## _wp10187 - 1.    GMM Dynamic Modeling

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---

### Introduction
- Research question: what pulls FDI into countries, distinguishing primary, secondary and tertiary FDI flows and comparing advanced and emerging economies.
- Sectoral focus: primary (petroleum, mining, agriculture), secondary (manufacturing), tertiary (services).
- Key motivation: FDI may bring foreign technology and management skills; causality between FDI and growth is unclear.
- Sample: annual FDI data 1985 to 2008 for 27 advanced and EM countries; analysis focused on 26 middle- and high-income economies (countries listed in source).

### Background (literature and hypotheses)
- Stylized determinants considered: market size and growth potential; openness; exchange rate valuation; clustering effects; political stability; institutional quality.
- Theoretical motivations cited: Dunning (1993) motives; Froot and Stein (1991) and Blonigen (1997) on exchange rates; evidence of agglomeration from Wheeler and Mody (1992), Barrell and Pain (1999), Campos and Kinoshita (2003).
- Empirical ambiguity noted for political risk and institutions (Wheeler and Mody (1992) vs. Root and Ahmed (1979), Schneider and Frey (1985), Wei (2000)).

### Data and methodology
- Dependent variable: inflow of FDI as a share of nominal GDP.
- FDI data: net FDI flows by primary, secondary, tertiary from UNCTAD.
- Explanatory variables:
  - Macroeconomic: openness (share of goods and services trade in GDP), log level of the multilateral real exchange rate (REER), trailing 3-year moving average inflation, stock of FDI, real GDP growth, log level of GDP per capita.
  - Qualitative/institutional: labor market flexibility (hiring and firing cost index), infrastructure quality, judicial independence, legal system efficiency, financial depth, school enrollment (primary, secondary, tertiary).
- Econometric approach:
  - Generalized Method of Moments (GMM) dynamic estimator based on Arellano-Bond methodology.
  - System GMM (Blundell and Bond (1988)) used to address weak instruments in small samples with persistent regressors.
- Estimated dynamic equation (notation preserved):
  - y denotes FDI as a share of GDP, X is the vector of macroeconomic and institutional/qualitative variables, μ represents time-invariant country-specific effects:
    - tiitititi vXyy ,'
    ,1,,
    
    
      (1)
  - First-differenced form:
    - )()()(
    1,,
    '
    1,
    '
    ,2,1,1,,
    
    titititititititi
    vvXXyyyy  (2)

### Results — A. Macroeconomic variables and FDI
- Baseline macro controls: openness, GDP growth, average inflation (3-year), log GDP per capita, log real exchange rate (REER), stock of FDI.
- Aggregated (total) FDI:
  - Clustering (FDI stock) significant.
  - Macro variables (openness, REER) show weak/puzzling results for total FDI.
- Sectoral heterogeneity:
  - Primary FDI:
    - Minimal linkage to macroeconomic variables; largely determined by natural resource location.
  - Secondary (manufacturing) FDI:
    - A more depreciated REER is associated with more manufacturing investment.
    - Higher GDP growth weakly associated with more manufacturing investment.
    - Richer countries attract a lower share of FDI relative to GDP (log GDP per capita negative).
    - Openness not clearly linked to secondary FDI.
  - Tertiary (services) FDI:
    - Openness is very important and positive (highly significant).
    - REER effect opposite to secondary FDI: tertiary FDI associated with more appreciated REER.
    - GDP growth and openness positively related to services FDI.
- Inflation: average CPI inflation over the past three years shows little relationship with FDI in any sector once REER is controlled for.
- Selected exact table summary items (Table 1):
  - Observations (Total FDI, Primary FDI, Secondary FDI, Tertiary FDI): 319, 320, 356, 330.
  - Sargan p-value (Total FDI, Primary FDI, Secondary FDI, Tertiary FDI): 0.95, 0.95, 0.55, 0.21.
  - Significance notation in tables: *** p<0.01, ** p<0.05, * p<0.1.

