metadata: authors: 0: author: Burns,Andrew
1: author: Jooste,Charl
count: World
docna: 0: docna: Estimating and Calibrating MFMod : A Panel
            Data Approach to Identifying the Parameters of Data Poor
            Countries in the World Bank's Structural Macro Model
docty: Policy Research Working Paper
subtopic: Macroeconomic Management,International Trade and Trade Rules,Inflation,Transport Services,Macro-Fiscal Policy,Economic Adjustment and Lending,Taxation & Subsidies,Public Finance Decentralization and
            Poverty Reduction,Public Sector Economics
teratopic: International Economics and Trade,Transport,Macroeconomics and Economic Growth,Public Sector Development
abstracts: cdata!: This paper summarizes the World
            Bank's approach to identifying parameters for key
            equations in its macro structural model for countries where
            short sample sizes or major structural changes render
            traditional time-series approaches infeasible or yield
            unstable estimates. To identify parameters that could be
            used in such cases, a cointegrating panel approach is
            followed that yields a common long-run estimate of
            parameters for key equations (to test the theoretical
            restrictions imposed in the model) and short-run
            disequilibrium estimates that vary by country. This approach
            is preferred to pure calibration or Bayesian estimation,
            because the functional forms imposed in the panel are
            consistent with those used in the macro structural model.
repnme: repnme: Estimating and Calibrating MFMod : A Panel
            Data Approach to Identifying the Parameters of Data Poor
            Countries in the World Bank's Structural Macro Model
display_title: Estimating and Calibrating MFMod : A
            Panel Data Approach to Identifying the Parameters of Data
            Poor Countries in the World Bank's Structural Macro Model
listing_relative_url: /research/2019/07/31240973/estimating-calibrating-mfmod-panel-data-approach-identifying-parameters-data-poor-countries-world-banks-structural-macro-model
topicv3: Transport m1326661 135,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Trade m1326924 698,Taxation m1327615 1121,MFMod m1504542 3120
publishtoextweb_dt: 2019-07-11T00:00:00Z
historic_topic: International Economics and Trade,Transport,Macroeconomics and Economic Growth,Public Sector Development
no_of_pages: 35
author_keys: 0: author_key: 759200
1: author_key: 1368476
model_extractions: Policy Research Working Paper 8939

# Estimating and Calibrating MFMod

A Panel Data Approach to Identifying the Parameters of Data Poor Countries in the World Bank’s Structural Macro Model _Andrew Burns Charl Jooste_ Macroeconomics, Trade and Investment Global Practice July 2019
Policy Research Working Paper 8939

# **Abstract**

This paper summarizes the World Bank’s approach to identifying parameters for key equations in its macro structural model for countries where short sample sizes or major structural changes render traditional time-series approaches infeasible or yield unstable estimates. To identify parameters that could be used in such cases, a cointegrating panel approach is followed that yields a common long-run estimate of parameters for key equations (to test the theoretical restrictions imposed in the model) and short-run disequilibrium estimates that vary by country. This approach is preferred to pure calibration or Bayesian estimation, because the functional forms imposed in the panel are consistent with those used in the macro structural model.

This paper is a product of the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at cjooste@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Estimating and Calibrating MFMod: A Panel Data Approach to Identifying the Parameters of Data Poor Countries in the World Bank’s Structural Macro Model

Andrew Burns Charl Jooste<sup>1</sup>

**JEL: C11, C33 Keywords: Structural equations, Cointegrated panels,**

> 1 The views in this paper are those of the authors and do not necessarily reflect the views of the World Bank. The authors thank Doerte Doemeland, David Stephan and Benoit Campagne for helpful comments and suggestions. Corresponding author: <u>cjooste@worldbank.org.</u>
# 1. Introduction

The World Bank’s Macro Structural Model (MFMod) is the main forecasting and analysis tool for World Bank staff (WBG, 2019). The model is deployed for 184 countries utilizing data from a wide range of sources. Individual country models have a similar structure and economic variables are made as consistent as possible to enhance cross-country comparability. Theory underpins the long-run solution of the model, while short-run dynamics are primarily driven by the data and reflect the historical behavior of the economy.

