# Algorithmic Modelling of Financial Conditions for Macro Predictive Purposes: Pilot Application to USA Data

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## Abstract

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## 1. Introduction

## 2. Algorithmic Model Design

#### 2.1. Macro Model Setting and Model Training

#### 2.2. Algorithm for FCI Construction

## 3. Data

## 4. Empirical Results

#### 4.1. Input Indicator Selection

#### 4.2. Aggregation

#### 4.3. Prediction

## 5. Concluding Discussion

- On model conceptualisation: Essentially, the model-based FCIs are pooled and partial predictors. However, it can be challenging to reach a consensus on the interpretation of these predictors, in view of the intense debates and discussions on the nature of latent variables or composite variates in PLS regression modelling and formative measurement modelling.15 From the stance of statistical modelling, the question of interpretability touches on the crux of under what conditions a theoretical identity has a one-to-one mapping from a statistical identity, see Markus (2016). Aside from epistemological concerns, the discussion highlights the primary importance of the algorithm design to ensure consistency between math/statistical aggregation rules and desired properties of the theoretical constructs, e.g., see Munda (2012).
- On model design: Improvements can be made from two sides. From the input side, more elaborate aggregation rules should be introduced with help from dimensionality reduction techniques in machine learning. For instance, multi-path or classification models should be experimented with to replace the man-made filtering step of redundant indicators. The possibility of interactive dynamics among indicators should also be considered to search for more effective and parsimonious ways to formulate dynamic input features. From the target side, more attention should be focused on how to exploit the target selection capacity of this modelling approach to better serve policy purposes.16
- On model testing: Improvements of methods of model evaluation are desired at various stages. Here, active research is worth tracking in two areas. One is concerned with the quality of composite indicators and tackled by sensitivity analysis, see Saisana et al. (2005), and Dobbie and Dail (2013). The other is on evaluation of various aspects of formative PLS path models, such as content, construct, convergent and discriminant validity, see Andreev et al. (2009), and Bentler and Huang (2014).

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Algorithm A1 Long-Run FCI Construction | |

1: | for each increasing update interval ${u}_{h},h\leftarrow 0$ to $N$ do |

2: | standardise each column of matrix ${\mathit{I}}_{T+{u}_{h}}$ by its mean ${\overline{\mathit{i}}}_{j,T+{u}_{h}}$ and sd ${s}_{{\mathit{i}}_{j,T+{u}_{h}}}$ |

3: | compute the weight vector ${\widehat{\mathit{\phi}}}_{i}={\mathit{I}}_{T+{u}_{h}}^{T}{\mathit{y}}_{T+{u}_{h}}$ |

4: | set ${\widehat{\mathit{\phi}}}_{h}={\widehat{\mathit{\phi}}}_{h}/\left|{\widehat{\mathit{\phi}}}_{h}\right|$ |

5: | for $j=1$ to $m$ do |

6: | for $k=0$ to $n$ do |

7: | if $\left|{\widehat{\phi}}_{j,k,h}\left|=ma{x}_{n}\right|{\widehat{\phi}}_{j,n,h}\right|$ then |

8: | ${\widehat{\phi}}_{j,k,h}={\widehat{\phi}}_{j,k,h}$ |

9: | else |

10: | ${\widehat{\phi}}_{j,k,h}=0$ |

11: | end if |

12: | end for |

13: | end for |

14: | compute the first factor ${\mathit{f}}_{T+{u}_{h}}={\mathit{I}}_{T+{u}_{h}}{\widehat{\mathit{\phi}}}_{h}$ |

15: | compute LRFCI ${\mathit{f}}_{T+{u}_{h}}^{L}={\mathit{f}}_{T+{u}_{h}}\times {s}_{\mathit{y}}{}_{T+{u}_{h}}+{\overline{\mathit{y}}}_{T+{u}_{h}}$ |

16: | end for |

Notes: Matrixes are bold and in capital letters and vectors are bold and in lower case. ${\mathit{y}}_{T}$ is the vector of the long-run target $({y}_{t}-{\kappa}_{1}{X}_{t})$ as specified in (3). ${\mathit{I}}_{T}$ is a $T$ by $m\times n$ matrix of financial indicators and their respective lagged versions. The selected ${\widehat{\phi}}_{j,k,h}$ in step 8 is ${\widehat{\phi}}_{j,{k}^{*}}$ in (4). ${s}_{{\mathit{x}}_{T}}$ indicates the standard deviation of vector ${\mathit{x}}_{T}$ and ${\overline{\mathit{x}}}_{T}$ its mean. |

