The relative importance of internal and external variables on the dynamics of Mexico's output and the calculation of the output gap : an SVAR approach

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Master’s Thesis

The Relative Importance of Internal and External Variables on

the Dynamics of Mexico’s Output and the Calculation of the

Output Gap: an SVAR approach.

Mariana Oviedo Pacheco

Student number: 10826300

Date of final version: January 23, 2016 Master’s programme: Econometrics

Specialisation: Free track

Supervisor: Prof. Andrew Pua Second reader: Prof. dr. Peter Boswijk

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i Statement of Originality

This document is written by Student Mariana Oviedo Pacheco who declares to take full respon-sibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Introduction

The aim of this thesis is to investigate the effects of shocks arising from both external and domes-tic factors on the Mexican economy. A by-product of the estimated model is some measure of the output gap. It is important for policy analysis to identify how the different macroeconomic variables interact in order to anticipate possible negative scenarios that an economy might face. Moreover, rulers and policymakers are not only interested to know whether a shock on the economy causes an increase or a fall on the Gross Domestic Product (GDP),1 but also if the economy is running in an efficient way, i.e., the economy’s capacity to generate full employment, which indicates the economy is reaching full capacity utilization (output gap equal to zero). The output gap is defined as the difference between the actual and potential output of the economy, that is, it gives us a measure of how far is the economy from the ideal situation. Moreover, the output gap is an economic concept that represents inflation pressures in the economy due to an excess demand (positive output gap) or excess supply (negative output gap), resulting in pressures on prices in the short run. The output gap is considered to be an important variable when formulating monetary and fiscal policies (Clarida, Gali and Gertler (1999), Svenson and Woodford (2000), among others), since it is through these policies that the authorities are able to influence the economy. The output gap provides some guidance on the adjustment that the economic variables need either to slow or stimulate growth.

Unfortunately, an official calculation of the output gap does not exist in Mexico. However, different institutions calculate their own estimates of this indicator, such as the Secretar´ıa de Hacienda y Crédito Público (SHCP)2 and Banco de México3. Given that the estimates not always coincide each other, in 2014, the Instituto Nacional de Estad´ıstica y Geograf´ıa (INEGI)4 expressed its intention to calculate an official measure of the potential output and the output

1

The Gross Domestic Product (GDP) is considered an official measure of the total production in a country and is commonly used to measure the economic performance. Following this practice, on this research ”GDP” and ”economy” are used as synonym.

2_{The agency that controls financial matters, taxes, spending, revenue and debt of the Mexican Government.} 3_{The central bank of Mexico.}

4_{The National Institute of Statistics in Mexico.}

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CHAPTER 1. INTRODUCTION 2 gap, however it has not been published at the time of writing this thesis.

With the purpose of capturing the dynamics of the economy and calculating a measure of the output gap for Mexico, time series techniques are going to be used, such as structural vector autoregressive (SVAR) models. Different shocks on output are studied: international shocks, monetary and fiscal shocks, aggregate demand shocks and labor supply shocks.

Since Mexico is a small open economy, the international environment may have a strong influence on it. However, it is not clear which of the economic fundamentals, e.g. inflation rate, unemployment, wages, etc., are explaining the dynamics. In addition, it is also unclear to what extent external variables, such as the economic activity of the USA5 and the international oil prices, affect the output of Mexico.

There are different methods to calculate the output gap. From an econometric point of view, potential output can be seen as the trend of the GDP while output gap can be seen as the cyclical component of the GDP. This idea comes from Blanchard and Quah (1989) where they considered that supply shocks are those affecting the output on the long-run while the demand shocks have no permanent effects on output. Following this idea, in the present thesis we use the SVAR model to calculate an output gap and we compare it with the Hodrick-Prescott fil-tered GDP series which is the method more commonly used and the one that Banco de M´exico currently uses.

As a result, the main aim of this thesis is to analyze the effects of shocks, both internal and external, on the Mexican economy. That is, we model the dynamics of the output and the related variables using a SVAR in order to calculate an output gap for Mexico. We use monthly macroeconomic data from 1995-2015 to construct a system of seven equations for the SVAR model.

The remainder of this thesis is organized as follows. Chapter 2 provides information about existing literature related with the SVAR models. Chapter 3 focuses on some stylized facts of the Mexican economy. Chapter 4 describes the econometric model. Chapter 5 resume the estimation and identification of the model. Chapter 6 presents the obtained outcome from the SVAR model. Chapter 7 concludes.

5_{Since the United States is the main trading partner of Mexico it is expected that it will be sufficient to}

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Chapter 2

Literature Review

Mexico is a developing small open economy, considered the second more important economy in Latin America and one of the more important emerging economies in the world. Mexico is the tenth largest oil producer in the world. Its geographical location in North America, right next to the United States, and the fact to having sign a free trade agreement with the United States and Canada in 1994, has contributed not only to promote and increase its commerce exchange with the United States, but also to improve its economic management during the last 20 years. Regarding the monetary authority, the autonomy of Banco de M´exico started in April 1994, later on December of that year a free floating exchange rate regime was adopted and, fi-nally, implementation of inflation targeting regime occured in 2001. In terms of fiscal situation, Mexico has promoted, approved and implemented a considerable number of structural reforms (legislative, fiscal and institutional reforms). All these changes have helped to achieve some stability on its inflation rate, however, the GDP displays more volatility.

Vector Autoregressive models (VAR) are used to describe the data generating process (DGP) of a set of time series. This type of model is very useful to analyze the relationships among a set of economic variables because these models allow for endogeneity of all the variables in-cluded in the system to be estimated. However, VAR models only give us the reduced form of the equations. In order to give an economic interpretation of the parameters it is necessary to impose some restrictions that give an specific structure to the system of equations.

Taking the above into account, Sims (1980) and Bernanke (1986) presented some objections about the macroeconomic models arguing that the way in which identification was achieved was inappropriate. They proposed an econometric model known as Structural Vector Autoregressive Models (SVARs), focusing to give an specific structure to the error terms. They managed to orthogonalize the reduced form errors using the Choleski decomposition. In such kind of mod-els, all variables are treated as endogenous therefore are unaffected by the restrictions imposed by the researchers to make the variables exogenous. The SVAR models are used to represent the dynamics of the series in the economy since these models allow to identify the sources of

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CHAPTER 2. LITERATURE REVIEW 4 fluctuations and also to quantify in what extent each variable affect the output.

Since then, several researchers have studied the sources of economic fluctuations by using SVAR Models. The present thesis is mainly based on the work developed by Blanchard and Quah (1989). They estimated a bi-variate model to explain the business cycle fluctuations in the U.S.A. They decomposed the real gross national product (GNP) into two components, the trend, considered as the permanent component, and a transitory component. Both of these components are uncorrelated with each other. They found that those disturbances that perma-nently affect the output are the supply disturbances and those that affect the output only in the short run are the demand disturbances. The variables included in the model were the first difference of the logarithm of GNP and the unemployment rate in levels.

Although Blanchard and Quah (1989) gave the basis to study the economic fluctuations with an SVAR, their model was very small because they only analyzed the interaction between two variables, however, many variables interact in the economy. Shapiro and Watson (1988) used Blanchard and Quah (1989) to identify a model to explain the sources of business cycle fluctuations in the U.S.A. Their research included five variables (labor supply, oil prices, output, inflation and money supply). In particular, to identify the model they used the lower triangular structure of the long-run restrictions C(1) matrix. Meanwhile, King, Plosser, Stock and Watson (1991), used a long-run restrictions to analyze the permanent shocks to productivity and their identifying restrictions were formally equivalent to those used by Blanchard and Quah (1989). They found that in systems with nominal variables, the permanent productivity shocks typically explain less than half of the business-cycle variability in output.

