Macroeconomic Effects of Fiscal Policy during the Covid-19 Crisis: Evidence from Bolivia at a Regional Level

2.1. Impact of Covid-19 in Bolivia

On March 10, 2020, the first two cases of Covid-19 were officially reported in Bolivia. According to Bolivia's Ministry of Health, the peak of the contagion curve, during the first phase of the pandemic, was reached in July and August 2020 (Figure 1). However, different waves of infections continued to affect the country in the following two years. Like most countries, Bolivia established a series of mobility restrictions to flatten the curve of infections and thus avoid the health system collapsing. Although this measure was effective for social distancing, it negatively impacted the country's economic activity and labor demand.

The lockdown measures resulted in a negative shock in both demand and supply. In terms of aggregate supply, private firms' marginal productivity of the labor force was affected due to transportation restrictions and a portion of their workers getting infected. Moreover, the restrictions on land and air borders had a negative impact on goods imported for firms. The lockdown decreased the population's consumption and aggregate demand. In addition, the decrease in economic activity and the restrictions applied to companies caused a significant reduction in the private businesses' generated income.

In this way, economic activity quickly declined. As can be seen in Figure 2, the variation in the same period in the General Index of Economic Activity (IGAE) was negative twice: 1) during November 2019, as a product of social and political conflicts, and 2) between March and June 2020, as a result of the implementation of the lockdown.

During the first quarter of 2020, there was a slowdown in economic activity of only 0.5 % in the cumulative growth rate for those months -the lowest economic growth rate since the beginning of the twenty-first century. During the second quarter, the economic contraction deepened even further. In addition to the consequences of the lockdown, a historic fall in oil and commodity prices should be noted, further weakening economic activity and deepening the government's tax revenues recession.

The national economy experienced a decline, and most economic activities showed considerable negative growth rates (Figure 3). The most contracted economic activities were construction, transportation, and mining. However, it cannot be considered a generalized effect, given that activities such as agriculture, communications, and public administration services grew.

Due to this economic scenario, Bolivia's unemployment rate increased since March 2020. As of July 2020, 11.8 %> of Bolivia's economically active population was unemployed (Figure 4). This employment behavior is in line with other countries in the region.

Two essential factors characterized Bolivia's 2020 public finances situation: 1) a decrease in tax revenue caused by the tax relief policies implemented and a decrease in economic activities due to the drastic reduction in mobility and trade among countries, and 2) an expansionary fiscal policy measures to counter the adverse economic effects of the Covid-19 pandemic.

As a result, in June 2020, Bolivia had a current fiscal deficit for the first time since 2004 (Figure 5), reaching a budget deficit of 12.7 % in relation to the GDP. On the other hand, the national public debt reached 19.4 billion dollars in the first months of 2020 (Figure 6) due to loans from international organizations and the Bolivian Central Bank to meet the needs generated by the health emergency. As of May 2020, the national public external debt in relation to the GDP reached 28.2 %, a number below the limit of 50 % recommended by the International Monetary Fund (IMF), which is a good indicator of debt sustainability.

In general, the pandemic affected the deterioration of the national economy, the deterioration of sectoral economic activity, unemployment, and other macroeconomic variables, but the effects at the regional level have not been quantified.

2.2. Stylized fact of economic growth by region in Bolivia

Figure 7 reflects the effects before the pandemic. Thus, before it, the real GDP growth of Santa Cruz was the highest compared to the other departments followed by La Paz and Beni, with a growth of 4.15 %, 3.21 %, and 3.09 %, respectively for 2019.

On the other hand, the annual GDP growth, in general, presents an erratic behavior for all departments, leaving aside Tarija, which presents a decreasing trend since 2013, due to its dependence on hydrocarbon production. It should be noted that only annual observations are available to measure the level of economic activity of the departments.

2.3. Economic Policy Measures in the Face of Covid-19 in Bolivia

To reactivate the economy, Bolivia's Ministry of Economy and Public Finance and the Central Bank designed and implemented an expansionary fiscal and monetary policy package. The following tables summarize the central economic policies performed in Bolivia.