Algorithm A2 Short-Run FCI Construction | |

1: | for each increasing update interval ${u}_{h},h\leftarrow 0$ to $N$ do |

2: | standardise each column of matrix ${\mathit{I}}_{T+{u}_{h}}$ by its mean ${\overline{\mathit{i}}}_{j,T+{u}_{h}}$ and sd ${s}_{{\mathit{i}}_{j,T+{u}_{h}}}$ |

3: | set ${m}^{*}=0$ and $c=0$ |

4: | for $j=1$ to $m$ do |

5: | regress ${\mathit{y}}_{T+{u}_{h}}$ on $\left[{\mathit{i}}_{j,T+{u}_{h}-1},{\mathit{i}}_{j,T+{u}_{h}-2},\dots ,{\mathit{i}}_{j,T+{u}_{h}-n}\right]$ |

6: | extract 3 coefficients with smallest p-value (including intercept) |

7: | regress on 3 selected variables |

8: | drop insignificant coefficients with p-value larger than threshold ${p}_{0}$ |

9: | if there is at least one remaining variable then |

10: | ${m}^{*}={m}^{*}+1$ |

11: | save the remaining coefficient estimates as ${\widehat{\mathit{\omega}}}_{j,h}$ |

12: | set the other insignificant coefficient estimates to zero |

13: | if intercept ${\beta}_{o}$ is significant then |

14: | $c=c+{\beta}_{o}$ |

15: | end if |

16: | else |

17: | set ${\widehat{\mathit{\omega}}}_{j,h}=0$ |

18: | end if |

19: | end for |

20: | compute SRFCI ${\mathit{f}}_{T+{u}_{h}}^{S}=1/{m}^{*}({\mathit{I}}_{T+{u}_{h}}{\widehat{\mathit{\omega}}}_{h}+c)$ |

21: | end for |

Notes: Matrixes are bold and in capital letters and vectors are bold and in lower case. ${\mathit{y}}_{T}$ is the vector of the short-run target $\Delta {y}_{t}$ as specified in (5). ${\mathit{I}}_{T}$ is a $T$ by $m\times n$ matrix of financial indicators and their respective lagged versions. ${s}_{{\mathit{x}}_{T}}$ indicates the standard deviation of vector ${\mathit{x}}_{T}$ and ${\overline{\mathit{x}}}_{T}$ its mean. |

## Appendix B

Variable | Description | Source | Series Title |
---|---|---|---|

O1 | 3-month market interest rate of US | Reuters | US INTERBANK RATE–3 MONTH |

O2 | 3-month market interest rate of UK | Bank of England | UK BOE LIBID/LIBOR–3 MONTH |

O3 | 3-month market interest rate of Canada | IMF, International Financial Statistics | CN interest rates: money market rate NADJ |

O4 | 3-month market interest rate of Sweden | Sveriges Riksbank | SD interbank money rate: 3 months (EP) NADJ |

O5 | Exchange rate of UK | Bank of England | GBP to USD (BOE)–Exchange rate |

O6 | Exchange rate of Canada | Reuters | Canadian $ to US $ (WMR)–Exchange Rate |

O7 | Exchange rate of Sweden | Bank of England | SEK to USD (BOE)–Exchange Rate |

O8 | Forward exchange rate of UK | Reuters | UK £ to US $ 3M FWD (WMR)–Exchange Rate |

O9 | Forward exchange rate of Canada | Barclays Bank PLC | Canadian $ to US $ 3M FWD (BBI)–Exchange Rate |

O10 | Forward exchange rate of Sweden | Barclays Bank PLC | Swedish Krona TO US $ 3M FWD (BBI)–Exchange Rate |

O11 | Stock market index of US | Standard and Poors (S&P) | S&P 500 Composite–Price index |

O12 | Stock market index of Canada | IMF, International Financial Statistics | CN Share prices, total NADJ |

O13 | Stock market index of Germany | Reuters | BD DAX Share Price Index, EP NADJ |

O14 | Stock market index of Japan | Tokyo Stock Exchange | TOPIX–Price Index |

O15 | Stock market index of UK | IMF, International Financial Statistics | UK Share Prices, TOTAL NADJ |

O16 | 1-year government bond | Thomson Reuters Datastream | United States GVT BMK Bid Yield 1 Year |

O17 | 10-year government bond | OECD, Main economic indicators | US Yield 10-Year FED GVT SECS NADJ |

O18 | 30-year government bond | Thomson Reuters Datastream | TR US GVT BMK BID YLD 30Y (U$)–RED. YIELD |

O19 | 3-month T bill | Federal Reserve | US T-BILL 3 Month (W) |

O20 | 6-month T bill | Federal Reserve | US T-BILL 6 Month (W) |

O26 | Lending rate | Federal Reserve | US Prime rate charged by banks (Month avg) NADJ |