A significant constraint in the modeling exercise is the availability of data over sufficiently long samples to estimate key parameters. As a general principle, most of the parameters should be time and policy invariant. With short sample sizes, econometrically estimated coefficients may be biased, have large standard errors and may therefore take the wrong size or sign, all of which renders analysis problematic. MFMod is an annual model. Across the 184 countries included in MFMod, time series for some countries can be as short as only five observations, partly because some countries have been publishing independent data for only a brief period. In other cases, data definitions have been significantly revised or upgraded. Combining the low-frequency nature of the data over short time horizons makes econometric identification of parameters close to impossible in some cases.

This paper describes the methodology used by the World Bank to estimate or calibrate the parameters for countries that suffer from short data samples. The paper’s objectives are to match the functional forms of MFMod and produce, as best possible, country estimates.

There are generally three approaches in dealing with these kinds of data constraints. One is to calibrate parameters using a meta-data approach based on the literature or from micro data (see Kydland and Prescott (1982) for calibration of general equilibrium models; Hansen and Heckman (1996) on a synthesis of calibration and simulation to identify parameters). Another is a Bayesian approach where a prior is imposed (see Smets and Wouters (2003) as an example). The last approach is a panel methodology – the approach used by the World Bank to identify some of the parameters.

The following section describes the various approaches to estimating parameters and juxtaposes it with the methodology employed in this paper. This is followed by a description of the econometric methodology used. The fourth section presents the key equations with references to the technical MFMod equations with the results. A final section concludes.

# 2. Methodological choice

Most estimation and calibration techniques have their pros and cons. It is inevitable that some assumption will be made to estimate/calibrate parameters for countries that have short sample sizes. As an example, one cannot adequately identify parameters for a country with say only five observations. Fixing that parameter to a certain value ignores all the country-characteristics (which 2
is unknowable, and at best approximated by studying countries that have a similar economy). This section describes some approaches to deal with this problem and finally motivates the use of a panel cointegrated method. Each approach is evaluated in terms of how it fits within the structure of MFMod. We do not claim that we adequately identify the parameters for data poor countries, but only approximate them in as much as we have evidence for how other countries (with more observations) behave.

**Calibration techniques** to identify parameters are complicated by the need to find studies that share similar functional forms for each of the equations in MFMod or finding a micro-data set from which to estimate the parameters. While a common approach, calibrating equations in either of these ways may be too restrictive, particularly as concerns accounting for country specific effects such as the speed of adjustment, and short-term sensitivities to external shocks – features that are critical to the out-of-equilibrium behavior of MFMod. A useful way to use calibration in cases where significant parameter uncertainty exists is to construct counterfactuals by varying the parameter. In single structural equations this might be permissible, however, for cases where equations are estimated jointly (i.e. reduced form systems) this will render problems.

**Bayesian** approaches marry the analyst’s specific view (informed or uninformed) of the world (prior) with what can be measured using data (likelihood function). A prior can be chosen based on some assumption on the distribution of parameters where the prior mean equals a value from the literature or from some available estimate. With large sample sizes, the prior weight is reduced to zero and coefficients resemble classical estimation – i.e. the posterior is determined by the data. With little data or short sample sizes, the likelihood function weight approaches zero while the prior gets a larger weight. Because a good prior is informed by the literature or a reasonable estimate, a large weight on the prior effectively reduces the problem to the calibration approach discussed above, while a low weight on the prior reduces to classical estimation. A classical example in the VAR literature requires assumptions about the distribution of the parameter, hyper parameters for the prior mean (i.e. the analyst’s view regarding a unit root assumption of the dependent variable), and the importance of own lags relative to the influence of the explanatory variable’s lags. It is important to note that this approach makes the analyst’s assumptions transparent – which in our view is a good thing. If the analyst acknowledges parameter uncertainty, then the precision of the posterior is low – this would entail that the estimate has wide variance.<sup>2</sup> A benefit with a Bayesian approach is that the prior gets updated with more available data – which represents learning and thus the parameter estimate gets closer the real parameter over time.

There exists yet a third approach, one that the World Bank employs: **estimation of dynamic panels** . Using a cointegrating panel, small sample bias becomes less of a problem. Grouped data greatly increases the degrees of freedom for estimating parameters, while still allowing for a differentiation of countries via fixed effects. The approach makes some assumptions; countries that form part of the panel are differentiated only is as much as their intercepts and error terms vary, while all sharing a common long-run slope (i.e. no long-run slope heterogeneity).