### Results — B. Qualitative / institutional variables
- Estimation approach: add qualitative variables one at a time to the macro baseline due to multicollinearity.
- Total and primary FDI:
  - Most institutional/development variables show no influence on total FDI or primary FDI.
  - Exception: a counter-intuitive negative finding for tertiary enrollment on total FDI in one specification.
  - FDI stock remains associated with higher flows.
  - Example Sargan p-values in Tables 2 and 3: 0.59, 0.56, 0.628, 0.576, 0.612, 0.765, 0.946, 0.759 (various specifications).
- Secondary FDI:
  - Labor market flexibility and financial depth are significant and positive determinants of manufacturing FDI.
  - GDP per capita coefficient is significant and negative in these specifications.
  - Infrastructure quality, school enrollment, and legal system efficiency generally not significant.
  - Selected coefficient details (Table 4 examples):
    - REER coefficient for column 1 is -0.73** (standard error (0.345)).
    - FDI Stock coefficient 2.18*** (standard error (0.511)) in one specification.
    - Observations reported in various columns: 271, 201, 134, 333, 260, 224, 225, 200.
- Tertiary FDI:
  - Judicial independence and infrastructure quality have significant and expected positive signs.
  - GDP per capita often negative and significant (example: -1.40*** with standard error (0.477) in Table 5 column 1).
  - Openness and REER strong positive determinants in services regressions (example: Openness 39.26*** (9.703) and REER 4.64*** (1.097) in Table 5 column 1).
  - Some puzzling negative relations with secondary and tertiary enrollment indices and services FDI.
  - Additional tertiary regression examples (Table 10 / column 1): Openness 49.19*** (10.845); REER 6.00*** (1.307); GDP per capita -1.91*** (0.546).

### Results — C. Developed versus developing economies
- Method: interact a developed-economy dummy with macro variables; base effect = effect in emerging markets; effect in developed = base + interaction coefficient.
- Primary FDI: macroeconomic variables largely unimportant; openness coefficient stronger for developed economies in this sample.
- Secondary FDI:
  - Broadly similar effects across advanced and emerging economies.
  - Labor market flexibility and financial depth matter much more for emerging markets than for advanced economies.
  - For financial depth, coefficient signs differ: positive for developing, negative for advanced (interaction terms significant).
  - Infrastructure improvements weakly associated with more secondary FDI into emerging markets, insignificant for advanced economies.
- Tertiary FDI:
  - Macro variables matter more for advanced economies than for emerging markets.
  - For developed economies, stronger REER and larger FDI stock lead to significantly more tertiary FDI.
  - Example interaction coefficient reported: GDP per capita -2.27*** in Table 6 developed interaction column (interpretation: developed-economy interaction result reported in source).
  - Judicial independence leads weakly to more FDI only in advanced economies.
  - Counterintuitive finding: more flexible labor markets linked with less tertiary FDI in advanced economies.

### Policy-relevant conclusions and implications
- Sectoral heterogeneity is crucial: determinants of FDI differ strongly across primary, secondary, tertiary sectors.
  - Primary FDI: little linkage to macroeconomic stability, development level, or institutional quality; clustering (FDI stock) matters.
  - Secondary FDI: attracted by depreciated REER, labor market flexibility, and deeper financial systems; GDP per capita negatively associated with FDI/GDP share.
  - Tertiary FDI: attracted by openness, appreciated REER, higher GDP growth, better infrastructure, and more independent judiciary.
- Advanced vs. emerging economies:
  - Secondary FDI determinants similar across development levels, but labor market flexibility and financial depth matter more for emerging markets.
  - Tertiary FDI determinants stronger in advanced economies: macroeconomic conditions (REER, inflation, openness) and FDI stock matter more for advanced economies.
- Policy prescriptions from results:
  - Do not treat aggregate FDI as homogeneous; target policies to sectoral composition.
  - For manufacturing (secondary FDI): policies improving labor market flexibility and financial depth can be effective, especially in emerging markets.
  - For services (tertiary FDI): maintaining openness, macroeconomic stability, good infrastructure, and judicial independence can attract more investment—particularly effective in advanced economies.
  - Reducing inflation from moderate to low levels may yield limited marginal benefits for attracting additional FDI within the relatively stable economies analyzed.
- Data and measurement caveats:
  - Institutional/qualitative variables are imperfect proxies (e.g., enrollment rates may not capture actual skill attainment).
  - Aggregation of heterogeneous FDI inflows can bias results; further firm- or project-level data would improve identification.

