Dynamic Panel Data Models

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Dynamic Panel Data Models

• Lecturer Zhigang Li

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Uses of Dynamic Panel Data Models

• yitayit-1ßXit?ieit
• Strict exogeneity assumption is obviously
  violated. When T is small, the estimates of all
  coefficients are generally inconsistent even if N
  is large.
• Ideas of solution
• Instrumental variables
• First estimate the model using OLS and then
  correct the bias used analytical formula.

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The IV Approach (J.F. Kiviet, 1995)

• Potential instrumental variables
• Lagged levels of independent variables
• Anderson and Hsiao (1981) For example, using
  yi,t-2 as the instrument for ?yt-1. (AHL)
• Arellano and Bond (1991) Using more lags as
  instruments. (GMM1 and GMM2)
• Lagged first difference of independent variables
• For example, using ?yt-1 as the instrument for
  yt-1. (IVAX)

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The Bias-correction Approach

• Step 1 Estimate the fixed effect model using OLS
  (sometimes referred as LSDV estimator).
• Step 2 Correct the estimate a by subtracting
  from it a measure of bias.
• For example, for a model with no exogenous
  regressor variables (X)

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Performance Comparison of Different Estimators

• The IVAX estimator generally provides the most
  consistent estimates.
• GMM estimators also provide quite good estimates.
• Compared with the above two, the LSDV estimators
  show large bias in the parameter estimates but
  smaller bias in standard errors.

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Simulation Results for Macroeconomic Panels
(Judson and Owen, 1999)

• Macroeconomic panel data generally have a larger
  T (as large as 30)
• Findings
• LSDV bias are still quite significant even for T
  as large as 30 (the bias may be as much as 20 of
  the true value).
• However, LSDV is preferable if we use mean square
  errors for comparison.
• GMM estimators typically perform better than the
  AHL estimator.
• A restricted GMM estimator that uses a subset
  of the available lagged values as instruments are
  easier to implement and still perform well.

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Growth Empirics (Islam, 1995)

• Objective Characterizing the pattern of
  convergence of different countries.
• Idea Using country fixed effects to control for
  unobserved country-specific factors (i.e.
  institution) that may affect the accumulation of
  production inputs (i.e. capital)
• Earlier studies only considered a cross section
  of countries and measure the relationship between
  their initial growth level and subsequent growth
  speed.

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The Model

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• Estimation method Least Squares with Dummy
  Variables (LSDV)
• Estimates are inconsistent in theory unless the
  time dimension is large (suggested by Amemiya,
  1967)
• Simulation by the author also finds the bias is
  small with the size of the given sample.

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Findings and Interpretation

• The estimated rates of conditional convergence
  prove to be higher than using OLS cross-country
  regressions.
• Persistent differences in technology level and
  institutions are a significant factor in
  understanding cross-country economic growth.
• If there had been no such differences,
  convergence would have proceeded at a faster
  rate.
• The estimated values of the elasticity of output
  with respect to capital are found to be much
  lower than the OLS estimates.
• Suggesting capital deepening.

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Testing for Fiscal Competition(Binet 2003)

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• NitdifGit-1eNit-1vit
• A Granger causality methodology
• The coefficient of interest is f, which indicates
  whether governmental fiscal policy affects (in
  the sense of Granger causality) local population
  changes
• Dynamic panel data regressions
• LSDV bias-corrected (Bun and Kiviet 2001)

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Methodology
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Empirical Results

• Data
• A sample of 27 French municipalities in the same
  suburban area for 1987-1996.
• Data from AUDIAR (Greater Rennes
  Inter-Municipality Development Agency)
  publications.
• Local public expenditure Municipal employee
  wages, debt services, and annual investment.
• Local public revenue policy Measured by fiscal
  effort (total tax revenue divided by the
  corresponding tax bases).
• Findings Both fiscal revenue and policy measures
  seem to affect local population.

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Democracy, Inequality, and Inflation (Desai et
al., 2003)

• Two theories
• The populist theory Inflation is the result of
  public demand for transfers financed by the
  inflation tax, suggesting that electoral
  competition will increase inflation.
• The state-capture theory Inflation is a result
  of pressure from elites who derive private
  benefits from money creation, suggesting that
  electoral competition may constrain inflation.
• Tested hypothesis More democratic countries will
  suffer from higher inflation as the distribution
  of income in those countries becomes more unequal.