The use of long-run restrictions and the identification scheme proposed by Blanchard and Quah (1989) increased when the SVAR models became widely used to calculate a measure of the output gap. In particular, Bjornland et all (2005) analyzed and compared a set of alterna-tive methods for estimating the output gap in Norway, the SVAR models, among them, with long-run restrictions based on the Blanchard and Quah identification scheme. The different methods, show a consistent pattern for the output gap, but they found also important differ-ences. Because of that, they conclude that the output gap should be calculated with different methods and not with only one method.

The research developed by Blanchard and Quah (1989) allow us to achieve our two main objectives for the thesis. First of all, it gives us some guidance to identify the reduced VAR model. Second, with the estimated SVAR we can get the relative importance of the macroe-conomic series on the economy. Third, it gives us the ingredients to construct an estimation of the output gap because with the estimated SVAR we can have a measure for the potential output.

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CHAPTER 2. LITERATURE REVIEW 5

Different econometric techniques have been developed to measure the output gap. The most used is the filter developed by Hodrick and Prescott (1980). They separated the time series in its permanent and transitory components. In this thesis we explore the SVAR models to calculate the Mexican output gap and we compare our results with the HP filtered series.

In this regard, the existing literature for Mexico is scarce. A similar research to ours re-garding the analysis of the relative importance of external and internal variables is the paper wrote by Sosa (2008) where he documented the importance of external shocks in the Mexican economy and how the North American Free Trade Agreement (NAFTA) increased the influence of the USA on the Mexican output behavior. However, he uses different variables and he did not calculate a measure for the output gap.

Regarding to the calculation for the output gap, Faal (2005) used the unobserved compo-nents (UC) approach and the Kalman filter to decompose the historical growth of the Mexican GDP into its trend and cycle components to calculate a measure of the output gap in order to analyze which factors are those causing the slowdown in output growth, like us, they found that the trend, i.e, the long-run are the most important factors underlying the behavior of the GDP. They compared their results with the Hodrick-Prescott filter. They conclude that reform of the labor markets would be crucial to improve the economic situation in Mexico.

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Chapter 3

Data and Stylized Facts

3.1 Data

The model is estimated using monthly time series from March 1995 to September 2015. Data were collected from Banco de M´exico, INEGI and Bloomberg. The variables included on the main SVAR model consider both foreign and domestic blocks. The foreign block includes the Industrial Production Index (IPI) as a proxy of the gross domestic product from USA and the World Oil Prices (WOP) considered as supply shocks to the Mexican economy. Oil prices are measured as the average of three crude oil spot prices (Dated Brent, West Texas Intermediate, and the Dubai Fateh). The external variables are included in order to capture the fact that Mexico is an small open economy which can be affected by the international economic envi-ronment but it cannot influence the world economy behavior. The Granger Causality test can confirm the influence of the external variables on the Mexican GDP.

The domestic block includes the Global Indicator of Economic Activity (IGAE as per its Spanish acronym) as a proxy of the Gross Domestic Product of Mexico; the prices level are represented by the Consumer Price Index (CPI); money supply is represented with the series of real monetary aggregate M1; the fiscal shock is measured with series of total fiscal expenditure; and the labor shock is measured with the monthly unemployment rate.

We first inspect the series for stationarity. The Ng and Perron test was performed. As shown in Table 3.1, all series are non stationary and integrated of order one, denoted as I(1). The series were tested by including an intercept and a trend in the model. The critical value of -2.91 show that the null hypothesis of the existence of a unit root can not be rejected.

The variables are seasonally adjusted and expressed in logarithms to avoid the problem of having different units.

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CHAPTER 3. DATA AND STYLIZED FACTS 7

Table 3.1: Time series properties 1995-2015

Variable Source Shock Unit root test statistic

IGAE INEGI Supply -1.560

CPI INEGI Demand -0.460

Gov. Exp. INEGI Demand -0.372

M1 Banco de M´exico Demand -1.948

WOP Bloomberg Supply -1.373

USA IPI Bloomberg Supply -1.652

Unemployment INEGI Supply -0.984

3.2 Stylized Facts

On this section, the empirical regularities of the Mexican economy are described. Given that the GDP is an aggregate measure of total economic production in Mexico, it is considered a good indicator of the economic activity in a country and it is, therefore, our variable of interest. However, there is no monthly data for the GDP, only quarterly data are available. We use the series of the Global Indicator of Economic Activity (IGAE as per its Spanish acronym) which is monthly published and it is a good proxy that captures the economic environment in Mexico.

The Mexican GDP and the IGAE are calculated by the INEGI which is the National Statis-tics Office in Mexico. To calculate both measures, INEGI uses the same methodology; the same classification of economic activities; and the same information sources, which ensure the com-patibility. The IGAE has a national geographical coverage and includes primary (agriculture, fishing, and extraction such as mining), secondary (manufacturing) and tertiary activities (ser-vice sector) reaching 93.9 per cent of the gross added value. However, what makes the difference with the GDP is that the information included in the IGAE is preliminary and therefore, it is subject to review by the public and private agencies; additionally, the IGAE does not include all of the activities as does the quarterly product but it is an excellent indicator of monthly timely product performance.

In order to verify the similarity of the IGAE with the DGP, we took the quarterly average of the IGAE monthly data to be compare with published quarterly data of the GDP. As can be observed in Figure 3.1, the IGAE is indeed a good proxy of the GDP. The graph has different scales on each axis because the series are expressed in different units, the IGAE is published as an index and the GDP is published in millions of Mexican pesos. The left hand side shows the units for the GDP and the right hand side shows the units for the IGAE. The correlation between these series is 0.98.

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Figure 3.1: IGAE as proxy of GDP

1995 to September 2015.

Figure 3.2: Macroeconomic variables time series (1995-2015)

Using statistical methods we separate the time series in different components. Fluctuations in the economy are captured by the cyclical component. Figure 3.3 shows the evolution of the IGAE cyclical component extracted with Hodrick-Prescott (HP) method.1 In this graph, it is possible to identify the expansions and recessions that Mexican economy has had during the study period. Notice that major recession was during 2008-2009.

1_{We also got the filtered series of the IGAE by using other filtering techniques: Baxter-King (BK),}

Christiano-Fitzgerald (CF), Linear Trend (LT) and First Difference (FOD), see Figure 1 in the Appendix. We can observe that the outcome for the different techniques are similar, however, the most commonly used in the literature is the Hodrick-Prescott.

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Figure 3.3: IGAE filtered series with Hodrick-Prescott (1995-2015)

The output gap is an economic concept defined as the difference between the actual and potential output of the economy but potential output is an unobservable variable that has to be estimated. There are different methods to measure a potential output and therefore, an output gap, as well. The Hodrick-Prescott filter is one of the statistical methods used by different countries and the one that Banco de M´exico uses to estimate the output gap in the economy. This univariate method involve the minimization of the difference between potential and actual output at each point in time, subject to the constraint of how much can vary the potential output. min_{y∗ t} T t=1 ( _T X t=1 (yt− yt∗)2+ λ T −1 X t=2 y_t+1∗ − y∗_t − y∗ t − yt−1∗ 2 ) (3.1) where yt is actual output, yt∗ is potential output and λ is the parameter that controls the

smoothness of the series of potential output.2

However, this method has the disadvantage that the level of potential output is more af-fected by variations in actual output at the beginning and at the end of the period than in the rest of the period (Bjornland et all, 2005).