### Exchange rate policy trade-off (explicit conclusion)
- Quoted key conclusion: "the role of exchange rate policy: while maintaining a weak exchange rate to stimulate manufacturing exports can lead to higher secondary sector FDI, it will at the margins reduce the amount of tertiary FDI received by the host country."
- Trade-off implication:
  - A weak exchange rate tends to increase secondary-sector FDI.
  - A weak exchange rate will at the margins reduce tertiary (services) FDI received by the host country.

### Appendix — GMM dynamic modeling formulation and estimators
- Model structure:
  - Regression structure includes a lagged dependent variable and a time-invariant cross-sectional factor μ_i; first-differencing eliminates μ_i but creates correlation between Δν_{i,t} and Δy_{i,t-1}.
- Arellano and Bond one-step estimator:
  - Instrumental matrix W constructed from lagged levels (block structure shown in source).
  - One-step consistent estimator presented as equation (4) in source.
- Two-step GMM estimator:
  - Arellano and Bond two-step estimator given as equation (5) in source.
  - Two-step estimator uses V = Σ_i v_i v_i' where v_i are residuals (source expression for 1/N Σ_i ...).
- Moment conditions and assumptions:
  - Under no serial correlation in errors and weak exogeneity of explanatory variables, moment conditions for difference GMM are:
    - 0]([1,, , = - - -titisti vyE ν for s≥2; t=3,...,T (equation (6) in source).
- Weak instrument problem in difference GMM:
  - In small samples with persistent regressors, lagged levels make weak instruments for the difference model; asymptotically, variance of coefficients would rise and coefficients could be biased.
- System GMM (Blundell and Bond, 1998):
  - Combines regressions in first differences and levels to strengthen instruments.
  - Instruments for differences regression are lagged levels; instruments for levels regression are lagged differences.
  - Additional moment conditions for the levels regression:
    - 0)]()[(
,1,,
=
tiististi yyE νμ for s=1 (equation (7) in source).
  - Instrument matrix W in expanded models includes lagged levels and (for system GMM) lagged differences of additional explanatory variables, with lag selection depending on whether variables are predetermined or strictly exogenous.

*Source: _wp10187 - 1.    GMM Dynamic Modeling (PDF chapter/section).*

### References .............................................................................................................

### _wp10187 - References

### Tables
- 1.    FDI and Macroeconomic Variables ..................................................................................11
- 2.    Total FDI and Institutions .................................................................................................12
- 3.    Primary FDI and Institutions ............................................................................................13
- 4.    Secondary FDI and Institutions ........................................................................................14
- 5.    Tertiary FDI and Institutions ............................................................................................15
- 6.    FDI and Macroeconomic Variables-By Level of Development .......................................16
- 7.    Total FDI and Qualitative Determinants-By Level of Development ................................17
- 8.    Primary FDI and Qualitative Determinants-By Level of Development ...........................18
- 9.    Secondary FDI and Qualitative Determinants-By Level of Development .......................19
- 10.  Tertiary FDI and Qualitative Deaterminants-By Level of Development .........................20

### Appendix
- Appendix

*Source: _wp10187 - References*

### 1.    GMM Dynamic Modeling .............................................................................................

### 1.    GMM Dynamic Modeling

### Introduction
- Research question: what pulls FDI into countries, distinguishing primary, secondary and tertiary FDI flows and comparing advanced and emerging economies.
- Key motivation: FDI may bring foreign technology and management skills; causality between FDI and growth is unclear.
- Sectoral focus: primary (petroleum, mining, agriculture), secondary (manufacturing), tertiary (services).
- Sample framing: emerging markets may trade off macro instability and weaker institutions for lower wages or protected markets.