O27 | Mortgage rate | Freddie Mac | Mortgage Lending Rates, Conforming 30-Year Fixed Rate Mortgage, Total, Average Interest Rate |

O28 | Mortgage volume of the banking sector | Federal Reserve | US Commercial Bank Assets–Real estate loans |

O29 | Loan volume of the banking sector | Federal Reserve | US Commercial Bank Assets–Loans & Leases in Bank credit |

O30 | Total liabilities of the banking sector | Federal Reserve | US Commercial Bank Liabilities–Total |

O31 | Equity of the banking sector | Federal Reserve | US Commercial Bank Residual (Assets less Liabilities) |

O32 | Deposit volume of the banking sector | Federal Reserve | US Commercial Bank Liabilities–Deposits |

O33 | M1 | Federal Reserve | US Money Supply M1 |

O34 | Real effective exchange rate | IMF, International Financial Statistics | US Real Effective FX Rate (REER) Based on Consumer price index |

O35 | Consumer Price Index | OECD, Main economic indicators | US CPI All items NADJ |

O36 | Producer Price Index | Bureau of Labor Statistics, U.S. Department of Labor | US PPI–All Commodities |

O37 | Industrial Production Index | Federal Reserve | US Industrial Production–Total Index VOLA |

O38 | GDP (quarterly) | OECD, Main economic indicators | US Gross Domestic Product (at COnstant PPP) |

O39 | Global output (quarterly) | From Di Mauro and Pesaran (2013) |

## Notes

1. | The inadequacy of capturing the financial sector impact in macro modelling has been highlighted recently from a broader angle in a special issue of Oxford Review of Economic Policy vol. 34, i.e., see Stiglitz (2018), and Vines and Wills (2018). |

2. | The PLS method was proposed by H. Wold (1966, 1975, 1980); for more background information, see Wegelin (2000), Sanchez (2013) and McIntosh et al. (2014). It has been extended into the causal interpretation of PLS path modelling in relation to measurement theory, see Vinzi et al. (2010), Howell et al. (2013) and Howell (2014). A few trial applications of PLS can be found in the econometric literature: e.g., Lin and Tsay (2005), Eickmeier and Ng (2011), Lannsjö (2014), Kelly and Pruitt (2015), Fuentes et al. (2015), Groen and Kapetanios (2016), and Kapetanios et al. (2018), but none has adopted the causal model basis of the method. |

3. | |

4. | Historically, the reflective model is referred to as ‘mode A’ and the formative model ‘mode B’, see Wold (1980) and also Vinzi et al. (2010). In a reflective model, weights are identified by the assumption of conditional independence, i.e., all the manifest indicators are effects of one common cause. In contrast, this assumption does not apply to the formative model. Hence, the weights of the indicators in a formative model cannot be identified by a single criterion, such as the common variance criterion of PCA. An additional criterion is needed for the identification (Markus and Borsboom 2013, p. 113). |

5. | Although the concept of supervised versus unsupervised data reduction is unfamiliar to economists, the idea of targeting the index construction process at dependent variables has been around since early warning systems research, e.g., Gramlich et al. (2010). The method of selecting indicators based on their ability to signal turning points in Levanon et al. (2015) effectively follows the supervised learning approach. |

6. | This incorrect formalization of problems falls into what is referred to as ‘Type III error’ by Hand (1994, p. 317). |

7. | |

8. | Evidence of lack of volatility synchronization among financial indicators has been discussed in the literature, e.g., Cesa-Bianchi et al. (2014). |

9. | When this long-run combination of the ECM fits the description of cointegration, our formulation can be interpreted as exploiting the Granger-Engle two-step procedure. |

10. | |

11. | See Di Mauro and Pesaran (2013) for the data source and definition. |

12. | Selection of the unprocessed series is carried out with reference to Alessi and Detken (2011), Hatzius et al. (2010), Bisias et al. (2012), and Moccero et al. (2014). Particular attention is paid to the coverage of credit and property price information, see Borio (2014b). The processed data series are downloaded from: https://sethpruitt.net/2016/03/31/systemic-risk-and-the-macroeconomy-an-empirical-evaluation/ (accessed on 11 April 2022); see Giglio et al. (2016) Table 1 Systemic Risk Measures. |

13. | |

14. | Estimating the unrestricted ECM showed that the imposition agrees with data information. A natural extension of this imposition is calibration, a commonly used method in macro DSGE modelling practice, i.e., experimenting with small variation of the imposed values to choose the best possible one by certain modelling criteria, see van Huellen et al. (2022). |

15. | For the recent literature, see Rigdon (2012), Rönkkö and Evermann (2013), Henseler et al. (2014), Bentler and Huang (2014), Hair et al. (2017) and also the November issue, vol. 44 (2013) of the DATABASE for Advances in Information Systems, Aguirre-Urreta et al. (2016) and all its commentaries in vol. 14 (3–4) of Measurement: Interdisciplinary Research and Perspectives. |

16. | Experiments in a subsequent research project have already yielded some encouraging results on this point, see van Huellen et al. (2022). |

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**Figure 2.**Short-Run Macro Targets and US Interest Rates. Note: Short-run macro targets in annual growth rates ${\Delta}_{12}{y}_{t}$ and US interest rates ${R}_{t}$. 1980M1–2017M12.

