# **5. Model calibration**

# _5.1 Setting up the baseline and scenarios_

To make empirical comparisons _between_ the Standard LTGM and the public capital extension (LTGM‐PC) as well as _within_ the public capital extension (public versus private investment, increasing quantity vs quality of public investment), we run simulations using both models for a sample of 147 countries. To solve each model, we need to first input baseline parameters, initial conditions and paths of variables for individual countries. Data sources and calculations are detailed in Table 3.

**<u>Table 3: Baseline Parameters, Initial Conditions and Paths of Variables</u>**

|<br>**Constant Parameters**|<br>**Model(s)**|<br>**Source/Calculation**|
|---|---|---|
|Labor shareβ|Std LTGM<br>LTGM‐PC|Latest individual countryβ, based on Penn World Tables (PWT) version 8.1,<br>or the Global Trade Analysis Project (GTAP) database. Labor shares below<br>0.45 or above 0.7 were trimmed to those values to remove outliers.|
|Elasticity of output to public<br>capitalφ|LTGM‐PC|0.170 (default) and 0.100 for all countries. See Section 5.2 for discussion of<br>this calibration.|
|Congestionζ|LTGM‐PC|1(congestion)or 0(purepublicgood)is assumed for all countries.|
|Efficient public capital stockθ|LTGM‐PC|Infrastructure Efficiency Index (IEI) – see Section 4. Unchanged efficiency is<br>assumed for all countries.|
|Aggregate depreciation rateδ|Std LTGM|Latest value from PWT 8.1.|
|Public capital and private capital<br>depreciation ratesδ<sup>�</sup>, δ<sup>�</sup>|LTGM‐PC|δ<sup>�</sup>= 2% for all countries, which is the average depreciation rate for<br>structures in the PWT 8.1.δ<sup>�</sup>, individual country‐specific, is the residual<br>from the weighted average calculation.|
|**Initial Conditions**|||
|Initial capital‐to‐output ratio<br>��<br>��|Std LTGM|Individual country values are based on the most recent data in PWT 8.1.<br>(Capital stock at constant 2005 national prices (2005 US$ mil.)/Real GDP at<br>constant 2005 national prices (2005 US$ mil.)). K/Y below 1.5 or above 3.5<br>were trimmed to those values to remove outliers.|
|Initial measured public capital‐<br>to‐output and private capital‐to‐<br>output ratios<br>��<br>��<br>��<br>~~,~~<br>��<sup>�</sup><br>��|LTGM‐PC|Individual country values are derived by applying 2015 shares of public and<br>private capital calculated by the IMF Fiscal Affairs Dept. to PWT data on<br>��<br>��<br>~~.~~<br>IMF data:http://www.imf.org/external/np/fad/publicinvestment/.|
|**Projected Paths**|||
|TFP growthg�|Std LTGM<br>LTGM‐PC|Individual country average value over 2001‐2010 based on PWT 8.1 (or<br>applying PWT methodology with GTAP labor shares). Missing TFP in PWT<br>calculated by Barrot (2016) using GTAP labor share. Negative TFP growth<br>adjusted upto zero.|
|Human capital growth rateg�|Std LTGM<br>LTGM‐PC|Individual country average value over 2001‐2010 from PWT 8.1, based on<br>years of schoolingand returns to education.|
|Growth in labor participation<br>rateg�|Std LTGM<br>LTGM‐PC|International Labor Organization (ILO) individual country data for 2014,<br>available from the World Development Indicators(WDI)Database.|
|Population growthg�|Std LTGM<br>LTGM‐PC|World Bank compilation of data sourced from the United Nations<br>Population Division and countrycensuses. Projections for 2016 to 2050.|
|Growth in the working age‐to‐<br>population rateg�|Std LTGM<br>LTGM‐PC|World Bank estimates based on United Nations Population Division data on<br>age and sex distribution ofpopulation. Projections for 2016 to 2050.|
|Investment‐to‐output ratio<br>�<br>�|Std LTGM|Individual country data is based on most recent data in WDI (Gross fixed<br>capital formation (constant 2010 US$)/GDP (constant 2010 US$)).|
|Public investment‐to‐output and<br>private investment‐to‐output<br>ratios<br>�<sup>�</sup><br>�<br>,<br>�<sup>�</sup><br>�|LTGM‐PC|Individual country values are derived by applying the 2015 shares of public<br>and private investment calculated by the IMF FAD to WDI data on<br>�<br>�<br>~~.~~IMF<br>data:http://www.imf.org/external/np/fad/publicinvestment/|
|The sample of countries is guided by t<br>affected countries based on the media<br>countries was reduced to 147 to exclu|he availability o<br>n value of avail<br>de outliers that|f human capital data. For missing data in other variables, these are interpolated for the<br>able data for the corresponding country groups by income. An initial sample of 151<br>appeared in the top graphs of Graph 2(The Bahamas,Egypt,Iran and Uzbekistan).|

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