Macroeconomic factors for inflation in Argentine 2013-2019
aa r X i v : . [ ec on . E M ] M a y MACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019
MANUEL LOPEZ GALVAN
Facultad de Ciencias Exactas y Naturales - Universidad de Buenos Aires
Abstract.
The aim of this paper is to investigate the use of the Factor Analysis in order toidentify the role of the relevant macroeconomic variables in driving the inflation. The Macroeco-nomic predictors that usually affect the inflation are summarized using a small number of factorsconstructed by the principal components. This allows us to identify the crucial role of moneygrowth, inflation expectation and exchange rate in driving the inflation. Then we use this factorsto build econometric models to forecast inflation. Specifically, we use univariate and multivariatemodels such as classical autoregressive, Factor models and FAVAR models. Results of forecastingsuggest that models which incorporate more economic information outperform the benchmark.Furthermore, causality test and impulse response are performed in order to examine the short-rundynamics of inflation to shocks in the principal factors.
JEL Classification : C38, E31, E37.
Keywords : Inflation rate, Factor Models, Money growth, Forecasting, Factor Analysis. Introduction
In the last 10 years, Argentine has experienced one of the highest inflation rates of any countryin the world and therefore it is an interesting case to study the effect and the relationships of theirmain macroeconomics variables on the inflation rate. There are various works on the effects ofthe relationship of monetary policy and inflation and also measures as the output gap or interestrate. Basco, D ’Amato and Garegnani (2006) studied the short-run dynamics of money andprices under high and low inflation and found that that proportionality holds for high inflationperiod but weakness under low regime. Most economists agree that high inflation usually beginswhen the Central Bank issues money to finance a fiscal disequilibrium; this argument was initiallydeveloped by Cagan (1956) to explain hyperinflation. The problem of inflation has been overcomedecades ago by developed countries focusing their attention primarily on monetary tools. InArgentine, the exchange rate plays a very import role on tradable goods pricing, however, it hasbeen seen that the inflation has continued for long term without suddenly changes on exchangerate. Wages are a very important component of production costs and impact on non-tradablegoods, furthermore, firms and agents take into account the expected rate of inflation on pricingdecisions and wage contracts. All of these reasons may have effect on inflation, however, it is notclear why a high rate persists, although the deficit does not grow, although there are no sharpvariations in the exchange rate. Thus, it is possible that prices dynamics could also be explained
E-mail address : [email protected] , [email protected] . by unobserved or latent factors related to the observable pressures of inflation and therefore itshould be studied from a multivariate point of view by using Factor Analysis. In this work weinvestigate what are the most important determinant of actual inflation and we will use thisinformation to build forecast models.Classical econometrics models, such as AR, ADL or VAR can be used for simultaneously mod-elling the interaction of only a handful of variables, for example, in VAR models the number ofparameters to be estimated increases geometrically with the number of variables and proportion-ally with the number of lags included. Factor Analysis is a technique used to discover clusters ofvariables so that the variables of each group are highly correlated, in this way this mode reduces anumber of variables intercorrelated to a lower number of factors, which explain most of variabilityof each of the variables. Stock and Watson (2002) had explored the use of Factor Analysis intoforecast models. Given a large number of macroeconomic variables, a time series of the factorsare estimated from the predictors and then a linear regression between the variable to be forecastand the factors is performed.The structure of this paper is as follows: Section 2 we develop the theoretical framework forfactor models with their respective assumptions, in Section 3 we analyze the data to be used andwe verify the assumption of the framework, in Section 4 we develop the Factor Analysis and weanalyze the relation between Factors and variables. In section 5 we start studying ceteris paribuseffect on static factor models, then Granger-Causality test and impulse response analysis andfinally we perform forecasting through Factor and FAVAR models. Section 6 concludes.2. Empirical Factor Model
Forecast Model.