### Background (literature and hypotheses)
- Stylized determinants considered: market size and growth potential; openness; exchange rate valuation; clustering effects; political stability; institutional quality.
- Theoretical motivations cited: Dunning(1993) motives (access to resources, markets, efficiency, strategic assets); Froot and Stein (1991) and Blonigen (1997) on exchange rates; evidence of agglomeration from Wheeler and Mody (1992), Barrell and Pain (1999), Campos and Kinoshita (2003).
- Empirical ambiguity noted for political risk and institutions (Wheeler and Mody (1992) vs. Root and Ahmed (1979), Schneider and Frey (1985), Wei (2000)).

### Data and methodology
- Data: annual FDI data with observations from 1985 to 2008 for 27 advanced and EM countries, analysis focusing on 26 middle- and high-income economies.
- Countries listed in sample: Argentina, Australia, Brazil, Canada, China, Colombia, the Czech Republic, France, Germany, Hungary, India, Indonesia, Italy, Japan, Korea, Malaysia, Mexico, the Philippines, Poland, Russia, South Africa, Saudi Arabia, Spain, Thailand, Turkey, the United Kingdom, and the United States.
- FDI data: net FDI flows by primary, secondary, tertiary from UNCTAD; institutional/qualitative indicators mainly from the Global Investment Report and World Bank development indicators.
- Dependent variable: inflow of FDI as a share of nominal GDP.
- Explanatory variables include: openness (share of goods and services trade in GDP), log level of the multilateral real exchange rate (REER), trailing 3-year moving average inflation, stock of FDI, real GDP growth, log level of GDP per capita; qualitative variables: labor market flexibility (hiring and firing cost index), infrastructure quality, judicial independence, legal system efficiency, financial depth, school enrollment (primary, secondary, tertiary).
- Econometric approach: Generalized Method of Moments (GMM) dynamic estimator based on Arellano-Bond methodology; system GMM (Blundell and Bond (1988)) used to address weak instruments in small samples with persistent regressors.
- Estimated dynamic equation (notation preserved):
  - y denotes FDI as a share of GDP, X is the vector of macroeconomic and institutional/qualitative variables, μ represents time-invariant country-specific effects:
    - tiitititi vXyy ,'
    ,1,,
    
    
      (1)
  - First-differenced form:
    - )()()(
    1,,
    '
    1,
    '
    ,2,1,1,,
    
    titititititititi
    vvXXyyyy  (2)

### Results — A. Macroeconomic variables and FDI
- Baseline macro controls: openness, GDP growth, average inflation (3-year), log GDP per capita, log real exchange rate (REER), stock of FDI.
- Aggregated (total) FDI: clustering (FDI stock) significant; macro variables (openness, REER) show weak/puzzling results for total FDI.
- Sectoral heterogeneity:
  - Primary FDI: minimal linkage to macroeconomic variables; primary FDI determined largely by natural resource location; macro variables make little difference.
  - Secondary (manufacturing) FDI:
    - A more depreciated REER is associated with more manufacturing investment.
    - Countries with higher GDP growth have (weakly) more manufacturing investment.
    - Richer countries attract a lower share of FDI relative to GDP (log GDP per capita negative).
    - Openness does not appear linked to secondary FDI.
  - Tertiary (services) FDI:
    - Openness is very important and positive, with a highly significant coefficient.
    - REER effect is the opposite of secondary FDI: tertiary FDI is at least weakly associated with more appreciated REER.
    - GDP growth and openness positively related to services FDI.
- Inflation: average CPI inflation over the past three years shows little relationship with FDI in any sector once REER is controlled for.
- Selected exact table summary items (Table 1):
  - Observations (Total FDI, Primary FDI, Secondary FDI, Tertiary FDI): 319, 320, 356, 330.
  - Sargan p-value (Total FDI, Primary FDI, Secondary FDI, Tertiary FDI): 0.95, 0.95, 0.55, 0.21.
  - Note on significance notation: *** p<0.01, ** p<0.05, * p<0.1.

