Nowcasting Indonesia

Abstract

We produce predictions of the current state of the Indonesian economy by estimating a dynamic factor model on a dataset of 11 indicators (followed closely by market operators) over the 2002–2014 period. Besides the standard difficulties associated with constructing timely indicators of current economic conditions, Indonesia presents additional challenges typical to emerging market economies where data are often scant and unreliable. By means of a pseudo-real-time forecasting exercise, we show that our model outperforms univariate benchmarks, and it does comparably well with predictions of market operators. Finally, we show that when quality of data is low, a careful selection of indicators is crucial for better forecast performance.

Appendix

1.1 Robustness

In this Appendix we show robustness checks with respect to the composition of the dataset.

The first robustrness check aims to answer the question “what if we had selected variables in a different way?”. As discussed in Sect. 3.1, we constructed the database by selecting variables from the set of indicators that market analysts are monitoring, however, a priori there are other equally valid selection criteria. In particular, in performing this robustness check we considered (a) the option of using all the indicators in Table 1 (labeled Bloomberg selection), and (b) the option of selecting indicators automatically by using a statistical technique (labeled as automatic selection).¹⁸

In Table 6, we show the RMSE for a DFM parameterized as described in Sect. 4.1 but estimated on the two datasets just described. As we can see, our database clearly delivers the best performance, though in forecasting the performance of the DFM estimated over the indicators followed by Bloomberg is comparable. The performance of the DFM is particularly disappointing when the indicators are selected with LARS. We believe that this is a consequence of having too few observations, and some missing values in the time series of our indicators.

The second robustness check aims to answer the question “what if we do not select indicators but include all variables that we are able to retrieve?”. To this end we use a bridge model as in Eq. (4), where the predictor $x_t^Q$ is a factor extracted from a panel of monthly variables by using principal component.¹⁹ The last column of Table 6 reports the RMSE for this model and the results confirm that including all variables does not appear to be a good strategy.

Table 6 Root mean squared error: different model specifications and datasets.

1.2 Technical aspects related to y-o-y transformations

In Sect. 3.2 we mention that to estimate the model we use the EM algorithm proposed by Bańbura and Modugno (2014), which can handle both mixed frequencies and missing data. While we refer the reader to Bańbura and Modugno (2014) and Bańbura et al. (2011, 2013) for detailed information on this algorithm and for a formal treatment, in this Appendix we provide basic information related to the use of year over year growth rates.

The first issue is to understand what is the relationship between monthly y-o-y growth rates, and quarterly y-o-y growth rates. Let t denotes months, and let $Y^Q_t$ be the log-level of a quarterly variable. The y-o-y growth rate is then equal to $Y^Q_t-Y^Q_{t-12}$ and we will denote it as $y_t^Q$. Then, let $Y^M_t$ be the monthly log-level of Y, and let $y_t^M=Y^M_t-Y^M_{t-12}$ be the monthly y-o-y growth rate. In order to link $y_t^Q$ and $y_t^M$ we follow Mariano and Murasawa (2003), and we make use of the approximation $Y_t^Q \approx Y_t^M + Y_{t-1}^M+Y_{t-2}^M$ which, after some simple algebra, allows us to write:

$$\begin{aligned} y_t^Q=y_t^M+y_{t-1}^M+y_{t-2}^M. \end{aligned}$$

(6)

The second issue is how to write the factor model when we have a vector of monthly and quarterly y-o-y growth rates. Bańbura and Modugno (2014) solved this by treating quarterly series as monthly series with missing observations, and by assigning the quarterly observation to the 3rd month. Suppose for simplicity that we have only one monthly variable $y_{1t}^M$, one quarterly variable $y_{2t}^Q$, and one (monthly) factor $f_t$, then by using (6) we have:

$$\begin{aligned} \begin{bmatrix} y_{1t}^M \\ y_{2t}^Q \end{bmatrix} = \begin{bmatrix} \lambda _m&0&0 \\ \lambda _q&\lambda _q&\lambda _q \end{bmatrix} \begin{bmatrix} f_t \\ f_{t-1} \\ f_{t-2} \end{bmatrix}+ \begin{bmatrix} 1&0&0&0 \\ 0&1&1&1 \end{bmatrix} \begin{bmatrix} \xi _{1t}^M \\ \xi _{2t}^Q \\ \xi ^Q_{2t-1} \\ \xi ^Q_{2t-2} \end{bmatrix}. \end{aligned}$$

(7)

1.3 Why two factors?

The literature on factor models has shown that it suffices to include a small number of factors for forecasting (e.g., Stock and Watson 2002b; Forni et al. 2003). Furthermore, recent literature on small-medium DFMs (Bańbura et al. 2013; Luciani and Ricci 2014; Giannone et al. 2014; Bragoli et al. 2015) often includes one factor only. Therefore, a natural choice would be to follow the literature and to set $r=1$.

However, these factor models are estimated for q-o-q growth rates, while we are estimating a model for y-o-y growth rates. So if the model for q-o-q growth rates has one factor, then the corresponding model for y-o-y growth rates has four factors: let $X_t$ be a non-stationary variable in log-levels, and let $x_t^y=X_t-X_{t-4}$ be the y-o-y growth rates and $x_t^q=X_t-X_{t-1}$ be the q-o-q growth rates, so that $x_t^y=x_t^q+x_{t-1}^q+x_{t-2}^q+x_{t-3}^q$. Then, if the true model is $x_t^q=\lambda f_t+e_t$, we have $x_t^y=\lambda (1+L+L^2+L^3)f_t+(1+L+L^2+L^3)e_t$, which can be rewritten as $x_t^y=\lambda {\mathbf {F}}_t+(1+L+L^2+L^3)e_t$ where ${\mathbf {F}}_t$ is a $4\times 1$ singular vector.

In light of this, we should set $r=4$, and, indeed, by looking at the eigenvalues of the covariance matrix of the first subsample (July 2002–December 2007), we can see clearly three/four diverging eigenvalues. However, among these three/four eigenvalues, the first two clearly dominate—the first eigenvalue accounts for 70% of the total variance, the second for 20%, the third for 5%, and the fourth for 3%—thus suggesting that the other two mainly carry noise, which is why we choose to set $r=2$. Furthermore, as a robustness check we estimated the DFM by setting either $r=1$ or $r=4$, and found (results not shown here) that including two factors proved optimal.

There are at least three possible alternatives to the strategy of setting $r=2$. The first would be to estimate a model with four common factors driven by only one common shock, so that the vector $\mathbf f_t$ in Eq. (2) is $4\times 1$, while the vector $\mathbf u_t$ is $1\times 1$. A second possibility would be to impose the specific lagged structure described above (see, e.g., Camacho and Perez-Quiros 2010), and a third possibility would be to estimate dynamic factor loadings by using the Dynamic Heterogeneous Factor Models of (D’Agostino et al. 2016).

The reason we prefer to use the model with $r=2$ to all the alternatives is that we want to keep the model as simple as possible, so that it easy to communicate the prediction obtained with our model to policy makers. Furthermore, all three alternatives complicate the state space representation and in our case where we have few time series observations, and the quality of the data is doubtful, while complicating the Kalman Filter is feasible it is costly in terms of computation accuracy.