**Figure 3.**Long-Run Macro Targets and Error Correction Terms. Note: Macro targets ${y}_{t}-{x}_{t}$ (

**left**) and error correction term ${e}_{t}^{*}={y}_{t}-{x}_{t}-{f}_{t}^{L}$ (

**right**). 1980M1–2017M12.

**Figure 4.**Short-Run FCIs. Note: SRFCI is ${f}_{t}^{S}$ constructed by targeting ${\Delta}_{12}{y}_{t}$ (

**left**). D12LRFCI is ${\Delta}_{12}{f}_{t}^{L}$ constructed by targeting long run macro targets and annual differencing of the resulting long run FCIs (

**right**). 1980M1–2017M12.

**Figure 5.**Squared Difference Concatenated versus Non-Concatenated FCI. Note: Squared difference between concatenated and non-concatenated short-run FCIs ${f}_{t}^{S}$ targeted at $\Delta {y}_{t}$ following (3) and (4) over repeated 12-month periods, updating 2001M1–2016M12.

**Figure 6.**MSFE Ratio Over Repeated Updates 2001M1–2006M12. Note: MSFE of baseline model (1) over the FCI-augmented model (2) over the testing period 2001M1–2006M12 for 1-step ahead forecasts over repeated 12-month updates. A value < 1 implies that (2) produces a smaller MSFE than (1).

**Figure 7.**MSFE Ratio Over Extended Testing Period 2001M1–2017M12. Note: MSFE of baseline model (1) over the FCI-augmented model (2) over the extended testing period 2001M1–2017M12 for 1-step to 6-step ahead forecasts. A value < 1 implies that (2) produces a smaller MSFE than (1).

Group | Ind. | Indicator Description | Construction |
---|---|---|---|

Forex Market | I1 | CIP vis-à-vis UK sterling | ln(O2)−ln(O1)−(ln(O8)−ln(O5)) |

I2 | CIP vis-à-vis Canadian dollar | ln(O3)−ln(O1)−(ln(O9)−ln(O6)) | |

I3 | CIP vis-à-vis Sweden krona | ln(O4)−ln(O1)−(ln(O10)−ln(O7)) | |

I4 | Real effective rate of US dollar | O29 | |

Equity Market | I5 | Ratio of SMI: Canada/USA | O12/O11 |

I6 | Ratio of SMI: Germany/USA | O13/O11 | |

I7 | Ratio of SMI: Japan/USA | O13/O11 | |

I8 | Ratio of SMI: UK/USA | O14/O11 | |

Fixed Income Market | I9 | TB spread: 10-to-1 years | O17−O16 |

I10 | TB spread: 30-to-10 years | O18−O17 | |

I11 | TB spread: 30-to-1 years | O18−O16 | |

I12 | TB spread: 6-to-3 months | O20−O19 | |

I13 | TED spread: interbank loan to TB rates | O19−O1 | |

Banking Sector | I14 | Total liability to equity ratio of the banking sector | O25/O26 |

I15 | Total lending to deposit ratio of the banking sector | O24/O27 | |

I16 | IR spread: lending-to-deposit rates | O21/O1 | |

I17 | Debt to liquidity ratio: M1 to liquidity | O28/O25 | |

I18 | IR spread: mortgage-to-bond rates | O22−O18 | |

I19 | Bank lending: mortgage to loan ratio | O23/O24 | |

Systemic Risk Measures | I22 | CatFin: Institution specific value-at-risk measure | Giglio et al. (2016) |

I23 | CoVar: Value-at-risk measure | Giglio et al. (2016) | |

I24 | Mes: Institution specific exposure to shocks measure | Giglio et al. (2016) | |

I25 | Mes_be: Variation of Mes | Giglio et al. (2016) | |

I26 | Dci: Interconnectedness of financial institutions | Giglio et al. (2016) | |

I27 | Size_conc: Size concentration of financial institutions | Giglio et al. (2016) |

**Table 2.**Representative Indicator Loadings ${\widehat{\phi}}_{j,{k}^{*}}$ for Long-Run Macro Targets ${y}_{t}-{x}_{t}$ Over the Testing Period 2001M1–2006M12.