> 2 See for example Koop and Korobilis (2010) on the Minnesota prior where the unknown variance‐covariance is replaced by an estimate, which does not necessarily reflect the degree of uncertainty in predictive densities.

3
The methodology, however, lends itself naturally to the one used in MFMod and allows for the estimation of parameters using the exact functional forms. Furthermore, the long-run (equilibrium) elasticities of different equations can be estimated (and the theoretical restrictions imposed on the long-run component of the ECMs in MFMod can be tested). The approach retains cross country heterogeneity in the estimation of short-run coefficients, including the speed of adjustment parameter in the ECM. Country-specific estimates of parameters can be used to calibrate parameters for countries where data constraints prevent more traditional time-series estimation, while the distribution of parameter estimates can be used to constrain outliers.

# 3. Econometric methodology

Most of the equations in MFMod<sup>3</sup> are written using a dynamic error-correction formulation (see Wickens and Breusch, 1988; Engel and Granger, 1987 and Johansen, 1991). This formulation lends itself naturally to test the theoretical restrictions of MFMod where the long-run conditions in the ECM are typically driven by theory. The standard ECM estimation methods used in MFMod allows a separate modeling of the short-run and long-run relationships between variables (for example allowing for short-run rigidities and larger long-run elasticities).

The methodology essentially separates two aspects of each equation; the equilibrium path of the dependent variable from the speed of adjustment of the model when it is away from equilibrium. In equation (1) below, the long run conditions are summarized by y� �ωx� �ε� where y� is a dependent variable or a vector of country dependent variables and x� resembles the explanatory variables. The long run expected value of the error term ε� is zero, the expression between the square brackets in �y��� �ωx��� ] reflects the deviation of the model from equilibrium. When the model is in equilibrium, i.e. y� �ωx� , the square bracketed component falls out. In the short run, the path of the dependent variable will reflect short-term influences ∑������ γ� ∆y��� �∑������ δ�∆x��� . The adjustment to equilibrium is determined by the speed of adjustment parameter θ and the distance from equilibrium in the previous period �y��� �ωx���� .

At a more technical level, (1) assumes that we have two nonstationary I(1) time series variables; the dependent variable is Y� and the explanatory variable is X� for every period t in history. Note that ∆��1 �L� is the difference operator and small case letters are the variables expressed in natural logs. The formulation in equation (1) exploits the equilibrium mechanism between Y� and X� , and summarizes the dynamic interplay. There exists a common stochastic trend if �1 �θ�0 and statistically significant. We interpret ω as the long-run elasticity of X� on Y� , while γ� and δ� are the short-run elasticities. ε�~iid and is the structural error term of equation (1).

> 3 World Bank (2019) provides an in‐depth discussion of the model’s structure and functional forms employed.

4
p-1 q-1 it = 9; it-1 t+ XieB + », Vij it-j t », Onj it-p te it Fie j=1 j=0 t=1,...,T i= P,q) i (-1,0) ~~B~~ <u>6:</u> it w) it _= ~~(7)~~ <u>(8b</u> Xie F eit |6; p-1 q-1 it = FilVit-1 — Xi.@] + >, Vij it-j+ >, Axit-j ig + de it it j=1 j=0

t i,t t i {6; i i} ~ ~~y~~ ii=t i
_ [DIRECT it_= % + 6gOi|Cye-1— Bln1 ~~|——.——it-1 it-1 ]~~ + yl 13 it-1 <u>| —</u> TPIRECT Aln ~~l, i,t~~ Cc ~~(as~~ it )- Biz" — We) + Eft

it C it it DIRECT t I ~~WNit-1-Tit-1~~ DIRECT Cit-1 — p n <u>pe</u> it-1 , € (-1,0 i i i2
income to consumption is slightly smaller than 1. Thus, for a 1% increase in permanent income, household consumption increases by 0.93%. The short-run elasticity of consumption to disposable income is 0.34 (implying that about 2/3 of consumption is subject to income smoothing). Interestingly the real interest rate is not statistically significant, perhaps a reflection of the lack of financial intermediation in many of the countries in the sample.