2

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CHAPTER 3. DATA AND STYLIZED FACTS 10 For the rest of the variables it was also obtained the cyclical component. Figure 3.4 shows a comparison between the cyclical component of each variable and the cyclical component of IGAE. As we can see, Industrial Production Index and World Oil Price have the same co-movement with IGAE so it is said that these series are procyclical; Consumer Price Index and Unemployment has a movement with IGAE so it is said that these series are counter-cyclical; while Money Supply and Government Expenditure are procyclical in some periods and countercyclical in other periods with respect to IGAE.

Figure 3.4: Cyclical components of macroeconomic variables with the HP filter (1995-2015)

Some statistics of the filtered series are reported in Table 3.2. It can be seen that the Consumer Price Index and unemployment have a negative correlation with the IGAE cyclical component; the World Oil Price is the most volatile series of the external variables and the Unemployment is the most volatile internal variable. Another important feature that can be observed is that external variables are highly correlated with the Mexican business cycle.

Table 3.2: Macroeconomic variables time series 1995-2015

Variable St. Dev. St. Dev. relative to IGAE Autocorr. Corr. with IGAE

IGAE 0.6782 0.5070 CPI 0.4916 0.7249 0.9321 -0.1937 Gov. Exp. 1.5184 2.2389 0.6926 0.1644 M1 0.8660 1.2769 0.7994 0.1197 WOP 7.2830 10.7391 0.9045 0.4788 USA IPI 0.8480 1.2504 0.9540 0.6689 Unemployment 3.2581 4.8042 0.6263 -0.4141

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Chapter 4

The Model

In the present chapter we describe the methodology to estimate the econometric model known as Structural Vector Autoregressive (SVAR) Model. This model, proposed by Sims (1980) and Bernanke (1986), is used to analyze the relative importance of each shock for each variable through the variance decomposition, and also to illustrate the future dynamic interactions be-tween the different macroeconomic variables through the impulse response functions.

4.1 Model Setup

4.1.1 The Reduced Form

Let z be the vector of k endogenous variables, the reduced form of the model is given by the VAR(p) representation:

zt= Γ1zt−1+ ... + Γpzt−p+ ut (4.1)

where Γi with i = 1, ...p are k × k matrices of coefficient and u0t = (u1t, ..., ukt) is an

unob-servable error term with positive definite variance matrix E(utu0t) = Ω and zero mean.

The model can also be written as MA representation:

Γ(L)zt= ut (4.2)

with:

Γ(L) = Ik−

Pp

i=1ΓiLi and L the lag operator.

Then we have a model with k economic shocks denoted by utand a vector ztof k observable

variables.

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CHAPTER 4. THE MODEL 12 The condition for the process to be stable is that all roots of the characteristic polynomial Γ(X) = (Ik− Γ1X − ... − ΓpXp) should lie outside the unit circle.

The optimal choice of lag p included in the VAR model can be determined by different information criteria: Akaike Information Criterion (AIC), Hannan-Quinn Criterion (HQ) and Schwarz Bayesian Criterion (SC).

AIC(m) = log det( ˜Σu(m)) +

2 Tmk 2 _(4.3) HQ(m) = log det( ˜Σu(m)) + 2log logT T mk 2 _(4.4) SC(m) = log det( ˜Σu(m)) + log T T mk 2 _(4.5)

where m = 0, ..., pmax is the order of the model, k is the number of variables and T is the

sample size.

The equations from (4.1) may be estimated separately by ordinary least squares (OLS). However, when the VAR equations does not have the same right hand side variables, the sys-tem should be estimated using seemingly unrelated regressions (SUR) to improve the efficiency of the estimates (Enders 2010, chapter 5).

4.1.2 The Structural Form

Since the Variance-Covariance matrix of the reduced VAR model is not diagonal, we cannot identify the effects of independent external shocks that we need in order to give an economic interpretation of the parameters. For that reason, we need a representation of the model where the residuals have a specific ’structure’.

Suppose that the structural form of the model given in (4.1) is:

A0zt= Γ1zt−1+ ... + Γpzt−p+ t (4.6)

where A0 is a full rank matrix that captures the instantaneous relations among the variables in

the vector of macroeconomic variables zt.

The structural form can be written also as the following equation:

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CHAPTER 4. THE MODEL 13 with A(L) = A0− Γ1L − Γ2L2... − ΓpLp.

Where t = A0ut is a (K × 1) structural form error that expresses the residuals of the

re-duced form ut as the linear combination of structural shocks t that are zero mean white noise

processes with time-invariant covariance matrix Σ.

The relationship between the covariance matrices is given by:

A0ΣA00= Ω (4.7)

The Wold representation theorem allows us to write the VAR as an invertible distributed lag of serially uncorrelated disturbances:

zt= C(L)t (4.8)

where C(L) = A(L)−1 represents the magnitude by which the ith variable is affected by jth structural shock.

We can rewrite the Wold moving average (MA) representation given in (4.8) as an infinite sum: zt= ∞ X i=0 Cit−i (4.9)

where zt is the k × 1 vector of endogenous variables, Ci is the i-th k × k MA coefficient

matrix defined earlier as C(L), t is a k × 1 vector of orthogonal white noise innovations.

This representation is useful to specify the structural long-run impact by using matrix C(1) which is obtained by evaluating in L = 1. This kind of representation is used in Blanchard and Quah (1989). The problem with the C matrix is that it is not unique, that is we can find different structural representations with the same reduced form that will depend on the im-posed restrictions. Because of that, we need additional information to distinguish among these representations. For exact identification of the structural shocks we need to define k(k + 1)/2 restrictions, where k is the number of endogenous variables (L¨utkepohl and Kr¨atzig (2004), chapter 4). In order to achieve this identification we will need to make some assumptions about the structure of the mechanism we are investigating.

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CHAPTER 4. THE MODEL 14

4.2 Impulse Response Function, Variance Decomposition and

Historical Decomposition

The main objectives of the thesis are achieved through the three outputs of the SVAR analysis: impulse response functions, variance decomposition and historical decomposition. The Impulse Response Function gives a representation of the dynamic responses of the economy to internal and external shocks. The Variance decomposition gives the relative importance of each of the shocks as sources of the variability of the output. The Historical decomposition is an extension of the variance decomposition used to estimate the individual contributions of each structural shock to the movements in the economy.

4.2.1 Impulse Response Function

Once we have the SVAR model we can use it to analyze the dynamic interaction between the variables with an impulse response analysis. We take the vector moving average representation given in equation (4.8) and we take conditional expectations based on information at time t − 1:

Et−1(zt) = Et−1(C(L)t) (4.10)

The right hand side of the equation (4.10) is a matrix of infinite sums. The expected value of the terms that involve t becomes zero because tis a zero mean structural shock. The other

terms in the equation are known in period t − 1, therefore they remain the same.

If we subtract the conditional expectation given in equation (4.10) from equation (4.8), the only terms that will remain are those that involve t:

zt− Et−1(zt) = t

Due to the interest of estimate the behavior of the variable one period ahead, we write the model at t + 1 and taking into consideration the results obtained above we get:

zt+1− Et−1(zt) = zt+1− (c2t−1+ ... + cp+1t−p+1+ ...) = t+1+ c1t

then by induction we conclude that t will affect zt+h for h = 0, 1, . . .. Therefore, in order

to understand the dynamics of the model, the coefficients of the moving average representation have to be analyzed.