Target | CPI | GDP | IP | ||||
---|---|---|---|---|---|---|---|

Indicator | Lag | Loading | Lag | Loading | Lag | Loading | |

Forex | I1 | 0 | 0.0537 | 0, 6 | −0.0448 | 0, 6 | −0.1395 |

I2 | 3, 5 | −0.0117 | 0, 2, 6 | 0.0144 | 6, 5 | −0.1122 | |

I3 | 2, 6, 0 | −0.0017 | 2, 6, 0 | 0.0065 | 0, 3, 6 | −0.1252 | |

I4 | 0 | −0.0544 | 6, 0 | 0.0655 | 0 | 0.0664 | |

Equity | I5 | 2, 4, 6 | −0.1534 | 0, 4, 6 | 0.1403 | 5, 6 | 0.0817 |

I6 | 0, 4 | 0.0612 | 6, 0 | −0.0493 | 0 | −0.0855 | |

I7 | 0 | −0.0488 | 0 | 0.0685 | 6 | −0.0535 | |

I8 | 0, 1 | −0.0783 | 0, 6 | 0.0815 | 6, 0 | −0.0158 | |

Fixed Income | I9 | 6 | 0.0450 | 0, 6 | −0.0387 | 0, 6 | −0.1185 |

I10 | 0, 5 | 0.0850 | 0, 6 | −0.0854 | 0 | −0.1047 | |

I11 | 6 | 0.0596 | 0, 6 | −0.0554 | 0, 6 | −0.1266 | |

I12 | 2 | −0.0189 | 1, 2 | 0.0114 | 2, 6 | 0.0071 | |

I13 | 4, 2 | 0.1150 | 0, 1 | −0.1022 | 0 | −0.1240 | |

Banking Sector | I14 | 0 | −0.1236 | 0 | 0.1274 | 0 | 0.0379 |

I15 | 1, 6 | 0.1331 | 3, 6, 0 | −0.1252 | 6 | −0.0325 | |

I16 | 0 | 0.1202 | 0 | −0.1299 | 0 | −0.0680 | |

I17 | 0 | −0.0684 | 0 | 0.0733 | 0, 6 | −0.0153 | |

I18 | 4 | −0.0909 | 4, 0, 6 | 0.0839 | 0 | 0.1004 | |

I19 | 0 | 0.1407 | 6 | −0.1546 | 0 | −0.1150 |

**Table 3.**Representative Indicator Loadings ${\widehat{\omega}}_{j}$ for Short-Run Macro Targets $\Delta {y}_{t}$ Over the Testing Period 2001M1–2006M12.

Target | CPI | GDP | IP | ||||
---|---|---|---|---|---|---|---|

Indicator | Lag | Loading | Lag | Loading | Lag | Loading | |

Forex | I1 | NA | −0.0058 | D12|L1 | −0.0093|−0.0037 | D16|L1 | −0.0143|−0.0053 |

I2 | - | 0.0000 | L1 | −0.0058 | L1 | −0.0099 | |

I3 | NA | −0.0027 | D16|L1 | −0.0095|−0.0027 | D16|L1 | −0.0260|−0.0031 | |

I4 | D16|L6 | 0.0099|−0.0026 | - | 0.0000 | - | 0.0000 | |

Equity | I5 | L4 | 0.0145 | D26|L6 | 0.0295|−0.0006 | D36|L6 | 0.0413|−0.0069 |

I6 | NA | −0.0028|−0.0021 | NA | 0.0033|−0.0020 | L1 | 0.0055 | |

I7 | - | 0.0000 | D16|L6 | 0.0106|−0.0006 | D16|L1 | 0.0144|0.0017 | |

I8 | L1 | 0.0074 | - | 0.0000 | - | 0.0000 | |

Fixed Income | I9 | L16 | −0.0131 | D16|L6 | −0.0103|0.0013 | D16|L6 | −0.0156|0.0031 |

I10 | L12 | −0.0128 | L6 | 0.0042 | L6 | 0.0121 | |

I11 | L16 | −0.0136 | D16|L6 | −0.0117|0.0018 | D16|L6 | −0.0183|0.0045 | |

I12 | NA | −0.0065 | - | 0.0000 | - | 0.0000 | |

I13 | L12 | −0.0192 | L2 | 0.0073 | L6 | 0.0147 | |

Banking Sector | I14 | D16|L1 | 0.0107|0.0062 | D16|L1 | −0.0271|−0.0003 | D16|L1 | −0.0403|−0.0039 |