### Results — B. Qualitative / institutional variables
- Approach: add qualitative variables one at a time to the macro baseline due to multicollinearity.
- Total and primary FDI:
  - Most institutional/development variables show no influence on total FDI or primary FDI.
  - Exception: a counter-intuitive negative finding for tertiary enrollment on total FDI in one specification.
  - FDI stock remains associated with higher flows.
  - Example table details (Tables 2 and 3): Sargan p-values for various specifications vary (e.g., Table 2 Sargan p-values 0.59, 0.56, 0.628, 0.576, 0.612, 0.765, 0.946, 0.759); observations vary across specifications.
- Secondary FDI:
  - Labor market flexibility and financial depth are significant and positive determinants of manufacturing FDI.
  - GDP per capita coefficient is significant and negative in these specifications.
  - Infrastructure quality, school enrollment, and legal system efficiency are generally not significant.
  - Selected table details (Table 4): REER coefficient for column 1 is -0.73** (standard error (0.345)); FDI Stock coefficients often significant and positive (e.g., 2.18*** in column 1 with standard error (0.511)); Observations vary (271, 201, 134, 333, 260, 224, 225, 200).
- Tertiary FDI:
  - Judicial independence and infrastructure quality have significant and expected signs (positive).
  - GDP per capita often negative and significant (e.g., -1.40*** in Table 5 column 1 with standard error (0.477)).
  - Openness and REER strong positive determinants in services regressions (e.g., Openness 39.26*** (9.703) in Table 5 column 1; REER 4.64*** (1.097) in Table 5 column 1).
  - Some puzzling negative relations with secondary and tertiary enrollment indices and services FDI.

### Results — C. Developed versus developing economies
- Method: interaction of developed-economy dummy with macro variables; coefficient interpretation: base effect = effect in emerging markets; effect in developed = base + interaction coefficient.
- Primary FDI: macroeconomic variables remain largely unimportant; openness coefficient stronger for developed economies in this sample (possibly driven by Canada, Australia).
- Secondary FDI: broadly similar effects across advanced and emerging economies; GDP per capita no longer as important when interacted.
- Tertiary FDI:
  - Macro variables matter more for advanced economies than for emerging markets.
  - For developed economies, stronger REER and larger FDI stock lead to significantly more tertiary FDI; GDP per capita may be negative and significant in developed-economy interaction (e.g., GDP per capita -2.27*** in Table 6 developed interaction column).
  - For developing economies, tertiary FDI appears less influenced by macro variables.
- Qualitative variables by development status:
  - Secondary FDI:
    - Labor market flexibility and financial depth matter much more for emerging markets than for advanced economies.
    - For financial depth, coefficient signs: positive for developing, negative for advanced (interaction terms significant).
    - Infrastructure improvements weakly associated with more secondary FDI into emerging markets, insignificant for advanced economies.
  - Tertiary FDI:
    - Significant qualitative determinants: labor market flexibility, infrastructure quality, judicial independence (but significance often weak).
    - Judicial independence leads weakly to more FDI only in advanced economies.
    - Counterintuitive finding: more flexible labor markets linked with less tertiary FDI in advanced economies.
  - Selected tertiary table details (Table 10): Openness 49.19*** (10.845) in column 1; REER 6.00*** (1.307) in column 1; GDP per capita -1.91*** (0.546) in column 1.