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Empirical Approach

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  Lit-1)eit
• Data
• Over 100 countries between 1960 and 1999.
• POL The Gastil index and the Polity index.
• Gini coefficient is from the UN-WIDER World
  Income Inequality Database.
• Other control variables Fiscal balance, GDP
  growth rates, the size of financial sector,
  foreign reserves, trade openness, central bank
  independence, instability.
• Estimated by LSDV and GMM.

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Arbitrage in International Telephone Service
(Gyimah and Karikari, 2002)

• International telephone calls are priced very
  differently in different countries. This provide
  an incentive for people to arbitrage through cost
  shifting (i.e. collect call, call me back)
• It is interesting to quantify peoples
  arbitraging behavior.
• Is there any evidence of this arbitrage effect?
• What is the magnitude of the arbitrage?

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Empirical Approach

• Model
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• ß5(lnptui-lnptai)ß6lnEmigrtaiß7lnTradetui?t?i
  t
• Data
• Mui is measured by average call duration (the
  ratio of total call minutes from the US to an
  African country to the total number of telephone
  calls from the US to that country).
• Neither prices of telephone calls from the
  African countries to the US nor total revenues
  from such calls were available. The authors use
  the pay-outs to US telephone companies by Arican
  countries for completing African-billed traffic
  to the US.

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Empirical Approach (Continued)

• Data on 45 African countries over the 1992-1996
  period are used.
• Dynamic Panel Estimator
• Arellano and Bond estimator
• Use all lagged values of endogenous and
  predetermined variables as well as current and
  lagged values of exogenous regressors as
  instruments in the differenced equaiton.

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Sensitivity Analysis

• Alternative measures of prices
• Excluding South Africa, which accounts for about
  15 of the volume of telephone calls between
  African countries and the US.

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Intangible resources and sustainability of firms
(Villalonga, 2004)

• Question Does greater degree of intangibility of
  a firms resources causes greater sustainability
  of its competitive advantage or disadvantage?

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Measures of Variables

• Intangibility
• Tobins Q The ratio of firms market value (the
  sum of the year-end market value of common stock
  and the book value of preferred stock and debt)
  to the replacement cost of their (tangible)
  assets
• Sustainability
• Persistence of firm-specific profits (FSP)
• FSP is the difference between the firms
  profitability and the average profitability of
  the industry in any given year.

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Empirical Approach

• Data
• The sample consists of 1641 US public
  corporations between 1981 and 1997.
• Data from Compustat annual company and industry
  segment files
• Model
• FSPitaiß0FSPit-1ß1qitS1JDjß2j FSPit-1qiteit
• Estimated by Arellano and Bond (1998) estimator
  (DPD98 program for GAUSS).

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Findings

• Resource intangibility is positively related to
  the persistence of firm-specific profits or
  losses.

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The Impact of Exchange Rate Uncertainty on
Investment (Byrne and Davis, 2005)

• How to measure ER uncertainty?
• This study utilizes the conditional volatility
  implied from GARCH models.
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• Empirical model
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• The pooled mean group estimator proposed by
  Pesaran et al. (1999) for a dynamic heterogeneous
  panel models.
• X includes lnY, lnC (user cost of capital), and
  conditional variance of exchange rate.

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Data

• OECD Business Sector Database
• Primark Dtatstream provide data on monthly
  exchange rate.

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Financial Depth and Economic Growth
(Christopoulos and Tsionas, 2004)

• Question Whether there is a long-run
  relationship between financial depth and economic
  growth?
• Data Panel data for 10 developing countries for
  the period 1970-2000.
• Methodology Panel unit root test and panel
  cointegration test.

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Panel Unit Root Test

• Im et al. (1997)
• Averaging individual Dickey-Fuller unit root
  tests according to
• Eti?i0 and varti?i0 are obtained by Monte
  Carlo simulation and are tabulated in Im et al.
  (1997).
• Maddala and Wu (1999)
• P-2Spi
• The P test is distributed as ?2 under the null
  (unit root).
• Comparison
• Both allow variables to have different dynamics
  in different countries.
• MW test seems to perform better.

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Panel Cointegration Test

• Levin and Lin (1993)
• Harris and Tzavalis (1999)
• Fishers test Aggregate the p-values of
  individual Johansen maximum likelihood
  cointegration test statistics.
• P-2Slnpi ?22N
• Comparison
• Neither the LL test nor the HT test allow for
  heterogeneity in the autoregressive coefficient.
• The Fishers test is easier to compute and allow
  for heterogeneity.