**Table 1: Real household consumption coefficients**

|Long-run<br>||
|---|---|
|ln~~�~~<sup>WN�,����T�,���</sup><br>������<br>~~�~~|0.93***|
|P�,���<br>�<br>||
|θ�<sup>�</sup>|-0.26***|
|Short-run(average over countrylist)||
|△ln~~�~~<sup>WN�,��T�,�</sup><br>������<br>~~�~~|0.34***|
|P�,�<br>�<br>||
|�r��π��|-0.01|
|α��|0.28***|
|n∗t|2794|

Notes: *,**,*** signify statistical significance at 10%, 5% and 1%, respectively.

Figure 1 displays the distribution of the error-correction terms and short-run parameters for all the countries. Most countries have an ECM term that falls within the expected range indicating that the theory and data match well. The short-run income elasticity is positive for most countries and in one case much larger than one. The outputs of the long and short-run elasticities are used as calibration inputs in countries where data are scarce. As an example, one may compute sample averages for country groups (e.g. based on some economic criteria or regional grouping) and use those estimates to calibrate parameters in countries where insufficient data exist to independently estimate parameters using standard single-country time-series techniques, and for countries that are not included in the sample. These estimates can also be used to calibrate the coefficients of outliers (Figure 1). In MFMod parameter estimates that lie outside the 80 and 20 percentile bounds are constrained to the closest boundary (in the case of positive interest rates, the parameter value is set equal to 0). Appendix B summarizes the short-run and ECM parameters for the countries in the sample.

**Figure 1: Real household consumption elasticities**

7
fest ; — ByIn| (Ay;e-1 + 62-1) — @) ~~_it-1 it-1~~ it-1

i,t piesty. (1- ~~—ito1 bto1~~ _ a) ( <u>Kitt</u> (1 -a) <mark>aa</mark> (Ay; ¢ + bit) <mark>(1—a)* Pe</mark> fest it i,t it
<!-- Start of picture text --> it<br>it<br>i<br><!-- End of picture text -->
x <u>it—1</u> it = aj + OF ia — wxmktjp-1 — €xln ~~(=~~ it-1) + Bi2A(xmkt;,) + E&x2Aln ~~(-#)~~ itx + Ef it it ~~Pit~~ PS <mark>(w =</mark> it = A+ 0x bie — axmkt;1 + &In ~~(|~~ i,t-i4USA,t-1 x + ~~Lt~~ Bi2A(xmkt;,) — €&,x2Aln ~~(——)~~ it USA + €f,

<mark>(w =</mark> 1)
<mark>Table 3 reports regression results for the two specifications, with the samples restricted to countries where price-taking behavior dominates (the second column) and countries where the</mark> price-making behavior dominates (column 3).

In the second column of Table **_3_** 3 the relative price has the wrong expected sign in the long-run – i.e. an increase in export prices relative to domestic consumer prices leads to a _reduction_ in exports. The third column, however, shows that the relative price has the expected sign, but is not statistically significant at 1% - an increase in the export price relative to the world priced _reduces_ exports. Running separate country regressions confirms the ambiguity with the export equation specification as many of the signs and statistical significance depends on which relative price measure is used. Interestingly, the ECM coefficient suggests that it takes approximately 10 years � for exports to equilibrate. The short-run elasticity is much smaller than the long-run elasticity ���<sup>�</sup> �� ~~�~~ which is close to 1.

|**Tabl**|**e 3: Export volume coeffici**|**ents**|
|---|---|---|
|Long-run|ln~~�~~<sup>P�,���</sup><br>�<br>~~�~~|ln~~�~~<br>P�,���<br>�<br>�|
||P�,���<br>�<br>|E�,���P�,���<br>∗<br>|
|xmkt�,���|0.87***|0.92***|
|Long-run relativeprice|-0.12***|-0.06|
|θ�<sup>�</sup>|-0.12***|-0.11***|
|Short-run (average over country<br>list)|||
|∆�xmkt�,��|0.03|0.03|
|Short-run relativeprice|0.20**|-0.30***|
|α��|0.24***|0.13***|
|n∗t|2224|2215|
|Notes:*,**,*** signify|statistical significance at 10%, 5% a|nd 1%, respectively.|

Most of the short-run elasticities fall within the expected ranges for the estimates in column 3. The slow equilibrating process is highlighted by the center of mass in Figure **3** 4 with the smallest ECM at around-0.5 (i.e. it takes two years to equilibrate). It is maintained that the price taking assumption holds for most of the developing countries in MFMod. In the case of MFMod, outliers from Figure 4 are restricted to the 80 and 20 percentile bounds and in the case of positive relative prices we set the parameter value equal to 0. Appendix B summarizes the short-run and ECM parameters for the countries that hit the bounds in the sample.