The forecasting model to be applied to inflation in Argentine follows thetwo step Principal Component approach of Stock and Watson (2002). First, a time series of thefactors are estimated from the predictors by using Principal Components methodology and thena linear regression is performed between the variable to be forecast and the estimated factors.More precisely, recalling Stock and Watson (2002), let π t be the time series to be forecast and let X t = ( X ti ) be a N -dimensional multiple time series of predictors ( t = 1 , , ..., T, i = 1 , , .., N ),the factor model representation for the data ( X ti , π t ) is, X t = F t Λ ′ + ǫ t (2.1)and π t + h = η + α ′ F t + β ′ Z t + ε t + h (2.2)where F t ∈ T × r matrix of r factors, Λ ∈ N × r is the factor loadings matrix, ǫ t is the matrix ofidiosyncratic error, cross-sectionally independent and temporally iid, where Z t is a m × π t ) and ε t + h is the forecast error. ACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 3
In order to estimate equation 2.1 one needs to estimate F t and the matrix Λ, assuming therestrictions Λ ′ Λ = I and T > N we minimize the following function, V ( F, Λ) = N X i =1 T X t =1 ( X it − λ i F ′ t ) = tr ( X ′ − Λ F ′ ) ′ ( X ′ − Λ F ′ ) (2.3)where λ i is the ith row of Λ and tr denotes the usual trace. Minimizing equation 2.3 isequivalent to maximizing tr (Λ ′ X ′ X Λ) and this is equivalent to the problem of finding maximunvariance linear combinations of components of vector X Λ under Λ ′ Λ = I . Therefore it is theclassical principal component problem and the resulting principal components estimator of F isthen, ˜ F = X ˜Λ (2.4)where ˜Λ has as its columns the first few eigenvectors of the covariance matrix of X .2.1.1. Out of the sample Static forecast (Or, one step ahead).
Let
P < T be a number of obser-vations, to build static out of sample forecast for π t on { t = T − P + 1 , ..., T } , firstly we formprincipal components of the data { X t } Tt =1 to serve as estimates of the factors and then up tomoment T − P we perform linear regression of π t on factor estimators ˜ F t − and Z t − . Let ˆ α, ˆ β and ˆ η be the estimated coefficient then the out of the sample forecasts is constructed as, b π t = ˆ η + ˆ α ′ ˜ F t − + ˆ β ′ Z t − (2.5)where t ranges from T − P + 1 up to T .2.1.2. Out of the sample Dynamic forecast.
To construct Dynamic forecast under Factor Modelmethodology we would need to assume a joint dynamics for ( F t , π t ), then two equations areestimated and the joint dynamics are given by, " F t π t = φ ( L ) " F t − π t − + ε t (2.6)where φ ( L ) is a conformable lag polynomial, Equation 5.4 is referred to as a FAVAR model asformal introduced by Bernanke (2005). More precisely, the FAVAR model assumes that F t and π t jointly follows a VAR process. Then, the forecast is obtained recursively by using the factorestimators ˜ F t , MACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 b ˜ F t = c φ b ˜ F t − + c φ b π t − (2.7) b π t = c φ b ˜ F t − + c φ b π t − (2.8)where t ranges from T − P + 1 up to T and c φ ij are the least square estimators up to moment T − P .2.2. Forecast evaluation.
Performance Measures.
In order to compare the forecast performance two metrics will beused in this work; the Root Mean Square Error (RMSE) and the Theils U statistics. Autoregres-sive model (AR(1)) will be used as benchmark. Given a number of observations
P < T , the RootMean Square Error (RMSE) is defined as,
RM SE P = " P T X t = T − P +1 ( π t − ˆ π t ) / (2.9)where { π t } are the observed values and { ˆ π t } are the forecast values. Theils U statistics orTheils coefficient of inequality is a relative Root Mean Square Error, more specifically we definethe U-Theil as, U P = (cid:20) P P Tt = T − P +1 ( π t − ˆ π t ) (cid:21) / h P P Tt = T − P +1 π t i / + h P P Tt = T − P +1 ˆ π t i / (2.10)The U-Theil measure is bounded between 0 and 1 and values closer to 0 indicate better fore-casting performance of the evaluated models. Other statistics are given as ratios to RMSE of theautoregressive (AR) model and U-Theil. More precisely we define, RRM SE P = RM SE P ( M odel ) RM SE P ( AR ) , RU P = U P ( M odel ) U P ( AR ) (2.11)Therefore, when the ratio is less than unity, the model (in RMSE or U-Theil - context) is betterthan the autoregresive benchmark model. ACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 5
Tests to compare forecast power.
Diebold and Mariano (1995) developed a hypothesis testto compare forecast power of two competing forecasts. Given two competing forecast b π t and b π t of a particular actual π t , let { e t } and { e t } be the associated forecast errors and let g ( e it )be the loss function of the forecast error. The loss differential is defined as d t = g ( e t ) − g ( e t ),the null hypothesis of equal forecast accuracy is H : E ( d t ) = 0 ∀ t against the alternative H a : E ( d t ) = 0 (or < > d be the sample mean of the loss differential ¯ d = T P ni =1 d t ,then by using a HAC estimator for the asymptotic variance of ¯ d ; that is \ Var( ¯ d ) = b γ + 2 K − X k =1 b γ k where b γ k denotes the lag- k sample covariance of the sequence { d t } and K the lag truncation.Under the null hypothesis of equal forecast accuracy we have the statistic, S (1) = √ T ¯ d q \ Var( ¯ d ) ∼ N (0 ,
1) (2.12)3.
