseppe De Arcangelis

The paperConclusions

Explaining Country Differences in Long-Run Trends

I Cross section regression of di (and others) on different sets ofexplanatory variables, representing geography, history,education, institutions

I Main advancement: avoid confounding short run and long run

I My main concern: representativeness of di per country since itmay have changed over time

I Surprising results: public expenditure (G/Y) has a negativeeffect on the own frontier level (parameter ei ) and uncertainon long-run growth (di ); education does not have along-runeffect (!!);we should probably be reminded that the globalfrontier is given by US growth

Giuseppe De Arcangelis

The paperConclusions

Explaining Country Differences in Long-Run Trends

I Cross section regression of di (and others) on different sets ofexplanatory variables, representing geography, history,education, institutions

I Main advancement: avoid confounding short run and long run

I My main concern: representativeness of di per country since itmay have changed over time

I Surprising results: public expenditure (G/Y) has a negativeeffect on the own frontier level (parameter ei ) and uncertainon long-run growth (di ); education does not have along-runeffect (!!);we should probably be reminded that the globalfrontier is given by US growth

Giuseppe De Arcangelis

The paperConclusions

Explaining Country Differences in Long-Run Trends

I Cross section regression of di (and others) on different sets ofexplanatory variables, representing geography, history,education, institutions

I Main advancement: avoid confounding short run and long run

I My main concern: representativeness of di per country since itmay have changed over time

I Surprising results: public expenditure (G/Y) has a negativeeffect on the own frontier level (parameter ei ) and uncertainon long-run growth (di );

education does not have along-runeffect (!!);we should probably be reminded that the globalfrontier is given by US growth

Giuseppe De Arcangelis

The paperConclusions

Explaining Country Differences in Long-Run Trends

I Cross section regression of di (and others) on different sets ofexplanatory variables, representing geography, history,education, institutions

I Main advancement: avoid confounding short run and long run

I My main concern: representativeness of di per country since itmay have changed over time

I Surprising results: public expenditure (G/Y) has a negativeeffect on the own frontier level (parameter ei ) and uncertainon long-run growth (di ); education does not have along-runeffect (!!);

we should probably be reminded that the globalfrontier is given by US growth

Giuseppe De Arcangelis

The paperConclusions

Explaining Country Differences in Long-Run Trends

I Cross section regression of di (and others) on different sets ofexplanatory variables, representing geography, history,education, institutions

I Main advancement: avoid confounding short run and long run

I My main concern: representativeness of di per country since itmay have changed over time

I Surprising results: public expenditure (G/Y) has a negativeeffect on the own frontier level (parameter ei ) and uncertainon long-run growth (di ); education does not have along-runeffect (!!);we should probably be reminded that the globalfrontier is given by US growth

Giuseppe De Arcangelis

The paperConclusions

Last ...

I Yet, another paper on the growth regression!!!

I But I really enjoy the reading!

I Thank you for your attention

Giuseppe De Arcangelis

The paperConclusions

Last ...

I Yet, another paper on the growth regression!!!

I But I really enjoy the reading!

I Thank you for your attention

Giuseppe De Arcangelis

The paperConclusions

Last ...

I Yet, another paper on the growth regression!!!

I But I really enjoy the reading!

I Thank you for your attention

Giuseppe De Arcangelis