11
**Figure 3: Export volume elasticities**

<!-- Start of picture text --> Error Correction SR Income Elasticity SR Price Competitiveness<br>28 36 60<br>24 32 50<br>28<br>20<br>24 40<br>16 20<br>30<br>12 16<br>12 20<br>8<br>8<br>4 4 10<br>0 0 0<br>-.6 -.5 -.4 -.3 -.2 -.1 .0 .1 .2 .3 -5 -4 -3 -2 -1 0 1 2 3 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5<br>Frequency Frequency Frequency<br><!-- End of picture text -->

# **Box 1: Export price elasticities: Price takers vs price makers**

<mark>The expected sign of the relative price variable in equation 5 or 6 depends on whether exporters in a country are price takers or price makers.</mark>

- <mark>A price-taker is sufficiently small enough that a producer cannot affect the world price with production decisions.  The empirical correlation between export price changes and a price-taker’s export volume will be positive.  Higher prices induce more output, lower prices induce less output (with the elasticity being dictated by the exporter’s supply curve).</mark>

- <mark>A price maker is either a sufficiently large producer on the global scale or produces a sufficiently differentiated product, that the producer can charge more or less as her costs rise or fall. For such producers the price elasticity of export volumes is expected to be negative: when prices rise, global demand falls; when prices fall, demand rises.</mark>

<mark>The exporters in any given country will be a mixture of price-takers and price-makers. As a result, the expected sign of the relative price variable in equations 5 and 6 is uncertain. Indeed empirically, about 30 of the countries have a positive price elasticity and 32 a negative – independent of the specification used, with many having coefficients close to zero (suggesting a mixture of price takers and price makers) and an overlap of 10 countries that have the correct</mark> sign in both specifications.

<mark>In MFMod when the price elasticity of exports is positive, the price-taker formulation is used,</mark> when the elasticity is negative the price taker formulation is used.

<mark>The two formulations used differ in the denominator of the relative price component of the equation. In the price-taker formulation the domestic price deflator is used as a proxy for local costs and competing domestic markets for export</mark> <u><mark>goods. As domestic costs / prices rise,</mark></u> 12
<!-- Start of picture text --> @ e<br>e@ @<br>|°<br>e<br>e<br>e @<br>e e° o*,<br>e° e > °<br>e@ ° @@<br>e .:e @ ? e@ @ @f. @6 °<br>2° e 4° e<br>@® @ e @<br>e %° e e<br>®e<br>@<br>e<br>e<br>—_ e @<br><!-- End of picture text -->

m de <u>i,t-1</u> de it = aj + OTM ao —Bir OS + eimin ~~(=|~~ i,tit—1 + Bi2A(ve"5) — Ei,m2Aln ~~(=)~~ itm + eft

gde <u>Pir,</u>
<mark>ensure that in the very long run imports remain as a steady share of GDP �β</mark> � <mark>�1� as in the first order condition. For the panel, it is estimated freely to test this hypothesis. It is also expected that</mark> ε�,� �0 suggesting that a rise in import prices relative to domestic prices will reduce imports.

<mark>The short-run elasticities and the error-correction parameter vary across countries. There are no a priori expectations about the size of the parameters, but it is expected that they have the correct theoretical sign (i.e. positive for domestic demand and negative for relative prices).</mark> To ensure stability of the current account balance under simulation (the Marshall-Lerner condition) the sum of the absolute elasticities of exports and imports to relative prices should be greater than unity ( |ε�| �|ε�| �1� .

All the estimated coefficients reported in Table **_4_** 4 are statistically significant, and the error correction estimate suggests that there is a common stochastic trend between import volumes, domestic demand and relative prices. The long-run elasticities meet a priori expectations and there is evidence for the Marshall-Lerner condition ( |ε�| �|ε�| �1� . As with export volumes, the equilibrating mechanism is close to 10 years – thus shocks that cause imports to deviate from their long-run path will take a considerable time to move back to that path.