Data
This section describe the variables to be included in all the models and how they should behandle.3.1.
Variables Handling.
The series chosen for the Dataset building are some of the mainmacroeconomics variables that cover the principal determinants of the inflation. The sample ofdata to be used includes the variables of the main inflation theories that are presented in theliterature. Also, in order to measure the different pressures of the different types of goods, weinclude different subindex of the general prices index. This is where we highlight the differentinflationary pressures, • Pressure of the prices of goods and services. • Pressure of cost. • Pressure of exchange. • Pressure of expectations. • Pressure of money issue and monetary policy rates. • Pressure of demand.The frequency of the data sample are, daily, monthly and quarterly; and the data sample rangefrom January 1st. 2013 until December 31th of 2019.The following list describes all the variables in the dataset: • IPCGL:
General Price Index Level of the City of Buenos Aires. Source: GCBA Instituteof Statistics. Frequency: Monthly. • IPCG:
Goods Price Index Level of the City of Buenos Aires. Source: GCBA Instituteof Statistics. Frequency: Monthly. • IPCS:
Services Price Index Level of the City of Buenos Aires. Source: GCBA Instituteof Statistics. Frequency: Monthly.
MACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 • W: Mean wage of stable workers (RIPTE). Source: Ministry of Labor, Employment andSocial Security of Argentine. Frequency: Monthly. • E: Nominal exchange peso-dollar. Source: Central Bank of Argentine (BCRA). Fre-quency: Daily. • E π : Inflation expectation. Source: CIF - UTDT. Frequency: Monthly. • Y: Output, no seasonally Real GDP at constant price. Source: National Institute ofStatistics and Census of Argentine (INDEC). Frequency: Quarterly. • M3:
Monetary aggregate. Source: Central Bank of Argentine (BCRA). Frequency: Daily. • M: Money held by the public. Source: Central Bank of Argentine (BCRA). Frequency:Daily. • r: Term fixed deposit rate. Source: Central Bank of Argentine (BCRA). Frequency:Daily. • FR:
Financial result, which is defined as Primary result minus debt interest. Source:Ministry of Treasury of Argentine. Frequency: Monthly. • D: Total external debt. Source: National Institute of Statistics and Census of Argentine(INDEC). Frequency: Quarterly.The inflation rate is the growth rate of the General Price Index Level of the City of BuenosAires (IPCBA) and it will be measured by the logarithmic change of the price index level, similarlywe also measure the growth rate of Goods and Services prices, π GLt = ∆ log(IPCGL t ) = log(IPCGL t ) − log(IPCGL t − ) , (3.1) π Gt = ∆ log(IPCG t ) = log(IPCG t ) − log(IPCG t − ) , (3.2) π St = ∆ log(IPCS t ) = log(IPCS t ) − log(IPCS t − ) (3.3)The treated dataset contains time series in different scales and frequencies. Since our studywill focus on a monthly base, first we need to transform the data. The process of transformationinvolved averaging the daily values as monthly values, and the quarterly values were interpolatedwith a cubic spline procedure as monthly values. Logarithms transform were applied in order toreduce possible source of heteroskedasticity and also to adapt the series to a same scale. Sincethe Principal Component approach of Stock-Watson requires stationary, the Dickey and Fuller(1969) (ADF) test was performed on all series and non-stationary series were differentiated. Thelag length for the ADF test were chosen by using the Akaike information criterion (AIC) ona maximum lag order defined by the Schwert rule. Indeed, let k max = " (cid:18) T (cid:19) / be themaximum lag suggested by Schwert rule, and let AIC ( k ) = log(ˆ σ ( k )) + 2 kT ACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 7 be the Akaike information criterion for k th order ADF regresion model,∆ y t = d t + ρy t − + k X j =1 γ j ∆ y t − j + u t , ( t = k max + 1 , ..., T ) , where d t denotes the drift or linear trend specification. Since the ADF regression model startsat k max + 1, all the competing models with different k are using the same number of effectiveobservations and therefore AIC criterion is comparable selecting the optimal lag as k opt = arg min k ≤ k max AIC ( k ) . The ADF test specification was chosen according to the general economic theory and also thoughta graphical inspection on all time series; variables regarding to prices, output, exchange and nom-inal quantities were considered as trending and the variables such as interest rate and expectationwere considered as drifting. The results of the ADF test are shown in Table 1.