The three levels of government implemented measures to expand current and capital expenditure: central, regional, and main local governments. The central government contributed to the implementation and disbursement of direct cash transfers such as Bono Familia, Canasta Familiar and Bono Universal, basic services payment deferrals, and deferral, and extension of tax payment, among others, to guarantee income for Bolivian families. In addition, the government transferred resources from the NT to the local governments for prevention, containment, and treatment of the Covid-19 pandemic.

The expenditure plan for the NT in 2020 aimed at dealing with the national emergency and lockdown measures. It focused on strengthening the country's health system (purchasing of medical supplies and hiring healthcare personnel), mitigating the contraction of economic activity (increasing public spending and tax reliefs), and protecting the vulnerable population (providing cash transfers).

3.1. Mixed Frequency Multivariate Autoregressive Vectors with Stochastic Volatility

We aimed to quantify the economic performance by region in Bolivia (quarterly economic growth) to improve the regional economic policy design data. This study adopted an empirical model in line with the methodology of Koop et al. (2018) and applied it to Bolivia. We used a Mixed Frequency Multivariate VAR model with stochastic volatility (MF-VAR-SV) and a Bayesian method using the machine learning algorithm known as Dirichlet-Laplace Hierarchical.

The MF-VAR-SV model allows the estimation of high-frequency unobserved variables (quarterly, monthly, or daily) by simultaneously modeling the data of high-frequency not observed variables and low-frequency observed variables, subject to temporal and spatial restrictions. The Kalman filter is used to fill in missing observations.

Following Kim and Nelson (1999), the Kalman filter, initially developed by Kalman (1960), is a recursive process used to compute the optimal estimator of the unobserved component of a system, also called the state vector, at time t, based on the information available up to that period. The Kalman filter has a long history in different fields. For economics, the original developers were Sargent and Sims (1977) and Geweke and Singleton (1981), who began to use this filter through frequency domain methods. Then, Engle and Watson (1981) and Watson and Engle (1983) showed that these models could be estimated using maximum likelihood and state-space models, which allows for estimating the values of the latent factor using the Kalman filter.

To use the Kalman filter, one must express the dynamic system, including the unobserved variable, through a state-space model. State-space models consist of the transition equation and the measurement equation. The estimation of the model used the maximum likelihood method. The estimated coefficients were then adjusted using the Kalman filter algorithm. The following is the notation of the model in the state-space form:

Where Z _t is the vector containing the unobserved state variables, which in this context is the regional gdp, the error terms of the measurement equation, and their innovations; Y _t is the vector containing the endogenous variables; X _t is the vector containing the exogenous variables, and ε_t is a vector containing the error terms of the measurement equation.

Whereas F, A, and C are the matrix that contains the time-invariant parameters of the model. It is assumed that the error terms of the measurement equation have a normal distribution, with zero mean and no serial correlation:

Our model was constructed using the quarterly logarithmic variation of the gdp for Bolivia's r regions (r - 9) and transition and measurement equations. The transition equation seeks to estimate the quarterly indicator of economic activity for the nine regions of Bolivia (Y _t ^Q ) using all the observable information available through the following var model:

Where Y _t is a vector of endogenous variables composed of three sets of variables:

All variables are in logarithmic differences with one period lag. We used Census-13 seasonal adjustment to all variables. The sample ranges from the first quarter of 2001 to the second quarter of 2020. In the second quarter of 2020, we used the IGAE variation as a proxy of the quarterly GDP variation, which was the indicator available at that time. Although it is a sample that could be considered small, our analysis period is restricted by the availability of fiscal information. As will be seen in the following sections, we used disaggregated information on current and capital expenditure for central, regional, and main local governments that we could only obtain from the year 2000. We want to point out that this is an unprecedented database that was possible to build thanks to close collaboration with the Ministry of Economy of Bolivia, to which we send our thanks.

The elements Y _t , are all observable and measurable except for the vector Y _t ^Q . In addition, u _t is the error of the estimation in equation (5), which is assumed to be independent and identically distributed with a distribution N(0, Σ_t).

We adopted a popular multivariate stochastic volatility specification (see Cogley and Sargent, 2005; Carriero et al., 2015). It decomposes the covari-ance matrix of the error as:

Where L is a lower triangular matrix and the diagonal D _t is formed by the volatilities, which follow a random walk.