As discussed in World Bank (2019) the coefficient on the ECM likely reflects rising import (and export) to GDP ratios during the 1990s and early 2000s. Indeed, the discussion in the Appendix demonstrates that the long-run elasticity is not constant without the trend – thus violating an important condition for interpreting the elasticities as structural. The historical increase in import penetration likely reflects a range of actors including: reduced shipping costs, access to credit markets, accession of China into the WTO, and economies of scale (Evenett and Keller, 2004). The third column in Table 4 summarizes results from an alternative specification, where a trend is assumed to capture the innovations. The income elasticity is still positive but slightly lower than one in Column 2, while the coefficient on the ECM is much larger, suggesting that, once the trend rise in import shares is accounted for, adjustment to equilibrium occurs much more quickly, in about four years _ceteris paribus._

**Table 4: Import volume coefficients**

|Long-run|Standard Specification|Specification includingtrend|
|---|---|---|
|y�,���<br>���|1.22***|0.78***|
|ln~~�~~<sup>P�,���</sup><br>~~�~~<br>P�,���<br>~~�~~|-0.57***|-0.35***|
|θ�<sup>�</sup>|-0.12***|-0.22***|
|trend||0.01***|
|Short-run(average over co|untrylist)||
|∆�y�,���<br>����|1.31***|1.31***|

14
|∆ln~~�~~<sup>P�,���</sup><br>~~�~~<br>P�,���<br>~~�~~|-0.10***|-0.10***|
|---|---|---|
|α��|-0.45***|0.24***|
|n∗t|5834|5834|

Notes:*,**,*** signify statistical significance at 10%, 5% and 1%, respectively.

The average short-run domestic demand elasticity is larger than one, while the dispersion by country is quite narrow (Figure **4** 5). In the case of MFMod, if traditional estimates of parameters follow outside the 80-20 bound, they are calibrated to the closest boundary, as are estimates for data poor countries that are among the outliers in Figure 5. In cases where relative prices have a positive effect on imports, the associated parameter is set equal to 0. Appendix B summarizes the short-run and ECM parameters for the countries that hit the bounds in the sample.

**Figure 4: Import volume elasticities**

<!-- Start of picture text --> Error Correction SR Income Elasticity SR Relative Prices<br>20 70 30<br>16 60 25<br>50<br>20<br>12 40<br>15<br>8 30<br>10<br>20<br>4 10 5<br>0 0 0<br>-.8 -.7 -.6 -.5 -.4 -.3 -.2 -.1 .0 .1 -28 -24 -20 -16 -12 -8 -4 0 4 8 -2.4 -2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6<br>Frequency Frequency Frequency<br><!-- End of picture text -->

# Producer prices

In MFMod producer prices are a function of the firm’s marginal costs expressed in nominal terms. This is obtained by substituting the marginal product of labor into the production function. The price equation shows the close relationship between prices and wages in the model. In the longrun, prices will grow at the rate of wages adjusted for productivity growth (provided that the capital-output ratio converges to a fixed point): Note that A�,� is the model’s trend TFP for each country, W�,� is the nominal wage, K�,�/Y�,� is the capital output ratio while α� is the labor share in output. In the model these equilibrium conditions are not assumed to hold in the short-term. Instead, short-term interaction of demand-side factors and the production factors will drive the economy back towards equilibrium over the medium- to long-term.

15
it = uit(MCir) Bi it it fest <mark>= ait 6,[pf ee — Spit-1| + Biz [est + Big itt</mark> ere

~~(¢~~ a = In(u; - 1)) 6=1

-1<6,<0

i,2 1 ~~——-~~ = 1.19 ~~(=|~~ )

<!-- Start of picture text --> ee ee<br>it-1<br>a a<br>i<br><!-- End of picture text -->
robust regardless of the lag structure used. As with other parameters, where MFMod estimates fall outside the 80 and 20 percent boundaries, then they are set to the closest bound, while if they cannot be estimated they are set to the modal value. Appendix B summarizes the short-run and ECM parameters for the countries that hit the bounds in the sample.