The structural shocks from equation (4.8) can also be expressed in terms of standardized structural shocks:

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CHAPTER 4. THE MODEL 15 where D is given by D = diag(var(1), . . . , var(k)).

We substitute (4.11) in (4.8):

zt= C(L)D1/2∗t = S(L) ∗

t (4.12)

where S(L) = C(L)D1/2.

The matrix Sh represents the one standard deviation orthogonalized impulse response

func-tions formally defined as:

IRFh=

∂zt+h

∂∗_t = Sh (4.13)

where Sh is the coefficient of Lh in the matrix polynomial S(L), with h = 1, 2, ...

4.2.2 Variance Decomposition

The Variance Decomposition or Forecast Error Variance Decomposition tell us how each of the different shocks contribute to the dynamic behavior of the variables in the model. It is con-cerned with the conditional variance of the impulse responses. Following L¨utkepohl and Kr¨atzig (2004), chapters 2 to 4, we know that forecasting vector processes is analogous to forecasting univariate processes.

At forecast origin T, one can write the h-step ahead forecast error for the process as :

zT +h− zT +h|T = h−1

X

i=0

CiT +h−i (4.14)

with z(h) being the optimal h-step forecast at period T for zT +h.

If we denote the ij-th element of Cn by cij,n, the k-th element of the forecast error vector

becomes: zk,T +h− zk,T +h/T = h−1 X n=0 (ck1,n1,T +h−n+ ... + ckK,nK,T +h−n) (4.15)

Given that kts are contemporaneously and serially uncorrelated and have unit variances by

construction, it follows that the corresponding forecast error variance is:

σ_k2(h) = h−1 X n=0 (c2_kl,n+ ... + c2_kK,n) = K X j=1 (c2_kj,0+ ... + c2_kj,h−1) (4.16)

The term (c2_kj,0+ ... + c2_kj,h−1) is interpreted as the contribution of variable j to the h-step forecast error variance of variable k. This interpretation makes sense if the its can be viewed as

shocks in variable i. Dividing the preceding terms by σ2_k(h) gives the percentage contribution of variable j to the h-step forecast error variance of variable k,

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CHAPTER 4. THE MODEL 16

wkj(h) = (c2kj,0+ ... + c2kj,h−1)/(σk2(h)) (4.17)

These variance decomposition is presented on Table 6.1.

4.2.3 Historical Decomposition

The historical decomposition reveals when the shocks occurred and whether such shocks in-creased or dein-creased the series because each variable zt is decomposed into its sub-components

with respect to the structural shocks, i.e., variations of the endogenous variables can only be explained by variations in the structural shocks. We re-construct the observed data if we fore-cast a VAR, adding at each stage the residuals generated using the estimated model. Through these technique we are able to examine what the path of each endogenous variable would have been conditioned to the presence of one or some of the structural shocks, by selecting which shocks are those affecting the behavior of a selected series.

Using the moving average representation, from equation (4.8) we have that the endogenous variables zt depend on an infinite number of past structural shocks. Following Ocampo and

Rodr´ıguez (2012), the historical decomposition is based upon the following reorganization of the MA representation for a vector time series z:

zT = T −1 X i=0 CiT −i+ ∞ X i=T CiT −i = T −1 X i=0 CiT −i+ KT (4.18)

KT represents the effect of all shocks that are realized previous to the sample, i.e., it

mea-sures the effect of the initial values over the period T realization of the endogenous variables, thus the effect of all shocks that occurred before the sample. If the VAR is stable, when T increase to ∞ this second sum will tend to zero because the shocks that are too far in the past have no effect in the current value of the variables. Therefore, KT is the reference value of the

historical decomposition.

The next step is to decompose the deviations of zT from KT into the effects of the current

and past values of the structural shocks T −i for i = 1, ...T . The decomposition is made over

the auxiliary variable ˜zT = zT − KT =PT −1i=0 CiT −i. The information needed to compute ˜zT

is contained in the first T matrices Ci and the first T rows of matrix ˆ.

Therefore the historical decomposition of the i-th variable of ˜zT into the j-th shock is given

by: ˜ z_T(i,j)= T −1 X i=0 cij_i ˆj_{T −i} (4.19)

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CHAPTER 4. THE MODEL 17 It must hold that the sum over j is equal to the actual value of the i-th element of ˜zT.

When KT is close to zero, i.e., when T → ∞, ˜z (i,j)

T can be interpreted as the deviation of the

i-th endogenous variable from its mean caused by the recovered sequence for the j-th structural shock. Therefore, the historical decomposition for the i-th endogenous variable into the j-th shock is given by:

z_T(i,j)= K_Ti + ˜z(i,j)_T = K_Ti +

T −1

X

i=0

cij_i ˆj_{T −i} (4.20)

where the variable z_T(i,j) is interpreted as what the i-th endogenous variable would have been if only realizations of the j-th shock had occurred. The value of KT can be obtained as

a residual of the historical decomposition, since zT is known and ˜zT can be computed from the

sum of the historical decomposition.

The procedure described above it is used to compute an historical decomposition, and builds a series of the potential IGAE. In order to do that, we calculated equation (4.20) for K_T4 because the IGAE is the fourth equation in our SVAR, plus the realizations of the first four shocks, i.e., the shocks given by the world oil prices, the Industrial Production Index of USA, unemployment and IGAE. We accumulated this values over the time to reconstruct the trend of the output (potential IGAE).

Finally, to construct the series of the output gap we took the difference between the observed output and the potential output (the series calculated with the historical decomposition). The resulting series are shown in chapter 6, Figure 6.2.

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Chapter 5

Estimation and Identification

5.1 Estimation

In order to study the forces driving Mexican economic fluctuations, we will focus on aggregate supply and aggregate demand curves, after all, business cycle will arise when demand and supply disturbances occur. The macroeconomic equilibrium is achieved when the production quantity demanded is equal to the quantity supplied. If the economy is in disequilibrium, pressures on production capacities will be identified. This disequilibrium is referred to as the output gap. Therefore, with the estimated model we can analyze the influence of the different macroeco-nomic variables in the economy, as well as obtain an output gap measure.

It is not possible to include in a model all the variables that are interacting in the economy, due to this we only consider the seven variables described on chapter three. With these seven variables it is expected to capture the international environment, aside from the performance of the Mexican economy to monetary and fiscal shocks, aggregate demand shocks and labor supply shocks.

An unexpected event that restrains output is considered as a supply shock. The external variables introduced in our model are associated with the supply shocks. Considering that Mexico is an oil producer country, we include the World Oil prices because it is expected that the changes in the oil prices can directly affect Mexican output. Moreover, since most of the world’s supply comes from the Middle East region, the World Oil prices are mainly affected by wars and because of that it is expected that these shocks affect Mexican output in the long-run. The second external variable included in the model is the Industrial Production Index of USA because the USA is the largest trading partner of Mexico. Furthermore, trade between Mexico and the USA not only affects output because of imports of different products but also because the trade relations include many manufacturing factories installed in Mexico that directly af-fect the supply side of output in Mexico. Therefore, we consider that both external variables directly affect Mexican economy and the inclusion of these variables in the model also allows us

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CHAPTER 5. ESTIMATION AND IDENTIFICATION 19 to capture the international economic environment. The third variable associated with supply shocks is the unemployment rate, which represents changes in the production conditions, that is the supply side of the economy. We include this variable to capture the shocks produced by the labor supply which can contribute to explaining movements in the output gap. The IGAE is included in our model because it is considered a good indicator of the economic activity in Mexico. Regarding the variables with demand shocks on the economy, we included the inflation rate. To account for the impact of monetary policy, we introduce the money supply, and the fiscal shock is captured with the government expenditure.

