About the Forecasting Model 

Back to the Forecasts

The forecasting model was developed and implemented by Doug McMillin, Professor Emeritus, Dept. of Economics, LSU. 

The state variables to be forecast are real GSP, employment, the unemployment rate, and the Louisiana house price index. The Louisiana forecasting model consists of two Bayesian Vector Autoregressive Models (BVARs), one for three of the state variables of interest and the other for national variables, and single equation autoregressive models for Louisiana house prices and employment in the state’s metro areas. BVARs are multivariate time series models in which a vector of variables depends on lagged values of the vector of variables. Single equation autoregressive (AR) models employ lagged values of the variable being forecast as explanatory variables. Both model types may also contain other variables not determined by the model (i.e., exogenous variables). Initially, single-equation AR models were estimated for all variables to be forecast. BVARs were employed only if forecast accuracy for the BVARs was better for all variables in the BVAR than for the corresponding AR equations. The accuracy of the BVARs was also compared to that of analogous standard VARs, but in all cases, the BVAR forecast errors were smaller than for the standard VARs. All estimation and forecasting were done with the RATS econometric software.

Specification of both the BVARs and AR models was based on the accuracy of out-of-sample forecasting. The models were estimated sequentially for samples that began in 1990:01 and that, alternatively, ended in 2007:04, 2008:01, 2008:02, etc. with the final sample period ending in 2020:04. For each sample period, 1-period ahead through 4-period ahead out-of-sample forecasts were generated and forecast errors (actual values minus forecast values) and relative forecast errors (forecast error/actual) were computed at each horizon. Except for the fact that the latest revised data are used, the procedure replicates what a forecaster would do in real-time to generate out-of-sample forecasts, i.e., estimate the forecasting model using data up to the point of the forecast and then forecast out-of-sample.

These error series were then used to compute root-mean-square-errors (RMSE) and root-mean-square-percent errors (RMSE%), two commonly used forecast error measures, for each forecasting horizon for each variable. The RMSE%s are used to specify the models. The RMSE values are a measure of the average size of the forecast errors at each horizon. Adding and subtracting the RMSE for a given horizon from the current forecast for that horizon provides a range of values within which we might reasonably expect current forecasts to lie, given the size of past forecast errors. Note that the forecast error measures were computed over time periods that included major hurricanes, a financial crisis, and a pandemic. Forecast errors immediately following essentially unforecastable major shocks are typically large, so the RMSE estimates reflect forecast errors in normal times as well as several very unusual times. This seems prudential given that major shocks hit the Louisiana (and national) economy during the 2008-2020 period, and major shocks can’t, unfortunately, be ruled out in the future.

The single equation autoregressive models were estimated using Ordinary Least Squares, and the key questions were how many lags of the variable itself to include and whether to include exogenous variables determined outside the Louisiana economy that might plausibly help explain the Louisiana economic variables. For example, the state of the national economy as measured by real GDP and the national unemployment rate and the price of oil as determined in world oil markets might be expected to have effects on the Louisiana economy. The final specification of the single equation models was the combination of own lags and exogenous variables that yielded the smallest out-of-sample forecast errors.

BVARs, like standard VARs, consist of an equation for each variable in the model in which that variable depends on lags of itself and lags of the other model variables as well as perhaps the values of exogenous variables. BVARs, unlike standard VARs, place initial (prior) restrictions on the model coefficients and their standard errors, although the data are allowed to override the restrictions if the data “speak” loudly enough. The goal is to find a set of restrictions that produce coefficient values that better capture the major forces driving the behavior of the model variables and hence deliver good forecasts than do unrestricted coefficients, which can reflect not only major forces but also less important relationships in the estimation period that may not be found in the future. In specifying BVARs, a search over alternative lag lengths, initial (prior) restrictions, and alternative exogenous variables is conducted for the combination of lag lengths of the model variables, prior restrictions, and exogenous variables that deliver the best out-of-sample forecasts, i.e., those that minimize out-of-sample forecast errors.

The BVAR for the state-wide variables comprises real GSP, employment, and the unemployment rate. The Louisiana house price index was also considered for inclusion in the BVAR, but adding this variable led to larger forecast errors for the other three variables. Further, the house price forecast errors from the BVAR were larger than from the house price AR equation. Consequently, only real GSP, employment, and the unemployment rate were included in the state-level BVAR, and an AR equation was used to forecast house prices.

The optimal lag for the BVAR was found to be 1 period. The optimal values of the Bayesian parameters are available on request. Several deterministic variables were included in each equation of the BVAR: a constant, two trend terms, a dummy variable to account for the back-to-back hurricanes Katrina and Rita, a financial crisis dummy variable, a covid pandemic lock-down dummy, and the current and 1 lag of real GDP, the national unemployment rate, and the West Texas Intermediate oil price. Other national variables were considered, but adding them did not improve forecast performance.

Because the state-level BVAR includes as exogenous variables the current and one lagged value of real GDP, the national unemployment rate, and oil prices, forecasts of these variables must be fed into the state-level BVAR to generate forecasts of the state variables. Consequently, a national BVAR was specified to generate forecasts of these national variables. Included in this BVAR are real GDP, the national unemployment rate, oil prices, the Wilshire 5000 stock price index, a national economic policy uncertainty index, the total capacity utilization index, and the 3-month Treasury bill rate. Although the latter 4 variables do not enter the state-level BVAR, including them in the national BVAR improved the forecasts of real GDP, the national unemployment rate, and oil prices. The more accurate are the forecasts of real GDP, the national unemployment rate, and oil prices, the more accurate are the forecasts of the state variables. Other national variables were also considered for inclusion in the national BVAR but didn’t make the cut. The national BVAR included an intercept term, the financial crisis and pandemic lock-down dummies, and a dummy for the Russian invasion of the Ukraine (which had a big effect on oil prices).