As it is well known, most empirical macroeconomic applications present evidence of changes in volatility. However, there is a tendency in mixed-frequency VAR literature to ignore this issue and work with homoscedastic models. As can be seen in Koop et al. (2018), which is the working paper version of Koop et al (2020), there is evidence in support of the use of this kind of MF-VAR-SV, because marginal likelihoods strongly indicated that stochastic volatility is present in real and nominal data.

We performed a robustness check using two quarterly exogenous variables per region: supermarket sales and consumption of concrete. The results from this exercise are not qualitatively different from the original specification. Given they restrict the sample, we did not use them for the rest of the document's analyses. They are available upon request to the users.

In line with Koop et al. (2018), Mariano and Murasawa (2003, 2010), Mitchell et al. (2005), and Schorfheide and Song (2015), the following mixed temporal frequency restriction was used:

Equation (10) is a restriction relating the endogenous variable observed at a regional level to the weighted sum of quarterly latent states. Specifically, it holds the relationship between the annual gdp growth rate (Y _t ^r - ^A ) and the quarterly growth rate (Y ^r _t ,Y ^r _t-1 ,...,Y ^r _t-6 ) for each region. In this way, we established a restriction between the annual frequency time series (Y _t ^r,A ) and the quarterly frequency (Y_t ^r), both expressed in logarithmic differences. This condition maintains the linear structure of the space state model. Note that (10) shows an approximate relationship between the annual and quarterly log differences. It does not represent the econometric specification but is a way to match quarterly and yearly growth rates.

To apply the restriction imposed in equation (10) to each of the country's regions, equation (11) was constructed:

The vector Y _t ^A contains the annual regional gdp growth rates and is mathematically represented as:

In equation (11), M _t ^A - 1. The matrix Ω ^A represents the numerical time constraints explained in equation (10), as presented in Koop et al. (2020). So, equation (11) links our quarterly regional data with the unobserved regional quarterly growth rates we wanted to estimate.

The vector z _t is a matrix composed of 6 column vectors with the respective quarterly lags expressed in (7) for each region. Therefore, z _t is defined as:

In addition, two restrictions were introduced for the country's GDP:

with µ_t ~ N(0,σ_cs ² ).

This last equation represents the transversal restriction we imposed, which dictates the sum of the regional GDP to be equal to the national GDP. The derivation of this equation, using data on logarithmic differences, can be found in Mitchell et al. (2005).

We resolved the notorious over-parametrization problem of the proposed VAR with a Bayesian estimation method and selected priors values using the Dirichlet-Laplace Hierarchical algorithm (Bhattacharya et al. 2015). In this model, the variance priors determine the degree of contraction of the coefficient matrix.

The state equations for our state space model can be written in multi-variate regression form, where β = vec([Φ ₀ , Φ ₁ , …, Φ _p ]′) is a k-dimensional vector of var coefficients. We define ß = (ß₁, ..., ß _k )', then the priors of each coefficient are independent:

Note that this prior would shrink the estimate of ß _j towards the prior mean of zero relatives to a maximum likelihood estimate (mle). The prior variance, ψ _k ^β υ² _j ,_β 2 ,τ_β ² determines the degree of shrinkage. Large values of variance priors imply a tiny contraction, and the Bayesian estimate is similar to that of maximum likelihood. However, if the variance priors are close to zero, the coefficient becomes zero, and the corresponding variable is removed from the model.

The determining factors of the previous variance priors were treated as unknown parameters and estimates. Therefore, the algorithm automatically decided whether these variance priors should be close to zero. The Dirichlet-Laplace priors were hierarchically chosen because they are expressed in unknown parameters requiring their priors. They involve only one prior hyperparameter α_ß. Bhattacharya et al. (2015) recommended setting it to 1 2 , and we use this recommendation.

The previous explanation regards the reduction of the MF-VAR coefficients matrix, but the Dirichlet-Laplace algorithm also chooses the coefficients of the covariances matrix for the error. Empirical evidence shows that this type of previous reduction in a high-dimensional parameters vector may help induce parsimony in a model (see Park and Casella, 2008). This model led to a posterior approximating to true value at a theoretically optimal rate, superior to other alternatives such as the Bayesian Lasso.