Variable Type Optimal AIC k Test Statistic p-value log (IPCGL) Trend -465.43 1 -1.29 0.889 log (IPCG) Trend -436.55 1 -0.97 0.948 log (IPCS) Trend -421.62 2 -2.35 0.403 log (W) Trend -416.63 0 -2.24 0.469 log (E) Trend -218.47 1 -1.82 0.697 log (E π GL ) Drift -148.61 1 -2.15 0.017 log (Y) Trend -874.11 10 -2.37 0.397 log (M3) Trend -411.97 8 -2.36 0.398 log (M) Trend -367.79 11 -2.48 0.336 log (r) Drift -182.66 1 -1.50 0.068 log (FR) Trend 47.83 11 -1.72 0.740 log (D) Trend -712.64 9 -2.32 0.422 Table 1.
ADF test at Levels.
The p -values used in the test correspond to MacKinnon (1994) approximation for the Trendspecification. The Drift specification, which include constant no zero term and no time trend,the Dickey-Fuller test statistic is asymptotically Gaussian due by Hamilton (1994) and thereforethe classical p -values could be used. At the 10 per cent level of significance, the ADF testindicated the presence of unit root in IPCBA price levels, Wages level, Exchange level, Outputlevel, M3 level, Public Money level, Financial result level and for other side the test confirmedthe stationary for Interest rate level and Expectation. The non-stationary series were differencedand then ADF test was performed again on all transformed series. Table 2 presents the ADF testfor all transformed series. MACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019
Variable Type Optimal AIC k Test Statistic p-value ∆ log (IPCGL) drift -459.36 0 -4.56 9.04e-06 ∆ log (IPCG) drift -431.47 0 -4.36 1.9e-05 ∆ log (IPCS) drift -413.98 0 -6.39 5.14e-09 ∆ log (W) drift -408.81 0 -9.35 9.10e-15 ∆ log (E) drift -215.35 1 -6.26 9.73e-09 ∆ log (Y) drift -859.19 9 -3.45 5.067e-04 ∆ log (M3) drift -403.31 7 -4.47 1.6e-05 ∆ log (M) drift -364.51 10 -2.32 .011 ∆ log (FR) drift 50.93 10 -4.82 1.3e-05 ∆ log (D) drift -683.66 6 -1.40 0.082
Table 2.
ADF test at first differences.
After differenced all the above series resulted stationary and therefore integrated of order one.Following this transformation, the N dimensional dataset to be used to form principal componentis, X t = { π Gt , π St , ∆ log( W ) t , ∆ log( E ) t , ∆ log( Y ) t , ∆ log( M t , ∆ log( M ) t , log( r ) t , log( Eπ GL t ) , ∆ log( F R ) t , ∆ log( D ) t } Finally all the series have been standardized to have sample mean zero and sample varianceone. 4.
Factor Analysis
In this section Factor Analysis is performed by using the Principal Component Methodology,we calculate principal component and also calculate the resulting principal components factorestimator ˜ F . Moreover, we will study the relation between factor and variables.We start the analysis by assessing the viability of the dataset ( X t ) to achieve Factor Analysis.In this way Kaiser-Meyer-Olkin and Bartlett test of sphericity were performed on the data sample.Kaiser-Meyer-Olkin is a measure of the sampling adequacy and values greater than 0.5 indicatethat the data is acceptable to perform factor analysis and the null hypothesis for Bartlett test is H : variables are not intercorrelated. Table 3 shows the test performance. KMO sampling measure 0.519Bartlett test of sphericity Chi-Square 219.439Degrees of freedom 55p-value 0.000
Table 3.
KMO and Bartlett test on data sample.
ACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 9
The tests have shown that the sample dataset ( X t ) could be used to perform Factor Analysis.In the next steps we calculate the principal components with the aim of summarize the totalvariance in the dataset. The eigenvalue greater than one (Kaiser criterion) leads to select fivecomponents, however, this is a lower bound for the number of components to extract in principlecomponents analysis. The scree plot shows that the slope of the graph goes from steep to flatafter the forth component and thus suggesting that four factor could be taken. Figure 1 illustratesthe scree plot and the variance distribution.
