Help with Panel Regression Analysis with Lagged Variables

[Jose Lizarraga]

Dear Statalisters,

I have been trying to estimate the responsiveness of national manufacturing output to changes in energy prices with a panel regression analysis, but I have not found intuitive results, so I would really appreciate if someone has some input for this exercise. In short, my equation looks like the following:

ΔY_it = a + B₀ΔY_it-1 + B₁ΔEL_t-1 + B₂ΔNG_{t-1 +} B₃ΔOD_t-1 + B₄ΔX_t-1 + e_t

Y_it -> Manufacturing output for subsector i, year t
EL_t-1 -> Electricity price, year t-1 (first energy price)
_NGt-1 -> Natural gas price, year t-1 (second energy price)
_ODt-1 -> Oil derivatives price, year t-1 (third energy price)
X_t-1 -> Vector of controls, year t-1 (includes the following variables: international oil prices, cost of capital, exchange rate, US industrial production, unit labor cost for subsector i)

All variables on the equation are in first-difference form, so I have been using % change to estimate this. Since I have monthly observations, % change has been measured for each month against the corresponding month last year (i.e, n-12). The purpose of lagging the regressors is to avoid simultaneity problems. This part of the code looks like the following (variable names in Spanish):

1) Generating % change variables

foreach i in tot_ali tot_alc_tab tot_tex tot_tex1 tot_ves tot_piel tot_mad tot_papel tot_impre tot_der_petr tot_quim tot_plas tot_mine tot_metal_ba tot_meta tot_maqui tot_compu tot_acce tot_trans tot_mueb tot_otros p_elec p_gas p_petro c_prec_petr c_costo_cap c_tc c_ipc cmo_tot_ali cmo_tot_alc_tab cmo_tot_tex cmo_tot_tex1 cmo_tot_ves cmo_tot_piel cmo_tot_mad cmo_tot_papel cmo_tot_impre cmo_tot_der_petr cmo_tot_quim cmo_tot_plas cmo_tot_mine cmo_tot_metal_ba cmo_tot_meta cmo_tot_maqui cmo_tot_compu cmo_tot_acce cmo_tot_trans cmo_tot_mueb cmo_tot_otros {

gen pc`i' = ((`i'[_n] / `i'[_n-12]) - 1)

}

2) Generating 1-period lagged % change variables

foreach i in pctot_ali pctot_alc_tab pctot_tex pctot_tex1 pctot_ves pctot_piel pctot_mad pctot_papel pctot_impre pctot_der_petr pctot_quim pctot_plas pctot_mine pctot_metal_ba pctot_meta pctot_maqui pctot_compu pctot_acce pctot_trans pctot_mueb pctot_otros pcp_elec pcp_gas pcp_petro pcc_prec_petr pcc_costo_cap pcc_tc pcc_ipc pccmo_tot_ali pccmo_tot_alc_tab pccmo_tot_tex pccmo_tot_tex1 pccmo_tot_ves pccmo_tot_piel pccmo_tot_mad pccmo_tot_papel pccmo_tot_impre pccmo_tot_der_petr pccmo_tot_quim pccmo_tot_plas pccmo_tot_mine pccmo_tot_metal_ba pccmo_tot_meta pccmo_tot_maqui pccmo_tot_compu pccmo_tot_acce pccmo_tot_trans pccmo_tot_mueb pccmo_tot_otros {

gen lag`i' = `i'[_n-12]

}

After that I just reshape some of the manufacturing and unit labor cost data to merge them according to the appropriate subsector, and, finally, regress the % manufacturing output variable against the lagged % change variables for energy prices and control variables. I feel I should be using xtreg, but I am not a very experienced in Stata so I might be doing an overkill.

Any thoughts would be greatly appreaciated. Thanks in advance.

Best,
Jose L.

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

You didn't get a quick answer. This is a very long complex posting. First, note that you're running differences against differences. It is not clear that you wouldn't be better off with levels on both sides. That is your parameter is the effect of a change in the change of x on the change in y. While in theory this can be the same as the levels analysis, no reason to complicate your life.

In generating the change variables, it is best to xtset your data at the beginning and then use lag (L.) or difference (D.) operators instead of [_n-1]. The [_n-1] formulation will lag across panels creating garbage. It is also often easiest not to do the lags up front but rather to put then in the regression: regress y L.x for example.

Without a clearer understanding of your structure, I can't say much about doing the manufacturing etc. data manipulation first and then merging them. Often it is easier to work with the full data set and use by variable along with generate or egen to calculation your variables.