Given the increased globalization, in macroeconometric analysis the assumption that some variables are exogenous is a very strong condition, even between variables from different coun-tries. However, we cannot really say that the Mexican economy has an influence on the dynamics of the world oil price or on the dynamics of the USA economy, because the total trade with Mexico account for a small percentage of the U.S. economy. Due to this reason, we model all the variables as endogenous but we do not include Mexican variables to explain the behavior of external variables. The World Oil prices will be explained by their own lags, meanwhile, the USA Industrial Production Index will be explained by the World Oil prices lags and its own lags.

We first check for cointegration. Several researchers as Chiquiar and Ramos-Francia (2005), Delajara (2012),1 among others, have documented a synchronization of the economic cycles between USA and Mexico, however, the Johansen cointegration test indicates no cointegration between the variables, this can be explained because of the small influence that Mexican econ-omy brings on the USA econecon-omy. The Johansen cointegration test between the IGAE and the oil prices also indicates no cointegration between these series. Finally, we also tested for cointegration between the internal variables and it was rejected.2

Chapter 2, it was shown that the time series to be considered on the model are I(1). With the purpose of estimating the VAR, it is necessary to have stationary series. For this, we transformed the integrated economic variables into stationary series by using the first difference operator. The criteria used to choose the number of lags to be included was the AIC. This lag selection criteria suggested the inclusion of 12 lags.

Once we have stationary series we estimate the VAR model. The representation of the

1_{Chiquiar and Ramos Francia (2005), documented the influence of the USA economy as external variable on}

the Mexican business cycle. They found a synchronization between the business cycle in both countries by using the Baxter and King filter, however they found an absence of cointegration between Mexico and U.S. economy. Moreover, Delajara (2012) found that the behavior of the business cycle in Mexico is more correlated with the USA economy on its north region compared with its center and south region, i.e., the variance of the business cycles in the North region is mostly associated with shocks to the US economy, while in the center and Southern region it is mostly related to specific shocks to the Mexican economy.

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CHAPTER 5. ESTIMATION AND IDENTIFICATION 20 model in the reduced form is given in equation 4.2, with the vector of endogenous variables zt=

(∆ot, ∆st, ∆lt, ∆yt, ∆mt, ∆pt, ∆dt), and the vector of shocks ut= (uot, ust, ult, u y t, umt , u

p t, udt).

Hence the equations of the VAR model to be estimated are:

∆ot= 12 X i=1 θoi∆ot−i+ uot ∆st= 12 X i=1 θoi∆ot−i+ 12 X i=1 θsi∆st−i+ ust ∆lt= 12 X i=1 θoi∆ot−i+ 12 X i=1 θsi∆st−i+ 12 X i=1 θli∆lt−i+ 12 X i=1 θyi∆yt−i+ 12 X i=1 θmi∆mt−i+ 12 X i=1 θpi∆pt−i+ 12 X i=1 θdi∆dt−i+ult ∆yt= 12 X i=1 θoi∆ot−i+ 12 X i=1 θsi∆st−i+ 12 X i=1 θli∆lt−i+ 12 X i=1 θyi∆yt−i+ 12 X i=1 θmi∆mt−i+ 12 X i=1 θpi∆pt−i+ 12 X i=1 θdi∆dt−i+uyt ∆pt= 12 X i=1 θoi∆ot−i+ 12 X i=1 θsi∆st−i+ 12 X i=1 θli∆lt−i+ 12 X i=1 θyi∆yt−i+ 12 X i=1 θmi∆mt−i+ 12 X i=1 θpi∆pt−i+ 12 X i=1 θdi∆dt−i+umt ∆dt= 12 X i=1 θoi∆ot−i+ 12 X i=1 θsi∆st−i+ 12 X i=1 θli∆lt−i+ 12 X i=1 θyi∆yt−i+ 12 X i=1 θmi∆mt−i+ 12 X i=1 θpi∆pt−i+ 12 X i=1 θdi∆dt−i+upt ∆mt= 12 X i=1 θoi∆ot−i+ 12 X i=1 θsi∆st−i+ 12 X i=1 θli∆lt−i+ 12 X i=1 θyi∆yt−i+ 12 X i=1 θmi∆mt−i+ 12 X i=1 θpi∆pt−i+ 12 X i=1 θdi∆dt−i+udt where:

ot: World Oil Price,

st: Industrial Production Index,

lt: Unemployment Rate,

yt: IGAE,

mt: Money supply M 1,

pt: Consumer Price Index,

dt: Fiscal Expenditure,

ut: shock of the reduced form,

∆ is the difference operator θ represent the coefficients of the model.

Given that not all the variables have the same components on the right hand side of the equation, the estimation method we use is the SUR method. The covariance matrix of the reduced form residuals and the correlation matrix are shown in the Appendix.

5.2 Stability

In chapter 4, it was mentioned that if reciprocals of λj lie inside the unit circle the VAR is stable. We

calculate the roots of the companion matrix, which are the inverse of the roots of the characteristic polynomial. The stability is tested for the largest eigenvalue to be less than one. We got a value of

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CHAPTER 5. ESTIMATION AND IDENTIFICATION 21

0.96144 for the largest eigenvalue. We can conclude that the model is stable.

To test whether the estimated VAR model gives a good representation of the DGP that lies behind the time series set of interest, we perform a multivariate Q test developed by Hosking (1981) for testing autocorrelation, which is an equivalent form of the Multivariate Portmanteu test. We included 12 lags. The degrees of freedom are given by k ∗ 2 ∗ l, where k are the endogenous variables and l is the maximum number of lags to test.3 _{If defects such as residual autocorrelation are detected at the stage of checking,}

we will need to find a better representation (L¨utkepohl and Kr¨atzig, 2004), since this is usually regarded as an indication that the model is a poor representation of the DGP. Results are shown on Table 5.2, as we can see there is no autocorrelation between model variables.

Table 5.1: Test for Autocorrelation

Test Test Statistic p-value

Multivariate Q Test (4 lags) 122.755 0.999 Multivariate Q Test (6 lags) 182.248 1.000 Multivariate Q Test (12 lags) 399.441 1.000

To test for Normality we perform a multivariate version of the Jarque-Bera test. Results are shown on Table 5.2. For the residuals of USA Industrial Production Index, the unemployment and the IGAE are not rejected the null hypothesis of normality but for the rest of the variables, the null hypothesis is rejected, however, much of the asymptotic theory on which inference in dynamic models is based, works also for certain nonnormal residual distributions (L¨utkepohl and Kr¨atzig (2004), chapter 2).

Table 5.2: Normality Test Jarque Bera

Variable JB p-value WOP 13.407 0.001 USA IPI 2.748 0.253 Unemployment 3.726 0.155 IGAE 3.434 0.180 M1 8.774 0.012 CPI 3.482 0.175 Gov. Exp. 43.382 0 All 78.953 0

As an additional tool to check stability in the VAR, we use the accumulated sum of the recursive residuals known as CUSUM test. Figures 5.1, 5.2, 5.3, 5.4, 5.6, 5.7 and 5.5 show that at the 5 per cent significance level the model is stable for the CUSUM test.