As noted earlier, an AR equation was used to forecast Louisiana house prices. The forecast equation includes an intercept term, two trend terms, the Katrina-Rita dummy, the financial crisis and pandemic lock-down dummies, a remote-work dummy that captures housing market effects from the increased working at home during and after the pandemic, 5 lags of the Louisiana house price index, and the current and 2 lags of the mortgage interest rate. Using this equation to forecast requires forecasts of the mortgage interest rate, and an AR equation was used to generate the mortgage rate forecasts. The mortgage rate AR equation includes an intercept term, a term that captures the steady downward drift in the mortgage rate over time, a dummy variable to account for the recent tightening of monetary policy, 2 lags of the mortgage rate, and the current value of the national unemployment rate. Note: adding the mortgage rate to the national BVAR did not improve the forecasts of real GDP, the national unemployment rate, and oil prices, and the forecasts of the mortgage rate from the expanded BVAR were not as accurate as those from the AR equation.

The remaining variables to be forecast are the employment levels of the state’s metro areas: Alexandria, Baton Rouge, Hammond, Houma-Thibodaux, Lafayette, Lake Charles, Monroe, New Orleans-Metairie, and Shreveport-Bossier City. Separate AR equations for each metro area were used to generate metro area forecasts. Conceptually a BVAR that includes lags of every variable in the model as explanatory variables in every equation doesn’t make much sense for the metro areas, and, not surprisingly, a BVAR that simultaneously included all metro areas didn’t forecast very well. It is, of course, possible for economic activity in a metro area to affect economic activity in contiguous metro areas and smaller BVARs that included two or three contiguous metro areas were tried but didn’t forecast as well as separate AR equations for each metro area. It is plausible that overall state economic activity and the price of oil affects the level of activity in a given metro area, and this was checked for each metro area.

The AR metro employment models all included an intercept term and the pandemic lock-down dummy, but other aspects of the equation differed across metro areas. The other explanatory variables are as follows.

Alexandria: the Katrina-Rita dummy, 1 lag of Alexandria employment, the current and 1 lagged value of the Louisiana unemployment rate, and the current values of real GSP and the price of oil.

Baton Rouge: a trend term, the Katrina-Rita dummy, 1 lag of Baton Rouge employment, the current and 4 lags of the state unemployment rate, and the current value of real GSP.

Hammond: the Katrina-Rita dummy, 1 lag of Hammond employment, the current and 3 lags of the state unemployment rate, and the current and 1 lag of real GSP.

Houma-Thibodaux: a trend term, 1 lag of Houma-Thibodaux employment, the current and 3 lags of the state unemployment rate, and the current values of real GSP and the oil price.

Lafayette: a trend term, the Katrina-Rita dummy, 1 lag of Lafayette employment, the current and 8 lagged values of the price of oil, and the current and 1 lagged value of both state real GSP and the state unemployment rate.

Lake Charles: two trend terms, a pandemic rebound dummy, 2 lags of Lake Charles employment, the current and 5 lags of the state unemployment rate, and the current oil price.

Monroe: a trend term, the Katrina-Rita dummy, 2 lags of Monroe employment, the current and 4 lagged values of the state unemployment rate, and the current and 8 lagged values of real GSP.

New Orleans-Metairie: a trend term, 1 lag of New Orleans-Metairie employment, and the current and 1 lagged value of the state unemployment rate.

Shreveport-Bossier City: two trend terms, the Katrina-Rita dummy, 1 lagged value of Shreveport-Bossier City employment, the current value of state real GSP, and the current and 1 lagged value of the state unemployment rate.

NOTE: for all the models described above, the natural logs of all variables except for the unemployment rate variables and the interest rate variables were used in the estimation and forecasts. However, the forecasts were converted back to the original form of the variable for presentation of the forecasts.

 

 

¹Data for all variables are from the Federal Reserve Bank of St. Louis FRED database (Federal Reserve Economic Data | FRED | St. Louis Fed (stlouisfed.org)).

²Quarterly Louisiana Real GSP is officially available only from 2005 on but is available annually from 1997 on. Estimates of real GSP before 2005 were generated in the following way. An older Louisiana Real GSP series (based on the SIC classification rather than the NACIS classification that is used now) is available annually through 1997. The old and the new series are thus both available in 1997. The old series from 1988-1996 was multiplied by the ratio of the new to old values of 1997 real GSP (1.594108) thereby producing an annual series consistent with the new basis for computing real GSP. This preserves the time series behavior of the old series but scales it to the level of the new series. The converted values from 1988-1996 were then appended to the annual official series. This generates an annual series from 1988 on. The annual series over the period 1988-2020 was then disaggregated into quarterly values using the @disaggregate procedure in RATS using random walk errors in a related series regression using U.S. real GDP, Louisiana real personal income, and the price of oil. The quarterly disaggregated values from 2005-2020 are almost identical to the official quarterly values for this period, so we know this procedure works very well from 2005-2020. We assume that the quarterly disaggregated values before 2005 are also close to the unobserved “true” quarterly values.