**Figure 5: Producer price elasticities**

<!-- Start of picture text --> Error Correction SR MC Persistence<br>20 12 16<br>14<br>16 10<br>12<br>8<br>12 10<br>6 8<br>8 6<br>4<br>4<br>4 2<br>2<br>0 0 0<br>-1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 -.4 -.3 -.2 -.1 .0 .1 .2 .3 .4 .5 .6 .7 .8<br>Frequency Frequency Frequency<br><!-- End of picture text -->

# Consumer prices

Consumer prices in MFMod are determined by a combination of domestic prices and import prices in the long-run. In addition to the same variables representing the short-run, the output gap is added to identify demand-pull pressures. Thus, any excess demand over supply will generate an increase in prices, which erodes real incomes and increases the cost of capital. Prices will continue to rise until the economy moves back into equilibrium. A priori it is expected that the long-run should have a homogeneity restriction on domestic and import prices. The elasticities σ� and σ� should sum to one and give an indication, econometrically, of the relative weight of imports in the consumption basket.

The estimated elasticities in Table **6** 6 are consistent with the theoretical expectations. The homogeneity condition is met ( σ� �σ� �1 ), while the data suggest that the equilibrium conditions are correctly identified (the ECM parameter is statistically significant). The output gap enters the equation with a positive sign, an indication that the Phillips curve holds on average.

**Table 6: Price equation for consumers**

Long-run

|p�,���<br>����|0.86***|
|---|---|
|p�,���<br>�|0.15***|
|θ�<sup>�</sup>|-0.22***|
|Short-run(average over countrylist)||

17
|△p�,���<br>����|0.36***|
|---|---|
|△p�,�<br>�|0.15***|
|∆p�,���<br>�|0.06|
|YGAP�,���|0.08**|
|α��|0.012***|
|n∗t|4029|

Notes: *,**,*** signify statistical significance at 10%, 5% and 1%, respectively.

For most countries the equation correctly identifies a common stochastic trend. The dispersion in the output gap is mainly positive – suggesting that there is some evidence of a short-run Phillips curve. However, the small output gap coefficient might imply that retail mark-ups are small for many of the countries in the sample or simply that the output gap is not the most robust explanatory variable, especially for data poor countries and countries with under-developed markets where external shocks (such as food prices) are the principal determinants of inflation. In the case of MFMod, when estimates fall outside the 80 and 20 percentile bounds, they are calibrated to the closest boundary, while parameters for data poor countries are calibrated to the modal parameter value. In the case, where the estimated parameter for the output gaps is negative it is calibrated to 0. Appendix B summarizes the short-run and ECM parameters for the countries that hit the bounds in the sample 18
Mit _— A — O|pit-4M —o,(1 + tEh4cust),,mKeyPit—1 it-1 — 9 fe-aIC + Cc cust mKey M Bir ie + Bi2AC + t744") * Pit it + Ejt

t mKey it Cct tcust a+ 2=1 j=l mKey it-1
a cointegrating relationship between import prices and the world import price. However, the homogeneity constraint does not hold ( σ� �σ� �0.79 ). In another formulation, adding in a timetrend the homogeneity restriction cannot be rejected (column 3 of Table 7), with the time-trend taking a coefficient of -.01 implying that import prices are growing 1 percentage point slower than can be explained by the other factors in the equation. Falling transport margins, changes in the composition of traded goods (notably manufacturing goods) or productivity differentials between exporting and importing countries may be among the factors that could explain that differential. With this specification, the error-correction parameter is also much higher, suggesting that it takes roughly three years to return to equilibrium holding all else constant.

**Table 7: Price equation for importers**

|Long-run|Standard specification|Specification with trend|
|---|---|---|
|�1 �τ�<br>�����p�,�<br>����e�,�|0.23***|0.23***|
|p�,�<br>�|0.56***|0.73***|
|θ�<sup>�</sup>|-0.19***|-0.31***|
|trend||-0.01|
|Short-run(average over country|list)||
|∆�1 �τ�<br>�����p�,�<br>����e�,�|0.35***|0.30***|
|∆p�,�<br>�|0.43***|0.35***|
|α��|-0.15***|-0.22***|
|n∗t|1639|1639|

Notes: *,**,*** signify statistical significance at 10%, 5% and 1%, respectively.

Figure 8 reports parameter estimates for the specification without a time trend. For most countries the ECM term falls within the negative unit interval, suggesting that the theoretical specification identifies the long-run. The impact of foreign prices on the import price deflator is very dispersed across countries, but primarily positive as expected. In MFMod, parameter estimates that fall outside the 80 and 20 percentiles are constrained to the closest boundary, and data poor countries are calibrated to the modal value of the associated parameter. Appendix B summarizes the shortrun and ECM parameters for the countries that hit the bounds in the sample.