I15 | L1 | −0.0120 | D14|L1 | 0.0501|0.0001 | D15|L1 | 0.1033|0.0052 | |

I16 | L46 | −0.0120 | L1 | −0.0045 | NA | −0.0009|−0.0055 | |

I17 | NA | 0.0145 | NA | −0.0366|0.0018 | D16|L6 | −0.0546|0.0079 | |

I18 | L26 | 0.0121 | NA | −0.0078 | L26 | −0.0208 | |

I19 | - | 0.0000 | NA | −0.0467|−0.0015 | NA | −0.1197|0.0040 |

**Table 4.**Representative Indicator Loadings for (

**A**) Long-Run and (

**B**) Short-Run Macro Targets for 2001M1–2006M12 (pre) and 2007M1–2016M12 (post) Testing Period.

(A) Long-Run Macro Targets ${\mathit{y}}_{\mathit{t}}-{\mathit{x}}_{\mathit{t}}$ | |||||||||||||

Target | CPI | IP | |||||||||||

Lag Cha. | Loadings | Lag Cha. | Loadings | ||||||||||

Ind. | Pre | Post | Pre | Post | Diff. | Pre | Post | Pre | Post | Diff. | |||

Forex | I1 | 0 | 3 | 0.0537 | 0.0583 | 0.01 | 1 | 3 | −0.1395 | −0.0799 | 0.06 | ||

I2 | 2 | 3 | −0.0117 | −0.0150 | 0.00 | 2 | 4 | −0.1122 | −0.0525 | 0.06 | |||

I3 | 2 | 0 | −0.0017 | −0.0147 | 0.01 | 2 | 4 | −0.1252 | −0.0607 | 0.07 | |||

I4 | 0 | 0 | −0.0544 | −0.0512 | 0.00 | 0 | 0 | 0.0664 | 0.0858 | 0.02 | |||

Equity | I5 | 2 | 0 | −0.1534 | −0.1674 | 0.01 | 1 | 0 | 0.0817 | 0.0356 | 0.05 | ||

I6 | 2 | 0 | 0.0612 | 0.0385 | 0.03 | 0 | 0 | −0.0855 | −0.1302 | 0.05 | |||

I7 | 0 | 0 | −0.0488 | −0.0602 | 0.01 | 0 | 2 | −0.0535 | 0.0342 | 0.09 | |||

I8 | 1 | 1 | −0.0783 | −0.0895 | 0.01 | 2 | 3 | −0.0158 | 0.0487 | 0.07 | |||

Fixed Income | I9 | 0 | 0 | 0.0450 | 0.0484 | 0.00 | 1 | 2 | −0.1185 | −0.1030 | 0.02 | ||

I10 | 1 | 2 | 0.0850 | 0.0792 | 0.01 | 0 | 0 | −0.1047 | −0.1218 | 0.02 | |||

I11 | 0 | 0 | 0.0596 | 0.0611 | 0.00 | 1 | 0 | −0.1266 | −0.1178 | 0.01 | |||

I12 | 0 | 0 | −0.0189 | −0.0185 | 0.00 | 2 | 3 | 0.0071 | 0.0012 | 0.01 | |||

I13 | 1 | 1 | 0.1150 | 0.1227 | 0.01 | 0 | 2 | −0.1240 | −0.0995 | 0.03 | |||

Banking Sector | I14 | 0 | 0 | −0.1236 | −0.1126 | 0.01 | 0 | 0 | 0.0379 | 0.1093 | 0.07 | ||

I15 | 1 | 0 | 0.1331 | 0.1315 | 0.00 | 0 | 1 | −0.0325 | −0.0231 | 0.01 | |||

I16 | 0 | 0 | 0.1202 | 0.1279 | 0.01 | 0 | 2 | −0.0680 | −0.0805 | 0.01 | |||

I17 | 0 | 0 | −0.0684 | −0.0684 | 0.00 | 1 | 0 | −0.0153 | 0.1007 | 0.12 | |||

I18 | 0 | 0 | −0.0909 | −0.0933 | 0.00 | 0 | 2 | 0.1004 | 0.0991 | 0.00 | |||

I19 | 0 | 0 | 0.1407 | 0.1233 | 0.02 | 0 | 1 | −0.1150 | −0.1425 | 0.03 | |||

(B) Short-Run Macro Targets $\mathsf{\Delta}{\mathit{y}}_{\mathit{i}\mathit{t}}$ | |||||||||||||

CPI | IP | ||||||||||||

Lag Cha. | Loadings | Lag Cha. | Loadings | ||||||||||

Ind. | Pre | Po | Pre | Post | Pre | Po | Pre | Post | |||||

Forex | I1 | 1 | 3 | −0.0058 | −0.0019 | 0 | 1 | −0.0143|−0.0053 | −0.0026|−0.0098 | ||||