3.2. Time-Varying Parameter Vector Autoregressions

Time-varying parameter vector autoregressions (TVP-VAR) have become widely used to analyze macroeconomic time series behavior. Chan and Eisenstat (2018) found that TVP-VAR with stochastic volatility works better than a VAR of constant coefficients for macroeconomic modeling. TVP-VARS often include stochastic volatility (sv), which allows variation over time in the variations in error processes affecting VAR. Thus, the method intended to capture the data's temporal variation using a parsimonious but flexible model as in the VAR. Generally, it works within a flexible framework with random time variation for a wide range of non-linear behaviors in the data. Following Cogley and Sargent (2001), a substantial part of the literature opted for a flexible specification that can be used for many temporal variation patterns.

Unlike the fixed coefficient version of the VAR, the intersection parameters and the matrix of lags are allowed to vary over time in a prescribed manner (Lubik & Matthes, 2015). The TVP-VAR was specified as follows:

However, as the subscript t indicates, the intersection of direction and strength of autoregressive effects in (19) can take on different values over time.⁴ The lagged values were collected as follows: X′ _t = I ∗ 1,′y _t−1 …,y′ _t−L ( ). θ _t collects the var time variable coefficients in the vectorized form: θ _t = vec, ([c _t A ₁ , _t A ₂ , t… A _{L, t} ]′) which allowed us to rewrite the previous equation as follows:

The commonly assumed law of motion for θ _t is a random walk:

Where µ_i ~ N(0, Q) is assumed to be independent of ε_t. The random walk specification is parsimonious because it can capture many patterns without introducing additional parameters. This assumption is primarily for parsimony and flexibility.

4.1. Analysis of the region's economic slowdown in Bolivia

We present the estimated series of quarterly growth rates for the nine regions from the second quarter of 2000 to the second quarter of 2020 and a robustness check using an alternative specification with two exogenous variables -supermarket sales and concrete consumption in each region (Figures 8, 9 and 10). The graph shows that both series behave consistently. To convince the reader that our estimation produced accurate results, we present a plot with annualized quarterly economic growth (calculated using equation 10) by region, along with credible intervals which cover the 16^th through 84^th percentiles in annex B.

The pandemic and the confinement of economic activity, through the ex-post situation, allowed to appreciate a decrease of 7.2 % in national production as of June 2020 (National Institute of Statistics). Therefore, Table 3 also displays the seasonally adjusted quarterly growth rate by region for the last four quarters.

The results show that the negative impact differed for each region, with Tarija, Oruro, Santa Cruz, and Pando being the most affected. In addition, from Figure 7, it can be deduced that the economic behavior is quite heterogeneous among regions, an example being Tarija, with a complicated economic situation since 2014, while others remained in a stable growth path at least until the second quarter of 2019.

4.2. Fiscal Policy Impact and Effectiveness Evaluation during Covid-19

Through the TVP-VAR models, we can appreciate that during the second quarter of 2020, the growth rate of the nine regions responded positively to the shocks of capital expenditure of the central government. Chuquisaca, La Paz, and Beni reacted positively to regional government capital expenditure shocks, while Santa Cruz, Chuquisaca, and La Paz responded positively to capital expenditure shocks made by main local governments (Table 4).

On the other hand, there is evidence that the regional growth rate did not respond to current expenditure shocks from regional and main local governments. However, Chuquisaca, Cochabamba, and Oruro's growth rates reacted positively to the current expenditure shocks of the central government.

To summarize, we noted that during the Covid-19 pandemic, central government capital spending was the most effective mechanism to mitigate the economic slowdown. We also identified that the response of economic activity to central government capital spending in the second quarter of 2020 was similar to that of the second quarter of 2009 and 2014 (time of economic slowdowns). Still, the magnitude of the former was much more significant (evidenced in annex B).

Finally, as a robustness check, we also made estimations using the variables of regional economic activity (supermarket sales and concrete consumption) following Koop et al. (2020). The results were consistent and very similar (see Figures 8, 9 and 10).