123 1 2 3 4 5 6 7 8 9 10 11 pc e i gen v a l ue pc P r opo r t i on o f v a r i an c e ( % ) C u m u l a t i v e v a r i an c e ( % ) Figure 1.
Scree plot and Variance distribution against principal components.
The first four components explain 62% of the total data variance which is considerable, the firstcomponent captures the major share of the variance 26%, the second 14%, the third 12%, andthe fourth 9.9%. Looking at the eigenvectors of the correlation matrix of the sample dataset, it ispossible to compute the factors estimators ˜ F or scores as the sum of products of the eigenvectorstimes the values observed for the original variable each period. Equation 4.1 and 4.2 describe theestimation of the two main factors and Figure 2 illustrate the inflation rate and the constructedfactor. ˜ F t = 0 . π Gt + 0 . π S t + 0 . W ) t + 0 . E ) t + 0 .
380 log( Eπ GL ) t + 0 .
348 log( r ) t − . M t − . M ) t (4.1) − . Y ) t − . F R ) t − . D ) t ˜ F t = 0 . π Gt + 0 . π S t − . W ) t + 0 . E ) t − .
080 log( Eπ GL ) t + 0 .
276 log( r ) t + 0 . M t + 0 . M ) t (4.2) − . Y ) t − . F R ) t + 0 . D ) t −4−2024 p G L , F m m m m m m m m p GL F Figure 2.
First principal component and standardized monthly inflation.
The visual analysis indicates that the first factor show either strong comovements or conversemovements with the inflation rate and this should improve predictive abilities.The correlation between the observed variables and factors may help to understand how thevariables are organized in the common factor space and therefore discover clusters of variables.The factor map is a scatter plot between Corr( X i , F ) and Corr( X i , F ) that shows the rela-tionships between variables and factors; positively correlated variables are grouped together andnegatively variables are positioned on opposite sides of the plot origin (opposed quadrants). Thequality of representation on the factor map is measured by the squared cosine, for a given variableand a given component we define ij -square cosine by,cos2 ij = Corr( X i , F j ) . The sum of the cos2 ij on all the principal components is equal to one, if a variable is perfectlyrepresented by only two principal components then the sum on these two PCs is equal to oneand in this case the variables will be positioned on the circle of correlations. Given a variable wedefine cos2 as the square norm of the vector (Corr( X i , F ) , Corr( X i , F )) i.e.,cos2 = Corr( X i , F ) + Corr( X i , F ) = cos2 i + cos2 i . Therefore a high cos2 indicates a good representation of the variable on the principal componentand in this case the variable is positioned close to the circumference of the correlation circle. Onother hand a low cos2 indicates that the variable is not perfectly represented by the PCs and inthis case the variable is close to the center of the circle. Its possible to color variables by theircos2 values and Figure 3 illustrates the factor map and the cos2 measure by a gradient color map.
ACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 11
Figure 3.
Factor map and cos2 for each variable.
In variable study, it is also very useful to look at the variable contributions of each axis for helpin interpreting axes. The contribution of a variable to a given principal component is defined asthe ratio between ij -square cosine and the total squared cosine of the component; ctr ij = cos2 ij P i cos2 ij (4.3)The larger the value of the contribution, the more the variable contributes to the component.Figure 4 illustrates a bar plot of variable contributions for the four principal components, Figure 4.
Contribution of the variables to the two principal components.
The red dashed line on the graph above indicates the average of the significantly contributionswhich could be used as a cutoff to consider a variable as important to the component. Given afactor j the cutoff contribution is calculated asmean( crt ij ) subjet Corr( X i , F j ) = 0 at 10% level , then a variable with a contribution larger than this cutoff could be considered as important incontributing to the component. From the contribution graph it can be seen that factors aremainly related to four different groups of variables; the first factor is mainly driven by goods andservice prices, inflation expectations and interest rate level. The most important contribution forthe first factor is given by goods price with 25% and then followed by inflation expectations witha contribution close to 15%. This show that the first factor tends to describe price components.For the second factor, variables such as M3 money growth, exchange rate, money growth by thepublic contribute the most. In this case the main contribution is driven by M3 money growthwith a level close to 30% and then followed by exchange rate with a contribution level close to23%. These finding indicate that the second factor tends to describe money growth and exchangesrate aspects. The third group is mainly related to debt growth with a contribution close to 33%and the fourth factor is strongly associate with the financial result with a contribution of morethan 60%. On the other hand, Wages and Output have shown a weak contribution into thefactors. Our components contributions analysis allowed us to have a better understanding of theeconomic interpretations of the latent factors. To sum up, Table 4 shows the groups of variablesthat contribute the most to the four main factors. F : Price F : Monetary and Exchange F : Debt F : Financial π G ∆ log( M
3) ∆ log( D ) ∆ log( RF )log( Eπ GL ) ∆ log( E ) ∆ log( M )log( r ) ∆ log( M ) π S Table 4.