I2 | 0 | 0 | 0.0000 | 0.0000 | 0 | 1 | −0.0099 | −0.0017 | |||||

I3 | 2 | 3 | −0.0027 | 0.0015|−0.0035 | 0 | 2 | −0.0260|−0.0031 | −0.0166|−0.0009 | |||||

I4 | 0 | 1 | 0.0099|−0.0026 | 0.0078|0.0005 | 0 | 0 | 0.0000 | 0.0000 | |||||

Equity | I5 | 0 | 4 | 0.0145 | 0.0077 | 0 | 2 | 0.0413|−0.0069 | 0.0245|−0.0081 | ||||

I6 | 1 | 1 | −0.0028|−0.0021 | −0.0009|−0.0086 | 1 | 3 | 0.0055 | 0.0008|−0.0110 | |||||

I7 | 0 | 0 | 0.0000 | 0.0000 | 0 | 1 | 0.0144|0.0017 | 0.0028|0.0126 | |||||

I8 | 0 | 0 | 0.0074 | 0.0072 | 0 | 6 | 0.0000 | 0.0009|0.0097 | |||||

Fixed Income | I9 | 0 | 1 | −0.0131 | −0.0118 | 0 | 0 | −0.0156|0.0031 | −0.0194|−0.0019 | ||||

I10 | 0 | 0 | −0.0128 | −0.0123 | 0 | 2 | 0.0121 | −0.0071|0.0020 | |||||

I11 | 0 | 0 | −0.0136 | −0.0125 | 0 | 0 | −0.0183|0.0045 | −0.0239|−0.0013 | |||||

I12 | 1 | 2 | −0.0065 | −0.0042 | 0 | 0 | 0.0000 | 0.0000 | |||||

I13 | 0 | 2 | −0.0192 | −0.0170 | 0 | 1 | 0.0147 | 0.0174 | |||||

Banking Sector | I14 | 0 | 3 | 0.0107|0.0062 | 0.0189|0.0080 | 0 | 0 | −0.0403|−0.0039 | −0.0475|0.0027 | ||||

I15 | 0 | 3 | −0.0120 | 0.0027|−0.0089 | 0 | 2 | 0.1033|0.0052 | 0.0875|−0.0021 | |||||

I16 | 0 | 2 | −0.0120 | −0.0110 | 1 | 3 | −0.0009|−0.0055 | −0.0052|−0.0001 | |||||

I17 | 1 | 4 | 0.0145 | −0.0231|0.0081 | 0 | 2 | −0.0546|0.0079 | −0.1116|0.0127 | |||||

I18 | 0 | 1 | 0.0121 | 0.0121 | 0 | 2 | −0.0208 | −0.0148 | |||||

I19 | 0 | 6 | 0.0000 | −0.0218|−0.0175 | 1 | 4 | −0.1197|0.0040 | −0.2585|−0.0038 |

(A) CPI-Based Annual Inflation${\mathit{y}}_{\mathit{t}}$ Is CPI. ${\mathit{x}}_{\mathit{t}}$ Is PPI. | |||

Model (1)–Baseline | Model (2)–FCI-Based | ||

${\alpha}_{0}$ | 0.0019 [0.0005] ** | ${\alpha}_{0}$ | 0.0021 [0.0005] ** |

${\Delta}_{12}{y}_{t-1}$ | 1.1278 [0.0567] ** | ${\Delta}_{12}{y}_{t-1}$ | 1.1362 [0.0566] ** |

${\Delta}_{12}{y}_{t-2}$ | −0.2065 [0.0516] ** | ${\Delta}_{12}{y}_{t-2}$ | −0.2233 [0.0513] ** |

${\Delta}_{12}{x}_{t}$ | 0.2074 [0.0214] ** | ${\Delta}_{12}{x}_{t}$ | 0.2114 [0.0214] ** |

${\Delta}_{12}{x}_{t-1}$ | −0.1797 [0.0226] ** | ${\Delta}_{12}{x}_{t-1}$ | −0.1790 [0.0226] ** |

${e}_{t-12}$ | −0.0049 [0.0019] * | ${e}_{t-12}$ | −0.0047 [0.0019] * |

$\Delta {r}_{t-4}^{S}$ | 0.1011 [0.0277] ** | ${\Delta}_{3}{\mathsf{\Delta}}_{12}{f}_{t-3}^{L}$ | −0.0130 [0.0034] ** |

(B) Annual GDP Growth${\mathit{y}}_{\mathit{t}}$ Is US GDP. ${\mathit{x}}_{\mathit{t}}$ Is GDP World. | |||