**Figure 7: Import price elasticities**

<!-- Start of picture text --> Error Correction SR Foreign Price Domestic Price<br>12 8 20<br>7<br>10 16<br>6<br>8<br>5 12<br>6 4<br>3 8<br>4<br>2<br>2 4<br>1<br>0 0 0<br>-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5<br>Frequency Frequency Frequency<br><!-- End of picture text --> 20
# Export prices

Using a similar approximation as the import price deflator, the panel version of the standard export price equation can be written as: <mark>This equation encapsulates the export price formation process of both price-takers and price makers. In instances where countries are pure price takers the price of export goods will be fully determined by the world USD prices of the exports of country i proxied by the Keyfitz export price multiplied by its bilateral exchange rate with respect to the US dollar e</mark> ��� <mark>. In this instance, domestic prices would be proxying for services prices, assuming that exporters price to market. In the case where countries are price-makers the expected coefficient on world prices will be smaller and the domestic inflation variable proxies for both service prices as above and cost pressures</mark> that leak into the export prices.

<mark>Table 8 indicates that the data do not reject the theoretical export price deflator equation, and that it takes approximately three years for export prices to converge to equilibrium once it is out of equilibrium. There is near homogeneity in the long-run ( σ</mark> � <mark>�σ</mark> � <mark>�0.95 ) (statistically indistinguishable from 1) and all the short-run parameters are statistically significant. In MFMod, parameter estimates that fall outside the 80 and 20 percentiles are constrained to the closest boundary, and data poor countries are calibrated to the modal value of the associated parameter. Appendix B summarizes the short-run and ECM parameters for the countries that hit the bounds in the sample.</mark>

**Table 8: Price equation for exporters**

|Long-run||
|---|---|
|p�,�<br>����e�,�|0.56***|
|p�,�<br>�|0.39***|
|θ�<sup>�</sup>|-0.29***|
|Short-run(average over countrylist)||
|∆p�,�<br>����e�,�|0.31***|
|∆p�,�<br>�|0.27***|
|α��|-0.53***|
|trend|-0.00|
|n∗t|5567|

Notes: *,**,*** signify statistical significance at 10%, 5% and 1%, respectively.

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**Figure 8: Export price elasticities**

<!-- Start of picture text --> Error Correction SR World Price SR Domestic Price<br>24 50 50<br>20 40 40<br>16<br>30 30<br>12<br>20 20<br>8<br>4 10 10<br>0 0 0<br>-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5<br>Frequency Frequency Frequency<br><!-- End of picture text -->

# 5. Conclusion

This paper uses a dynamic panel approach (a natural extension to the methodology employed in MFMod) to estimate parameters from several of the key equations in the World Bank’s macro structural model (MFMod). The objective is to find an empirical basis for imposing parameters for countries where a short sample period (or regime change) precludes the identification of countryspecific parameters using standard time-series techniques.

For most of the equations, the panel estimation results support (do not reject) the theoretically derived long-run relationships and restrictions. They indicate that there is significant variation across countries in terms of short-run elasticities and the movement towards equilibrium when they are perturbed. Taken together these results support imposing long-run theoretical parameters on equations, when country-specific data are scarce, but suggest more work may be required to identify the factors (such as income levels, commodity dependency, exchange rate regime) that might be influencing the wider dispersion observed for short-term parameters.

The country specific short-term elasticities with the error-correction components are used when calibrating data poor countries in MFMod. The 80<sup>th</sup> and 20<sup>th</sup> percentiles for each variable in the panel are used as cut-off points to force outlier countries within reasonable estimates. Future work may entail finding country groups that share similar economic structures to find appropriate bounds for outlier data poor countries.

While most of the results fall within a priori expectations, further work on both the trade deflators and trade volumes is warranted. The results suggest that it is hard to pin down the effects of relative prices on export volumes – the elasticities suggest that several countries set prices independently of world prices. One explanation is that the number of variables does not adequately explain the trade behavior over the last decade – as such additional variables identified in the literature should be added to obtain unbiased trade elasticities.

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