### Conclusions (policy-relevant findings and implications)
- Sectoral heterogeneity is crucial: determinants of FDI differ strongly across primary, secondary, tertiary sectors.
  - Primary FDI: little linkage to macroeconomic stability, development level, or institutional quality; clustering (FDI stock) matters.
  - Secondary FDI: attracted by depreciated REER, labor market flexibility, and deeper financial systems; GDP per capita negatively associated with FDI/GDP share.
  - Tertiary FDI: attracted by openness, appreciated REER, higher GDP growth, better infrastructure, and more independent judiciary.
- Advanced vs. emerging economies:
  - Secondary FDI determinants similar across development levels, but labor market flexibility and financial depth matter more for emerging markets.
  - Tertiary FDI determinants stronger in advanced economies: macroeconomic conditions (REER, inflation, openness) and FDI stock matter more for advanced economies.
- Policy implications:
  - Policymakers should avoid treating aggregate FDI as homogeneous; sectoral composition matters for policy targeting.
  - For manufacturing (secondary FDI), policies improving labor market flexibility and financial depth can be effective, especially in emerging markets.
  - For services (tertiary FDI), maintaining openness, macroeconomic stability, good infrastructure, and judicial independence can attract more investment—particularly effective in advanced economies.
  - Reducing inflation from moderate to low levels may yield limited marginal benefits for attracting additional FDI within relatively stable economies analyzed here.
- Data and measurement caveats:
  - Institutional/qualitative variables are imperfect proxies (e.g., enrollment rates may not capture actual skills attainment).
  - Aggregation of heterogeneous FDI inflows can bias results; further firm- or project-level data would improve identification.

*Source: _wp10187 - 1.    GMM Dynamic Modeling (PDF chapter/section).*

### conclusion is the role of exchange rate policy: while maintaining a weak exchange rate to

### _wp10187 - conclusion is the role of exchange rate policy: while maintaining a weak exchange rate to

### Key conclusions on exchange rate policy and FDI
- "the role of exchange rate policy: while maintaining a weak exchange rate to stimulate manufacturing exports can lead to higher secondary sector FDI, it will at the margins reduce the amount of tertiary FDI received by the host country."
- The trade-off highlighted: policies that favor a weak exchange rate to boost manufacturing exports tend to increase secondary-sector FDI but marginally reduce tertiary (services) FDI.

### Institutional and qualitative determinants of FDI
- "Liberalizing labor markets and measures to increase financial deepening could attract more secondary FDI into emerging markets, though these effects are weaker among advanced economies."
- "A more independent judiciary and better infrastructure appear to attract more services FDI to both types of economies."

### GMM dynamic modeling — formulation and estimators
- The appendix outlines a Generalized Method of Moment (GMM) dynamic model built on a lagged dependent variable and a time-invariant cross-sectional factor:
  - Regression structure (equation (1) in source): y_{i,t} is regressed on its lag and time-invariant cross-sectional factor μ_i.
  - First-differenced form eliminates μ_i but introduces correlation between Δν_{i,t} and Δy_{i,t-1}.
- Arellano and Bond (1991) instrumental matrix and one-step estimator:
  - Instrumental matrix W is constructed from lagged levels as in the source (block structure shown for W).
  - Pre-multiplication leads to equation (3): ΔWy = ΔWy W'...? (see source for exact matrix expressions).
  - The one-step consistent estimator is presented in the source as equation (4).
- Two-step GMM estimator:
  - Arellano and Bond two-step estimator is given as equation (5) in the source.
  - The two-step estimator uses V = Σ_i v_i v_i' where v_i are residuals (see source expression for 1/N Σ_i ...).
- Moment conditions and assumptions:
  - Under no serial correlation in errors and weak exogeneity of explanatory variables, moment conditions for difference GMM are:
    - 0]([1,, , = - - -titisti vyE ν for s≥2; t=3,...,T (equation (6) in source).
  - Weak instrument problem in difference GMM:
    - "In a small sample where some explanatory variables are persistent over time, lagged levels make weak instruments for the difference model regression. Asymptotically, the variance of the coefficients would rise and coefficients could be biased."
- System GMM (Blundell and Bond, 1998):
  - To address weak instruments, the system GMM combines regressions in first differences and levels.
  - Instruments for the differences regression are lagged levels; instruments for the levels regression are lagged differences.
  - Additional moment conditions for the levels regression are:
    - 0)]()[(
,1,,
=
tiististi yyE νμ for s=1 (equation (7) in source).
  - The instrument matrix W in expanded models includes lagged levels and (for system GMM) lagged differences of additional explanatory variables, with the number of lags depending on whether variables are predetermined or strictly exogenous.

*Source: IMF working paper content (conclusion and Appendix I: GMM Dynamic Modeling).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10187.pdf_