Main contributions to the components and components interpretations. Factor Model Estimation and Forecast results
Implications for Static Factor regressions.
Consider the regression model given by themain unobserved four factor, π GL t = α F t + α F t + α F t + α F t + ε t (5.1)Since the estimated factor have economic interpretation we can give economic interpretationto the coefficient when we use as regressor ˜ F it . Table 5 shows the estimated model, ACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 13
Parameters Estimation α ∗∗∗ (0.0453) α ∗∗∗ (0.0453) α -0.012(0.0453) α -0.209 ∗∗∗ (0.0453) R Standard errors in parentheses ∗ p < . , ∗∗ p < . , ∗∗∗ p < . Table 5.
Factor Model regresion for Equation 5.1
The result of the regression showed that factors 1, 2 and 4 were statistically significant at lessthan 5% level. According to the interpretation of the factors, the signs obtained are in line withthe literature having a positive effect on price level. An increase of one unit in factor one, relatedto prices, increases the general price level by 0.829%, while an increase in factor two, associatedwith monetary growth and the exchange rate, also increases the general price level by around0.297%. The effect of the deterioration of the fiscal accounts on the price level is confirmed bythe negative sign of factor 4 associated with the financial result, here a drop of one unit generatesa 0.209% increase on prices. On the other hand, factor 3, associated with debt growth, was notsignificant for any acceptable level of confidence; thus it could suggest that financing of the deficitthrough debt issuance has a lesser impact on inflation than financing with monetary issue.5.2.
Granger-causality and Impulse response functions on FAVAR model.
Hence, weconduct Granger-causality test on the FAVAR model by using the main four factors. The causalitytests performed by Granger (1969) suggest which variables in the system have significant impactson the future values of each of the variables in the system. However, the results do not, byconstruction, indicate how long these impacts will remain effective and impulse response functionsmay give this information. After fitting the FAVAR model we can know whether one variableGranger-causes another, for each equation in FAVAR model we can test the hypotheses thateach of the other endogenous variables does not Granger-cause the dependent variable in thatequation. We consider the following FAVAR Model by using factors 1,2,3 and 4 with one lagspecification, ˜ F t ˜ F t ˜ F t ˜ F t π GLt = φ . . . φ φ . . . φ ... . . . ... φ . . . φ ˜ F t − ˜ F t − ˜ F t − ˜ F t − π GLt − + ε t ε t ε t ε t ε t (5.2)Table 6 reports Granger tests that the coefficients on all the lags of an endogenous variable arejointly zero. Equation Excluded F df p -value ˜ F ˜ F ˜ F ˜ F π GL ˜ F ˜ F ˜ F ˜ F π GL ˜ F ˜ F ˜ F ˜ F π GL ˜ F ˜ F ˜ F ˜ F π GL ˜ F ˜ F π GL ˜ F ˜ F Table 6.
Granger causality tests for FAVAR model.
ACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 15
The table 6 read as follow, for each equation in the FAVAR system Granger F test is performedby assuming zero the excluded variable. For example, on the first equation for ˜ F a F test isperformed on the lag of ˜ F and in this case the null hypothesis that ˜ F does not Granger-cause˜ F is rejected. The second test and third test on the excluded variables ˜ F and ˜ F respectivelyare not rejected, and the last two test for π GL and all excluded variables are rejected.In summary we have the following pairwise Granger-Causality maps;˜ F → ˜ F , π GL → ˜ F , ˜ F ˜ F ˜ F π GL → ˜ F ˜ F → ˜ F , ˜ F ˜ F ˜ F π GL → ˜ F ˜ F → ˜ F , π GL → ˜ F , ˜ F ˜ F ˜ F π GL → ˜ F ˜ F → ˜ F , ˜ F → ˜ F , ˜ F → ˜ F , π GL → ˜ F , ˜ F ˜ F ˜ F π GL → ˜ F ˜ F → π GL , ˜ F → π GL , ˜ F ˜ F ˜ F ˜ F → π GL According to the factors identifications, these results are in line with the literature. Since thesecond factor is associated to unobserved facts of Monetary and Exchanges rates aspect it ishighly probable that this variable may have a contemporaneous effect on the first factor which isrepresented as inflation expectation and goods price and therefore effect on the general level ofthe inflation rate. Another economic interpretation is given with factor 4 and factor 2, respondingto the financing budget equation.The Impulse Response Functions trace out responsiveness of dependent variables in the VARto shocks to each of the variables. A distinguishing feature of these generalized approaches is thatthe results from these analyses are invariant to the ordering of the variables entering the VARsystem. For each variable from each equation separately, a unit shock is applied to the error,and the effects upon the VAR system over time are noted. The results of the impulse responsefunctions are presented in Figure 5. −.3−.1.1.3.5.7.9 0 2 4 6 8 10step
FAVAR: F1 −> p GL −.3−.1.1.3.5.7.9 0 2 4 6 8 10step FAVAR: F2 −> p GL −.3−.1.1.3.5.7.9 0 2 4 6 8 10step FAVAR: F2 −> F1 −.6−.4−.20.2 0 2 4 6 8 10step
FAVAR: p GL −> F1 −.20.2.4 0 2 4 6 8 10step FAVAR: F4 −> F2 −.4−.20.2 0 2 4 6 8 10step
FAVAR: F3 −> F4
Figure 5.
Impulse Response Function for FAVAR model.
According to these results, the general level inflation rate response from a unit shock in thefirst factor has a positive response and after one month it was close to 0.6. The conventionalinterpretation for this is that shocks to the first factor are mainly driven by inflation expectationsand goods prices and therefore responding to inflation pressures. Shocks to the second factor hasalso a positive effect on inflation rate with a maximum level of 0.3 after two months. Since thesecond factor is mostly driven by monetary and exchange facts, the inflation response is in linewith what is expected. The first factor response from a shock in the second factor is also expected;the exchange rate contribution of the second factor impulse tradable goods and therefore inflationexpectations. Response on factor two from a shock on factor 4 is also expected, since factor 4is related to financial result an improvement of it should be in line with an increasing of themonetary issue and therefore on the aggregate. The fourth factor response from a shock onfactor 3 cuold be explained by the increasing of the participation of the interest rate for debt intothe financial result balance.5.3.
Forecast.
In this section we perform the Factor Model following the methodology givenin Section 2. The aim is to forecast the inflation rate π GL under the two forecasting approachby using out of the sample data on different forecast horizon. The benchmark model chosen tocompare was an autoregressive model (AR) whose structure was determined through the analysisof the partial autocorrelation function and the Akaike information criterion and the resulted orderwas one. The model performance is compared against an AR(1) benchmark model and the relativeRMSE and U-Theil measure are calculated. Low values of RMSE and U-Theil indicate smallerforecast error and the lowest relative RMSE and U-Theil indicates the highest predictive abilities. ACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 17
Also Diebold and Mariano (1995) (DM) test is performed against benchmark by using the Statamodule created by Baum (2003), which follows the theoretical framework given in Section 2.2.2.The loss function considered is g ( e it ) = e it and the autocovariance of the loss differential is givenby taking the lag structure close to the cubic root over the number of observations. Since thetest is a two-sided, the rejection of the null hypothesis against the alternative suggest that if theS(1)-statistic is negative the benchmark model is preferred, and if S(1)-statistic is positive FactorModel is preferred. Three different forecast horizon are defined; the first ( P ) from January 2019until December 2019, the second ( P ) from May 2019 until December 2019 and the third ( P )from September 2019 until December 2019.5.3.1. Performance for Static forecast.
Here we present the performance for the forecast modelgiven by Equation 2.5 by using one factor and two factors. Specifically, we consider the followingtwo Factor Model forms (1 FM) and (2 FM) respectively, π GLt = η + π GLt − + α ˜ F t − + ε t π GLt = η + π GLt − + α ˜ F t − + α ˜ F t − + ε t Figure 6 illustrates the static forecasting and Table 7 presents the forecast performance underRMSE, U-Theil measures and Diebold and Mariano test results. −.50.511.52 m m m m m m m m m m
10 2019 m
11 2019 m −.50.511.52 m m m m m m
10 2019 m
11 2019 m AR 1 FM2 FM Actual m m
10 2019 m
11 2019 m Figure 6.
Comparison of the Static inflation forecasts using different models and differentout of the sample horizon.