3

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Figure 5.1: CUSUM test-World Oil Price

Figure 5.2: CUSUM test-Industrial Production Index

Figure 5.3: CUSUM test-Unemployment Rate

Figure 5.4: CUSUM test-IGAE

Figure 5.5: CUSUM test-Money Supply

Figure 5.6: CUSUM test-Consumer Price Index

Finally, we tested the stability of the covariance matrix. The p-value we got is 0.069 so then we cannot reject the null hypothesis of stability of the variance covariance matrix at 5 per cent level of

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Figure 5.7: CUSUM test-Government Expenditure

confidence. The analysis performed so far do not give rise to concern about the model stability.

5.3 Identification

To identify the required restrictions, we use a recursive identification scheme and impose restrictions on the long-run multipliers of the C(L), i.e., on C(1). We use the identification that Blanchard and Quah (1989) proposed to explain the business cycle fluctuations in the U.S.A., along with some charac-teristics of the Mexican economy. This approach primarily focuses on the identification of supply and demand innovations, i.e., the supply disturbances are expected to have a permanent effect on output while demand disturbances have only a transitory effect. Following this idea, the trend of the estimated series of the output gap will be given by the variables affecting the output in the long-run (supply dis-turbances). While the cyclical component of the estimated series of the output gap will be given by the variables affecting the output only with a transitory effect (demand disturbances). Moreover, we use a lower triangular structure of the long-run restrictions C(1) matrix, like Shapiro and Watson (1988).

Once we estimate the VAR model we get the matrix of coefficients Γi and the variance matrix Ω

from equation (4.1). However, we are interested in the economic interpretation of the model so we need to estimate the structural form. To estimate the SVAR model we use the Wold representation theorem given in the equation (4.8). We are allowed to use the moving average representation, given that all the variables defined in ztare stationary and the model is stable and invertible. It will be through the

identification that we will be able to give an economic interpretation of the model, i.e., we will restrict which variables will not have a permanent effect on the economy. In order to achieve exact identification of the SVAR we need to impose 28 restrictions45_.

The normalization of the variance-covariance matrix Σ = I (where I is the identity matrix) gives us 7 restrictions, therefore the relationship between the covariance matrices given in equation (4.7) is reduced to A0A00 = Ω. The 21 missing restrictions6 to exact identify the model will be achieved by

imposing zero restrictions on the long-run effect of t on zt, i.e., on the matrix C(1) that measures the

long run impact of the structural shocks.7 _{The restrictions are imposed by creating a recursive ordering}

in C(1). Imposing cij(1) = 0 means that the long-run effect on the i-th element of zt, of the j-th element

of tis zero. This identification scheme means that variables in zt does not depend in the long-run on

the innovations of the variables ordered after. Being ztour (7 × 1) vector of macroeconomic variables,

4_{k × (k + 1)/2} 5

To use the Wold representation we need to have an exactly identified model.

6

k × (k − 1)/2

7

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and the uncorrelated structural shocks ordered as t = (ot, st, lt, y t, mt , p t, dt), where ot, st, lt and y t

represent the supply shocks while the remaining shocks correspond to demand disturbances, we describe the 21 restrictions placed on matrix C(1).

The assumption that cki = 0 and ckj 6= 0 captures the idea that the i-th shock do not affect

the k-th variable on the long-run but the j-th shock do. The World Oil price is considered to cause supply-side disturbances in the long term. Since most of the world’s oil supply comes from the Middle East region whose unexpected events like wars are of long duration.8 _{Hence c}

41 6= 0. Moreover, the

VAR was defined such that non of the other variables has an impact on the world oil price. Hence c12= c13= c14= c15= c16= c17= 0.

The VAR was also defined such that only shocks on the world oil price has an impact on the dynamics of the USA Industrial Production Index, this because the USA is not an oil producer but is one of the major consumers worldwide, i.e., it cannot affect the oil prices but it is affected by them. Hence c216= 0

and c23= c24= c25= c26= c27= 0.

Unemployment does have long-run impact on economy because it represents changes in the pro-duction conditions but it is only permanent affected by changes in external conditions. The output is expected to be fixed in the long-run so then is only affected by external variables and unemployment. These assumptions rely on the identification used by Blanchard and Quah (1989). Additionally, as it is mentioned in L¨utkepohl and Kr¨atzig (2004), the effect of nominal shocks on real variables like output or unemployment vanishes as time goes by, so then the effect of money supply and government expenditure on output is transitory. Moreover, prices does not have run impact on output because at the long-run everything is assumed to be optimally used. Therefore, c34= c35= c36= c37= c45= c46= c47= 0.

Money supply is affected by the Central Bank to influence the inflation behavior, so then the effect of the money supply on inflation it is expected to be stronger than the effect of inflation in money supply on the long-run. So then c54 = c55= 0. Only the government expenditure does not affect prices in the

long-run, c67= 0, and finally, no restrictions are placed on the government expenditure.

The assumption that the demand variables does not have effect on the output in the long-run can be seem quite strong and rigid and it might be that they actually have effect on the dynamics of the output, but it is expected that those effects are smaller than the supply disturbances (Blanchard and Quah, 1998).

The estimated coefficients for the long-run impact matrix C(1) are shown below:               1 0 0 0 0 0 0 −0.471∗ ₁ ₀ ₀ ₀ ₀ ₀ −0.095 −0.307∗ ₁ ₀ ₀ ₀ ₀ 0.025∗ 0.099∗∗ −0.117∗∗∗ ₁ ₀ ₀ ₀ 0.06 −0.249∗∗ _0.615∗ _0.04∗∗∗ ₁ ₀ ₀ −0.055∗∗ 0.287∗∗ −0.55∗∗ 0.239∗∗∗ −0.787∗∗∗ 1 0 −0.148∗∗∗ _0.174 _−0.658∗ _0.078∗∗ _−0.67∗∗∗ _−0.383∗∗∗ ₁              

8_{Estrada and Hernandez de Cos (2009) and DePratto et al. (2009) documented that oil prices impact supply}

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Where stars denote statistical significance at the 10 per cent level for * , 5 per cent level for **, and 1 per cent level for ***.

The relevant information obtained from this matrix are the sign of the coefficients for the long-run impact. We can see that an innovation on the world oil price affect in a negative way the USA Industrial Production Index, however the impact on the Mexican economy is positive. This can be explained by the fact that the USA is an oil consumer while Mexico is a producer country so that an increase on oil prices can also contributes to an increase in the GDP. On the other hand, oil prices have a negative impact on Mexican inflation, this may be because oil is a production input whose innovations are directly reflected in the price of products and services. Oil prices also affect government expenditure in a negative way, this can be explained because the dependence of the Mexican fiscal revenue on oil revenues is very high, around of 35 per cent so this variable is more sensible to innovations on the oil prices. As it can be expected, the USA Industrial Production Index have a positive impact on the IGAE on the long-run while unemployment have a negative impact on the IGAE on the long-run. Finally, is also interesting to see that the money supply innovations has a negative impact on inflation, this coefficient reflect the effort of the Central Bank to maintain a low and stable inflation rate through affectations to the money supply.

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Chapter 6

Results

6.1 Results

The impulse response functions of the Mexican economy when internal and external shocks occur, are shown on Figure 6.1. The graphs represent the response of the IGAE to one standard deviation positive shock in each of the variables, assuming the rest remains the same.