Model (1)–Baseline | Model (2)–FCI-Based | ||

${\alpha}_{0}$ | −0.0200 [0.0051] ** | ${\alpha}_{0}$ | −0.0022 [0.0014] |

${\Delta}_{12}{y}_{t-1}$ | 0.8632 [0.0281] ** | ${\Delta}_{12}{y}_{t-1}$ | 0.8227 [0.0296] ** |

${\Delta}_{12}{x}_{t}$ | 1.0090 [0.0528] ** | ${\Delta}_{12}{x}_{t}$ | 0.9854 [0.9854] ** |

${\Delta}_{12}{x}_{t-1}$ | −0.8279 [0.0590] ** | ${\Delta}_{12}{x}_{t-1}$ | −0.7831 [0.0584] ** |

${e}_{t-12}$ | −0.0643 [0.0151] ** | ${e}_{t-12}^{*}$ | −0.1464 [0.0261] ** |

${\Delta}_{2}{({r}^{L}-{r}^{S})}_{t-3}$ | −0.2394 [0.0754] ** | $\Delta {f}_{t-3}^{S}$ | 0.8527 [0.3809] * |

(C) Annual IP Growth${\mathit{y}}_{\mathit{t}}$ Is US Industrial Production. ${\mathit{x}}_{\mathit{t}}$ is US GDP. | |||

Model (1)–Baseline | Model (2)–FCI-Based | ||

${\alpha}_{0}$ | 0.1361 [0.0221] ** | ${\alpha}_{0}$ | 0.0607 [0.0102] ** |

${\Delta}_{12}{y}_{t-1}$ | 0.8471 [0.0239] ** | ${\Delta}_{12}{y}_{t-1}$ | 0.8741 [0.0217] ** |

${\Delta}_{12}{x}_{t}$ | 0.6300 [0.0420] ** | ${\Delta}_{12}{x}_{t}$ | 0.6068 [0.0408] ** |

${\Delta}_{12}{x}_{t-1}$ | −0.3308 [0.0470] ** | ${\Delta}_{12}{x}_{t-1}$ | −0.4186 [0.0456] ** |

${e}_{t-12}$ | −0.1124 [0.0179] ** | ${e}_{t-12}^{*}$ | −0.1688 [0.0275] ** |

${\Delta}_{4}{({r}^{L}-{r}^{S})}_{t-2}$ | 0.1659 [0.0519] ** | $\Delta {f}_{t-6}^{S}$ | 0.7402 [0.2152] ** |

Forecast Encompassing Tests ^{†} | ||||||
---|---|---|---|---|---|---|

MSFE Baseline (1) | MSFE FCI-Based (2) | Harvey et al. (1997) | Ericsson (1992) | |||

H1 | H2 | H1 | H2 | |||

2001M1–2006M12 | ||||||

CPI | 0.0027 | 0.0027 | 0.4082 | 0.5500 | 0.2754 | 0.0443 * |

GDP | 0.0066 | 0.0068 | 0.4147 | 0.4762 | 0.9357 | 0.0028 ** |

IP | 0.0065 | 0.0064 | 0.4336 | 0.4200 | 0.7381 | 0.0029 ** |

2001M1–2010M12 | ||||||

CPI | 0.0028 | 0.0028 | 0.4239 | 0.5161 | 0.6715 | 0.0526 |

IP | 0.0096 | 0.0095 | 0.4760 | 0.4361 | 0.4272 | 0.0221 * |

2001M1–2017M12 | ||||||

CPI | 0.0024 | 0.0024 | 0.4431 | 0.5072 | 0.7815 | 0.0341 * |

IP | 0.0087 | 0.0085 | 0.4809 | 0.4199 | 0.0424* | 0.0092 ** |

^{†}H1: the FCI-based model (2) encompasses the baseline model (1); H2: the baseline model (1) encompasses the FCI-based model (2). * indicates 5% significance level and ** indicates 1%.

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## Share and Cite

**MDPI and ACS Style**

Qin, D.; van Huellen, S.; Wang, Q.C.; Moraitis, T. Algorithmic Modelling of Financial Conditions for Macro Predictive Purposes: Pilot Application to USA Data. *Econometrics* **2022**, *10*, 22.
https://doi.org/10.3390/econometrics10020022

**AMA Style**

Qin D, van Huellen S, Wang QC, Moraitis T. Algorithmic Modelling of Financial Conditions for Macro Predictive Purposes: Pilot Application to USA Data. *Econometrics*. 2022; 10(2):22.
https://doi.org/10.3390/econometrics10020022

**Chicago/Turabian Style**

Qin, Duo, Sophie van Huellen, Qing Chao Wang, and Thanos Moraitis. 2022. "Algorithmic Modelling of Financial Conditions for Macro Predictive Purposes: Pilot Application to USA Data" *Econometrics* 10, no. 2: 22.
https://doi.org/10.3390/econometrics10020022