Period Model
RM SE P U P RRM SE P RU P DM-testS(1)-stadistic p -value K lagAR 0.824 0.565 1 1 P P P Table 7.
Static Forecast evaluations criterions.
All ratios of the Root Mean Square Error and U-Theil against autoregresive model are lessthan unity on all horizon and also it can be seem that the 2 Factor Model is better than the 1Factor Model on all horizon. The S(1)-statistic was statistically significant at the 10% level andtherefore suggesting that factors extracted from observed group of series have a certain potentialin forecasting the dynamics of consumer prices index.5.3.2.
Performance for Dynamic forecast.
In order to perform the Dynamic forecasting Equation2.7 was performed to get the forecast of factor estimator and then the inflation forecast wascomputed by using Equation 2.8. Specifically, we consider the following two FAVAR Model withone lag specification,FAVAR1 : " ˜ F t π GLt = φ φ φ φ ! " ˜ F t − π GLt − + " ε t ε t (5.3)FAVAR2 : ˜ F t ˜ F t π GLt = φ φ φ φ φ φ φ φ φ ˜ F t − ˜ F t − π GLt − + ε t ε t ε t (5.4)Figure 7 illustrates the dynamic forecasting and Table 8 presents the forecast performanceunder RMSE and U-Theil measures. ACROECONOMIC FACTORS FOR INFLATION IN ARGENTINE 2013-2019 19
Period Model
RM SE P U P RRM SE P RU P DM-testS(1)-stadistic p -value K lagAR 1.011 0.981 1 1 P FAVAR1 1.016 0.980 1.004 0.998 -3.370 0.0008 3FAVAR2 0.862 0.797 0.852 0.812 2.311 0.0208 3AR 0.886 0.755 1 1 P FAVAR1 0.814 0.579 0.918 0.766 0.9217 0.3567 3FAVAR2 0.841 0.561 0.949 0.743 0.4282 0.6685 3AR 1.013 0.684 1 1 P FAVAR1 0.808 0.456 0.797 0.666 5.155 0.0000 2FAVAR2 0.681 0.287 0.672 0.419 3.276 0.0011 2
Table 8.
Dynamic Forecast evaluations criterions. −.2−.10.1.2.3 m m m m m m m m m m
10 2019 m
11 2019 m m m m m m m
10 2019 m
11 2019 m AR FAVAR1FAVAR2 m m
10 2019 m
11 2019 m Figure 7.
Comparison of Dynamic inflation forecasts using different models and differentout of the sample horizon.
For dynamic forecast the best performance was achieved for FAVAR2 on the first and thirdperiod showing both ratios far less than the unity and also with the S(1)-statistic statisticallysignificant at the 10% level. For the second period FAVAR1 and FAVAR2 performed very similar for both metrics and also better than benchmark in terms of the performance measures, howeverS(1)-statistic did not result statistically significant in both cases.6.
Conclusion
This paper has two main goals; firstly investigates the relation between several macroeconomicsvariables and the inflation rate by using Factor Analysis and secondly focuses on the performanceof Factor Model when it is used to predict the Argentinian inflation rate. The study of contri-butions indicated that the four main factors have an economic interpretation. The first factor isstrongly associated with the aspects of goods prices and inflation expectations, the second onedeals with monetary growth and exchange aspects, the third is related to debt growth and thefourth is related to financial results. The identification of the static factor model allowed us tointerpret the ceteris paribus effect of each factor on the inflation rate. Here factors 1 and 2 hadpositive effects, with factor 1 having the greatest impact. The effect of factor 3 was close to zeroand statistically not significant, evidencing a possible low impact of debt growth on inflation. Onthe other hand, factor 4 was negative, thus positively impacting the inflation rate against thedeterioration of the financial result. Output and wages have not shown significant contributionson the main factors and therefore evidencing that inflation is far to be a problem related withaggregate demand and wages. Granger-Causality tests and the impulse response functions alsosuggested a positive effect of factors 1 and 2 on inflation and therefore identifying the crucial roleof goods prices, inflation expectation, monetary growth and exchange in driving the dynamicsof inflation. Secondly, we have presented forecasting models by using one and two factors andthe findings provided evidence that factor model forecasts improve upon the benchmark modelon static and dynamic forecasting. Thus, factors extracted from observed group of series havea certain potential in forecasting the dynamics of consumer prices index. All of these findingsindicate that multivariate analysis allows a better understanding of the sources of the differentinflation drivers.
References
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