We first analyze the dynamic response of Mexico’s GDP to a shock on the external variables. The shock in the world oil prices has a positive and permanent effect on the economy. The effect stabilizes at the end of the first year and throughout the entire period the effect is between 7 to 12 per cent. This direction of influence can be explained by the fact that Mexico is an oil producer so the innovations on the oil prices can contribute to an increase on the IGAE due to oil revenues. However, we will see that the contribution of the world oil prices to the variance of IGAE is very small. The shock on the USA Industrial Production Index also has a positive and permanent effect on the dynamics of the IGAE between 7 and 13 per cent. This behavior is expected due to the synchronization between both economies.

Regarding in the internal variables, a shock to unemployment rate has a negative and permanent effect on the Mexican economy. The mentioned effect has a decreasing behavior during the first semester between −30 to −50 per cent approximately, and it has a negative permanent effect from the second semester onwards. According to the Okun’s Law this negative relationship is expected, i.e., if the un-employment increases the production will decrease. The variance decomposition also show that the unemployment is the variable that has more influence on the variance of the IGAE.

When an innovation or shock occurs on production (shock on IGAE) it can be observed in the graph that these shocks have a great impact on the economy of around 35 per cent in the first period and it increases to 55 per cent during the first months, however, within the first year this variable has a slightly fall to finally stabilize from the first year onwards. This stabilization above zero means that the innovations on IGAE cause a change on the level of the output in the long-run. Sosa (2008) does not report the impulse response for Mexican GDP he only report the variance decomposition so we can not compare the GDP response to a shock on its own innovations.

The money supply has a negative effect on the IGAE during the first months, between −10 and −15 per cent. This negative effect reverts after approximately 3 months, during the following months the

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CHAPTER 6. RESULTS 27

effect of a shock on the money supply has a positive effect on IGAE which disappears in the long-run.

Figure 6.1: Impulse Response functions of the SVAR. The effects on IGAE to a one standard deviation shock in:

This implies that a positive shock on the money supply will increase the production but not immedi-ately. According to monetarism theory mainly promoted by the economists Milton Friedman and Anna Schwartz, this behavior of the economy is expected because an increase in the money supply should

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lower the interest rate leading to a more consumption that can lead to an increase in the demand and therefore an increase in the production.1 _{We can see on the graph that a positive shock on the money}

supply increases the production in approximately 15 per cent during the first year, however, these effect is not permanent and disappear on the long-run.

The positive shock on inflation increases IGAE in around 7.5 per cent in the first period. Given that the simulated shock is only in inflation this scenario implies that the production amount is the same but available at higher prices, causing an increases of the GDP. This kind of behavior is observed when the supply of key commodities and the consumer expectations decreases making the prices to increase without an increment on the demand.

Finally, we analyze the shock on the government expenditure. An increase of government expendi-ture on infrastrucexpendi-ture investment or gross capital formation can be used to stabilize the economy and to recover from a recessions (Romer, 1999). Because of this, it was expected that the shock on government expenditure increases the IGAE. We can see on the graph that the shock indeed leads to an increase in production during the first six months, however, the production reverts to its pre-shock level after one year. We can conclude that for the Mexican economy, it is not enough to increase the government expenditure to increase the IGAE in the long-run, it will be necessary to implement other policies at the same time.

Having analyzed the impulse response functions, the next step, and one of the main objectives on this research is to check the forecast error variance decomposition. Table 6.1 shows the variance decomposi-tion of the SVAR model for 24 forecast horizons (denoted by h). The results of variance decomposidecomposi-tion for IGAE show that the relative importance of the external variables on the Mexican economy on the first period is around 4 per cent, while the internal variables contribute 60 per cent to the variance of the IGAE. We also can see that 35.9 per cent of the variation corresponds to its own innovations.2 _{It is}

important to mention that the model only contain seven variables so there are several omitted variables whose innovations are contained on the errors of the variable IGAE estimated by the model. Additionally, the Variance decomposition allows us to appreciate that the relative importance of the Unemployment to the variance of the IGAE is of 34.72 per cent in the first period. This result gives some guidance about the problems that public policies should focus and try to solve in order to improve the economic situation. As it was found by Blanchard an Quah (1989), the supply shocks included on the model have a greater effect on the economy as time passes, while the demand effect have a bigger effect on the short run but in the long-run tend to decrease.

The Historical decomposition is performed with the objective to obtain an estimation of the Mexican output gap. As it is mentioned on chapter 3, the Output gap is calculated by the difference between the actual and the potential output. The potential output is considered to be the highest level of production that the economy could have if all its resources were fully employed. The dynamics of the demand disturbances represent the output gap while the supply shocks represent the trend of the output. The potential IGAE is obtained by adding the forecast for the IGAE estimated with the SVAR model plus

1

Consulted on http://www.econlib.org/library/Enc/MoneySupply.html

2

Sosa (2008) found for Mexico that the own innovations of the GDP contributes on 49.23 per cent on the first period to the variance decomposition of the Mexican output. The difference between our results may be due to the inclusion of different variables in our model like the unemployment.

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the accumulated effect of the first four shocks to IGAE. The output gap is generated as the difference between the original series of the IGAE and the constructed series of the potential output.

Figure 6.2 show the estimated series of the output gap. As convenient reference, our estimated series with the SVAR model is compared with the Hodrick-Prescott filtered series of the IGAE, that is the method that Banco de M´exico uses to estimate a measure of the output gap.

Figure 6.2: Output Gap

A positive output gap occurs when the actual output is greater than the product at full capacity, i.e., both firms and employees are working above its maximum capacity which implies an excess of de-mand. A negative output gap occurs when the effective production is less than the production at full capacity, and denotes a weak demand. An output gap indicates that the economy is inefficient because the consumption of the resources is too many or not enough.

On the graph we can see that the output gap have five periods with positive outcomes, according to the HP filtered series (1997-1999, 2000-2001, 2004, 2006-2008 and 2011-2012), and five periods with negative outcomes (1999, 2002-2004, 2005, 2009 and 2013-2015). While the output gap according to the SVAR model has four periods with positive outcomes (1996-1998, 2000, 2006-2008, 2010-2014), and four periods with negative outcomes (1999, 2001-2005, 2009 and 2015).

The measures of the output gap obtained with the HP filter and the SVAR do not coincide in some periods. During period 2000-2001, the HP filtered series report a positive output gap while the SVAR series report a negative outcome. We consider that the behavior of the SVAR measure is more consistent with the economic situation reported by Banco de M´exico because during that period the demand was weak because the consumer confidence was low. During 2004, the measure obtained with the SVAR model indicates a negative outcome while the description given by Banco de M´exico indicates an ex-pansion in the economy, as it is captured by the HP filtered series. However, the minimum wage at real prices reported by the Secretariat of Labor and Social Welfare in Mexico show that in 2004 the real minimum wage was lower than in 2003,3 as we already mentioned, a negative output gap denotes a weak demand so the SVAR could be showing that the decline in real wage during 2004 resulted in

3_{In 2003 the real minimum wage it was equal to 43.69 Mexican pesos while during 2004 it was equal to 43.30}

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weak demand. Finally, during 2013, the Mexican economy seems to have had an expansion period as it is described by the SVAR series. Table 6.2 describes the economic situation in Mexico during the study period according to the annual reports published by Banco de M´exico.

Mexico had its worst economic crisis during the study period in 2009 due not only to the global financial crisis in the USA but also to a flu pandemic that occurred in M´exico during the second quarter of 2009 so it was necessary to stop the economic activity for almost one month. We can observe that the measure of the output gap with the two different methods coincide giving a negative output gap during 2009.

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Table 6.1: Variance Decomposition

h World Oil USA Unem- IGAE Money Inflation Government External Internal Supply Demand

Price IPI ployment Supply Expenditure Shocks Shocks

1 1.37 2.67 34.72 35.91 7.87 5.81 11.65 4.04 60.06 38.76 25.34 2 1.37 2.68 34.91 35.85 7.87 5.73 11.60 4.59 60.11 38.95 25.20 3 1.38 2.67 35.18 36.08 7.75 5.58 11.36 4.55 59.87 39.23 24.69 4 1.38 2.68 35.54 36.39 7.66 5.26 11.08 4.55 59.55 39.60 24.01 8 1.44 2.78 36.89 38.09 6.77 4.13 9.91 4.22 57.69 41.11 20.80 12 1.45 3.10 38.37 41.13 5.65 2.77 7.54 4.06 54.32 42.92 15.95 16 1.45 3.10 38.44 41.18 5.55 2.72 7.55 4.05 54.26 43.00 15.82 20 1.44 3.15 38.38 41.70 5.59 2.22 7.52 4.05 53.71 42.97 15.33 24 1.47 3.18 39.04 42.53 5.47 2.22 6.09 4.04 52.82 43.69 13.78

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6.

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Table 6.2: Summary of the economic performance in Mexico from 1995-2015 reported by Banco de M´exico

Year Economic situation

1995-1998 During 1995 Mexico had one of the worst economic crises in its history. In 1996 Mexico began a successful economic recovery. In subsequent years it continues to increase investor confidence mainly because of the implementation of a consistent set of macroeconomic policies among themselves, emphasizing fiscal, public debt, monetary, exchange rate and structural change. 1999 The average growth in Latin America was the lowest of the decade. It was affected by a devaluation of the Brazilian

currency thus affecting the financial markets in Mexico. Additionally, in Mexico there was uncertainty about the political situation in the country because in 2000 was going to be presidential elections.

2000 There was uncertainty about the political situation. In July it was elected a new party (after 70 years with the same governing party). Additionally, during the final months of 2000 the United States economy had a less vigorous growth and the price of the Mexican crude oil export mix fell sharply in December. These circumstances caused uncertainty among investors regarding their possible impact on the Mexican economy, and caused upward pressure on both interest and exchange rates. Moreover, the deceleration of domestic output was made evident by the fact that GDP showed practically no growth in the fourth quarter according to the seasonally adjusted figures while domestic demand weakened less.

2004 Mexican economic growth, which had begun towards the end of 2003, strengthened during 2004. The world economy, recorded its highest rate of growth since the mid-seventies.

2005 Due to natural disasters the economic growth in late 2005 slowed down.

2006-2007 The global economic expansion remained robust during 2006. Mexico’s economic growth was higher than expected. 2008 The global financial crisis significantly affected the performance of the world economy including Mexico.

2009 Additionally to the global financial crisis, there was a flu pandemic in Mexico during the second quarter of 2009 that stopped the economic activity for almost one month.

2010-2013 The world economy consolidated its recovery which started in the second half of 2009. Mexican economy had a period of expansion. During this period the aggregate demand increases.

2014 Given the increment in international financial volatility, markets in Mexico were also affected. 2015 The political situation in Mexico has decreased aggregate demand.

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6.2 Sensitivity analysis

In order to be sure that the results obtained with the SVAR are not highly sensitive to the order of the variables. The sensitivity analysis is based on estimating the SVAR for different orderings of the variables: money supply, inflation and government expenditure. We did not change the order of the other variables (world oil prices, USA Industrial Production Index, unemployment and IGAE) because we consider that the world oil prices are not significantly affected by the rest of the variables, the USA Industrial Production Index is only affected by the world oil prices. Regarding with the unemployment and the IGAE variables, we consider that the relationship between unemployment and IGAE in the long run given by the aggregate production function relates the total amount of employment in the economy with the total output on the economy, i.e., usually it is analyzed how the amount of labor affects output and not vice versa.

The SVAR model is alternatively estimated by ordering money supply, inflation and government ex-penditure in the six different possible ways. Table 6.2 show the order for the 6 models that were estimated.

Table 6.3: Order of the variables for the sensitive analysis

Base Model Model 1 Model 2 Model 3 Model 4 Model 5

WOP WOP WOP WOP WOP WOP

USA IPI USA IPI USA IPI USA IPI USA IPI USA IPI

Unempl. Unempl. Unempl. Unempl. Unempl. Unempl.

IGAE IGAE IGAE IGAE IGAE IGAE

Money Sup. Money Sup. Inflation Inflation Gov. exp. Gov. exp.

Inflation Gov. exp. Money Sup. Gov. exp. Inflation Money Sup.

Gov. exp. Inflation Gov. exp. Money Sup. Money Sup. Inflation

The base model order first the money supply, then the inflation and last the fiscal expenditure. Figures 5 to 9 on the appendix show the Impulse Response Functions and the out put gap series of the money supply, inflation and government expenditure for the other 5 models, we only included the graphs for the variables we have changed the order, for the rest of the variables the shocks remain the same. Shock of money supply has an effect between −15 and 20 per cent and a similar behavior for all the models except for the Model 4 whose effect is between 0 and −25 per cent. Shock of inflation rate is between −5 and 25 per cent and it has a similar shape for all the models except for Models 4 and 5. The effect of government expenditure shock is between −7 and 12 per cent except for Models 4 and 5 that it has an effect between −20 and 10 although the behavior of the government expenditure shock is very similar for the 6 models. Finally the measure of the output gap is similar for most of the different orderings. This analysis suggests that the model is not very sensible to the order of the variables.

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Chapter 7

Conclusion

One of the important issues for policy makers is to know how the economy behaves in a country. The information that can be useful to them is on one hand, to know how much the macroeconomic variables are contributing to the dynamics of the GDP. On the other hand, it is also useful to know if the economy is working on an efficient and stable way or if it is under or above its optimal production level. Since the IGAE turned out to be a good proxy of GDP, we used the IGAE as the variable representing the economy. The advantage of using the GDP instead of the IGAE is because it allows us to analyze the economy in a monthly basis instead of quarterly.

This thesis construct and estimate an SVAR model for the Mexican economy from March 1995 to September 2015, in order to identify the relative importance of the external and internal variables in the dynamics of the IGAE. Additionally, the model is used to give a measure of the output gap taking as a benchmark measure the IGAE filtered series with the Hodrick-Prescott method.

We estimated a system of seven equations. The World oil prices and USA Industrial Production Index were considered into the model in order to capture the fact that M´exico is an open economy, i.e., it has trade with other countries.

Regarding to the macroeconomic internal variables, aside of the IGAE, four variables were elected. Taking into account that policymakers intend to smooth the dynamics of the economy, in order to min-imize the magnitude of variations in time, they use both fiscal and monetary policies. Therefore, we include Government expenditure to represent fiscal policies, and Money supply and Inflation rate to represent monetary policies. The fifth internal variable included was the unemployment rate, in order to capture labor supply shocks.

The estimated VAR model did not give evidence neither instability nor nonstationarity, therefore the Wold representation was used to estimate the SVAR model. Based on the research developed by Blanchard and Quah (1989) and the characteristics of the Mexican economy, the system was identified with a recursive representation.

The empirical results obtained through the impulse response functions together with the variance decomposition forecast suggest that the internal macroeconomic variables are those mainly affecting the dynamics of the Mexican economy. In particular the unemployment rate shocks contributes to the

The relative importance of internal and external variables on the dynamics of Mexico's output and the calculation of the output gap : an SVAR approach

Master’s Thesis